Finite Group Databasebeta

← #14262256

Subgroups — #14262256

Order 1792.

7104 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3482C211yesmaximal, characteristic, complemented
2#11744092C211yesmaximal, characteristic, complemented
3#11744086C211yesmaximal, characteristic, complemented
4#11744058C213yesmaximal, complemented
5#11744051C213yesmaximal, complemented
6#11743905C216yesmaximal, complemented
7#11743899C216yesmaximal, complemented
8#11743821C211yesmaximal, characteristic, complemented
9#11743814C211yesmaximal, characteristic, complemented
10#11743788C212yesmaximal, complemented
11#11743782C212yesmaximal, complemented
12#11743754C213yesmaximal, complemented
13#11743748C213yesmaximal, complemented
14#11743346C213yesmaximal, complemented
15D7×#533C213yesmaximal, complemented
16#11743219C216yesmaximal, complemented
17#11743217C216yesmaximal, complemented
18#11742912C213yesmaximal, complemented
19#11742912C211yesmaximal, characteristic, complemented
20#11742904C213yesmaximal, complemented
21C4×D7×#41C211yesmaximal, characteristic, complemented
22Q8×#1157C212yesmaximal, complemented
23C4×#6551C212yesmaximal, complemented
24C2×D7×#41C2211yescharacteristic
25C2×#6551C2212yes—
26C7×#557C2211yescharacteristic, complemented
27C7×#556C2213yescomplemented
28C7×#552C2216yescomplemented
29C7×D4×Q8C2211yescharacteristic, complemented
30C7×#548C2212yes—
31C7×#547C2213yescomplemented
32C7×#533C2213yescomplemented
33C7×#529C2216yescomplemented
34C4×C7×#41C2211yescharacteristic
35C4×C7×#41C2213yescomplemented
36C2×C4×C7×Q8C2212yescomplemented
37#90523C2213yescomplemented
38#90522C2212yes—
39#90522C2216yescomplemented
40#90519C2213yes—
41#41×Dic7C2211yescharacteristic
42Q8×C22⋊D7C2212yes—
43Q8×C22⋊D7C2212yescomplemented
44#90503C2212yescomplemented
45#90423C2213yescomplemented
46#90419C2213yes—
47#90419C2213yes—
48#90418C2213yescomplemented
49#90417C2213yescomplemented
50D7×C4⋊Q8C2213yescomplemented
51D7×C4⋊Q8C2213yescomplemented
52#90412C2213yescomplemented
53#90399C22112yescomplemented
54#90398C22112yescomplemented
55#90396C22112yes—
56#90392C22112yescomplemented
57#90388C2216yescomplemented
58#90385C2216yes—
59#90384C22112yescomplemented
60#90381C2216yescomplemented
61#90380C2216yescomplemented
62#90379C2216yes—
63D7×#125C2216yescomplemented
64#90373C2216yescomplemented
65#90367C2216yes—
66#90366C2216yes—
67#90362C2216yescomplemented
68#90353C22112yescomplemented
69#90352C22112yescomplemented
70#90351C22112yescomplemented
71#90350C22112yes—
72#90332C2216yescomplemented
73#90330C2216yes—
74#90330C2216yescomplemented
75#90324C2216yescomplemented
76#90322C2216yes—
77#90322C2216yescomplemented
78#90319C2216yescomplemented
79D7×C22⋊Q8C2216yes—
80D7×C22⋊Q8C2216yes—
81#90316C2216yescomplemented
82#90313C2216yescomplemented
83#90313C2216yescomplemented
84#90307C2216yescomplemented
85#90303C2216yes—
86#90299C2216yes—
87#90294C2216yescomplemented
88#90271C2213yes—
89#90271C2213yescomplemented
90#90270C2216yes—
91#90269C2213yes—
92#90269C2216yes—
93#90269C2213yescomplemented
94#90269C2216yescomplemented
95Q8×D28C2212yes—
96Q8×D28C2213yescomplemented
97Q8×D28C2211yescharacteristic, complemented
98#90265C2212yes—
99#90265C2216yescomplemented
100C4×#1161C2211yescharacteristic
101C4×#1161C2211yescharacteristic
102C4×#1161C2216yescomplemented
103#90263C2212yescomplemented
104#90263C2216yescomplemented
105C4×Q8×D7C2211yescharacteristic
106C4×Q8×D7C2211yescharacteristic
107C4×Q8×D7C2216yescomplemented
108C4×Q8×D7C2216yescomplemented
109C4×Q8×D7C2212yescomplemented
110#90261C2213yescomplemented
111#90261C2211yescharacteristic, complemented
112#90258C2216yescomplemented
113Q8×Dic14C2212yescomplemented
114#90248C2213yes—
115#90248C2213yescomplemented
116#90248C2216yescomplemented
117#90248C22112yescomplemented
