Finite Group Databasebeta

← #14262325

Subgroups — #14262325

Order 1792.

7220 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3504C211yesmaximal, characteristic, complemented
2#11744094C212yesmaximal, complemented
3#11744090C212yesmaximal, complemented
4#11744085C212yesmaximal, complemented
5#11744084C212yesmaximal, complemented
6#11744003C216yesmaximal, complemented
7#11743997C216yesmaximal, complemented
8#11743992C216yesmaximal, complemented
9#11743990C216yesmaximal, complemented
10#11743666C213yesmaximal, complemented
11#11743665C213yesmaximal, complemented
12#11743651C213yesmaximal, complemented
13#11743650C213yesmaximal, complemented
14#11743331C213yesmaximal, complemented
15#11743325C213yesmaximal, complemented
16#11743155C213yesmaximal, complemented
17C2×#90382C213yesmaximal, complemented
18#11742969C211yesmaximal, characteristic, complemented
19#11742968C211yesmaximal, characteristic, complemented
20#11742955C211yesmaximal, characteristic, complemented
21#11742954C211yesmaximal, characteristic, complemented
22#11742915C211yesmaximal, characteristic, complemented
23C4×D7×#41C211yesmaximal, characteristic, complemented
24C2×#6554C2211yescharacteristic
25C2×#6553C2211yescharacteristic
26C2×D7×#41C2211yescharacteristic
27C7×#557C2212yescomplemented
28C7×#557C2212yescomplemented
29C7×#554C2216yescomplemented
30C7×#554C2216yescomplemented
31C7×#544C2213yescomplemented
32C7×#544C2213yescomplemented
33C7×#533C2213yescomplemented
34C2×C7×#125C2213yescomplemented
35C7×#520C2211yescharacteristic
36C7×#520C2211yescharacteristic
37C4×C7×#41C2211yescharacteristic
38#41×Dic7C2211yescharacteristic
39#90425C2216yescomplemented
40#90424C2216yescomplemented
41#90424C2216yescomplemented
42#90424C2216yescomplemented
43#90424C2216yescomplemented
44#90423C2216yescomplemented
45#90421C2216yescomplemented
46#90419C2216yescomplemented
47#90419C2213yescomplemented
48#90419C2213yescomplemented
49#90417C2216yescomplemented
50#90416C2216yescomplemented
51#90416C2213yescomplemented
52#90416C2213yescomplemented
53#90389C2216yescomplemented
54#90389C2216yescomplemented
55#90388C2216yescomplemented
56#90388C2216yescomplemented
57#90386C2216yescomplemented
58#90386C2216yescomplemented
59#90386C2216yescomplemented
60#90386C2216yescomplemented
61#90385C2216yescomplemented
62#90385C2216yescomplemented
63#90385C2216yescomplemented
64#90385C2216yescomplemented
65#90382C2216yescomplemented
66#90382C2216yescomplemented
67#90382C2216yescomplemented
68#90382C2216yescomplemented
69#90382C2216yescomplemented
70#90382C2216yescomplemented
71#90382C2211yescharacteristic, complemented
72#90382C2213yescomplemented
73#90382C2213yescomplemented
74#90382C2213yescomplemented
75#90382C2216yescomplemented
76#90382C2216yescomplemented
77#90382C2216yescomplemented
78#90336C22112yescomplemented
79#90335C22112yescomplemented
80#90333C22112yescomplemented
81#90328C22112yescomplemented
82#90328C22112yescomplemented
83#90328C22112yescomplemented
84#90328C22112yescomplemented
85#90321C22112yescomplemented
86#90318C2216yescomplemented
87#90318C2216yescomplemented
88#90318C22112yescomplemented
89#90315C2216yescomplemented
90#90315C2216yescomplemented
91#90315C22112yescomplemented
92#90276C2216yescomplemented
93#90276C2216yescomplemented
94#90275C2216yescomplemented
95#90275C2216yescomplemented
96#90271C2216yescomplemented
97#90271C2216yescomplemented
98#90268C2212yes—
99#90267C2212yes—
100#90267C2212yescomplemented
101#90267C2212yescomplemented
102#90267C2212yescomplemented
103Q8×D28C2212yescomplemented
104#90265C2212yescomplemented
105C4×#1161C2211yescharacteristic, complemented
106C4×#1161C2212yescomplemented
107C4×#1161C2216yescomplemented
108C4×#1161C2216yescomplemented
109C4×#1161C2211yescharacteristic, complemented
110#90263C2212yescomplemented
111C4×Q8×D7C2212yescomplemented
112C4×Q8×D7C2211yescharacteristic, complemented
113C4×Q8×D7C2211yescharacteristic, complemented
114#90246C2216yescomplemented
115#90245C2216yes—
116#90245C2216yescomplemented
