Finite Group Databasebeta

← #14218483

Subgroups — #14218483

Order 1792.

1914 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11742908C211yesmaximal, characteristic
2C4×C7×#131C211yesmaximal, characteristic, complemented
3#11741241C212yesmaximal, complemented
4#11741240C212yesmaximal, complemented
5#11739960C211yesmaximal, characteristic, complemented
6#11736004C214yesmaximal, complemented
7#11736002C214yesmaximal, complemented
8#11735996C212yesmaximal, complemented
9#11735993C212yesmaximal, complemented
10M16×D28C211yesmaximal, characteristic, complemented
11#11735957C212yesmaximal, complemented
12#11735956C212yesmaximal, complemented
13#11735953C211yesmaximal, characteristic, complemented
14C2×#89460C211yesmaximal, characteristic, complemented
15#11735893C212yesmaximal, complemented
16#11735892C212yesmaximal, complemented
17#11735890C211yesmaximal, characteristic, complemented
18C2×C7×#131C2211yescharacteristic
19C2×C7×#131C2211yescharacteristic
20C4×C7×#41C2211yescharacteristic
21#90519C2212yes—
22C2×D7×M16C2212yes—
23C22×#1131C2212yes—
24#90275C411yescharacteristic
25#90272C412yes—
26#90270C411yescharacteristic
27#90254C411yescharacteristic
28#90249C412yes—
29#90247C414yes—
30#90242C411yescharacteristic
31#90241C412yes—
32#90232C412yes—
33#90219C2214yes—
34D7×#117C2212yes—
35#90170C2212yes—
36C4×#1157C2212yes—
37C2×C4×D28C2211yescharacteristic
38#90161C2211yescharacteristic
39C7×#405C2211yescharacteristic
40C7×#405C2211yescharacteristic
41C7×#405C2212yescomplemented
42C7×#405C2212yescomplemented
43C4×C7×M16C2211yescharacteristic
44C4×C7×M16C2212yescomplemented
45C2×C4×C7×C8C2211yescharacteristic
46C2×C4×C7×C8C2212yescomplemented
47#90006C2212yes—
48#89900C2214yescomplemented
49#89900C2214yescomplemented
50#89900C2214yescomplemented
51#89899C2214yescomplemented
52#89898C2212yes—
53#89894C2212yes—
54#89891C2212yes—
55#89883C2214yescomplemented
56#89883C2214yescomplemented
57#89883C2214yescomplemented
58C8×C22⋊D7C2214yescomplemented
59C2×(C2×D7)⋊C8C2212yes—
60#89874C2212yes—
61#89873C2212yes—
62#89772C2214yescomplemented
63#89769C2212yes—
64#89698C2212yescomplemented
65#89697C2212yescomplemented
66#89696C2211yescharacteristic
67C2×C4⋊(C7⋊C8)C2211yescharacteristic
68#89481C2214yescomplemented
69#89480C2214yescomplemented
70#89479C2214yescomplemented
71#89478C2214yes—
72#89477C2214yescomplemented
73#89473C2214yescomplemented
74#89462C2214yescomplemented
75#89461C2214yescomplemented
76#89460C2211yescharacteristic
77#89460C2212yes—
78#89460C2211yescharacteristic
79#89460C2211yescharacteristic
80#89460C2211yescharacteristic
81#89460C2212yes—
82#89460C2212yes—
83C4×#1131C2214yescomplemented
84C8×D28C2212yes—
85#89457C2214yescomplemented
86#89451C2212yescomplemented