118#90242C2216yes—
119#90242C2213yescomplemented
120#90242C2213yescomplemented
121#90239C2211yescharacteristic
122#90239C2213yescomplemented
123#90238C2216yes—
124#90238C2216yes—
125C4×D4×D7C2213yes—
126C4×D4×D7C2213yes—
127#90233C2213yescomplemented
128#90233C2213yescomplemented
129#90233C2216yescomplemented
130#90229C2216yescomplemented
131#90229C2216yescomplemented
132C4×#1159C2213yes—
133C4×#1159C2213yes—
134#90220C2216yescomplemented
135#90220C2216yescomplemented
136#90220C22112yescomplemented
137#90219C2216yes—
138#90219C22112yescomplemented
139#90219C2216yescomplemented
140#90215C2213yes—
141#90213C2213yes—
142D7×#117C2216yes—
143D7×#117C2213yes—
144#90208C2213yescomplemented
145#90208C2216yescomplemented
146#90202C2216yes—
147#90202C2216yescomplemented
148#90195C2216yescomplemented
149#90195C2216yescomplemented
150C4×#1157C2213yes—
151C4×#1157C2216yes—
152C4×#1157C2213yescomplemented
153C4×#1157C2216yescomplemented
154C4×#1157C2216yescomplemented
155C2×C42×D7C2213yes—
156#90161C2213yescomplemented
157#90161C2216yescomplemented
158#62805—71nomaximal, Sylow
159C2×C7×#41C2311yescharacteristic
160C2×C7×#41C2313yes—
161C22×C7×Q8C2312yes—
162D7×#41—28no—
163#6551—216no—
164C2×#1161C2316yes—
165C2×#1161C2311yescharacteristic
166C2×Q8×D7C2316yes—
167C2×Q8×D7C2311yescharacteristic
168C2×Q8×D7C2312yes—
169C2×Q8×D7C2316yes—
170C2×#1159C2313yes—
171C2×D4×D7C2313yes—
172C2×#1157C2312yes—
173C2×#1157C2313yes—
174C2×#1157C2316yes—
175C2×#1157C2316yes—
176C2×#1157C2313yes—
177C22×C4×D7C2313yes—
178C22×C4×D7C2313yes—
179C22×C4×D7C2313yes—
180C7×C4⋊Q8C2313yes—
181C7×C4⋊Q8C2313yes—
182C7×#126C23112yes—
183C7×#125C2316yes—
184C7×#125C2316yes—
185C7×#124C2316yes—
186C7×#123C23112yes—
187C7×C22⋊Q8C2316yes—
188C7×C22⋊Q8C2316yes—
189C7×C22⋊Q8C2316yes—
190C7×#121C2316yes—
191C4×C7×Q8C2312yes—
192C4×C7×Q8C2316yes—
193C4×C7×Q8C2311yescharacteristic
194C4×C7×Q8C2313yes—
195C4×C7×Q8C2311yescharacteristic
196C4×C7×Q8C2313yes—
197C4×C7×Q8C2316yes—
198C4×C7×D4C2313yes—
199C4×C7×D4C2313yes—
200C4×C7×D4C2316yes—
201C4×C7×D4C2316yes—
202C4×C7×D4C2313yes—
203C4×C7×D4C2311yescharacteristic
204C7×#117C2316yes—
205C7×#117C2313yes—
206C7×#117C2313yes—
207C7×#117C2316yes—
208C2×C7×C4⋊C4C2316yes—
209C2×C42×C7C2313yes—
210C2×C42×C7C2316yes—
211#6510C2313yes—
212#6509C2316yes—
213#6509C2313yes—
214#6509C2313yes—
215#6509C2316yes—
216Q8×Dic7C2316yes—
217Q8×Dic7C2316yes—
218Q8×Dic7C2316yes—
219Q8×Dic7C2311yescharacteristic
220Q8×Dic7C2312yes—
221Q8×Dic7C2311yescharacteristic
222#6507C2316yes—
223#6507C2313yes—
224#6507C2316yes—
225#6503C2311yescharacteristic
226#6502C2316yes—
227#6502C2316yes—
228#6501C2316yes—
229#6501C2311yescharacteristic
230#6501C2313yes—
231#6501C23112yes—
232#6500C2316yes—
233#6499C2313yes—
234#6499C2316yes—
235#6499C23112yes—
236#6498C2316yes—
237D4×Dic7C2313yes—
238D4×Dic7C2313yes—
239C4×C22⋊D7C2316yes—
240C4×C22⋊D7C2316yes—
241C4×C22⋊D7C2316yes—
242C4×C22⋊D7C2316yes—
243C4×C22⋊D7C2316yes—
244C4×C22⋊D7C2316yes—
245C4×C22⋊D7C2312yes—
246C4×C22⋊D7C2316yes—
247C4×C22⋊D7C2316yes—
248C4×C22⋊D7C2316yes—
249C4×C22⋊D7C23112yes—
250C4×C22⋊D7C2316yes—
251C4×C22⋊D7C2316yes—
252#6489C2316yes—
253#6489C2316yes—
254#6489C2313yes—
255#6489C2316yes—
256#6489C2316yes—
257#6489C2313yes—
258#6487C23112yes—
259#6487C2316yes—
260#6487C2316yes—
261#6487C2316yes—
262#6487C2316yes—
263C2×C4×Dic7C2313yes—
264C2×C4×Dic7C2313yes—
265C2×C4×Dic7C2313yes—
266#6461C2316yes—
267#6461C23112yes—
268#6461C2316yes—
269#6460C23112yes—
270#6460C2316yes—
271#6460C2316yes—
272#6460C2316yes—
273#6460C2313yes—
274#6460C2313yes—
275#6459C2316yes—
276#6459C23112yes—
277#6459C23112yes—
278#6459C2316yes—
279#6459C23112yes—
280#6458C2313yes—
281#6458C2311yescharacteristic
282#6457C2316yes—
283#6457C23112yes—
284#6457C2316yes—
285#6456C2313yes—
