Finite Group Databasebeta

← C2×#22600466 #32874170

Subgroups — C2×#22600466 #32874170

Order 18176.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986689C211yesmaximal, characteristic, complemented
2#22600466C2116yesmaximal, direct product factor
3C2×#17986363C211yesmaximal, characteristic, complemented
4C2×#17986315C211yesmaximal, characteristic, complemented
5C2×#17986320C211yesmaximal, characteristic, complemented
6C2×#17986306C211yesmaximal, characteristic, complemented
7C2×#17986243C211yesmaximal, characteristic, complemented
8C2×#17986226C211yesmaximal, characteristic, complemented
9C2×#17986196C211yesmaximal, characteristic, complemented
10C2×#17986161C211yesmaximal, characteristic, complemented
11C2×#17986161C211yesmaximal, characteristic, complemented
12C2×#17986104C211yesmaximal, characteristic, complemented
13C2×#17986071C211yesmaximal, characteristic, complemented
14C2×#17986000C211yesmaximal, characteristic, complemented
15C2×#17985995C211yesmaximal, characteristic, complemented
16C2×#550×C71C211yesmaximal, characteristic
17C22×#11765855C2211yescharacteristic
18C22×#11765853C2211yescharacteristic
19C22×#11765853C2211yescharacteristic
20C22×#11765849C2211yescharacteristic
21C23×C71⋊C8C2211yescharacteristic
22#17986689—24no—
23#17986689C2218yescomplemented
24C2×#14556121—21no—
25C2×#14556120C2211yescharacteristic
26C2×#14556118—21no—
27C2×#14556109—21no—
28C2×#14556107C2211yescharacteristic
29C2×#14556107C2211yescharacteristic
30C2×C4×Dic142C2211yescharacteristic
31C2×#14556087C2211yescharacteristic
32C2×#14556084—21no—
33C22×C4⋊Dic71C2211yescharacteristic
34#17986363C2218yescomplemented
35#17986320C2218yescomplemented
36#17986315C2218yescomplemented
37#17986306C2218yescomplemented
38#17986243C2218yescomplemented
39#17986226C2218yescomplemented
40#17986196C2218yescomplemented
41#17986161C2218yescomplemented
42#17986161C2218yescomplemented
43#17986104C2218yescomplemented
44#17986071C2218yescomplemented
45C2×#14556061C2211yescharacteristic
46C2×#14556059C2211yescharacteristic
47C2×#14556059C2211yescharacteristic
48C2×C4⋊(C71⋊C8)C2211yescharacteristic
49#17986000C2218yescomplemented
50#17985995C2218yescomplemented
51C2×#14556052C2211yescharacteristic
52C2×#14556052C2211yescharacteristic
53C2×#14556052C2211yescharacteristic
54C2×#14556051C2211yescharacteristic
55C2×#14556049C2211yescharacteristic
56C2×#14556049C2211yescharacteristic
57C2×#14556049C2211yescharacteristic
58C2×#14556049C2211yescharacteristic
59C2×#14556049C2211yescharacteristic
60C2×#14556049C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×C22⋊(C71⋊C8)C2211yescharacteristic
