Finite Group Databasebeta

← #14262324

Subgroups — #14262324

Order 1792.

7220 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C7×2−1+4C211yesmaximal, characteristic, complemented
2#11744363C211yesmaximal, characteristic, complemented
3#11744361C211yesmaximal, characteristic, complemented
4#11742973C216yesmaximal, complemented
5#11742971C213yesmaximal, complemented
6#11742968C211yesmaximal, characteristic, complemented
7#11742965C216yesmaximal, complemented
8#11742962C213yesmaximal, complemented
9#11742958C211yesmaximal, characteristic, complemented
10#11742951C212yesmaximal, complemented
11#11742950C213yesmaximal, complemented
12#11742947C212yesmaximal, complemented
13#11742945C213yesmaximal, complemented
14#11742911C216yesmaximal, complemented
15#11742909C216yesmaximal, complemented
16#11742906C213yesmaximal, complemented
17#11742904C213yesmaximal, complemented
18C4×#6553C211yesmaximal, characteristic, complemented
19C4×D7×#41C211yesmaximal, characteristic, complemented
20#11742885C212yesmaximal, complemented
21#11742879C213yesmaximal, complemented
22C2×#90271C213yesmaximal, complemented
23#11742870C212yesmaximal, complemented
24C2×C7×2−1+4C2211yescharacteristic
25C2×#6553C2211yescharacteristic
26C2×D7×#41C2211yescharacteristic
27C7×#520C2211yescharacteristic
28C7×#520C2213yescomplemented
29C7×#520C2216yescomplemented
30C7×#519C2213yescomplemented
31C7×#519C2212yescomplemented
32C4×C7×#41C2211yescharacteristic
33C4×C7×#41C2213yescomplemented
34C4×C7×#41C2216yescomplemented
35C2×C4×C7×Q8C2212yescomplemented
36C2×C4×C7×Q8C2213yescomplemented
37#90524C2213yescomplemented
38#90523C2213yescomplemented
39#90521C2213yescomplemented
40#90520C2216yescomplemented
41#90520C2216yescomplemented
42#90520C2216yescomplemented
43#90519C2213yescomplemented
44#90518C2211yescharacteristic
45#41×Dic7C2211yescharacteristic
46#90515C2216yescomplemented
47#90508C2212yescomplemented
48#90508C2212yescomplemented
49#90508C2212yescomplemented
50#90507C2213yescomplemented
51#90507C2213yescomplemented
52Q8×C22⋊D7C2212yescomplemented
53C2×#6510C2213yescomplemented
54C2×#6509C2213yescomplemented
55#90276C2216yescomplemented
56#90276C2216yescomplemented
57#90275C2216yescomplemented
58#90274C2216yescomplemented
59#90274C2216yescomplemented
60#90273C2216yescomplemented
61#90273C2216yescomplemented
62#90273C2216yescomplemented
63#90272C2216yescomplemented
64#90272C2216yescomplemented
65#90271C2216yescomplemented
66#90271C2216yescomplemented
67#90271C2213yescomplemented
68#90271C2216yescomplemented
69#90271C2216yescomplemented
70#90271C2216yescomplemented
71#90271C2216yescomplemented
72#90271C2216yescomplemented
73#90271C2216yescomplemented
74#90271C2213yescomplemented
75#90270C2216yescomplemented
76#90269C2213yescomplemented
77#90269C2216yescomplemented
78#90269C2213yescomplemented
79#90268C2212yes—
80#90267C2212yes—
81#90265C2212yescomplemented
82C4×#1161C2211yescharacteristic, complemented
83C4×#1161C2212yescomplemented
84C4×#1161C2211yescharacteristic, complemented
85C4×Q8×D7C2211yescharacteristic, complemented
86C4×Q8×D7C2211yescharacteristic, complemented
87#90261C2212yescomplemented
88#90260C2212yescomplemented
89#90259C2216yescomplemented
90#90259C2216yescomplemented
91#90256C22112yescomplemented
92#90253C2216yescomplemented
93#90251C22112yescomplemented
94#90248C2211yescharacteristic, complemented
95#90248C2213yescomplemented
96#90247C22112yescomplemented
97#90245C2216yes—
98#90241C22112yescomplemented
99D4×D28C2216yes—
100#90239C2213yescomplemented
101#90239C2213yescomplemented
102#90238C2216yescomplemented
103#90238C2216yescomplemented
104#90238C22112yescomplemented
105#90236C2216yescomplemented
106C4×D4×D7C2213yescomplemented
107C4×D4×D7C2213yescomplemented
108C4×D4×D7C2216yescomplemented
109#90234C2216yescomplemented
110#90231C22112yescomplemented
111#90230C2216yescomplemented
112#90229C2216yescomplemented
113#90229C2216yescomplemented
114C4×#1159C2213yescomplemented
115C4×#1159C2213yescomplemented
