Finite Group Databasebeta

← #33249520

Subgroups — #33249520

Order 18688.

2522 conjugacy classes of subgroups.

The subgroup lattice has 1608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989170C211yesmaximal, characteristic
2#22613122C211yesmaximal, characteristic, complemented
3#22613102C211yesmaximal, characteristic, complemented
4#22613087C211yesmaximal, characteristic, complemented
5#22613075C211yesmaximal, characteristic, complemented
6#22613054C211yesmaximal, characteristic, complemented
7#22613012C211yesmaximal, characteristic, complemented
8#22613002C211yesmaximal, characteristic, complemented
9#22612976C211yesmaximal, characteristic, complemented
10#22612950C211yesmaximal, characteristic, complemented
11#22612948C211yesmaximal, characteristic, complemented
12#22612931C211yesmaximal, characteristic, complemented
13#22612919C211yesmaximal, characteristic, complemented
14#22612867C211yesmaximal, characteristic, complemented
15#22612860C211yesmaximal, characteristic, complemented
16#22612827C211yesmaximal, characteristic, complemented
17#22612745C211yesmaximal, characteristic, complemented
18#22612724C211yesmaximal, characteristic, complemented
19#22612706C211yesmaximal, characteristic, complemented
20#22612702C211yesmaximal, characteristic, complemented
21#22612637C211yesmaximal, characteristic, complemented
22#22612634C211yesmaximal, characteristic, complemented
23#22612620C211yesmaximal, characteristic, complemented
24#22612595C211yesmaximal, characteristic, complemented
25#22612588C211yesmaximal, characteristic, complemented
26#22612585C211yesmaximal, characteristic, complemented
27#22612528C211yesmaximal, characteristic, complemented
28#22612432C211yesmaximal, characteristic, complemented
29C4×#14556559C211yesmaximal, characteristic, complemented
30C2×#17988461C211yesmaximal, characteristic, complemented
31C73×#2349C211yesmaximal, characteristic, complemented
32C23×C4×D73C2211yescharacteristic
33#17989170C4116yescomplemented
34C2×#14556586C2211yescharacteristic
35C2×#14556585C2211yescharacteristic
36C2×#14556579C2211yescharacteristic
37C2×#14556577C2211yescharacteristic
38C2×#14556576C2211yescharacteristic
39C2×#14556574C2211yescharacteristic
40C2×#14556568C2211yescharacteristic
41C2×#14556565C2211yescharacteristic
42C2×#14556564C2211yescharacteristic
43C2×#14556563C2211yescharacteristic
44C2×#14556561C2211yescharacteristic
45C2×#14556559C2211yescharacteristic
46C2×#14556556C2211yescharacteristic, complemented
47C2×#14556553C2211yescharacteristic
48C2×#14556553C2211yescharacteristic
49C2×C4×C22⋊D73C2211yescharacteristic
50C2×C4×C22⋊D73C2211yescharacteristic
51C2×C4×C22⋊D73C2211yescharacteristic
52C2×C4×C22⋊D73C2211yescharacteristic, complemented
53C2×#14556551C2211yescharacteristic
54C2×#14556551C2211yescharacteristic
55C2×#14556550C2211yescharacteristic, complemented
56C22×C4⋊Dic73C2211yescharacteristic
57C22×#11924007C2211yescharacteristic
58C2×C4⋊C4×D73C2211yescharacteristic, complemented
59C22×#11924005C2211yescharacteristic
60C22×#11924005C2211yescharacteristic
61#17988492C2211yescharacteristic, complemented
62#17988491C2211yescharacteristic, complemented
63#17988491C2211yescharacteristic, complemented
64#17988488C2211yescharacteristic
65#17988488C2211yescharacteristic
66#17988487C2211yescharacteristic
67#17988487C2211yescharacteristic
68#17988487C2211yescharacteristic, complemented
69#17988484C2211yescharacteristic, complemented
70#17988484C2211yescharacteristic, complemented
71#17988483C2211yescharacteristic, complemented
72#17988482C2211yescharacteristic, complemented
73#17988482C2211yescharacteristic, complemented
74#17988482C2211yescharacteristic, complemented
75#17988481C2211yescharacteristic, complemented
76#17988480C2211yescharacteristic, complemented
77#17988480C2211yescharacteristic, complemented
78#17988479C2211yescharacteristic
79#17988479C2211yescharacteristic
80#17988479C2211yescharacteristic
81#17988479C2211yescharacteristic
82#17988479C2211yescharacteristic, complemented
83#17988479C2211yescharacteristic, complemented
84#17988478C2211yescharacteristic
85#17988478C2211yescharacteristic
86#17988478C2211yescharacteristic, complemented
87#17988477C2211yescharacteristic
88#17988477C2211yescharacteristic
89#17988477C2211yescharacteristic
90#17988477C2211yescharacteristic
91#17988477C2211yescharacteristic
92#17988477C2211yescharacteristic
93#17988477C2211yescharacteristic
94#17988477C2211yescharacteristic
95#17988477C2211yescharacteristic, complemented
96#17988476C2211yescharacteristic
97#17988476C2211yescharacteristic
98#17988475C2211yescharacteristic, complemented
99#17988474C2211yescharacteristic, complemented
100#17988474C2211yescharacteristic, complemented
101#17988473C2211yescharacteristic, complemented
102#17988473C2211yescharacteristic, complemented
103#17988472C2211yescharacteristic, complemented
104#17988472C2211yescharacteristic, complemented
105#17988471C2211yescharacteristic, complemented
106#17988469C2211yescharacteristic, complemented
107#17988469C2211yescharacteristic, complemented
108#17988468C2211yescharacteristic, complemented
109#17988468C2211yescharacteristic, complemented
110#17988468C2211yescharacteristic, complemented
111#17988467C2211yescharacteristic
112#17988467C2211yescharacteristic
113#17988466C2211yescharacteristic
114#17988466C2211yescharacteristic
115#17988466C2211yescharacteristic
116#17988466C2211yescharacteristic
117#17988466C2211yescharacteristic, complemented
