Finite Group Databasebeta

← #14219014

Subgroups — #14219014

Order 1792.

1882 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11742832C211yesmaximal, characteristic
2C2×C7×C8×D4C211yesmaximal, characteristic, complemented
3#11741179C212yesmaximal, complemented
4C2×#89874C212yesmaximal, complemented
5D4×#1136C211yesmaximal, characteristic, complemented
6#11736855C212yesmaximal, complemented
7#11736854C214yesmaximal, complemented
8#11736853C212yesmaximal, complemented
9#11736852C214yesmaximal, complemented
10#11736851C212yesmaximal, complemented
11#11736850C212yesmaximal, complemented
12#11736457C211yesmaximal, characteristic, complemented
13#11736453C211yesmaximal, characteristic, complemented
14#11736041C212yesmaximal, complemented
15#11736029C212yesmaximal, complemented
16#11735900C211yesmaximal, characteristic, complemented
17#11735890C211yesmaximal, characteristic, complemented
18C23×C7×C8C2212yes—
19C2×C4×C7×D4C2211yescharacteristic
20#90497C412yes—
21#90482C2212yes—
22C2×#6489C2212yes—
23C22×#1136C2212yes—
24C2×#6464C2212yes—
25#90256C412yes—
26#90254C411yescharacteristic
27#90248C2212yes—
28#90246C411yescharacteristic
29#90234C411yescharacteristic
30#90233C411yescharacteristic
31#90232C412yes—
32#90229C2214yes—
33C4×#1159C2212yes—
34#90204C412yes—
35#90186C414yes—
36C4×#1157C2211yescharacteristic
37#90161C2211yescharacteristic
38C7×C8×D4C2211yescharacteristic
39C7×C8×D4C2211yescharacteristic
40C7×C8×D4C2212yes—
41C7×C8×D4C2211yescharacteristic
42C7×C8×D4C2212yes—
43C7×C8×D4C2211yescharacteristic
44C2×C7×C4⋊C8C2211yescharacteristic
45C2×C7×C22⋊C8C2212yes—
46C2×C4×C7×C8C2211yescharacteristic
47#89979C2212yes—
48#89883C2214yescomplemented
49#89883C2214yescomplemented
50#89882C2211yescharacteristic
51#89882C2211yescharacteristic
52C8×C22⋊D7C2214yescomplemented
53C8×C22⋊D7C2214yescomplemented
54#89874C2212yes—
55#89874C2211yescharacteristic
56#89874C2211yescharacteristic
57#89874C2212yes—
58#89874C2212yes—
59#89874C2214yescomplemented
60#89874C2214yescomplemented
61#89873C2212yes—
62#89873C2212yes—
63C2×Dic7⋊C8C2214yescomplemented
64C2×Dic7⋊C8C2214yescomplemented
65#89784C2212yes—
66#89783C2214yes—
67D4×C7⋊C8C2212yes—
68#89696C2211yescharacteristic
69C4×#1136C2211yescharacteristic
70#89611C2214yescomplemented
71#89609C2212yescomplemented
72D7×C4⋊C8C2212yescomplemented
73#89603C2212yescomplemented
74#89602C2212yescomplemented
75#89600C2214yescomplemented
76#89502C2214yescomplemented
77#89501C2214yescomplemented
78#89500C2214yescomplemented
79(C22⋊D7)⋊C8C2214yescomplemented
80#89492C2214yescomplemented
81#89492C2214yescomplemented
82#89491C2214yescomplemented
83#89490C2214yescomplemented