117#90245C2216yescomplemented
118#90245C2216yescomplemented
119D4×D28C2216yes—
120#90237C2216yescomplemented
121#90236C2216yescomplemented
122C4×D4×D7C2213yescomplemented
123C4×D4×D7C2213yescomplemented
124C4×D4×D7C2216yescomplemented
125C4×#1159C2213yescomplemented
126C4×#1159C2213yescomplemented
127C4×#1159C2216yescomplemented
128#90217C2213yescomplemented
129#90217C2213yescomplemented
130#90216C2213yes—
131#90216C2213yescomplemented
132#90215C2213yes—
133#90215C2213yescomplemented
134#90213C2213yescomplemented
135#90213C2213yescomplemented
136#90213C2213yescomplemented
137#90212C2213yescomplemented
138D7×#117C2213yescomplemented
139#90207C2213yescomplemented
140#90205C22112yescomplemented
141#90205C22112yescomplemented
142C2×#6461C2216yescomplemented
143#90201C2213yes—
144#90201C2213yescomplemented
145C2×#6460C2213yescomplemented
146C2×#6458C2213yes—
147C2×#6457C2216yescomplemented
148#90195C2213yescomplemented
149#90195C2213yescomplemented
150C2×#6456C2213yescomplemented
151C2×#6456C2216yescomplemented
152C2×#6455C2216yescomplemented
153C2×#6450C2213yescomplemented
154#90168C2213yescomplemented
155C2×#6438C2213yescomplemented
156C4×#1157C2213yescomplemented
157C2×C42×D7C2213yescomplemented
158#62810—71nomaximal, Sylow
159C2×C7×#41C2311yescharacteristic
160#6554—28no—
161#6553—28no—
162D7×#41—28no—
163C2×#1161C2311yescharacteristic
164C2×#1161C2312yes—
165C2×#1161C2316yes—
166C2×#1161C2316yes—
167C2×Q8×D7C2311yescharacteristic
168C2×Q8×D7C2312yes—
169C2×#1159C2313yes—
170C2×#1159C2316yes—
171C2×D4×D7C2313yes—
172C2×D4×D7C2316yes—
173C2×#1157C2313yes—
174C2×#1157C2313yes—
175C2×#1157C2313yes—
176C22×D28C2313yes—
177C22×D28C2316yes—
178C22×C4×D7C2313yes—
179C22×C4×D7C2313yes—
180C22×C4×D7C2313yes—
181C22×C4×D7C2316yes—
182C22×Dic14C2313yes—
183C7×C4⋊Q8C2313yes—
184C7×C4⋊Q8C2313yes—
185C7×C4⋊Q8C2316yes—
186C7×C4⋊Q8C2316yes—
187C7×#125C2313yes—
188C7×#125C2311yescharacteristic
189C7×#125C2316yes—
190C7×#125C2316yes—
191C7×#125C2316yes—
192C7×#125C2316yes—
193C7×#125C2316yes—
194C7×C22⋊Q8C2316yes—
195C7×C22⋊Q8C2316yes—
196C7×C22⋊Q8C23112yes—
197C7×C22⋊Q8C23112yes—
198C4×C7×Q8C2312yes—
199C4×C7×Q8C2311yescharacteristic
200C4×C7×Q8C2311yescharacteristic
201C4×C7×Q8C2312yes—
202C4×C7×Q8C2316yes—
203C4×C7×Q8C2316yes—
204C4×C7×D4C2313yes—
205C4×C7×D4C2313yes—
206C4×C7×D4C2316yes—
207C4×C7×D4C2316yes—
208C7×#117C2313yes—
209C7×#117C2313yes—
210C7×#117C2313yes—
211C2×C7×C4⋊C4C2313yes—
212C2×C7×C4⋊C4C2316yes—
213C2×C7×C4⋊C4C2313yes—
214C2×C7×C4⋊C4C2316yes—
215C2×C42×C7C2313yes—
216#6510C23112yes—
217#6510C2316yes—
218#6510C2316yes—
219#6510C23112yes—
220#6509C23112yes—
221#6509C2316yes—
222#6509C2316yes—
223#6509C23112yes—
224Q8×Dic7C2316yes—
225Q8×Dic7C2316yes—
226Q8×Dic7C2311yescharacteristic
227Q8×Dic7C2311yescharacteristic
228D4×Dic7C2313yes—
229D4×Dic7C2313yes—
230#6493C2316yes—
231#6493C2316yes—
232#6493C23112yes—
233#6493C23112yes—
234C4×C22⋊D7C2316yes—
235C4×C22⋊D7C2316yes—
236C4×C22⋊D7C23112yes—
237C4×C22⋊D7C23112yes—
238C2×(C2×D7)⋊C4C2316yes—
239C2×(C2×D7)⋊C4C2316yes—
240C2×(C2×D7)⋊C4C2316yes—
241C2×(C2×D7)⋊C4C2316yes—
242C2×(C2×D7)⋊C4C2316yes—
243#6489C2313yes—
244C2×C4⋊Dic7C2316yes—
245C2×Dic7⋊C4C2316yes—
246C2×C4×Dic7C2313yes—
247C2×C4×Dic7C2313yes—
248C2×C4×Dic7C2313yes—
249C2×C4×Dic7C2316yes—
250#6461C2316yes—
251#6461C23112yes—
252#6461C23112yes—
253#6461C23112yes—
254#6461C2316yes—
255#6461C23112yes—
256#6461C23112yes—
257#6461C2312yes—
258#6461C2316yes—
259#6461C23112yes—
260#6461C23112yes—
261#6460C2313yes—
262#6460C2316yes—
263#6460C2316yes—
264#6460C2316yes—
265#6460C2316yes—
266#6460C2313yes—
267#6460C2316yes—
268#6460C2311yescharacteristic
269#6460C2313yes—
270#6460C2316yes—
271#6460C2316yes—
272#6458C2313yes—
273#6458C2316yes—
274#6458C2316yes—
275#6458C2316yes—
276#6458C2316yes—
277#6458C2313yes—
278#6458C2316yes—
279#6458C2311yescharacteristic
280#6458C2313yes—
281#6458C2316yes—
282#6458C23112yes—
283#6458C2316yes—
284#6458C2316yes—
285#6458C23112yes—
