Finite Group Databasebeta

← #33249535

Subgroups — #33249535

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×#17989173C211yesmaximal, characteristic
2#22613118C211yesmaximal, characteristic, complemented
3#22613100C211yesmaximal, characteristic, complemented
4#22613083C211yesmaximal, characteristic, complemented
5#22613079C211yesmaximal, characteristic, complemented
6#22613053C211yesmaximal, characteristic, complemented
7#22613013C211yesmaximal, characteristic, complemented
8#22612999C211yesmaximal, characteristic, complemented
9#22612982C211yesmaximal, characteristic, complemented
10#22612950C211yesmaximal, characteristic, complemented
11#22612943C211yesmaximal, characteristic, complemented
12#22612938C211yesmaximal, characteristic, complemented
13#22612870C211yesmaximal, characteristic, complemented
14#22612861C211yesmaximal, characteristic, complemented
15#22612838C211yesmaximal, characteristic, complemented
16#22612832C211yesmaximal, characteristic, complemented
17#22612739C211yesmaximal, characteristic, complemented
18#22612715C211yesmaximal, characteristic, complemented
19#22612709C211yesmaximal, characteristic, complemented
20#22612699C211yesmaximal, characteristic, complemented
21#22612637C211yesmaximal, characteristic, complemented
22#22612634C211yesmaximal, characteristic, complemented
23#22612624C211yesmaximal, characteristic, complemented
24#22612604C211yesmaximal, characteristic, complemented
25#22612587C211yesmaximal, characteristic, complemented
26#22612584C211yesmaximal, characteristic, complemented
27#22612525C211yesmaximal, characteristic, complemented
28C4×#14556561C211yesmaximal, characteristic, complemented
29C4×#14556559C211yesmaximal, characteristic, complemented
30#385×D73C211yesmaximal, characteristic, complemented
31C73×#2359C211yesmaximal, characteristic, complemented
32C23×C4×D73C2211yescharacteristic
33#17989173C4116yescomplemented
34C2×#14556586C2211yescharacteristic
35C2×#14556584C2211yescharacteristic
36C2×#14556577C2211yescharacteristic
37C2×#14556577C2211yescharacteristic
38C2×#14556576C2211yescharacteristic
39C2×#14556571C2211yescharacteristic
40C2×#14556565C2211yescharacteristic
41C2×#14556564C2211yescharacteristic
42C2×#14556562C2211yescharacteristic
43C2×#14556561C2211yescharacteristic
44C2×#14556559C2211yescharacteristic
45C2×#14556556C2211yescharacteristic, complemented
46C2×C4×D292C2211yescharacteristic
47C2×C4×D292C2211yescharacteristic
48C2×#14556553C2211yescharacteristic
49C2×#14556553C2211yescharacteristic
50C2×C4×C22⋊D73C2211yescharacteristic
51C2×C4×C22⋊D73C2211yescharacteristic
52C2×C4×C22⋊D73C2211yescharacteristic
53C2×C4×C22⋊D73C2211yescharacteristic
54C2×C4×C22⋊D73C2211yescharacteristic
55C2×C4×C22⋊D73C2211yescharacteristic, complemented
56C2×C4⋊C4×D73C2211yescharacteristic
57C2×C4⋊C4×D73C2211yescharacteristic
58C2×C4⋊C4×D73C2211yescharacteristic, complemented
59C2×C22⋊C4×D73C2211yescharacteristic
60C2×C22⋊C4×D73C2211yescharacteristic
61#17988493C2211yescharacteristic, complemented
62#17988491C2211yescharacteristic, complemented
63#17988491C2211yescharacteristic, complemented
64#17988490C2211yescharacteristic
65#17988489C2211yescharacteristic
66#17988487C2211yescharacteristic
