Finite Group Databasebeta

← C2×#22600451 #32874042

Subgroups — C2×#22600451 #32874042

Order 18176.

2158 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
1C2×#17986706C211yesmaximal, characteristic, complemented
2#22600451C2116yesmaximal, direct product factor
3C2×#17986358C211yesmaximal, characteristic, complemented
4C2×#17986315C211yesmaximal, characteristic, complemented
5C2×#17986327C211yesmaximal, characteristic, complemented
6C2×#17986284C211yesmaximal, characteristic, complemented
7C2×#17986255C211yesmaximal, characteristic, complemented
8C2×#17986226C211yesmaximal, characteristic, complemented
9C2×#17986218C211yesmaximal, characteristic, complemented
10C2×#17986161C211yesmaximal, characteristic, complemented
11C2×#17986155C211yesmaximal, characteristic, complemented
12C2×#17986104C211yesmaximal, characteristic, complemented
13C2×#17986071C211yesmaximal, characteristic, complemented
14C2×#17986000C211yesmaximal, characteristic, complemented
15C22×#14556052C211yesmaximal, characteristic, complemented
16C2×#548×C71C211yesmaximal, characteristic
17C22×#11765855C2211yescharacteristic
18C22×#11765855C2211yescharacteristic
19C22×#11765853C2211yescharacteristic
20C22×#11765849C2211yescharacteristic
21C23×C71⋊C8C2211yescharacteristic
22#17986706—24no—
23#17986706C2218yescomplemented
24C2×#14556128C2211yescharacteristic
25C2×#14556119—21no—
26C2×#14556107C2211yescharacteristic
27C2×#14556107C2211yescharacteristic
28C2×#14556105—21no—
29C2×#14556105—21no—
30C2×C4×Dic142C2211yescharacteristic
31C2×D4×Dic71—21no—
32C22×C4⋊Dic71C2211yescharacteristic
33C22×C4⋊Dic71C2211yescharacteristic
34#17986358C2218yescomplemented
35#17986327C2218yescomplemented
36#17986315C2218yescomplemented
37#17986284C2218yescomplemented
38#17986255C2218yescomplemented
39#17986226C2218yescomplemented
40#17986218C2218yescomplemented
41#17986161C2218yescomplemented
42#17986155C2218yescomplemented
43#17986104C2218yescomplemented
44#17986071C2218yescomplemented
45C2×#14556059C2211yescharacteristic
46C2×#14556059C2211yescharacteristic
47C2×#14556059C2211yescharacteristic
48C2×C4⋊(C71⋊C8)C2211yescharacteristic
49#17986000C2218yescomplemented
50C2×#14556052C2211yescharacteristic
51C2×#14556052C2211yescharacteristic
52C2×#14556052C2211yescharacteristic
53C2×#14556052C2211yescharacteristic
54C2×#14556052C2211yescharacteristic
55C2×#14556052C2211yescharacteristic
56C2×#14556052C2218yescomplemented
57C2×#14556051C2211yescharacteristic
58C2×#14556049C2211yescharacteristic
59C2×#14556049C2211yescharacteristic
