Finite Group Databasebeta

← #14249440

Subgroups — #14249440

Order 1792.

1784 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3480C211yesmaximal, characteristic, complemented
2#11742918C211yesmaximal, characteristic, complemented
3#11741158C212yesmaximal, complemented
4#11741138C212yesmaximal, complemented
5#11741103C212yesmaximal, complemented
6#11741052C214yesmaximal, complemented
7#11741016C212yesmaximal, complemented
8#11740980C214yesmaximal, complemented
9#11740755C211yesmaximal, characteristic, complemented
10#11740716C211yesmaximal, characteristic, complemented
11#11740593C212yesmaximal, complemented
12#11740567C212yesmaximal, complemented
13#11739974C212yesmaximal, complemented
14#11739965C211yesmaximal, characteristic, complemented
15#11739952C212yesmaximal, complemented
16#11739887C211yesmaximal, characteristic, complemented
17C2×#89793C211yesmaximal, characteristic, complemented
18C7×#559—21no—
19C7×#559C2211yescharacteristic
20C7×#557C2211yescharacteristic
21C7×#556—21no—
22C7×#556C2211yescharacteristic
23C7×#553—22no—
24C7×#553C2212yes—
25C7×#550C2211yescharacteristic
26C7×#548C2212yes—
27C7×#532—21no—
28C7×#532C2211yescharacteristic
29C7×#529—22no—
30C7×#529C2212yes—
31C4×C7×#41—21no—
32C4×C7×#41C2212yes—
33C4×C7×#41C2211yescharacteristic
34C2×C4×C7×Q8C2211yescharacteristic
35#90524—21no—
36#90275—21no—
37#90270C2212yes—
38#90256C2214yes—
39#90254C2212yes—
40#90243—22no—
41#90242—21no—
42#90225—22no—
43#90214—21no—
44#90168C2212yes—
45#90168C2211yescharacteristic
46#90161C2212yes—
47C2×#6432C2211yescharacteristic
48#90010C2214yes—
49#90005C2214yes—
50#89999C2212yes—
51C2×#6409C2212yes—
52#89859C2212yes—
53#89851C2212yes—
54#89844C2212yes—
55#89842C2212yes—
56#89838C2214yes—
57#89836C2214yes—
58#89829C2214yes—
59#89828C2214yes—
60#89820C2214yes—
61#89817C2214yes—
62#89810C2214yes—
63#89810C2214yes—
64#89807C2214yes—
65#89806C2214yes—
66#89799C2211yescharacteristic
67#89799C2211yescharacteristic
68C4×#1143C2214yes—
69C4×#1143C2212yes—
70C4×#1143C2212yes—
71Q8×C7⋊C8C2212yes—
72#89794C2214yes—
73#89793C2212yes—
74#89793C2212yes—
75#89793C2212yes—
76#89793C2212yes—
77#89792C2211yescharacteristic
78#89792C2211yescharacteristic
79#89787C2212yes—
80C4×#1141C2214yes—
81D4×C7⋊C8C2214yes—
82D4×C7⋊C8C2212yes—
83#89781C2214yes—
84#89780C2212yes—
85#89780C2212yes—
86#89779C2212yes—
87#89775C2214yes—
88#89770C2214yes—
89#89740C2212yes—
90C2×#6381C2212yes—
91#89697C2211yescharacteristic
92#89697C2212yes—
93C2×C4⋊(C7⋊C8)C2212yes—
94C2×C4⋊(C7⋊C8)C2211yescharacteristic
95#62102—71nomaximal, Sylow
96C2×C7×#41—21no—