67#17988487C2211yescharacteristic
68#17988487C2211yescharacteristic, complemented
69#17988486C2211yescharacteristic, complemented
70#17988486C2211yescharacteristic, complemented
71#17988485C2211yescharacteristic, complemented
72#17988485C2211yescharacteristic, complemented
73#17988484C2211yescharacteristic, complemented
74#17988484C2211yescharacteristic, complemented
75#17988482C2211yescharacteristic, complemented
76#17988481C2211yescharacteristic
77#17988481C2211yescharacteristic, complemented
78#17988481C2211yescharacteristic, complemented
79#17988480C2211yescharacteristic
80#17988480C2211yescharacteristic
81#17988480C2211yescharacteristic, complemented
82#17988480C2211yescharacteristic, complemented
83#17988479C2211yescharacteristic
84#17988479C2211yescharacteristic
85#17988479C2211yescharacteristic, complemented
86#17988478C2211yescharacteristic
87#17988478C2211yescharacteristic, complemented
88#17988477C2211yescharacteristic
89#17988477C2211yescharacteristic
90#17988477C2211yescharacteristic, complemented
91#17988477C2211yescharacteristic, complemented
92#17988476C2211yescharacteristic
93#17988476C2211yescharacteristic
94#17988476C2211yescharacteristic
95#17988475C2211yescharacteristic
96#17988475C2211yescharacteristic
97#17988475C2211yescharacteristic
98#17988474C2211yescharacteristic, complemented
99#17988473C2211yescharacteristic, complemented
100#17988473C2211yescharacteristic, complemented
101#17988472C2211yescharacteristic, complemented
102#17988472C2211yescharacteristic, complemented
103#17988472C2211yescharacteristic, complemented
104#17988471C2211yescharacteristic, complemented
105#17988471C2211yescharacteristic, complemented
106#17988471C2211yescharacteristic, complemented
107#17988470C2211yescharacteristic, complemented
108#17988467C2211yescharacteristic
109#17988466C2211yescharacteristic
110#17988466C2211yescharacteristic, complemented
111#17988465C2211yescharacteristic
112#17988465C2211yescharacteristic
113#17988465C2211yescharacteristic
114#17988465C2211yescharacteristic
115#17988464C2211yescharacteristic
116#17988463C2211yescharacteristic
117#17988463C2211yescharacteristic
118#17988463C2211yescharacteristic
119#17988463C2211yescharacteristic
120#17988463C2211yescharacteristic, complemented
121#17988462C2211yescharacteristic
122#17988462C2211yescharacteristic
123#17988461C2211yescharacteristic
124#17988461C2211yescharacteristic
125#17988461C2211yescharacteristic
126#17988461C2211yescharacteristic
127#17988461C2211yescharacteristic
128#17988461C2211yescharacteristic
129#17988461C2211yescharacteristic, complemented
130#17988461C2211yescharacteristic, complemented
131#17988460C2211yescharacteristic
132#17988460C2211yescharacteristic, complemented
133#17988460C2211yescharacteristic, complemented
134#17988459C2211yescharacteristic
135#17988459C2211yescharacteristic
136#17988458C2211yescharacteristic
137#17988458C2211yescharacteristic
138#17988458C2211yescharacteristic
139#17988458C2211yescharacteristic
140#17988458C2211yescharacteristic, complemented
141#17988456C2211yescharacteristic, complemented
142#17988454C2211yescharacteristic, complemented
143#17988452C2211yescharacteristic, complemented
144#17988451C2211yescharacteristic, complemented