116#90226C2216yescomplemented
117#90225C2216yescomplemented
118#90223C2216yescomplemented
119#90222C22112yescomplemented
120#90221C2216yescomplemented
121#90221C2216yescomplemented
122#90220C2216yescomplemented
123#90219C2216yescomplemented
124#90219C2216yescomplemented
125#90218C22112yescomplemented
126#90218C22112yescomplemented
127#90218C22112yescomplemented
128#90216C2213yes—
129#90215C2213yes—
130#90214C2213yescomplemented
131#90213C2213yescomplemented
132#90212C2213yescomplemented
133D7×#117C2213yescomplemented
134#90210C2213yescomplemented
135#90208C2213yescomplemented
136#90206C22112yescomplemented
137#90205C2216yescomplemented
138#90205C2216yescomplemented
139#90204C2216yescomplemented
140C2×#6461C2216yescomplemented
141#90201C2213yes—
142#90198C2216yescomplemented
143C2×#6458C2213yes—
144C2×#6457C2216yescomplemented
145#90191C2213yescomplemented
146C2×#6453C2213yescomplemented
147#90170C22112yescomplemented
148#90170C2216yescomplemented
149#90168C2216yescomplemented
150C4×#1157C2216yescomplemented
151C4×#1157C2213yescomplemented
152C4×#1157C2213yescomplemented
153C4×#1157C2216yescomplemented
154C2×C4×D28C2213yescomplemented
155C2×C4×D28C2216yescomplemented
156C2×#6435C2216yescomplemented
157C2×C42×D7C2213yescomplemented
158#62810—71nomaximal, Sylow
159C7×2−1+4—28no—
160C2×C7×#41C2316yes—
161C2×C7×#41C2313yes—
162C2×C7×#41C2311yescharacteristic
163C22×C7×Q8C2313yes—
164C22×C7×Q8C2312yes—
165#6553—28no—
166D7×#41—28no—
167C2×#1161C2311yescharacteristic
168C2×#1161C2312yes—
169C2×Q8×D7C2311yescharacteristic
170C2×#1159C2313yes—
171C2×D4×D7C2313yes—
172C2×D4×D7C2316yes—
173C2×#1157C2313yes—
174C2×#1157C2313yes—
175C2×#1157C2316yes—
176C2×#1157C2316yes—
177C22×D28C2313yes—
178C22×D28C2316yes—
179C22×C4×D7C2313yes—
180C22×C4×D7C2313yes—
181C22×C4×D7C2313yes—
182C22×C4×D7C2316yes—
183C4×C7×Q8C2316yes—
184C4×C7×Q8C2316yes—
185C4×C7×Q8C2312yes—
186C4×C7×Q8C2311yescharacteristic
187C4×C7×Q8C2311yescharacteristic
188C4×C7×Q8C2313yes—
189C4×C7×Q8C2316yes—
190C4×C7×Q8C2313yes—
191C4×C7×Q8C2316yes—
192C4×C7×Q8C2316yes—
193C4×C7×D4C2313yes—
194C4×C7×D4C2313yes—
195C4×C7×D4C2316yes—
196C4×C7×D4C2316yes—
197C4×C7×D4C2316yes—
198C4×C7×D4C23112yes—
199C4×C7×D4C2311yescharacteristic
200C4×C7×D4C2313yes—
201C7×#117C2313yes—
202C7×#117C2313yes—
203C7×#117C23112yes—
204C7×#117C2316yes—
205C7×#117C2316yes—
206C2×C7×C4⋊C4C2313yes—
207C2×C7×C4⋊C4C2316yes—
208C2×C7×C4⋊C4C2316yes—
209C2×C42×C7C2313yes—
210C2×C42×C7C2316yes—
211C2×C42×C7C2316yes—
212#6510C2313yes—
213#6510C2316yes—
214#6510C2316yes—
215#6510C2316yes—
216#6510C2316yes—
217#6509C2313yes—
218#6509C2316yes—
219#6509C2316yes—
220#6509C2316yes—
221#6509C2313yes—
222#6509C2316yes—
223#6509C2316yes—
224Q8×Dic7C2312yes—
225Q8×Dic7C2311yescharacteristic
226Q8×Dic7C2311yescharacteristic
227#6507C2316yes—
228#6507C2313yes—
229#6503C2313yes—
230#6502C2316yes—
231#6502C2316yes—
232#6502C23112yes—
233#6501C2311yescharacteristic
234#6501C2313yes—
235#6500C2316yes—
236#6500C23112yes—
237#6499C2311yescharacteristic
238#6498C2316yes—
239D4×Dic7C2313yes—
240D4×Dic7C2313yes—
241D4×Dic7C2316yes—
242#6493C23112yes—
243#6493C2316yes—
244#6493C2316yes—
245#6493C2316yes—
246#6493C23112yes—
247#6492C23112yes—
248#6492C23112yes—
249#6492C23112yes—
250C4×C22⋊D7C2312yes—
251C4×C22⋊D7C2316yes—
252C4×C22⋊D7C2316yes—
253C4×C22⋊D7C2316yes—
254C4×C22⋊D7C2316yes—
255C4×C22⋊D7C2316yes—
256C4×C22⋊D7C2316yes—
257C4×C22⋊D7C2316yes—
258C4×C22⋊D7C2316yes—
259C4×C22⋊D7C2316yes—
260C4×C22⋊D7C2316yes—
261C4×C22⋊D7C2316yes—
262C2×(C2×D7)⋊C4C2316yes—
263C2×(C2×D7)⋊C4C2316yes—
264C2×(C2×D7)⋊C4C2316yes—
265C2×(C2×D7)⋊C4C2316yes—
266C2×(C2×D7)⋊C4C2316yes—
267#6489C2312yes—
268#6489C2313yes—
269#6489C2313yes—
270#6489C2316yes—
271C2×C4⋊Dic7C2316yes—
272C2×C4⋊Dic7C2313yes—
273#6487C23112yes—
274#6487C2316yes—
275C2×Dic7⋊C4C2316yes—
276C2×Dic7⋊C4C2316yes—
277C2×C4×Dic7C2313yes—
278C2×C4×Dic7C2313yes—
279C2×C4×Dic7C2313yes—
280#6461C2316yes—
281#6461C23112yes—
282#6461C23112yes—
283#6461C23112yes—
284#6461C23112yes—