97C2×C7×#41D411yescharacteristic
98C2×C7×#41C2312yes—
99C22×C7×Q8C2311yescharacteristic
100C2×#1157—21no—
101C2×#1157—22no—
102C22×Dic14—21no—
103C7×C4⋊Q8—21no—
104C7×C4⋊Q8C2311yescharacteristic
105C7×#127—21no—
106C7×#127C2311yescharacteristic
107C7×#126—22no—
108C7×#126—22no—
109C7×#126—22no—
110C7×#125—22no—
111C7×#125C2312yes—
112C7×#124—21no—
113C7×#124—21no—
114C7×#124—22no—
115C7×#124—21no—
116C7×#124C2312yes—
117C7×#123—22no—
118C7×#123—22no—
119C7×#123—22no—
120C7×C22⋊Q8—22no—
121C7×C22⋊Q8C2312yes—
122C7×#121—22no—
123C7×#121—22no—
124C7×#121—21no—
125C7×#121—22no—
126C7×#121C2312yes—
127C7×#121C2312yes—
128C4×C7×Q8—21no—
129C4×C7×Q8—21no—
130C4×C7×Q8—21no—
131C4×C7×Q8—21no—
132C4×C7×Q8D411yescharacteristic
133C4×C7×Q8C2311yescharacteristic
134C4×C7×Q8C2311yescharacteristic
135C4×C7×Q8C2311yescharacteristic
136C4×C7×Q8C2311yescharacteristic
137C4×C7×Q8C2312yes—
138C4×C7×Q8C2311yescharacteristic
139C4×C7×D4—22no—
140C4×C7×D4—22no—
141C4×C7×D4—22no—
142C4×C7×D4—21no—
143C4×C7×D4—21no—
144C4×C7×D4—22no—
145C4×C7×D4—22no—
146C4×C7×D4—21no—
147C4×C7×D4D411yescharacteristic
148C4×C7×D4D412yes—
149C4×C7×D4C2312yes—
150C4×C7×D4C2312yes—
151C4×C7×D4C2311yescharacteristic
152C4×C7×D4C2312yes—
153C7×#117—22no—
154C7×#117—22no—
155C7×#117D411yescharacteristic
156C7×#117D412yes—
157C7×#117C2312yes—
158C2×C7×C4⋊C4—21no—
159C2×C7×C4⋊C4C2311yescharacteristic
160C2×C42×C7—21no—
161C2×C42×C7—22no—
162C2×C42×C7C2311yescharacteristic
163C2×C42×C7C2312yes—
164#6509—22no—
165C2×#1143C2312yes—
166C2×#1143C2312yes—
167#6502—24no—
168#6501—22no—
169C2×#1141C2314yes—
170#6493—22no—
171#6493—21no—
172#6493C2312yes—
173#6493C2314yes—
174#6489C2314yes—
175C2×C4⋊Dic7—21no—
176C2×C4⋊Dic7C2312yes—
177#6487—22no—
178#6487—22no—
179C22×C7⋊C8C2312yes—
180C22×C7⋊C8C2314yes—
181#6461—24no—
182#6459—24no—
183#6455—22no—
184D7×C4⋊C4—22no—
185#6448—24no—
186#6446—24no—
187(C22⋊D7)⋊C4—24no—
188#6438—21no—
189#6438—22no—
190#6437C2311yescharacteristic
191C4×D28—22no—
192C4×D28—21no—
193C4×D28C2312yes—
194C4×D28C2314yes—
195#6433C2314yes—
196#6432—21no—
197#6432—21no—
198#6432C2312yes—
199#6432C2312yes—
200#6432C2311yescharacteristic
201C4×Dic14—22no—
202C4×Dic14—22no—
203#6409C2314yes—
204#6409C2314yes—
205#6409C2312yes—
206#6409C2312yes—
207#6406C2314yes—
208#6406C2314yes—
209#6406C2314yes—
210C22⋊(C7⋊C8)C2312yes—
211C22⋊(C7⋊C8)C2314yes—
212#6383C2314yes—
213#6383C2312yes—
214#6383C2312yes—
215#6382C2312yes—
216#6382C2312yes—
217#6382C2314yes—
218#6382C2314yes—
219#6381C2314yes—
220#6381C2314yes—
221#6381C2314yes—
222C4⋊(C7⋊C8)C2312yes—
223C4⋊(C7⋊C8)C2312yes—