145#17988449C2211yescharacteristic, complemented
146#17988447C2211yescharacteristic, complemented
147#17988447C2211yescharacteristic, complemented
148#17988446C2211yescharacteristic
149#17988446C2211yescharacteristic, complemented
150#17988444C2211yescharacteristic
151#17988442C2211yescharacteristic
152#17988442C2211yescharacteristic
153C4⋊C4×Dic73C2211yescharacteristic, complemented
154C4⋊C4×Dic73C2211yescharacteristic, complemented
155C4×#11924007C2211yescharacteristic, complemented
156C4×C4⋊Dic73C2211yescharacteristic, complemented
157#17988438C2211yescharacteristic, complemented
158#17988438C2211yescharacteristic, complemented
159C4×#11924005C2211yescharacteristic
160C4×#11924005C2211yescharacteristic
161C4×#11924005C2211yescharacteristic
162C4×#11924005C2211yescharacteristic
163C4×#11924005C2211yescharacteristic
164C4×#11924005C2211yescharacteristic
165C4×#11924005C2211yescharacteristic, complemented
166C4×C22⋊Dic73C2211yescharacteristic
167#17988434C2211yescharacteristic
168#17988434C2211yescharacteristic
169#17988434C2211yescharacteristic, complemented
170#17988432C2211yescharacteristic, complemented
171#95×D73C2211yescharacteristic
172#95×D73C2211yescharacteristic
173C2×#123×C73C2211yescharacteristic
174C2×C4×D4×C73C2211yescharacteristic
175C2×#117×C73C2211yescharacteristic, complemented
176#389×C73C2211yescharacteristic, complemented
177#388×C73C2211yescharacteristic
178#388×C73C2211yescharacteristic
179#387×C73C2211yescharacteristic, complemented
180#387×C73C2211yescharacteristic, complemented
181#386×C73C2211yescharacteristic
182#385×C73C2211yescharacteristic
183#385×C73C2211yescharacteristic, complemented
184C4×C4⋊C4×C73C2211yescharacteristic, complemented
185C4×C22⋊C4×C73C2211yescharacteristic
186C4×C22⋊C4×C73C2211yescharacteristic, complemented
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
197C22×C4×D73—42no—
198C22×C4×D73—42no—
199C22×C4×D73—42no—
200C22×C4×D73C2311yescharacteristic
201C22×C4×D73C2311yescharacteristic
202C22×C4×D73C2311yescharacteristic
203C22×C4×D73C2311yescharacteristic
204C22×C4×D73C2311yescharacteristic
205C22×C4×D73C2311yescharacteristic
206C22×C4×D73C2311yescharacteristic
207C22×C4×D73C2311yescharacteristic
208C22×C4×D73C2311yescharacteristic
209C22×C4×D73C2311yescharacteristic
210C22×C4×D73C2311yescharacteristic
211#14556586C2×C418yescomplemented
212#14556584C2×C418yescomplemented
213#14556577C2×C418yescomplemented
214#14556577C2×C418yescomplemented
215#14556576C2×C418yescomplemented
216#14556571C2×C418yescomplemented
217#14556565C2×C418yescomplemented
218#14556564C2×C418yescomplemented
219#14556562C2×C418yescomplemented
220#14556561C2×C418yescomplemented
221#14556559C2×C418yescomplemented
222#14556556—42no—
223C4×D292—42no—
224C4×D292—42no—
225#14556553—42no—
226#14556553C2×C418yescomplemented
227C4×C22⋊D73—42no—
228C4×C22⋊D73—42no—
229C4×C22⋊D73—42no—
230C4×C22⋊D73—42no—
231C4×C22⋊D73—42no—
232C4×C22⋊D73C2×C418yescomplemented
233C2×C4⋊Dic73C2311yescharacteristic
234C2×C4⋊Dic73C2311yescharacteristic
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
256C4⋊C4×D73—42no—
257C4⋊C4×D73—42no—
258C4⋊C4×D73—42no—
259C2×C22⋊Dic73C2311yescharacteristic
260C2×C22⋊Dic73C2311yescharacteristic