87#89451C2212yescomplemented
88#89451C2212yescomplemented
89C8×Dic14C2212yescomplemented
90C8×Dic14C2212yescomplemented
91C8×Dic14C2212yescomplemented
92#60217—71nomaximal, Sylow
93C2×C7×#41C2311yescharacteristic
94C2×#1157C2×C412yes—
95C22×D28C2×C411yescharacteristic
96C22×C4×D7C2312yes—
97C7×#131—24no—
98C7×#131—24no—
99C2×C7×M16C2311yescharacteristic
100C2×C7×M16C2312yes—
101C2×C7×M16C2312yes—
102C2×C7×M16C2311yescharacteristic
103C22×C7×C8C2311yescharacteristic
104C22×C7×C8C2312yes—
105C22×C7×C8C2312yes—
106C22×C7×C8C2311yescharacteristic
107C4×C7×Q8C2×C411yescharacteristic
108C4×C7×Q8C2×C411yescharacteristic
109C4×C7×D4C2×C412yes—
110C4×C7×D4C2×C411yescharacteristic
111C4×C7×D4C2×C412yes—
112C4×C7×D4C2×C411yescharacteristic
113C7×#117C2311yescharacteristic
114C7×#117C2312yes—
115C2×C42×C7C2311yescharacteristic
116C2×C42×C7C2312yes—
117#6509C2×C412yes—
118#6509C2×C412yes—
119#6501C2×C412yes—
120#6501C2×C412yes—
121#6500C2×C414yes—
122#6498C2×C414yes—
123#6493C2×C412yes—
124#6492C2×C414yes—
125C4×C22⋊D7C2×C414yes—
126C4×C22⋊D7C2314yes—
127C4×C22⋊D7C2314yes—
128C2×(C2×D7)⋊C4C2×C412yes—
129#6489C2×C412yes—
130#6489C2312yes—
131C2×C4⋊Dic7C2×C411yescharacteristic
132#6487C2×C412yes—
133#6487C2×C412yes—
134#6487C2×C412yes—
135C2×#1136C2312yes—
136C22×C7⋊C8C2312yes—
137D7×M16—28no—
138C2×#1131—28no—
139C2×#1131C2312yes—
140C2×#1131C2312yes—
141C2×#1131C2314yes—
142C2×#1131C2312yes—
143C2×#1131C2312yes—
144C2×C8×D7C2314yes—
145#6461C2×C414yes—
146#6459C2×C414yes—
147#6457C2×C414yes—
148#6455C2×C412yes—
149#6455C2×C412yes—
150D7×C4⋊C4C2×C412yes—
151D7×C4⋊C4C2×C412yes—
152#6452C2×C414yes—
153#6448C2×C414yes—
154#6447C2×C414yes—
155#6446C2×C414yes—
156D7×C22⋊C4C2×C414yes—
157#6442C2×C414yes—
158#6440C2×C414yes—
159#6439C2×C414yes—
160#6438C2×C412yes—
161C4×D28C2×C411yescharacteristic
162C4×D28C2×C412yes—
163C4×D28C2×C411yescharacteristic
164C4×D28C2×C412yes—
165C4×D28C2311yescharacteristic
166C4×D28C2311yescharacteristic
167C4×D28C2312yes—
168#6435C2×C414yes—
169#6435C2314yes—
170C42×D7C2314yes—
171#6433C2×C412yes—
172#6433C2×C412yes—
173#6432C2×C411yescharacteristic
174#6432C2×C411yescharacteristic
175C4×Dic14C2×C412yes—
176C4×Dic14C2312yes—
177C4×Dic14C2312yes—
178C7×#97C2312yes—
179C7×#97C2312yes—
180C7×#97C2312yes—
181C4×C7×C8C2311yescharacteristic
182C4×C7×C8C2311yescharacteristic
183C4×C7×C8C2312yes—
184C4×C7×C8C2311yescharacteristic
185C4×C7×C8C2311yescharacteristic
186C4×C7×C8C2312yes—
187C4×C7×C8C2312yes—
188C22⋊(C7⋊C8)C2314yes—
189C22⋊(C7⋊C8)C2314yes—
190(C2×D7)⋊C8C2312yes—
191(C2×D7)⋊C8C2312yes—
192(C2×D7)⋊C8C2312yes—
193(C2×D7)⋊C8C2312yes—
194(C2×D7)⋊C8C2314yes—
195(C2×D7)⋊C8C2314yes—
196#6389C2314yes—
197#6389C2314yes—
198Dic7⋊C8C2314yes—
199Dic7⋊C8C2314yes—