224C4⋊(C7⋊C8)C2311yescharacteristic
225C4⋊(C7⋊C8)C2314yes—
226C4⋊(C7⋊C8)C2311yescharacteristic
227C4×C7⋊C8C2314yes—
228C4×C7⋊C8C2312yes—
229#3511—71no—
230#3480D711yescharacteristic, complemented
231#3381—72no—
232#3361—72no—
233#3340—72no—
234#3339—74no—
235#3305—72no—
236#3301—74no—
237#3247—72no—
238#3245—71no—
239#3233—72no—
240#3227—71no—
241#3106—72no—
242#3103—71no—
243#3076—72no—
244C2×#477—71no—
245#2988—71no—
246C7×#41—24no—
247C7×#41—24no—
248C7×#41—42no—
249C7×#41—44no—
250C2×C7×Q8—21no—
251C2×C7×Q8—21no—
252C2×C7×Q8—22no—
253C2×C7×Q8—41no—
254C2×C7×Q8C2×D411yescharacteristic
255C2×C7×Q8C2411yescharacteristic
256C2×C7×Q8C2411yescharacteristic
257C2×C7×D4—22no—
258C2×C7×D4—22no—
259C2×C7×D4—22no—
260C2×C7×D4—21no—
261C2×C7×D4—21no—
262C2×C7×D4C2×D411yescharacteristic
263C2×C7×D4C2×D412yes—
264C2×C7×D4C2412yes—
265C22×C4×C7—21no—
266C22×C4×C7—21no—
267C22×C4×C7—22no—
268C22×C4×C7—22no—
269C22×C4×C7—22no—
270C22×C4×C7C2×D412yes—
271C22×C4×C7C2×D412yes—
272C22×C4×C7C2×D411yescharacteristic
273C22×C4×C7C2×D411yescharacteristic
274C22×C4×C7C2411yescharacteristic
275C22×C4×C7C2412yes—
276C2×C22⋊D7—22no—
277C2×C22⋊D7—24no—
278C22×Dic7—22no—
279#1157—44no—
280#1157—84no—
281C2×D28—21no—
282C2×D28—21no—
283C2×D28C2412yes—
284C2×C4×D7—22no—
285C2×C4×D7—24no—
286C2×Dic14—21no—
287C2×Dic14—22no—
288C2×Dic14—22no—
289C2×Dic14—82no—
290C7×C4⋊C4—21no—
291C7×C4⋊C4—21no—
292C7×C4⋊C4—21no—
293C7×C4⋊C4—21no—
294C7×C4⋊C4—21no—
295C7×C4⋊C4—22no—
296C7×C4⋊C4—22no—
297C7×C4⋊C4—22no—
298C7×C4⋊C4—21no—
299C7×C4⋊C4—22no—
300C7×C4⋊C4C2×D411yescharacteristic
301C7×C4⋊C4C2×D411yescharacteristic
302C7×C4⋊C4C2×D412yes—
303C7×C4⋊C4C2×D412yes—
304C7×C4⋊C4C2411yescharacteristic
305C7×C4⋊C4C2411yescharacteristic
306C7×C4⋊C4C2412yes—
307C7×C22⋊C4—22no—
308C7×C22⋊C4—22no—
309C7×C22⋊C4—22no—
310C7×C22⋊C4—22no—
311C7×C22⋊C4—22no—
312C7×C22⋊C4—22no—
313C7×C22⋊C4—22no—
314C7×C22⋊C4—22no—
315C7×C22⋊C4C2×D412yes—
316C7×C22⋊C4C2×D412yes—
317C7×C22⋊C4C2×D412yes—
318C42×C7—21no—
319C42×C7—21no—
320C42×C7—22no—
321C42×C7—22no—
322C42×C7—21no—
323C42×C7—21no—
324C42×C7C2×D412yes—
325C42×C7C2×D412yes—
326C42×C7C2×D411yescharacteristic
327C42×C7C2×D411yescharacteristic
328C42×C7C2411yescharacteristic
329C42×C7C2411yescharacteristic
330C42×C7C2412yes—
331C22⋊Dic7—24no—
332#1143—24no—
333#1143—42no—
334#1141—44no—
335(C2×D7)⋊C4—24no—
336(C2×D7)⋊C4—22no—
337(C2×D7)⋊C4—22no—
338(C2×D7)⋊C4—24no—
339C4⋊Dic7—21no—
340C4⋊Dic7—22no—
341C4⋊Dic7—22no—
342C4⋊Dic7—22no—
343C4⋊Dic7C2414yes—
344C4⋊Dic7C2412yes—
345Dic7⋊C4—24no—
346Dic7⋊C4—24no—
347C4×Dic7—24no—
