Finite Group Databasebeta

← #33249531

Subgroups — #33249531

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×#17989169C211yesmaximal, characteristic
2#22613119C211yesmaximal, characteristic, complemented
3#22613101C211yesmaximal, characteristic, complemented
4#22613074C211yesmaximal, characteristic, complemented
5#22613058C211yesmaximal, characteristic, complemented
6#22613008C211yesmaximal, characteristic, complemented
7#22613001C211yesmaximal, characteristic, complemented
8#22612980C211yesmaximal, characteristic, complemented
9#22612952C211yesmaximal, characteristic, complemented
10#22612951C211yesmaximal, characteristic, complemented
11#22612939C211yesmaximal, characteristic, complemented
12#22612929C211yesmaximal, characteristic, complemented
13#22612868C211yesmaximal, characteristic, complemented
14#22612859C211yesmaximal, characteristic, complemented
15#22612837C211yesmaximal, characteristic, complemented
16#22612827C211yesmaximal, characteristic, complemented
17#22612745C211yesmaximal, characteristic, complemented
18#22612717C211yesmaximal, characteristic, complemented
19#22612712C211yesmaximal, characteristic, complemented
20#22612711C211yesmaximal, characteristic, complemented
21#22612640C211yesmaximal, characteristic, complemented
22#22612632C211yesmaximal, characteristic, complemented
23#22612617C211yesmaximal, characteristic, complemented
24#22612597C211yesmaximal, characteristic, complemented
25#22612590C211yesmaximal, characteristic, complemented
26#22612587C211yesmaximal, characteristic, complemented
27#22612525C211yesmaximal, characteristic, complemented
28#22612436C211yesmaximal, characteristic, complemented
29#22612436C211yesmaximal, characteristic, complemented
30#385×D73C211yesmaximal, characteristic, complemented
31C73×#2377C211yesmaximal, characteristic, complemented
32C23×C4×D73C2211yescharacteristic
33#17989169C4116yescomplemented
34C2×#14556586C2211yescharacteristic
35C2×#14556584C2211yescharacteristic
36C2×#14556578C2211yescharacteristic
37C2×#14556577C2211yescharacteristic
38C2×#14556574C2211yescharacteristic
39C2×#14556572C2211yescharacteristic
40C2×#14556569C2211yescharacteristic
41C2×#14556563C2211yescharacteristic
42C2×#14556562C2211yescharacteristic
43C2×#14556559C2211yescharacteristic
44C2×#14556559C2211yescharacteristic
45C2×C4×Dic146C2211yescharacteristic, complemented
46C2×D4×Dic73C2211yescharacteristic
47C2×D4×Dic73C2211yescharacteristic
48C2×D4×Dic73C2211yescharacteristic, complemented
49C2×C4×C22⋊D73C2211yescharacteristic
50C2×C4×C22⋊D73C2211yescharacteristic
51C2×#14556551C2211yescharacteristic
52C2×#14556551C2211yescharacteristic
53C2×#14556551C2211yescharacteristic
54C2×#14556551C2211yescharacteristic
55C2×#14556551C2211yescharacteristic
56C2×#14556551C2211yescharacteristic
57C2×#14556547C2211yescharacteristic, complemented
58C22×C4⋊Dic73C2211yescharacteristic, complemented
59C2×C4⋊C4×D73C2211yescharacteristic
60C2×C4⋊C4×D73C2211yescharacteristic
61C2×C22⋊C4×D73C2211yescharacteristic
62C2×C22⋊C4×D73C2211yescharacteristic
63#17988492C2211yescharacteristic, complemented
64#17988491C2211yescharacteristic, complemented
65#17988491C2211yescharacteristic, complemented
66#17988490C2211yescharacteristic
67#17988487C2211yescharacteristic
68#17988487C2211yescharacteristic
69#17988486C2211yescharacteristic, complemented
70#17988484C2211yescharacteristic, complemented
71#17988484C2211yescharacteristic, complemented
72#17988484C2211yescharacteristic, complemented
73#17988484C2211yescharacteristic, complemented
74#17988483C2211yescharacteristic, complemented
75#17988482C2211yescharacteristic, complemented
76#17988482C2211yescharacteristic, complemented
77#17988481C2211yescharacteristic
78#17988481C2211yescharacteristic