118#17988465C2211yescharacteristic
119#17988465C2211yescharacteristic
120#17988465C2211yescharacteristic
121#17988465C2211yescharacteristic
122#17988463C2211yescharacteristic
123#17988463C2211yescharacteristic
124#17988463C2211yescharacteristic, complemented
125#17988461C2211yescharacteristic
126#17988461C2211yescharacteristic
127#17988461C2211yescharacteristic
128#17988461C2211yescharacteristic
129#17988461C2211yescharacteristic
130#17988461C2211yescharacteristic
131#17988461C2211yescharacteristic
132#17988461C2211yescharacteristic
133#17988461C2211yescharacteristic, complemented
134#17988461C2211yescharacteristic, complemented
135#17988460C2211yescharacteristic, complemented
136#17988459C2211yescharacteristic
137#17988459C2211yescharacteristic
138#17988458C2211yescharacteristic
139#17988458C2211yescharacteristic
140#17988458C2211yescharacteristic
141#17988458C2211yescharacteristic
142#17988458C2211yescharacteristic, complemented
143#17988456C2211yescharacteristic, complemented
144#17988454C2211yescharacteristic, complemented
145#17988453C2211yescharacteristic, complemented
146#17988449C2211yescharacteristic, complemented
147#17988447C2211yescharacteristic
148#17988447C2211yescharacteristic, complemented
149#17988444C2211yescharacteristic, complemented
150#17988442C2211yescharacteristic
151#17988442C2211yescharacteristic
152C4⋊C4×Dic73C2211yescharacteristic, complemented
153C4⋊C4×Dic73C2211yescharacteristic, complemented
154C4×#11924007C2211yescharacteristic, complemented
155C4×C4⋊Dic73C2211yescharacteristic, complemented
156#17988438C2211yescharacteristic, complemented
157#17988438C2211yescharacteristic, complemented
158C22⋊C4×Dic73C2211yescharacteristic
159C22⋊C4×Dic73C2211yescharacteristic
160C22⋊C4×Dic73C2211yescharacteristic
161C22⋊C4×Dic73C2211yescharacteristic
162C4×#11924005C2211yescharacteristic
163C4×#11924005C2211yescharacteristic
164C4×#11924005C2211yescharacteristic, complemented
165C4×C22⋊Dic73C2211yescharacteristic
166C4×C22⋊Dic73C2211yescharacteristic
167C4×C22⋊Dic73C2211yescharacteristic, complemented
168#17988434C2211yescharacteristic
169#17988434C2211yescharacteristic
170#17988434C2211yescharacteristic, complemented
171#17988432C2211yescharacteristic, complemented
172C2×#14556498C2211yescharacteristic
173C2×C4×D4×C73C2211yescharacteristic
174C2×C4×D4×C73C2211yescharacteristic
175C2×C4×D4×C73C2211yescharacteristic
176#389×C73C2211yescharacteristic, complemented
177#389×C73C2211yescharacteristic, complemented
178#385×C73C2211yescharacteristic
179#385×C73C2211yescharacteristic
180#385×C73C2211yescharacteristic, complemented
181#385×C73C2211yescharacteristic, complemented
182#382×C73C2211yescharacteristic, complemented
183#380×C73C2211yescharacteristic
184#380×C73C2211yescharacteristic, complemented
185C4×C4⋊C4×C73C2211yescharacteristic, complemented
186C2×#95×C73C2211yescharacteristic
187C2×#95×C73C2211yescharacteristic, complemented
188C24×D73C2311yescharacteristic
189C22×Dic146C2311yescharacteristic
190C22×D292C2311yescharacteristic
191C22×D292C2311yescharacteristic
192C22×C22⋊D73C2311yescharacteristic
193C22×C22⋊D73C2311yescharacteristic
194C22×C22⋊D73C2311yescharacteristic
195C22×C22⋊D73C2311yescharacteristic
196C23×Dic73C2311yescharacteristic
197C23×Dic73C2311yescharacteristic
198C23×Dic73C2311yescharacteristic
199C22×C4×D73—42no—
200C22×C4×D73—42no—
201C22×C4×D73—42no—
202C22×C4×D73C2311yescharacteristic
203C22×C4×D73C2311yescharacteristic
204C22×C4×D73C2311yescharacteristic
205C22×C4×D73C2311yescharacteristic
206C22×C4×D73C2311yescharacteristic
207C22×C4×D73C2311yescharacteristic
208C22×C4×D73C2311yescharacteristic
209#14556586C2×C418yescomplemented
210#14556585C2×C418yescomplemented
211#14556579C2×C418yescomplemented
212#14556577C2×C418yescomplemented
213#14556576C2×C418yescomplemented
214#14556574C2×C418yescomplemented
215#14556568C2×C418yescomplemented
216#14556565C2×C418yescomplemented
217#14556564C2×C418yescomplemented
218#14556563C2×C418yescomplemented
219#14556561C2×C418yescomplemented
220#14556559C2×C418yescomplemented
221#14556556—42no—
222#14556553—42no—
223#14556553—42no—
224C4×C22⋊D73—42no—
225C4×C22⋊D73—42no—
226C4×C22⋊D73—42no—
227C4×C22⋊D73C2×C418yescomplemented
228#14556551—42no—
229#14556551—42no—
230#14556550—42no—
231C2×C4⋊Dic73—42no—
232C2×C4⋊Dic73C2311yescharacteristic
233C2×C4⋊Dic73C2311yescharacteristic
234C2×C4⋊Dic73C2311yescharacteristic
235C2×C4⋊Dic73C2311yescharacteristic
236C2×C4⋊Dic73C2311yescharacteristic
237C2×C4⋊Dic73C2311yescharacteristic
238C2×C4⋊Dic73C2311yescharacteristic
239C2×#11924007—42no—
240C2×#11924007C2311yescharacteristic
241C2×#11924007C2311yescharacteristic
242C2×#11924007C2311yescharacteristic
243C2×#11924007C2311yescharacteristic
244C2×#11924007C2311yescharacteristic
245C2×#11924007C2311yescharacteristic
246C2×#11924007C2311yescharacteristic
247C2×#11924007C2311yescharacteristic
248C2×#11924007C2311yescharacteristic
249C2×#11924007C2311yescharacteristic
250C2×#11924007C2311yescharacteristic
251C2×#11924007C2311yescharacteristic
252C2×#11924007C2311yescharacteristic
253C2×#11924007C2311yescharacteristic
254C4⋊C4×D73—42no—
255C2×C22⋊Dic73C2311yescharacteristic
256C2×C22⋊Dic73C2311yescharacteristic
257C2×C22⋊Dic73C2311yescharacteristic
258C2×C22⋊Dic73C2311yescharacteristic
259C2×C22⋊Dic73C2311yescharacteristic
260C2×C22⋊Dic73C2311yescharacteristic
261C2×C22⋊Dic73C2311yescharacteristic
262C2×C22⋊Dic73C2311yescharacteristic
263C2×#11924005—42no—
264C2×#11924005C2×C418yescomplemented
