Finite Group Databasebeta

← #14261663

Subgroups — #14261663

Order 1792.

6624 conjugacy classes of subgroups.

The subgroup lattice has 1400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3444C211yesmaximal, characteristic, complemented
2#11743355C212yesmaximal, complemented
3#11743346C212yesmaximal, complemented
4#11743337C212yesmaximal, complemented
5#11743318C212yesmaximal, complemented
6#11743307C211yesmaximal, characteristic, complemented
7#11743300C212yesmaximal, complemented
8#11743289C211yesmaximal, characteristic, complemented
9#11743252C218yesmaximal, complemented
10#11743250C214yesmaximal, complemented
11#11743248C214yesmaximal, complemented
12#11743217C214yesmaximal, complemented
13#11743216C214yesmaximal, complemented
14#11743122C214yesmaximal, complemented
15#11743116C214yesmaximal, complemented
16#11743100C214yesmaximal, complemented
17#11742910C214yesmaximal, complemented
18#11742909C214yesmaximal, complemented
19#11742905C214yesmaximal, complemented
20#11742748C212yesmaximal, complemented
21C7×#533C2212yescomplemented
22C7×#533C2211yescharacteristic, complemented
23C7×#532C2211yescharacteristic
24C7×#532C2212yes—
25C7×#529C2214yescomplemented
26C7×#529C2214yescomplemented
27C7×#529C2214yescomplemented
28C7×#525C2214yescomplemented
29C7×#525C2212yescomplemented
30C4×C7×#41C2212yescomplemented
31C4×C7×#41C2214yescomplemented
32C22×C42×C7C2211yescharacteristic, complemented
33#90525C2214yes—
34#90523C2214yescomplemented
35#90522C2214yescomplemented
36#90520C2214yes—
37#90519C2214yes—
38#90515C2214yescomplemented
39#90482C2212yes—
40#90482C2214yescomplemented
41#90482C2214yescomplemented
42#90482C2212yescomplemented
43#90425C2211yescharacteristic, complemented
44#90423C2212yescomplemented
45#90421C2212yescomplemented
46#90418C2212yescomplemented
47#90417C2212yescomplemented
48#90413C2211yescharacteristic, complemented
49#90412C2212yescomplemented
50#90409C2212yescomplemented
51#90408C2211yescharacteristic, complemented
52#90404C2211yescharacteristic, complemented
53#90401C2218yescomplemented
54#90398C2218yescomplemented
55#90395C2218yescomplemented
56#90392C2218yescomplemented
57#90389C2214yescomplemented
58#90388C2214yescomplemented
59#90384C2218yescomplemented
60#90380C2214yescomplemented
61#90380C2214yescomplemented
62#90373C2214yescomplemented
63#90373C2214yescomplemented
64#90370C2214yescomplemented
65#90366C2214yescomplemented
66#90365C2214yescomplemented
67#90361C2214yescomplemented
68#90358C2218yescomplemented
69#90357C2214yescomplemented
70#90354C2218yescomplemented
71#90353C2218yescomplemented
72#90351C2218yescomplemented
73#90348C2218yescomplemented
74#90342C2214yescomplemented
75#90338C2218yescomplemented
76#90337C2218yescomplemented
77#90334C2214yes—
78#90332C2214yescomplemented
79#90330C2214yescomplemented
80#90324C2214yes—
81#90322C2214yescomplemented
82#90320C2214yescomplemented
83#90319C2214yescomplemented
84#90316C2214yescomplemented
85#90312C2218yescomplemented
86#90311C2218yes—
87#90310C2214yescomplemented
88#90307C2214yescomplemented
89#90305C2214yes—
90#90303C2214yes—
91#90299C2214yes—
92#90298C2214yes—
93#90294C2214yescomplemented
94#90290C2214yescomplemented
95#90286C2218yescomplemented
96#90286C2214yescomplemented
97#90285C2214yescomplemented
98#90274C2218yescomplemented
99#90273C2218yescomplemented
100#90272C2214yescomplemented
101#90271C2214yescomplemented
102#90269C2214yescomplemented
103#90267C2214yescomplemented
104C4×#1161C2214yescomplemented
105C4×Q8×D7C2214yescomplemented
106#90260C2214yescomplemented
107#90259C2214yescomplemented
108#90255C2218yescomplemented
109#90255C2218yescomplemented
110#90253C2218yescomplemented
111#90252C2218yescomplemented
112#90251C2218yescomplemented
113#90251C2218yescomplemented
114#90250C2214yescomplemented
115#90250C2218yescomplemented
116#90249C2214yescomplemented
117#90249C2218yescomplemented
118#90248C2214yescomplemented
119#90248C2218yescomplemented
120#90247C2218yescomplemented