286#6456C2316yes—
287#6456C23112yes—
288#6456C2313yes—
289#6455C2316yes—
290#6455C2316yes—
291#6455C2313yes—
292#6455C23112yes—
293#6455C2316yes—
294#6455C2313yes—
295D7×C4⋊C4C2316yes—
296D7×C4⋊C4C23112yes—
297D7×C4⋊C4C23112yes—
298D7×C4⋊C4C2316yes—
299D7×C4⋊C4C2316yes—
300D7×C4⋊C4C2313yes—
301D7×C4⋊C4C2316yes—
302D7×C4⋊C4C2316yes—
303D7×C4⋊C4C2313yes—
304#6453C2316yes—
305#6453C2316yes—
306#6453C2316yes—
307#6453C23112yes—
308#6453C2313yes—
309#6453C2313yes—
310#6452C2316yes—
311#6452C23112yes—
312#6452C2316yes—
313#6452C23112yes—
314#6452C23112yes—
315#6451C2316yes—
316#6451C2316yes—
317#6451C2316yes—
318#6451C2316yes—
319#6451C2313yes—
320#6451C2311yescharacteristic
321#6450C23112yes—
322#6450C23112yes—
323#6450C2313yes—
324#6450C2316yes—
325#6450C2316yes—
326#6450C2316yes—
327#6450C2313yes—
328#6449C2316yes—
329#6448C23112yes—
330#6448C2316yes—
331#6448C2312yes—
332#6447C23112yes—
333#6447C2312yes—
334#6447C2316yes—
335#6446C23112yes—
336#6446C23112yes—
337#6446C23112yes—
338#6446C2316yes—
339#6446C2316yes—
340#6446C23112yes—
341#6445C2316yes—
342(C22⋊D7)⋊C4C2316yes—
343(C22⋊D7)⋊C4C2316yes—
344D7×C22⋊C4C2316yes—
345D7×C22⋊C4C23112yes—
346#6442C23112yes—
347#6442C23112yes—
348#6442C23112yes—
349#6442C2316yes—
350#6442C2316yes—
351#6442C23112yes—
352#6441C23112yes—
353#6441C2316yes—
354#6441C23112yes—
355#6441C2316yes—
356#6440C2316yes—
357#6440C23112yes—
358C4×D28C2316yes—
359C4×D28C2316yes—
360C4×D28C2316yes—
361C4×D28C2316yes—
362C4×D28C2313yes—
363C4×D28C2313yes—
364C4×D28C2313yes—
365C4×D28C2311yescharacteristic
366C4×D28C2316yes—
367#6435C2316yes—
368#6435C2316yes—
369#6435C2316yes—
370#6435C2316yes—
371#6435C23112yes—
372#6435C2316yes—
373#6435C2316yes—
374C42×D7C2313yes—
375C42×D7C2313yes—
376C42×D7C2313yes—
377C42×D7C2311yescharacteristic
378C42×D7C2313yes—
379C42×D7C2313yes—
380C42×D7C2313yes—
381C42×D7C2313yes—
382C42×D7C2316yes—
383C42×D7C23112yes—
384#6433C2316yes—
385#6433C23112yes—
386#6432C2316yes—
387#6432C2316yes—
388#6432C2313yes—
389#6432C2313yes—
390C4×Dic14C2316yes—
391C4×Dic14C2316yes—
392C4×Dic14C2316yes—
393C4×Dic14C2316yes—
394C4×Dic14C2313yes—
395C4×Dic14C2313yes—
396C4×Dic14C2313yes—
397C4×Dic14C2313yes—
398C4×Dic14C2316yes—
399C4×Dic14C23112yes—
400C4×Dic14C2316yes—
401#3523—71no—
402#3523—71no—
403#3520—73no—
404#3520—73no—
405#3518—72no—
406#3515—76no—
407#3511—73no—
408#3509—73no—
409#3503—71no—
410#3499—71no—
411#3495—76no—
412#3489—72no—
413#3482—73no—
414#3482—71no—
415#3482—73no—
416#3482D711yescharacteristic, complemented
417Q8×#41—72no—
418#3475—76no—
419#3461—76no—
420#3444—73no—
421C2×#533—73no—
422C4×2−1+4—72no—
423C2×C4×#41—71no—
424C23×D7C2413yes—
425C7×#41—24no—
426C7×#41—46no—
427C2×C7×Q8—28no—
428C2×C7×Q8C2416yes—
429C2×C7×Q8C2413yes—
430C2×C7×Q8C2411yescharacteristic
431C2×C7×D4C2413yes—
432C2×C7×D4C2411yescharacteristic
433C2×C7×D4C2416yes—
434C22×C4×C7C2413yes—
435C22×C4×C7C2413yes—
436C22×C4×C7C2413yes—
437C22×C4×C7C2416yes—
438C22×C4×C7C2412yes—
439C22×C4×C7C2416yes—
440C2×C22⋊D7C2416yes—
441C2×C22⋊D7C2412yes—
442C2×C22⋊D7C2416yes—
443C2×C22⋊D7C2412yes—
444C2×C22⋊D7C2412yes—
445C2×C22⋊D7C2416yes—
446C22×Dic7C2413yes—
447C22×Dic7C2413yes—
448C22×Dic7C2413yes—
449#1161—224no—
450#1161#4118yescomplemented
451Q8×D7—28no—
452Q8×D7—24no—
453Q8×D7—224no—
454Q8×D7—412no—
455#1159—212no—
456D4×D7—212no—
457#1157—224no—
458#1157—212no—
459#1157—224no—
460#1157—28no—
461#1157—46no—
462C2×D28C2412yes—
463C2×D28C2411yescharacteristic
464C2×D28C2416yes—
465C2×D28C2413yes—
466C2×C4×D7—212no—
467C2×C4×D7—212no—
468C2×C4×D7—46no—
469C2×C4×D7C2413yes—
470C2×C4×D7C2411yescharacteristic
471C2×C4×D7C2411yescharacteristic
472C2×C4×D7C2412yes—
473C2×C4×D7C2413yes—
474C2×C4×D7C2413yes—
475C2×C4×D7C2413yes—
476C2×C4×D7C2413yes—
477C2×C4×D7C2413yes—
478C2×C4×D7C2416yes—