265C2×#11924005C2311yescharacteristic
266C2×#11924005C2311yescharacteristic
267C2×#11924005C2311yescharacteristic
268C2×#11924005C2311yescharacteristic
269C2×#11924005C2311yescharacteristic
270C2×#11924005C2311yescharacteristic
271C2×#11924005C2311yescharacteristic
272C2×#11924005C2311yescharacteristic
273C2×#11924005C2311yescharacteristic
274C2×#11924005C2311yescharacteristic
275C2×#11924005C2311yescharacteristic
276C2×#11924005C2311yescharacteristic
277C2×#11924005C2311yescharacteristic
278C2×#11924005C2311yescharacteristic
279C2×#11924005C2311yescharacteristic
280C2×#11924005C2311yescharacteristic
281C2×#11924005C2311yescharacteristic
282C2×#11924005C2311yescharacteristic
283C2×#11924005C2311yescharacteristic
284C2×#11924005C2311yescharacteristic
285C2×#11924005C2311yescharacteristic
286C2×#11924005C2311yescharacteristic
287C2×#11924005C2311yescharacteristic
288C2×#11924005C2311yescharacteristic
289C2×#11924005C2311yescharacteristic
290C2×#11924005C2311yescharacteristic
291C2×#11924005C2311yescharacteristic
292C2×#11924005C2311yescharacteristic
293C2×C4×Dic73C2311yescharacteristic
294C2×C4×Dic73C2311yescharacteristic
295C2×C4×Dic73C2311yescharacteristic
296C2×C4×Dic73C2311yescharacteristic
297C2×C4×Dic73C2311yescharacteristic
298C2×C4×Dic73C2311yescharacteristic
299C2×C4×Dic73C2311yescharacteristic
300C2×C4×Dic73C2311yescharacteristic
301C2×C4×Dic73C2311yescharacteristic
302C2×C4×Dic73C2311yescharacteristic
303C2×C4×Dic73C2311yescharacteristic
304C2×C4×Dic73C2311yescharacteristic
305C2×C4×Dic73C2311yescharacteristic
306C2×C4×Dic73C2311yescharacteristic
307C2×C4×Dic73C2311yescharacteristic
308#14556498C2311yescharacteristic
309#14556498C2311yescharacteristic
310#14556498C2311yescharacteristic
311#14556498C2311yescharacteristic
312#14556498C2311yescharacteristic
313#14556498C2311yescharacteristic
314#14556498C2311yescharacteristic
315#14556498C2311yescharacteristic
316#14556498C2311yescharacteristic
317#14556498C2311yescharacteristic
318#14556498C2311yescharacteristic
319#14556498C2311yescharacteristic
320#14556498C2311yescharacteristic
321#14556498C2311yescharacteristic
322#14556498C2311yescharacteristic
323#14556498C2311yescharacteristic
324#14556498C2311yescharacteristic
325#14556498C2311yescharacteristic
326#14556498C2311yescharacteristic
327#14556498C2311yescharacteristic
328#14556498C2311yescharacteristic
329#14556498C2311yescharacteristic
330#14556498C2311yescharacteristic
331#14556498C2311yescharacteristic
332#14556498C2311yescharacteristic
333#14556498C2311yescharacteristic
334#14556498C2311yescharacteristic
335#14556498C2311yescharacteristic
336#14556498C2311yescharacteristic
337#14556498C2311yescharacteristic
338C22×D4×C73C2311yescharacteristic
339C23×C4×C73C2311yescharacteristic
340C23×C4×C73C2311yescharacteristic
341C23×C4×C73C2311yescharacteristic
342C23×C4×C73C2311yescharacteristic
343C23×C4×C73C2311yescharacteristic
344C23×C4×C73C2311yescharacteristic
345C4×D4×C73—42no—
346C4×D4×C73—42no—
347C4×D4×C73C2×C418yescomplemented
348C2×C4⋊C4×C73C2311yescharacteristic
349C2×C4⋊C4×C73C2311yescharacteristic
350C2×C4⋊C4×C73C2311yescharacteristic
351C2×C4⋊C4×C73C2311yescharacteristic
352C2×C4⋊C4×C73C2311yescharacteristic
353C2×C4⋊C4×C73C2311yescharacteristic
354C2×C4⋊C4×C73C2311yescharacteristic
355C2×C4⋊C4×C73C2311yescharacteristic
356C2×C4⋊C4×C73C2311yescharacteristic
357C2×C22⋊C4×C73C2311yescharacteristic
358C2×C22⋊C4×C73C2311yescharacteristic
359C2×C22⋊C4×C73C2311yescharacteristic
360C2×C22⋊C4×C73C2311yescharacteristic
361C2×C22⋊C4×C73C2311yescharacteristic
362C2×C22⋊C4×C73C2311yescharacteristic
363C2×C42×C73C2311yescharacteristic
364C2×C42×C73C2311yescharacteristic
365C2×C42×C73C2311yescharacteristic
366#95×C73C2311yescharacteristic
367#95×C73C2311yescharacteristic
368#95×C73C2311yescharacteristic
369#95×C73C2311yescharacteristic
370#95×C73C2311yescharacteristic
371#95×C73C2311yescharacteristic
372#95×C73C2311yescharacteristic
373#95×C73C2311yescharacteristic
374#95×C73C2311yescharacteristic
375#95×C73C2311yescharacteristic
376C23×D73—22no—
377C23×D73—22no—
378C23×D73—41no—
379C23×D73—41no—
380C23×D73—41no—
381C23×D73—41no—
382C23×D73C22×C414yes—
383C23×D73C2411yescharacteristic
384C23×D73C2411yescharacteristic
385C23×D73C2411yescharacteristic
386C2×Dic146—41no—
387C2×Dic146—41no—
388C2×Dic146C22×C414yescomplemented
389C2×D292—41no—
390C2×D292—41no—
391C2×D292—41no—
392C2×D292—41no—
393C2×D292C22×C414yes—
394C2×D292C22×C414yes—
395C2×C22⋊D73—22no—
396C2×C22⋊D73—22no—
397C2×C22⋊D73—41no—
398C2×C22⋊D73—41no—
399C2×C22⋊D73—41no—
400C2×C22⋊D73—41no—
401C2×C22⋊D73—41no—
402C2×C22⋊D73—41no—
403C2×C22⋊D73C22×C414yes—
404C2×C22⋊D73C22×C414yes—
405C2×C22⋊D73C22×C414yes—
406C2×C22⋊D73C22×C414yescomplemented
407C22×Dic73—22no—
408C22×Dic73—22no—
409C22×Dic73—22no—
410C22×Dic73—41no—
411C22×Dic73—41no—
412C22×Dic73—41no—
413C22×Dic73—41no—
414C22×Dic73—41no—
415C22×Dic73C22×C414yes—
416C22×Dic73C2411yescharacteristic
417C22×Dic73C2411yescharacteristic
418C22×Dic73C2411yescharacteristic
419C22×Dic73C2411yescharacteristic
420C22×Dic73C2411yescharacteristic
421C22×Dic73C2411yescharacteristic
422C22×Dic73C2411yescharacteristic
423C22×Dic73C2411yescharacteristic
424C22×Dic73C2411yescharacteristic
425C22×Dic73C2411yescharacteristic
426C22×Dic73C2411yescharacteristic
427C22×Dic73C2411yescharacteristic
428C22×Dic73C2411yescharacteristic
429C2×C4×D73—22no—
430C2×C4×D73—22no—
431C2×C4×D73—22no—
432C2×C4×D73—22no—
433C2×C4×D73—22no—