63C2×#14556039C2211yescharacteristic
64C22×#41×C71C2211yescharacteristic
65C22×#41×C71C2211yescharacteristic
66#550×C71—24no—
67#550×C71C2218yes—
68C2×#127×C71—21no—
69C2×#127×C71C2211yescharacteristic
70C2×#121×C71—21no—
71C2×#121×C71—21no—
72C2×#121×C71C2211yescharacteristic
73C2×#121×C71C2211yescharacteristic
74C2×C4×Q8×C71C2211yescharacteristic
75C2×C4×D4×C71—21no—
76C2×C4×D4×C71C2211yescharacteristic
77C22×Dic142C2311yescharacteristic
78C23×Dic71—21no—
79C2×#11765855—24no—
80C2×#11765855C2314yes—
81C2×#11765853—42no—
82C2×#11765853—42no—
83C2×#11765853C2314yes—
84C2×#11765853C2314yes—
85C2×#11765849—42no—
86C2×#11765849C2314yes—
87C22×C71⋊C8—42no—
88C22×C71⋊C8C2311yescharacteristic
89C22×C71⋊C8C2311yescharacteristic
90C22×C71⋊C8C2311yescharacteristic
91C22×C71⋊C8C2311yescharacteristic
92C22×C71⋊C8C2314yes—
93#14556121—28no—
94#14556120—22no—
95#14556120C2314yes—
96#14556118—28no—
97#14556109—28no—
98#14556107—22no—
99#14556107—22no—
100#14556107C2314yes—
101#14556107C2314yes—
102C4×Dic142—22no—
103C4×Dic142C2314yes—
104#14556087—22no—
105#14556087C2314yes—
106#14556084—28no—
107C2×C4⋊Dic71—22no—
108C2×C4⋊Dic71—21no—
109C2×C4⋊Dic71C2314yes—
110C2×C4⋊Dic71C2311yescharacteristic
111C2×C4⋊Dic71C2311yescharacteristic
112C2×C4⋊Dic71C2311yescharacteristic
113C2×Dic71⋊C4—21no—
114C2×Dic71⋊C4—21no—
115C2×Dic71⋊C4—21no—
116C2×Dic71⋊C4—21no—
117C2×Dic71⋊C4—21no—
118C2×C22⋊Dic71—21no—
119C2×C22⋊Dic71—21no—
120C2×C22⋊Dic71—21no—
121C2×C4×Dic71—21no—
122C2×C4×Dic71—21no—
123#14556061C2314yes—
124#14556059C2314yes—
125#14556059C2314yes—
126C4⋊(C71⋊C8)C2314yes—
127#14556052C2314yes—
128#14556052C2314yes—
129#14556052C2314yes—
130#14556051C2314yes—
131#14556049C2314yes—
132#14556049C2314yes—
133#14556049C2314yes—
134#14556049C2314yes—
135#14556049C2314yes—
136#14556049C2314yes—
137C22⋊(C71⋊C8)C2314yes—
138C22⋊(C71⋊C8)C2314yes—
139#14556039C2314yes—
140C2×#41×C71—22no—
141C2×#41×C71—22no—
142C2×#41×C71—24no—
143C2×#41×C71—24no—
144C2×#41×C71—42no—
145C2×#41×C71—42no—
146C2×#41×C71C2314yes—
147C2×#41×C71C2314yes—
148C22×Q8×C71C2311yescharacteristic
149C22×D4×C71—21no—
150C22×D4×C71—21no—
151C22×D4×C71—21no—
152C22×D4×C71—21no—
153C22×D4×C71—21no—
154C22×D4×C71—21no—
155C22×D4×C71D411yescharacteristic
156C22×D4×C71C2311yescharacteristic
157C22×D4×C71C2311yescharacteristic
158C23×C4×C71—21no—
159C23×C4×C71—21no—
160C23×C4×C71C2311yescharacteristic
161C23×C4×C71C2311yescharacteristic
162#127×C71—28no—
163#127×C71—22no—
164#127×C71C2314yes—
165#121×C71—22no—
166#121×C71—22no—
167#121×C71—28no—
168#121×C71—28no—
169#121×C71C2314yes—
170#121×C71C2314yes—
171C4×Q8×C71—22no—
172C4×Q8×C71C2314yes—