348C2×C7⋊C8—42no—
349C2×C7⋊C8—44no—
350C2×C7⋊C8C2412yes—
351C2×C7⋊C8C2412yes—
352C2×C7⋊C8C2414yes—
353#559—21no—
354#559C2×D711yescharacteristic
355#557C2×D711yescharacteristic
356#556—21no—
357#556—141no—
358#556C2×D711yescharacteristic
359#555—72no—
360#554—72no—
361#553—22no—
362#553—74no—
363#553C2×D712yes—
364#550C2×D711yescharacteristic
365#548—142no—
366#548C2×D712yes—
367#547—141no—
368#542—142no—
369#537—141no—
370#533—72no—
371#532—21no—
372#532—71no—
373#532—72no—
374#532C2×D711yescharacteristic
375C2×C4⋊Q8—71no—
376#529—22no—
377#529C2×D712yes—
378#520—141no—
379C4×#41—21no—
380C4×#41C2×D712yes—
381C4×#41C2×D711yescharacteristic
382C2×C4×Q8C2×D711yescharacteristic
383#499—74no—
384#498—72no—
385#488—74no—
386#486—72no—
387#485—74no—
388#482—74no—
389#482—74no—
390#481—74no—
391#481—72no—
392#479—74no—
393#478—74no—
394#478—74no—
395#477—72no—
396#477—72no—
397#477—72no—
398#477—72no—
399#476—72no—
400#476—72no—
401#475—71no—
402#475—71no—
403#474—72no—
404#474—72no—
405#466—74no—
406#466—74no—
407#465—74no—
408#463—74no—
409#460—71no—
410#460—71no—
411#459—72no—
412#459—72no—
413#449—74no—
414#448—72no—
415C8×Q8—72no—
416C4×SD16—72no—
417C4×SD16—72no—
418C4×SD16—74no—
419C4×D8—74no—
420C8×D4—74no—
421C8×D4—72no—
422#431—71no—
423#431—72no—
424#427—74no—
425C2×#107—72no—
426C2×C4⋊C8—71no—
427C2×C4⋊C8—72no—
428#416—74no—
429C2×#103—72no—
430C23×C7—22no—
431C23×C7C22×D412yes—
432C23×C7C22×D411yescharacteristic
433C22×D7—22no—
434C7×Q8—22no—
435C7×Q8—21no—
436C7×Q8—21no—
437C7×Q8—21no—
438C7×Q8—42no—
439C7×Q8—42no—
440C7×Q82−1+412yes—
441C7×D4—24no—
442C7×D4—22no—
443C7×D4—22no—
444C7×D4—22no—
445C7×D4—44no—
446C7×D4—44no—
447C7×D4—42no—
448C7×D4—81no—
449C7×D4—82no—
450C2×C4×C7—21no—
451C2×C4×C7—24no—
452C2×C4×C7—21no—
453C2×C4×C7—22no—
454C2×C4×C7—21no—
455C2×C4×C7—22no—
456C2×C4×C7—21no—
457C2×C4×C7—21no—
458C2×C4×C7—22no—
459C2×C4×C7—21no—
460C2×C4×C7—41no—
461C2×C4×C7—42no—
462C2×C4×C7—44no—
463C2×C4×C7—42no—
464C2×C4×C7—44no—
465C2×C4×C7—82no—
466C2×C4×C7—81no—
467C2×C4×C7#13514yes—
468C2×C4×C7C22×D412yes—
469C2×C4×C7C22×D412yes—
470C2×C4×C7C22×D412yes—
471C2×C4×C7C22×D411yescharacteristic
472C2×C4×C7C22×D411yescharacteristic
473C2×C4×C7C22×D411yescharacteristic
474C2×C4×C7C22×D411yescharacteristic
475C2×C4×C7C22×D411yescharacteristic
476C2×C4×C7C2511yescharacteristic
477C22⋊D7—44no—
478C22⋊D7—84no—
479C2×Dic7—22no—
480C2×Dic7—24no—
481C2×Dic7—82no—
482D28—22no—
483D28—22no—
484D28—42no—
485D28—42no—
486C4×D7—44no—
487C4×D7—84no—
488Dic14—44no—
489Dic14—42no—
490Dic14—82no—
491C7⋊C8—22no—
492C7⋊C8—24no—