479C2×C4×D7C24112yes—
480C2×C4×D7C2413yes—
481C2×C4×D7C2413yes—
482C2×C4×D7C2416yes—
483C2×C4×D7C24112yes—
484C2×C4×D7C2413yes—
485C2×C4×D7C2411yescharacteristic
486C2×Dic14C2412yes—
487C2×Dic14C2416yes—
488C2×Dic14C2413yes—
489C2×Dic14C2413yes—
490C2×Dic14C2416yes—
491C2×Dic14C24112yes—
492C7×C4⋊C4C2413yes—
493C7×C4⋊C4C2413yes—
494C7×C4⋊C4C2416yes—
495C7×C4⋊C4C2416yes—
496C7×C4⋊C4C24112yes—
497C7×C4⋊C4C2413yes—
498C7×C4⋊C4C2416yes—
499C7×C4⋊C4C2411yescharacteristic
500C7×C4⋊C4C2416yes—
501C7×C4⋊C4C2416yes—
502C7×C22⋊C4C24112yes—
503C7×C22⋊C4C2416yes—
504C7×C22⋊C4C2416yes—
505C7×C22⋊C4C2412yes—
506C7×C22⋊C4C2416yes—
507C42×C7C2413yes—
508C42×C7C2411yescharacteristic
509C42×C7C2416yes—
510C42×C7C2413yes—
511C42×C7C2416yes—
512C42×C7C2416yes—
513C42×C7C2413yes—
514C22⋊Dic7C24112yes—
515C22⋊Dic7C2416yes—
516C22⋊Dic7C2416yes—
517C22⋊Dic7C2416yes—
518C22⋊Dic7C2416yes—
519C22⋊Dic7C2412yes—
520C22⋊Dic7C2416yes—
521(C2×D7)⋊C4C2416yes—
522(C2×D7)⋊C4C2412yes—
523(C2×D7)⋊C4C2416yes—
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)⋊C4C2416yes—
531(C2×D7)⋊C4C2416yes—
532(C2×D7)⋊C4C2416yes—
533C4⋊Dic7C2411yescharacteristic
534C4⋊Dic7C2413yes—
535C4⋊Dic7C2416yes—
536C4⋊Dic7C2416yes—
537C4⋊Dic7C2413yes—
538C4⋊Dic7C2416yes—
539C4⋊Dic7C2413yes—
540C4⋊Dic7C24112yes—
541C4⋊Dic7C2416yes—
542C4⋊Dic7C2416yes—
543C4⋊Dic7C2416yes—
544C4⋊Dic7C2416yes—
545Dic7⋊C4C2412yes—
546Dic7⋊C4C2416yes—
547Dic7⋊C4C2416yes—
548Dic7⋊C4C2416yes—
549Dic7⋊C4C24112yes—
550Dic7⋊C4C24112yes—
551Dic7⋊C4C24112yes—
552Dic7⋊C4C2416yes—
553Dic7⋊C4C2416yes—
554Dic7⋊C4C2416yes—
555Dic7⋊C4C2416yes—
556Dic7⋊C4C2416yes—
557Dic7⋊C4C2416yes—
558Dic7⋊C4C2416yes—
559Dic7⋊C4C2416yes—
560C4×Dic7C2411yescharacteristic
561C4×Dic7C2416yes—
562C4×Dic7C2413yes—
563C4×Dic7C2413yes—
564C4×Dic7C2413yes—
565C4×Dic7C2413yes—
566C4×Dic7C2413yes—
567C4×Dic7C2416yes—
568C4×Dic7C2416yes—
569C4×Dic7C24112yes—
570C4×Dic7C2411yescharacteristic
571C4×Dic7C2411yescharacteristic
572C4×Dic7C2413yes—
573C4×Dic7C2413yes—
574C4×Dic7C2413yes—
575C4×Dic7C2413yes—
576C4×Dic7C24112yes—
577C2×2−1+4—72no—
578C22×#41—71no—
579Q82—72no—
580#557—73no—
581#557—76no—
582#557—71no—
583#557—73no—
584#557C2×D711yescharacteristic, complemented
585#556—73no—
586#556—76no—
587#556—76no—
588#556—76no—
589#556—73no—
590#556—73no—
591#556C2×D713yescomplemented
592#555—76no—
593#554—76no—
594#554—76no—
595#554—76no—
596#554—76no—
597#553—712no—
598#552—712no—
599#552—712no—
600#552—76no—
601#552—76no—
602#552—76no—
603#552—76no—
604#552—712no—
605#552—76no—
606#552C2×D716yescomplemented
607#551—712no—
608#551—712no—
609D4×Q8—72no—
610D4×Q8—72no—
611D4×Q8—73no—
612D4×Q8—72no—
613D4×Q8—71no—
614D4×Q8—73no—
615D4×Q8C2×D711yescharacteristic, complemented
616#548—72no—
617#548—76no—
618#548—76no—
619#548C2×D712yes—
620#547—73no—
621#547—76no—
622#547—76no—
623#547—76no—
624#547—73no—
625#547—73no—
626#547C2×D713yescomplemented
627#546—76no—
628#546—76no—
629#544—76no—
630#542—76no—
631#542—712no—
632#542—76no—
633#541—712no—
634#541—76no—
635#541—76no—
636#539—712no—
637#539—712no—
638#537—76no—
639#536—76no—
640#536—76no—
641#533—73no—
642#533—73no—
643#533—76no—
644#533—76no—
645#533—76no—
646#533—73no—
647#533—76no—
648#533—73no—
649#533—76no—
650#533—76no—
651#533—73no—
652#533—73no—
653#533—76no—
654#533C2×D713yescomplemented
655#532—73no—
656#532—71no—
657#532—73no—
658C2×C4⋊Q8—73no—
659C2×C4⋊Q8—73no—
660#529—73no—
661#529—73no—
662#529—76no—
663#529—76no—
664#529—73no—
665#529—73no—
666#529—712no—
667#529—76no—
668#529—76no—
669#529—76no—
670#529—712no—
671#529C2×D716yescomplemented
672C2×#125—76no—
673#525—73no—
674#525—76no—
675#525—76no—
676#525—73no—
677C2×C22⋊Q8—76no—
678C2×C22⋊Q8—76no—
679#520—72no—
680#520—76no—
681#520—76no—
682#520—76no—
683#519—72no—
684#519—76no—