173C4×D4×C71—28no—
174C4×D4×C71D414yes—
175C4×D4×C71C2314yes—
176C2×C4⋊C4×C71—21no—
177C2×C4⋊C4×C71D411yescharacteristic
178C2×C4⋊C4×C71C2311yescharacteristic
179C2×C22⋊C4×C71—21no—
180C2×C22⋊C4×C71—21no—
181C2×C22⋊C4×C71D411yescharacteristic
182C2×C22⋊C4×C71D411yescharacteristic
183C2×C42×C71—21no—
184C2×C42×C71C2311yescharacteristic
185C2×Dic142—22no—
186C2×Dic142—22no—
187C2×Dic142—21no—
188C2×Dic142C2412yes—
189C22×Dic71—21no—
190C22×Dic71—21no—
191C22×Dic71—24no—
192C22×Dic71—21no—
193C22×Dic71—21no—
194C22×Dic71—44no—
195#11765855—28no—
196#11765853—44no—
197#11765853—44no—
198#11765849—44no—
199C2×C71⋊C8—22no—
200C2×C71⋊C8—22no—
201C2×C71⋊C8—22no—
202C2×C71⋊C8—22no—
203C2×C71⋊C8—44no—
204C2×C71⋊C8C2412yes—
205C2×C71⋊C8C2412yes—
206C2×C71⋊C8C2412yes—
207C2×C71⋊C8C2412yes—
208C4⋊Dic71—21no—
209C4⋊Dic71—21no—
210C4⋊Dic71—24no—
211C4⋊Dic71—21no—
212C4⋊Dic71C2412yes—
213C4⋊Dic71C2412yes—
214C4⋊Dic71C2412yes—
215Dic71⋊C4—24no—
216Dic71⋊C4—24no—
217Dic71⋊C4—24no—
218Dic71⋊C4—24no—
219Dic71⋊C4—24no—
220C22⋊Dic71—24no—
221C22⋊Dic71—24no—
222C22⋊Dic71—24no—
223C4×Dic71—24no—
224C4×Dic71—24no—
225C24×C71—21no—
226C24×C71—21no—
227C24×C71C2×D411yescharacteristic
228C24×C71C2×D411yescharacteristic
229#41×C71—28no—
230#41×C71—28no—
231#41×C71—44no—
232#41×C71—44no—
233#41×C71—48no—
234#41×C71—48no—
235C2×Q8×C71—21no—
236C2×Q8×C71—22no—
237C2×Q8×C71#4114yes—
238C2×Q8×C71C2412yes—
239C2×D4×C71—24no—
240C2×D4×C71—24no—
241C2×D4×C71—24no—
242C2×D4×C71—24no—
243C2×D4×C71—24no—
244C2×D4×C71—21no—
245C2×D4×C71—21no—
246C2×D4×C71—24no—
247C2×D4×C71—22no—
248C2×D4×C71—22no—
249C2×D4×C71—22no—
250C2×D4×C71—22no—
251C2×D4×C71—42no—
252C2×D4×C71—44no—
253C2×D4×C71—44no—
254C2×D4×C71—44no—
255C2×D4×C71—82no—
256C2×D4×C71—82no—
257C2×D4×C71—82no—
258C2×D4×C71C2×D414yes—
259C2×D4×C71C2412yes—
260C2×D4×C71C2412yes—
261C22×C4×C71—21no—
262C22×C4×C71—22no—
263C22×C4×C71—22no—
264C22×C4×C71—22no—
265C22×C4×C71—22no—
266C22×C4×C71—21no—
267C22×C4×C71—24no—
268C22×C4×C71—24no—
269C22×C4×C71—44no—
270C22×C4×C71—44no—
271C22×C4×C71C2×D411yescharacteristic
272C22×C4×C71C2×D411yescharacteristic
273C22×C4×C71C2×D411yescharacteristic
274C22×C4×C71C2×D411yescharacteristic
275C22×C4×C71C2×D412yes—
276C22×C4×C71C2×D412yes—
277C22×C4×C71C2412yes—
278C22×C4×C71C2412yes—
279C22×C4×C71C2411yescharacteristic
280C4⋊C4×C71—24no—
281C4⋊C4×C71—21no—
282C4⋊C4×C71C2×D414yes—
283C4⋊C4×C71C2412yes—
284C22⋊C4×C71—24no—
285C22⋊C4×C71—24no—
286C22⋊C4×C71C2×D414yes—
287C22⋊C4×C71C2×D414yes—
288C42×C71—24no—
289C42×C71C2×D412yes—
290C42×C71C2412yes—
291C23×C71—22no—
292C23×C71—22no—
293C23×C71—22no—