200Dic7⋊C8C2314yes—
201Dic7⋊C8C2314yes—
202C8×Dic7C2314yes—
203C8×Dic7C2314yes—
204C4⋊(C7⋊C8)C2311yescharacteristic
205C4⋊(C7⋊C8)C2311yescharacteristic
206C4⋊(C7⋊C8)C2312yes—
207C4⋊(C7⋊C8)C2312yes—
208C4⋊(C7⋊C8)C2312yes—
209#6377C2314yes—
210C4×C7⋊C8C2314yes—
211#3475—71no—
212#2971—72no—
213#2969—74no—
214#2969—72no—
215#2967—74no—
216#2966—72no—
217#2965—72no—
218#2962—71no—
219#2960—71no—
220D4×M16—71no—
221#2933—72no—
222#2930—72no—
223C2×#436—71no—
224#2925—71no—
225#2924—72no—
226C4×#131D711yescharacteristic, complemented
227#2873—72no—
228C23×D7C22×C412yes—
229C7×#41—22no—
230C7×#41—22no—
231C2×C7×Q8C22×C411yescharacteristic
232C2×C7×D4C22×C412yes—
233C2×C7×D4C22×C411yescharacteristic
234C22×C4×C7C22×C411yescharacteristic
235C22×C4×C7C22×C412yes—
236C22×C4×C7C22×C411yescharacteristic
237C22×C4×C7C22×C412yes—
238C22×C4×C7C2412yes—
239C22×C4×C7C2411yescharacteristic
240C2×C22⋊D7C22×C414yes—
241C2×C22⋊D7C22×C414yes—
242C22×Dic7C22×C412yes—
243#1157—44no—
244C2×D28—42no—
245C2×D28C22×C411yescharacteristic
246C2×D28C22×C411yescharacteristic
247C2×D28C22×C412yes—
248C2×C4×D7—24no—
249C2×C4×D7—24no—
250C2×C4×D7C22×C412yes—
251C2×C4×D7C22×C412yes—
252C2×C4×D7C22×C414yes—
253C2×C4×D7C22×C414yes—
254C2×C4×D7C2412yes—
255C2×C4×D7C2412yes—
256C2×Dic14C22×C412yes—
257C2×Dic14C22×C412yes—
258C7×M16—22no—
259C7×M16—24no—
260C7×M16—24no—
261C7×M16#4114yescomplemented
262C2×C7×C8—22no—
263C2×C7×C8—24no—
264C2×C7×C8—24no—
265C2×C7×C8#4114yescomplemented
266C2×C7×C8C2411yescharacteristic
267C2×C7×C8C2411yescharacteristic
268C2×C7×C8C2412yes—
269C2×C7×C8C2411yescharacteristic
270C2×C7×C8C2412yes—
271C2×C7×C8C2411yescharacteristic
272C7×C4⋊C4C22×C412yes—
273C7×C4⋊C4C22×C411yescharacteristic
274C7×C4⋊C4C22×C411yescharacteristic
275C7×C4⋊C4C22×C412yes—
276C7×C22⋊C4C22×C412yes—
277C7×C22⋊C4C22×C412yes—
278C7×C22⋊C4C22×C412yes—
279C42×C7C22×C412yes—
280C42×C7C22×C411yescharacteristic
281C42×C7C22×C411yescharacteristic
282C42×C7C22×C412yes—
283C42×C7C2411yescharacteristic
284C42×C7C2411yescharacteristic
285C42×C7C2412yes—
286C22⋊Dic7C22×C414yes—
287C22⋊Dic7C22×C414yes—
288C22⋊Dic7C22×C414yes—
289(C2×D7)⋊C4C22×C412yes—
290(C2×D7)⋊C4C22×C414yes—
291(C2×D7)⋊C4C22×C414yes—
292(C2×D7)⋊C4C22×C414yes—
293(C2×D7)⋊C4C22×C412yes—
294(C2×D7)⋊C4C22×C412yes—
295(C2×D7)⋊C4C22×C412yes—
296(C2×D7)⋊C4C22×C414yes—
297C4⋊Dic7C22×C411yescharacteristic
298C4⋊Dic7C22×C412yes—
299C4⋊Dic7C22×C412yes—
300C4⋊Dic7C22×C412yes—
301C4⋊Dic7C22×C412yes—
302C4⋊Dic7C22×C411yescharacteristic
303C4⋊Dic7C22×C412yes—
304Dic7⋊C4C22×C414yes—
305Dic7⋊C4C22×C414yes—
306Dic7⋊C4C22×C414yes—
307Dic7⋊C4C22×C414yes—
308Dic7⋊C4C22×C414yes—
309Dic7⋊C4C22×C414yes—
310C4×Dic7C22×C414yes—
311C4×Dic7C22×C414yes—
312C4×Dic7C2414yes—
313#1136—24no—