685#519—72no—
686C4×#41—71no—
687C4×#41—71no—
688C4×#41—71no—
689C4×#41—76no—
690C4×#41—73no—
691C4×#41—73no—
692C4×#41—73no—
693C4×#41—73no—
694C4×#41—76no—
695C4×#41—76no—
696C4×#41—76no—
697C4×#41—73no—
698C4×#41C2×D711yescharacteristic
699C4×#41C2×D713yescomplemented
700C2×C4×Q8—71no—
701C2×C4×Q8—71no—
702C2×C4×Q8—76no—
703C2×C4×Q8—72no—
704C2×C4×Q8—76no—
705C2×C4×Q8C2×D712yescomplemented
706C2×C4×D4—73no—
707C2×C4×D4—73no—
708C2×#117—73no—
709C2×#117—76no—
710C22×C42—73no—
711C23×C7C2512yes—
712C23×C7C2513yes—
713C22×D7—26no—
714C22×D7—26no—
715C22×D7—43no—
716C22×D7C2512yes—
717C22×D7C2513yes—
718C22×D7C2511yescharacteristic
719C7×Q8—212no—
720C7×Q8—26no—
721C7×Q8C2×#4114yes—
722C7×D4—26no—
723C7×D4—22no—
724C7×D4—46no—
725C2×C4×C7—26no—
726C2×C4×C7—212no—
727C2×C4×C7—26no—
728C2×C4×C7—24no—
729C2×C4×C7—26no—
730C2×C4×C7—46no—
731C2×C4×C7C2511yescharacteristic
732C2×C4×C7C2513yes—
733C2×C4×C7C2516yes—
734C2×C4×C7C2513yes—
735C2×C4×C7C2516yes—
736C2×C4×C7C2512yes—
737C2×C4×C7C2513yes—
738C2×C4×C7C2511yescharacteristic
739C2×C4×C7C2511yescharacteristic
740C22⋊D7—212no—
741C22⋊D7—212no—
742C22⋊D7—24no—
743C22⋊D7—24no—
744C22⋊D7—24no—
745C22⋊D7—46no—
746C2×Dic7—26no—
747C2×Dic7—26no—
748C2×Dic7—43no—
749C2×Dic7C2513yes—
750C2×Dic7C2511yescharacteristic
751C2×Dic7C2512yes—
752C2×Dic7C2513yes—
753C2×Dic7C2516yes—
754C2×Dic7C2516yes—
755C2×Dic7C2513yes—
756C2×Dic7C2511yescharacteristic
757C2×Dic7C2511yescharacteristic
758D28—212no—
759D28—24no—
760D28—22no—
761D28C2×#41112yes—
762C4×D7—26no—
763C4×D7—224no—
764C4×D7—26no—
765C4×D7—26no—
766C4×D7—212no—
767C4×D7—26no—
768C4×D7—24no—
769C4×D7—22no—
770C4×D7—26no—
771C4×D7—22no—
772C4×D7—26no—
773C4×D7—43no—
774C4×D7—43no—
775C4×D7—46no—
776C4×D7—412no—
777C4×D7C2×#41112yes—
778C4×D72−1+414yescomplemented
779Dic14—26no—
780Dic14—212no—
781Dic14—26no—
782Dic14—212no—
783Dic14—24no—
784Dic14—412no—
7852−1+4—1416no—
786C2×#41—71no—
787C2×#41—76no—
788C2×#41—73no—
789C2×#41—72no—
790C2×#41—73no—
791C2×#41—76no—
792C2×#41—76no—
793C2×#41—73no—
794C2×#41—148no—
795C2×#41C22×D711yescharacteristic
796C2×#41C22×D713yes—
797C22×Q8—71no—
798C22×Q8—76no—
799C22×Q8—72no—
800C22×Q8—76no—
801C22×Q8C22×D712yes—
802C22×D4—73no—
803C23×C4—73no—
804C23×C4—73no—
805C23×C4—73no—
806C4⋊Q8—73no—
807C4⋊Q8—76no—
808C4⋊Q8—76no—
809C4⋊Q8—73no—
810C4⋊Q8—76no—
811C4⋊Q8—76no—
812C4⋊Q8—76no—
813C4⋊Q8—71no—
814C4⋊Q8—76no—
815C4⋊Q8—73no—
816C4⋊Q8—73no—
817C4⋊Q8—76no—
818C4⋊Q8—76no—
819C4⋊Q8C22×D713yes—
820C4⋊Q8C22×D713yes—
821#127—71no—
822#126—76no—
823#126—76no—
824#126—712no—
825#126—76no—
826#126—76no—
827#126—712no—
828#126—712no—
829#126—712no—
830#126—712no—
831#126C22×D7112yes—
832#125—76no—
833#125—76no—
834#125—76no—
835#125—712no—
836#125—76no—
837#125—73no—
838#125—73no—
839#125—712no—
840#125—712no—
841#125—76no—
842#125—712no—
843#125—76no—
844#125—712no—
845#125C22×D716yes—
846#125C22×D716yes—
847#124—73no—
848#124—73no—
849#124—76no—
850#124—712no—
851#124—72no—
852#124—76no—
853#124—712no—
854#124C22×D716yes—
855#123—76no—
856#123—76no—
857#123—76no—
858#123—712no—
859#123—76no—
860#123—76no—
861#123—76no—
862#123—712no—
863#123—712no—
864#123—712no—
865#123—712no—
866#123C22×D7112yes—
867C22⋊Q8—73no—
868C22⋊Q8—76no—
869C22⋊Q8—73no—
870C22⋊Q8—76no—
871C22⋊Q8—76no—
872C22⋊Q8—76no—
873C22⋊Q8—76no—
874C22⋊Q8—76no—
875C22⋊Q8—712no—
876C22⋊Q8—76no—
877C22⋊Q8—73no—
878C22⋊Q8—76no—
879C22⋊Q8—712no—
880C22⋊Q8—73no—
881C22⋊Q8—76no—
882C22⋊Q8—76no—
883C22⋊Q8—712no—
884C22⋊Q8—712no—
885C22⋊Q8—76no—
886C22⋊Q8—712no—
887C22⋊Q8—712no—
888C22⋊Q8—712no—
889C22⋊Q8—76no—
890C22⋊Q8—76no—
891C22⋊Q8C22×D716yes—
892C22⋊Q8C22×D716yes—
893C22⋊Q8C22×D716yes—
894#121—71no—
895#121—76no—
896#121—73no—
897#121—76no—
898#121—712no—
899#121—76no—
900#121—71no—
901#121—73no—
902#121—72no—