434C2×C4×D73—41no—
435C2×C4×D73—41no—
436C2×C4×D73—41no—
437C2×C4×D73—41no—
438C2×C4×D73—41no—
439C2×C4×D73—41no—
440C2×C4×D73—41no—
441C2×C4×D73—41no—
442C2×C4×D73—41no—
443C2×C4×D73—41no—
444C2×C4×D73—416no—
445C2×C4×D73—41no—
446C2×C4×D73—41no—
447C2×C4×D73—41no—
448C2×C4×D73—41no—
449C2×C4×D73—41no—
450C2×C4×D73C22×C414yescomplemented
451C4⋊Dic73—22no—
452C4⋊Dic73—22no—
453C4⋊Dic73—41no—
454C4⋊Dic73—41no—
455C4⋊Dic73—41no—
456C4⋊Dic73—41no—
457C4⋊Dic73C22×C414yescomplemented
458#11924007—22no—
459#11924007—22no—
460#11924007—22no—
461#11924007—41no—
462#11924007—41no—
463#11924007—41no—
464#11924007—41no—
465#11924007—41no—
466#11924007—41no—
467#11924007—41no—
468#11924007C22×C414yescomplemented
469#11924007C22×C414yescomplemented
470#11924007C22×C414yescomplemented
471#11924007C22×C414yescomplemented
472C22⋊Dic73—22no—
473C22⋊Dic73—22no—
474C22⋊Dic73—22no—
475C22⋊Dic73—41no—
476C22⋊Dic73—41no—
477C22⋊Dic73—41no—
478C22⋊Dic73C22×C414yes—
479C22⋊Dic73C22×C414yescomplemented
480#11924005—22no—
481#11924005—41no—
482#11924005—41no—
483#11924005—41no—
484#11924005—41no—
485#11924005—41no—
486#11924005—41no—
487#11924005—41no—
488#11924005—41no—
489#11924005—41no—
490#11924005—41no—
491#11924005—41no—
492#11924005—41no—
493#11924005—41no—
494#11924005—41no—
495#11924005—41no—
496#11924005—41no—
497#11924005—41no—
498#11924005C22×C414yes—
499#11924005C22×C414yes—
500#11924005C22×C414yes—
501#11924005C22×C414yes—
502#11924005C22×C414yes—
503#11924005C22×C414yes—
504#11924005C22×C414yes—
505#11924005C22×C414yes—
506#11924005C22×C414yescomplemented
507#11924005C22×C414yescomplemented
508C4×Dic73—22no—
509C4×Dic73—22no—
510C4×Dic73—41no—
511C4×Dic73—41no—
512C4×Dic73—41no—
513C4×Dic73—41no—
514C4×Dic73—41no—
515C4×Dic73—41no—
516C4×Dic73—41no—
517C4×Dic73—41no—
518C4×Dic73—41no—
519C4×Dic73—41no—
520C4×Dic73—41no—
521C4×Dic73—41no—
522C4×Dic73C22×C414yescomplemented
523C24×C73C2411yescharacteristic
524C24×C73C2411yescharacteristic
525C2×D4×C73—22no—
526C2×D4×C73—22no—
527C2×D4×C73C22×C414yes—
528C22×C4×C73—22no—
529C22×C4×C73—22no—
530C22×C4×C73—22no—
531C22×C4×C73—22no—
532C22×C4×C73—41no—
533C22×C4×C73—41no—
534C22×C4×C73—41no—
535C22×C4×C73—41no—
536C22×C4×C73—41no—
537C22×C4×C73—41no—
538C22×C4×C73—41no—
539C22×C4×C73—41no—
540C22×C4×C73—41no—
541C22×C4×C73—41no—
542C22×C4×C73—41no—
543C22×C4×C73—41no—
544C22×C4×C73C22×C414yes—
545C22×C4×C73C22×C414yescomplemented
546C22×C4×C73C2411yescharacteristic
547C22×C4×C73C2411yescharacteristic
548C22×C4×C73C2411yescharacteristic
549C22×C4×C73C2411yescharacteristic
550C22×C4×C73C2411yescharacteristic
551C22×C4×C73C2411yescharacteristic
552C22×C4×C73C2411yescharacteristic
553C22×C4×C73C2411yescharacteristic
554C22×C4×C73C2411yescharacteristic
555C22×C4×C73C2411yescharacteristic
556C22×C4×C73C2411yescharacteristic
557C22×C4×C73C2411yescharacteristic
558C22×C4×C73C2411yescharacteristic
559C4⋊C4×C73—22no—
560C4⋊C4×C73—41no—
561C4⋊C4×C73—41no—
562C4⋊C4×C73—41no—
563C4⋊C4×C73—41no—
564C4⋊C4×C73—41no—
565C4⋊C4×C73—41no—
566C4⋊C4×C73—41no—
567C4⋊C4×C73C22×C414yescomplemented
568C22⋊C4×C73—22no—
569C22⋊C4×C73—22no—
570C22⋊C4×C73—41no—
571C22⋊C4×C73—41no—
572C22⋊C4×C73C22×C414yes—
573C22⋊C4×C73C22×C414yescomplemented
574C42×C73—41no—
575C42×C73—41no—
576C42×C73C22×C414yescomplemented
577C23×C73—21no—
578C23×C73—21no—
579C23×C73—21no—
580C23×C73—21no—
581C23×C73—21no—
582C23×C73—21no—
583C23×C73—21no—
584C23×C73—21no—
585C23×C73—21no—
586C23×C73—21no—
587C23×C73C23×C412yes—
588C23×C73C23×C412yes—
589C23×C73H(5,𝔽2)12yes—
590C23×C732−1+412yes—
591C23×C73C2511yescharacteristic
592C22×D73—28no—
593C22×D73—21no—
594C22×D73—21no—
595C22×D73—21no—
596C22×D73—21no—
597C22×D73—21no—
598C22×D73—21no—
599C22×D73—21no—
600C22×D73—21no—
601C22×D73—21no—
602C22×D73—21no—
603C22×D73—21no—
604C22×D73—21no—
605C22×D73—21no—
606C22×D73—21no—
607C22×D73—21no—
608C22×D73—21no—
609C22×D73—21no—
610C22×D73—21no—
611C22×D73—44no—
612C22×D73—44no—
613C22×D73—44no—
614C22×D73—44no—
615C22×D73—44no—
616C22×D73—44no—
617C22×D73C23×C412yes—
618C22×D73C23×C412yes—
619C22×D73C23×C412yes—
620D4×C73—28no—
621C2×C4×C73—21no—
622C2×C4×C73—21no—
623C2×C4×C73—21no—
624C2×C4×C73—21no—
625C2×C4×C73—21no—
626C2×C4×C73—21no—
627C2×C4×C73—21no—
628C2×C4×C73—21no—
629C2×C4×C73—21no—
630C2×C4×C73—21no—
631C2×C4×C73—21no—
632C2×C4×C73—21no—
633C2×C4×C73—21no—
634C2×C4×C73—21no—
635C2×C4×C73—21no—
636C2×C4×C73—21no—
637C2×C4×C73—21no—
638C2×C4×C73—21no—
639C2×C4×C73—21no—
640C2×C4×C73—21no—
641C2×C4×C73—21no—
642C2×C4×C73—21no—
643C2×C4×C73—21no—
644C2×C4×C73—21no—
645C2×C4×C73—21no—
646C2×C4×C73—21no—
647C2×C4×C73—21no—
648C2×C4×C73—21no—
649C2×C4×C73—21no—
650C2×C4×C73—21no—
651C2×C4×C73—21no—
652C2×C4×C73—21no—
653C2×C4×C73—21no—
654C2×C4×C73—44no—
655C2×C4×C73—44no—
656C2×C4×C73—44no—
657C2×C4×C73—82no—
658C2×C4×C73—82no—
659C2×C4×C73—82no—
660C2×C4×C73C23×C412yes—
661C2×C4×C73C23×C412yes—
662C2×C4×C73C23×C412yes—
663C2×C4×C73C23×C412yes—
664C2×C4×C73C23×C412yes—
665C2×C4×C73H(5,𝔽2)12yes—
666C22⋊D73—28no—
667C22⋊D73—44no—
668C22⋊D73—44no—
669C22⋊D73—44no—
670C2×Dic73—21no—
671C2×Dic73—21no—
672C2×Dic73—21no—
673C2×Dic73—21no—
674C2×Dic73—21no—
675C2×Dic73—21no—
676C2×Dic73—21no—
677C2×Dic73—21no—
678C2×Dic73—21no—
679C2×Dic73—21no—
680C2×Dic73—21no—
681C2×Dic73—21no—
682C2×Dic73—21no—
683C2×Dic73—21no—
684C2×Dic73—21no—
685C2×Dic73—21no—
686C2×Dic73—21no—
687C2×Dic73—21no—
688C2×Dic73—21no—
689C2×Dic73—21no—
690C2×Dic73—21no—
691C2×Dic73—21no—