79#17988481C2211yescharacteristic
80#17988481C2211yescharacteristic, complemented
81#17988481C2211yescharacteristic, complemented
82#17988481C2211yescharacteristic, complemented
83#17988480C2211yescharacteristic
84#17988480C2211yescharacteristic, complemented
85#17988479C2211yescharacteristic
86#17988479C2211yescharacteristic
87#17988478C2211yescharacteristic
88#17988478C2211yescharacteristic
89#17988477C2211yescharacteristic
90#17988477C2211yescharacteristic
91#17988476C2211yescharacteristic
92#17988476C2211yescharacteristic
93#17988475C2211yescharacteristic
94#17988475C2211yescharacteristic
95#17988475C2211yescharacteristic
96#17988475C2211yescharacteristic, complemented
97#17988475C2211yescharacteristic, complemented
98#17988475C2211yescharacteristic, complemented
99#17988474C2211yescharacteristic, complemented
100#17988474C2211yescharacteristic, complemented
101#17988474C2211yescharacteristic, complemented
102#17988472C2211yescharacteristic, complemented
103#17988470C2211yescharacteristic, complemented
104#17988469C2211yescharacteristic, complemented
105#17988469C2211yescharacteristic, complemented
106#17988469C2211yescharacteristic, complemented
107#17988469C2211yescharacteristic, complemented
108#17988468C2211yescharacteristic, complemented
109#17988467C2211yescharacteristic
110#17988467C2211yescharacteristic, complemented
111#17988466C2211yescharacteristic
112#17988464C2211yescharacteristic
113#17988463C2211yescharacteristic
114#17988463C2211yescharacteristic
115#17988463C2211yescharacteristic
116#17988463C2211yescharacteristic
117#17988463C2211yescharacteristic
118#17988463C2211yescharacteristic
119#17988462C2211yescharacteristic
120#17988462C2211yescharacteristic, complemented
121#17988461C2211yescharacteristic
122#17988461C2211yescharacteristic
123#17988461C2211yescharacteristic
124#17988461C2211yescharacteristic
125#17988461C2211yescharacteristic
126#17988461C2211yescharacteristic
127#17988461C2211yescharacteristic
128#17988460C2211yescharacteristic
129#17988460C2211yescharacteristic
130#17988460C2211yescharacteristic
131#17988459C2211yescharacteristic
132#17988459C2211yescharacteristic, complemented
133#17988459C2211yescharacteristic, complemented
134#17988459C2211yescharacteristic, complemented
135#17988459C2211yescharacteristic, complemented
136#17988458C2211yescharacteristic
137#17988458C2211yescharacteristic
138#17988458C2211yescharacteristic
139#17988456C2211yescharacteristic, complemented
140#17988454C2211yescharacteristic, complemented
141#17988451C2211yescharacteristic, complemented
142#17988451C2211yescharacteristic, complemented
143#17988446C2211yescharacteristic
144#17988445C2211yescharacteristic, complemented
145#17988445C2211yescharacteristic, complemented
146#17988444C2211yescharacteristic
147#17988442C2211yescharacteristic
148#17988442C2211yescharacteristic
149C4⋊C4×Dic73C2211yescharacteristic, complemented
150C4⋊C4×Dic73C2211yescharacteristic, complemented
151C4⋊C4×Dic73C2211yescharacteristic, complemented
152C4×#11924007C2211yescharacteristic, complemented
153C4×#11924007C2211yescharacteristic, complemented
154C4×C4⋊Dic73C2211yescharacteristic, complemented
155#17988438C2211yescharacteristic, complemented
156C22⋊C4×Dic73C2211yescharacteristic
157C22⋊C4×Dic73C2211yescharacteristic
158C22⋊C4×Dic73C2211yescharacteristic, complemented
159C4×#11924005C2211yescharacteristic
160C4×#11924005C2211yescharacteristic
161C4×C22⋊Dic73C2211yescharacteristic, complemented
162C4×C22⋊Dic73C2211yescharacteristic, complemented
163#17988434C2211yescharacteristic
164#17988434C2211yescharacteristic
165#17988434C2211yescharacteristic
166#17988434C2211yescharacteristic
167#17988434C2211yescharacteristic
168#17988434C2211yescharacteristic
169#17988432C2211yescharacteristic, complemented