903#121—76no—
904#121—712no—
905#121C22×D716yes—
906#120—76no—
907#120—76no—
908C4×Q8—71no—
909C4×Q8—71no—
910C4×Q8—76no—
911C4×Q8—72no—
912C4×Q8—76no—
913C4×Q8—76no—
914C4×Q8—73no—
915C4×Q8—73no—
916C4×Q8—712no—
917C4×Q8—76no—
918C4×Q8—76no—
919C4×Q8—76no—
920C4×Q8—712no—
921C4×Q8—76no—
922C4×Q8—76no—
923C4×Q8—73no—
924C4×Q8—73no—
925C4×Q8—73no—
926C4×Q8—712no—
927C4×Q8—76no—
928C4×Q8—76no—
929C4×Q8—73no—
930C4×Q8—76no—
931C4×Q8—76no—
932C4×Q8C22×D711yescharacteristic
933C4×Q8C22×D713yes—
934C4×Q8C22×D716yes—
935C4×Q8C22×D711yescharacteristic
936C4×Q8C22×D712yes—
937C4×Q8C22×D716yes—
938C4×Q8C22×D713yes—
939C4×D4—73no—
940C4×D4—73no—
941C4×D4—76no—
942C4×D4—76no—
943C4×D4—76no—
944C4×D4—72no—
945C4×D4—76no—
946C4×D4—76no—
947C4×D4—712no—
948C4×D4—76no—
949C4×D4—76no—
950C4×D4—76no—
951C4×D4—76no—
952C4×D4—76no—
953C4×D4—76no—
954C4×D4—73no—
955C4×D4—73no—
956C4×D4—76no—
957C4×D4—712no—
958C4×D4—76no—
959C4×D4—76no—
960C4×D4—73no—
961C4×D4—73no—
962C4×D4—76no—
963C4×D4—71no—
964C4×D4—76no—
965C4×D4—76no—
966C4×D4—76no—
967C4×D4—76no—
968C4×D4—73no—
969C4×D4C22×D713yes—
970C4×D4C22×D713yes—
971C4×D4C22×D711yescharacteristic
972C4×D4C22×D716yes—
973C4×D4C22×D716yes—
974C4×D4C22×D713yes—
975#117—73no—
976#117—76no—
977#117—76no—
978#117—76no—
979#117—73no—
980#117—76no—
981#117—73no—
982#117—73no—
983#117—76no—
984#117—76no—
985#117—712no—
986#117—76no—
987#117—76no—
988#117—712no—
989#117—76no—
990#117—76no—
991#117—76no—
992#117—76no—
993#117—712no—
994#117—76no—
995#117—76no—
996#117C22×D713yes—
997#117C22×D716yes—
998#117C22×D713yes—
999#117C22×D716yes—
1000C2×C4⋊C4—73no—
1001C2×C4⋊C4—73no—
1002C2×C4⋊C4—76no—
1003C2×C4⋊C4—76no—
1004C2×C4⋊C4—712no—
1005C2×C4⋊C4—76no—
1006C2×C4⋊C4—76no—
1007C2×C4⋊C4—712no—
1008C2×C4⋊C4—76no—
1009C2×C4⋊C4C22×D716yes—
1010C2×C22⋊C4—76no—
1011C2×C22⋊C4—712no—
1012C2×C42—73no—
1013C2×C42—73no—
1014C2×C42—73no—
1015C2×C42—73no—
1016C2×C42—712no—
1017C2×C42—73no—
1018C2×C42—73no—
1019C2×C42—73no—
1020C2×C42—73no—
1021C2×C42—76no—
1022C2×C42—73no—
1023C2×C42—73no—
1024C2×C42—71no—
1025C2×C42C22×D716yes—
1026C2×C42C22×D713yes—
1027C22×C7—23no—
1028C22×C7—22no—
1029C22×C7—23no—
1030C22×C7—22no—
1031C22×C7—23no—
1032C22×C7—22no—
1033C22×C7C2611yescharacteristic
1034C2×D7—21no—
1035C2×D7—23no—
1036C2×D7—23no—
1037C2×D7—21no—
1038C2×D7—22no—
1039C2×D7—22no—
1040C2×D7—22no—
1041C2×D7—412no—
1042C2×D7C22×#4116yes—
1043C2×D7C2×2−1+412yes—
1044C4×C7—26no—
1045C4×C7—21no—
1046C4×C7—22no—
1047C4×C7—23no—
1048C4×C7—26no—
1049C4×C7—23no—
1050C4×C7C22×#4116yes—
1051C4×C7C2×2−1+412yes—
1052C4×C7#58512yes—
1053Dic7—26no—
1054Dic7—23no—
1055Dic7—22no—
1056Dic7—23no—
1057Dic7—26no—
1058Dic7—23no—
1059Dic7—21no—
1060Dic7C22×#4112yes—
1061Dic7C2×2−1+412yes—
1062C24—73no—
1063#41—24no—
1064#41—46no—
1065#41—78no—
1066#41—148no—
1067#41—1424no—
1068#41—1412no—
1069#41—1424no—
1070#41—1412no—
1071#41—1424no—
1072#41—286no—
1073C2×Q8—28no—
1074C2×Q8—72no—
1075C2×Q8—76no—
1076C2×Q8—76no—
1077C2×Q8—73no—
1078C2×Q8—73no—
1079C2×Q8—712no—
1080C2×Q8—1424no—
1081C2×Q8—144no—
1082C2×Q8—148no—
1083C2×Q8—2812no—
1084C2×Q8C23×D713yes—
1085C2×Q8C23×D716yes—
1086C2×Q8C23×D711yescharacteristic
1087C2×D4—72no—
1088C2×D4—72no—
1089C2×D4—76no—
1090C2×D4—76no—
1091C2×D4—72no—
1092C2×D4—76no—
1093C2×D4—73no—
1094C2×D4—72no—
1095C2×D4—76no—
1096C2×D4—71no—
1097C2×D4—1412no—
1098C2×D4C23×D713yes—
1099C2×D4C23×D711yescharacteristic
1100C2×D4C23×D716yes—
1101C22×C4—73no—
1102C22×C4—71no—
1103C22×C4—73no—
1104C22×C4—73no—
1105C22×C4—73no—
1106C22×C4—71no—
1107C22×C4—71no—
1108C22×C4—73no—
1109C22×C4—73no—
1110C22×C4—73no—
1111C22×C4—73no—
1112C22×C4—73no—
1113C22×C4—712no—
1114C22×C4—76no—
1115C22×C4—73no—
1116C22×C4—72no—
1117C22×C4—73no—
1118C22×C4—73no—
1119C22×C4—712no—
1120C22×C4—76no—
1121C22×C4—1412no—