294C23×C71—22no—
295C23×C71—22no—
296C23×C71—22no—
297C23×C71—22no—
298C23×C71—22no—
299C23×C71—42no—
300C23×C71—42no—
301C23×C71—42no—
302C23×C71—42no—
303C23×C71—42no—
304C23×C71—42no—
305C23×C71C22×D412yes—
306C23×C71C22×D412yes—
307C23×C71C22×D411yescharacteristic
308Q8×C71—24no—
309Q8×C71—22no—
310Q8×C71C2×#4114yes—
311D4×C71—22no—
312D4×C71—22no—
313D4×C71—22no—
314D4×C71—22no—
315D4×C71—44no—
316D4×C71—48no—
317D4×C71—48no—
318D4×C71—48no—
319D4×C71—42no—
320D4×C71—42no—
321D4×C71—84no—
322D4×C71—84no—
323D4×C71—84no—
324C2×C4×C71—22no—
325C2×C4×C71—22no—
326C2×C4×C71—24no—
327C2×C4×C71—22no—
328C2×C4×C71—22no—
329C2×C4×C71—22no—
330C2×C4×C71—24no—
331C2×C4×C71—24no—
332C2×C4×C71—22no—
333C2×C4×C71—22no—
334C2×C4×C71—22no—
335C2×C4×C71—22no—
336C2×C4×C71—22no—
337C2×C4×C71—48no—
338C2×C4×C71—48no—
339C2×C4×C71—42no—
340C2×C4×C71C22×D412yes—
341C2×C4×C71C22×D412yes—
342C2×C4×C71C22×D412yes—
343C2×C4×C71C22×D412yes—
344C2×C4×C71C22×D411yescharacteristic
345C2×C4×C71C2×#4112yes—
346C2×C4×C71H(5,𝔽2)12yes—
347C2×C4×C71C2511yescharacteristic
348C2×Dic71—22no—
349C2×Dic71—22no—
350C2×Dic71—22no—
351C2×Dic71—22no—
352C2×Dic71—48no—
353C2×Dic71—42no—
354C2×Dic71—42no—
355C2×Dic71—42no—
356C2×Dic71—42no—
357Dic142—22no—
358Dic142—22no—
359Dic142—42no—
360C71⋊C8—22no—
361C71⋊C8—22no—
362C71⋊C8—22no—
363C71⋊C8—22no—
364C22×C71—22no—
365C22×C71—22no—
366C22×C71—22no—
367C22×C71—22no—
368C22×C71—22no—
369C22×C71—22no—
370C22×C71—44no—
371C22×C71—44no—
372C22×C71—42no—
373C22×C71—42no—
374C22×C71—42no—
375C22×C71—42no—
376C22×C71—42no—
377C22×C71—42no—
378C22×C71—84no—
379C22×C71—84no—
380C22×C71#54612yes—
381C22×C71#57512yes—
382C22×C71#57712yes—
383C22×C71C23×D411yescharacteristic
384C4×C71—22no—
385C4×C71—22no—
386C4×C71—24no—
387C4×C71—22no—
388C4×C71—22no—
389C4×C71—42no—
390C4×C71#54612yes—
391C4×C71C22×#4111yescharacteristic
392C4×C71C2×H(5,𝔽2)11yescharacteristic
393Dic71—42no—
394Dic71—42no—
395Dic71—42no—
396Dic71—42no—
397C2×#3317—711nomaximal, Sylow
398C2×C71—42no—
399C2×C71—42no—
400C2×C71—82no—
401C2×C71—82no—
402C2×C71#331714yescomplemented
403C2×C71C2×#54611yescharacteristic
404C2×C71C2×#57511yescharacteristic
405C2×C71C2×#57711yescharacteristic
406C2×#552—711no—
407C2×#550D7111yescharacteristic
408#3317—7116no—
409C2×#490—711no—
410C2×#481—711no—
411C2×#482—711no—
412C2×#479—711no—
413C2×#468—711no—
414C2×#465—711no—
415C2×#460—711no—
416C2×#452—711no—
417C2×#452—711no—
418C2×#441—711no—
419C2×#435—711no—
420C2×#417—711no—
421C2×#416—711no—
422C71C2×#331711yescharacteristic, complemented, Sylow
423C22×#41C2×D7111yescharacteristic
424C22×#41C2×D7111yescharacteristic