314C2×C7⋊C8—24no—
315C2×C7⋊C8C2414yes—
316C2×C7⋊C8C2412yes—
317C2×C7⋊C8C2412yes—
318#1131—24no—
319#1131—24no—
320#1131—24no—
321#1131—24no—
322#1131—28no—
323C8×D7—28no—
324C2×#131C2×D711yescharacteristic
325C2×#131C2×D711yescharacteristic
326C22×M16—72no—
327C22×M16—72no—
328#556—71no—
329#555—71no—
330#554—71no—
331#553—72no—
332#552—72no—
333#552—72no—
334#551—74no—
335#547—71no—
336#546—72no—
337#533—71no—
338#529—74no—
339#529—72no—
340#525—72no—
341C4×#41—72no—
342C4×#41C2×D711yescharacteristic
343C2×C4×D4—71no—
344C2×#117—72no—
345#446—74no—
346#446—72no—
347#446—72no—
348#446—72no—
349C8×Q8—72no—
350C8×Q8—72no—
351C8×Q8—72no—
352#436—74no—
353#436—74no—
354#436—74no—
355#436—71no—
356#436—71no—
357#436—72no—
358#436—71no—
359#436—72no—
360#436—71no—
361#436—72no—
362#435—74no—
363#435—74no—
364#435—74no—
365#435—74no—
366#435—74no—
367C8×D4—74no—
368C8×D4—72no—
369#433—74no—
370#433—74no—
371#433—74no—
372#432—72no—
373#432—74no—
374#431—72no—
375#431—74no—
376#424—72no—
377#424—72no—
378#423—71no—
379C2×C4⋊C8—71no—
380#408—72no—
381#407—72no—
382C2×C22⋊C8—72no—
383#405—72no—
384#405—72no—
385#405—72no—
386#405—74no—
387#405—74no—
388#405C2×D711yescharacteristic
389#405C2×D711yescharacteristic
390#405C2×D712yescomplemented
391#405C2×D712yescomplemented
392C4×M16—74no—
393C4×M16—74no—
394C4×M16C2×D711yescharacteristic
395C4×M16C2×D712yescomplemented
396C2×C4×C8C2×D711yescharacteristic
397C2×C4×C8C2×D712yescomplemented
398C23×C7C23×C412yes—
399C23×C7C23×C411yescharacteristic
400C22×D7—24no—
401C22×D7—42no—
402C22×D7—42no—
403C22×D7C23×C412yes—
404C22×D7C23×C412yes—
405C7×Q8—22no—
406C7×D4—24no—
407C7×D4—22no—
408C2×C4×C7—22no—
409C2×C4×C7—24no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—41no—
413C2×C4×C7—42no—
414C2×C4×C7C23×C412yes—
415C2×C4×C7C23×C412yes—
416C2×C4×C7C23×C411yescharacteristic
417C2×C4×C7C23×C411yescharacteristic
418C2×C4×C7C23×C412yes—
419C2×C4×C7C23×C411yescharacteristic
420C2×C4×C7C23×C411yescharacteristic
421C2×C4×C7C23×C411yescharacteristic
422C2×C4×C7C2×#4112yes—
423C2×C4×C7C2×#4112yes—
424C2×C4×C7C2511yescharacteristic
425C22⋊D7—44no—
426C22⋊D7—44no—
427C2×Dic7—24no—
428C2×Dic7C23×C412yes—
429C2×Dic7C23×C414yes—
430C2×Dic7C23×C414yes—
431C2×Dic7C23×C412yes—
432D28—22no—
433D28—22no—
434D28—42no—
435C4×D7—24no—
436C4×D7—24no—
437C4×D7—22no—
438C4×D7—22no—
439C4×D7—22no—
440C4×D7—22no—
441C4×D7—44no—
442C4×D7—44no—
443Dic14—24no—
444Dic14—42no—
445C7×C8—21no—
446C7×C8—21no—
447C7×C8—22no—
448C7×C8C2×#4114yes—
449C7×C8C2×#4112yes—
450C7×C8C2×#4112yes—
451C7⋊C8—24no—
452C7⋊C8—22no—
453C7⋊C8—22no—
454C2×#41—72no—
455C2×#41C22×D711yescharacteristic
456C22×D4—71no—
457C23×C4—72no—
458#131—24no—
459#131—24no—
460C2×M16—72no—
461C2×M16—74no—