692C2×Dic73—21no—
693C2×Dic73—21no—
694C2×Dic73—21no—
695C2×Dic73—21no—
696C2×Dic73—21no—
697C2×Dic73—21no—
698C2×Dic73—21no—
699C2×Dic73—21no—
700C2×Dic73—21no—
701C2×Dic73—21no—
702C2×Dic73—21no—
703C2×Dic73—44no—
704C2×Dic73—44no—
705C2×Dic73—82no—
706C2×Dic73C23×C412yes—
707C2×Dic73C23×C412yes—
708C2×Dic73C23×C412yes—
709C2×Dic73C23×C412yes—
710C2×Dic73C23×C412yes—
711C2×Dic73H(5,𝔽2)12yes—
712D292—44no—
713D292—44no—
714C4×D73—44no—
715C4×D73—44no—
716C4×D73—44no—
717C4×D73—44no—
718C4×D73—44no—
719C4×D73—82no—
720C4×D73—82no—
721Dic146—44no—
722C22×C73—22no—
723C22×C73—22no—
724C22×C73—22no—
725C22×C73—22no—
726C22×C73—22no—
727C22×C73—22no—
728C22×C73—22no—
729C22×C73—22no—
730C22×C73—22no—
731C22×C73—41no—
732C22×C73—41no—
733C22×C73—41no—
734C22×C73—41no—
735C22×C73#52014yes—
736C22×C73C24×C411yescharacteristic
737C22×C73C2×H(5,𝔽2)11yescharacteristic
738C22×C73C2×H(5,𝔽2)11yescharacteristic
739C22×C73C2×H(5,𝔽2)11yescharacteristic
740C22×C73C2×2−1+411yescharacteristic
741C22×C73#58511yescharacteristic
742C22×C73#58511yescharacteristic
743C2×D73—22no—
744C2×D73—22no—
745C2×D73—22no—
746C2×D73—22no—
747C2×D73—22no—
748C2×D73—22no—
749C2×D73—22no—
750C2×D73—22no—
751C2×D73—22no—
752C2×D73—416no—
753C2×D73—41no—
754C2×D73—41no—
755C2×D73—41no—
756C2×D73—41no—
757C2×D73—41no—
758C2×D73—41no—
759C2×D73—41no—
760C2×D73—41no—
761C2×D73—41no—
762C2×D73—41no—
763C2×D73—41no—
764C2×D73—41no—
765C4×C73—22no—
766C4×C73—22no—
767C4×C73—22no—
768C4×C73—22no—
769C4×C73—22no—
770C4×C73—22no—
771C4×C73—41no—
772C4×C73—41no—
773C4×C73—41no—
774C4×C73—41no—
775C4×C73—41no—
776C4×C73—41no—
777C4×C73—41no—
778Dic73—22no—
779Dic73—22no—
780Dic73—22no—
781Dic73—22no—
782Dic73—22no—
783Dic73—22no—
784Dic73—41no—
785Dic73—41no—
786Dic73—41no—
787Dic73—41no—
788Dic73—41no—
789Dic73—41no—
790Dic73—41no—
791#34416—731nomaximal, Sylow
792C2×C73—24no—
793C2×C73—42no—
794C2×C73C2×#52011yescharacteristic
795C2×C73C4×H(5,𝔽2)11yescharacteristic
796C2×C73C4×H(5,𝔽2)11yescharacteristic
797C2×C73#353211yescharacteristic
798C2×C73#353311yescharacteristic
799C2×C73#354111yescharacteristic
800C2×C73#354111yescharacteristic
801D73—42no—
802D73—42no—
803D73—42no—
804C2×#538—731no—
805#2383—731no—
806#2379—731no—
807#2377—731no—
808#2376—731no—
809#2373—731no—
810#2368—731no—
811#2367—731no—
812#2364—731no—
813#2361—731no—
814#2361—731no—
815#2360—731no—
816#2359—731no—
817#2353—731no—
818#2352—731no—
819#2349D7311yescharacteristic, complemented
820D4×C4⋊C4—731no—
821#2337—731no—
822#2335—731no—
823#2334—731no—
824#2334—731no—
825#2326—731no—
826#2325—731no—
827#2324—731no—
828#2322—731no—
829#2321—731no—
830#2321—731no—
831#2312—731no—
832C4×#120—731no—
833C4×#120—731no—
834C2×#385—731no—
835C73#3441611yescharacteristic, complemented, Sylow
836C24×C4—731no—
837#538—7316no—
838C2×#126—731no—
839C2×#126—731no—
840C2×#124—731no—
841C2×#124—731no—
842C2×#123—731no—
843C2×#123—731no—
844C2×C22⋊Q8—731no—
845C2×#121—731no—
846C2×#121—731no—
847C2×#121—731no—
848C2×#120—731no—
849C2×#120—731no—
850C2×C4×Q8—731no—
851C2×C4×D4—731no—
852C2×C4×D4—731no—
853C2×C4×D4—731no—
854C2×C4×D4—731no—
855C2×C4×D4—731no—
856C2×C4×D4—731no—
857C2×C4×D4—731no—
858C2×C4×D4—731no—
859C2×C4×D4C2×D7311yescharacteristic
860C2×C4×D4C2×D7311yescharacteristic
861C2×C4×D4C2×D7311yescharacteristic
862C2×#117—731no—
863C22×C4⋊C4—731no—
864C22×C4⋊C4—731no—
865C22×C4⋊C4—731no—
866C22×C22⋊C4—731no—
867C22×C22⋊C4—731no—
868#391—731no—
869#391—731no—
870#391—731no—
871#390—731no—
872#390—731no—
873#390—731no—
874#390—731no—
875#390—731no—
876#389—731no—
877#389—731no—
878#389—731no—
879#389—731no—
880#389—731no—
881#389—731no—
882#389C2×D7311yescharacteristic, complemented
883#389C2×D7311yescharacteristic, complemented
884#388—731no—
885#388—731no—
886#388—731no—
887#388—731no—
888#388—731no—
889#388—731no—
890#388—731no—
891#388—731no—
892#388—731no—
893#388—731no—
894#388—731no—
895#388—731no—
896#388—731no—
897#388—731no—
898#388—731no—
899#388—731no—
900#388—731no—
901#388—731no—
902#388—731no—
903#388—731no—
904#388—731no—
905#388—731no—
906#388—731no—
907#388—731no—
908#387—731no—
909#387—731no—
910#387—731no—
911#387—731no—
912#387—731no—
913#387—731no—
914#387—731no—
915#387—731no—
916#387—731no—
917#387—731no—
918#387—731no—
919#387—731no—
920#386—731no—
921#386—731no—
922#386—731no—
923#386—731no—
924#386—731no—
925#386—731no—
926#386—731no—
927#386—731no—
928#386—731no—
929#386—731no—
930#386—731no—
931#386—731no—
932#386—731no—
933#386—731no—
934#385—731no—
935#385—731no—
936#385—731no—
937#385—731no—
938#385—731no—
939#385—731no—
940#385—731no—
941#385—731no—
942#385—731no—
943#385—731no—
944#385—731no—
945#385—731no—
946#385—731no—
947#385—731no—
948#385—731no—
949#385—731no—
950#385—731no—
951#385—731no—
952#385C2×D7311yescharacteristic
953#385C2×D7311yescharacteristic
954#385C2×D7311yescharacteristic, complemented
955#385C2×D7311yescharacteristic, complemented
956#384—731no—
957#383—731no—
958#382—731no—
959#382C2×D7311yescharacteristic, complemented
960#381—731no—
961#380—731no—
962#380—731no—
963#380—731no—
964#380C2×D7311yescharacteristic
965#380C2×D7311yescharacteristic, complemented
966#379—731no—
967#379—731no—
968C4×C4⋊C4—731no—
969C4×C4⋊C4—731no—
970C4×C4⋊C4—731no—
971C4×C4⋊C4—731no—
972C4×C4⋊C4—731no—
973C4×C4⋊C4—731no—
974C4×C4⋊C4C2×D7311yescharacteristic, complemented
975C4×C22⋊C4—731no—
976C4×C22⋊C4—731no—
977C4×C22⋊C4—731no—
978C4×C22⋊C4—731no—
979C4×C22⋊C4—731no—
980C4×C22⋊C4—731no—