261C2×C22⋊Dic73C2311yescharacteristic
262C2×C22⋊Dic73C2311yescharacteristic
263C2×C22⋊Dic73C2311yescharacteristic
264C2×C22⋊Dic73C2311yescharacteristic
265C2×C22⋊Dic73C2311yescharacteristic
266C2×C22⋊Dic73C2311yescharacteristic
267C2×C22⋊Dic73C2311yescharacteristic
268C2×C22⋊Dic73C2311yescharacteristic
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
293C22⋊C4×D73—42no—
294C22⋊C4×D73C2×C418yescomplemented
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
343#123×C73C2×C418yescomplemented
344C4×D4×C73—42no—
345#117×C73—42no—
346C2×C4⋊C4×C73C2311yescharacteristic
347C2×C4⋊C4×C73C2311yescharacteristic
348C2×C4⋊C4×C73C2311yescharacteristic
349C2×C4⋊C4×C73C2311yescharacteristic
350C2×C4⋊C4×C73C2311yescharacteristic
351C2×C4⋊C4×C73C2311yescharacteristic
352C2×C4⋊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×C42×C73C2311yescharacteristic
362C2×C42×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—22no—
390C2×D292—22no—
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—41no—
408C22×Dic73—41no—
409C22×Dic73—41no—
410C22×Dic73C2411yescharacteristic
411C22×Dic73C2411yescharacteristic
412C22×Dic73C2411yescharacteristic
413C22×Dic73C2411yescharacteristic
414C22×Dic73C2411yescharacteristic
415C22×Dic73C2411yescharacteristic
416C22×Dic73C2411yescharacteristic
417C22×Dic73C2411yescharacteristic
418C22×Dic73C2411yescharacteristic
419C22×Dic73C2411yescharacteristic
420C22×Dic73C2411yescharacteristic
421C22×Dic73C2411yescharacteristic
422C22×Dic73C2411yescharacteristic
423C2×C4×D73—22no—
424C2×C4×D73—22no—
425C2×C4×D73—22no—
426C2×C4×D73—22no—
427C2×C4×D73—22no—
428C2×C4×D73—22no—
429C2×C4×D73—22no—
430C2×C4×D73—22no—
431C2×C4×D73—22no—
432C2×C4×D73—41no—
433C2×C4×D73—41no—
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×D73—41no—
451C2×C4×D73—41no—
452C2×C4×D73—41no—
453C2×C4×D73—41no—
454C2×C4×D73C22×C414yes—
455C2×C4×D73C22×C414yes—
456C2×C4×D73C22×C414yescomplemented
457C4⋊Dic73—41no—
458C4⋊Dic73—41no—
459C4⋊Dic73—41no—
460C4⋊Dic73—41no—
461C4⋊Dic73—41no—
462C4⋊Dic73—41no—
463C4⋊Dic73—41no—
464C4⋊Dic73C22×C414yescomplemented
465C4⋊Dic73C22×C414yescomplemented
466#11924007—22no—
467#11924007—22no—
468#11924007—22no—
469#11924007—41no—
470#11924007—41no—
471#11924007—41no—
472#11924007—41no—
473#11924007—41no—
474#11924007—41no—
475#11924007—41no—
476#11924007—41no—
477#11924007—41no—
478#11924007C22×C414yescomplemented
479#11924007C22×C414yescomplemented
480C22⋊Dic73—41no—
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×C414yescomplemented
490#11924005—22no—
491#11924005—22no—
492#11924005—22no—
493#11924005—22no—
494#11924005—22no—
495#11924005—41no—
496#11924005—41no—
497#11924005—41no—
498#11924005—41no—
499#11924005—41no—
500#11924005—41no—
501#11924005—41no—
502#11924005—41no—
503#11924005—41no—
504#11924005—41no—
505#11924005—41no—
506#11924005C22×C414yes—
507#11924005C22×C414yes—
508#11924005C22×C414yes—
509#11924005C22×C414yes—
510#11924005C22×C414yes—
511#11924005C22×C414yes—
512#11924005C22×C414yescomplemented
513#11924005C22×C414yescomplemented
514C4×Dic73—22no—
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×Dic73—41no—
524C4×Dic73—41no—
525C4×Dic73C22×C414yescomplemented
526C4×Dic73C22×C414yescomplemented