60C2×#14556049C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×C22⋊(C71⋊C8)C2211yescharacteristic
63C2×#14556039C2211yescharacteristic
64C22×#41×C71C2211yescharacteristic
65C23×Q8×C71C2211yescharacteristic
66#548×C71—24no—
67#548×C71C2218yes—
68C2×#124×C71—21no—
69C2×#124×C71C2211yescharacteristic
70C2×C22⋊Q8×C71—21no—
71C2×C22⋊Q8×C71C2211yescharacteristic
72C2×#121×C71—21no—
73C2×#121×C71C2211yescharacteristic
74C2×C4×Q8×C71C2211yescharacteristic
75C2×C4×D4×C71—21no—
76C2×C4×D4×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142C2311yescharacteristic
79C23×Dic71—21no—
80C23×Dic71—21no—
81C2×#11765855—24no—
82C2×#11765855—42no—
83C2×#11765855C2314yes—
84C2×#11765855C2314yes—
85C2×#11765853—42no—
86C2×#11765853C2314yes—
87C2×#11765849—42no—
88C2×#11765849C2314yes—
89C22×C71⋊C8—42no—
90C22×C71⋊C8C2311yescharacteristic
91C22×C71⋊C8C2311yescharacteristic
92C22×C71⋊C8C2311yescharacteristic
93C22×C71⋊C8C2311yescharacteristic
94C22×C71⋊C8C2314yes—
95#14556128—22no—
96#14556128C2314yes—
97#14556119—28no—
98#14556107—22no—
99#14556107—22no—
100#14556107C2314yes—
101#14556107C2314yes—
102#14556105—28no—
103#14556105—28no—
104C4×Dic142—22no—
105C4×Dic142C2314yes—
106D4×Dic71—28no—
107C2×C4⋊Dic71—22no—
108C2×C4⋊Dic71—22no—
109C2×C4⋊Dic71—21no—
110C2×C4⋊Dic71—21no—
111C2×C4⋊Dic71—21no—
112C2×C4⋊Dic71C2314yes—
113C2×C4⋊Dic71C2314yes—
114C2×C4⋊Dic71C2311yescharacteristic
115C2×C4⋊Dic71C2311yescharacteristic
116C2×C4⋊Dic71C2311yescharacteristic
117C2×Dic71⋊C4—21no—
118C2×Dic71⋊C4—21no—
119C2×Dic71⋊C4—21no—
120C2×C22⋊Dic71—21no—
121C2×C22⋊Dic71—21no—
122C2×C4×Dic71—21no—
123#14556059C2314yes—
124#14556059C2314yes—
125#14556059C2314yes—
126C4⋊(C71⋊C8)C2314yes—
127#14556052C2314yes—
128#14556052C2314yes—
129#14556052C2314yes—
130#14556052C2314yes—
131#14556052C2314yes—
132#14556052C2314yes—
133#14556051C2314yes—
134#14556049C2314yes—
135#14556049C2314yes—
136#14556049C2314yes—
137C22⋊(C71⋊C8)C2314yes—
138C22⋊(C71⋊C8)C2314yes—
139#14556039C2314yes—
140C2×#41×C71—22no—
141C2×#41×C71—24no—
142C2×#41×C71—42no—
143C2×#41×C71C2314yes—
144C22×Q8×C71—21no—
145C22×Q8×C71—22no—
146C22×Q8×C71—24no—
147C22×Q8×C71—42no—
148C22×Q8×C71C2311yescharacteristic
149C22×Q8×C71C2314yes—
150C22×Q8×C71C2311yescharacteristic
151C22×D4×C71—21no—
152C22×D4×C71—21no—
153C22×D4×C71D411yescharacteristic
154C22×D4×C71C2311yescharacteristic
155C23×C4×C71—21no—
156C23×C4×C71—21no—
157C23×C4×C71C2311yescharacteristic
158C23×C4×C71C2311yescharacteristic
159#124×C71—28no—
160#124×C71—22no—
161#124×C71C2314yes—
162C22⋊Q8×C71—22no—
163C22⋊Q8×C71—28no—