121#90245C2214yescomplemented
122#90239C2214yescomplemented
123#90239C2218yescomplemented
124#90238C2218yescomplemented
125C4×D4×D7C2214yescomplemented
126#90231C2218yescomplemented
127#90230C2214yescomplemented
128#90229C2218yescomplemented
129C4×#1159C2214yescomplemented
130#90224C2218yescomplemented
131#90224C2214yescomplemented
132#90223C2214yes—
133#90222C2218yescomplemented
134#90221C2218yescomplemented
135#90221C2214yescomplemented
136#90220C2214yescomplemented
137#90219C2218yescomplemented
138#90219C2218yescomplemented
139#90218C2218yescomplemented
140#90215C2214yescomplemented
141#90208C2214yescomplemented
142#90170C2212yes—
143#90170C2212yes—
144#90170C2214yescomplemented
145#90170C2214yescomplemented
146#90170C2214yescomplemented
147#90170C2212yescomplemented
148#90170C2214yescomplemented
149#90170C2212yescomplemented
150#90170C2218yescomplemented
151#90168C2212yes—
152#90168C2212yes—
153#90168C2212yes—
154C4×#1157C2212yes—
155C4×#1157C2212yescomplemented
156C4×#1157C2214yescomplemented
157C4×#1157C2214yescomplemented
158C4×#1157C2214yescomplemented
159C2×#6435C2214yescomplemented
160#90161C2212yescomplemented
161#90161C2212yescomplemented
162#90161C2212yescomplemented
163#62762—71nomaximal, Sylow
164C2×C7×#41C2314yes—
165C2×C7×#41C2312yes—
166C23×C4×C7C2312yes—
167C23×C4×C7C2311yescharacteristic
168C2×#1161C2314yes—
169C2×Q8×D7C2314yes—
170C2×#1159C2314yes—
171C2×D4×D7C2314yes—
172C2×#1157C2312yes—
173C2×#1157C2314yes—
174C2×#1157C2312yes—
175C2×#1157C2314yes—
176C2×#1157C2314yes—
177C22×C4×D7C2314yes—
178C7×C4⋊Q8C2312yes—
179C7×C4⋊Q8C2311yescharacteristic
180C7×#127C2311yescharacteristic
181C7×#126C2318yes—
182C7×#125C2314yes—
183C7×#125C2312yes—
184C7×#124C2312yes—
185C7×#124C2314yes—
186C7×#123C2314yes—
187C7×#123C2318yes—
188C7×C22⋊Q8C2314yes—
189C7×C22⋊Q8C2314yes—
190C7×C22⋊Q8C2314yes—
191C7×#121C2314yes—
192C7×#121C2314yes—
193C7×#121C2314yes—
194C7×#120C2314yes—
195C4×C7×Q8C2314yes—
196C4×C7×Q8C2314yes—
197C4×C7×Q8C2314yes—
198C4×C7×D4C2314yes—
199C4×C7×D4C2318yes—
200C4×C7×D4C2314yes—
201C4×C7×D4C2318yes—
202C4×C7×D4C2314yes—
203C4×C7×D4C2318yes—
204C7×#117C2314yes—
205C7×#117C2318yes—
206C7×#117C2312yes—
207C7×#117C2314yes—
208C2×C42×C7C2312yes—
209C2×C42×C7C2312yes—
210C2×C42×C7C2312yes—
211C2×C42×C7C2314yes—
212C2×C42×C7C2311yescharacteristic
213C2×C42×C7C2312yes—
214C2×C42×C7C2311yescharacteristic
215C2×C42×C7C2312yes—
216#6516C2314yes—
217#6516C2314yes—
218#6510C2314yes—
219#6510C2314yes—
220#6509C2318yes—
221#6509C2314yes—
222#6509C2314yes—
223Q8×Dic7C2314yes—
224Q8×Dic7C2314yes—
225#6507C2314yes—
226#6507C2314yes—
227#6503C2314yes—
228#6503C2318yes—
229#6503C2314yes—
230#6502C2318yes—
231#6502C2318yes—
232#6502C2318yes—
233#6502C2318yes—
234#6501C2314yes—
235#6501C2314yes—
236#6501C2318yes—
237#6501C2318yes—
238#6501C2318yes—
239#6500C2314yes—
240#6500C2318yes—
241#6500C2314yes—
242#6499C2314yes—
243#6499C2318yes—
244#6499C2314yes—
245#6498C2314yes—
246#6498C2318yes—
247#6498C2314yes—
248D4×Dic7C2314yes—
249D4×Dic7C2314yes—
250#6493C2312yes—
251#6493C2312yes—
252#6493C2312yes—
253#6493C2314yes—
254#6493C2312yes—
255#6493C2314yes—
256#6493C2314yes—
257#6493C2314yes—
258#6493C2318yes—
259#6492C2314yes—
260#6492C2314yes—
261#6492C2314yes—
262#6492C2314yes—
263#6492C2314yes—
264#6492C2314yes—
265#6492C2318yes—
266#6492C2318yes—
267C4×C22⋊D7C2314yes—
268C4×C22⋊D7C2314yes—
269C4×C22⋊D7C2314yes—
270C4×C22⋊D7C2314yes—
271C4×C22⋊D7C2314yes—
272C4×C22⋊D7C2314yes—
273C4×C22⋊D7C2314yes—
274C4×C22⋊D7C2314yes—
275C4×C22⋊D7C2314yes—
276C4×C22⋊D7C2314yes—
277C4×C22⋊D7C2314yes—
278C4×C22⋊D7C2314yes—
279C4×C22⋊D7C2318yes—
280C4×C22⋊D7C2318yes—
281C4×C22⋊D7C2318yes—
282C4×C22⋊D7C2318yes—
283C2×(C2×D7)⋊C4C2318yes—
284#6489C2312yes—
285#6489C2312yes—
286#6489C2314yes—
287#6489C2314yes—
288#6489C2314yes—
289#6487C2312yes—
290#6487C2312yes—
291#6487C2312yes—
292#6487C2312yes—
293#6487C2314yes—
294#6487C2314yes—
295#6487C2314yes—
296#6487C2314yes—
297#6487C2318yes—