285#6461C2316yes—
286#6460C2313yes—
287#6460C2316yes—
288#6460C2311yescharacteristic
289#6459C23112yes—
290#6459C2316yes—
291#6459C2316yes—
292#6459C23112yes—
293#6458C2313yes—
294#6458C2316yes—
295#6458C2316yes—
296#6458C2316yes—
297#6458C2316yes—
298#6458C2313yes—
299#6457C2316yes—
300#6457C23112yes—
301#6457C23112yes—
302#6457C23112yes—
303#6457C23112yes—
304#6457C2316yes—
305#6457C23112yes—
306#6456C2316yes—
307#6456C2313yes—
308#6456C2316yes—
309#6456C2313yes—
310#6455C2316yes—
311#6455C2313yes—
312#6455C2313yes—
313D7×C4⋊C4C2313yes—
314D7×C4⋊C4C2313yes—
315D7×C4⋊C4C2316yes—
316#6453C2313yes—
317#6453C2316yes—
318#6453C2316yes—
319#6453C2316yes—
320#6453C2316yes—
321#6453C2311yescharacteristic
322#6452C23112yes—
323#6452C2316yes—
324#6452C2316yes—
325#6451C2313yes—
326#6451C2316yes—
327#6451C2313yes—
328#6450C2313yes—
329#6450C2313yes—
330#6449C2316yes—
331#6448C2316yes—
332#6448C2316yes—
333#6447C2316yes—
334#6447C2316yes—
335#6447C23112yes—
336#6446C2312yes—
337#6446C2316yes—
338#6446C23112yes—
339#6445C2316yes—
340#6445C23112yes—
341(C22⋊D7)⋊C4C2316yes—
342(C22⋊D7)⋊C4C2316yes—
343(C22⋊D7)⋊C4C23112yes—
344D7×C22⋊C4C2316yes—
345D7×C22⋊C4C23112yes—
346#6442C2312yes—
347#6442C2316yes—
348#6441C2316yes—
349#6441C2316yes—
350#6441C23112yes—
351#6440C2316yes—
352#6439C23112yes—
353#6439C23112yes—
354#6439C23112yes—
355#6438C23112yes—
356#6438C2316yes—
357#6438C23112yes—
358#6437C2316yes—
359C4×D28C2316yes—
360C4×D28C2313yes—
361C4×D28C2316yes—
362C4×D28C23112yes—
363C4×D28C2316yes—
364C4×D28C23112yes—
365C4×D28C23112yes—
366C4×D28C2316yes—
367C4×D28C2313yes—
368C4×D28C2313yes—
369C4×D28C2316yes—
370C4×D28C2316yes—
371C4×D28C2316yes—
372C4×D28C2313yes—
373#6435C2316yes—
374#6435C23112yes—
375#6435C23112yes—
376#6435C23112yes—
377#6435C2316yes—
378#6435C2316yes—
379#6435C2316yes—
380#6435C2316yes—
381#6435C2316yes—
382C42×D7C2311yescharacteristic
383C42×D7C2313yes—
384C42×D7C2313yes—
385C42×D7C2313yes—
386C42×D7C2313yes—
387C42×D7C2313yes—
388C42×D7C2313yes—
389C42×D7C2313yes—
390C42×D7C2316yes—
391#6433C2316yes—
392#6433C23112yes—
393#6432C2316yes—
394C4×Dic14C2311yescharacteristic
395C4×Dic14C2313yes—
396C4×Dic14C2316yes—
397C4×Dic14C2316yes—
398C4×Dic14C2316yes—
399C4×Dic14C2313yes—
400C4×Dic14C2316yes—
401C4×Dic14C2313yes—
402#3524—72no—
403#3521—76no—
404#3516—72no—
405#3513—76no—
406#3512—73no—
407#3510—73no—
408#3504—71no—
409#3500—71no—
410#3495—73no—
411#3494—73no—
412#3489—71no—
413#3488—71no—
414#3482—72no—
415#3481—76no—
416#3480—72no—
417#3475—76no—
418#3461—73no—
419#3460—73no—
420#3444—73no—
421C2×#529—73no—
422C4×2−1+4D711yescharacteristic, complemented
423C4×H(5,𝔽2)—71no—
424C2×C4×#41—71no—
425C23×D7C2413yes—
426C23×D7C2416yes—
427C7×#41—224no—
428C7×#41—212no—
429C7×#41#4118yescomplemented
430C2×C7×Q8—28no—
431C2×C7×Q8—212no—
432C2×C7×Q8C2416yes—
433C2×C7×Q8C2413yes—
434C2×C7×Q8C2411yescharacteristic
435C2×C7×D4C2416yes—
436C2×C7×D4C2411yescharacteristic
437C2×C7×D4C2413yes—
438C22×C4×C7C2413yes—
439C22×C4×C7C2416yes—
440C22×C4×C7C2416yes—
441C22×C4×C7C2412yes—
442C22×C4×C7C2413yes—
443C22×C4×C7C2416yes—
444C22×C4×C7C2416yes—
445C22×C4×C7C2413yes—
446C2×C22⋊D7C2416yes—
447C2×C22⋊D7C2416yes—
448C2×C22⋊D7C2412yes—
449C2×C22⋊D7C2416yes—
450C2×C22⋊D7C2416yes—
451C2×C22⋊D7C2416yes—
452C22×Dic7C2413yes—
453C22×Dic7C2413yes—
454C22×Dic7C2413yes—
455C22×Dic7C2416yes—
456#1161—24no—
457#1161—28no—
458Q8×D7—24no—
459#1159—212no—
460D4×D7—212no—
461D4×D7—224no—
462#1157—212no—
463#1157—212no—
464#1157—412no—
465#1157—412no—
466C2×D28—212no—
467C2×D28—412no—
468C2×D28C2416yes—
469C2×D28C2413yes—
470C2×D28C2413yes—
471C2×D28C2416yes—
472C2×D28C2416yes—
473C2×D28C24112yes—
474C2×C4×D7—212no—
475C2×C4×D7—46no—
476C2×C4×D7—412no—
477C2×C4×D7—46no—
478C2×C4×D7C2411yescharacteristic
479C2×C4×D7C2411yescharacteristic
480C2×C4×D7C2411yescharacteristic
481C2×C4×D7C2413yes—
482C2×C4×D7C2413yes—
483C2×C4×D7C2413yes—
484C2×C4×D7C2413yes—
485C2×C4×D7C2413yes—
486C2×C4×D7C2416yes—
487C2×C4×D7C2416yes—