164C22⋊Q8×C71C2314yes—
165#121×C71—28no—
166#121×C71—22no—
167#121×C71C2314yes—
168C4×Q8×C71—22no—
169C4×Q8×C71C2314yes—
170C4×D4×C71—28no—
171C4×D4×C71D414yes—
172C4×D4×C71C2314yes—
173C2×C4⋊C4×C71—21no—
174C2×C4⋊C4×C71—21no—
175C2×C4⋊C4×C71D411yescharacteristic
176C2×C4⋊C4×C71C2311yescharacteristic
177C2×C22⋊C4×C71—21no—
178C2×C22⋊C4×C71—21no—
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×Dic142—24no—
189C2×Dic142—82no—
190C2×Dic142C2412yes—
191C22×Dic71—21no—
192C22×Dic71—21no—
193C22×Dic71—21no—
194C22×Dic71—21no—
195C22×Dic71—24no—
196C22×Dic71—24no—
197C22×Dic71—82no—
198C22×Dic71—82no—
199#11765855—28no—
200#11765855—44no—
201#11765853—44no—
202#11765849—44no—
203C2×C71⋊C8—22no—
204C2×C71⋊C8—22no—
205C2×C71⋊C8—22no—
206C2×C71⋊C8—22no—
207C2×C71⋊C8—44no—
208C2×C71⋊C8C2412yes—
209C2×C71⋊C8C2412yes—
210C2×C71⋊C8C2412yes—
211C2×C71⋊C8C2412yes—
212C4⋊Dic71—21no—
213C4⋊Dic71—24no—
214C4⋊Dic71—24no—
215C4⋊Dic71—21no—
216C4⋊Dic71—21no—
217C4⋊Dic71—24no—
218C4⋊Dic71C2412yes—
219C4⋊Dic71C2412yes—
220C4⋊Dic71C2412yes—
221Dic71⋊C4—24no—
222Dic71⋊C4—24no—
223Dic71⋊C4—24no—
224C22⋊Dic71—24no—
225C22⋊Dic71—24no—
226C4×Dic71—24no—
227C24×C71—21no—
228C24×C71C2×D411yescharacteristic
229C24×C71C2×D411yescharacteristic
230#41×C71—28no—
231#41×C71—44no—
232#41×C71—48no—
233C2×Q8×C71—21no—
234C2×Q8×C71—24no—
235C2×Q8×C71—21no—
236C2×Q8×C71—22no—
237C2×Q8×C71—28no—
238C2×Q8×C71—22no—
239C2×Q8×C71—22no—
240C2×Q8×C71—44no—
241C2×Q8×C71—44no—
242C2×Q8×C71—48no—
243C2×Q8×C71#4114yes—
244C2×Q8×C71C2412yes—
245C2×Q8×C71C2412yes—
246C2×D4×C71—24no—
247C2×D4×C71—24no—
248C2×D4×C71—24no—
249C2×D4×C71—21no—
250C2×D4×C71—22no—
251C2×D4×C71—22no—
252C2×D4×C71—44no—
253C2×D4×C71—44no—
254C2×D4×C71C2×D414yes—
255C2×D4×C71C2412yes—
256C22×C4×C71—21no—
257C22×C4×C71—22no—
258C22×C4×C71—22no—
259C22×C4×C71—22no—
260C22×C4×C71—22no—
261C22×C4×C71—21no—
262C22×C4×C71—21no—
263C22×C4×C71—24no—
264C22×C4×C71—24no—
265C22×C4×C71—44no—
266C22×C4×C71—44no—
267C22×C4×C71C2×D411yescharacteristic
268C22×C4×C71C2×D411yescharacteristic
269C22×C4×C71C2×D411yescharacteristic
270C22×C4×C71C2×D411yescharacteristic
271C22×C4×C71C2×D412yes—
272C22×C4×C71C2×D412yes—
273C22×C4×C71C2412yes—
274C22×C4×C71C2412yes—
275C22×C4×C71C2411yescharacteristic
276C4⋊C4×C71—24no—
277C4⋊C4×C71—24no—
278C4⋊C4×C71—21no—
279C4⋊C4×C71C2×D414yes—
280C4⋊C4×C71C2412yes—
281C22⋊C4×C71—24no—
282C22⋊C4×C71—24no—
283C22⋊C4×C71—24no—
284C22⋊C4×C71—24no—
285C22⋊C4×C71C2×D414yes—
286C22⋊C4×C71C2×D414yes—
287C42×C71—24no—
288C42×C71C2×D412yes—