286#6458C2316yes—
287#6457C2316yes—
288#6457C23112yes—
289#6457C23112yes—
290#6457C23112yes—
291#6457C23112yes—
292#6457C2316yes—
293#6457C23112yes—
294#6457C2312yes—
295#6457C2316yes—
296#6457C23112yes—
297#6457C23112yes—
298#6456C2313yes—
299#6456C2316yes—
300#6456C23112yes—
301#6456C2316yes—
302#6456C23112yes—
303#6456C23112yes—
304#6456C2316yes—
305#6456C2316yes—
306#6456C2313yes—
307#6456C2316yes—
308#6456C2316yes—
309#6456C2313yes—
310#6456C2311yescharacteristic
311#6456C2313yes—
312#6456C2312yes—
313#6456C2316yes—
314#6456C2316yes—
315#6456C2313yes—
316#6455C23112yes—
317#6455C2316yes—
318#6455C23112yes—
319#6455C23112yes—
320#6455C2316yes—
321#6455C2316yes—
322#6455C2312yes—
323#6455C2316yes—
324#6455C2316yes—
325#6455C2316yes—
326#6455C2313yes—
327#6455C2316yes—
328#6455C2313yes—
329D7×C4⋊C4C2316yes—
330D7×C4⋊C4C2313yes—
331D7×C4⋊C4C2316yes—
332D7×C4⋊C4C2313yes—
333#6453C23112yes—
334#6453C2316yes—
335#6453C23112yes—
336#6453C2316yes—
337#6450C2313yes—
338#6450C2316yes—
339#6450C2316yes—
340#6450C2316yes—
341#6450C2313yes—
342#6450C2313yes—
343#6450C2311yescharacteristic
344#6450C2313yes—
345#6450C2313yes—
346#6449C2316yes—
347#6449C2316yes—
348#6449C23112yes—
349#6449C23112yes—
350#6445C2316yes—
351#6445C2316yes—
352#6445C23112yes—
353#6445C23112yes—
354(C22⋊D7)⋊C4C2316yes—
355(C22⋊D7)⋊C4C2316yes—
356(C22⋊D7)⋊C4C2316yes—
357(C22⋊D7)⋊C4C2316yes—
358(C22⋊D7)⋊C4C2316yes—
359(C22⋊D7)⋊C4C2316yes—
360D7×C22⋊C4C2316yes—
361D7×C22⋊C4C23112yes—
362#6440C23112yes—
363#6440C2316yes—
364#6438C2313yes—
365#6438C2311yescharacteristic
366#6438C2316yes—
367#6438C2316yes—
368#6438C2316yes—
369#6438C2316yes—
370#6438C2316yes—
371#6437C2313yes—
372#6437C2316yes—
373C4×D28C2316yes—
374C4×D28C2316yes—
375C4×D28C2316yes—
376C4×D28C2316yes—
377C4×D28C2313yes—
378C4×D28C2313yes—
379C4×D28C2316yes—
380C4×D28C2316yes—
381C4×D28C2316yes—
382C4×D28C2316yes—
383#6435C2316yes—
384#6435C2316yes—
385#6435C2316yes—
386C42×D7C2311yescharacteristic
387C42×D7C2313yes—
388C42×D7C2313yes—
389C42×D7C2313yes—
390C42×D7C2313yes—
391C42×D7C2313yes—
392C42×D7C2313yes—
393C42×D7C2313yes—
394C42×D7C2316yes—
395C42×D7C2316yes—
396#6432C2313yes—
397#6432C2316yes—
398C4×Dic14C2313yes—
399C4×Dic14C2313yes—
400C4×Dic14C2316yes—
401C4×Dic14C2316yes—
402#3524—72no—
403#3521—76no—
404#3516—72no—
405#3513—76no—
406#3512—73no—
407#3510—73no—
408#3504D711yescharacteristic, complemented
409#3500—71no—
410#3495—73no—
411#3494—73no—
412#3489—71no—
413#3488—71no—
414#3482—72no—
415#3481—76no—
416#3480—72no—
417#3475—76no—
418#3461—73no—
419#3460—73no—
420#3444—73no—
421C2×#529—73no—
422C4×2−1+4—71no—
423C4×H(5,𝔽2)—71no—
424C2×C4×#41—71no—
425C23×D7C2413yes—
426C23×D7C2416yes—
427C7×#41#4118yescomplemented
428C2×C7×Q8C2416yes—
429C2×C7×Q8C2416yes—
430C2×C7×Q8C2411yescharacteristic
431C2×C7×D4C2413yes—
432C22×C4×C7C2416yes—
433C22×C4×C7C2413yes—
434C22×C4×C7C2413yes—
435C22×C4×C7C2416yes—
436C22×C4×C7C2413yes—
437C2×C22⋊D7C2416yes—
438C2×C22⋊D7C2416yes—
439C2×C22⋊D7C2416yes—
440C22×Dic7C2413yes—
441C22×Dic7C2416yes—
442C22×Dic7C2413yes—
443C22×Dic7C2413yes—
444#1161—24no—
445#1161—28no—
446#1161—412no—
447#1161—412no—
448Q8×D7—24no—
449Q8×D7—28no—
450#1159—212no—
451#1159—224no—
452D4×D7—212no—
453D4×D7—224no—
454#1157—212no—
455#1157—212no—
456#1157—212no—
457C2×D28—212no—
458C2×D28—412no—
459C2×D28C2412yes—
460C2×D28C2413yes—
461C2×D28C2416yes—
462C2×D28C2416yes—
463C2×D28C2411yescharacteristic
464C2×D28C2413yes—
465C2×D28C2416yes—
466C2×D28C2416yes—
467C2×D28C2416yes—
468C2×D28C2416yes—
469C2×D28C24112yes—
470C2×C4×D7—212no—
471C2×C4×D7—46no—
472C2×C4×D7—412no—
473C2×C4×D7—46no—
474C2×C4×D7C2411yescharacteristic
475C2×C4×D7C2411yescharacteristic
476C2×C4×D7C2411yescharacteristic
477C2×C4×D7C2412yes—
478C2×C4×D7C2413yes—
479C2×C4×D7C2413yes—
480C2×C4×D7C2413yes—
481C2×C4×D7C2413yes—
482C2×C4×D7C2413yes—
483C2×C4×D7C2416yes—
484C2×C4×D7C2416yes—
485C2×C4×D7C2416yes—
486C2×C4×D7C2413yes—
487C2×C4×D7C2413yes—
488C2×C4×D7C2413yes—
489C2×C4×D7C2413yes—