170C2×#14556498C2211yescharacteristic, complemented
171#95×D73C2211yescharacteristic
172#95×D73C2211yescharacteristic
173C2×#121×C73C2211yescharacteristic
174#390×C73C2211yescharacteristic
175#390×C73C2211yescharacteristic, complemented
176#388×C73C2211yescharacteristic
177#388×C73C2211yescharacteristic, complemented
178#387×C73C2211yescharacteristic, complemented
179#387×C73C2211yescharacteristic, complemented
180#386×C73C2211yescharacteristic
181#386×C73C2211yescharacteristic
182#386×C73C2211yescharacteristic
183#386×C73C2211yescharacteristic, complemented
184#385×C73C2211yescharacteristic
185#385×C73C2211yescharacteristic, complemented
186#381×C73C2211yescharacteristic, complemented
187#380×C73C2211yescharacteristic, complemented
188C24×D73C2311yescharacteristic
189C22×Dic146C2311yescharacteristic
190C22×C22⋊D73C2311yescharacteristic
191C22×C22⋊D73C2311yescharacteristic
192C22×C22⋊D73C2311yescharacteristic
193C22×C22⋊D73C2311yescharacteristic
194C23×Dic73C2311yescharacteristic
195C23×Dic73C2311yescharacteristic
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
209C22×C4×D73C2311yescharacteristic
210#14556586C2×C418yescomplemented
211#14556584C2×C418yescomplemented
212#14556578C2×C418yescomplemented
213#14556577C2×C418yescomplemented
214#14556574C2×C418yescomplemented
215#14556572C2×C418yescomplemented
216#14556569C2×C418yescomplemented
217#14556563C2×C418yescomplemented
218#14556562C2×C418yescomplemented
219#14556559C2×C418yescomplemented
220#14556559C2×C418yescomplemented
221C4×Dic146—42no—
222D4×Dic73—42no—
223D4×Dic73—42no—
224D4×Dic73—42no—
225C4×C22⋊D73—42no—
226C4×C22⋊D73C2×C418yescomplemented
227#14556551—42no—
228#14556551—42no—
229#14556551—42no—
230#14556551—42no—
231#14556551—42no—
232#14556551C2×C418yescomplemented
233#14556547—42no—
234C2×C4⋊Dic73—42no—
235C2×C4⋊Dic73C2311yescharacteristic
236C2×C4⋊Dic73C2311yescharacteristic
237C2×C4⋊Dic73C2311yescharacteristic
238C2×C4⋊Dic73C2311yescharacteristic
239C2×C4⋊Dic73C2311yescharacteristic
240C2×C4⋊Dic73C2311yescharacteristic
241C2×C4⋊Dic73C2311yescharacteristic
242C2×#11924007C2311yescharacteristic
243C2×#11924007C2311yescharacteristic
244C2×#11924007C2311yescharacteristic
245C2×#11924007C2311yescharacteristic
246C2×#11924007C2311yescharacteristic
247C2×#11924007C2311yescharacteristic
248C2×#11924007C2311yescharacteristic
249C2×#11924007C2311yescharacteristic
250C2×#11924007C2311yescharacteristic
251C2×#11924007C2311yescharacteristic
252C2×#11924007C2311yescharacteristic
253C2×#11924007C2311yescharacteristic
254C2×#11924007C2311yescharacteristic
255C2×#11924007C2311yescharacteristic
256C2×#11924007C2311yescharacteristic
257C2×#11924007C2311yescharacteristic
258C2×#11924007C2311yescharacteristic
259C2×#11924007C2311yescharacteristic
260C4⋊C4×D73—42no—
261C4⋊C4×D73—42no—
262C2×C22⋊Dic73C2311yescharacteristic
263C2×C22⋊Dic73C2311yescharacteristic
264C2×C22⋊Dic73C2311yescharacteristic
265C2×C22⋊Dic73C2311yescharacteristic
266C2×C22⋊Dic73C2311yescharacteristic
267C2×C22⋊Dic73C2311yescharacteristic
268C2×C22⋊Dic73C2311yescharacteristic
269C2×C22⋊Dic73C2311yescharacteristic
270C2×C22⋊Dic73C2311yescharacteristic
271C2×C22⋊Dic73C2311yescharacteristic
272C2×C22⋊Dic73C2311yescharacteristic
273C2×C22⋊Dic73C2311yescharacteristic
274C2×C22⋊Dic73C2311yescharacteristic
275C2×C22⋊Dic73C2311yescharacteristic
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
292C22⋊C4×D73—42no—
293C22⋊C4×D73C2×C418yescomplemented
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
308C2×C4×Dic73C2311yescharacteristic
309C2×C4×Dic73C2311yescharacteristic
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
338#14556498C2311yescharacteristic
339#14556498C2311yescharacteristic
340C22×D4×C73C2311yescharacteristic
341C22×D4×C73C2311yescharacteristic