84#89462C2212yescomplemented
85#89462C2212yescomplemented
86#89457C2212yescomplemented
87#89457C2212yescomplemented
88#89451C2212yescomplemented
89#89451C2212yescomplemented
90C8×Dic14C2212yescomplemented
91C8×Dic14C2212yescomplemented
92#60271—71nomaximal, Sylow
93C22×C7×D4C2×C411yescharacteristic
94C23×C4×C7C2312yes—
95C2×#1159C2×C412yes—
96C2×#1157C2311yescharacteristic
97C22×C7×C8—44no—
98C22×C7×C8C2311yescharacteristic
99C22×C7×C8C2312yes—
100C22×C7×C8C2311yescharacteristic
101C22×C7×C8C2312yes—
102C22×C7×C8C2312yes—
103C22×C7×C8C2312yes—
104C22×C7×C8C2312yes—
105C4×C7×D4C2×C412yes—
106C4×C7×D4C2×C411yescharacteristic
107C4×C7×D4C2×C411yescharacteristic
108C4×C7×D4C2311yescharacteristic
109C4×C7×D4C2312yes—
110C4×C7×D4C2311yescharacteristic
111C2×C7×C4⋊C4C2×C411yescharacteristic
112C2×C7×C22⋊C4C2×C412yes—
113C2×C42×C7C2311yescharacteristic
114#6516C2×C414yes—
115C2×C22⋊Dic7C2×C414yes—
116#6502C2×C414yes—
117#6501C2×C412yes—
118#6499C2×C412yes—
119#6498C2×C414yes—
120D4×Dic7C2×C412yes—
121#6493C2×C412yes—
122#6493C2×C412yes—
123#6492C2×C414yes—
124C4×C22⋊D7C2×C412yes—
125C4×C22⋊D7C2×C412yes—
126C4×C22⋊D7C2314yes—
127C4×C22⋊D7C2314yes—
128#6489C2×C414yes—
129#6489C2×C412yes—
130#6489C2×C412yes—
131#6489C2312yes—
132#6489C2311yescharacteristic
133#6489C2314yes—
134C2×C4⋊Dic7C2×C412yes—
135C2×C4⋊Dic7C2×C412yes—
136#6487C2×C412yes—
137#6487C2×C412yes—
138#6487C2×C412yes—
139#6487C2×C412yes—
140C2×C4×Dic7C2314yes—
141C2×#1136—44no—
142C2×#1136C2311yescharacteristic
143C2×#1136C2312yes—
144C2×#1136C2311yescharacteristic
145C2×#1136C2314yes—
146C22×C7⋊C8C2314yes—
147#6464—44no—
148C2×#1131C2314yes—
149C2×C8×D7C2314yes—
150#6461C2×C414yes—
151#6460C2×C412yes—
152#6455C2×C412yes—
153#6453C2×C412yes—
154#6452C2×C414yes—
155#6450C2×C412yes—
156#6449C2×C414yes—
157#6448C2×C414yes—
158#6446C2×C414yes—
159(C22⋊D7)⋊C4C2×C414yes—
160#6442C2×C414yes—
161#6442C2×C414yes—
162#6441C2×C414yes—
163#6440C2×C414yes—
164C4×D28C2×C411yescharacteristic
165C4×D28C2×C411yescharacteristic
166#6435C2312yes—
167C42×D7C2312yes—
168#6433C2×C412yes—
169#6432C2×C411yescharacteristic
170#6432C2×C411yescharacteristic
171C4×Dic14C2×C411yescharacteristic
172C4×Dic14C2×C411yescharacteristic
173C4×Dic14C2312yes—
174C4×Dic14C2312yes—
175C7×C4⋊C8C2312yes—
176C7×C4⋊C8C2311yescharacteristic
177C7×C4⋊C8C2311yescharacteristic
178C7×C22⋊C8C2312yes—
179C7×C22⋊C8C2312yes—
180C7×C22⋊C8C2312yes—
181C7×C22⋊C8C2312yes—
182C4×C7×C8C2311yescharacteristic
183C4×C7×C8C2311yescharacteristic
184C4×C7×C8C2311yescharacteristic
185C4×C7×C8C2311yescharacteristic
186C22⋊(C7⋊C8)C2314yes—
187C22⋊(C7⋊C8)C2314yes—
188(C2×D7)⋊C8C2312yes—
189(C2×D7)⋊C8C2312yes—
190(C2×D7)⋊C8C2312yes—