488C2×C4×D7C2413yes—
489C2×C4×D7C2413yes—
490C2×C4×D7C2413yes—
491C2×C4×D7C2413yes—
492C2×C4×D7C2416yes—
493C2×C4×D7C24112yes—
494C2×Dic14C2411yescharacteristic
495C2×Dic14C2413yes—
496C2×Dic14C2416yes—
497C2×Dic14C2416yes—
498C7×C4⋊C4C2413yes—
499C7×C4⋊C4C2413yes—
500C7×C4⋊C4C2411yescharacteristic
501C7×C4⋊C4C2413yes—
502C7×C4⋊C4C2416yes—
503C7×C4⋊C4C2416yes—
504C7×C4⋊C4C24112yes—
505C7×C4⋊C4C2416yes—
506C7×C22⋊C4C2416yes—
507C7×C22⋊C4C2416yes—
508C7×C22⋊C4C2416yes—
509C7×C22⋊C4C2412yes—
510C42×C7C2416yes—
511C42×C7C2411yescharacteristic
512C42×C7C2413yes—
513C42×C7C2413yes—
514C42×C7C2413yes—
515C42×C7C2416yes—
516C42×C7C2416yes—
517C42×C7C24112yes—
518C22⋊Dic7C2416yes—
519C22⋊Dic7C2416yes—
520C22⋊Dic7C2412yes—
521C22⋊Dic7C2412yes—
522C22⋊Dic7C2416yes—
523C22⋊Dic7C2412yes—
524(C2×D7)⋊C4C2412yes—
525(C2×D7)⋊C4C2416yes—
526(C2×D7)⋊C4C2416yes—
527(C2×D7)⋊C4C24112yes—
528(C2×D7)⋊C4C24112yes—
529(C2×D7)⋊C4C2416yes—
530(C2×D7)⋊C4C2416yes—
531(C2×D7)⋊C4C2416yes—
532(C2×D7)⋊C4C2416yes—
533(C2×D7)⋊C4C2416yes—
534(C2×D7)⋊C4C2416yes—
535(C2×D7)⋊C4C2416yes—
536(C2×D7)⋊C4C2416yes—
537(C2×D7)⋊C4C2416yes—
538(C2×D7)⋊C4C24112yes—
539(C2×D7)⋊C4C24112yes—
540(C2×D7)⋊C4C24112yes—
541C4⋊Dic7C2412yes—
542C4⋊Dic7C2412yes—
543C4⋊Dic7C2413yes—
544C4⋊Dic7C2416yes—
545C4⋊Dic7C2413yes—
546C4⋊Dic7C2416yes—
547C4⋊Dic7C2411yescharacteristic
548C4⋊Dic7C2413yes—
549C4⋊Dic7C24112yes—
550C4⋊Dic7C2416yes—
551Dic7⋊C4C2412yes—
552Dic7⋊C4C2416yes—
553Dic7⋊C4C2416yes—
554Dic7⋊C4C2416yes—
555Dic7⋊C4C2416yes—
556Dic7⋊C4C2416yes—
557Dic7⋊C4C2412yes—
558Dic7⋊C4C2416yes—
559Dic7⋊C4C2416yes—
560Dic7⋊C4C2416yes—
561Dic7⋊C4C2416yes—
562Dic7⋊C4C2416yes—
563Dic7⋊C4C24112yes—
564Dic7⋊C4C24112yes—
565C4×Dic7C2412yes—
566C4×Dic7C2413yes—
567C4×Dic7C2413yes—
568C4×Dic7C2413yes—
569C4×Dic7C2413yes—
570C4×Dic7C2413yes—
571C4×Dic7C2416yes—
572C4×Dic7C2416yes—
573C4×Dic7C2411yescharacteristic
574C4×Dic7C2411yescharacteristic
575C4×Dic7C2411yescharacteristic
576C4×Dic7C2413yes—
577C4×Dic7C2413yes—
578C4×Dic7C2413yes—
579C4×Dic7C2413yes—
580C2×2−1+4C2×D711yescharacteristic
581C2×H(5,𝔽2)—71no—
582C22×#41—71no—
583#559—76no—
584#559—76no—
585#557—72no—
586#557—72no—
587#556—76no—
588#556—76no—
589#556—76no—
590#555—76no—
591#554—76no—
592#554—76no—
593#554—76no—
594#553—712no—
595#553—712no—
596#553—76no—
597#553—76no—
598#553—76no—
599#553—76no—
600#552—76no—
601#552—76no—
602#552—76no—
603#552—712no—
604#552—76no—
605#551—712no—
606#551—712no—
607#551—712no—
608#551—712no—
609#550—72no—
610D4×Q8—72no—
611#548—72no—
612#548—72no—
613#548—72no—
614#548—72no—
615#547—76no—
616#547—76no—
617#546—76no—
618#546—76no—
619#546—76no—
620#546—712no—
621#546—76no—
622D42—76no—
623#544—73no—
624#544—73no—
625#542—76no—
626#542—76no—
627#542—76no—
628#542—76no—
629#541—76no—
630#541—76no—
631#540—76no—
632#540—76no—
633#539—712no—
634#538—712no—
635#537—73no—
636#537—73no—
637#536—73no—
638#536—73no—
639#535—73no—
640#535—73no—
641#533—73no—
642#533—73no—
643#533—76no—
644#533—73no—
645#532—73no—
646#532—73no—
647#532—73no—
648#532—76no—
649#529—73no—
650#529—76no—
651#529—76no—
652#529—76no—
653#529—76no—
654#529—76no—
655#529—76no—
656#529—76no—
657#529—73no—
658#529—76no—
659#529—71no—
660#529—76no—
661#529—76no—
662#529—73no—
663#529—76no—
664#529—76no—
665#529—76no—
666#529—712no—
667C2×#126—76no—
668C2×#125—73no—
669C2×#124—73no—
670#525—73no—
671#525—76no—
672#525—76no—
673#525—712no—
674#525—73no—
675C2×#123—76no—
676C2×C22⋊Q8—73no—
677C2×#121—73no—
678#520—71no—
679#520—72no—
680#520—73no—
681#520C2×D711yescharacteristic
682#520C2×D713yescomplemented
683#520C2×D716yescomplemented
684#519C2×D713yescomplemented
685#519C2×D712yescomplemented
686#518—76no—
687#518—73no—
688C4×#41—71no—
689C4×#41—71no—
690C4×#41—71no—
691C4×#41—72no—
692C4×#41—73no—
693C4×#41—73no—
694C4×#41—73no—
695C4×#41—73no—
696C4×#41—73no—
697C4×#41—76no—
698C4×#41—76no—
699C4×#41C2×D711yescharacteristic
700C4×#41C2×D713yescomplemented
701C4×#41C2×D716yescomplemented
702C2×C4×Q8—71no—