298C2×Dic7⋊C4C2318yes—
299C2×C4×Dic7C2314yes—
300#6461C2318yes—
301#6461C2318yes—
302#6461C2318yes—
303#6461C2318yes—
304#6460C2318yes—
305#6460C2318yes—
306#6460C2314yes—
307#6460C2314yes—
308#6459C2318yes—
309#6459C2318yes—
310#6459C2318yes—
311#6459C2318yes—
312#6458C2318yes—
313#6458C2318yes—
314#6458C2314yes—
315#6458C2314yes—
316#6457C2318yes—
317#6457C2318yes—
318#6457C2318yes—
319#6457C2318yes—
320#6456C2318yes—
321#6456C2314yes—
322#6456C2314yes—
323#6455C2314yes—
324#6455C2314yes—
325#6455C2318yes—
326D7×C4⋊C4C2314yes—
327D7×C4⋊C4C2314yes—
328D7×C4⋊C4C2318yes—
329#6453C2314yes—
330#6453C2314yes—
331#6453C2318yes—
332#6453C2318yes—
333#6452C2318yes—
334#6452C2318yes—
335#6452C2318yes—
336#6452C2318yes—
337#6451C2318yes—
338#6451C2318yes—
339#6451C2314yes—
340#6451C2314yes—
341#6450C2318yes—
342#6450C2314yes—
343#6450C2314yes—
344#6449C2318yes—
345#6449C2318yes—
346#6448C2318yes—
347#6448C2318yes—
348#6448C2318yes—
349#6448C2318yes—
350#6448C2318yes—
351#6448C2318yes—
352#6447C2318yes—
353#6447C2318yes—
354#6447C2318yes—
355#6447C2318yes—
356#6447C2318yes—
357#6447C2318yes—
358#6446C2318yes—
359#6446C2318yes—
360#6446C2318yes—
361#6446C2318yes—
362#6446C2318yes—
363#6446C2318yes—
364#6445C2318yes—
365#6445C2318yes—
366(C22⋊D7)⋊C4C2318yes—
367(C22⋊D7)⋊C4C2318yes—
368D7×C22⋊C4C2318yes—
369#6442C2318yes—
370#6442C2318yes—
371#6442C2318yes—
372#6442C2318yes—
373#6442C2318yes—
374#6442C2318yes—
375#6441C2318yes—
376#6441C2318yes—
377#6441C2318yes—
378#6441C2318yes—
379#6440C2318yes—
380#6439C2314yes—
381#6439C2314yes—
382#6439C2314yes—
383#6439C2314yes—
384#6439C2318yes—
385#6439C2318yes—
386#6438C2314yes—
387#6438C2312yes—
388#6438C2312yes—
389#6438C2314yes—
390#6438C2318yes—
391#6437C2312yes—
392C4×D28C2314yes—
393C4×D28C2312yes—
394C4×D28C2312yes—
395C4×D28C2312yes—
396C4×D28C2314yes—
397C4×D28C2314yes—
398C4×D28C2312yes—
399C4×D28C2314yes—
400C4×D28C2318yes—
401C4×D28C2318yes—
402#6435C2314yes—
403#6435C2314yes—
404#6435C2314yes—
405#6435C2314yes—
406#6435C2314yes—
407#6435C2318yes—
408#6435C2318yes—
409#6435C2318yes—
410#6435C2314yes—
411C42×D7C2314yes—
412C42×D7C2314yes—
413C42×D7C2318yes—
414#6433C2314yes—
415#6433C2312yes—
416#6433C2312yes—
417#6433C2314yes—
418#6433C2318yes—
419#6432C2312yes—
420#6432C2312yes—
421#6432C2312yes—
422C4×Dic14C2314yes—
423C4×Dic14C2312yes—
424C4×Dic14C2312yes—
425C4×Dic14C2312yes—
426C4×Dic14C2312yes—
427C4×Dic14C2314yes—
428C4×Dic14C2314yes—
429C4×Dic14C2314yes—
430C4×Dic14C2318yes—
431C4×Dic14C2318yes—
432#3566—78no—
433#3565—74no—
434#3562—74no—
435#3555—72no—
436#3554—72no—
437#3547—72no—
438#3546—72no—
439#3540—74no—
440#3539—74no—
441#3529—74no—
442#3483—71no—
443#3482—72no—
444#3481—71no—
445#3480—74no—
446#3475—74no—
447#3461—74no—
448#3460—74no—
449#3455—74no—
450#3444—72no—
451#3444D711yescharacteristic, complemented
452C24×C7C2411yescharacteristic
453C23×D7C2414yes—
454C7×#41—44no—
455C7×#41—48no—
456C2×C7×Q8C2414yes—
457C2×C7×Q8C2412yes—
458C2×C7×D4C2414yes—
459C2×C7×D4C2412yes—
460C2×C7×D4C2418yes—
461C2×C7×D4C2414yes—
462C22×C4×C7—44no—
463C22×C4×C7—42no—
464C22×C4×C7C2414yes—
465C22×C4×C7C2412yes—
466C22×C4×C7C2412yes—
467C22×C4×C7C2412yes—
468C22×C4×C7C2412yes—
469C22×C4×C7C2411yescharacteristic
470C22×C4×C7C2418yes—
471C22×C4×C7C2411yescharacteristic
472C22×C4×C7C2412yes—
473C22×C4×C7C2412yes—
474C22×C4×C7C2412yes—
475C22×C4×C7C2412yes—
476C2×C22⋊D7C2418yes—
477C2×C22⋊D7C2418yes—
478C2×C22⋊D7C2418yes—
479C2×C22⋊D7C2414yes—
480C2×C22⋊D7C2414yes—
481C2×C22⋊D7C2414yes—
482C2×C22⋊D7C2414yes—
483C2×C22⋊D7C2414yes—
484C2×C22⋊D7C2414yes—
485C22×Dic7C2418yes—
486C22×Dic7C2414yes—
487#1161—48no—
488Q8×D7—48no—
489#1159—48no—
490D4×D7—48no—
491#1157—44no—
492#1157—44no—
493#1157—48no—
494#1157—48no—
495#1157—48no—
496C2×D28C2412yes—
497C2×D28C2412yes—
498C2×D28C2414yes—
499C2×D28C2414yes—
500C2×D28C2414yes—
501C2×D28C2418yes—
502C2×C4×D7—48no—
503C2×C4×D7C2414yes—
504C2×C4×D7C2414yes—
505C2×C4×D7C2414yes—
506C2×C4×D7C2414yes—