425C22×Q16—711no—
426C22×SD16—711no—
427C22×SD16—711no—
428C22×M16—711no—
429C23×C8—711no—
430#552—718no—
431#552—1424no—
432#550—24no—
433#550C2×D7118yes—
434C2×#127—21no—
435C2×#127C2×D7111yescharacteristic
436C2×#126—1421no—
437C2×#125—711no—
438C2×#125—1421no—
439C2×#123—1421no—
440C2×C22⋊Q8—711no—
441C2×C22⋊Q8—711no—
442C2×#121—21no—
443C2×#121—21no—
444C2×#121C2×D7111yescharacteristic
445C2×#121C2×D7111yescharacteristic
446C2×C4×Q8—711no—
447C2×C4×Q8C2×D7111yescharacteristic
448C2×C4×D4—21no—
449C2×C4×D4C2×D7111yescharacteristic
450C2×#117—711no—
451C2×#117—1421no—
452C22×C4⋊C4—711no—
453#490—718no—
454#482—718no—
455#481—718no—
456#479—718no—
457#468—718no—
458#465—718no—
459#460—718no—
460#452—718no—
461#452—718no—
462#441—718no—
463#435—718no—
464C2×#107—711no—
465C2×#106—711no—
466C2×#106—711no—
467C2×C4⋊C8—711no—
468#417—718no—
469#416—718no—
470C2×#103—711no—
471C2×#103—711no—
472C2×#103—711no—
473C2×#103—711no—
474C2×#102—711no—
475C2×#102—711no—
476C2×#102—711no—
477C2×#102—711no—
478C2×#102—711no—
479C2×#102—711no—
480C2×C22⋊C8—711no—
481C2×C22⋊C8—711no—
482C2×#97—711no—
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—24no—
486C2×#41—24no—
487C2×#41—42no—
488C2×#41—42no—
489C2×#41C22×D7114yes—
490C2×#41C22×D7114yes—
491C22×Q8—711no—
492C22×Q8C22×D7111yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C22⋊D7111yescharacteristic
500C22×D4C22×D7111yescharacteristic
501C22×D4C22×D7111yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—1421no—
505C23×C4C22×D7111yescharacteristic
506C23×C4C22×D7111yescharacteristic
507C2×Q16—714no—
508C2×Q16—1424no—
509C2×SD16—2842no—
510C2×SD16—2842no—
511C2×SD16—714no—
512C2×SD16—714no—
513C2×M16—2842no—
514C2×M16—714no—
515C22×C8—2842no—
516C22×C8—714no—
517C22×C8—711no—
518C22×C8—711no—
519C22×C8—711no—
520C22×C8—711no—
521#127—28no—
522#127—22no—
523#127C22×D7114yes—
524#126—1428no—
525#125—714no—
526#125—1428no—
527#125—1422no—
528#123—1428no—
529C22⋊Q8—714no—
530C22⋊Q8—714no—
531C22⋊Q8—1422no—
532C22⋊Q8—1422no—
533#121—22no—
534#121—22no—
535#121—28no—
536#121—28no—
537#121C22×D7114yes—
538#121C22×D7114yes—
539C4×Q8—22no—
540C4×Q8—714no—
541C4×Q8—1422no—
542C4×Q8C22×D7114yes—
543C4×D4—28no—
544C4×D4C22⋊D7114yes—
545C4×D4C22×D7114yes—
546#117—714no—
547#117—1422no—
548#117—1428no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—711no—
551C2×C4⋊C4—711no—
552C2×C4⋊C4—714no—
553C2×C4⋊C4—711no—
554C2×C4⋊C4—1421no—
555C2×C4⋊C4—1422no—
556C2×C4⋊C4—1421no—
557C2×C4⋊C4—1421no—
558C2×C4⋊C4—1421no—
559C2×C4⋊C4—1421no—
560C2×C4⋊C4—1421no—
561C2×C4⋊C4C22⋊D7111yescharacteristic