490C2×C4×D7C2416yes—
491C2×C4×D7C2416yes—
492C2×C4×D7C24112yes—
493C2×Dic14—212no—
494C2×Dic14C2413yes—
495C2×Dic14C2416yes—
496C2×Dic14C2411yescharacteristic
497C2×Dic14C2413yes—
498C7×C4⋊C4C2413yes—
499C7×C4⋊C4C2411yescharacteristic
500C7×C4⋊C4C2416yes—
501C7×C4⋊C4C2413yes—
502C7×C4⋊C4C2413yes—
503C7×C4⋊C4C2413yes—
504C7×C4⋊C4C2411yescharacteristic
505C7×C4⋊C4C24112yes—
506C7×C4⋊C4C2416yes—
507C7×C4⋊C4C2416yes—
508C7×C4⋊C4C24112yes—
509C7×C4⋊C4C2416yes—
510C7×C4⋊C4C2416yes—
511C7×C4⋊C4C2412yes—
512C7×C4⋊C4C2416yes—
513C7×C4⋊C4C2412yes—
514C7×C22⋊C4C2416yes—
515C7×C22⋊C4C2416yes—
516C7×C22⋊C4C2416yes—
517C42×C7C2416yes—
518C42×C7C2413yes—
519C42×C7C2413yes—
520C42×C7C2413yes—
521C42×C7C2416yes—
522C42×C7C2411yescharacteristic
523C22⋊Dic7C2416yes—
524(C2×D7)⋊C4C2412yes—
525(C2×D7)⋊C4C2416yes—
526(C2×D7)⋊C4C2416yes—
527(C2×D7)⋊C4C2416yes—
528(C2×D7)⋊C4C2416yes—
529(C2×D7)⋊C4C2416yes—
530(C2×D7)⋊C4C2412yes—
531(C2×D7)⋊C4C2412yes—
532(C2×D7)⋊C4C2412yes—
533(C2×D7)⋊C4C2412yes—
534(C2×D7)⋊C4C2416yes—
535(C2×D7)⋊C4C2416yes—
536(C2×D7)⋊C4C2416yes—
537(C2×D7)⋊C4C2416yes—
538(C2×D7)⋊C4C24112yes—
539(C2×D7)⋊C4C2416yes—
540(C2×D7)⋊C4C2416yes—
541(C2×D7)⋊C4C2416yes—
542(C2×D7)⋊C4C2416yes—
543(C2×D7)⋊C4C24112yes—
544(C2×D7)⋊C4C24112yes—
545(C2×D7)⋊C4C24112yes—
546(C2×D7)⋊C4C24112yes—
547C4⋊Dic7C2413yes—
548C4⋊Dic7C2413yes—
549C4⋊Dic7C2416yes—
550C4⋊Dic7C2416yes—
551C4⋊Dic7C2416yes—
552C4⋊Dic7C24112yes—
553C4⋊Dic7C2412yes—
554C4⋊Dic7C2416yes—
555C4⋊Dic7C2416yes—
556Dic7⋊C4C2416yes—
557Dic7⋊C4C2416yes—
558Dic7⋊C4C2416yes—
559Dic7⋊C4C24112yes—
560Dic7⋊C4C2412yes—
561Dic7⋊C4C2416yes—
562Dic7⋊C4C2416yes—
563C4×Dic7C2413yes—
564C4×Dic7C2413yes—
565C4×Dic7C2416yes—
566C4×Dic7C24112yes—
567C4×Dic7C2413yes—
568C4×Dic7C2411yescharacteristic
569C4×Dic7C2411yescharacteristic
570C4×Dic7C2411yescharacteristic
571C4×Dic7C2412yes—
572C4×Dic7C2413yes—
573C4×Dic7C2413yes—
574C4×Dic7C2413yes—
575C4×Dic7C2413yes—
576C4×Dic7C2413yes—
577C4×Dic7C2413yes—
578C4×Dic7C2416yes—
579C4×Dic7C2416yes—
580C2×2−1+4—71no—
581C2×H(5,𝔽2)—71no—
582C22×#41—71no—
583#559—76no—
584#559—76no—
585#557C2×D712yescomplemented
586#557C2×D712yescomplemented
587#556—76no—
588#556—76no—
589#556—76no—
590#555—76no—
591#554—76no—
592#554C2×D716yescomplemented
593#554C2×D716yescomplemented
594#553—76no—
595#553—76no—
596#553—76no—
597#553—76no—
598#553—712no—
599#553—712no—
600#552—76no—
601#552—76no—
602#552—76no—
603#552—76no—
604#552—712no—
605#551—712no—
606#551—712no—
607#551—712no—
608#551—712no—
609#550—72no—
610D4×Q8—72no—
611#548—72no—
612#548—72no—
613#548—72no—
614#548—72no—
615#547—76no—
616#547—76no—
617#546—712no—
618#546—76no—
619#546—76no—
620#546—76no—
621#546—76no—
622D42—76no—
623#544C2×D713yescomplemented
624#544C2×D713yescomplemented
625#542—76no—
626#542—76no—
627#542—76no—
628#542—76no—
629#541—76no—
630#541—76no—
631#540—76no—
632#540—76no—
633#539—712no—
634#538—712no—
635#537—73no—
636#537—73no—
637#536—73no—
638#536—73no—
639#535—73no—
640#535—73no—
641#533—73no—
642#533—73no—
643#533—76no—
644#533C2×D713yescomplemented
645#532—73no—
646#532—73no—
647#532—76no—
648#532—73no—
649#529—73no—
650#529—76no—
651#529—76no—
652#529—76no—
653#529—76no—
654#529—76no—
655#529—76no—
656#529—76no—
657#529—71no—
658#529—73no—
659#529—73no—
660#529—76no—
661#529—76no—
662#529—76no—
663#529—76no—
664#529—712no—
665#529—76no—
666#529—76no—
667C2×#126—76no—
668C2×#125C2×D713yescomplemented
669C2×#124—73no—
670#525—76no—
671#525—76no—
672#525—712no—
673#525—73no—
674#525—73no—
675C2×#123—76no—
676C2×C22⋊Q8—73no—
677C2×#121—73no—
678#520—72no—
679#520—76no—
680#520—73no—
681#520—73no—
682#520C2×D711yescharacteristic
683#520C2×D711yescharacteristic
684#519—72no—
685#519—73no—
686#518—76no—
687#518—73no—
688C4×#41—71no—
689C4×#41—71no—
690C4×#41—71no—
691C4×#41—72no—
692C4×#41—76no—
693C4×#41—76no—
694C4×#41—73no—
695C4×#41—73no—
696C4×#41—76no—
697C4×#41—73no—
698C4×#41—73no—
699C4×#41—73no—
700C4×#41—73no—
701C4×#41C2×D711yescharacteristic