191(C2×D7)⋊C8C2312yes—
192#6389C2314yes—
193#6389C2314yes—
194Dic7⋊C8C2314yes—
195Dic7⋊C8C2314yes—
196Dic7⋊C8C2314yes—
197Dic7⋊C8C2314yes—
198Dic7⋊C8C2312yes—
199Dic7⋊C8C2312yes—
200Dic7⋊C8C2314yes—
201Dic7⋊C8C2314yes—
202Dic7⋊C8C2312yes—
203Dic7⋊C8C2312yes—
204C8×Dic7C2314yes—
205C8×Dic7C2314yes—
206C4⋊(C7⋊C8)C2312yes—
207C4⋊(C7⋊C8)C2312yes—
208#6377C2312yes—
209C4×C7⋊C8C2312yes—
210#3475—71no—
211#2994—74no—
212#2994—72no—
213#2993—72no—
214#2992—74no—
215#2990—72no—
216#2988—72no—
217#2962—71no—
218#2960—71no—
219D4×M16—71no—
220#2933—72no—
221#2929—72no—
222C2×C8×D4D711yescharacteristic, complemented
223#2924—72no—
224#2922—71no—
225#2906—71no—
226C2×#424—72no—
227C24×C7C22×C412yes—
228C2×C7×D4—24no—
229C2×C7×D4C22×C412yes—
230C2×C7×D4C22×C411yescharacteristic
231C2×C7×D4C22×C411yescharacteristic
232C22×C4×C7—24no—
233C22×C4×C7—24no—
234C22×C4×C7C22×C411yescharacteristic
235C22×C4×C7C22×C412yes—
236C22×C4×C7C22×C412yes—
237C22×C4×C7C22×C412yes—
238C22×C4×C7C22×C411yescharacteristic
239C22×C4×C7C2412yes—
240C22×C4×C7C2412yes—
241C22×C4×C7C2411yescharacteristic
242C2×C22⋊D7C22×C414yes—
243C2×C22⋊D7C22×C412yes—
244C2×C22⋊D7C22×C414yes—
245C22×Dic7C22×C414yes—
246C22×Dic7C22×C414yes—
247#1159—28no—
248#1157—22no—
249#1157—22no—
250C2×D28C22×C411yescharacteristic
251C2×C4×D7C22×C412yes—
252C2×C4×D7C22×C412yes—
253C2×C4×D7C2412yes—
254C2×Dic14C22×C411yescharacteristic
255C2×Dic14C22×C412yes—
256C2×Dic14C22×C412yes—
257C2×C7×C8—24no—
258C2×C7×C8—22no—
259C2×C7×C8—22no—
260C2×C7×C8—42no—
261C2×C7×C8—42no—
262C2×C7×C8—42no—
263C2×C7×C8—42no—
264C2×C7×C8C2411yescharacteristic
265C2×C7×C8C2411yescharacteristic
266C2×C7×C8C2411yescharacteristic
267C2×C7×C8C2411yescharacteristic
268C2×C7×C8C2412yes—
269C2×C7×C8C2412yes—
270C7×C4⋊C4C22×C411yescharacteristic
271C7×C4⋊C4C22×C412yes—
272C7×C4⋊C4C22×C411yescharacteristic
273C7×C22⋊C4C22×C412yes—
274C7×C22⋊C4C22×C412yes—
275C7×C22⋊C4C22×C412yes—
276C7×C22⋊C4C22×C412yes—
277C42×C7C22×C411yescharacteristic
278C42×C7C22×C411yescharacteristic
279C42×C7C2411yescharacteristic
280C42×C7C2411yescharacteristic
281C22⋊Dic7C22×C414yes—
282C22⋊Dic7C22×C414yes—
283C22⋊Dic7C22×C414yes—
284C22⋊Dic7C22×C414yes—
285C22⋊Dic7C22×C414yes—
286C22⋊Dic7C22×C412yes—
287(C2×D7)⋊C4C22×C412yes—
288(C2×D7)⋊C4C22×C412yes—
289(C2×D7)⋊C4C22×C414yes—
290(C2×D7)⋊C4C22×C414yes—
291C4⋊Dic7C22×C411yescharacteristic
292C4⋊Dic7C22×C411yescharacteristic
293C4⋊Dic7C22×C412yes—
294C4⋊Dic7C22×C412yes—
295C4⋊Dic7C22×C412yes—
296C4⋊Dic7C22×C412yes—
297C4⋊Dic7C22×C414yes—
298C4⋊Dic7C22×C414yes—
299Dic7⋊C4C22×C412yes—
300Dic7⋊C4C22×C412yes—
301Dic7⋊C4C22×C414yes—
302Dic7⋊C4C22×C414yes—
303Dic7⋊C4C22×C414yes—
304Dic7⋊C4C22×C414yes—