1122C22×C4—1412no—
1123C22×C4—286no—
1124C22×C4C23×D713yes—
1125C22×C4C23×D713yes—
1126C22×C4C23×D716yes—
1127C22×C4C23×D713yes—
1128C22×C4C23×D712yes—
1129C22×C4C23×D716yes—
1130C4⋊C4—76no—
1131C4⋊C4—76no—
1132C4⋊C4—76no—
1133C4⋊C4—76no—
1134C4⋊C4—712no—
1135C4⋊C4—76no—
1136C4⋊C4—76no—
1137C4⋊C4—76no—
1138C4⋊C4—712no—
1139C4⋊C4—712no—
1140C4⋊C4—72no—
1141C4⋊C4—76no—
1142C4⋊C4—76no—
1143C4⋊C4—76no—
1144C4⋊C4—76no—
1145C4⋊C4—76no—
1146C4⋊C4—73no—
1147C4⋊C4—76no—
1148C4⋊C4—73no—
1149C4⋊C4—73no—
1150C4⋊C4—76no—
1151C4⋊C4—76no—
1152C4⋊C4—712no—
1153C4⋊C4—71no—
1154C4⋊C4—76no—
1155C4⋊C4—76no—
1156C4⋊C4—76no—
1157C4⋊C4C23×D713yes—
1158C4⋊C4C23×D713yes—
1159C4⋊C4C23×D716yes—
1160C4⋊C4C23×D716yes—
1161C4⋊C4C23×D7112yes—
1162C4⋊C4C23×D713yes—
1163C4⋊C4C23×D716yes—
1164C4⋊C4C23×D716yes—
1165C4⋊C4C23×D711yescharacteristic
1166C4⋊C4C23×D716yes—
1167C22⋊C4—76no—
1168C22⋊C4—712no—
1169C22⋊C4—72no—
1170C22⋊C4—76no—
1171C22⋊C4—76no—
1172C22⋊C4—76no—
1173C22⋊C4—76no—
1174C22⋊C4—76no—
1175C22⋊C4—76no—
1176C22⋊C4—76no—
1177C22⋊C4—76no—
1178C22⋊C4—76no—
1179C22⋊C4—76no—
1180C22⋊C4—72no—
1181C22⋊C4—72no—
1182C22⋊C4—76no—
1183C22⋊C4—76no—
1184C22⋊C4—76no—
1185C22⋊C4—76no—
1186C22⋊C4C23×D716yes—
1187C22⋊C4C23×D7112yes—
1188C22⋊C4C23×D712yes—
1189C22⋊C4C23×D716yes—
1190C22⋊C4C23×D716yes—
1191C42—71no—
1192C42—71no—
1193C42—73no—
1194C42—73no—
1195C42—73no—
1196C42—73no—
1197C42—73no—
1198C42—73no—
1199C42—73no—
1200C42—73no—
1201C42—76no—
1202C42—712no—
1203C42—712no—
1204C42—76no—
1205C42—71no—
1206C42—73no—
1207C42—76no—
1208C42C23×D713yes—
1209C42C23×D713yes—
1210C42C23×D716yes—
1211C42C23×D716yes—
1212C42C23×D713yes—
1213C42C23×D711yescharacteristic
1214C42C23×D716yes—
1215C2×C7—43no—
1216C2×C7—42no—
1217C2×C7C23×#4111yescharacteristic
1218C2×C7C22×2−1+411yescharacteristic
1219C2×C7C2×#58511yescharacteristic
1220D7—22no—
1221D7—26no—
1222D7—42no—
1223C23—71no—
1224C23—73no—
1225C23—72no—
1226C23—146no—
1227C23—146no—
1228C23—283no—
1229C23C24×D712yes—
1230C23C24×D713yes—
1231Q8—212no—
1232Q8—26no—
1233Q8—1412no—
1234Q8—144no—
1235Q8—1412no—
1236Q8—146no—
1237Q8—146no—
1238Q8—2812no—
1239Q8D7×#4114yes—
1240D4—26no—
1241D4—22no—
1242D4—46no—
1243D4—712no—
1244D4—144no—
1245D4—1412no—
1246D4—144no—
1247D4—144no—
1248D4—1412no—
1249D4—144no—
1250D4—1412no—
1251D4—142no—
1252D4—286no—
1253C2×C4—26no—
1254C2×C4—212no—
1255C2×C4—26no—
1256C2×C4—26no—
1257C2×C4—24no—
1258C2×C4—46no—
1259C2×C4—71no—
1260C2×C4—71no—
1261C2×C4—712no—
1262C2×C4—74no—
1263C2×C4—73no—
1264C2×C4—71no—
1265C2×C4—72no—
1266C2×C4—73no—
1267C2×C4—76no—
1268C2×C4—76no—
1269C2×C4—73no—
1270C2×C4—146no—
1271C2×C4—142no—
1272C2×C4—146no—
1273C2×C4—146no—
1274C2×C4—1424no—
1275C2×C4—146no—
1276C2×C4—146no—
1277C2×C4—146no—
1278C2×C4—1412no—
1279C2×C4—142no—
1280C2×C4—146no—
1281C2×C4—146no—
1282C2×C4—144no—
1283C2×C4—283no—
1284C2×C4—283no—
1285C2×C4—2812no—
1286C2×C4—286no—
1287C2×C4—283no—
1288C2×C4C24×D711yescharacteristic
1289C2×C4C24×D713yes—
1290C2×C4C24×D713yes—
1291C2×C4C24×D716yes—
1292C2×C4C24×D716yes—
1293C2×C4C24×D712yes—
1294C2×C4C24×D713yes—
1295C2×C4C24×D711yescharacteristic
1296C2×C4C24×D711yescharacteristic
1297C7#6280511yescharacteristic, complemented, Sylow
1298C22—22no—
1299C22—23no—
1300C22—23no—
1301C22—22no—
1302C22—23no—
1303C22—22no—
1304C22—76no—
1305C22—72no—
1306C22—141no—
1307C22—143no—
1308C22—141no—
1309C22—143no—
1310C22—142no—
1311C22—142no—
1312C22—142no—
1313C22—2812no—
1314C22C25×D711yescharacteristic
1315C4—21no—
1316C4—26no—
1317C4—23no—
1318C4—26no—
1319C4—23no—
1320C4—22no—
1321C4—72no—
1322C4—72no—
1323C4—143no—
1324C4—146no—
1325C4—141no—
1326C4—143no—
1327C4—146no—
1328C4—143no—
1329C4—142no—
1330C4C2×D7×#4116yes—
1331C4#9061612yes—
1332C4D7×2−1+412yes—
1333C2—43no—
1334C2—42no—
1335C2—142no—
1336C2—146no—