342C22×D4×C73C2311yescharacteristic
343C23×C4×C73C2311yescharacteristic
344C23×C4×C73C2311yescharacteristic
345C23×C4×C73C2311yescharacteristic
346#121×C73C2×C418yescomplemented
347C2×C4⋊C4×C73C2311yescharacteristic
348C2×C4⋊C4×C73C2311yescharacteristic
349C2×C4⋊C4×C73C2311yescharacteristic
350C2×C4⋊C4×C73C2311yescharacteristic
351C2×C4⋊C4×C73C2311yescharacteristic
352C2×C22⋊C4×C73C2311yescharacteristic
353C2×C22⋊C4×C73C2311yescharacteristic
354C2×C22⋊C4×C73C2311yescharacteristic
355C2×C22⋊C4×C73C2311yescharacteristic
356C2×C22⋊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×C22⋊C4×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
385C2×Dic146—41no—
386C2×Dic146—41no—
387C2×Dic146C22×C414yescomplemented
388C2×C22⋊D73—22no—
389C2×C22⋊D73—22no—
390C2×C22⋊D73—22no—
391C2×C22⋊D73—22no—
392C2×C22⋊D73—41no—
393C2×C22⋊D73—41no—
394C2×C22⋊D73—41no—
395C2×C22⋊D73—41no—
396C2×C22⋊D73C22×C414yes—
397C2×C22⋊D73C22×C414yes—
398C2×C22⋊D73C22×C414yes—
399C2×C22⋊D73C22×C414yes—
400C22×Dic73—22no—
401C22×Dic73—22no—
402C22×Dic73—22no—
403C22×Dic73—22no—
404C22×Dic73—41no—
405C22×Dic73—41no—
406C22×Dic73—41no—
407C22×Dic73—41no—
408C22×Dic73—41no—
409C22×Dic73—41no—
410C22×Dic73—41no—
411C22×Dic73—41no—
412C22×Dic73—41no—
413C22×Dic73—41no—
414C22×Dic73C22×C414yescomplemented
415C22×Dic73C2411yescharacteristic
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—22no—
435C2×C4×D73—22no—
436C2×C4×D73—22no—
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—41no—
445C2×C4×D73—41no—
446C2×C4×D73—41no—
447C2×C4×D73—416no—
448C2×C4×D73—41no—
449C2×C4×D73—41no—
450C2×C4×D73—41no—
451C2×C4×D73—41no—
452C2×C4×D73C22×C414yes—
453C2×C4×D73C22×C414yes—
454C4⋊Dic73—22no—
455C4⋊Dic73—22no—
456C4⋊Dic73—22no—
457C4⋊Dic73—22no—
458C4⋊Dic73—41no—
459C4⋊Dic73—41no—
460C4⋊Dic73C22×C414yescomplemented
461#11924007—22no—
462#11924007—22no—
463#11924007—41no—
464#11924007—41no—
465#11924007—41no—
466#11924007—41no—
467#11924007—41no—
468#11924007—41no—
469#11924007—41no—
470#11924007—41no—
471#11924007—41no—
472#11924007—41no—
473#11924007—41no—
474#11924007—41no—
475#11924007C22×C414yescomplemented
476#11924007C22×C414yescomplemented
477#11924007C22×C414yescomplemented
478#11924007C22×C414yescomplemented
479C22⋊Dic73—22no—
480C22⋊Dic73—22no—
481C22⋊Dic73—41no—
482C22⋊Dic73—41no—
483C22⋊Dic73—41no—
484C22⋊Dic73—41no—
485C22⋊Dic73—41no—
486C22⋊Dic73—41no—
487C22⋊Dic73C22×C414yes—
488C22⋊Dic73C22×C414yes—
489C22⋊Dic73C22×C414yes—
490C22⋊Dic73C22×C414yescomplemented
491C22⋊Dic73C22×C414yescomplemented
492C22⋊Dic73C22×C414yescomplemented
493#11924005—22no—
494#11924005—22no—
495#11924005—22no—
496#11924005—22no—
497#11924005—41no—
498#11924005—41no—
499#11924005—41no—
500#11924005—41no—
501#11924005—41no—
502#11924005—41no—
503#11924005C22×C414yes—
504#11924005C22×C414yes—
505#11924005C22×C414yes—
506#11924005C22×C414yes—
507#11924005C22×C414yes—
508#11924005C22×C414yes—
509C4×Dic73—22no—
510C4×Dic73—22no—
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×Dic73—41no—
523C4×Dic73C22×C414yescomplemented
524C4×Dic73C22×C414yescomplemented
525C24×C73C2411yescharacteristic
526C24×C73C2411yescharacteristic
527C24×C73C2411yescharacteristic
528C2×D4×C73—41no—
529C2×D4×C73—41no—
530C2×D4×C73—41no—
531C2×D4×C73—41no—
532C2×D4×C73—41no—
533C2×D4×C73—41no—
534C2×D4×C73C22×C414yes—
535C2×D4×C73C22×C414yes—
536C2×D4×C73C22×C414yescomplemented
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×C73—41no—
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
558C4⋊C4×C73—41no—
559C4⋊C4×C73—41no—
560C4⋊C4×C73—41no—
561C4⋊C4×C73—41no—
562C4⋊C4×C73C22×C414yescomplemented
563C22⋊C4×C73—41no—
564C22⋊C4×C73—41no—
565C22⋊C4×C73—41no—
566C22⋊C4×C73—41no—
567C22⋊C4×C73—41no—
568C22⋊C4×C73—41no—
569C22⋊C4×C73—41no—
