Finite Group Databasebeta

← #14261666

Subgroups — #14261666

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×#3481C211yesmaximal, characteristic, complemented
2#11744135C212yesmaximal, complemented
3#11744024C212yesmaximal, complemented
4#11744022C212yesmaximal, complemented
5#11743985C214yesmaximal, complemented
6#11743971C214yesmaximal, complemented
7#11743892C218yesmaximal, complemented
8#11743739C214yesmaximal, complemented
9#11743727C214yesmaximal, complemented
10#11743693C212yesmaximal, complemented
11#11743289C211yesmaximal, characteristic, complemented
12#11743287C211yesmaximal, characteristic, complemented
13#11743220C214yesmaximal, complemented
14#11743217C214yesmaximal, complemented
15#11743116C214yesmaximal, complemented
16#11743087C214yesmaximal, complemented
17#11742912C212yesmaximal, complemented
18#11742904C212yesmaximal, complemented
19#11742845C214yesmaximal, complemented
20#11742832C214yesmaximal, complemented
21C7×#559C2211yescharacteristic, complemented
22C7×#554C2212yescomplemented
23C7×#553C2214yes—
24C7×#551C2214yescomplemented
25C7×#546C2214yes—
26C7×D42C2211yescharacteristic, complemented
27C7×#532C2211yescharacteristic
28C7×#529C2214yescomplemented
29C7×#525C2214yes—
30C4×C7×#41C2212yes—
31C2×C4×C7×D4C2214yescomplemented
32#90523C2212yes—
33#90523C2214yescomplemented
34#90522C2214yes—
35#90519C2212yes—
36#90519C2212yescomplemented
37#41×Dic7C2212yescomplemented
38#90497C2214yes—
39#90497C2214yescomplemented
40#90496C2214yes—
41#90496C2214yescomplemented
42#90482C2214yescomplemented
43#90482C2218yescomplemented
44C2×#6489C2214yescomplemented
45#90425C2211yescharacteristic, complemented
46#90419C2212yescomplemented
47#90413C2211yescharacteristic, complemented
48#90409C2212yescomplemented
49#90407C2212yes—
50#90400C2218yescomplemented
51#90398C2218yescomplemented
52#90393C2218yescomplemented
53#90392C2218yescomplemented
54#90388C2214yescomplemented
55#90386C2214yescomplemented
56#90380C2214yescomplemented
57#90376C2214yescomplemented
58#90373C2214yescomplemented
59#90372C2214yescomplemented
60#90371C2214yescomplemented
61#90368C2214yescomplemented
62#90366C2214yescomplemented
63#90361C2214yescomplemented
64#90358C2218yescomplemented
65#90357C2214yescomplemented
66#90356C2218yescomplemented
67#90356C2218yescomplemented
68#90355C2218yescomplemented
69#90353C2218yescomplemented
70#90352C2218yescomplemented
71#90351C2218yescomplemented
72#90342C2214yescomplemented
73#90338C2218yescomplemented
74#90337C2218yescomplemented
75#90334C2218yescomplemented
76#90332C2214yescomplemented
77#90324C2214yescomplemented
78#90319C2214yescomplemented
79#90316C2218yescomplemented
80#90316C2214yescomplemented
81#90312C2218yescomplemented
82#90311C2218yescomplemented
83#90310C2218yescomplemented
84#90307C2214yescomplemented
85#90305C2214yescomplemented
86#90299C2214yes—
87#90297C2214yescomplemented
88#90294C2218yescomplemented
89#90294C2214yescomplemented
90#90291C2214yescomplemented
91#90290C2214yes—
92#90290C2214yescomplemented
93#90286C2218yes—
94#90286C2214yescomplemented
95#90285C2214yescomplemented
96#90284C2218yescomplemented
97#90284C2218yescomplemented
98#90271C2212yescomplemented
99#90271C2212yescomplemented
100#90269C2212yescomplemented
101#90269C2212yescomplemented
102Q8×D28C2212yescomplemented
103C4×Q8×D7C2214yescomplemented
104#90261C2212yescomplemented
105#90256C2218yescomplemented
106#90254C2214yes—
107#90253C2214yescomplemented
108#90253C2214yescomplemented
109#90253C2218yescomplemented
110#90252C2214yes—
111#90252C2214yescomplemented
112#90252C2218yescomplemented
113#90248C2212yes—
114#90248C2212yes—
115#90248C2214yescomplemented
116#90248C2218yescomplemented
117#90248C2218yescomplemented
118#90248C2214yescomplemented
119#90246C2214yescomplemented
120#90242C2212yescomplemented
121#90242C2214yescomplemented
122#90239C2212yes—