527C24×C73C2411yescharacteristic
528C24×C73C2411yescharacteristic
529C2×D4×C73—41no—
530C2×D4×C73—41no—
531C2×D4×C73C22×C414yes—
532C22×C4×C73—22no—
533C22×C4×C73—22no—
534C22×C4×C73—22no—
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×C73C22×C414yescomplemented
544C22×C4×C73C2411yescharacteristic
545C22×C4×C73C2411yescharacteristic
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
557C4⋊C4×C73—22no—
558C4⋊C4×C73—22no—
559C4⋊C4×C73—22no—
560C4⋊C4×C73—41no—
561C4⋊C4×C73—41no—
562C4⋊C4×C73C22×C414yescomplemented
563C4⋊C4×C73C22×C414yescomplemented
564C22⋊C4×C73—22no—
565C22⋊C4×C73—41no—
566C22⋊C4×C73—41no—
567C22⋊C4×C73—41no—
568C22⋊C4×C73—41no—
569C22⋊C4×C73C22×C414yes—
570C22⋊C4×C73C22×C414yes—
571C22⋊C4×C73C22×C414yescomplemented
572C42×C73—22no—
573C42×C73—41no—
574C42×C73—41no—
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×C73C23×C412yes—
590C23×C73C23×C412yes—
591C23×C73C2511yescharacteristic
592C22×D73—21no—
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—28no—
609C22×D73—44no—
610C22×D73—44no—
611C22×D73—44no—
612C22×D73—44no—
613C22×D73—44no—
614C22×D73—44no—
615C22×D73C23×C412yes—
616C22×D73C23×C412yes—
617C22×D73C23×C412yes—
618C22×D73H(5,𝔽2)12yes—
619C22×D732−1+412yes—
620D4×C73—44no—
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—44no—
654C2×C4×C73—44no—
655C2×C4×C73—82no—
656C2×C4×C73—82no—
657C2×C4×C73C23×C412yes—
658C2×C4×C73C23×C412yes—
659C2×C4×C73C23×C412yes—
660C2×C4×C73C23×C412yes—
661C2×C4×C73C23×C412yes—
662C2×C4×C73H(5,𝔽2)12yes—
663C2×C4×C73H(5,𝔽2)12yes—
664C22⋊D73—28no—
665C22⋊D73—44no—
666C22⋊D73—44no—
667C22⋊D73—44no—
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—21no—
701C2×Dic73—21no—
702C2×Dic73—44no—
703C2×Dic73C23×C412yes—
704C2×Dic73C23×C412yes—
705C2×Dic73C23×C412yes—
706C2×Dic73C23×C412yes—
707C2×Dic73C23×C412yes—
708D292—28no—
709D292—44no—
710C4×D73—44no—
711C4×D73—44no—
712C4×D73—44no—
713C4×D73—44no—
714C4×D73—44no—
715C4×D73—44no—
716C4×D73—44no—
717C4×D73—82no—
718C4×D73—82no—
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—41no—
729C22×C73—41no—
730C22×C73—41no—
731C22×C73—41no—
732C22×C73—41no—
733C22×C73—41no—
734C22×C73—41no—
735C22×C73—41no—
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—22no—
753C2×D73—22no—
754C2×D73—22no—
755C2×D73—416no—
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#52014yes—
765C4×C73—22no—
766C4×C73—22no—
767C4×C73—22no—
768C4×C73—22no—
769C4×C73—22no—
770C4×C73—22no—
771C4×C73—22no—
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—41no—
784Dic73—41no—
785Dic73—41no—
786Dic73—41no—
787Dic73—41no—
788Dic73—41no—
789Dic73—41no—
790Dic73—41no—
791#34416—731nomaximal, Sylow
792C2×C73—42no—
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—24no—
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#2359D7311yescharacteristic, complemented
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×#123C2×D7311yescharacteristic
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×D4—731no—
860C2×C4×D4—731no—
861C2×C4×D4C2×D7311yescharacteristic
862C2×#117C2×D7311yescharacteristic, complemented
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#389—731no—
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#388C2×D7311yescharacteristic