570C22⋊C4×C73—41no—
571C22⋊C4×C73—41no—
572C22⋊C4×C73—41no—
573C22⋊C4×C73C22×C414yes—
574C22⋊C4×C73C22×C414yescomplemented
575C42×C73—41no—
576C42×C73—41no—
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×C73—21no—
588C23×C73—21no—
589C23×C73—21no—
590C23×C73—21no—
591C23×C73—21no—
592C23×C73—21no—
593C23×C73—21no—
594C23×C73—21no—
595C23×C73C23×C412yes—
596C23×C73C23×C412yes—
597C23×C73C23×C412yes—
598C23×C73C2511yescharacteristic
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—28no—
610C22×D73—44no—
611C22×D73—44no—
612C22×D73—44no—
613C22×D73—44no—
614C22×D73—44no—
615C22×D73—44no—
616C22×D73C23×C412yes—
617C22×D73C23×C412yes—
618C22×D73H(5,𝔽2)12yes—
619C22×D732−1+412yes—
620D4×C73—44no—
621D4×C73—44no—
622D4×C73—44no—
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—21no—
655C2×C4×C73—44no—
656C2×C4×C73—44no—
657C2×C4×C73—82no—
658C2×C4×C73C23×C412yes—
659C2×C4×C73C23×C412yes—
660C2×C4×C73C23×C412yes—
661C2×C4×C73C23×C412yes—
662C22⋊D73—28no—
663C22⋊D73—28no—
664C22⋊D73—44no—
665C22⋊D73—44no—
666C2×Dic73—21no—
667C2×Dic73—21no—
668C2×Dic73—21no—
669C2×Dic73—21no—
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—44no—
701C2×Dic73—44no—
702C2×Dic73—82no—
703C2×Dic73—82no—
704C2×Dic73—82no—
705C2×Dic73C23×C412yes—
706C2×Dic73C23×C412yes—
707C2×Dic73C23×C412yes—
708C2×Dic73C23×C412yes—
709C2×Dic73C23×C412yes—
710C2×Dic73C23×C412yes—
711C2×Dic73H(5,𝔽2)12yes—
712C2×Dic73H(5,𝔽2)12yes—
713C4×D73—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—41no—
736C22×C73—41no—
737C22×C73—41no—
738C22×C73—41no—
739C22×C73—41no—
740C22×C73—41no—
741C22×C73—41no—
742C22×C73—41no—
743C22×C73C24×C411yescharacteristic
744C22×C73C2×H(5,𝔽2)11yescharacteristic
745C22×C73C2×H(5,𝔽2)11yescharacteristic
746C22×C73C2×H(5,𝔽2)11yescharacteristic
747C22×C73C2×2−1+411yescharacteristic
748C22×C73#58511yescharacteristic
749C22×C73#58511yescharacteristic
750C2×D73—22no—
751C2×D73—22no—
752C2×D73—22no—
753C2×D73—22no—
754C2×D73—22no—
755C2×D73—22no—
756C2×D73—22no—
757C2×D73—22no—
758C2×D73—22no—
759C2×D73—416no—
760C2×D73—41no—
761C2×D73—41no—
762C2×D73—41no—
763C2×D73—41no—
764C2×D73#52014yes—
765C4×C73—22no—
766C4×C73—22no—
767C4×C73—22no—
768C4×C73—22no—
769C4×C73—41no—
770C4×C73—41no—
771C4×C73—41no—
772C4×C73—41no—
773C4×C73—41no—
774C4×C73—41no—
775C4×C73—41no—
776C4×C73—41no—
777Dic73—22no—
778Dic73—22no—
779Dic73—22no—
780Dic73—22no—
781Dic73—22no—
782Dic73—22no—
783Dic73—22no—
784Dic73—22no—
785Dic73—41no—
786Dic73—41no—
787Dic73—41no—
788Dic73—41no—
789Dic73—41no—
790Dic73—41no—
791#34416—731nomaximal, Sylow
792C2×C73—42no—
793C2×C73—42no—
794C2×C73—42no—
795C2×C73C2×#52011yescharacteristic
796C2×C73C4×H(5,𝔽2)11yescharacteristic
797C2×C73C4×H(5,𝔽2)11yescharacteristic
798C2×C73#353211yescharacteristic
799C2×C73#353311yescharacteristic
800C2×C73#354111yescharacteristic
801C2×C73#354111yescharacteristic
802D73—24no—
803D73—42no—
804C2×#538—731no—
805#2383—731no—
806#2379—731no—
807#2377D7311yescharacteristic, complemented
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#2349—731no—
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×#121C2×D7311yescharacteristic
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×D4—731no—
860C2×C4×D4—731no—
861C2×C4×D4—731no—
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#390C2×D7311yescharacteristic
875#390C2×D7311yescharacteristic, complemented
876#389—731no—
877#389—731no—
878#389—731no—
879#389—731no—
880#389—731no—
881#389—731no—
882#389—731no—
883#389—731no—
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#388C2×D7311yescharacteristic
907#388C2×D7311yescharacteristic, complemented
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#387C2×D7311yescharacteristic, complemented
919#387C2×D7311yescharacteristic, complemented