123#90239C2212yes—
124#90239C2214yescomplemented
125#90239C2218yescomplemented
126#90238C2214yescomplemented
127#90238C2214yescomplemented
128#90234C2214yescomplemented
129#90233C2214yescomplemented
130#90233C2212yescomplemented
131#90233C2214yescomplemented
132#90232C2218yescomplemented
133#90229C2214yescomplemented
134#90229C2218yescomplemented
135#90229C2218yescomplemented
136#90229C2214yescomplemented
137C4×#1159C2214yescomplemented
138C4×#1159C2214yescomplemented
139#90220C2218yescomplemented
140#90220C2214yescomplemented
141#90219C2218yescomplemented
142#90219C2214yescomplemented
143#90219C2214yescomplemented
144#90215C2212yescomplemented
145#90213C2214yescomplemented
146#90208C2214yescomplemented
147#90208C2212yescomplemented
148#90204C2214yescomplemented
149#90204C2214yescomplemented
150#90201C2214yescomplemented
151#90191C2214yescomplemented
152#90186C2218yescomplemented
153#90186C2218yescomplemented
154#90185C2218yescomplemented
155#90185C2218yescomplemented
156C4×#1157C2212yescomplemented
157C4×#1157C2214yescomplemented
158C4×#1157C2214yescomplemented
159C4×#1157C2214yescomplemented
160C2×C42×D7C2211yescharacteristic, complemented
161#90161C2211yescharacteristic, complemented
162#90161C2214yescomplemented
163#62762—71nomaximal, Sylow
164C2×C7×#41C2312yes—
165C2×C7×#41C2312yes—
166C22×C7×D4C2314yes—
167C23×C4×C7C2314yes—
168C2×Q8×D7C2314yes—
169C2×#1159C2314yes—
170C2×#1159C2314yes—
171C2×#1157C2314yes—
172C2×#1157C2314yes—
173C2×#1157C2312yes—
174C2×#1157C2314yes—
175C2×#1157C2314yes—
176C22×C4×D7C2312yes—
177C22×C4×D7C2311yescharacteristic
178C7×C4⋊Q8C2311yescharacteristic
179C7×#127C2311yescharacteristic
180C7×#126C2318yes—
181C7×#125C2314yes—
182C7×#124C2314yes—
183C7×#124C2312yes—
184C7×#123C2314yes—
185C7×#123C2314yes—
186C7×#123C2318yes—
187C7×C22⋊Q8C2318yes—
188C7×C22⋊Q8C2314yes—
189C7×#121C2314yes—
190C7×#121C2314yes—
191C7×#121C2318yes—
192C7×#120C2314yes—
193C7×#120C2314yes—
194C4×C7×Q8C2312yes—
195C4×C7×Q8C2312yes—
196C4×C7×D4C2314yes—
197C4×C7×D4C2318yes—
198C4×C7×D4C2314yes—
199C4×C7×D4C2314yes—
200C4×C7×D4C2318yes—
201C4×C7×D4C2312yes—
202C4×C7×D4C2314yes—
203C4×C7×D4C2314yes—
204C4×C7×D4C2312yes—
205C7×#117C2314yes—
206C7×#117C2312yes—
207C7×#117C2314yes—
208C2×C7×C4⋊C4C2314yes—
209C2×C7×C22⋊C4C2318yes—
210C2×C42×C7C2311yescharacteristic
211C2×C42×C7C2314yes—
212#6516C2318yes—
213#6516C2318yes—
214#6516C2318yes—
215C2×C22⋊Dic7C2318yes—
216#6510C2312yes—
217#6510C2314yes—
218#6509C2312yes—
219#6509C2314yes—
220#6509C2312yes—
221Q8×Dic7C2314yes—
222Q8×Dic7C2314yes—
223#6507C2314yes—
224#6507C2312yes—
225#6503C2314yes—
226#6503C2312yes—
227#6503C2318yes—
228#6503C2314yes—
229#6502C2318yes—
230#6502C2314yes—
231#6502C2314yes—
232#6502C2318yes—
233#6502C2318yes—
234#6502C2318yes—
235#6501C2314yes—
236#6501C2314yes—
237#6501C2314yes—
238#6501C2312yes—
239#6501C2312yes—
240#6501C2318yes—
241#6501C2314yes—
242#6501C2318yes—
243#6501C2318yes—
244#6500C2314yes—
245#6500C2314yes—
246#6499C2314yes—
247#6499C2314yes—
248#6499C2312yes—
249#6499C2318yes—
250#6499C2318yes—
251#6499C2314yes—
252#6498C2314yes—
253#6498C2318yes—
254#6498C2318yes—
255#6498C2314yes—
256D4×Dic7C2314yes—
257D4×Dic7C2314yes—
258D4×Dic7C2314yes—
259D4×Dic7C2318yes—
260#6493C2318yes—
261#6493C2318yes—
262#6493C2318yes—
263#6492C2318yes—
264#6492C2318yes—
265#6492C2318yes—
266C4×C22⋊D7C2314yes—
267C4×C22⋊D7C2314yes—
268C4×C22⋊D7C2318yes—
269C4×C22⋊D7C2314yes—
270C4×C22⋊D7C2314yes—
271C4×C22⋊D7C2314yes—
272C4×C22⋊D7C2314yes—
273C4×C22⋊D7C2314yes—
274C4×C22⋊D7C2314yes—
275C4×C22⋊D7C2314yes—
276C4×C22⋊D7C2318yes—
277C4×C22⋊D7C2314yes—
278C4×C22⋊D7C2318yes—
279C4×C22⋊D7C2318yes—
280#6489C2318yes—
281#6489C2312yes—
282#6489C2314yes—
283#6489C2314yes—
284#6489C2312yes—
285#6489C2314yes—
286#6489C2318yes—
287#6489C2318yes—
288#6489C2314yes—
289C2×C4⋊Dic7C2318yes—
290#6487C2318yes—