981C4×C22⋊C4—731no—
982C4×C22⋊C4—731no—
983C4×C22⋊C4—731no—
984C4×C22⋊C4—731no—
985C4×C22⋊C4—731no—
986C4×C22⋊C4—731no—
987C4×C22⋊C4—731no—
988#376—731no—
989C2×#95—731no—
990C2×#95C2×D7311yescharacteristic
991C2×#95C2×D7311yescharacteristic, complemented
992C25—731no—
993C22×Q8—731no—
994C22×D4—731no—
995C22×D4—731no—
996C22×D4—731no—
997C22×D4—731no—
998C22×D4—731no—
999C22×D4—731no—
1000C22×D4C22×D7311yescharacteristic
1001C23×C4—2922no—
1002C23×C4—2922no—
1003C23×C4—2922no—
1004C23×C4—731no—
1005C23×C4—731no—
1006C23×C4—731no—
1007C23×C4—731no—
1008C23×C4—731no—
1009C23×C4—731no—
1010C23×C4—731no—
1011C23×C4—731no—
1012C23×C4—731no—
1013C23×C4—731no—
1014C23×C4C22×D7311yescharacteristic
1015C23×C4C22×D7311yescharacteristic
1016C23×C4C22×D7311yescharacteristic
1017C23×C4C22×D7311yescharacteristic
1018C23×C4C22×D7311yescharacteristic
1019C23×C4C22×D7311yescharacteristic
1020#126—738no—
1021#126—738no—
1022#124—738no—
1023#124—738no—
1024#123—738no—
1025#123—738no—
1026C22⋊Q8—738no—
1027#121—738no—
1028#121—738no—
1029#121—738no—
1030#120—738no—
1031#120—738no—
1032C4×Q8—2922no—
1033C4×D4—42no—
1034C4×D4—42no—
1035C4×D4—2922no—
1036C4×D4—2922no—
1037C4×D4—2922no—
1038C4×D4—2922no—
1039C4×D4—2922no—
1040C4×D4—2922no—
1041C4×D4—2922no—
1042C4×D4—738no—
1043C4×D4C4×D7318yescomplemented
1044#117—2922no—
1045C2×C4⋊C4—2922no—
1046C2×C4⋊C4—2922no—
1047C2×C4⋊C4—2922no—
1048C2×C4⋊C4—731no—
1049C2×C4⋊C4—731no—
1050C2×C4⋊C4—731no—
1051C2×C4⋊C4—731no—
1052C2×C4⋊C4—731no—
1053C2×C4⋊C4—731no—
1054C2×C4⋊C4—731no—
1055C2×C4⋊C4—731no—
1056C2×C4⋊C4—731no—
1057C2×C4⋊C4—731no—
1058C2×C4⋊C4—731no—
1059C2×C4⋊C4—731no—
1060C2×C4⋊C4—731no—
1061C2×C4⋊C4—731no—
1062C2×C4⋊C4—731no—
1063C2×C4⋊C4—731no—
1064C2×C4⋊C4—731no—
1065C2×C4⋊C4—731no—
1066C2×C4⋊C4—731no—
1067C2×C4⋊C4—731no—
1068C2×C4⋊C4—731no—
1069C2×C4⋊C4C22×D7311yescharacteristic
1070C2×C4⋊C4C22×D7311yescharacteristic
1071C2×C4⋊C4C22×D7311yescharacteristic
1072C2×C4⋊C4C22×D7311yescharacteristic
1073C2×C4⋊C4C22×D7311yescharacteristic
1074C2×C4⋊C4C22×D7311yescharacteristic
1075C2×C4⋊C4C22×D7311yescharacteristic
1076C2×C4⋊C4C22×D7311yescharacteristic
1077C2×C4⋊C4C22×D7311yescharacteristic
1078C2×C22⋊C4—2922no—
1079C2×C22⋊C4—731no—
1080C2×C22⋊C4—731no—
1081C2×C22⋊C4—731no—
1082C2×C22⋊C4—731no—
1083C2×C22⋊C4—731no—
1084C2×C22⋊C4—731no—
1085C2×C22⋊C4—731no—
1086C2×C22⋊C4—731no—
1087C2×C22⋊C4—731no—
1088C2×C22⋊C4—731no—
1089C2×C22⋊C4—731no—
1090C2×C22⋊C4—731no—
1091C2×C22⋊C4—731no—
1092C2×C22⋊C4—731no—
1093C2×C22⋊C4—731no—
1094C2×C22⋊C4—731no—
1095C2×C22⋊C4—731no—
1096C2×C22⋊C4—731no—
1097C2×C22⋊C4—731no—
1098C2×C22⋊C4—731no—
1099C2×C22⋊C4—731no—
1100C2×C22⋊C4—731no—
1101C2×C22⋊C4—738no—
1102C2×C22⋊C4—731no—
1103C2×C22⋊C4—731no—
1104C2×C22⋊C4—731no—
1105C2×C22⋊C4—731no—
1106C2×C22⋊C4—731no—
1107C2×C22⋊C4—731no—
1108C2×C22⋊C4—731no—
1109C2×C22⋊C4—731no—
1110C2×C22⋊C4—731no—
1111C2×C22⋊C4—731no—
1112C2×C22⋊C4—731no—
1113C2×C22⋊C4—731no—
1114C2×C22⋊C4—731no—
1115C2×C22⋊C4—731no—
1116C2×C22⋊C4C22×D7311yescharacteristic
1117C2×C22⋊C4C22×D7311yescharacteristic
1118C2×C22⋊C4C22×D7311yescharacteristic
1119C2×C22⋊C4C22×D7311yescharacteristic
1120C2×C22⋊C4C22×D7311yescharacteristic
1121C2×C22⋊C4C22×D7311yescharacteristic
1122C2×C42—731no—
1123C2×C42—731no—
1124C2×C42—731no—
1125C2×C42—731no—
1126C2×C42—731no—
1127C2×C42—731no—
1128C2×C42—731no—
1129C2×C42—731no—
1130C2×C42—731no—
1131C2×C42—731no—
1132C2×C42—731no—
1133C2×C42—731no—
1134C2×C42—731no—
1135C2×C42—731no—
1136C2×C42—731no—
1137C2×C42C22×D7311yescharacteristic
1138C2×C42C22×D7311yescharacteristic
1139C2×C42C22×D7311yescharacteristic
1140#95—731no—
1141#95—731no—
1142#95—731no—
1143#95—731no—
1144#95—731no—
1145#95—731no—
1146#95—731no—
1147#95—731no—
1148#95—731no—
1149#95—731no—
1150#95—731no—
1151#95—731no—
1152#95—731no—
1153#95—731no—
1154#95—731no—
1155#95—731no—
1156#95—731no—
1157#95—731no—
1158#95—731no—
1159#95—731no—
1160#95—731no—
1161#95—731no—
1162#95—731no—
1163#95—731no—
1164#95—731no—
1165#95—731no—
1166#95—731no—
1167#95—731no—
1168#95—731no—
1169#95—731no—
1170#95C22×D7311yescharacteristic
1171#95C22×D7311yescharacteristic
1172#95C22×D7311yescharacteristic
1173#95C22×D7311yescharacteristic
1174#95C22×D7311yescharacteristic
1175#95C22×D7311yescharacteristic
1176#95C22×D7311yescharacteristic
1177#95C22×D7311yescharacteristic
1178#95C22×D7311yescharacteristic
1179#95C22×D7311yescharacteristic
1180C24—2921no—
1181C24—2921no—
1182C24—2921no—
1183C24—2921no—
1184C24—734no—
1185C24—731no—
1186C24—731no—
1187C24—731no—
1188C24—1462no—
1189C24—1462no—
1190C24C23×D7311yescharacteristic
1191C24C23×D7311yescharacteristic
1192C2×Q8—2921no—
1193C2×Q8—2921no—
1194C2×Q8—734no—
1195C2×D4—22no—
1196C2×D4—22no—
1197C2×D4—2921no—
1198C2×D4—2921no—
1199C2×D4—2921no—
1200C2×D4—2921no—
1201C2×D4—2921no—
1202C2×D4—2921no—
1203C2×D4—2921no—
1204C2×D4—2921no—
1205C2×D4—2921no—
1206C2×D4—2921no—
1207C2×D4—734no—
1208C2×D4—734no—
1209C2×D4—734no—
1210C2×D4—734no—
1211C2×D4—734no—
1212C2×D4—734no—
1213C2×D4—1462no—
1214C2×D4—1462no—
1215C2×D4C2×C4×D7314yes—
1216C22×C4—22no—
1217C22×C4—22no—
1218C22×C4—22no—
1219C22×C4—22no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—41no—
1224C22×C4—41no—
1225C22×C4—41no—
1226C22×C4—41no—
1227C22×C4—41no—
1228C22×C4—41no—
1229C22×C4—41no—
1230C22×C4—41no—
1231C22×C4—41no—
1232C22×C4—2921no—
1233C22×C4—2921no—
1234C22×C4—2921no—
1235C22×C4—2921no—
1236C22×C4—2921no—
1237C22×C4—2921no—
1238C22×C4—2921no—
1239C22×C4—2921no—