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#386C2×D7311yescharacteristic
931#386C2×D7311yescharacteristic
932#386C2×D7311yescharacteristic
933#386C2×D7311yescharacteristic, complemented
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#385—731no—
953#385—731no—
954#385C2×D7311yescharacteristic
955#385C2×D7311yescharacteristic, complemented
956#384—731no—
957#383—731no—
958#382—731no—
959#382—731no—
960#381C2×D7311yescharacteristic, complemented
961#380—731no—
962#380—731no—
963#380—731no—
964#380—731no—
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⋊C4—731no—
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×#95—731no—
991C2×#95—731no—
992C25—731no—
993C22×Q8—731no—
994C22×D4—731no—
995C22×D4—731no—
996C22×D4—731no—
997C22×D4—731no—
998C22×D4C22×D7311yescharacteristic
999C22×D4C22×D7311yescharacteristic
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×C4—731no—
1015C23×C4—731no—
1016C23×C4—731no—
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#121C4×D7318yescomplemented
1030#120—738no—
1031#120—738no—
1032C4×Q8—2922no—
1033C4×D4—2922no—
1034C4×D4—2922no—
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×D4—738no—
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⋊C4—731no—
1070C2×C4⋊C4—731no—
1071C2×C4⋊C4—731no—
1072C2×C4⋊C4—731no—
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—731no—
1102C2×C22⋊C4—731no—
1103C2×C22⋊C4—738no—
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⋊C4C22×D7311yescharacteristic
1111C2×C22⋊C4C22×D7311yescharacteristic
1112C2×C22⋊C4C22×D7311yescharacteristic
1113C2×C22⋊C4C22×D7311yescharacteristic
1114C2×C22⋊C4C22×D7311yescharacteristic
1115C2×C22⋊C4C22×D7311yescharacteristic
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×C42—731no—
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—1462no—
1188C24—1462no—
1189C24C23×D7311yescharacteristic
1190C24C23×D7311yescharacteristic
1191C24C23×D7311yescharacteristic
1192C2×Q8—2921no—
1193C2×Q8—2921no—
1194C2×Q8—734no—
1195C2×D4—41no—
1196C2×D4—41no—
1197C2×D4—41no—
1198C2×D4—41no—
1199C2×D4—41no—
1200C2×D4—41no—
1201C2×D4—2921no—
1202C2×D4—2921no—
1203C2×D4—2921no—
1204C2×D4—2921no—
1205C2×D4—734no—
1206C2×D4—734no—
1207C2×D4—734no—
1208C2×D4—734no—
1209C2×D4—1462no—
1210C2×D4—1462no—
1211C2×D4—1462no—
1212C2×D4—1462no—
1213C2×D4C2×C4×D7314yes—
1214C2×D4C2×C4×D7314yes—
1215C2×D4C2×C4×D7314yescomplemented
1216C22×C4—41no—
1217C22×C4—41no—
1218C22×C4—41no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—41no—
1224C22×C4—2921no—
1225C22×C4—2921no—
1226C22×C4—2921no—
1227C22×C4—2921no—
1228C22×C4—2921no—
1229C22×C4—2921no—
1230C22×C4—2921no—
1231C22×C4—2921no—
1232C22×C4—2921no—
1233C22×C4—2921no—
1234C22×C4—2921no—
1235C22×C4—2921no—
1236C22×C4—2921no—
1237C22×C4—2921no—
1238C22×C4—29216no—
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—2921no—
1248C22×C4—2921no—
1249C22×C4—734no—
1250C22×C4—734no—
1251C22×C4—734no—
1252C22×C4—731no—
1253C22×C4—731no—
1254C22×C4—731no—
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—1462no—
1267C22×C4—1462no—
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×C4—1462no—
1277C22×C4—1462no—
1278C22×C4C2×C4×D7314yescomplemented
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—41no—
1292C4⋊C4—41no—
1293C4⋊C4—41no—
1294C4⋊C4—41no—
1295C4⋊C4—2921no—
1296C4⋊C4—2921no—
1297C4⋊C4—2921no—
1298C4⋊C4—2921no—
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—734no—
1310C4⋊C4—734no—
1311C4⋊C4—734no—
1312C4⋊C4—734no—
1313C4⋊C4—734no—
1314C4⋊C4—1462no—
1315C4⋊C4—1462no—
1316C4⋊C4—1462no—
1317C4⋊C4—1462no—
1318C4⋊C4—1462no—
1319C4⋊C4—1462no—
1320C4⋊C4C2×C4×D7314yescomplemented
1321C22⋊C4—41no—
1322C22⋊C4—41no—
1323C22⋊C4—41no—
1324C22⋊C4—41no—
1325C22⋊C4—41no—
1326C22⋊C4—41no—