291#6487C2314yes—
292#6487C2314yes—
293#6487C2314yes—
294#6487C2318yes—
295#6487C2318yes—
296#6487C2318yes—
297C2×C4×Dic7C2312yes—
298C2×C4×Dic7C2311yescharacteristic
299C2×C4×Dic7C2314yes—
300C2×C4×Dic7C2314yes—
301#6461C2318yes—
302#6461C2318yes—
303#6461C2318yes—
304#6461C2314yes—
305#6461C2314yes—
306#6460C2318yes—
307#6460C2312yes—
308#6460C2314yes—
309#6460C2314yes—
310#6460C2312yes—
311#6460C2318yes—
312#6459C2318yes—
313#6459C2314yes—
314#6459C2314yes—
315#6458C2312yes—
316#6458C2318yes—
317#6458C2314yes—
318#6458C2312yes—
319#6457C2318yes—
320#6457C2314yes—
321#6457C2314yes—
322#6456C2318yes—
323#6455C2314yes—
324#6455C2314yes—
325D7×C4⋊C4C2314yes—
326D7×C4⋊C4C2318yes—
327#6453C2312yes—
328#6453C2314yes—
329#6453C2318yes—
330#6453C2318yes—
331#6453C2314yes—
332#6453C2312yes—
333#6453C2318yes—
334#6452C2318yes—
335#6452C2318yes—
336#6452C2318yes—
337#6452C2314yes—
338#6452C2314yes—
339#6451C2318yes—
340#6451C2314yes—
341#6451C2312yes—
342#6451C2318yes—
343#6451C2312yes—
344#6450C2314yes—
345#6450C2318yes—
346#6450C2314yes—
347#6450C2314yes—
348#6450C2318yes—
349#6449C2318yes—
350#6449C2318yes—
351#6449C2314yes—
352#6448C2318yes—
353#6448C2318yes—
354#6448C2318yes—
355#6448C2314yes—
356#6448C2318yes—
357#6448C2318yes—
358#6448C2318yes—
359#6448C2314yes—
360#6447C2318yes—
361#6447C2318yes—
362#6447C2318yes—
363#6447C2314yes—
364#6447C2318yes—
365#6447C2314yes—
366#6446C2318yes—
367#6446C2318yes—
368#6446C2318yes—
369#6446C2318yes—
370#6446C2318yes—
371#6446C2314yes—
372#6446C2314yes—
373#6446C2318yes—
374#6446C2318yes—
375#6445C2314yes—
376(C22⋊D7)⋊C4C2318yes—
377(C22⋊D7)⋊C4C2318yes—
378(C22⋊D7)⋊C4C2318yes—
379(C22⋊D7)⋊C4C2318yes—
380#6442C2318yes—
381#6442C2318yes—
382#6442C2318yes—
383#6442C2318yes—
384#6442C2318yes—
385#6442C2314yes—
386#6442C2318yes—
387#6442C2318yes—
388#6442C2314yes—
389#6442C2318yes—
390#6442C2318yes—
391#6441C2318yes—
392#6441C2318yes—
393#6441C2318yes—
394#6441C2318yes—
395#6441C2314yes—
396#6441C2314yes—
397#6440C2318yes—
398#6440C2318yes—
399C4×D28C2314yes—
400C4×D28C2314yes—
401C4×D28C2314yes—
402C4×D28C2314yes—
403C4×D28C2312yes—
404C4×D28C2312yes—
405C4×D28C2314yes—
406#6435C2314yes—
407#6435C2314yes—
408#6435C2318yes—
409#6435C2314yes—
410#6435C2314yes—
411#6435C2314yes—
412C42×D7C2312yes—
413C42×D7C2312yes—
414C42×D7C2312yes—
415C42×D7C2312yes—
416C42×D7C2314yes—
417C42×D7C2318yes—
418#6433C2312yes—
419#6433C2318yes—
420#6432C2314yes—
421#6432C2314yes—
422#6432C2312yes—
423C4×Dic14C2314yes—
424C4×Dic14C2314yes—
425C4×Dic14C2314yes—
426C4×Dic14C2314yes—
427C4×Dic14C2312yes—
428C4×Dic14C2312yes—
429C4×Dic14C2314yes—
430C4×Dic14C2318yes—
431C4×Dic14C2314yes—
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#3481D711yescharacteristic, complemented
445#3480—74no—
446#3475—74no—
447#3461—74no—
448#3460—74no—
449#3455—74no—
450#3444—71no—
451#3444—72no—
452C24×C7C2414yes—
453C23×D7C2411yescharacteristic
454C7×#41—44no—
455C7×#41—44no—
456C2×C7×Q8C2412yes—
457C2×C7×Q8C2412yes—
458C2×C7×D4—48no—
459C2×C7×D4C2414yes—
460C2×C7×D4C2412yes—
461C2×C7×D4C2414yes—
462C2×C7×D4C2412yes—
463C2×C7×D4C2418yes—
464C2×C7×D4C2414yes—
465C22×C4×C7—48no—
466C22×C4×C7C2414yes—
467C22×C4×C7C2412yes—
468C22×C4×C7C2411yescharacteristic
469C22×C4×C7C2414yes—
470C22×C4×C7C2414yes—
471C22×C4×C7C2414yes—
472C22×C4×C7C2418yes—
473C22×C4×C7C2414yes—
474C2×C22⋊D7C2418yes—
475C2×C22⋊D7C2418yes—
476C2×C22⋊D7C2418yes—
477C2×C22⋊D7C2414yes—
478C2×C22⋊D7C2418yes—
479C2×C22⋊D7C2414yes—
480C2×C22⋊D7C2414yes—
481C2×C22⋊D7C2414yes—
482C2×C22⋊D7C2414yes—
483C22×Dic7C2418yes—
484C22×Dic7C2418yes—
485C22×Dic7C2411yescharacteristic
486C22×Dic7C2412yes—
487Q8×D7—48no—
488#1159—48no—
489#1159—48no—
490#1157—44no—
491#1157—48no—
492#1157—48no—
493#1157—48no—
494#1157—48no—
495C2×D28C2412yes—
496C2×D28C2414yes—
497C2×D28C2414yes—
498C2×D28C2414yes—
499C2×C4×D7—42no—