907#388C2×D7311yescharacteristic
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#386—731no—
931#386—731no—
932#386—731no—
933#386C2×D7311yescharacteristic
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#381—731no—
961#380—731no—
962#380—731no—
963#380—731no—
964#380—731no—
965#380—731no—
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⋊C4C2×D7311yescharacteristic
987C4×C22⋊C4C2×D7311yescharacteristic, complemented
988#376—731no—
989C2×#95—731no—
990C2×#95—731no—
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×C4—731no—
1015C23×C4—731no—
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#123C4×D7318yescomplemented
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—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—42no—
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⋊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—731no—
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—738no—
1109C2×C22⋊C4—731no—
1110C2×C22⋊C4—731no—
1111C2×C22⋊C4—731no—
1112C2×C22⋊C4—731no—
1113C2×C22⋊C4—731no—
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×C42C22×D7311yescharacteristic
1136C2×C42C22×D7311yescharacteristic
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—41no—
1196C2×D4—41no—
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—734no—
1206C2×D4—734no—
1207C2×D4—734no—
1208C2×D4—734no—
1209C2×D4—734no—
1210C2×D4—734no—
1211C2×D4—1462no—
1212C2×D4—1462no—
1213C2×D4—1462no—
1214C2×D4—1462no—
1215C2×D4C2×C4×D7314yes—
1216C22×C4—22no—
1217C22×C4—22no—
1218C22×C4—22no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—41no—
1224C22×C4—41no—
1225C22×C4—41no—
1226C22×C4—41no—
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—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—2921no—
1248C22×C4—29216no—
1249C22×C4—2921no—
1250C22×C4—2921no—
1251C22×C4—2921no—
1252C22×C4—734no—
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×C4—1462no—
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—22no—
1293C4⋊C4—22no—
1294C4⋊C4—41no—
1295C4⋊C4—41no—
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—2921no—
1310C4⋊C4—2921no—
1311C4⋊C4—2921no—
1312C4⋊C4—734no—
1313C4⋊C4—734no—
1314C4⋊C4—734no—
1315C4⋊C4—734no—
1316C4⋊C4—1462no—
1317C4⋊C4—1462no—
1318C4⋊C4—1462no—
1319C4⋊C4C2×C4×D7314yescomplemented
1320C4⋊C4C2×C4×D7314yescomplemented
1321C22⋊C4—22no—
1322C22⋊C4—41no—
1323C22⋊C4—41no—
1324C22⋊C4—41no—
1325C22⋊C4—41no—
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—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⋊C4C2×C4×D7314yes—
1361C22⋊C4C2×C4×D7314yes—
1362C22⋊C4C2×C4×D7314yescomplemented
1363C42—22no—
1364C42—41no—
1365C42—41no—
1366C42—41no—
1367C42—41no—
1368C42—2921no—
1369C42—2921no—
1370C42—2921no—
1371C42—2921no—
1372C42—2921no—
1373C42—2921no—
1374C42—2921no—
1375C42—2921no—
1376C42—2921no—
1377C42—2921no—
1378C42—734no—
1379C42—734no—
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—2924no—
1394C23—2924no—
1395C23—2924no—
1396C23—2924no—
1397C23—2924no—
1398C23—2924no—
1399C23—732no—
1400C23—732no—
1401C23—732no—
1402C23—732no—
1403C23—732no—
1404C23—1468no—
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—1461no—
1419C23—1461no—
1420C23—1461no—