507C2×C4×D7C2414yes—
508C2×C4×D7C2414yes—
509C2×C4×D7C2418yes—
510C2×C4×D7C2418yes—
511C2×C4×D7C2418yes—
512C2×Dic14C2412yes—
513C2×Dic14C2412yes—
514C2×Dic14C2414yes—
515C2×Dic14C2414yes—
516C2×Dic14C2414yes—
517C2×Dic14C2418yes—
518C7×C4⋊C4C2414yes—
519C7×C4⋊C4C2414yes—
520C7×C4⋊C4C2418yes—
521C7×C4⋊C4C2418yes—
522C7×C4⋊C4C2418yes—
523C7×C4⋊C4C2414yes—
524C7×C22⋊C4C2418yes—
525C7×C22⋊C4C2418yes—
526C7×C22⋊C4C2418yes—
527C7×C22⋊C4C2414yes—
528C7×C22⋊C4C2418yes—
529C42×C7C2411yescharacteristic
530C42×C7C2411yescharacteristic
531C42×C7C2412yes—
532C42×C7C2412yes—
533C42×C7C2412yes—
534C42×C7C2414yes—
535C42×C7C2412yes—
536C42×C7C2418yes—
537C42×C7C2412yes—
538C42×C7C2412yes—
539C42×C7C2411yescharacteristic
540C42×C7C2411yescharacteristic
541C22⋊Dic7C2418yes—
542C22⋊Dic7C2414yes—
543C22⋊Dic7C2414yes—
544C22⋊Dic7C2418yes—
545C22⋊Dic7C2414yes—
546C22⋊Dic7C2414yes—
547C22⋊Dic7C2414yes—
548C22⋊Dic7C2414yes—
549C22⋊Dic7C2414yes—
550C22⋊Dic7C2414yes—
551(C2×D7)⋊C4C2414yes—
552(C2×D7)⋊C4C2414yes—
553(C2×D7)⋊C4C2418yes—
554(C2×D7)⋊C4C2418yes—
555(C2×D7)⋊C4C2414yes—
556(C2×D7)⋊C4C2414yes—
557(C2×D7)⋊C4C2414yes—
558(C2×D7)⋊C4C2414yes—
559(C2×D7)⋊C4C2414yes—
560(C2×D7)⋊C4C2414yes—
561(C2×D7)⋊C4C2414yes—
562(C2×D7)⋊C4C2414yes—
563(C2×D7)⋊C4C2414yes—
564(C2×D7)⋊C4C2414yes—
565(C2×D7)⋊C4C2418yes—
566(C2×D7)⋊C4C2418yes—
567(C2×D7)⋊C4C2418yes—
568(C2×D7)⋊C4C2418yes—
569C4⋊Dic7C2414yes—
570C4⋊Dic7C2414yes—
571C4⋊Dic7C2414yes—
572C4⋊Dic7C2414yes—
573C4⋊Dic7C2412yes—
574C4⋊Dic7C2412yes—
575C4⋊Dic7C2412yes—
576C4⋊Dic7C2412yes—
577C4⋊Dic7C2418yes—
578C4⋊Dic7C2418yes—
579C4⋊Dic7C2418yes—
580Dic7⋊C4C2414yes—
581Dic7⋊C4C2414yes—
582Dic7⋊C4C2414yes—
583Dic7⋊C4C2414yes—
584Dic7⋊C4C2414yes—
585Dic7⋊C4C2414yes—
586Dic7⋊C4C2414yes—
587Dic7⋊C4C2414yes—
588Dic7⋊C4C2414yes—
589Dic7⋊C4C2414yes—
590Dic7⋊C4C2414yes—
591Dic7⋊C4C2414yes—
592Dic7⋊C4C2418yes—
593Dic7⋊C4C2418yes—
594Dic7⋊C4C2418yes—
595Dic7⋊C4C2418yes—
596Dic7⋊C4C2418yes—
597Dic7⋊C4C2418yes—
598C4×Dic7C2414yes—
599C4×Dic7C2414yes—
600C4×Dic7C2414yes—
601C4×Dic7C2414yes—
602C4×Dic7C2414yes—
603C4×Dic7C2414yes—
604C4×Dic7C2418yes—
605C4×Dic7C2418yes—
606C4×Dic7C2414yes—
607C4×Dic7C2414yes—
608#563—74no—
609#563—78no—
610#562—78no—
611#562—78no—
612#562—78no—
613H(3,𝔽4)—74no—
614#560—74no—
615#560—78no—
616#560—74no—
617#560—78no—
618#559—71no—
619#559—78no—
620#559—74no—
621Q82—71no—
622#557—72no—
623#557—74no—
624#556—72no—
625#556—74no—
626#556—74no—
627#556—74no—
628#556—78no—
629#555—71no—
630#555—74no—
631#555—74no—
632#555—74no—
633#554—72no—
634#554—74no—
635#553—74no—
636#553—78no—
637#553—78no—
638#553—74no—
639#553—74no—
640#553—78no—
641#552—78no—
642#552—74no—
643#552—74no—
644#552—74no—
645#552—78no—
646#551—74no—
647#551—78no—
648#551—78no—
649#550—74no—
650#550—72no—
651#550—74no—
652D4×Q8—72no—
653#548—74no—
654#548—74no—
655#548—74no—
656#547—74no—
657#547—72no—
658#547—74no—
659#546—74no—
660#546—74no—
661#546—74no—
662D42—71no—
663#544—74no—
664#544—74no—
665#542—78no—
666#542—74no—
667#542—74no—
668#542—78no—
669#542—74no—
670#542—74no—
671#542—78no—
672#542—78no—
673#541—78no—
674#541—74no—
675#541—74no—
676#541—78no—
677#540—74no—
678#540—78no—
679#540—74no—
680#540—78no—
681#539—78no—
682#539—78no—
683#539—78no—
684#539—78no—
685#538—78no—
686#538—78no—
687#538—78no—
688#538—78no—
689#537—74no—
690#537—74no—
691#536—74no—
692#536—74no—
693#535—74no—
694#535—74no—
695#533—74no—
696#533—74no—
697#533—72no—
698#533—72no—
699#533—72no—
700#533C2×D711yescharacteristic, complemented
701#533C2×D712yescomplemented
702#532—74no—
703#532—74no—
704#532—78no—
705#532—72no—
706#532—72no—
707#532—72no—
708#532C2×D711yescharacteristic
709#532C2×D712yes—
710#529—74no—
711#529—78no—
712#529—74no—
713#529—78no—
714#529—78no—
715#529—78no—
716#529—72no—
717#529—72no—
718#529—74no—
719#529—72no—
720#529—72no—
721#529—74no—
722#529—74no—
723#529—74no—
724#529—78no—
725#529C2×D714yescomplemented
726#529C2×D714yescomplemented
727#529C2×D714yescomplemented