702C2×C4×Q8—71no—
703C2×C4×Q8—71no—
704C2×C4×Q8—72no—
705C2×C4×Q8—73no—
706C2×C4×D4—73no—
707C2×C4×D4—73no—
708C2×C4×D4—76no—
709C2×C4×D4—73no—
710C2×C4×D4—76no—
711C2×#117—73no—
712C2×#117—76no—
713C22×C42—73no—
714C23×C7C2513yes—
715C22×D7—26no—
716C22×D7—212no—
717C22×D7—26no—
718C22×D7—43no—
719C22×D7—46no—
720C22×D7—46no—
721C22×D7C2516yes—
722C22×D7C2513yes—
723C22×D7C2512yes—
724C22×D7C2511yescharacteristic
725C7×Q8—46no—
726C7×Q8—46no—
727C7×Q8C2×#4114yes—
728C7×D4C2×#41112yes—
729C2×C4×C7—43no—
730C2×C4×C7—43no—
731C2×C4×C7—46no—
732C2×C4×C7—46no—
733C2×C4×C7C2×#41112yes—
734C2×C4×C7C2511yescharacteristic
735C2×C4×C7C2511yescharacteristic
736C2×C4×C7C2512yes—
737C2×C4×C7C2516yes—
738C2×C4×C7C2513yes—
739C2×C4×C7C2513yes—
740C2×C4×C7C2512yes—
741C2×C4×C7C2516yes—
742C2×C4×C7C2511yescharacteristic
743C2×C4×C7C2513yes—
744C22⋊D7—212no—
745C22⋊D7—212no—
746C22⋊D7—212no—
747C2×Dic7—212no—
748C2×Dic7—26no—
749C2×Dic7—26no—
750C2×Dic7—43no—
751C2×Dic7C2511yescharacteristic
752C2×Dic7C2513yes—
753C2×Dic7C2513yes—
754C2×Dic7C2511yescharacteristic
755C2×Dic7C2512yes—
756C2×Dic7C2513yes—
757C2×Dic7C2516yes—
758C2×Dic7C2511yescharacteristic
759D28—212no—
760D28—24no—
761D28—26no—
762D28—212no—
763D28—22no—
764D28—26no—
765D28—412no—
766D28—46no—
767D28—46no—
768D28—46no—
769D28—46no—
770C4×D7—22no—
771C4×D7—26no—
772C4×D7—22no—
773C4×D7—26no—
774C4×D7—26no—
775C4×D7—26no—
776C4×D7—212no—
777C4×D7—212no—
778C4×D7—22no—
779C4×D7—212no—
780C4×D7—26no—
781C4×D7—24no—
782C4×D7—43no—
783C4×D7—43no—
784C4×D7—43no—
785C4×D7—412no—
786C4×D7—43no—
787C4×D7—46no—
788C4×D7—46no—
789Dic14—26no—
790Dic14—212no—
791Dic14—22no—
792Dic14—26no—
7932−1+4—148no—
794H(5,𝔽2)—148no—
795C2×#41—71no—
796C2×#41—72no—
797C2×#41—76no—
798C2×#41—76no—
799C2×#41—73no—
800C2×#41—76no—
801C2×#41—73no—
802C2×#41—73no—
803C2×#41—73no—
804C2×#41—148no—
805C2×#41C22×D711yescharacteristic
806C22×Q8—71no—
807C22×Q8—72no—
808C22×Q8—73no—
809C22×D4—73no—
810C22×D4—76no—
811C22×D4—73no—
812C22×D4—76no—
813C23×C4—73no—
814C23×C4—76no—
815C23×C4—73no—
816C23×C4—73no—
817C4⋊Q8—73no—
818C4⋊Q8—76no—
819C4⋊Q8C22×D713yes—
820C4⋊Q8C22×D713yes—
821C4⋊Q8C22×D716yes—
822C4⋊Q8C22×D716yes—
823#127—73no—
824#127—76no—
825#126—76no—
826#126—712no—
827#126—712no—
828#126—712no—
829#126—72no—
830#126—76no—
831#126—76no—
832#126—712no—
833#126—712no—
834#126—712no—
835#126—712no—
836#125—76no—
837#125—76no—
838#125—712no—
839#125—712no—
840#125C22×D713yes—
841#125C22×D716yes—
842#125C22×D716yes—
843#125C22×D716yes—
844#125C22×D711yescharacteristic
845#125C22×D716yes—
846#125C22×D716yes—
847#124—76no—
848#124—76no—
849#124—712no—
850#124—712no—
851#124—73no—
852#124—76no—
853#124—76no—
854#124—76no—
855#124—71no—
856#124—76no—
857#124—76no—
858#123—76no—
859#123—712no—
860#123—712no—
861#123—712no—
862#123—72no—
863#123—76no—
864#123—76no—
865#123—712no—
866#123—712no—
867#123—712no—
868#123—712no—
869#123—76no—
870#123—76no—
871#123—712no—
872#123—712no—
873C22⋊Q8—76no—
874C22⋊Q8—76no—
875C22⋊Q8—712no—
876C22⋊Q8—712no—
877C22⋊Q8—73no—
878C22⋊Q8—76no—
879C22⋊Q8—76no—
880C22⋊Q8—76no—
881C22⋊Q8—71no—
882C22⋊Q8—73no—
883C22⋊Q8—73no—
884C22⋊Q8—76no—
885C22⋊Q8—76no—
886C22⋊Q8—76no—
887C22⋊Q8—76no—
888C22⋊Q8C22×D716yes—
889C22⋊Q8C22×D716yes—
890C22⋊Q8C22×D7112yes—
891C22⋊Q8C22×D7112yes—
892#121—76no—
893#121—76no—
894#121—712no—
895#121—712no—
896#121—73no—
897#121—76no—
898#121—76no—
899#121—76no—
900#121—71no—
901#121—73no—
902#121—73no—
903#121—76no—
904#121—76no—
905#121—712no—
906#121—76no—
907#121—76no—
908#121—76no—
909#121—76no—
910#121—712no—
911#120—76no—
912#120—76no—
913#120—712no—
914#120—712no—
915C4×Q8—71no—
916C4×Q8—71no—
917C4×Q8—76no—
918C4×Q8—76no—
919C4×Q8—76no—
920C4×Q8—73no—
921C4×Q8—73no—
922C4×Q8—73no—
923C4×Q8—76no—
924C4×Q8—76no—
925C4×Q8—71no—
926C4×Q8—73no—
927C4×Q8—73no—
928C4×Q8—73no—
929C4×Q8—73no—
930C4×Q8—76no—
931C4×Q8—76no—
932C4×Q8C22×D711yescharacteristic
933C4×Q8C22×D711yescharacteristic
934C4×Q8C22×D712yes—
935C4×Q8C22×D712yes—