1327C22⋊C4—41no—
1328C22⋊C4—41no—
1329C22⋊C4—41no—
1330C22⋊C4—41no—
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—734no—
1344C22⋊C4—734no—
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—1462no—
1356C22⋊C4—1462no—
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—734no—
1379C42—1462no—
1380C42—1462no—
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—2924no—
1400C23—2924no—
1401C23—2924no—
1402C23—2924no—
1403C23—2924no—
1404C23—2924no—
1405C23—732no—
1406C23—732no—
1407C23—732no—
1408C23—732no—
1409C23—1468no—
1410C23—1461no—
1411C23—1461no—
1412C23—1461no—
1413C23—1461no—
1414C23—1461no—
1415C23—1461no—
1416C23—1461no—
1417C23—1461no—
1418C23—1461no—
1419C23—1461no—
1420C23C22×C4×D7312yes—
1421C23C22×C4×D7312yes—
1422C23C22×C4×D7312yes—
1423C23C24×D7311yescharacteristic
1424Q8—2924no—
1425D4—44no—
1426D4—44no—
1427D4—44no—
1428D4—2924no—
1429D4—2924no—
1430D4—1468no—
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—44no—
1465C2×C4—44no—
1466C2×C4—82no—
1467C2×C4—2924no—
1468C2×C4—2924no—
1469C2×C4—2924no—
1470C2×C4—2924no—
1471C2×C4—2924no—
1472C2×C4—2924no—
1473C2×C4—2924no—
1474C2×C4—2924no—
1475C2×C4—5842no—
1476C2×C4—5842no—
1477C2×C4—5842no—
1478C2×C4—5842no—
1479C2×C4—5842no—
1480C2×C4—732no—
1481C2×C4—732no—
1482C2×C4—732no—
1483C2×C4—732no—
1484C2×C4—732no—
1485C2×C4—732no—
1486C2×C4—732no—
1487C2×C4—732no—
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×C4—1461no—
1521C2×C4—1461no—
1522C2×C4C22×C4×D7312yes—
1523C2×C4C22×C4×D7312yes—
1524C2×C4C22×C4×D7312yes—
1525C2×C4C22×C4×D7312yes—
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—41no—
1540C22—41no—
1541C22—41no—
1542C22—41no—
1543C22—41no—
1544C22—41no—
1545C22—41no—
1546C22—41no—
1547C22—29216no—
1548C22—2921no—
1549C22—2921no—
1550C22—2921no—
1551C22—2921no—
1552C22—734no—
1553C22—1462no—
1554C22—1462no—
1555C22—1462no—
1556C22—1462no—
1557C22—1462no—
1558C22—1462no—
1559C22—1462no—
1560C22—1462no—
1561C22—1462no—
1562C22C23×C4×D7311yescharacteristic
1563C22H(5,𝔽2)×D7311yescharacteristic
1564C22H(5,𝔽2)×D7311yescharacteristic
1565C22H(5,𝔽2)×D7311yescharacteristic
1566C222−1+4×D7311yescharacteristic
1567C22#1798942211yescharacteristic
1568C22#1798942211yescharacteristic
1569C4—22no—
1570C4—22no—
1571C4—22no—
1572C4—22no—
1573C4—41no—
1574C4—41no—
1575C4—41no—
1576C4—41no—
1577C4—41no—
1578C4—41no—
1579C4—41no—
1580C4—41no—
1581C4—2921no—
1582C4—2921no—
1583C4—2921no—
1584C4—2921no—
1585C4—2921no—
1586C4—2921no—
1587C4—1462no—
1588C4—1462no—
1589C4—1462no—
1590C4—1462no—
1591C4—1462no—
1592C4—1462no—
1593C4—1462no—
1594C4—1462no—
1595C2—42no—
1596C2—42no—
1597C2—42no—
1598C2—2922no—
1599C2—1464no—
1600C2#520×D7311yescharacteristic
1601C2#2262313511yescharacteristic
1602C2#2262313511yescharacteristic
1603C2#2262408411yescharacteristic
1604C2#2262410011yescharacteristic
1605C2#2262421311yescharacteristic
1606C2#2262421311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2377C2
socle, cosocleC23×C73C25
prime radicalC2×#17989169C2
hypercenter#2377D73
hypocenterC73#34416
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2377

Complements

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

NH ≅ G/Ntype
2. #22613119C2semidirect
3. #22613101C2semidirect
4. #22613074C2semidirect
5. #22613058C2semidirect
6. #22613008C2semidirect
7. #22613001C2semidirect
8. #22612980C2semidirect
9. #22612952C2semidirect
10. #22612951C2semidirect
11. #22612939C2semidirect
12. #22612929C2semidirect
13. #22612868C2semidirect
14. #22612859C2semidirect
15. #22612837C2semidirect
16. #22612827C2semidirect
17. #22612745C2semidirect
18. #22612717C2semidirect
19. #22612712C2semidirect
20. #22612711C2semidirect
21. #22612640C2semidirect
22. #22612632C2semidirect
23. #22612617C2semidirect
24. #22612597C2semidirect