305C4×Dic7C22×C412yes—
306C4×Dic7C22×C412yes—
307C4×Dic7C22×C414yes—
308C4×Dic7C22×C414yes—
309C4×Dic7C2414yes—
310C4×Dic7C2412yes—
311#1136—24no—
312#1136—22no—
313#1136—22no—
314#1136—44no—
315C2×C7⋊C8—44no—
316C2×C7⋊C8C2412yes—
317C2×C7⋊C8C2414yes—
318C2×C7⋊C8C2412yes—
319#1131—44no—
320C8×D7—44no—
321C2×#131—72no—
322C22×M16—72no—
323C23×C8C2×D712yes—
324#556—71no—
325#555—71no—
326#554—71no—
327#553—72no—
328#552—72no—
329#552—72no—
330#551—74no—
331#547—71no—
332#546—72no—
333#533—71no—
334#529—74no—
335#529—72no—
336#525—72no—
337C4×#41—72no—
338C4×#41—71no—
339C2×C4×D4C2×D711yescharacteristic
340C2×#117—72no—
341#446—74no—
342#446—72no—
343#446—72no—
344#446—72no—
345C8×Q8—72no—
346C8×Q8—72no—
347C8×Q8—72no—
348#436—72no—
349#436—74no—
350#435—74no—
351#435—74no—
352#435—74no—
353#435—74no—
354#435—74no—
355C8×D4—74no—
356C8×D4—74no—
357C8×D4—72no—
358C8×D4—74no—
359C8×D4C2×D711yescharacteristic
360C8×D4C2×D711yescharacteristic
361C8×D4C2×D712yes—
362C8×D4C2×D711yescharacteristic
363C8×D4C2×D711yescharacteristic
364C8×D4C2×D712yes—
365#433—74no—
366#433—74no—
367#433—72no—
368#433—72no—
369#432—74no—
370#431—74no—
371#431—72no—
372#431—72no—
373#424—71no—
374#424—72no—
375#424—72no—
376#424—72no—
377#424—71no—
378#424—74no—
379#424—74no—
380#424—74no—
381#423—71no—
382#423—72no—
383C2×C4⋊C8—74no—
384C2×C4⋊C8—74no—
385C2×C4⋊C8—72no—
386C2×C4⋊C8C2×D711yescharacteristic
387#408—71no—
388#408—71no—
389#407—72no—
390C2×C22⋊C8C2×D712yes—
391#405—72no—
392#405—72no—
393C4×M16—71no—
394C2×C4×C8C2×D711yescharacteristic
395C23×C7—24no—
396C23×C7—24no—
397C23×C7—42no—
398C23×C7C23×C412yes—
399C23×C7C23×C411yescharacteristic
400C23×C7C23×C412yes—
401C22×D7C23×C412yes—
402C7×D4—24no—
403C7×D4—22no—
404C7×D4#13114yescomplemented
405C2×C4×C7—24no—
406C2×C4×C7—24no—
407C2×C4×C7—24no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—41no—
414C2×C4×C7C23×C412yes—
415C2×C4×C7C23×C411yescharacteristic
416C2×C4×C7C23×C411yescharacteristic
417C2×C4×C7C23×C412yes—
418C2×C4×C7C23×C411yescharacteristic
419C2×C4×C7C23×C411yescharacteristic
420C2×C4×C7C23×C411yescharacteristic
421C2×C4×C7H(5,𝔽2)12yes—
422C2×C4×C72−1+412yes—
423C2×C4×C7C2511yescharacteristic
424C22⋊D7—24no—
425C22⋊D7—28no—
426C22⋊D7—44no—
427C2×Dic7—28no—
428C2×Dic7—44no—
429C2×Dic7C23×C412yes—
430C2×Dic7C23×C412yes—
431C2×Dic7C23×C412yes—
432C2×Dic7C23×C414yes—
433C2×Dic7C23×C414yes—
434D28—22no—
435C4×D7—24no—
436C4×D7—22no—
437C4×D7—22no—
438C4×D7—42no—
439Dic14—22no—
440Dic14—24no—
441Dic14—42no—
442C7×C8—22no—
443C7×C8—22no—
444C7×C8—21no—
445C7×C8—21no—
446C7×C8—21no—
447C7×C8—21no—
448C7⋊C8—24no—
449C7⋊C8—22no—
450C7⋊C8—22no—
451C2×#41—72no—