936C4×Q8C22×D716yes—
937C4×Q8C22×D716yes—
938C4×D4—73no—
939C4×D4—73no—
940C4×D4—76no—
941C4×D4—76no—
942C4×D4—712no—
943C4×D4—712no—
944C4×D4—76no—
945C4×D4—76no—
946C4×D4—73no—
947C4×D4—73no—
948C4×D4—73no—
949C4×D4—76no—
950C4×D4—76no—
951C4×D4—712no—
952C4×D4—712no—
953C4×D4—712no—
954C4×D4—72no—
955C4×D4—71no—
956C4×D4—73no—
957C4×D4—73no—
958C4×D4—76no—
959C4×D4—76no—
960C4×D4—76no—
961C4×D4—76no—
962C4×D4—76no—
963C4×D4—76no—
964C4×D4—76no—
965C4×D4—76no—
966C4×D4—76no—
967C4×D4—76no—
968C4×D4—73no—
969C4×D4—73no—
970C4×D4—76no—
971C4×D4—76no—
972C4×D4—76no—
973C4×D4—76no—
974C4×D4—76no—
975C4×D4—76no—
976C4×D4—76no—
977C4×D4—76no—
978C4×D4C22×D713yes—
979C4×D4C22×D713yes—
980C4×D4C22×D716yes—
981C4×D4C22×D716yes—
982#117—73no—
983#117—76no—
984#117—73no—
985#117—73no—
986#117—712no—
987#117—712no—
988#117—712no—
989#117—72no—
990#117—76no—
991#117—76no—
992#117—76no—
993#117—76no—
994#117—76no—
995#117—76no—
996#117—76no—
997#117—712no—
998#117—76no—
999#117—76no—
1000#117—76no—
1001#117C22×D713yes—
1002#117C22×D713yes—
1003#117C22×D713yes—
1004C2×C4⋊C4—76no—
1005C2×C4⋊C4—76no—
1006C2×C4⋊C4—73no—
1007C2×C4⋊C4—73no—
1008C2×C4⋊C4—76no—
1009C2×C4⋊C4—76no—
1010C2×C4⋊C4C22×D716yes—
1011C2×C4⋊C4C22×D713yes—
1012C2×C4⋊C4C22×D716yes—
1013C2×C4⋊C4C22×D713yes—
1014C2×C22⋊C4—76no—
1015C2×C22⋊C4—76no—
1016C2×C22⋊C4—76no—
1017C2×C22⋊C4—76no—
1018C2×C22⋊C4—76no—
1019C2×C22⋊C4—76no—
1020C2×C22⋊C4—712no—
1021C2×C42—73no—
1022C2×C42—76no—
1023C2×C42—73no—
1024C2×C42—73no—
1025C2×C42—73no—
1026C2×C42—73no—
1027C2×C42—73no—
1028C2×C42—76no—
1029C2×C42—76no—
1030C2×C42—73no—
1031C2×C42—73no—
1032C2×C42—73no—
1033C2×C42—73no—
1034C2×C42—71no—
1035C2×C42C22×D713yes—
1036C22×C7—23no—
1037C22×C7—23no—
1038C22×C7C22×#4116yes—
1039C22×C7C2611yescharacteristic
1040C2×D7—21no—
1041C2×D7—21no—
1042C2×D7—22no—
1043C2×D7—23no—
1044C2×D7—26no—
1045C2×D7—26no—
1046C2×D7—23no—
1047C2×D7—22no—
1048C2×D7—22no—
1049C2×D7—23no—
1050C2×D7—26no—
1051C2×D7—412no—
1052C2×D7—812no—
1053C2×D7#58512yes—
1054C4×C7—21no—
1055C4×C7—21no—
1056C4×C7—26no—
1057C4×C7—23no—
1058C4×C7—23no—
1059C4×C7—22no—
1060C4×C7—22no—
1061C4×C7—26no—
1062C4×C7C22×#4112yes—
1063C4×C7C22×#4116yes—
1064Dic7—26no—
1065Dic7—23no—
1066Dic7—22no—
1067Dic7—21no—
1068Dic7—23no—
1069Dic7—21no—
1070Dic7—23no—
1071Dic7#58512yes—
1072C24—73no—
1073C24—76no—
1074#41—144no—
1075#41—148no—
1076#41—1412no—
1077#41—1424no—
1078#41—1412no—
1079#41—1412no—
1080#41—1412no—
1081#41—2812no—
1082#41—2812no—
1083#41#116118yescomplemented
1084C2×Q8—73no—
1085C2×Q8—76no—
1086C2×Q8—73no—
1087C2×Q8—71no—
1088C2×Q8—144no—
1089C2×Q8—148no—
1090C2×Q8—1412no—
1091C2×Q8C23×D716yes—
1092C2×Q8C23×D716yes—
1093C2×Q8C23×D711yescharacteristic
1094C2×D4—76no—
1095C2×D4—76no—
1096C2×D4—76no—
1097C2×D4—72no—
1098C2×D4—76no—
1099C2×D4—73no—
1100C2×D4—76no—
1101C2×D4—73no—
1102C2×D4—71no—
1103C2×D4—76no—
1104C2×D4—76no—
1105C2×D4—76no—
1106C2×D4—76no—
1107C2×D4—712no—
1108C2×D4—1412no—
1109C2×D4—1424no—
1110C2×D4—1412no—
1111C2×D4—2812no—
1112C2×D4C23×D713yes—
1113C22×C4—73no—
1114C22×C4—73no—
1115C22×C4—76no—
1116C22×C4—73no—
1117C22×C4—71no—
1118C22×C4—71no—
1119C22×C4—71no—
1120C22×C4—72no—
1121C22×C4—73no—
1122C22×C4—73no—
1123C22×C4—73no—
1124C22×C4—73no—
1125C22×C4—73no—
1126C22×C4—76no—
1127C22×C4—76no—
1128C22×C4—76no—
1129C22×C4—73no—
1130C22×C4—73no—
1131C22×C4—73no—
1132C22×C4—73no—
1133C22×C4—76no—
1134C22×C4—76no—
1135C22×C4—712no—
1136C22×C4—1412no—
1137C22×C4—286no—
1138C22×C4—2812no—
1139C22×C4—286no—
1140C22×C4C23×D713yes—
1141C22×C4C23×D713yes—
1142C22×C4C23×D716yes—
1143C22×C4C23×D716yes—
1144C22×C4C23×D713yes—
1145C4⋊C4—76no—
1146C4⋊C4—712no—
1147C4⋊C4—76no—
1148C4⋊C4—76no—
1149C4⋊C4—76no—
1150C4⋊C4—72no—
1151C4⋊C4—76no—
1152C4⋊C4—73no—
1153C4⋊C4—73no—
1154C4⋊C4—76no—
1155C4⋊C4—712no—
1156C4⋊C4—72no—
1157C4⋊C4—76no—
1158C4⋊C4—76no—
1159C4⋊C4—76no—
1160C4⋊C4—76no—
1161C4⋊C4C23×D716yes—
1162C4⋊C4C23×D716yes—
1163C4⋊C4C23×D713yes—
1164C4⋊C4C23×D713yes—
1165C4⋊C4C23×D716yes—