703C2×C4×Q8—71no—
704C2×C4×Q8C2×D713yescomplemented
705C2×C4×Q8C2×D712yescomplemented
706C2×C4×D4—73no—
707C2×C4×D4—73no—
708C2×C4×D4—76no—
709C2×C4×D4—73no—
710C2×C4×D4—76no—
711C2×#117—73no—
712C2×#117—76no—
713C22×C42—73no—
714C23×C7C2512yes—
715C23×C7C2513yes—
716C22×D7—26no—
717C22×D7—212no—
718C22×D7—26no—
719C22×D7—43no—
720C22×D7—46no—
721C22×D7—46no—
722C22×D7C2516yes—
723C22×D7C2513yes—
724C22×D7C2511yescharacteristic
725C7×Q8—212no—
726C7×Q8—26no—
727C7×Q8C2×#4114yes—
728C7×D4—212no—
729C7×D4—22no—
730C7×D4C2×#41112yes—
731C2×C4×C7—212no—
732C2×C4×C7—212no—
733C2×C4×C7—26no—
734C2×C4×C7—24no—
735C2×C4×C7—43no—
736C2×C4×C7—46no—
737C2×C4×C7—46no—
738C2×C4×C7C2×#41112yes—
739C2×C4×C7C2513yes—
740C2×C4×C7C2511yescharacteristic
741C2×C4×C7C2513yes—
742C2×C4×C7C2516yes—
743C2×C4×C7C2516yes—
744C2×C4×C7C2512yes—
745C2×C4×C7C2513yes—
746C2×C4×C7C2511yescharacteristic
747C2×C4×C7C2511yescharacteristic
748C22⋊D7—212no—
749C22⋊D7—212no—
750C22⋊D7—24no—
751C22⋊D7—46no—
752C22⋊D7—46no—
753C22⋊D7—46no—
754C2×Dic7—26no—
755C2×Dic7—43no—
756C2×Dic7—43no—
757C2×Dic7—46no—
758C2×Dic7C2511yescharacteristic
759C2×Dic7C2511yescharacteristic
760C2×Dic7C2511yescharacteristic
761C2×Dic7C2512yes—
762C2×Dic7C2513yes—
763C2×Dic7C2513yes—
764C2×Dic7C2512yes—
765C2×Dic7C2513yes—
766C2×Dic7C2516yes—
767D28—212no—
768D28—26no—
769D28—212no—
770D28—26no—
771D28—412no—
772D28—46no—
773C4×D7—22no—
774C4×D7—26no—
775C4×D7—22no—
776C4×D7—26no—
777C4×D7—26no—
778C4×D7—26no—
779C4×D7—212no—
780C4×D7—22no—
781C4×D7—212no—
782C4×D7—26no—
783C4×D7—43no—
784C4×D7—43no—
785C4×D7—412no—
786C4×D7—43no—
787C4×D7—43no—
788C4×D7—46no—
789Dic14—22no—
790Dic14—26no—
791Dic14—46no—
792Dic14—46no—
7932−1+4—28no—
794H(5,𝔽2)—148no—
795C2×#41—71no—
796C2×#41—72no—
797C2×#41—73no—
798C2×#41—73no—
799C2×#41—73no—
800C2×#41—76no—
801C2×#41—76no—
802C2×#41—148no—
803C2×#41C22×D713yes—
804C2×#41C22×D716yes—
805C2×#41C22×D711yescharacteristic
806C22×Q8—71no—
807C22×Q8C22×D713yes—
808C22×Q8C22×D712yes—
809C22×D4—73no—
810C22×D4—76no—
811C22×D4—73no—
812C22×D4—76no—
813C23×C4—73no—
814C23×C4—76no—
815C23×C4—73no—
816C23×C4—73no—
817C4⋊Q8—73no—
818C4⋊Q8—76no—
819C4⋊Q8—73no—
820C4⋊Q8—73no—
821C4⋊Q8—76no—
822C4⋊Q8—76no—
823#127—73no—
824#127—76no—
825#126—76no—
826#126—712no—
827#126—712no—
828#126—712no—
829#126—76no—
830#126—712no—
831#126—72no—
832#126—76no—
833#126—712no—
834#126—712no—
835#126—712no—
836#125—73no—
837#125—76no—
838#125—76no—
839#125—76no—
840#125—71no—
841#125—76no—
842#125—76no—
843#125—76no—
844#125—712no—
845#125—76no—
846#125—712no—
847#124—73no—
848#124—76no—
849#124—76no—
850#124—76no—
851#124—76no—
852#124—71no—
853#124—76no—
854#124—76no—
855#124—76no—
856#124—712no—
857#124—712no—
858#123—76no—
859#123—712no—
860#123—712no—
861#123—712no—
862#123—76no—
863#123—712no—
864#123—712no—
865#123—712no—
866#123—76no—
867#123—712no—
868#123—712no—
869#123—72no—
870#123—76no—
871#123—76no—
872#123—712no—
873C22⋊Q8—73no—
874C22⋊Q8—76no—
875C22⋊Q8—76no—
876C22⋊Q8—76no—
877C22⋊Q8—73no—
878C22⋊Q8—76no—
879C22⋊Q8—76no—
880C22⋊Q8—76no—
881C22⋊Q8—712no—
882C22⋊Q8—71no—
883C22⋊Q8—73no—
884C22⋊Q8—76no—
885C22⋊Q8—76no—
886C22⋊Q8—712no—
887C22⋊Q8—76no—
888C22⋊Q8—712no—
889C22⋊Q8—76no—
890C22⋊Q8—76no—
891C22⋊Q8—712no—
892#121—71no—
893#121—73no—
894#121—76no—
895#121—76no—
896#121—712no—
897#121—76no—
898#121—712no—
899#121—76no—
900#121—76no—
901#121—712no—
902#121—73no—
903#121—76no—
904#121—76no—
905#121—76no—
906#121—73no—
907#121—76no—
908#121—76no—
909#121—76no—
910#121—712no—
911#120—76no—
912#120—712no—
913#120—76no—
914#120—712no—
915C4×Q8—71no—
916C4×Q8—71no—
917C4×Q8—72no—
918C4×Q8—73no—
919C4×Q8—73no—
920C4×Q8—73no—
921C4×Q8—73no—
922C4×Q8—71no—
923C4×Q8—73no—
924C4×Q8—76no—
925C4×Q8—76no—
926C4×Q8—76no—
927C4×Q8—76no—
928C4×Q8C22×D711yescharacteristic
929C4×Q8C22×D711yescharacteristic
930C4×Q8C22×D713yes—
931C4×Q8C22×D716yes—
932C4×Q8C22×D712yes—
933C4×Q8C22×D716yes—
934C4×Q8C22×D716yes—
935C4×Q8C22×D716yes—