493C7⋊C8—22no—
494C2×#41—21no—
495C2×#41—141no—
496C2×#41—142no—
497C2×#41C22⋊D711yescharacteristic
498C2×#41C22×D712yes—
499C22×Q8—141no—
500C22×Q8C22×D711yescharacteristic
501C2×SD16—72no—
502C2×SD16—72no—
503C2×D8—74no—
504C22×C8—72no—
505C22×C8—74no—
506C4⋊Q8—21no—
507C4⋊Q8—72no—
508C4⋊Q8—72no—
509C4⋊Q8—71no—
510C4⋊Q8—141no—
511C4⋊Q8—141no—
512C4⋊Q8C22×D711yescharacteristic
513#127—21no—
514#127—71no—
515#127C22×D711yescharacteristic
516#126—22no—
517#126—22no—
518#126—22no—
519#126—144no—
520#125—22no—
521#125—74no—
522#125C22×D712yes—
523#124—21no—
524#124—21no—
525#124—22no—
526#124—21no—
527#124—144no—
528#124—141no—
529#124—142no—
530#124C22×D712yes—
531#123—22no—
532#123—22no—
533#123—22no—
534#123—144no—
535C22⋊Q8—22no—
536C22⋊Q8—142no—
537C22⋊Q8—142no—
538C22⋊Q8—142no—
539C22⋊Q8—144no—
540C22⋊Q8C22×D712yes—
541#121—22no—
542#121—22no—
543#121—21no—
544#121—22no—
545#121—72no—
546#121—74no—
547#121—142no—
548#121—144no—
549#121—142no—
550#121—141no—
551#121C22×D712yes—
552#121C22×D712yes—
553C4×Q8—21no—
554C4×Q8—21no—
555C4×Q8—21no—
556C4×Q8—21no—
557C4×Q8—142no—
558C4×Q8—142no—
559C4×Q8C22⋊D711yescharacteristic
560C4×Q8C22×D711yescharacteristic
561C4×Q8C22×D711yescharacteristic
562C4×Q8C22×D711yescharacteristic
563C4×Q8C22×D711yescharacteristic
564C4×Q8C22×D712yes—
565C4×Q8C22×D711yescharacteristic
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—21no—
570C4×D4—21no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—21no—
574C4×D4—74no—
575C4×D4—72no—
576C4×D4—144no—
577C4×D4—142no—
578C4×D4—141no—
579C4×D4C22⋊D711yescharacteristic
580C4×D4C22⋊D712yes—
581C4×D4C22×D712yes—
582C4×D4C22×D712yes—
583C4×D4C22×D712yes—
584C4×D4C22×D711yescharacteristic
585#117—22no—
586#117—22no—
587#117—74no—
588#117—142no—
589#117C22⋊D711yescharacteristic
590#117C22⋊D712yes—
591#117C22×D712yes—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—72no—
594C2×C4⋊C4—141no—
595C2×C4⋊C4—142no—
596C2×C4⋊C4C22×D711yescharacteristic
597C2×C42—21no—
598C2×C42—22no—
599C2×C42C22×D711yescharacteristic
600C2×C42C22×D712yes—
601#107—74no—
602#107—74no—
603#107—74no—
604#106—72no—
605#106—74no—
606#106—72no—
607#106—74no—
608C4⋊C8—72no—
609C4⋊C8—71no—
610C4⋊C8—72no—
611C4⋊C8—74no—
612C4⋊C8—71no—
613#103—74no—
614#103—74no—
615#103—72no—
616#103—72no—
617#102—74no—
618#102—74no—
619#102—74no—
620#102—72no—
621#102—74no—
622#102—72no—
623C22⋊C8—72no—
624C22⋊C8—74no—
625C4×C8—74no—
626C4×C8—72no—
627C22×C7—21no—
628C22×C7—21no—
629C22×C7—22no—
630C22×C7—22no—
631C22×C7—22no—
632C22×C7—42no—
633C22×C7—42no—
634C22×C7—42no—
635C22×C7C2×#13512yes—