1337C2—282no—
1338C2C22×D7×#4111yescharacteristic
1339C2C2×#9061611yescharacteristic
1340C2C2×D7×2−1+411yescharacteristic
subgroupG/H
centerC2×C4C24×D7
commutator, socle, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC7×#3482C2
hypercenter#3482D7
hypocenterC7#62805
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ #3482

Complements

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

NH ≅ G/Ntype
1. C7×#3482C2semidirect
2. #11744092C2semidirect
3. #11744086C2semidirect
4. #11744058C2semidirect
5. #11744051C2semidirect
6. #11743905C2semidirect
7. #11743899C2semidirect
8. #11743821C2semidirect
9. #11743814C2semidirect
10. #11743788C2semidirect
11. #11743782C2semidirect
12. #11743754C2semidirect
13. #11743748C2semidirect
14. #11743346C2semidirect
15. D7×#533C2semidirect
16. #11743219C2semidirect
17. #11743217C2semidirect
18. #11742912C2semidirect
19. #11742912C2semidirect
20. #11742904C2semidirect
21. C4×D7×#41C2semidirect
22. Q8×#1157C2semidirect
23. C4×#6551C2semidirect
26. C7×#557C22semidirect
27. C7×#556C22semidirect
28. C7×#552C22semidirect
29. C7×D4×Q8C22semidirect
31. C7×#547C22semidirect
32. C7×#533C22semidirect
33. C7×#529C22semidirect
35. C4×C7×#41C22semidirect
36. C2×C4×C7×Q8C22semidirect
37. #90523C22semidirect
39. #90522C22semidirect
43. Q8×C22⋊D7C22semidirect
44. #90503C22semidirect
45. #90423C22semidirect
48. #90418C22semidirect
49. #90417C22semidirect
50. D7×C4⋊Q8C22semidirect
51. D7×C4⋊Q8C22semidirect
52. #90412C22semidirect
53. #90399C22semidirect
54. #90398C22semidirect
56. #90392C22semidirect
57. #90388C22semidirect
59. #90384C22semidirect
60. #90381C22semidirect
61. #90380C22semidirect
63. D7×#125C22semidirect
64. #90373C22semidirect
67. #90362C22semidirect
68. #90353C22semidirect
69. #90352C22semidirect
70. #90351C22semidirect
72. #90332C22semidirect
74. #90330C22semidirect
75. #90324C22semidirect
77. #90322C22semidirect
78. #90319C22semidirect
81. #90316C22semidirect
82. #90313C22semidirect
83. #90313C22semidirect
84. #90307C22semidirect
87. #90294C22semidirect
89. #90271C22semidirect
93. #90269C22semidirect
94. #90269C22semidirect
96. Q8×D28C22semidirect
97. Q8×D28C22semidirect
99. #90265C22semidirect
102. C4×#1161C22semidirect
103. #90263C22semidirect
104. #90263C22semidirect
107. C4×Q8×D7C22semidirect
108. C4×Q8×D7C22semidirect
109. C4×Q8×D7C22semidirect
110. #90261C22semidirect
111. #90261C22semidirect
112. #90258C22semidirect
113. Q8×Dic14C22semidirect
115. #90248C22semidirect
116. #90248C22semidirect
117. #90248C22semidirect
119. #90242C22semidirect
120. #90242C22semidirect
122. #90239C22semidirect
127. #90233C22semidirect
128. #90233C22semidirect
129. #90233C22semidirect
130. #90229C22semidirect
131. #90229C22semidirect
134. #90220C22semidirect
135. #90220C22semidirect
136. #90220C22semidirect
138. #90219C22semidirect
139. #90219C22semidirect
144. #90208C22semidirect
145. #90208C22semidirect
147. #90202C22semidirect
148. #90195C22semidirect
149. #90195C22semidirect
152. C4×#1157C22semidirect
153. C4×#1157C22semidirect
154. C4×#1157C22semidirect
156. #90161C22semidirect
157. #90161C22semidirect
416. #3482D7semidirect
450. #1161#41semidirect
584. #557C2×D7semidirect
591. #556C2×D7semidirect
606. #552C2×D7semidirect
615. D4×Q8C2×D7semidirect
626. #547C2×D7semidirect
654. #533C2×D7semidirect
671. #529C2×D7semidirect
699. C4×#41C2×D7semidirect
705. C2×C4×Q8C2×D7semidirect
778. C4×D72−1+4semidirect
1297. C7#62805semidirect

Maximal subgroups

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

subgroupindex
C7×#34822
#117440922
#117440862
#117440582
#117440512
#117439052
#117438992
#117438212
#117438142
#117437882
#117437822
#117437542
#117437482
#117433462
D7×#5332
#117432192
#117432172
#117429122
#117429042
C4×D7×#412
Q8×#11572
C4×#65512
#628057