500C2×C4×D7—44no—
501C2×C4×D7C2414yes—
502C2×C4×D7C2412yes—
503C2×C4×D7C2412yes—
504C2×C4×D7C2412yes—
505C2×C4×D7C2414yes—
506C2×C4×D7C2412yes—
507C2×C4×D7C2412yes—
508C2×C4×D7C2412yes—
509C2×C4×D7C2414yes—
510C2×C4×D7C2418yes—
511C2×C4×D7C2418yes—
512C2×Dic14C2414yes—
513C2×Dic14C2412yes—
514C2×Dic14C2414yes—
515C2×Dic14C2414yes—
516C2×Dic14C2418yes—
517C2×Dic14C2414yes—
518C7×C4⋊C4C2412yes—
519C7×C4⋊C4C2414yes—
520C7×C4⋊C4C2414yes—
521C7×C4⋊C4C2418yes—
522C7×C4⋊C4C2418yes—
523C7×C4⋊C4C2412yes—
524C7×C4⋊C4C2414yes—
525C7×C22⋊C4C2418yes—
526C7×C22⋊C4C2414yes—
527C7×C22⋊C4C2414yes—
528C7×C22⋊C4C2418yes—
529C7×C22⋊C4C2414yes—
530C7×C22⋊C4C2414yes—
531C7×C22⋊C4C2414yes—
532C7×C22⋊C4C2418yes—
533C42×C7C2412yes—
534C42×C7C2414yes—
535C42×C7C2411yescharacteristic
536C42×C7C2414yes—
537C42×C7C2414yes—
538C42×C7C2411yescharacteristic
539C22⋊Dic7C2418yes—
540C22⋊Dic7C2418yes—
541C22⋊Dic7C2418yes—
542C22⋊Dic7C2414yes—
543C22⋊Dic7C2418yes—
544C22⋊Dic7C2414yes—
545C22⋊Dic7C2414yes—
546C22⋊Dic7C2418yes—
547C22⋊Dic7C2414yes—
548C22⋊Dic7C2414yes—
549C22⋊Dic7C2418yes—
550C22⋊Dic7C2414yes—
551(C2×D7)⋊C4C2414yes—
552(C2×D7)⋊C4C2414yes—
553(C2×D7)⋊C4C2414yes—
554(C2×D7)⋊C4C2414yes—
555(C2×D7)⋊C4C2414yes—
556(C2×D7)⋊C4C2414yes—
557(C2×D7)⋊C4C2414yes—
558(C2×D7)⋊C4C2414yes—
559(C2×D7)⋊C4C2418yes—
560(C2×D7)⋊C4C2414yes—
561(C2×D7)⋊C4C2414yes—
562(C2×D7)⋊C4C2418yes—
563(C2×D7)⋊C4C2418yes—
564C4⋊Dic7C2412yes—
565C4⋊Dic7C2412yes—
566C4⋊Dic7C2414yes—
567C4⋊Dic7C2418yes—
568C4⋊Dic7C2414yes—
569C4⋊Dic7C2414yes—
570C4⋊Dic7C2414yes—
571C4⋊Dic7C2414yes—
572C4⋊Dic7C2418yes—
573C4⋊Dic7C2418yes—
574C4⋊Dic7C2414yes—
575C4⋊Dic7C2418yes—
576Dic7⋊C4C2414yes—
577Dic7⋊C4C2418yes—
578Dic7⋊C4C2418yes—
579Dic7⋊C4C2418yes—
580Dic7⋊C4C2414yes—
581Dic7⋊C4C2414yes—
582Dic7⋊C4C2414yes—
583Dic7⋊C4C2414yes—
584Dic7⋊C4C2414yes—
585Dic7⋊C4C2414yes—
586Dic7⋊C4C2418yes—
587Dic7⋊C4C2414yes—
588Dic7⋊C4C2414yes—
589Dic7⋊C4C2414yes—
590Dic7⋊C4C2418yes—
591Dic7⋊C4C2418yes—
592C4×Dic7C2414yes—
593C4×Dic7C2411yescharacteristic
594C4×Dic7C2414yes—
595C4×Dic7C2412yes—
596C4×Dic7C2412yes—
597C4×Dic7C2412yes—
598C4×Dic7C2414yes—
599C4×Dic7C2414yes—
600C4×Dic7C2418yes—
601C4×Dic7C2411yescharacteristic
602C4×Dic7C2412yes—
603C4×Dic7C2412yes—
604C4×Dic7C2418yes—
605C4×Dic7C2414yes—
606C4×Dic7C2418yes—
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—78no—
617#560—74no—
618#559—74no—
619#559—78no—
620#559C2×D711yescharacteristic, complemented
621Q82—71no—
622#557—74no—
623#557—72no—
624#556—78no—
625#556—74no—
626#556—74no—
627#556—74no—
628#556—72no—
629#555—71no—
630#555—74no—
631#555—74no—
632#555—74no—
633#554—74no—
634#554C2×D712yescomplemented
635#553—78no—
636#553—74no—
637#553—78no—
638#553—74no—
639#553—78no—
640#553C2×D714yes—
641#552—78no—
642#552—74no—
643#552—78no—
644#552—74no—
645#552—74no—
646#551—78no—
647#551—78no—
648#551C2×D714yescomplemented
649#550—72no—
650#550—74no—
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#546C2×D714yes—
662D42C2×D711yescharacteristic, complemented
663#544—74no—
664#544—74no—
665#542—74no—
666#542—78no—
667#542—78no—
668#542—78no—
669#542—74no—
670#542—74no—
671#542—74no—
672#542—78no—
673#541—78no—
674#541—74no—
675#541—78no—
676#541—74no—
677#540—78no—
678#540—74no—
679#540—78no—
680#540—74no—
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—72no—
696#533—72no—
697#533—72no—
698#533—72no—
699#533—74no—
700#533—71no—
701#533—74no—
702#532—72no—
703#532—74no—
704#532—72no—
705#532—72no—
706#532—72no—
707#532—74no—
708#532—78no—
709#532C2×D711yescharacteristic
710#529—74no—
711#529—74no—
712#529—72no—
713#529—72no—
714#529—74no—
715#529—74no—
716#529—74no—
717#529—72no—
718#529—72no—
719#529—78no—
720#529—78no—
721#529—78no—
722#529—78no—
723#529—74no—
724#529—74no—
725#529—74no—
726#529—78no—
727#529C2×D714yescomplemented
728#525—72no—
729#525—72no—
730#525—74no—