936C4×Q8C22×D713yes—
937C4×Q8C22×D716yes—
938C4×D4—73no—
939C4×D4—73no—
940C4×D4—76no—
941C4×D4—76no—
942C4×D4—76no—
943C4×D4—76no—
944C4×D4—72no—
945C4×D4—76no—
946C4×D4—76no—
947C4×D4—76no—
948C4×D4—76no—
949C4×D4—76no—
950C4×D4—76no—
951C4×D4—76no—
952C4×D4—76no—
953C4×D4—73no—
954C4×D4—73no—
955C4×D4—76no—
956C4×D4—76no—
957C4×D4—76no—
958C4×D4—76no—
959C4×D4—712no—
960C4×D4—76no—
961C4×D4—76no—
962C4×D4—73no—
963C4×D4—73no—
964C4×D4—73no—
965C4×D4—76no—
966C4×D4—76no—
967C4×D4—712no—
968C4×D4—712no—
969C4×D4—712no—
970C4×D4—73no—
971C4×D4—76no—
972C4×D4—76no—
973C4×D4—76no—
974C4×D4C22×D713yes—
975C4×D4C22×D713yes—
976C4×D4C22×D716yes—
977C4×D4C22×D711yescharacteristic
978C4×D4C22×D716yes—
979C4×D4C22×D716yes—
980C4×D4C22×D713yes—
981C4×D4C22×D7112yes—
982#117—73no—
983#117—72no—
984#117—73no—
985#117—76no—
986#117—73no—
987#117—73no—
988#117—76no—
989#117—76no—
990#117—76no—
991#117—76no—
992#117—712no—
993#117—712no—
994#117—712no—
995#117—76no—
996#117—76no—
997#117—76no—
998#117—76no—
999#117C22×D713yes—
1000#117C22×D713yes—
1001#117C22×D716yes—
1002#117C22×D7112yes—
1003#117C22×D716yes—
1004C2×C4⋊C4—76no—
1005C2×C4⋊C4—76no—
1006C2×C4⋊C4—73no—
1007C2×C4⋊C4—76no—
1008C2×C4⋊C4—73no—
1009C2×C4⋊C4—73no—
1010C2×C4⋊C4—76no—
1011C2×C4⋊C4C22×D713yes—
1012C2×C4⋊C4C22×D716yes—
1013C2×C4⋊C4C22×D716yes—
1014C2×C22⋊C4—76no—
1015C2×C22⋊C4—76no—
1016C2×C22⋊C4—76no—
1017C2×C22⋊C4—76no—
1018C2×C22⋊C4—76no—
1019C2×C22⋊C4—76no—
1020C2×C22⋊C4—712no—
1021C2×C42—73no—
1022C2×C42—73no—
1023C2×C42—73no—
1024C2×C42—73no—
1025C2×C42—73no—
1026C2×C42—73no—
1027C2×C42—76no—
1028C2×C42—73no—
1029C2×C42—73no—
1030C2×C42—73no—
1031C2×C42—73no—
1032C2×C42—71no—
1033C2×C42C22×D716yes—
1034C2×C42C22×D713yes—
1035C2×C42C22×D716yes—
1036C22×C7—23no—
1037C22×C7—23no—
1038C22×C7—22no—
1039C22×C7—22no—
1040C22×C7—22no—
1041C22×C7C22×#4116yes—
1042C22×C7C2611yescharacteristic
1043C2×D7—21no—
1044C2×D7—21no—
1045C2×D7—23no—
1046C2×D7—26no—
1047C2×D7—26no—
1048C2×D7—23no—
1049C2×D7—23no—
1050C2×D7—26no—
1051C2×D7—412no—
1052C2×D7—812no—
1053C2×D7#58512yes—
1054C4×C7—26no—
1055C4×C7—22no—
1056C4×C7—26no—
1057C4×C7—21no—
1058C4×C7—23no—
1059C4×C7—23no—
1060C4×C7C22×#4116yes—
1061C4×C7C22×#4112yes—
1062C4×C7#58512yes—
1063Dic7—23no—
1064Dic7—22no—
1065Dic7—21no—
1066Dic7—22no—
1067Dic7—23no—
1068Dic7—23no—
1069Dic7—26no—
1070Dic7—21no—
1071Dic7—21no—
1072C24—73no—
1073C24—76no—
1074#41—224no—
1075#41—212no—
1076#41—144no—
1077#41—148no—
1078#41—1412no—
1079#41—1412no—
1080#41—1412no—
1081#41—2812no—
1082#41—2812no—
1083#41#115718yescomplemented
1084C2×Q8—28no—
1085C2×Q8—212no—
1086C2×Q8—73no—
1087C2×Q8—71no—
1088C2×Q8—76no—
1089C2×Q8—76no—
1090C2×Q8—144no—
1091C2×Q8C23×D713yes—
1092C2×Q8C23×D716yes—
1093C2×Q8C23×D711yescharacteristic
1094C2×D4—72no—
1095C2×D4—76no—
1096C2×D4—76no—
1097C2×D4—76no—
1098C2×D4—76no—
1099C2×D4—76no—
1100C2×D4—76no—
1101C2×D4—76no—
1102C2×D4—73no—
1103C2×D4—73no—
1104C2×D4—76no—
1105C2×D4—712no—
1106C2×D4—1412no—
1107C2×D4—1424no—
1108C2×D4—1412no—
1109C2×D4—2812no—
1110C2×D4C23×D716yes—
1111C2×D4C23×D711yescharacteristic
1112C2×D4C23×D713yes—
1113C22×C4—73no—
1114C22×C4—73no—
1115C22×C4—73no—
1116C22×C4—76no—
1117C22×C4—71no—
1118C22×C4—71no—
1119C22×C4—73no—
1120C22×C4—73no—
1121C22×C4—73no—
1122C22×C4—73no—
1123C22×C4—76no—
1124C22×C4—71no—
1125C22×C4—73no—
1126C22×C4—76no—
1127C22×C4—73no—
1128C22×C4—73no—
1129C22×C4—73no—
1130C22×C4—73no—
1131C22×C4—76no—
1132C22×C4—712no—
1133C22×C4—1412no—
1134C22×C4—286no—
1135C22×C4—2812no—
1136C22×C4—286no—
1137C22×C4C23×D716yes—
1138C22×C4C23×D716yes—
1139C22×C4C23×D713yes—
1140C22×C4C23×D712yes—
1141C22×C4C23×D713yes—
1142C22×C4C23×D716yes—
1143C22×C4C23×D716yes—
1144C22×C4C23×D713yes—
1145C4⋊C4—76no—
1146C4⋊C4—76no—
1147C4⋊C4—76no—
1148C4⋊C4—76no—
1149C4⋊C4—76no—
1150C4⋊C4—712no—
1151C4⋊C4—712no—
1152C4⋊C4—72no—
1153C4⋊C4—72no—
1154C4⋊C4—76no—
1155C4⋊C4—76no—
1156C4⋊C4—76no—
1157C4⋊C4—76no—
1158C4⋊C4—76no—
1159C4⋊C4—73no—
1160C4⋊C4—76no—
1161C4⋊C4—76no—
1162C4⋊C4—73no—