728#525—74no—
729#525—72no—
730#525—74no—
731#525—72no—
732#525—74no—
733#525—78no—
734#525—74no—
735#525C2×D712yescomplemented
736#525C2×D714yescomplemented
737C4×#41—74no—
738C4×#41—74no—
739C4×#41—72no—
740C4×#41—74no—
741C4×#41—74no—
742C4×#41—72no—
743C4×#41—74no—
744C4×#41C2×D712yescomplemented
745C4×#41C2×D714yescomplemented
746C2×C4×Q8—74no—
747C2×C4×D4—74no—
748C2×#117—74no—
749C22×C42C2×D711yescharacteristic, complemented
750C23×C7—42no—
751C23×C7—41no—
752C23×C7C2512yes—
753C23×C7C2511yescharacteristic
754C23×C7C2514yes—
755C22×D7—44no—
756C22×D7—48no—
757C22×D7C2514yes—
758C22×D7C2514yes—
759C7×Q8—28no—
760C7×Q8—42no—
761C7×D4—28no—
762C7×D4—44no—
763C7×D4—48no—
764C7×D4—42no—
765C2×C4×C7—28no—
766C2×C4×C7—24no—
767C2×C4×C7—24no—
768C2×C4×C7—24no—
769C2×C4×C7—24no—
770C2×C4×C7—22no—
771C2×C4×C7—41no—
772C2×C4×C7—42no—
773C2×C4×C7—42no—
774C2×C4×C7—42no—
775C2×C4×C7—42no—
776C2×C4×C7—48no—
777C2×C4×C7C2512yes—
778C2×C4×C7C2514yes—
779C2×C4×C7C2518yes—
780C2×C4×C7C2512yes—
781C2×C4×C7C2511yescharacteristic
782C2×C4×C7C2512yes—
783C2×C4×C7C2512yes—
784C2×C4×C7C2512yes—
785C2×C4×C7C2511yescharacteristic
786C22⋊D7—44no—
787C22⋊D7—44no—
788C22⋊D7—44no—
789C22⋊D7—44no—
790C22⋊D7—48no—
791C22⋊D7—44no—
792C22⋊D7—44no—
793C22⋊D7—48no—
794C22⋊D7—48no—
795C2×Dic7—44no—
796C2×Dic7—48no—
797C2×Dic7C2514yes—
798C2×Dic7C2514yes—
799C2×Dic7C2514yes—
800C2×Dic7C2514yes—
801C2×Dic7C2514yes—
802C2×Dic7C2514yes—
803D28—24no—
804D28—24no—
805D28—44no—
806D28—44no—
807D28—44no—
808D28—48no—
809C4×D7—28no—
810C4×D7—28no—
811C4×D7—28no—
812C4×D7—28no—
813C4×D7—48no—
814C4×D7—44no—
815C4×D7—44no—
816C4×D7—48no—
817C4×D7—48no—
818Dic14—24no—
819Dic14—24no—
820Dic14—44no—
821Dic14—44no—
822Dic14—44no—
823Dic14—48no—
824C2×#41—74no—
825C2×#41—74no—
826C2×#41—74no—
827C2×#41—74no—
828C2×#41—74no—
829C2×#41—72no—
830C2×#41—72no—
831C2×#41C22×D712yes—
832C2×#41C22×D714yes—
833C22×Q8—74no—
834C22×D4—74no—
835C23×C4—74no—
836C23×C4C22×D712yes—
837C23×C4C22×D711yescharacteristic
838C4⋊Q8—74no—
839C4⋊Q8—74no—
840C4⋊Q8—74no—
841C4⋊Q8—78no—
842C4⋊Q8—78no—
843C4⋊Q8—74no—
844C4⋊Q8—72no—
845C4⋊Q8—72no—
846C4⋊Q8—72no—
847C4⋊Q8C22×D712yes—
848C4⋊Q8C22×D711yescharacteristic
849#127—74no—
850#127—78no—
851#127—74no—
852#127—72no—
853#127C22×D711yescharacteristic
854#126—78no—
855#126—78no—
856#126—78no—
857#126—78no—
858#126—78no—
859#126—78no—
860#126—78no—
861#126—78no—
862#126—78no—
863#126—78no—
864#126—74no—
865#126—74no—
866#126—74no—
867#126—74no—
868#126—78no—
869#126—78no—
870#126C22×D718yes—
871#125—78no—
872#125—78no—
873#125—74no—
874#125—78no—
875#125—78no—
876#125—74no—
877#125—78no—
878#125—78no—
879#125—74no—
880#125—74no—
881#125—72no—
882#125—72no—
883#125—78no—
884#125C22×D714yes—
885#125C22×D712yes—
886#124—74no—
887#124—74no—
888#124—74no—
889#124—78no—
890#124—74no—
891#124—78no—
892#124—78no—
893#124—78no—
894#124—78no—
895#124—78no—
896#124—78no—
897#124—74no—
898#124—74no—
899#124—72no—
900#124—72no—
901#124—78no—
902#124C22×D714yes—
903#124C22×D712yes—
904#123—74no—
905#123—74no—
906#123—78no—
907#123—74no—
908#123—74no—
909#123—74no—
910#123—74no—
911#123—74no—
912#123—74no—
913#123—78no—
914#123—78no—
915#123—78no—
916#123—78no—
917#123—78no—
918#123—78no—
919#123—78no—
920#123—78no—
921#123—78no—
922#123—78no—
923#123—78no—
924#123—78no—
925#123—78no—
926#123—78no—
927#123C22×D718yes—
928#123C22×D714yes—
929C22⋊Q8—78no—
930C22⋊Q8—74no—
931C22⋊Q8—74no—
932C22⋊Q8—72no—
933C22⋊Q8—72no—
934C22⋊Q8—74no—
935C22⋊Q8—74no—
936C22⋊Q8—72no—
937C22⋊Q8—72no—
938C22⋊Q8—74no—
939C22⋊Q8—74no—
940C22⋊Q8—78no—
941C22⋊Q8—78no—
942C22⋊Q8—78no—
943C22⋊Q8—74no—
944C22⋊Q8—78no—
945C22⋊Q8—78no—
946C22⋊Q8—78no—
947C22⋊Q8—74no—
948C22⋊Q8—78no—
949C22⋊Q8—78no—
950C22⋊Q8—78no—
951C22⋊Q8—78no—
952C22⋊Q8—78no—
953C22⋊Q8C22×D714yes—
954C22⋊Q8C22×D714yes—
955C22⋊Q8C22×D714yes—
956#121—78no—
957#121—78no—
958#121—78no—
959#121—74no—
960#121—78no—
961#121—74no—
962#121—78no—
963#121—78no—
964#121—78no—