731#525—78no—
732#525—74no—
733#525—74no—
734#525—74no—
735#525—72no—
736#525C2×D714yes—
737C4×#41—72no—
738C4×#41—74no—
739C4×#41—74no—
740C4×#41—74no—
741C4×#41—74no—
742C4×#41—74no—
743C4×#41—72no—
744C4×#41—74no—
745C4×#41C2×D712yes—
746C2×C4×Q8—74no—
747C2×C4×D4C2×D714yescomplemented
748C2×#117—74no—
749C22×C42—71no—
750C23×C7—44no—
751C23×C7—48no—
752C23×C7C2514yes—
753C23×C7C2511yescharacteristic
754C23×C7C2514yes—
755C22×D7—41no—
756C22×D7—42no—
757C22×D7C2512yes—
758C22×D7C2514yes—
759C7×Q8—24no—
760C7×Q8—42no—
761C7×D4—28no—
762C7×D4—24no—
763C7×D4—48no—
764C7×D4—44no—
765C7×D4—44no—
766C7×D4—42no—
767C2×C4×C7—24no—
768C2×C4×C7—22no—
769C2×C4×C7—28no—
770C2×C4×C7—28no—
771C2×C4×C7—28no—
772C2×C4×C7—44no—
773C2×C4×C7—48no—
774C2×C4×C7—44no—
775C2×C4×C7C2512yes—
776C2×C4×C7C2514yes—
777C2×C4×C7C2514yes—
778C2×C4×C7C2511yescharacteristic
779C2×C4×C7C2514yes—
780C2×C4×C7C2514yes—
781C2×C4×C7C2512yes—
782C2×C4×C7C2511yescharacteristic
783C22⋊D7—48no—
784C22⋊D7—44no—
785C22⋊D7—44no—
786C22⋊D7—44no—
787C22⋊D7—48no—
788C22⋊D7—44no—
789C22⋊D7—44no—
790C22⋊D7—48no—
791C22⋊D7—48no—
792C2×Dic7—41no—
793C2×Dic7—42no—
794C2×Dic7—48no—
795C2×Dic7—48no—
796C2×Dic7C2512yes—
797C2×Dic7C2514yes—
798C2×Dic7C2512yes—
799C2×Dic7C2514yes—
800C2×Dic7C2518yes—
801C2×Dic7C2512yes—
802C2×Dic7C2514yes—
803D28—24no—
804D28—44no—
805D28—44no—
806D28—44no—
807C4×D7—24no—
808C4×D7—24no—
809C4×D7—24no—
810C4×D7—28no—
811C4×D7—28no—
812C4×D7—42no—
813C4×D7—42no—
814C4×D7—42no—
815C4×D7—48no—
816C4×D7—44no—
817C4×D7—48no—
818Dic14—24no—
819Dic14—28no—
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—74no—
831C2×#41C22×D712yes—
832C2×#41C22×D712yes—
833C22×Q8—74no—
834C22×D4C22×D714yes—
835C23×C4—72no—
836C23×C4—71no—
837C23×C4C22×D714yes—
838C4⋊Q8—72no—
839C4⋊Q8—74no—
840C4⋊Q8—72no—
841C4⋊Q8—72no—
842C4⋊Q8—74no—
843C4⋊Q8—78no—
844C4⋊Q8—78no—
845C4⋊Q8—72no—
846C4⋊Q8—74no—
847C4⋊Q8—74no—
848C4⋊Q8C22×D711yescharacteristic
849#127—72no—
850#127—74no—
851#127—78no—
852#127—74no—
853#127C22×D711yescharacteristic
854#126—74no—
855#126—74no—
856#126—78no—
857#126—78no—
858#126—78no—
859#126—74no—
860#126—78no—
861#126—74no—
862#126—78no—
863#126—78no—
864#126—78no—
865#126—78no—
866#126—78no—
867#126—78no—
868#126—78no—
869#126—78no—
870#126C22×D718yes—
871#125—74no—
872#125—74no—
873#125—74no—
874#125—72no—
875#125—72no—
876#125—78no—
877#125—78no—
878#125—78no—
879#125—74no—
880#125—78no—
881#125—78no—
882#125—78no—
883#125—72no—
884#125—78no—
885#125C22×D714yes—
886#124—72no—
887#124—74no—
888#124—74no—
889#124—72no—
890#124—78no—
891#124—74no—
892#124—78no—
893#124—74no—
894#124—74no—
895#124—74no—
896#124—78no—
897#124—78no—
898#124—78no—
899#124—78no—
900#124—78no—
901#124—78no—
902#124C22×D712yes—
903#124C22×D714yes—
904#123—74no—
905#123—74no—
906#123—78no—
907#123—78no—
908#123—78no—
909#123—78no—
910#123—78no—
911#123—74no—
912#123—74no—
913#123—78no—
914#123—78no—
915#123—74no—
916#123—74no—
917#123—74no—
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#123C22×D714yes—
927#123C22×D714yes—
928#123C22×D718yes—
929C22⋊Q8—72no—
930C22⋊Q8—72no—
931C22⋊Q8—74no—
932C22⋊Q8—74no—
933C22⋊Q8—78no—
934C22⋊Q8—78no—
935C22⋊Q8—78no—
936C22⋊Q8—74no—
937C22⋊Q8—74no—
938C22⋊Q8—78no—
939C22⋊Q8—74no—
940C22⋊Q8—72no—
941C22⋊Q8—74no—
942C22⋊Q8—72no—
943C22⋊Q8—74no—
944C22⋊Q8—78no—
945C22⋊Q8—74no—
946C22⋊Q8—78no—
947C22⋊Q8—78no—
948C22⋊Q8—74no—
949C22⋊Q8—74no—
950C22⋊Q8—78no—
951C22⋊Q8—78no—
952C22⋊Q8—78no—
953C22⋊Q8—78no—
954C22⋊Q8C22×D718yes—
955C22⋊Q8C22×D714yes—
956#121—72no—
957#121—74no—
958#121—74no—
959#121—72no—
960#121—74no—
961#121—74no—
962#121—78no—
963#121—74no—
964#121—78no—
965#121—78no—
966#121—78no—
967#121—74no—
968#121—78no—
969#121—78no—
970#121—78no—
971#121—78no—
972#121—78no—
973#121—78no—
974#121—72no—
975#121—72no—
976#121—74no—
977#121—78no—
978#121—74no—