562C2×C4⋊C4C22×D7111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—1421no—
566C2×C22⋊C4—1421no—
567C2×C22⋊C4—1421no—
568C2×C22⋊C4C22⋊D7111yescharacteristic
569C2×C22⋊C4C22⋊D7111yescharacteristic
570C2×C42—21no—
571C2×C42—1421no—
572C2×C42—1421no—
573C2×C42C22×D7111yescharacteristic
574#107—714no—
575#106—714no—
576#106—714no—
577C4⋊C8—714no—
578#103—714no—
579#103—714no—
580#103—714no—
581#103—714no—
582#102—714no—
583#102—714no—
584#102—714no—
585#102—714no—
586#102—714no—
587#102—714no—
588C22⋊C8—714no—
589C22⋊C8—714no—
590#97—714no—
591C24—21no—
592C24—21no—
593C24C2×C22⋊D7111yescharacteristic
594C24C2×C22⋊D7111yescharacteristic
595#41—28no—
596#41—28no—
597#41—44no—
598#41—44no—
599#41—48no—
600#41—48no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—712no—
604C2×Q8—1422no—
605C2×Q8—1422no—
606C2×Q8—1421no—
607C2×Q8#1176586414yes—
608C2×Q8C23×D7112yes—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—24no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—24no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—42no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—44no—
625C2×D4—82no—
626C2×D4—82no—
627C2×D4—82no—
628C2×D4C2×C22⋊D7114yes—
629C2×D4C23×D7112yes—
630C2×D4C23×D7112yes—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—24no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—2844no—
642C22×C4—1424no—
643C22×C4—1421no—
644C22×C4—1421no—
645C22×C4—1421no—
646C22×C4—1421no—
647C22×C4C2×C22⋊D7112yes—
648C22×C4C2×C22⋊D7112yes—
649C22×C4C2×C22⋊D7111yescharacteristic
650C22×C4C2×C22⋊D7111yescharacteristic
651C22×C4C2×C22⋊D7111yescharacteristic
652C22×C4C2×C22⋊D7111yescharacteristic
653C22×C4C23×D7112yes—
654C22×C4C23×D7112yes—
655C22×C4C23×D7111yescharacteristic
656Q16—1428no—
657SD16—2844no—
658SD16—2844no—
659M16—2844no—
660C2×C8—2844no—
661C2×C8—712no—
662C2×C8—712no—
663C2×C8—712no—
664C2×C8—712no—
665C2×C8—1422no—
666C2×C8—1422no—
667C2×C8—1422no—
668C2×C8—1422no—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—712no—
672C4⋊C4—712no—
673C4⋊C4—712no—
674C4⋊C4—1424no—
675C4⋊C4—1424no—
676C4⋊C4—1424no—
677C4⋊C4—1424no—
678C4⋊C4—1424no—
679C4⋊C4—1421no—
680C4⋊C4—1421no—
681C4⋊C4—1424no—
682C4⋊C4—1421no—
683C4⋊C4C2×C22⋊D7114yes—
684C4⋊C4C23×D7112yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—1424no—
688C22⋊C4—1424no—
689C22⋊C4—1424no—
690C22⋊C4C2×C22⋊D7114yes—
691C22⋊C4C2×C22⋊D7114yes—
692C42—24no—
693C42—1424no—
694C42—1424no—
695C42C2×C22⋊D7112yes—
696C42C23×D7112yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23C22×C22⋊D7112yes—
712C23C22×C22⋊D7112yes—
713C23C22×C22⋊D7111yescharacteristic
714Q8—22no—
715Q8—24no—
716Q8—2842no—