965#121—72no—
966#121—72no—
967#121—74no—
968#121—74no—
969#121—72no—
970#121—72no—
971#121—74no—
972#121—74no—
973#121—78no—
974#121—78no—
975#121—74no—
976#121—74no—
977#121—78no—
978#121—78no—
979#121—78no—
980#121—78no—
981#121—78no—
982#121—78no—
983#121—78no—
984#121C22×D714yes—
985#121C22×D714yes—
986#121C22×D714yes—
987#120—74no—
988#120—74no—
989#120—78no—
990#120—74no—
991#120—74no—
992#120—78no—
993#120—78no—
994#120C22×D714yes—
995C4×Q8—74no—
996C4×Q8—74no—
997C4×Q8—74no—
998C4×Q8—78no—
999C4×Q8—74no—
1000C4×Q8—72no—
1001C4×Q8—78no—
1002C4×Q8—72no—
1003C4×Q8—74no—
1004C4×Q8—74no—
1005C4×Q8—72no—
1006C4×Q8—72no—
1007C4×Q8—74no—
1008C4×Q8—74no—
1009C4×Q8—78no—
1010C4×Q8C22×D714yes—
1011C4×Q8C22×D714yes—
1012C4×Q8C22×D714yes—
1013C4×D4—74no—
1014C4×D4—74no—
1015C4×D4—78no—
1016C4×D4—74no—
1017C4×D4—74no—
1018C4×D4—78no—
1019C4×D4—74no—
1020C4×D4—74no—
1021C4×D4—74no—
1022C4×D4—74no—
1023C4×D4—74no—
1024C4×D4—74no—
1025C4×D4—74no—
1026C4×D4—74no—
1027C4×D4—74no—
1028C4×D4—74no—
1029C4×D4—78no—
1030C4×D4—78no—
1031C4×D4—74no—
1032C4×D4—78no—
1033C4×D4—74no—
1034C4×D4—78no—
1035C4×D4—78no—
1036C4×D4—72no—
1037C4×D4—72no—
1038C4×D4—78no—
1039C4×D4—74no—
1040C4×D4—74no—
1041C4×D4—72no—
1042C4×D4—74no—
1043C4×D4—72no—
1044C4×D4—74no—
1045C4×D4—78no—
1046C4×D4C22×D714yes—
1047C4×D4C22×D718yes—
1048C4×D4C22×D718yes—
1049C4×D4C22×D718yes—
1050C4×D4C22×D714yes—
1051C4×D4C22×D714yes—
1052#117—74no—
1053#117—74no—
1054#117—74no—
1055#117—72no—
1056#117—72no—
1057#117—74no—
1058#117—74no—
1059#117—78no—
1060#117—78no—
1061#117—74no—
1062#117—78no—
1063#117—78no—
1064#117—78no—
1065#117—74no—
1066#117—74no—
1067#117—74no—
1068#117—74no—
1069#117—74no—
1070#117C22×D714yes—
1071#117C22×D712yes—
1072#117C22×D714yes—
1073#117C22×D718yes—
1074C2×C4⋊C4—78no—
1075C2×C4⋊C4—74no—
1076C2×C4⋊C4—74no—
1077C2×C4⋊C4—78no—
1078C2×C22⋊C4—78no—
1079C2×C22⋊C4—78no—
1080C2×C42—74no—
1081C2×C42—74no—
1082C2×C42—74no—
1083C2×C42—78no—
1084C2×C42C22×D714yes—
1085C2×C42C22×D711yescharacteristic
1086C2×C42C22×D712yes—
1087C2×C42C22×D712yes—
1088C2×C42C22×D711yescharacteristic
1089C2×C42C22×D712yes—
1090C2×C42C22×D712yes—
1091C2×C42C22×D712yes—
1092C22×C7—24no—
1093C22×C7—28no—
1094C22×C7—22no—
1095C22×C7—22no—
1096C22×C7—22no—
1097C22×C7—22no—
1098C22×C7—21no—
1099C22×C7—44no—
1100C22×C7C2611yescharacteristic
1101C2×D7—24no—
1102C2×D7—24no—
1103C2×D7—24no—
1104C2×D7—24no—
1105C2×D7—24no—
1106C2×D7—24no—
1107C2×D7—88no—
1108C4×C7—22no—
1109C4×C7—22no—
1110C4×C7—24no—
1111C4×C7—28no—
1112C4×C7—22no—
1113C4×C7—22no—
1114C4×C7—21no—
1115C4×C7#58514yes—
1116C4×C7#58512yes—
1117Dic7—24no—
1118Dic7—24no—
1119Dic7—24no—
1120Dic7—24no—
1121Dic7—24no—
1122Dic7—24no—
1123C24—74no—
1124C24C23×D711yescharacteristic
1125#41—44no—
1126#41—48no—
1127#41—288no—
1128#41—288no—
1129#41—288no—
1130#41—284no—
1131#41—284no—
1132#41—288no—
1133#41—288no—
1134C2×Q8—72no—
1135C2×Q8—72no—
1136C2×Q8—78no—
1137C2×Q8—74no—
1138C2×Q8—74no—
1139C2×Q8—74no—
1140C2×Q8—288no—
1141C2×Q8C23×D714yes—
1142C2×Q8C23×D712yes—
1143C2×D4—74no—
1144C2×D4—74no—
1145C2×D4—74no—
1146C2×D4—74no—
1147C2×D4—78no—
1148C2×D4—74no—
1149C2×D4—74no—
1150C2×D4—78no—
1151C2×D4—78no—
1152C2×D4—72no—
1153C2×D4—72no—
1154C2×D4—78no—
1155C2×D4—74no—
1156C2×D4—74no—
1157C2×D4—74no—
1158C2×D4—288no—
1159C2×D4C23×D714yes—
1160C2×D4C23×D712yes—
1161C2×D4C23×D718yes—
1162C2×D4C23×D714yes—
1163C22×C4—44no—
1164C22×C4—42no—
1165C22×C4—78no—
1166C22×C4—74no—
1167C22×C4—74no—
1168C22×C4—74no—
1169C22×C4—74no—
1170C22×C4—74no—
1171C22×C4—74no—
1172C22×C4—74no—
1173C22×C4—78no—
1174C22×C4—78no—
1175C22×C4—78no—
1176C22×C4—288no—
1177C22×C4C23×D712yes—
1178C22×C4C23×D712yes—
1179C22×C4C23×D712yes—
1180C22×C4C23×D714yes—
1181C22×C4C23×D712yes—
1182C22×C4C23×D711yescharacteristic
1183C22×C4C23×D712yes—
1184C22×C4C23×D712yes—
1185C22×C4C23×D712yes—
1186C22×C4C23×D711yescharacteristic
1187C22×C4C23×D712yes—
1188C22×C4C23×D718yes—
1189C4⋊C4—74no—
1190C4⋊C4—74no—
1191C4⋊C4—74no—