979#121—74no—
980#121—78no—
981#121—78no—
982#121—78no—
983#121—78no—
984#121C22×D714yes—
985#121C22×D718yes—
986#121C22×D714yes—
987#120—78no—
988#120—78no—
989#120—78no—
990#120—74no—
991#120—74no—
992#120—74no—
993#120C22×D714yes—
994#120C22×D714yes—
995C4×Q8—74no—
996C4×Q8—74no—
997C4×Q8—74no—
998C4×Q8—78no—
999C4×Q8—74no—
1000C4×Q8—74no—
1001C4×Q8—78no—
1002C4×Q8—74no—
1003C4×Q8—78no—
1004C4×Q8—72no—
1005C4×Q8—74no—
1006C4×Q8—74no—
1007C4×Q8—72no—
1008C4×Q8—74no—
1009C4×Q8—74no—
1010C4×Q8—74no—
1011C4×Q8C22×D712yes—
1012C4×Q8C22×D712yes—
1013C4×D4—78no—
1014C4×D4—74no—
1015C4×D4—74no—
1016C4×D4—74no—
1017C4×D4—74no—
1018C4×D4—74no—
1019C4×D4—78no—
1020C4×D4—78no—
1021C4×D4—78no—
1022C4×D4—74no—
1023C4×D4—74no—
1024C4×D4—74no—
1025C4×D4—74no—
1026C4×D4—74no—
1027C4×D4—74no—
1028C4×D4—74no—
1029C4×D4—74no—
1030C4×D4—78no—
1031C4×D4—78no—
1032C4×D4—78no—
1033C4×D4—78no—
1034C4×D4—78no—
1035C4×D4—78no—
1036C4×D4—72no—
1037C4×D4—74no—
1038C4×D4—74no—
1039C4×D4—74no—
1040C4×D4—74no—
1041C4×D4—72no—
1042C4×D4—74no—
1043C4×D4C22×D712yes—
1044C4×D4C22×D714yes—
1045C4×D4C22×D718yes—
1046C4×D4C22×D714yes—
1047C4×D4C22×D714yes—
1048C4×D4C22×D718yes—
1049C4×D4C22×D714yes—
1050C4×D4C22×D714yes—
1051C4×D4C22×D712yes—
1052#117—74no—
1053#117—78no—
1054#117—78no—
1055#117—78no—
1056#117—74no—
1057#117—72no—
1058#117—72no—
1059#117—74no—
1060#117—74no—
1061#117—74no—
1062#117—74no—
1063#117—78no—
1064#117—78no—
1065#117—74no—
1066#117—74no—
1067#117—74no—
1068#117—74no—
1069#117—74no—
1070#117—78no—
1071#117C22×D714yes—
1072#117C22×D712yes—
1073#117C22×D714yes—
1074C2×C4⋊C4—78no—
1075C2×C4⋊C4—74no—
1076C2×C4⋊C4—78no—
1077C2×C4⋊C4C22×D714yes—
1078C2×C22⋊C4—78no—
1079C2×C22⋊C4C22×D718yes—
1080C2×C42—74no—
1081C2×C42—74no—
1082C2×C42—71no—
1083C2×C42—72no—
1084C2×C42—74no—
1085C2×C42—78no—
1086C2×C42—72no—
1087C2×C42—72no—
1088C2×C42—72no—
1089C2×C42—72no—
1090C2×C42C22×D714yes—
1091C2×C42C22×D711yescharacteristic
1092C22×C7—28no—
1093C22×C7—22no—
1094C22×C7—21no—
1095C22×C7—24no—
1096C22×C7—24no—
1097C22×C7—24no—
1098C22×C7—24no—
1099C22×C7—88no—
1100C22×C7C2611yescharacteristic
1101C2×D7—24no—
1102C2×D7—22no—
1103C2×D7—22no—
1104C2×D7—22no—
1105C2×D7—24no—
1106C2×D7—24no—
1107C2×D7—44no—
1108C4×C7—24no—
1109C4×C7—24no—
1110C4×C7—24no—
1111C4×C7—24no—
1112C4×C7—22no—
1113C4×C7—21no—
1114C4×C7#58514yes—
1115C4×C7#58512yes—
1116Dic7—28no—
1117Dic7—24no—
1118Dic7—24no—
1119Dic7—24no—
1120Dic7—22no—
1121Dic7—22no—
1122Dic7—22no—
1123C24—71no—
1124C24C23×D714yes—
1125#41—44no—
1126#41—44no—
1127#41—288no—
1128#41—288no—
1129#41—288no—
1130#41—284no—
1131#41—288no—
1132#41—288no—
1133#41—288no—
1134C2×Q8—74no—
1135C2×Q8—72no—
1136C2×Q8—78no—
1137C2×Q8—74no—
1138C2×Q8—74no—
1139C2×Q8—74no—
1140C2×Q8—288no—
1141C2×Q8C23×D712yes—
1142C2×Q8C23×D712yes—
1143C2×D4—48no—
1144C2×D4—74no—
1145C2×D4—74no—
1146C2×D4—78no—
1147C2×D4—74no—
1148C2×D4—78no—
1149C2×D4—74no—
1150C2×D4—74no—
1151C2×D4—78no—
1152C2×D4—78no—
1153C2×D4—72no—
1154C2×D4—74no—
1155C2×D4—74no—
1156C2×D4—74no—
1157C2×D4C23×D714yes—
1158C2×D4C23×D712yes—
1159C2×D4C23×D714yes—
1160C2×D4C23×D712yes—
1161C2×D4C23×D714yes—
1162C2×D4C23×D718yes—
1163C22×C4—48no—
1164C22×C4—72no—
1165C22×C4—71no—
1166C22×C4—78no—
1167C22×C4—78no—
1168C22×C4—72no—
1169C22×C4—72no—
1170C22×C4—74no—
1171C22×C4—74no—
1172C22×C4—72no—
1173C22×C4—72no—
1174C22×C4—72no—
1175C22×C4—72no—
1176C22×C4—74no—
1177C22×C4—78no—
1178C22×C4—78no—
1179C22×C4—284no—
1180C22×C4—282no—
1181C22×C4C23×D712yes—
1182C22×C4C23×D714yes—
1183C22×C4C23×D714yes—
1184C22×C4C23×D711yescharacteristic
1185C22×C4C23×D714yes—
1186C22×C4C23×D714yes—
1187C22×C4C23×D718yes—
1188C22×C4C23×D714yes—
1189C4⋊C4—78no—
1190C4⋊C4—78no—
1191C4⋊C4—78no—
1192C4⋊C4—74no—
1193C4⋊C4—74no—
1194C4⋊C4—74no—
1195C4⋊C4—78no—
1196C4⋊C4—74no—
1197C4⋊C4—74no—
1198C4⋊C4—78no—
1199C4⋊C4—74no—
1200C4⋊C4—78no—