452C2×#41—71no—
453C22×D4C4×D711yescharacteristic
454C23×C4C22×D712yes—
455#131—284no—
456C2×M16—71no—
457C2×M16—72no—
458C2×M16—71no—
459C2×M16—74no—
460C2×M16—74no—
461C2×M16—284no—
462C22×C8—44no—
463C22×C8—74no—
464C22×C8—74no—
465C22×C8C22×D711yescharacteristic
466C22×C8C22×D712yes—
467C22×C8C22×D711yescharacteristic
468C22×C8C22×D712yes—
469C22×C8C22×D712yes—
470C22×C8C22×D712yes—
471C22×C8C22×D712yes—
472C4⋊Q8—71no—
473C4⋊Q8—71no—
474#126—74no—
475#126—74no—
476#126—74no—
477#125—74no—
478#125—72no—
479#125—72no—
480#124—72no—
481#124—74no—
482#123—74no—
483#123—74no—
484#123—74no—
485#123—74no—
486C22⋊Q8—72no—
487C22⋊Q8—72no—
488C22⋊Q8—72no—
489C22⋊Q8—72no—
490C22⋊Q8—72no—
491C22⋊Q8—74no—
492#121—74no—
493#121—72no—
494#121—72no—
495#121—72no—
496#120—74no—
497C4×Q8—72no—
498C4×Q8—71no—
499C4×Q8—71no—
500C4×Q8—72no—
501C4×Q8—72no—
502C4×D4—72no—
503C4×D4—72no—
504C4×D4—72no—
505C4×D4—74no—
506C4×D4—74no—
507C4×D4—74no—
508C4×D4—71no—
509C4×D4—71no—
510C4×D4C4×D711yescharacteristic
511C4×D4C4×D712yes—
512C4×D4C4×D711yescharacteristic
513C4×D4C22×D711yescharacteristic
514C4×D4C22×D712yes—
515C4×D4C22×D711yescharacteristic
516#117—74no—
517#117—72no—
518#117—72no—
519#117—71no—
520#117—72no—
521#117—74no—
522#117—72no—
523#117—74no—
524#117—72no—
525C2×C4⋊C4—72no—
526C2×C4⋊C4—72no—
527C2×C4⋊C4C4×D711yescharacteristic
528C2×C22⋊C4—74no—
529C2×C22⋊C4C4×D712yes—
530C2×C42—74no—
531C2×C42—72no—
532C2×C42C22×D711yescharacteristic
533C4⋊C8—74no—
534C4⋊C8—72no—
535C4⋊C8—72no—
536C4⋊C8—74no—
537C4⋊C8—74no—
538C4⋊C8—74no—
539C4⋊C8—74no—
540C4⋊C8—74no—
541C4⋊C8—72no—
542C4⋊C8—72no—
543C4⋊C8—72no—
544C4⋊C8—72no—
545C4⋊C8C22×D711yescharacteristic
546C4⋊C8C22×D711yescharacteristic
547C4⋊C8C22×D712yes—
548C22⋊C8—74no—
549C22⋊C8—74no—
550C22⋊C8—72no—
551C22⋊C8—72no—
552C22⋊C8—72no—
553C22⋊C8—72no—
554C22⋊C8C22×D712yes—
555C22⋊C8C22×D712yes—
556C22⋊C8C22×D712yes—
557C22⋊C8C22×D712yes—
558#97—74no—
559#97—74no—
560#97—72no—
561C4×C8—74no—
562C4×C8—74no—
563C4×C8—72no—
564C4×C8C22×D711yescharacteristic
565C4×C8C22×D711yescharacteristic
566C4×C8C22×D711yescharacteristic
567C4×C8C22×D711yescharacteristic
568C22×C7—22no—
569C22×C7—21no—
570C22×C7—22no—
571C22×C7—21no—
572C22×C7—22no—
573C22×C7—22no—
574C22×C7—22no—
575C22×C7—48no—
576C22×C7#52012yes—
577C22×C7C2×#13114yes—
578C22×C7C24×C411yescharacteristic
579C2×D7—22no—
580C2×D7—22no—
581C2×D7—22no—
582C4×C7—22no—
583C4×C7—22no—
584C4×C7—21no—
585C4×C7—21no—
586C4×C7—21no—
587C4×C7#52012yes—
588C4×C7C2×#13112yes—
589C4×C7C2×H(5,𝔽2)11yescharacteristic
590C4×C7C2×2−1+411yescharacteristic
591Dic7—22no—
592Dic7—24no—
593Dic7—22no—
594Dic7—24no—
595Dic7—22no—
596C24C2×C4×D712yes—