1166C4⋊C4C23×D716yes—
1167C4⋊C4C23×D713yes—
1168C4⋊C4C23×D713yes—
1169C4⋊C4C23×D7112yes—
1170C4⋊C4C23×D7112yes—
1171C4⋊C4C23×D712yes—
1172C4⋊C4C23×D712yes—
1173C4⋊C4C23×D716yes—
1174C4⋊C4C23×D716yes—
1175C4⋊C4C23×D711yescharacteristic
1176C4⋊C4C23×D711yescharacteristic
1177C22⋊C4—76no—
1178C22⋊C4—76no—
1179C22⋊C4—76no—
1180C22⋊C4—76no—
1181C22⋊C4—76no—
1182C22⋊C4—712no—
1183C22⋊C4—76no—
1184C22⋊C4—76no—
1185C22⋊C4—76no—
1186C22⋊C4—76no—
1187C22⋊C4—712no—
1188C22⋊C4—712no—
1189C22⋊C4—712no—
1190C22⋊C4—712no—
1191C22⋊C4—72no—
1192C22⋊C4—76no—
1193C22⋊C4—72no—
1194C22⋊C4—72no—
1195C22⋊C4—72no—
1196C22⋊C4—72no—
1197C22⋊C4—76no—
1198C22⋊C4—76no—
1199C22⋊C4—76no—
1200C22⋊C4—76no—
1201C22⋊C4C23×D716yes—
1202C22⋊C4C23×D716yes—
1203C22⋊C4C23×D716yes—
1204C42—71no—
1205C42—71no—
1206C42—73no—
1207C42—71no—
1208C42—73no—
1209C42—76no—
1210C42—73no—
1211C42—72no—
1212C42—73no—
1213C42—73no—
1214C42—73no—
1215C42—73no—
1216C42—73no—
1217C42—73no—
1218C42—76no—
1219C42—712no—
1220C42—76no—
1221C42C23×D711yescharacteristic
1222C42C23×D713yes—
1223C42C23×D713yes—
1224C42C23×D713yes—
1225C42C23×D716yes—
1226C42C23×D716yes—
1227C2×C7—26no—
1228C2×C7C23×#4111yescharacteristic
1229C2×C7C2×#58511yescharacteristic
1230C2×C7C2×#58511yescharacteristic
1231D7—22no—
1232D7—42no—
1233D7—43no—
1234D7—46no—
1235C23—71no—
1236C23—76no—
1237C23—73no—
1238C23—72no—
1239C23—146no—
1240C23—146no—
1241C23—1412no—
1242C23—283no—
1243C23—286no—
1244C23—286no—
1245C23C24×D713yes—
1246Q8—46no—
1247Q8—46no—
1248Q8—1412no—
1249Q8—146no—
1250Q8—146no—
1251Q8—142no—
1252Q8C2×#116114yes—
1253D4—1412no—
1254D4—144no—
1255D4—1412no—
1256D4—1412no—
1257D4—1412no—
1258D4—1412no—
1259D4—146no—
1260D4—146no—
1261D4—142no—
1262D4—2812no—
1263D4—286no—
1264D4—286no—
1265D4—286no—
1266D4—286no—
1267D4C2×#1161112yes—
1268C2×C4—43no—
1269C2×C4—43no—
1270C2×C4—46no—
1271C2×C4—46no—
1272C2×C4—71no—
1273C2×C4—71no—
1274C2×C4—71no—
1275C2×C4—73no—
1276C2×C4—73no—
1277C2×C4—76no—
1278C2×C4—73no—
1279C2×C4—72no—
1280C2×C4—142no—
1281C2×C4—1412no—
1282C2×C4—146no—
1283C2×C4—144no—
1284C2×C4—142no—
1285C2×C4—146no—
1286C2×C4—146no—
1287C2×C4—146no—
1288C2×C4—1412no—
1289C2×C4—142no—
1290C2×C4—146no—
1291C2×C4—146no—
1292C2×C4—146no—
1293C2×C4—1412no—
1294C2×C4—1412no—
1295C2×C4—283no—
1296C2×C4—283no—
1297C2×C4—2812no—
1298C2×C4—283no—
1299C2×C4—283no—
1300C2×C4—286no—
1301C2×C4—286no—
1302C2×C4—283no—
1303C2×C4C2×#1161112yes—
1304C2×C4C24×D711yescharacteristic
1305C2×C4C24×D711yescharacteristic
1306C2×C4C24×D712yes—
1307C2×C4C24×D716yes—
1308C2×C4C24×D713yes—
1309C2×C4C24×D713yes—
1310C2×C4C24×D712yes—
1311C2×C4C24×D716yes—
1312C2×C4C24×D711yescharacteristic
1313C2×C4C24×D713yes—
1314C7#6281011yescharacteristic, complemented, Sylow
1315C22—23no—
1316C22—23no—
1317C22—72no—
1318C22—141no—
1319C22—141no—
1320C22—142no—
1321C22—143no—
1322C22—146no—
1323C22—146no—
1324C22—143no—
1325C22—142no—
1326C22—142no—
1327C22—143no—
1328C22—146no—
1329C22—2812no—
1330C22—5612no—
1331C22C22×#116116yes—
1332C22C25×D711yescharacteristic
1333C4—21no—
1334C4—21no—
1335C4—26no—
1336C4—26no—
1337C4—23no—
1338C4—23no—
1339C4—22no—
1340C4—22no—
1341C4—72no—
1342C4—141no—
1343C4—142no—
1344C4—143no—
1345C4—146no—
1346C4—143no—
1347C4—141no—
1348C4—143no—
1349C4C22×#116116yes—
1350C4C22×#116112yes—
1351C2—26no—
1352C2—142no—
1353C2—283no—
1354C2—286no—
1355C2—282no—
1356C2C23×#116111yescharacteristic
1357C2D7×#58511yescharacteristic
1358C2D7×#58511yescharacteristic
subgroupG/H
center, FrattiniC22C25×D7
commutator, socle, cosocleC22×C7C26
FittingC7×#3504C2
hypercenter#3504D7
hypocenterC7#62810
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ #3504

Complements

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

NH ≅ G/Ntype
1. C7×#3504C2semidirect
2. #11744094C2semidirect
3. #11744090C2semidirect
4. #11744085C2semidirect
5. #11744084C2semidirect
6. #11744003C2semidirect
7. #11743997C2semidirect
8. #11743992C2semidirect
9. #11743990C2semidirect
10. #11743666C2semidirect