1421C23C22×C4×D7312yes—
1422C23C22×C4×D7312yes—
1423C23C24×D7311yescharacteristic
1424Q8—2924no—
1425D4—44no—
1426D4—2924no—
1427D4—2924no—
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—82no—
1468C2×C4—2924no—
1469C2×C4—2924no—
1470C2×C4—2924no—
1471C2×C4—2924no—
1472C2×C4—2924no—
1473C2×C4—2924no—
1474C2×C4—2924no—
1475C2×C4—2924no—
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—1461no—
1486C2×C4—1461no—
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×C4C22×C4×D7312yes—
1520C2×C4C22×C4×D7312yes—
1521C2×C4C22×C4×D7312yes—
1522C2×C4C22×C4×D7312yes—
1523C2×C4C22×C4×D7312yes—
1524C2×C4#1455663612yes—
1525C2×C4#1455663712yes—
1526C22—22no—
1527C22—22no—
1528C22—22no—
1529C22—22no—
1530C22—22no—
1531C22—22no—
1532C22—41no—
1533C22—41no—
1534C22—41no—
1535C22—41no—
1536C22—41no—
1537C22—41no—
1538C22—41no—
1539C22—41no—
1540C22—29216no—
1541C22—2921no—
1542C22—2921no—
1543C22—2921no—
1544C22—2921no—
1545C22—2921no—
1546C22—2921no—
1547C22—2921no—
1548C22—2921no—
1549C22—734no—
1550C22—1462no—
1551C22—1462no—
1552C22—1462no—
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
1564C22C2×#1455663611yescharacteristic
1565C22C2×#1455663711yescharacteristic
1566C222−1+4×D7311yescharacteristic
1567C22#1798942311yescharacteristic
1568C22#1798942311yescharacteristic
1569C4—22no—
1570C4—22no—
1571C4—22no—
1572C4—22no—
1573C4—22no—
1574C4—22no—
1575C4—22no—
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—2921no—
1590C4—1462no—
1591C4—1462no—
1592C4—1462no—
1593C4—1462no—
1594C4—1462no—
1595C2—42no—
1596C2—42no—
1597C2—2922no—
1598C2—2922no—
1599C2—1464no—
1600C2#520×D7311yescharacteristic
1601C2C4×#1455663611yescharacteristic
1602C2C4×#1455663711yescharacteristic
1603C2#2262408011yescharacteristic
1604C2#2262409611yescharacteristic
1605C2#2262421411yescharacteristic
1606C2#2262422711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2359C2
socle, cosocleC23×C73C25
prime radicalC2×#17989173C2
hypercenter#2359D73
hypocenterC73#34416
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2359

Complements

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

NH ≅ G/Ntype
2. #22613118C2semidirect
3. #22613100C2semidirect
4. #22613083C2semidirect
5. #22613079C2semidirect
6. #22613053C2semidirect
7. #22613013C2semidirect
8. #22612999C2semidirect
9. #22612982C2semidirect
10. #22612950C2semidirect
11. #22612943C2semidirect
12. #22612938C2semidirect
13. #22612870C2semidirect
14. #22612861C2semidirect
15. #22612838C2semidirect
16. #22612832C2semidirect
17. #22612739C2semidirect
18. #22612715C2semidirect
19. #22612709C2semidirect
20. #22612699C2semidirect
21. #22612637C2semidirect
22. #22612634C2semidirect
23. #22612624C2semidirect
24. #22612604C2semidirect
25. #22612587C2semidirect
26. #22612584C2semidirect
27. #22612525C2semidirect
28. C4×#14556561C2semidirect
29. C4×#14556559C2semidirect
30. #385×D73C2semidirect
31. C73×#2359C2semidirect
33. #17989173C4semidirect
45. C2×#14556556C22semidirect
55. C2×C4×C22⋊D73C22semidirect
58. C2×C4⋊C4×D73C22semidirect
61. #17988493C22semidirect
62. #17988491C22semidirect
63. #17988491C22semidirect
68. #17988487C22semidirect
69. #17988486C22semidirect
70. #17988486C22semidirect
71. #17988485C22semidirect