717Q8—1422no—
718Q8—1422no—
719Q8C2×#1176586414yes—
720D4—22no—
721D4—22no—
722D4—22no—
723D4—22no—
724D4—44no—
725D4—48no—
726D4—48no—
727D4—48no—
728D4—42no—
729D4—42no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—48no—
747C2×C4—48no—
748C2×C4—42no—
749C2×C4—2848no—
750C2×C4—2842no—
751C2×C4—2842no—
752C2×C4—2842no—
753C2×C4—2842no—
754C2×C4—1422no—
755C2×C4—1422no—
756C2×C4—1422no—
757C2×C4—1422no—
758C2×C4C22×C22⋊D7112yes—
759C2×C4C22×C22⋊D7112yes—
760C2×C4C22×C22⋊D7112yes—
761C2×C4C22×C22⋊D7112yes—
762C2×C4C22×C22⋊D7111yescharacteristic
763C2×C4C2×#1176586412yes—
764C2×C4#1455617312yes—
765C2×C4C24×D7111yescharacteristic
766C8—1422no—
767C8—1422no—
768C8—1422no—
769C8—1422no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—84no—
785C22—84no—
786C22#1798664312yes—
787C22#1798679712yes—
788C22#1798681012yes—
789C22C23×C22⋊D7111yescharacteristic
790C4—22no—
791C4—22no—
792C4—24no—
793C4—22no—
794C4—22no—
795C4—42no—
796C4—2842no—
797C4—2842no—
798C4—2842no—
799C4—2842no—
800C4#1798664312yes—
801C4C22×#1176586411yescharacteristic
802C4C2×#1455617311yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—82no—
807C2#2260046614yesdirect product factor
808C2C2×#1798664311yescharacteristic
809C2C2×#1798679711yescharacteristic
810C2C2×#1798681011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
Fitting, prime radicalC2×#550×C71C2
socleC23×C71C22×D4
hypercenterC2×#550D71
hypocenterC71C2×#3317
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#17986689C2semidirect
2. #22600466C2direct (N × H)
3. C2×#17986363C2semidirect
4. C2×#17986315C2semidirect
5. C2×#17986320C2semidirect
6. C2×#17986306C2semidirect
7. C2×#17986243C2semidirect
8. C2×#17986226C2semidirect
9. C2×#17986196C2semidirect
10. C2×#17986161C2semidirect
11. C2×#17986161C2semidirect
12. C2×#17986104C2semidirect
13. C2×#17986071C2semidirect
14. C2×#17986000C2semidirect
15. C2×#17985995C2semidirect
23. #17986689C22semidirect
34. #17986363C22semidirect
35. #17986320C22semidirect
36. #17986315C22semidirect
37. #17986306C22semidirect
38. #17986243C22semidirect
39. #17986226C22semidirect
40. #17986196C22semidirect
41. #17986161C22semidirect
42. #17986161C22semidirect
43. #17986104C22semidirect
44. #17986071C22semidirect
49. #17986000C22semidirect
50. #17985995C22semidirect
402. C2×C71#3317semidirect
422. C71C2×#3317semidirect
807. C2#22600466direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866892
#226004662
C2×#179863632
C2×#179863152
C2×#179863202
C2×#179863062
C2×#179862432
C2×#179862262
C2×#179861962
C2×#179861612
C2×#179861042
C2×#179860712
C2×#179860002
C2×#179859952
C2×#550×C712
C2×#331771