636C22×C7C23×D411yescharacteristic
637C2×D7—42no—
638C2×D7—42no—
639C2×D7—42no—
640C4×C7—21no—
641C4×C7—21no—
642C4×C7—22no—
643C4×C7—22no—
644C4×C7—21no—
645C4×C7—22no—
646C4×C7—22no—
647C4×C7—41no—
648C4×C7—41no—
649C4×C7—41no—
650C4×C7—42no—
651C4×C7C2×#13512yes—
652C4×C7C2×#13512yes—
653C4×C7C2×2−1+411yescharacteristic
654C4×C7#58511yescharacteristic
655Dic7—44no—
656Dic7—42no—
657#41—24no—
658#41—24no—
659#41—42no—
660#41—44no—
661#41—284no—
662#41—564no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—22no—
666C2×Q8—41no—
667C2×Q8—141no—
668C2×Q8—142no—
669C2×Q8—142no—
670C2×Q8—562no—
671C2×Q8C2×C22⋊D711yescharacteristic
672C2×Q8C23×D711yescharacteristic
673C2×Q8C23×D711yescharacteristic
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—72no—
680C2×D4—142no—
681C2×D4—144no—
682C2×D4—141no—
683C2×D4—141no—
684C2×D4C2×C22⋊D712yes—
685C2×D4C2×C22⋊D711yescharacteristic
686C2×D4C23×D712yes—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—142no—
693C22×C4—142no—
694C22×C4—144no—
695C22×C4C2×C22⋊D712yes—
696C22×C4C2×C22⋊D711yescharacteristic
697C22×C4C2×C22⋊D712yes—
698C22×C4C2×C22⋊D711yescharacteristic
699C22×C4C23×D711yescharacteristic
700C22×C4C23×D712yes—
701SD16—144no—
702SD16—282no—
703D8—284no—
704C2×C8—72no—
705C2×C8—72no—
706C2×C8—74no—
707C2×C8—282no—
708C2×C8—284no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—22no—
715C4⋊C4—22no—
716C4⋊C4—22no—
717C4⋊C4—21no—
718C4⋊C4—22no—
719C4⋊C4—74no—
720C4⋊C4—72no—
721C4⋊C4—144no—
722C4⋊C4—144no—
723C4⋊C4—142no—
724C4⋊C4—142no—
725C4⋊C4—142no—
726C4⋊C4—141no—
727C4⋊C4C2×C22⋊D711yescharacteristic
728C4⋊C4C2×C22⋊D711yescharacteristic
729C4⋊C4C2×C22⋊D712yes—
730C4⋊C4C2×C22⋊D712yes—
731C4⋊C4C23×D712yes—
732C4⋊C4C23×D711yescharacteristic
733C4⋊C4C23×D711yescharacteristic
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—144no—
743C22⋊C4—144no—
744C22⋊C4—144no—
745C22⋊C4—142no—
746C22⋊C4—142no—
747C22⋊C4C2×C22⋊D712yes—
748C22⋊C4C2×C22⋊D712yes—
749C22⋊C4C2×C22⋊D712yes—
750C42—21no—
751C42—21no—
752C42—22no—
753C42—22no—
754C42—21no—
755C42—21no—
756C42—144no—
757C42C2×C22⋊D712yes—
758C42C2×C22⋊D712yes—
759C42C2×C22⋊D711yescharacteristic
760C42C2×C22⋊D711yescharacteristic
761C42C23×D712yes—
762C42C23×D711yescharacteristic
763C42C23×D711yescharacteristic
764C2×C7—22no—
765C2×C7—42no—
766C2×C7—82no—
767C2×C7#348911yescharacteristic
768C2×C7C22×#13511yescharacteristic
769C2×C7#358511yescharacteristic
770D7—82no—
771C23—22no—
772C23—142no—
773C23C22×C22⋊D712yes—
774C23C22×C22⋊D711yescharacteristic
775Q8—22no—
776Q8—21no—
777Q8—21no—
778Q8—21no—