1163C4⋊C4—73no—
1164C4⋊C4—712no—
1165C4⋊C4—71no—
1166C4⋊C4—72no—
1167C4⋊C4—72no—
1168C4⋊C4—76no—
1169C4⋊C4C23×D713yes—
1170C4⋊C4C23×D713yes—
1171C4⋊C4C23×D713yes—
1172C4⋊C4C23×D716yes—
1173C4⋊C4C23×D716yes—
1174C4⋊C4C23×D7112yes—
1175C4⋊C4C23×D711yescharacteristic
1176C4⋊C4C23×D716yes—
1177C22⋊C4—76no—
1178C22⋊C4—76no—
1179C22⋊C4—72no—
1180C22⋊C4—72no—
1181C22⋊C4—72no—
1182C22⋊C4—76no—
1183C22⋊C4—76no—
1184C22⋊C4—76no—
1185C22⋊C4—76no—
1186C22⋊C4—76no—
1187C22⋊C4—712no—
1188C22⋊C4—76no—
1189C22⋊C4—76no—
1190C22⋊C4—76no—
1191C22⋊C4—76no—
1192C22⋊C4—712no—
1193C22⋊C4—712no—
1194C22⋊C4—712no—
1195C22⋊C4—712no—
1196C22⋊C4—72no—
1197C22⋊C4—76no—
1198C22⋊C4—76no—
1199C22⋊C4—76no—
1200C22⋊C4C23×D716yes—
1201C22⋊C4C23×D716yes—
1202C22⋊C4C23×D716yes—
1203C22⋊C4C23×D712yes—
1204C42—71no—
1205C42—71no—
1206C42—73no—
1207C42—73no—
1208C42—73no—
1209C42—73no—
1210C42—73no—
1211C42—73no—
1212C42—73no—
1213C42—73no—
1214C42—76no—
1215C42—76no—
1216C42—71no—
1217C42—72no—
1218C42—73no—
1219C42C23×D713yes—
1220C42C23×D713yes—
1221C42C23×D7112yes—
1222C42C23×D716yes—
1223C42C23×D716yes—
1224C42C23×D713yes—
1225C42C23×D711yescharacteristic
1226C42C23×D716yes—
1227C2×C7—26no—
1228C2×C7—42no—
1229C2×C7C23×#4111yescharacteristic
1230C2×C7C2×#58511yescharacteristic
1231C2×C7C2×#58511yescharacteristic
1232D7—22no—
1233D7—43no—
1234D7—46no—
1235C23—71no—
1236C23—76no—
1237C23—73no—
1238C23—146no—
1239C23—146no—
1240C23—1412no—
1241C23—283no—
1242C23—286no—
1243C23—286no—
1244C23C24×D712yes—
1245C23C24×D713yes—
1246Q8—212no—
1247Q8—26no—
1248Q8—146no—
1249Q8—142no—
1250Q8—286no—
1251Q8—286no—
1252Q8C2×#115714yes—
1253D4—212no—
1254D4—22no—
1255D4—1412no—
1256D4—144no—
1257D4—1412no—
1258D4—1412no—
1259D4—1412no—
1260D4—146no—
1261D4—146no—
1262D4—2812no—
1263D4—286no—
1264D4—286no—
1265D4—286no—
1266D4—286no—
1267D4C2×#1157112yes—
1268C2×C4—212no—
1269C2×C4—212no—
1270C2×C4—26no—
1271C2×C4—24no—
1272C2×C4—43no—
1273C2×C4—46no—
1274C2×C4—46no—
1275C2×C4—71no—
1276C2×C4—71no—
1277C2×C4—71no—
1278C2×C4—72no—
1279C2×C4—73no—
1280C2×C4—73no—
1281C2×C4—73no—
1282C2×C4—72no—
1283C2×C4—76no—
1284C2×C4—142no—
1285C2×C4—146no—
1286C2×C4—146no—
1287C2×C4—142no—
1288C2×C4—146no—
1289C2×C4—146no—
1290C2×C4—146no—
1291C2×C4—1412no—
1292C2×C4—142no—
1293C2×C4—1412no—
1294C2×C4—146no—
1295C2×C4—283no—
1296C2×C4—2812no—
1297C2×C4—283no—
1298C2×C4—283no—
1299C2×C4—283no—
1300C2×C4—286no—
1301C2×C4—283no—
1302C2×C4—286no—
1303C2×C4—283no—
1304C2×C4C2×#1157112yes—
1305C2×C4C24×D711yescharacteristic
1306C2×C4C24×D713yes—
1307C2×C4C24×D713yes—
1308C2×C4C24×D712yes—
1309C2×C4C24×D716yes—
1310C2×C4C24×D716yes—
1311C2×C4C24×D713yes—
1312C2×C4C24×D711yescharacteristic
1313C2×C4C24×D711yescharacteristic
1314C7#6281011yescharacteristic, complemented, Sylow
1315C22—23no—
1316C22—23no—
1317C22—22no—
1318C22—22no—
1319C22—22no—
1320C22—72no—
1321C22—141no—
1322C22—141no—
1323C22—143no—
1324C22—146no—
1325C22—146no—
1326C22—143no—
1327C22—143no—
1328C22—146no—
1329C22—2812no—
1330C22—5612no—
1331C22C22×#115716yes—
1332C22C25×D711yescharacteristic
1333C4—26no—
1334C4—23no—
1335C4—22no—
1336C4—21no—
1337C4—23no—
1338C4—26no—
1339C4—141no—
1340C4—142no—
1341C4—143no—
1342C4—141no—
1343C4—146no—
1344C4—143no—
1345C4—141no—
1346C4—143no—
1347C4—142no—
1348C4C22×#115716yes—
1349C4C22×#115712yes—
1350C4#9062012yes—
1351C2—26no—
1352C2—42no—
1353C2—142no—
1354C2—283no—
1355C2—286no—
1356C2C23×#115711yescharacteristic
1357C2C2×#9062011yescharacteristic
1358C2D7×#58511yescharacteristic
subgroupG/H
centerC2×C4C24×D7
commutator, socle, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC4×C7×2−1+4C2
hypercenterC4×2−1+4D7
hypocenterC7#62810
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. C4×C7×2−1+4C2semidirect
2. #11744363C2semidirect
3. #11744361C2semidirect
4. #11742973C2semidirect
5. #11742971C2semidirect
6. #11742968C2semidirect
7. #11742965C2semidirect
8. #11742962C2semidirect
9. #11742958C2semidirect
10. #11742951C2semidirect
11. #11742950C2semidirect