1240C22×C4—2921no—
1241C22×C4—2921no—
1242C22×C4—2921no—
1243C22×C4—2921no—
1244C22×C4—2921no—
1245C22×C4—2921no—
1246C22×C4—2921no—
1247C22×C4—29216no—
1248C22×C4—2921no—
1249C22×C4—2921no—
1250C22×C4—2921no—
1251C22×C4—2921no—
1252C22×C4—2921no—
1253C22×C4—734no—
1254C22×C4—734no—
1255C22×C4—731no—
1256C22×C4—731no—
1257C22×C4—731no—
1258C22×C4—731no—
1259C22×C4—731no—
1260C22×C4—731no—
1261C22×C4—731no—
1262C22×C4—731no—
1263C22×C4—731no—
1264C22×C4—731no—
1265C22×C4—731no—
1266C22×C4—731no—
1267C22×C4—731no—
1268C22×C4—1462no—
1269C22×C4—1462no—
1270C22×C4—1462no—
1271C22×C4—1462no—
1272C22×C4—1462no—
1273C22×C4—1462no—
1274C22×C4—1462no—
1275C22×C4—1462no—
1276C22×C4C2×C4×D7314yes—
1277C22×C4C2×C4×D7314yescomplemented
1278C22×C4C23×D7311yescharacteristic
1279C22×C4C23×D7311yescharacteristic
1280C22×C4C23×D7311yescharacteristic
1281C22×C4C23×D7311yescharacteristic
1282C22×C4C23×D7311yescharacteristic
1283C22×C4C23×D7311yescharacteristic
1284C22×C4C23×D7311yescharacteristic
1285C22×C4C23×D7311yescharacteristic
1286C22×C4C23×D7311yescharacteristic
1287C22×C4C23×D7311yescharacteristic
1288C22×C4C23×D7311yescharacteristic
1289C22×C4C23×D7311yescharacteristic
1290C22×C4C23×D7311yescharacteristic
1291C4⋊C4—22no—
1292C4⋊C4—41no—
1293C4⋊C4—41no—
1294C4⋊C4—41no—
1295C4⋊C4—41no—
1296C4⋊C4—41no—
1297C4⋊C4—41no—
1298C4⋊C4—41no—
1299C4⋊C4—2921no—
1300C4⋊C4—2921no—
1301C4⋊C4—2921no—
1302C4⋊C4—2921no—
1303C4⋊C4—2921no—
1304C4⋊C4—2921no—
1305C4⋊C4—2921no—
1306C4⋊C4—2921no—
1307C4⋊C4—2921no—
1308C4⋊C4—2921no—
1309C4⋊C4—2921no—
1310C4⋊C4—734no—
1311C4⋊C4—734no—
1312C4⋊C4—734no—
1313C4⋊C4—734no—
1314C4⋊C4—734no—
1315C4⋊C4—1462no—
1316C4⋊C4—1462no—
1317C4⋊C4—1462no—
1318C4⋊C4—1462no—
1319C4⋊C4—1462no—
1320C4⋊C4C2×C4×D7314yescomplemented
1321C22⋊C4—22no—
1322C22⋊C4—22no—
1323C22⋊C4—41no—
1324C22⋊C4—41no—
1325C22⋊C4—2921no—
1326C22⋊C4—2921no—
1327C22⋊C4—2921no—
1328C22⋊C4—2921no—
1329C22⋊C4—2921no—
1330C22⋊C4—2921no—
1331C22⋊C4—2921no—
1332C22⋊C4—2921no—
1333C22⋊C4—2921no—
1334C22⋊C4—2921no—
1335C22⋊C4—2921no—
1336C22⋊C4—2921no—
1337C22⋊C4—2921no—
1338C22⋊C4—2921no—
1339C22⋊C4—2921no—
1340C22⋊C4—2921no—
1341C22⋊C4—2921no—
1342C22⋊C4—2921no—
1343C22⋊C4—2921no—
1344C22⋊C4—2921no—
1345C22⋊C4—734no—
1346C22⋊C4—734no—
1347C22⋊C4—734no—
1348C22⋊C4—734no—
1349C22⋊C4—734no—
1350C22⋊C4—734no—
1351C22⋊C4—734no—
1352C22⋊C4—734no—
1353C22⋊C4—734no—
1354C22⋊C4—734no—
1355C22⋊C4—734no—
1356C22⋊C4—734no—
1357C22⋊C4—1462no—
1358C22⋊C4—1462no—
1359C22⋊C4—1462no—
1360C22⋊C4—1462no—
1361C22⋊C4C2×C4×D7314yes—
1362C22⋊C4C2×C4×D7314yescomplemented
1363C42—41no—
1364C42—41no—
1365C42—2921no—
1366C42—2921no—
1367C42—2921no—
1368C42—2921no—
1369C42—2921no—
1370C42—2921no—
1371C42—2921no—
1372C42—2921no—
1373C42—2921no—
1374C42—2921no—
1375C42—2921no—
1376C42—2921no—
1377C42—734no—
1378C42—1462no—
1379C42—1462no—
1380C42C2×C4×D7314yescomplemented
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—2924no—
1392C23—2924no—
1393C23—2924no—
1394C23—2924no—
1395C23—2924no—
1396C23—2924no—
1397C23—732no—
1398C23—732no—
1399C23—732no—
1400C23—1461no—
1401C23—1461no—
1402C23—1461no—
1403C23—1461no—
1404C23—1461no—
1405C23—1461no—
1406C23—1461no—
1407C23—1461no—
1408C23—1461no—
1409C23—1461no—
1410C23—1461no—
1411C23—1461no—
1412C23—1461no—
1413C23—1461no—
1414C23—1461no—
1415C23—1461no—
1416C23—1461no—
1417C23—1461no—
1418C23—1468no—
1419C23C22×C4×D7312yes—
1420C23C22×C4×D7312yes—
1421C23#1455663612yes—
1422C23#1455663912yes—
1423C23C24×D7311yescharacteristic
1424Q8—2924no—
1425D4—28no—
1426D4—2924no—
1427D4—2924no—
1428D4—2924no—
1429D4—2924no—
1430D4—2924no—
1431D4—1468no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—44no—
1466C2×C4—44no—
1467C2×C4—44no—
1468C2×C4—82no—
1469C2×C4—82no—
1470C2×C4—82no—
1471C2×C4—2924no—
1472C2×C4—2924no—
1473C2×C4—2924no—
1474C2×C4—2924no—
1475C2×C4—2924no—
1476C2×C4—2924no—
1477C2×C4—2924no—
1478C2×C4—5842no—
1479C2×C4—5842no—
1480C2×C4—5842no—
1481C2×C4—732no—
1482C2×C4—732no—
1483C2×C4—732no—
1484C2×C4—732no—
1485C2×C4—732no—
1486C2×C4—732no—
1487C2×C4—1461no—
1488C2×C4—1461no—
1489C2×C4—1461no—
1490C2×C4—1461no—
1491C2×C4—1461no—
1492C2×C4—1461no—
1493C2×C4—1461no—
1494C2×C4—1461no—
1495C2×C4—1461no—
1496C2×C4—1461no—
1497C2×C4—1461no—
1498C2×C4—1461no—
1499C2×C4—1461no—
1500C2×C4—1461no—
1501C2×C4—1461no—
1502C2×C4—1461no—
1503C2×C4—1461no—
1504C2×C4—1461no—
1505C2×C4—1461no—
1506C2×C4—1461no—
1507C2×C4—1461no—
1508C2×C4—1461no—
1509C2×C4—1461no—
1510C2×C4—1461no—
1511C2×C4—1461no—
1512C2×C4—1461no—
1513C2×C4—1461no—
1514C2×C4—1461no—
1515C2×C4—1461no—
1516C2×C4—1461no—
1517C2×C4—1461no—
1518C2×C4—1461no—
1519C2×C4—1461no—
1520C2×C4C22×C4×D7312yes—
1521C2×C4C22×C4×D7312yes—
1522C2×C4C22×C4×D7312yes—
1523C2×C4C22×C4×D7312yes—
1524C2×C4C22×C4×D7312yes—
1525C2×C4#1455663712yes—
1526C22—22no—
1527C22—22no—
1528C22—22no—
1529C22—22no—
1530C22—22no—
1531C22—22no—
1532C22—22no—
1533C22—22no—
1534C22—22no—
1535C22—41no—
1536C22—41no—
1537C22—41no—
1538C22—41no—
1539C22—29216no—
1540C22—2921no—
1541C22—2921no—
1542C22—2921no—
1543C22—2921no—
1544C22—2921no—
1545C22—2921no—
1546C22—2921no—
1547C22—2921no—
1548C22—2921no—
1549C22—2921no—
1550C22—2921no—
1551C22—2921no—
1552C22—1462no—
1553C22—1462no—
1554C22—1462no—
1555C22—1462no—
1556C22—1462no—
1557C22—1462no—
1558C22—1462no—
1559C22—1462no—
1560C22—1462no—
1561C22#1798906814yes—
1562C22C23×C4×D7311yescharacteristic
1563C22H(5,𝔽2)×D7311yescharacteristic
1564C22C2×#1455663611yescharacteristic