25. #22612590C2semidirect
26. #22612587C2semidirect
27. #22612525C2semidirect
28. #22612436C2semidirect
29. #22612436C2semidirect
30. #385×D73C2semidirect
31. C73×#2377C2semidirect
33. #17989169C4semidirect
45. C2×C4×Dic146C22semidirect
48. C2×D4×Dic73C22semidirect
57. C2×#14556547C22semidirect
58. C22×C4⋊Dic73C22semidirect
63. #17988492C22semidirect
64. #17988491C22semidirect
65. #17988491C22semidirect
69. #17988486C22semidirect
70. #17988484C22semidirect
71. #17988484C22semidirect
72. #17988484C22semidirect
73. #17988484C22semidirect
74. #17988483C22semidirect
75. #17988482C22semidirect
76. #17988482C22semidirect
80. #17988481C22semidirect
81. #17988481C22semidirect
82. #17988481C22semidirect
84. #17988480C22semidirect
96. #17988475C22semidirect
97. #17988475C22semidirect
98. #17988475C22semidirect
99. #17988474C22semidirect
100. #17988474C22semidirect
101. #17988474C22semidirect
102. #17988472C22semidirect
103. #17988470C22semidirect
104. #17988469C22semidirect
105. #17988469C22semidirect
106. #17988469C22semidirect
107. #17988469C22semidirect
108. #17988468C22semidirect
110. #17988467C22semidirect
120. #17988462C22semidirect
132. #17988459C22semidirect
133. #17988459C22semidirect
134. #17988459C22semidirect
135. #17988459C22semidirect
139. #17988456C22semidirect
140. #17988454C22semidirect
141. #17988451C22semidirect
142. #17988451C22semidirect
144. #17988445C22semidirect
145. #17988445C22semidirect
149. C4⋊C4×Dic73C22semidirect
150. C4⋊C4×Dic73C22semidirect
151. C4⋊C4×Dic73C22semidirect
152. C4×#11924007C22semidirect
153. C4×#11924007C22semidirect
154. C4×C4⋊Dic73C22semidirect
155. #17988438C22semidirect
158. C22⋊C4×Dic73C22semidirect
161. C4×C22⋊Dic73C22semidirect
162. C4×C22⋊Dic73C22semidirect
169. #17988432C22semidirect
170. C2×#14556498C22semidirect
175. #390×C73C22semidirect
177. #388×C73C22semidirect
178. #387×C73C22semidirect
179. #387×C73C22semidirect
183. #386×C73C22semidirect
185. #385×C73C22semidirect
186. #381×C73C22semidirect
187. #380×C73C22semidirect
210. #14556586C2×C4semidirect
211. #14556584C2×C4semidirect
212. #14556578C2×C4semidirect
213. #14556577C2×C4semidirect
214. #14556574C2×C4semidirect
215. #14556572C2×C4semidirect
216. #14556569C2×C4semidirect
217. #14556563C2×C4semidirect
218. #14556562C2×C4semidirect
219. #14556559C2×C4semidirect
220. #14556559C2×C4semidirect
226. C4×C22⋊D73C2×C4semidirect
232. #14556551C2×C4semidirect
293. C22⋊C4×D73C2×C4semidirect
346. #121×C73C2×C4semidirect
387. C2×Dic146C22×C4semidirect
414. C22×Dic73C22×C4semidirect
460. C4⋊Dic73C22×C4semidirect
475. #11924007C22×C4semidirect
476. #11924007C22×C4semidirect
477. #11924007C22×C4semidirect
478. #11924007C22×C4semidirect
490. C22⋊Dic73C22×C4semidirect
491. C22⋊Dic73C22×C4semidirect
492. C22⋊Dic73C22×C4semidirect
523. C4×Dic73C22×C4semidirect
524. C4×Dic73C22×C4semidirect
536. C2×D4×C73C22×C4semidirect
545. C22×C4×C73C22×C4semidirect
562. C4⋊C4×C73C22×C4semidirect
574. C22⋊C4×C73C22×C4semidirect
807. #2377D73semidirect
835. C73#34416semidirect
875. #390C2×D73semidirect
907. #388C2×D73semidirect
918. #387C2×D73semidirect
919. #387C2×D73semidirect
933. #386C2×D73semidirect
955. #385C2×D73semidirect
960. #381C2×D73semidirect
965. #380C2×D73semidirect
1029. #121C4×D73semidirect
1215. C2×D4C2×C4×D73semidirect
1278. C22×C4C2×C4×D73semidirect
1320. C4⋊C4C2×C4×D73semidirect
1362. C22⋊C4C2×C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179891692
#226131192
#226131012
#226130742
#226130582
#226130082
#226130012
#226129802
#226129522
#226129512
#226129392
#226129292
#226128682
#226128592
#226128372
#226128272
#226127452
#226127172
#226127122
#226127112
#226126402
#226126322
#226126172
#226125972
#226125902
#226125872
#226125252
#226124362
#385×D732
C73×#23772
#3441673