1201C4⋊C4—74no—
1202C4⋊C4—74no—
1203C4⋊C4—74no—
1204C4⋊C4—74no—
1205C4⋊C4—74no—
1206C4⋊C4—74no—
1207C4⋊C4—74no—
1208C4⋊C4—78no—
1209C4⋊C4—78no—
1210C4⋊C4—78no—
1211C4⋊C4—72no—
1212C4⋊C4—72no—
1213C4⋊C4—74no—
1214C4⋊C4—74no—
1215C4⋊C4—78no—
1216C4⋊C4—74no—
1217C4⋊C4C23×D712yes—
1218C4⋊C4C23×D714yes—
1219C4⋊C4C23×D712yes—
1220C4⋊C4C23×D714yes—
1221C4⋊C4C23×D718yes—
1222C4⋊C4C23×D718yes—
1223C4⋊C4C23×D714yes—
1224C22⋊C4—74no—
1225C22⋊C4—74no—
1226C22⋊C4—78no—
1227C22⋊C4—78no—
1228C22⋊C4—74no—
1229C22⋊C4—74no—
1230C22⋊C4—78no—
1231C22⋊C4—74no—
1232C22⋊C4—78no—
1233C22⋊C4—78no—
1234C22⋊C4—74no—
1235C22⋊C4—78no—
1236C22⋊C4—74no—
1237C22⋊C4—74no—
1238C22⋊C4—74no—
1239C22⋊C4—74no—
1240C22⋊C4—74no—
1241C22⋊C4—78no—
1242C22⋊C4—74no—
1243C22⋊C4—74no—
1244C22⋊C4—74no—
1245C22⋊C4—78no—
1246C22⋊C4—78no—
1247C22⋊C4—74no—
1248C22⋊C4—74no—
1249C22⋊C4C23×D714yes—
1250C22⋊C4C23×D718yes—
1251C22⋊C4C23×D718yes—
1252C22⋊C4C23×D718yes—
1253C22⋊C4C23×D714yes—
1254C22⋊C4C23×D714yes—
1255C22⋊C4C23×D714yes—
1256C22⋊C4C23×D714yes—
1257C42—72no—
1258C42—72no—
1259C42—72no—
1260C42—72no—
1261C42—72no—
1262C42—74no—
1263C42—78no—
1264C42—74no—
1265C42—74no—
1266C42—74no—
1267C42—78no—
1268C42—78no—
1269C42—71no—
1270C42—74no—
1271C42—74no—
1272C42—71no—
1273C42C23×D711yescharacteristic
1274C42C23×D711yescharacteristic
1275C42C23×D714yes—
1276C42C23×D714yes—
1277C42C23×D712yes—
1278C42C23×D714yes—
1279C2×C7—41no—
1280C2×C7—44no—
1281C2×C7—44no—
1282C2×C7C2×#58512yes—
1283C2×C7C2×#58511yescharacteristic
1284D7—44no—
1285D7—42no—
1286C23—44no—
1287C23—48no—
1288C23—72no—
1289C23—74no—
1290C23—282no—
1291C23—281no—
1292C23C24×D714yes—
1293C23C24×D711yescharacteristic
1294C23C24×D714yes—
1295Q8—24no—
1296Q8—42no—
1297Q8—148no—
1298Q8—144no—
1299Q8—288no—
1300Q8—284no—
1301Q8—284no—
1302Q8—284no—
1303D4—24no—
1304D4—28no—
1305D4—48no—
1306D4—44no—
1307D4—44no—
1308D4—42no—
1309D4—144no—
1310D4—284no—
1311D4—284no—
1312D4—284no—
1313D4—284no—
1314D4—284no—
1315D4—284no—
1316D4—288no—
1317D4—288no—
1318D4—288no—
1319D4—284no—
1320D4—284no—
1321D4—288no—
1322C2×C4—24no—
1323C2×C4—28no—
1324C2×C4—28no—
1325C2×C4—28no—
1326C2×C4—22no—
1327C2×C4—44no—
1328C2×C4—48no—
1329C2×C4—44no—
1330C2×C4—72no—
1331C2×C4—74no—
1332C2×C4—74no—
1333C2×C4—72no—
1334C2×C4—78no—
1335C2×C4—72no—
1336C2×C4—74no—
1337C2×C4—144no—
1338C2×C4—144no—
1339C2×C4—148no—
1340C2×C4—144no—
1341C2×C4—148no—
1342C2×C4—282no—
1343C2×C4—282no—
1344C2×C4—282no—
1345C2×C4—288no—
1346C2×C4—284no—
1347C2×C4—288no—
1348C2×C4—282no—
1349C2×C4—281no—
1350C2×C4—288no—
1351C2×C4—288no—
1352C2×C4C24×D712yes—
1353C2×C4C24×D714yes—
1354C2×C4C24×D714yes—
1355C2×C4C24×D711yescharacteristic
1356C2×C4C24×D714yes—
1357C2×C4C24×D714yes—
1358C2×C4C24×D712yes—
1359C2×C4C24×D711yescharacteristic
1360C7#6276211yescharacteristic, complemented, Sylow
1361C22—22no—
1362C22—24no—
1363C22—24no—
1364C22—28no—
1365C22—24no—
1366C22—24no—
1367C22—21no—
1368C22—88no—
1369C22—144no—
1370C22—142no—
1371C22—142no—
1372C22—144no—
1373C22—142no—
1374C22—144no—
1375C22—284no—
1376C22C25×D711yescharacteristic
1377C4—22no—
1378C4—24no—
1379C4—24no—
1380C4—24no—
1381C4—24no—
1382C4—21no—
1383C4—142no—
1384C4—142no—
1385C4—144no—
1386C4—144no—
1387C4—148no—
1388C4—142no—
1389C4—144no—
1390C4#9061614yes—
1391C4#9061812yes—
1392C2—44no—
1393C2—44no—
1394C2—41no—
1395C2—282no—
1396C2—284no—
1397C2C2×#9061612yes—
1398C2C2×#9061811yescharacteristic
subgroupG/H
centerC2×C4C24×D7
commutator, socle, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC7×#3481C2
hypercenter#3481D7
hypocenterC7#62762
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ #3481

Complements

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

NH ≅ G/Ntype
1. C7×#3481C2semidirect
2. #11744135C2semidirect
3. #11744024C2semidirect
4. #11744022C2semidirect
5. #11743985C2semidirect
6. #11743971C2semidirect