462C2×M16—72no—
463C2×M16—72no—
464C2×M16—72no—
465C2×M16—72no—
466C2×M16—148no—
467C2×M16—148no—
468C2×M16C22×D711yescharacteristic
469C2×M16C22×D712yes—
470C2×M16C22×D712yes—
471C2×M16C22×D711yescharacteristic
472C22×C8—72no—
473C22×C8—74no—
474C22×C8C22×D711yescharacteristic
475C22×C8C22×D712yes—
476C22×C8C22×D712yes—
477C22×C8C22×D711yescharacteristic
478C4⋊Q8—71no—
479C4⋊Q8—71no—
480#126—74no—
481#126—74no—
482#126—74no—
483#125—74no—
484#125—72no—
485#125—72no—
486#124—74no—
487#124—72no—
488#123—74no—
489#123—74no—
490#123—74no—
491#123—74no—
492C22⋊Q8—72no—
493C22⋊Q8—72no—
494C22⋊Q8—72no—
495C22⋊Q8—72no—
496C22⋊Q8—72no—
497C22⋊Q8—74no—
498#121—72no—
499#121—72no—
500#121—72no—
501#121—74no—
502#120—74no—
503C4×Q8—72no—
504C4×Q8—72no—
505C4×Q8—72no—
506C4×Q8C4×D711yescharacteristic
507C4×Q8C4×D711yescharacteristic
508C4×D4—74no—
509C4×D4—74no—
510C4×D4—74no—
511C4×D4—71no—
512C4×D4—72no—
513C4×D4—71no—
514C4×D4—72no—
515C4×D4—71no—
516C4×D4—71no—
517C4×D4—72no—
518C4×D4C4×D712yes—
519C4×D4C4×D711yescharacteristic
520C4×D4C4×D712yes—
521C4×D4C4×D711yescharacteristic
522#117—72no—
523#117—72no—
524#117—72no—
525#117—72no—
526#117—74no—
527#117—74no—
528#117—74no—
529#117C22×D711yescharacteristic
530#117C22×D712yes—
531C2×C4⋊C4—71no—
532C2×C4⋊C4—72no—
533C2×C4⋊C4—72no—
534C2×C22⋊C4—72no—
535C2×C22⋊C4—74no—
536C2×C42—74no—
537C2×C42C22×D711yescharacteristic
538C2×C42C22×D712yes—
539C4⋊C8—74no—
540C4⋊C8—74no—
541C4⋊C8—74no—
542C4⋊C8—74no—
543C4⋊C8—71no—
544C4⋊C8—71no—
545C4⋊C8—72no—
546C4⋊C8—72no—
547C4⋊C8—72no—
548C22⋊C8—74no—
549C22⋊C8—74no—
550C22⋊C8—72no—
551C22⋊C8—72no—
552C22⋊C8—72no—
553C22⋊C8—72no—
554C22⋊C8—74no—
555C22⋊C8—74no—
556#97—74no—
557#97—74no—
558#97—74no—
559#97C22×D712yes—
560#97C22×D712yes—
561#97C22×D712yes—
562C4×C8—74no—
563C4×C8—74no—
564C4×C8—74no—
565C4×C8C22×D711yescharacteristic
566C4×C8C22×D711yescharacteristic
567C4×C8C22×D711yescharacteristic
568C4×C8C22×D711yescharacteristic
569C4×C8C22×D712yes—
570C4×C8C22×D712yes—
571C4×C8C22×D712yes—
572C22×C7—21no—
573C22×C7—21no—
574C22×C7—22no—
575C22×C7—22no—
576C22×C7—22no—
577C22×C7C4×#4112yes—
578C22×C7C24×C411yescharacteristic
579C2×D7—22no—
580C2×D7—22no—
581C2×D7—22no—
582C2×D7—22no—
583C2×D7—22no—
584C2×D7—22no—
585C2×D7—84no—
586C4×C7—22no—
587C4×C7—22no—
588C4×C7—21no—
589C4×C7—21no—
590C4×C7—22no—
591C4×C7—21no—
592C4×C7C4×#4112yes—
593C4×C7#56812yes—
594C4×C7C22×#4111yescharacteristic
595C4×C7C22×#4111yescharacteristic
596Dic7—22no—
597Dic7—22no—
598Dic7—24no—
599Dic7—24no—
600C24—72no—
601#41—22no—
602#41—22no—
603#41—284no—
604C2×Q8—72no—
605C2×Q8—72no—
606C2×Q8C2×C4×D711yescharacteristic
607C2×D4—74no—
608C2×D4—74no—
609C2×D4—71no—
610C2×D4—71no—
611C2×D4—72no—
612C2×D4—282no—