597#41—148no—
598#41—142no—
599#41—142no—
600C2×Q8—71no—
601C2×Q8—72no—
602C2×Q8—72no—
603C2×D4—24no—
604C2×D4—72no—
605C2×D4—74no—
606C2×D4—74no—
607C2×D4—71no—
608C2×D4C2×C4×D712yes—
609C2×D4C2×C4×D711yescharacteristic
610C2×D4C2×C4×D711yescharacteristic
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—74no—
614C22×C4—74no—
615C22×C4—72no—
616C22×C4—72no—
617C22×C4—72no—
618C22×C4C2×C4×D711yescharacteristic
619C22×C4C2×C4×D712yes—
620C22×C4C2×C4×D712yes—
621C22×C4C2×C4×D712yes—
622C22×C4C2×C4×D711yescharacteristic
623C22×C4C23×D712yes—
624C22×C4C23×D712yes—
625C22×C4C23×D711yescharacteristic
626M16—142no—
627M16—144no—
628M16—142no—
629M16—284no—
630M16—284no—
631C2×C8—22no—
632C2×C8—24no—
633C2×C8—22no—
634C2×C8—42no—
635C2×C8—42no—
636C2×C8—42no—
637C2×C8—42no—
638C2×C8—72no—
639C2×C8—74no—
640C2×C8—72no—
641C2×C8—284no—
642C2×C8—284no—
643C2×C8C23×D711yescharacteristic
644C2×C8C23×D712yes—
645C2×C8C23×D711yescharacteristic
646C2×C8C23×D711yescharacteristic
647C2×C8C23×D711yescharacteristic
648C2×C8C23×D712yes—
649C4⋊C4—72no—
650C4⋊C4—74no—
651C4⋊C4—74no—
652C4⋊C4—72no—
653C4⋊C4—74no—
654C4⋊C4—74no—
655C4⋊C4—71no—
656C4⋊C4—71no—
657C4⋊C4—72no—
658C4⋊C4—72no—
659C4⋊C4—74no—
660C4⋊C4—74no—
661C4⋊C4—72no—
662C4⋊C4—72no—
663C4⋊C4C2×C4×D711yescharacteristic
664C4⋊C4C2×C4×D711yescharacteristic
665C4⋊C4C2×C4×D712yes—
666C22⋊C4—72no—
667C22⋊C4—74no—
668C22⋊C4—74no—
669C22⋊C4—74no—
670C22⋊C4—74no—
671C22⋊C4—74no—
672C22⋊C4—72no—
673C22⋊C4—74no—
674C22⋊C4—72no—
675C22⋊C4—74no—
676C22⋊C4C2×C4×D712yes—
677C22⋊C4C2×C4×D712yes—
678C22⋊C4C2×C4×D712yes—
679C22⋊C4C2×C4×D712yes—
680C42—74no—
681C42—74no—
682C42—72no—
683C42—72no—
684C42—74no—
685C42—72no—
686C42C2×C4×D711yescharacteristic
687C42C2×C4×D711yescharacteristic
688C42C23×D711yescharacteristic
689C42C23×D711yescharacteristic
690C2×C7—22no—
691C2×C7—24no—
692C2×C7—42no—
693C2×C7C2×#52011yescharacteristic
694C2×C7C22×#13111yescharacteristic
695C2×C7#357311yescharacteristic
696D7—42no—
697C23—24no—
698C23—24no—
699C23—42no—
700C23—72no—
701C23C22×C4×D712yes—
702C23C22×C4×D712yes—
703C23C22×C4×D711yescharacteristic
704Q8—144no—
705Q8—142no—
706Q8—282no—
707D4—24no—
708D4—22no—
709D4—148no—
710D4—144no—
711D4—142no—
712D4—284no—
713D4#646414yescomplemented
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—41no—
723C2×C4—72no—
724C2×C4—72no—
725C2×C4—72no—
726C2×C4—74no—
727C2×C4—74no—
728C2×C4—148no—
729C2×C4—144no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—282no—
733C2×C4—284no—
734C2×C4C22×C4×D712yes—
735C2×C4C22×C4×D711yescharacteristic
736C2×C4C22×C4×D711yescharacteristic
737C2×C4C22×C4×D711yescharacteristic
738C2×C4C22×C4×D712yes—