779Q8—42no—
780Q8—42no—
781Q8—284no—
782Q8—282no—
783Q8—562no—
784Q8#655412yes—
785D4—24no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—44no—
790D4—44no—
791D4—42no—
792D4—81no—
793D4—82no—
794D4—142no—
795D4—142no—
796D4—282no—
797D4—284no—
798D4—282no—
799D4—564no—
800C2×C4—21no—
801C2×C4—24no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—21no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—44no—
813C2×C4—42no—
814C2×C4—44no—
815C2×C4—82no—
816C2×C4—81no—
817C2×C4—142no—
818C2×C4—144no—
819C2×C4—284no—
820C2×C4—564no—
821C2×C4—562no—
822C2×C4#651314yes—
823C2×C4C22×C22⋊D712yes—
824C2×C4C22×C22⋊D712yes—
825C2×C4C22×C22⋊D711yescharacteristic
826C2×C4C22×C22⋊D711yescharacteristic
827C2×C4C22×C22⋊D712yes—
828C2×C4C22×C22⋊D711yescharacteristic
829C2×C4C22×C22⋊D711yescharacteristic
830C2×C4C22×C22⋊D711yescharacteristic
831C2×C4C24×D711yescharacteristic
832C8—142no—
833C8—144no—
834C8—142no—
835C7#6210211yescharacteristic, complemented, Sylow
836C22—21no—
837C22—21no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—282no—
845C22—282no—
846C22—282no—
847C22C2×#651312yes—
848C22C23×C22⋊D711yescharacteristic
849C4—22no—
850C4—22no—
851C4—21no—
852C4—22no—
853C4—21no—
854C4—22no—
855C4—21no—
856C4—42no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—282no—
861C4—284no—
862C4C2×#651312yes—
863C4C2×#651312yes—
864C4C2×#655411yescharacteristic
865C4#9061611yescharacteristic
866C2—22no—
867C2—42no—
868C2—82no—
869C2—562no—
870C2C22×#651311yescharacteristic
871C2#1174433211yescharacteristic
872C2#1174436611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC7×#3480C2
socleC22×C7C23×D4
hypercenter#3480D7
hypocenterC7#62102
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3480

Complements

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

NH ≅ G/Ntype
1. C7×#3480C2semidirect
2. #11742918C2semidirect
3. #11741158C2semidirect
4. #11741138C2semidirect
5. #11741103C2semidirect
6. #11741052C2semidirect
7. #11741016C2semidirect
8. #11740980C2semidirect
9. #11740755C2semidirect
10. #11740716C2semidirect
11. #11740593C2semidirect
12. #11740567C2semidirect
13. #11739974C2semidirect
14. #11739965C2semidirect
15. #11739952C2semidirect
16. #11739887C2semidirect
17. C2×#89793C2semidirect
230. #3480D7semidirect
835. C7#62102semidirect

Maximal subgroups

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

subgroupindex
C7×#34802
#117429182
#117411582
#117411382
#117411032
#117410522
#117410162
#117409802
#117407552
#117407162
#117405932
#117405672
#117399742
#117399652
#117399522
#117398872
C2×#897932
#621027