613C2×D4C2×C4×D712yes—
614C2×D4C2×C4×D711yescharacteristic
615C22×C4—72no—
616C22×C4—72no—
617C22×C4—72no—
618C22×C4—72no—
619C22×C4—72no—
620C22×C4—74no—
621C22×C4—74no—
622C22×C4—144no—
623C22×C4—144no—
624C22×C4C2×C4×D711yescharacteristic
625C22×C4C2×C4×D712yes—
626C22×C4C2×C4×D711yescharacteristic
627C22×C4C2×C4×D712yes—
628C22×C4C23×D712yes—
629C22×C4C23×D711yescharacteristic
630M16—22no—
631M16—24no—
632M16—24no—
633M16—144no—
634M16—144no—
635M16—144no—
636M16—148no—
637M16—144no—
638M16—144no—
639M16#115714yescomplemented
640C2×C8—22no—
641C2×C8—24no—
642C2×C8—24no—
643C2×C8—72no—
644C2×C8—74no—
645C2×C8—72no—
646C2×C8—144no—
647C2×C8—148no—
648C2×C8#115714yescomplemented
649C2×C8C23×D711yescharacteristic
650C2×C8C23×D711yescharacteristic
651C2×C8C23×D712yes—
652C2×C8C23×D711yescharacteristic
653C2×C8C23×D712yes—
654C2×C8C23×D711yescharacteristic
655C4⋊C4—74no—
656C4⋊C4—74no—
657C4⋊C4—74no—
658C4⋊C4—74no—
659C4⋊C4—74no—
660C4⋊C4—74no—
661C4⋊C4—71no—
662C4⋊C4—72no—
663C4⋊C4—72no—
664C4⋊C4—71no—
665C4⋊C4—72no—
666C4⋊C4—72no—
667C4⋊C4—72no—
668C4⋊C4C2×C4×D711yescharacteristic
669C4⋊C4C2×C4×D711yescharacteristic
670C4⋊C4C2×C4×D712yes—
671C4⋊C4C2×C4×D712yes—
672C22⋊C4—74no—
673C22⋊C4—74no—
674C22⋊C4—74no—
675C22⋊C4—72no—
676C22⋊C4—74no—
677C22⋊C4—74no—
678C22⋊C4—72no—
679C22⋊C4—72no—
680C22⋊C4—72no—
681C22⋊C4—74no—
682C22⋊C4—74no—
683C22⋊C4C2×C4×D712yes—
684C22⋊C4C2×C4×D712yes—
685C22⋊C4C2×C4×D712yes—
686C42—74no—
687C42—74no—
688C42—74no—
689C42C2×C4×D712yes—
690C42C2×C4×D711yescharacteristic
691C42C2×C4×D711yescharacteristic
692C42C2×C4×D712yes—
693C42C23×D712yes—
694C42C23×D711yescharacteristic
695C42C23×D711yescharacteristic
696C2×C7—22no—
697C2×C7—42no—
698C2×C7C2×C4×#4111yescharacteristic
699C2×C7C2×#56811yescharacteristic
700C2×C7#357311yescharacteristic
701D7—42no—
702D7—42no—
703C23—72no—
704C23—72no—
705C23—144no—
706C23—282no—
707C23—282no—
708C23C22×C4×D712yes—
709C23C22×C4×D711yescharacteristic
710Q8—22no—
711Q8—144no—
712Q8—282no—
713D4—24no—
714D4—22no—
715D4—142no—
716D4—142no—
717D4—282no—
718D4—284no—
719D4—284no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—72no—
727C2×C4—74no—
728C2×C4—74no—
729C2×C4—72no—
730C2×C4—144no—
731C2×C4—144no—
732C2×C4—144no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—284no—
738C2×C4—284no—
739C2×C4C22×C4×D712yes—
740C2×C4C22×C4×D712yes—
741C2×C4C22×C4×D711yescharacteristic
742C2×C4C22×C4×D712yes—
743C2×C4C22×C4×D711yescharacteristic
744C2×C4C22×C4×D711yescharacteristic
745C2×C4C22×C4×D711yescharacteristic
746C2×C4C22×C4×D711yescharacteristic
747C2×C4C2×#115712yes—
748C2×C4C2×#115712yes—
749C2×C4C24×D711yescharacteristic
750C8—21no—
751C8—21no—
752C8—22no—
753C8—144no—
754C8—142no—
755C8—142no—