1192C4⋊C4—78no—
1193C4⋊C4—78no—
1194C4⋊C4—78no—
1195C4⋊C4—78no—
1196C4⋊C4—78no—
1197C4⋊C4—74no—
1198C4⋊C4—74no—
1199C4⋊C4—74no—
1200C4⋊C4—74no—
1201C4⋊C4—78no—
1202C4⋊C4—74no—
1203C4⋊C4—74no—
1204C4⋊C4—74no—
1205C4⋊C4—74no—
1206C4⋊C4—74no—
1207C4⋊C4—72no—
1208C4⋊C4—72no—
1209C4⋊C4—78no—
1210C4⋊C4—72no—
1211C4⋊C4—72no—
1212C4⋊C4—78no—
1213C4⋊C4—74no—
1214C4⋊C4—78no—
1215C4⋊C4—74no—
1216C4⋊C4—74no—
1217C4⋊C4—74no—
1218C4⋊C4C23×D714yes—
1219C4⋊C4C23×D714yes—
1220C4⋊C4C23×D718yes—
1221C4⋊C4C23×D718yes—
1222C4⋊C4C23×D718yes—
1223C4⋊C4C23×D714yes—
1224C22⋊C4—78no—
1225C22⋊C4—74no—
1226C22⋊C4—74no—
1227C22⋊C4—74no—
1228C22⋊C4—74no—
1229C22⋊C4—74no—
1230C22⋊C4—74no—
1231C22⋊C4—78no—
1232C22⋊C4—74no—
1233C22⋊C4—74no—
1234C22⋊C4—74no—
1235C22⋊C4—74no—
1236C22⋊C4—74no—
1237C22⋊C4—78no—
1238C22⋊C4—78no—
1239C22⋊C4—78no—
1240C22⋊C4—74no—
1241C22⋊C4—74no—
1242C22⋊C4—74no—
1243C22⋊C4—74no—
1244C22⋊C4—74no—
1245C22⋊C4—78no—
1246C22⋊C4—74no—
1247C22⋊C4—78no—
1248C22⋊C4—74no—
1249C22⋊C4—78no—
1250C22⋊C4—74no—
1251C22⋊C4—74no—
1252C22⋊C4C23×D718yes—
1253C22⋊C4C23×D718yes—
1254C22⋊C4C23×D718yes—
1255C22⋊C4C23×D714yes—
1256C22⋊C4C23×D718yes—
1257C42—74no—
1258C42—74no—
1259C42—74no—
1260C42—74no—
1261C42—74no—
1262C42—74no—
1263C42—78no—
1264C42—78no—
1265C42—74no—
1266C42—74no—
1267C42C23×D711yescharacteristic
1268C42C23×D712yes—
1269C42C23×D712yes—
1270C42C23×D711yescharacteristic
1271C42C23×D712yes—
1272C42C23×D712yes—
1273C42C23×D712yes—
1274C42C23×D718yes—
1275C42C23×D712yes—
1276C42C23×D714yes—
1277C42C23×D711yescharacteristic
1278C42C23×D711yescharacteristic
1279C2×C7—44no—
1280C2×C7—41no—
1281C2×C7—42no—
1282C2×C7C2×#58512yes—
1283C2×C7C2×#58511yescharacteristic
1284D7—44no—
1285D7—44no—
1286C23—42no—
1287C23—41no—
1288C23—74no—
1289C23—74no—
1290C23—284no—
1291C23—288no—
1292C23C24×D712yes—
1293C23C24×D711yescharacteristic
1294C23C24×D714yes—
1295Q8—28no—
1296Q8—42no—
1297Q8—144no—
1298Q8—144no—
1299Q8—288no—
1300Q8—284no—
1301Q8—284no—
1302Q8—284no—
1303D4—28no—
1304D4—42no—
1305D4—44no—
1306D4—48no—
1307D4—144no—
1308D4—144no—
1309D4—284no—
1310D4—284no—
1311D4—284no—
1312D4—288no—
1313D4—288no—
1314D4—284no—
1315D4—284no—
1316D4—284no—
1317D4—284no—
1318D4—288no—
1319D4—284no—
1320D4—288no—
1321D4—284no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—28no—
1328C2×C4—42no—
1329C2×C4—42no—
1330C2×C4—42no—
1331C2×C4—42no—
1332C2×C4—41no—
1333C2×C4—48no—
1334C2×C4—74no—
1335C2×C4—74no—
1336C2×C4—74no—
1337C2×C4—74no—
1338C2×C4—74no—
1339C2×C4—74no—
1340C2×C4—148no—
1341C2×C4—148no—
1342C2×C4—148no—
1343C2×C4—148no—
1344C2×C4—288no—
1345C2×C4—288no—
1346C2×C4—284no—
1347C2×C4—284no—
1348C2×C4—288no—
1349C2×C4—284no—
1350C2×C4—288no—
1351C2×C4C24×D712yes—
1352C2×C4C24×D714yes—
1353C2×C4C24×D718yes—
1354C2×C4C24×D712yes—
1355C2×C4C24×D711yescharacteristic
1356C2×C4C24×D712yes—
1357C2×C4C24×D712yes—
1358C2×C4C24×D712yes—
1359C2×C4C24×D711yescharacteristic
1360C7#6276211yescharacteristic, complemented, Sylow
1361C22—22no—
1362C22—21no—
1363C22—22no—
1364C22—22no—
1365C22—22no—
1366C22—24no—
1367C22—28no—
1368C22—44no—
1369C22—144no—
1370C22—144no—
1371C22—144no—
1372C22—144no—
1373C22—144no—
1374C22—144no—
1375C22—568no—
1376C22C25×D711yescharacteristic
1377C4—22no—
1378C4—22no—
1379C4—21no—
1380C4—22no—
1381C4—22no—
1382C4—24no—
1383C4—28no—
1384C4—144no—
1385C4—144no—
1386C4—144no—
1387C4—144no—
1388C4—144no—
1389C4—144no—
1390C4#9061612yes—
1391C4#9061614yes—
1392C2—42no—
1393C2—41no—
1394C2—44no—
1395C2—284no—
1396C2—284no—
1397C2C2×#9061612yes—
1398C2C2×#9061611yescharacteristic
subgroupG/H
centerC2×C4C24×D7
commutator, socle, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC7×#3444C2
hypercenter#3444D7
hypocenterC7#62762
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. C7×#3444C2semidirect
2. #11743355C2semidirect
3. #11743346C2semidirect
4. #11743337C2semidirect
5. #11743318C2semidirect
6. #11743307C2semidirect
7. #11743300C2semidirect
8. #11743289C2semidirect