11. #11743665C2semidirect
12. #11743651C2semidirect
13. #11743650C2semidirect
14. #11743331C2semidirect
15. #11743325C2semidirect
16. #11743155C2semidirect
17. C2×#90382C2semidirect
18. #11742969C2semidirect
19. #11742968C2semidirect
20. #11742955C2semidirect
21. #11742954C2semidirect
22. #11742915C2semidirect
23. C4×D7×#41C2semidirect
27. C7×#557C22semidirect
28. C7×#557C22semidirect
29. C7×#554C22semidirect
30. C7×#554C22semidirect
31. C7×#544C22semidirect
32. C7×#544C22semidirect
33. C7×#533C22semidirect
34. C2×C7×#125C22semidirect
39. #90425C22semidirect
40. #90424C22semidirect
41. #90424C22semidirect
42. #90424C22semidirect
43. #90424C22semidirect
44. #90423C22semidirect
45. #90421C22semidirect
46. #90419C22semidirect
47. #90419C22semidirect
48. #90419C22semidirect
49. #90417C22semidirect
50. #90416C22semidirect
51. #90416C22semidirect
52. #90416C22semidirect
53. #90389C22semidirect
54. #90389C22semidirect
55. #90388C22semidirect
56. #90388C22semidirect
57. #90386C22semidirect
58. #90386C22semidirect
59. #90386C22semidirect
60. #90386C22semidirect
61. #90385C22semidirect
62. #90385C22semidirect
63. #90385C22semidirect
64. #90385C22semidirect
65. #90382C22semidirect
66. #90382C22semidirect
67. #90382C22semidirect
68. #90382C22semidirect
69. #90382C22semidirect
70. #90382C22semidirect
71. #90382C22semidirect
72. #90382C22semidirect
73. #90382C22semidirect
74. #90382C22semidirect
75. #90382C22semidirect
76. #90382C22semidirect
77. #90382C22semidirect
78. #90336C22semidirect
79. #90335C22semidirect
80. #90333C22semidirect
81. #90328C22semidirect
82. #90328C22semidirect
83. #90328C22semidirect
84. #90328C22semidirect
85. #90321C22semidirect
86. #90318C22semidirect
87. #90318C22semidirect
88. #90318C22semidirect
89. #90315C22semidirect
90. #90315C22semidirect
91. #90315C22semidirect
92. #90276C22semidirect
93. #90276C22semidirect
94. #90275C22semidirect
95. #90275C22semidirect
96. #90271C22semidirect
97. #90271C22semidirect
100. #90267C22semidirect
101. #90267C22semidirect
102. #90267C22semidirect
103. Q8×D28C22semidirect
104. #90265C22semidirect
105. C4×#1161C22semidirect
106. C4×#1161C22semidirect
107. C4×#1161C22semidirect
108. C4×#1161C22semidirect
109. C4×#1161C22semidirect
110. #90263C22semidirect
111. C4×Q8×D7C22semidirect
112. C4×Q8×D7C22semidirect
113. C4×Q8×D7C22semidirect
114. #90246C22semidirect
116. #90245C22semidirect
117. #90245C22semidirect
118. #90245C22semidirect
120. #90237C22semidirect
121. #90236C22semidirect
122. C4×D4×D7C22semidirect
123. C4×D4×D7C22semidirect
124. C4×D4×D7C22semidirect
125. C4×#1159C22semidirect
126. C4×#1159C22semidirect
127. C4×#1159C22semidirect
128. #90217C22semidirect
129. #90217C22semidirect
131. #90216C22semidirect
133. #90215C22semidirect
134. #90213C22semidirect
135. #90213C22semidirect
136. #90213C22semidirect
137. #90212C22semidirect
138. D7×#117C22semidirect
139. #90207C22semidirect
140. #90205C22semidirect
141. #90205C22semidirect
142. C2×#6461C22semidirect
144. #90201C22semidirect
145. C2×#6460C22semidirect
147. C2×#6457C22semidirect
148. #90195C22semidirect
149. #90195C22semidirect
150. C2×#6456C22semidirect
151. C2×#6456C22semidirect
152. C2×#6455C22semidirect
153. C2×#6450C22semidirect
154. #90168C22semidirect
155. C2×#6438C22semidirect
156. C4×#1157C22semidirect
157. C2×C42×D7C22semidirect
408. #3504D7semidirect
427. C7×#41#41semidirect
585. #557C2×D7semidirect
586. #557C2×D7semidirect
592. #554C2×D7semidirect
593. #554C2×D7semidirect
623. #544C2×D7semidirect
624. #544C2×D7semidirect
644. #533C2×D7semidirect
668. C2×#125C2×D7semidirect
1083. #41#1161semidirect
1314. C7#62810semidirect

Maximal subgroups

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

subgroupindex
C7×#35042
#117440942
#117440902
#117440852
#117440842
#117440032
#117439972
#117439922
#117439902
#117436662
#117436652
#117436512
#117436502
#117433312
#117433252
#117431552
C2×#903822
#117429692
#117429682
#117429552
#117429542
#117429152
C4×D7×#412
#628107