1565C22C2×#1455663711yescharacteristic
1566C22C2×#1455663911yescharacteristic
1567C22#1798942211yescharacteristic
1568C22#1798942311yescharacteristic
1569C4—22no—
1570C4—22no—
1571C4—22no—
1572C4—22no—
1573C4—22no—
1574C4—22no—
1575C4—41no—
1576C4—41no—
1577C4—41no—
1578C4—41no—
1579C4—41no—
1580C4—41no—
1581C4—41no—
1582C4—2921no—
1583C4—2921no—
1584C4—2921no—
1585C4—2921no—
1586C4—2921no—
1587C4—2921no—
1588C4—2921no—
1589C4—1462no—
1590C4—1462no—
1591C4—1462no—
1592C4—1462no—
1593C4—1462no—
1594C4—1462no—
1595C2—24no—
1596C2—42no—
1597C2—2922no—
1598C2—2922no—
1599C2—2922no—
1600C2C2×#1798906811yescharacteristic
1601C2#2262313511yescharacteristic
1602C2C4×#1455663711yescharacteristic
1603C2#2262408011yescharacteristic
1604C2#2262409011yescharacteristic
1605C2#2262421711yescharacteristic
1606C2#2262422511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2349C2
socle, cosocleC23×C73C25
prime radicalC2×#17989170C2
hypercenter#2349D73
hypocenterC73#34416
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2349

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #22613122C2semidirect
3. #22613102C2semidirect
4. #22613087C2semidirect
5. #22613075C2semidirect
6. #22613054C2semidirect
7. #22613012C2semidirect
8. #22613002C2semidirect
9. #22612976C2semidirect
10. #22612950C2semidirect
11. #22612948C2semidirect
12. #22612931C2semidirect
13. #22612919C2semidirect
14. #22612867C2semidirect
15. #22612860C2semidirect
16. #22612827C2semidirect
17. #22612745C2semidirect
18. #22612724C2semidirect
19. #22612706C2semidirect
20. #22612702C2semidirect
21. #22612637C2semidirect
22. #22612634C2semidirect
23. #22612620C2semidirect
24. #22612595C2semidirect
25. #22612588C2semidirect
26. #22612585C2semidirect
27. #22612528C2semidirect
28. #22612432C2semidirect
29. C4×#14556559C2semidirect
30. C2×#17988461C2semidirect
31. C73×#2349C2semidirect
33. #17989170C4semidirect
46. C2×#14556556C22semidirect
52. C2×C4×C22⋊D73C22semidirect
55. C2×#14556550C22semidirect
58. C2×C4⋊C4×D73C22semidirect
61. #17988492C22semidirect
62. #17988491C22semidirect
63. #17988491C22semidirect
68. #17988487C22semidirect
69. #17988484C22semidirect
70. #17988484C22semidirect
71. #17988483C22semidirect
72. #17988482C22semidirect
73. #17988482C22semidirect
74. #17988482C22semidirect
75. #17988481C22semidirect
76. #17988480C22semidirect
77. #17988480C22semidirect
82. #17988479C22semidirect
83. #17988479C22semidirect
86. #17988478C22semidirect
95. #17988477C22semidirect
98. #17988475C22semidirect
99. #17988474C22semidirect
100. #17988474C22semidirect
101. #17988473C22semidirect
102. #17988473C22semidirect
103. #17988472C22semidirect
104. #17988472C22semidirect
105. #17988471C22semidirect
106. #17988469C22semidirect
107. #17988469C22semidirect
108. #17988468C22semidirect
109. #17988468C22semidirect
110. #17988468C22semidirect
117. #17988466C22semidirect
124. #17988463C22semidirect
133. #17988461C22semidirect
134. #17988461C22semidirect
135. #17988460C22semidirect
142. #17988458C22semidirect
143. #17988456C22semidirect
144. #17988454C22semidirect
145. #17988453C22semidirect
146. #17988449C22semidirect
148. #17988447C22semidirect
149. #17988444C22semidirect
152. C4⋊C4×Dic73C22semidirect
153. C4⋊C4×Dic73C22semidirect
154. C4×#11924007C22semidirect
155. C4×C4⋊Dic73C22semidirect
156. #17988438C22semidirect
157. #17988438C22semidirect
164. C4×#11924005C22semidirect
167. C4×C22⋊Dic73C22semidirect
170. #17988434C22semidirect
171. #17988432C22semidirect
176. #389×C73C22semidirect
177. #389×C73C22semidirect
180. #385×C73C22semidirect
181. #385×C73C22semidirect
182. #382×C73C22semidirect
184. #380×C73C22semidirect
185. C4×C4⋊C4×C73C22semidirect
187. C2×#95×C73C22semidirect
209. #14556586C2×C4semidirect
210. #14556585C2×C4semidirect
211. #14556579C2×C4semidirect
212. #14556577C2×C4semidirect
213. #14556576C2×C4semidirect
214. #14556574C2×C4semidirect
215. #14556568C2×C4semidirect
216. #14556565C2×C4semidirect
217. #14556564C2×C4semidirect
218. #14556563C2×C4semidirect
219. #14556561C2×C4semidirect
220. #14556559C2×C4semidirect
227. C4×C22⋊D73C2×C4semidirect
264. C2×#11924005C2×C4semidirect
347. C4×D4×C73C2×C4semidirect
388. C2×Dic146C22×C4semidirect
406. C2×C22⋊D73C22×C4semidirect
450. C2×C4×D73C22×C4semidirect
457. C4⋊Dic73C22×C4semidirect
468. #11924007C22×C4semidirect
469. #11924007C22×C4semidirect
470. #11924007C22×C4semidirect
471. #11924007C22×C4semidirect
479. C22⋊Dic73C22×C4semidirect
506. #11924005C22×C4semidirect
507. #11924005C22×C4semidirect
522. C4×Dic73C22×C4semidirect
545. C22×C4×C73C22×C4semidirect
567. C4⋊C4×C73C22×C4semidirect
573. C22⋊C4×C73C22×C4semidirect
576. C42×C73C22×C4semidirect
819. #2349D73semidirect
835. C73#34416semidirect
882. #389C2×D73semidirect
883. #389C2×D73semidirect
954. #385C2×D73semidirect
955. #385C2×D73semidirect
959. #382C2×D73semidirect
965. #380C2×D73semidirect
974. C4×C4⋊C4C2×D73semidirect
991. C2×#95C2×D73semidirect
1043. C4×D4C4×D73semidirect
1277. C22×C4C2×C4×D73semidirect
1320. C4⋊C4C2×C4×D73semidirect
1362. C22⋊C4C2×C4×D73semidirect
1380. C42C2×C4×D73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179891702
#226131222
#226131022
#226130872
#226130752
#226130542
#226130122
#226130022
#226129762
#226129502
#226129482
#226129312
#226129192
#226128672
#226128602
#226128272
#226127452
#226127242
#226127062
#226127022
#226126372
#226126342
#226126202
#226125952
#226125882
#226125852
#226125282
#226124322
C4×#145565592
C2×#179884612
C73×#23492
#3441673