9. #11743252C2semidirect
10. #11743250C2semidirect
11. #11743248C2semidirect
12. #11743217C2semidirect
13. #11743216C2semidirect
14. #11743122C2semidirect
15. #11743116C2semidirect
16. #11743100C2semidirect
17. #11742910C2semidirect
18. #11742909C2semidirect
19. #11742905C2semidirect
20. #11742748C2semidirect
21. C7×#533C22semidirect
22. C7×#533C22semidirect
25. C7×#529C22semidirect
26. C7×#529C22semidirect
27. C7×#529C22semidirect
28. C7×#525C22semidirect
29. C7×#525C22semidirect
30. C4×C7×#41C22semidirect
31. C4×C7×#41C22semidirect
32. C22×C42×C7C22semidirect
34. #90523C22semidirect
35. #90522C22semidirect
38. #90515C22semidirect
40. #90482C22semidirect
41. #90482C22semidirect
42. #90482C22semidirect
43. #90425C22semidirect
44. #90423C22semidirect
45. #90421C22semidirect
46. #90418C22semidirect
47. #90417C22semidirect
48. #90413C22semidirect
49. #90412C22semidirect
50. #90409C22semidirect
51. #90408C22semidirect
52. #90404C22semidirect
53. #90401C22semidirect
54. #90398C22semidirect
55. #90395C22semidirect
56. #90392C22semidirect
57. #90389C22semidirect
58. #90388C22semidirect
59. #90384C22semidirect
60. #90380C22semidirect
61. #90380C22semidirect
62. #90373C22semidirect
63. #90373C22semidirect
64. #90370C22semidirect
65. #90366C22semidirect
66. #90365C22semidirect
67. #90361C22semidirect
68. #90358C22semidirect
69. #90357C22semidirect
70. #90354C22semidirect
71. #90353C22semidirect
72. #90351C22semidirect
73. #90348C22semidirect
74. #90342C22semidirect
75. #90338C22semidirect
76. #90337C22semidirect
78. #90332C22semidirect
79. #90330C22semidirect
81. #90322C22semidirect
82. #90320C22semidirect
83. #90319C22semidirect
84. #90316C22semidirect
85. #90312C22semidirect
87. #90310C22semidirect
88. #90307C22semidirect
93. #90294C22semidirect
94. #90290C22semidirect
95. #90286C22semidirect
96. #90286C22semidirect
97. #90285C22semidirect
98. #90274C22semidirect
99. #90273C22semidirect
100. #90272C22semidirect
101. #90271C22semidirect
102. #90269C22semidirect
103. #90267C22semidirect
104. C4×#1161C22semidirect
105. C4×Q8×D7C22semidirect
106. #90260C22semidirect
107. #90259C22semidirect
108. #90255C22semidirect
109. #90255C22semidirect
110. #90253C22semidirect
111. #90252C22semidirect
112. #90251C22semidirect
113. #90251C22semidirect
114. #90250C22semidirect
115. #90250C22semidirect
116. #90249C22semidirect
117. #90249C22semidirect
118. #90248C22semidirect
119. #90248C22semidirect
120. #90247C22semidirect
121. #90245C22semidirect
122. #90239C22semidirect
123. #90239C22semidirect
124. #90238C22semidirect
125. C4×D4×D7C22semidirect
126. #90231C22semidirect
127. #90230C22semidirect
128. #90229C22semidirect
129. C4×#1159C22semidirect
130. #90224C22semidirect
131. #90224C22semidirect
133. #90222C22semidirect
134. #90221C22semidirect
135. #90221C22semidirect
136. #90220C22semidirect
137. #90219C22semidirect
138. #90219C22semidirect
139. #90218C22semidirect
140. #90215C22semidirect
141. #90208C22semidirect
144. #90170C22semidirect
145. #90170C22semidirect
146. #90170C22semidirect
147. #90170C22semidirect
148. #90170C22semidirect
149. #90170C22semidirect
150. #90170C22semidirect
155. C4×#1157C22semidirect
156. C4×#1157C22semidirect
157. C4×#1157C22semidirect
158. C4×#1157C22semidirect
159. C2×#6435C22semidirect
160. #90161C22semidirect
161. #90161C22semidirect
162. #90161C22semidirect
451. #3444D7semidirect
700. #533C2×D7semidirect
701. #533C2×D7semidirect
725. #529C2×D7semidirect
726. #529C2×D7semidirect
727. #529C2×D7semidirect
735. #525C2×D7semidirect
736. #525C2×D7semidirect
744. C4×#41C2×D7semidirect
745. C4×#41C2×D7semidirect
749. C22×C42C2×D7semidirect
1360. C7#62762semidirect

Maximal subgroups

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

subgroupindex
C7×#34442
#117433552
#117433462
#117433372
#117433182
#117433072
#117433002
#117432892
#117432522
#117432502
#117432482
#117432172
#117432162
#117431222
#117431162
#117431002
#117429102
#117429092
#117429052
#117427482
#627627