739C2×C4C22×C4×D711yescharacteristic
740C2×C4C22×C4×D711yescharacteristic
741C2×C4#654812yes—
742C2×C4#655412yes—
743C2×C4C24×D711yescharacteristic
744C8—21no—
745C8—21no—
746C8—22no—
747C8—22no—
748C8—21no—
749C8—21no—
750C8—144no—
751C8—142no—
752C8—142no—
753C7#6027111yescharacteristic, complemented, Sylow
754C22—22no—
755C22—21no—
756C22—21no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—48no—
762C22—142no—
763C22—142no—
764C22—142no—
765C22#9023712yes—
766C22C2×#646414yes—
767C22C23×C4×D711yescharacteristic
768C4—22no—
769C4—22no—
770C4—21no—
771C4—21no—
772C4—21no—
773C4—142no—
774C4—142no—
775C4—144no—
776C4—142no—
777C4—144no—
778C4#9023712yes—
779C4C2×#646412yes—
780C4C2×#654811yescharacteristic
781C4C2×#655411yescharacteristic
782C2—22no—
783C2—24no—
784C2—42no—
785C2—282no—
786C2C2×#9023711yescharacteristic
787C2C22×#646411yescharacteristic
788C2#1174422811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D7
commutator, socleC22×C7C24×C4
FittingC2×C7×C8×D4C2
prime radical#11742832C2
cosocleC2×C4×C7C25
hypercenterC2×C8×D4D7
hypocenterC7#60271
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
2. C2×C7×C8×D4C2semidirect
3. #11741179C2semidirect
4. C2×#89874C2semidirect
5. D4×#1136C2semidirect
6. #11736855C2semidirect
7. #11736854C2semidirect
8. #11736853C2semidirect
9. #11736852C2semidirect
10. #11736851C2semidirect
11. #11736850C2semidirect
12. #11736457C2semidirect
13. #11736453C2semidirect
14. #11736041C2semidirect
15. #11736029C2semidirect
16. #11735900C2semidirect
17. #11735890C2semidirect
48. #89883C22semidirect
49. #89883C22semidirect
52. C8×C22⋊D7C22semidirect
53. C8×C22⋊D7C22semidirect
59. #89874C22semidirect
60. #89874C22semidirect
63. C2×Dic7⋊C8C22semidirect
64. C2×Dic7⋊C8C22semidirect
70. #89611C22semidirect
71. #89609C22semidirect
72. D7×C4⋊C8C22semidirect
73. #89603C22semidirect
74. #89602C22semidirect
75. #89600C22semidirect
76. #89502C22semidirect
77. #89501C22semidirect
78. #89500C22semidirect
79. (C22⋊D7)⋊C8C22semidirect
80. #89492C22semidirect
81. #89492C22semidirect
82. #89491C22semidirect
83. #89490C22semidirect
84. #89462C22semidirect
85. #89462C22semidirect
86. #89457C22semidirect
87. #89457C22semidirect
88. #89451C22semidirect
89. #89451C22semidirect
90. C8×Dic14C22semidirect
91. C8×Dic14C22semidirect
222. C2×C8×D4D7semidirect
404. C7×D4#131semidirect
713. D4#6464semidirect
753. C7#60271semidirect

Maximal subgroups

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

subgroupindex
#117428322
C2×C7×C8×D42
#117411792
C2×#898742
D4×#11362
#117368552
#117368542
#117368532
#117368522
#117368512
#117368502
#117364572
#117364532
#117360412
#117360292
#117359002
#117358902
#602717