12. #11742947C2semidirect
13. #11742945C2semidirect
14. #11742911C2semidirect
15. #11742909C2semidirect
16. #11742906C2semidirect
17. #11742904C2semidirect
18. C4×#6553C2semidirect
19. C4×D7×#41C2semidirect
20. #11742885C2semidirect
21. #11742879C2semidirect
22. C2×#90271C2semidirect
23. #11742870C2semidirect
28. C7×#520C22semidirect
29. C7×#520C22semidirect
30. C7×#519C22semidirect
31. C7×#519C22semidirect
33. C4×C7×#41C22semidirect
34. C4×C7×#41C22semidirect
35. C2×C4×C7×Q8C22semidirect
36. C2×C4×C7×Q8C22semidirect
37. #90524C22semidirect
38. #90523C22semidirect
39. #90521C22semidirect
40. #90520C22semidirect
41. #90520C22semidirect
42. #90520C22semidirect
43. #90519C22semidirect
46. #90515C22semidirect
47. #90508C22semidirect
48. #90508C22semidirect
49. #90508C22semidirect
50. #90507C22semidirect
51. #90507C22semidirect
52. Q8×C22⋊D7C22semidirect
53. C2×#6510C22semidirect
54. C2×#6509C22semidirect
55. #90276C22semidirect
56. #90276C22semidirect
57. #90275C22semidirect
58. #90274C22semidirect
59. #90274C22semidirect
60. #90273C22semidirect
61. #90273C22semidirect
62. #90273C22semidirect
63. #90272C22semidirect
64. #90272C22semidirect
65. #90271C22semidirect
66. #90271C22semidirect
67. #90271C22semidirect
68. #90271C22semidirect
69. #90271C22semidirect
70. #90271C22semidirect
71. #90271C22semidirect
72. #90271C22semidirect
73. #90271C22semidirect
74. #90271C22semidirect
75. #90270C22semidirect
76. #90269C22semidirect
77. #90269C22semidirect
78. #90269C22semidirect
81. #90265C22semidirect
82. C4×#1161C22semidirect
83. C4×#1161C22semidirect
84. C4×#1161C22semidirect
85. C4×Q8×D7C22semidirect
86. C4×Q8×D7C22semidirect
87. #90261C22semidirect
88. #90260C22semidirect
89. #90259C22semidirect
90. #90259C22semidirect
91. #90256C22semidirect
92. #90253C22semidirect
93. #90251C22semidirect
94. #90248C22semidirect
95. #90248C22semidirect
96. #90247C22semidirect
98. #90241C22semidirect
100. #90239C22semidirect
101. #90239C22semidirect
102. #90238C22semidirect
103. #90238C22semidirect
104. #90238C22semidirect
105. #90236C22semidirect
106. C4×D4×D7C22semidirect
107. C4×D4×D7C22semidirect
108. C4×D4×D7C22semidirect
109. #90234C22semidirect
110. #90231C22semidirect
111. #90230C22semidirect
112. #90229C22semidirect
113. #90229C22semidirect
114. C4×#1159C22semidirect
115. C4×#1159C22semidirect
116. #90226C22semidirect
117. #90225C22semidirect
118. #90223C22semidirect
119. #90222C22semidirect
120. #90221C22semidirect
121. #90221C22semidirect
122. #90220C22semidirect
123. #90219C22semidirect
124. #90219C22semidirect
125. #90218C22semidirect
126. #90218C22semidirect
127. #90218C22semidirect
130. #90214C22semidirect
131. #90213C22semidirect
132. #90212C22semidirect
133. D7×#117C22semidirect
134. #90210C22semidirect
135. #90208C22semidirect
136. #90206C22semidirect
137. #90205C22semidirect
138. #90205C22semidirect
139. #90204C22semidirect
140. C2×#6461C22semidirect
142. #90198C22semidirect
144. C2×#6457C22semidirect
145. #90191C22semidirect
146. C2×#6453C22semidirect
147. #90170C22semidirect
148. #90170C22semidirect
149. #90168C22semidirect
150. C4×#1157C22semidirect
151. C4×#1157C22semidirect
152. C4×#1157C22semidirect
153. C4×#1157C22semidirect
154. C2×C4×D28C22semidirect
155. C2×C4×D28C22semidirect
156. C2×#6435C22semidirect
157. C2×C42×D7C22semidirect
422. C4×2−1+4D7semidirect
429. C7×#41#41semidirect
682. #520C2×D7semidirect
683. #520C2×D7semidirect
684. #519C2×D7semidirect
685. #519C2×D7semidirect
700. C4×#41C2×D7semidirect
701. C4×#41C2×D7semidirect
704. C2×C4×Q8C2×D7semidirect
705. C2×C4×Q8C2×D7semidirect
1083. #41#1157semidirect
1314. C7#62810semidirect

Maximal subgroups

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

subgroupindex
C4×C7×2−1+42
#117443632
#117443612
#117429732
#117429712
#117429682
#117429652
#117429622
#117429582
#117429512
#117429502
#117429472
#117429452
#117429112
#117429092
#117429062
#117429042
C4×#65532
C4×D7×#412
#117428852
#117428792
C2×#902712
#117428702
#628107