72. #17988485C22semidirect
73. #17988484C22semidirect
74. #17988484C22semidirect
75. #17988482C22semidirect
77. #17988481C22semidirect
78. #17988481C22semidirect
81. #17988480C22semidirect
82. #17988480C22semidirect
85. #17988479C22semidirect
87. #17988478C22semidirect
90. #17988477C22semidirect
91. #17988477C22semidirect
98. #17988474C22semidirect
99. #17988473C22semidirect
100. #17988473C22semidirect
101. #17988472C22semidirect
102. #17988472C22semidirect
103. #17988472C22semidirect
104. #17988471C22semidirect
105. #17988471C22semidirect
106. #17988471C22semidirect
107. #17988470C22semidirect
110. #17988466C22semidirect
120. #17988463C22semidirect
129. #17988461C22semidirect
130. #17988461C22semidirect
132. #17988460C22semidirect
133. #17988460C22semidirect
140. #17988458C22semidirect
141. #17988456C22semidirect
142. #17988454C22semidirect
143. #17988452C22semidirect
144. #17988451C22semidirect
145. #17988449C22semidirect
146. #17988447C22semidirect
147. #17988447C22semidirect
149. #17988446C22semidirect
153. C4⋊C4×Dic73C22semidirect
154. C4⋊C4×Dic73C22semidirect
155. C4×#11924007C22semidirect
156. C4×C4⋊Dic73C22semidirect
157. #17988438C22semidirect
158. #17988438C22semidirect
165. C4×#11924005C22semidirect
169. #17988434C22semidirect
170. #17988432C22semidirect
175. C2×#117×C73C22semidirect
176. #389×C73C22semidirect
179. #387×C73C22semidirect
180. #387×C73C22semidirect
183. #385×C73C22semidirect
184. C4×C4⋊C4×C73C22semidirect
186. C4×C22⋊C4×C73C22semidirect
187. C2×#95×C73C22semidirect
211. #14556586C2×C4semidirect
212. #14556584C2×C4semidirect
213. #14556577C2×C4semidirect
214. #14556577C2×C4semidirect
215. #14556576C2×C4semidirect
216. #14556571C2×C4semidirect
217. #14556565C2×C4semidirect
218. #14556564C2×C4semidirect
219. #14556562C2×C4semidirect
220. #14556561C2×C4semidirect
221. #14556559C2×C4semidirect
226. #14556553C2×C4semidirect
232. C4×C22⋊D73C2×C4semidirect
294. C22⋊C4×D73C2×C4semidirect
343. #123×C73C2×C4semidirect
388. C2×Dic146C22×C4semidirect
406. C2×C22⋊D73C22×C4semidirect
456. C2×C4×D73C22×C4semidirect
464. C4⋊Dic73C22×C4semidirect
465. C4⋊Dic73C22×C4semidirect
478. #11924007C22×C4semidirect
479. #11924007C22×C4semidirect
489. C22⋊Dic73C22×C4semidirect
512. #11924005C22×C4semidirect
513. #11924005C22×C4semidirect
525. C4×Dic73C22×C4semidirect
526. C4×Dic73C22×C4semidirect
543. C22×C4×C73C22×C4semidirect
562. C4⋊C4×C73C22×C4semidirect
563. C4⋊C4×C73C22×C4semidirect
571. C22⋊C4×C73C22×C4semidirect
816. #2359D73semidirect
835. C73#34416semidirect
862. C2×#117C2×D73semidirect
883. #389C2×D73semidirect
918. #387C2×D73semidirect
919. #387C2×D73semidirect
955. #385C2×D73semidirect
974. C4×C4⋊C4C2×D73semidirect
987. C4×C22⋊C4C2×D73semidirect
991. C2×#95C2×D73semidirect
1025. #123C4×D73semidirect
1277. C22×C4C2×C4×D73semidirect
1319. C4⋊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×#179891732
#226131182
#226131002
#226130832
#226130792
#226130532
#226130132
#226129992
#226129822
#226129502
#226129432
#226129382
#226128702
#226128612
#226128382
#226128322
#226127392
#226127152
#226127092
#226126992
#226126372
#226126342
#226126242
#226126042
#226125872
#226125842
#226125252
C4×#145565612
C4×#145565592
#385×D732
C73×#23592
#3441673