756C8C2×#115712yes—
757C8C2×#115714yes—
758C8C2×#115712yes—
759C7#6021711yescharacteristic, complemented, Sylow
760C22—21no—
761C22—21no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—142no—
766C22—142no—
767C22—142no—
768C22—142no—
769C22—142no—
770C22—142no—
771C22—564no—
772C22C4×#115712yes—
773C22C23×C4×D711yescharacteristic
774C4—22no—
775C4—22no—
776C4—21no—
777C4—21no—
778C4—22no—
779C4—21no—
780C4—142no—
781C4—142no—
782C4—144no—
783C4—144no—
784C4C4×#115712yes—
785C4#9044112yes—
786C4C22×#115711yescharacteristic
787C4C22×#115711yescharacteristic
788C2—22no—
789C2—42no—
790C2—282no—
791C2—282no—
792C2C2×C4×#115711yescharacteristic
793C2C2×#9044111yescharacteristic
794C2#1174422811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D7
commutator, socleC22×C7C24×C4
FittingC4×C7×#131C2
prime radical#11742908C2
cosocleC2×C4×C7C25
hypercenterC4×#131D7
hypocenterC7#60217
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C4×#131

Complements

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

NH ≅ G/Ntype
2. C4×C7×#131C2semidirect
3. #11741241C2semidirect
4. #11741240C2semidirect
5. #11739960C2semidirect
6. #11736004C2semidirect
7. #11736002C2semidirect
8. #11735996C2semidirect
9. #11735993C2semidirect
10. M16×D28C2semidirect
11. #11735957C2semidirect
12. #11735956C2semidirect
13. #11735953C2semidirect
14. C2×#89460C2semidirect
15. #11735893C2semidirect
16. #11735892C2semidirect
17. #11735890C2semidirect
41. C7×#405C22semidirect
42. C7×#405C22semidirect
44. C4×C7×M16C22semidirect
46. C2×C4×C7×C8C22semidirect
48. #89900C22semidirect
49. #89900C22semidirect
50. #89900C22semidirect
51. #89899C22semidirect
55. #89883C22semidirect
56. #89883C22semidirect
57. #89883C22semidirect
58. C8×C22⋊D7C22semidirect
62. #89772C22semidirect
64. #89698C22semidirect
65. #89697C22semidirect
68. #89481C22semidirect
69. #89480C22semidirect
70. #89479C22semidirect
72. #89477C22semidirect
73. #89473C22semidirect
74. #89462C22semidirect
75. #89461C22semidirect
83. C4×#1131C22semidirect
85. #89457C22semidirect
86. #89451C22semidirect
87. #89451C22semidirect
88. #89451C22semidirect
89. C8×Dic14C22semidirect
90. C8×Dic14C22semidirect
91. C8×Dic14C22semidirect
226. C4×#131D7semidirect
261. C7×M16#41semidirect
265. C2×C7×C8#41semidirect
390. #405C2×D7semidirect
391. #405C2×D7semidirect
395. C4×M16C2×D7semidirect
397. C2×C4×C8C2×D7semidirect
639. M16#1157semidirect
648. C2×C8#1157semidirect
759. C7#60217semidirect

Maximal subgroups

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

subgroupindex
#117429082
C4×C7×#1312
#117412412
#117412402
#117399602
#117360042
#117360022
#117359962
#117359932
M16×D282
#117359572
#117359562
#117359532
C2×#894602
#117358932
#117358922
#117358902
#602177