7. #11743892C2semidirect
8. #11743739C2semidirect
9. #11743727C2semidirect
10. #11743693C2semidirect
11. #11743289C2semidirect
12. #11743287C2semidirect
13. #11743220C2semidirect
14. #11743217C2semidirect
15. #11743116C2semidirect
16. #11743087C2semidirect
17. #11742912C2semidirect
18. #11742904C2semidirect
19. #11742845C2semidirect
20. #11742832C2semidirect
21. C7×#559C22semidirect
22. C7×#554C22semidirect
24. C7×#551C22semidirect
26. C7×D42C22semidirect
28. C7×#529C22semidirect
31. C2×C4×C7×D4C22semidirect
33. #90523C22semidirect
36. #90519C22semidirect
37. #41×Dic7C22semidirect
39. #90497C22semidirect
41. #90496C22semidirect
42. #90482C22semidirect
43. #90482C22semidirect
44. C2×#6489C22semidirect
45. #90425C22semidirect
46. #90419C22semidirect
47. #90413C22semidirect
48. #90409C22semidirect
50. #90400C22semidirect
51. #90398C22semidirect
52. #90393C22semidirect
53. #90392C22semidirect
54. #90388C22semidirect
55. #90386C22semidirect
56. #90380C22semidirect
57. #90376C22semidirect
58. #90373C22semidirect
59. #90372C22semidirect
60. #90371C22semidirect
61. #90368C22semidirect
62. #90366C22semidirect
63. #90361C22semidirect
64. #90358C22semidirect
65. #90357C22semidirect
66. #90356C22semidirect
67. #90356C22semidirect
68. #90355C22semidirect
69. #90353C22semidirect
70. #90352C22semidirect
71. #90351C22semidirect
72. #90342C22semidirect
73. #90338C22semidirect
74. #90337C22semidirect
75. #90334C22semidirect
76. #90332C22semidirect
77. #90324C22semidirect
78. #90319C22semidirect
79. #90316C22semidirect
80. #90316C22semidirect
81. #90312C22semidirect
82. #90311C22semidirect
83. #90310C22semidirect
84. #90307C22semidirect
85. #90305C22semidirect
87. #90297C22semidirect
88. #90294C22semidirect
89. #90294C22semidirect
90. #90291C22semidirect
92. #90290C22semidirect
94. #90286C22semidirect
95. #90285C22semidirect
96. #90284C22semidirect
97. #90284C22semidirect
98. #90271C22semidirect
99. #90271C22semidirect
100. #90269C22semidirect
101. #90269C22semidirect
102. Q8×D28C22semidirect
103. C4×Q8×D7C22semidirect
104. #90261C22semidirect
105. #90256C22semidirect
107. #90253C22semidirect
108. #90253C22semidirect
109. #90253C22semidirect
111. #90252C22semidirect
112. #90252C22semidirect
115. #90248C22semidirect
116. #90248C22semidirect
117. #90248C22semidirect
118. #90248C22semidirect
119. #90246C22semidirect
120. #90242C22semidirect
121. #90242C22semidirect
124. #90239C22semidirect
125. #90239C22semidirect
126. #90238C22semidirect
127. #90238C22semidirect
128. #90234C22semidirect
129. #90233C22semidirect
130. #90233C22semidirect
131. #90233C22semidirect
132. #90232C22semidirect
133. #90229C22semidirect
134. #90229C22semidirect
135. #90229C22semidirect
136. #90229C22semidirect
137. C4×#1159C22semidirect
138. C4×#1159C22semidirect
139. #90220C22semidirect
140. #90220C22semidirect
141. #90219C22semidirect
142. #90219C22semidirect
143. #90219C22semidirect
144. #90215C22semidirect
145. #90213C22semidirect
146. #90208C22semidirect
147. #90208C22semidirect
148. #90204C22semidirect
149. #90204C22semidirect
150. #90201C22semidirect
151. #90191C22semidirect
152. #90186C22semidirect
153. #90186C22semidirect
154. #90185C22semidirect
155. #90185C22semidirect
156. C4×#1157C22semidirect
157. C4×#1157C22semidirect
158. C4×#1157C22semidirect
159. C4×#1157C22semidirect
160. C2×C42×D7C22semidirect
161. #90161C22semidirect
162. #90161C22semidirect
444. #3481D7semidirect
620. #559C2×D7semidirect
634. #554C2×D7semidirect
648. #551C2×D7semidirect
662. D42C2×D7semidirect
727. #529C2×D7semidirect
747. C2×C4×D4C2×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×#34812
#117441352
#117440242
#117440222
#117439852
#117439712
#117438922
#117437392
#117437272
#117436932
#117432892
#117432872
#117432202
#117432172
#117431162
#117430872
#117429122
#117429042
#117428452
#117428322
#627627