289C42×C71C2412yes—
290C23×C71—22no—
291C23×C71—22no—
292C23×C71—22no—
293C23×C71—22no—
294C23×C71—22no—
295C23×C71—22no—
296C23×C71—42no—
297C23×C71—42no—
298C23×C71—42no—
299C23×C71#13714yes—
300C23×C71C22×D412yes—
301C23×C71C22×D412yes—
302C23×C71C22×D411yescharacteristic
303Q8×C71—24no—
304Q8×C71—22no—
305Q8×C71—22no—
306Q8×C71—22no—
307Q8×C71—48no—
308Q8×C71—42no—
309Q8×C71C2×#4114yes—
310D4×C71—28no—
311D4×C71—22no—
312D4×C71—22no—
313D4×C71—48no—
314D4×C71—48no—
315D4×C71—42no—
316C2×C4×C71—22no—
317C2×C4×C71—22no—
318C2×C4×C71—24no—
319C2×C4×C71—22no—
320C2×C4×C71—22no—
321C2×C4×C71—22no—
322C2×C4×C71—24no—
323C2×C4×C71—24no—
324C2×C4×C71—22no—
325C2×C4×C71—22no—
326C2×C4×C71—22no—
327C2×C4×C71—22no—
328C2×C4×C71—22no—
329C2×C4×C71—22no—
330C2×C4×C71—48no—
331C2×C4×C71—48no—
332C2×C4×C71—42no—
333C2×C4×C71—42no—
334C2×C4×C71C22×D412yes—
335C2×C4×C71C22×D412yes—
336C2×C4×C71C22×D412yes—
337C2×C4×C71C22×D412yes—
338C2×C4×C71C22×D411yescharacteristic
339C2×C4×C71C2×#4112yes—
340C2×C4×C71H(5,𝔽2)12yes—
341C2×C4×C71C2511yescharacteristic
342C2×Dic71—22no—
343C2×Dic71—22no—
344C2×Dic71—22no—
345C2×Dic71—22no—
346C2×Dic71—42no—
347C2×Dic71—42no—
348C2×Dic71—42no—
349C2×Dic71—42no—
350C2×Dic71—84no—
351C2×Dic71—84no—
352Dic142—22no—
353Dic142—22no—
354Dic142—42no—
355Dic142—84no—
356C71⋊C8—22no—
357C71⋊C8—22no—
358C71⋊C8—22no—
359C71⋊C8—22no—
360C22×C71—22no—
361C22×C71—28no—
362C22×C71—22no—
363C22×C71—22no—
364C22×C71—22no—
365C22×C71—22no—
366C22×C71—44no—
367C22×C71—42no—
368C22×C71—42no—
369C22×C71—42no—
370C22×C71—84no—
371C22×C71#54612yes—
372C22×C71C2×#13714yes—
373C22×C71C2×#13712yes—
374C22×C71#57712yes—
375C22×C71C23×D411yescharacteristic
376C4×C71—22no—
377C4×C71—22no—
378C4×C71—24no—
379C4×C71—22no—
380C4×C71—22no—
381C4×C71—42no—
382C4×C71—42no—
383C4×C71#54612yes—
384C4×C71C22×#4111yescharacteristic
385C4×C71C2×H(5,𝔽2)11yescharacteristic
386Dic71—42no—
387Dic71—42no—
388Dic71—42no—
389Dic71—42no—
390C2×#3316—711nomaximal, Sylow
391C2×C71—24no—
392C2×C71—42no—
393C2×C71—82no—
394C2×C71#331614yescomplemented
395C2×C71C2×#54611yescharacteristic
396C2×C71C22×#13711yescharacteristic
397C2×C71C2×#57711yescharacteristic
398C2×#554—711no—
399C2×#548D7111yescharacteristic
400#3316—7116no—
401C2×#489—711no—
402C2×#481—711no—
403C2×#483—711no—
404C2×#475—711no—
405C2×#470—711no—
406C2×#465—711no—
407C2×#464—711no—
408C2×#452—711no—
409C2×#451—711no—
410C2×#441—711no—
411C2×#435—711no—
412C2×#417—711no—
413C22×#103—711no—
414C71C2×#331611yescharacteristic, complemented, Sylow
415C22×#41C2×D7111yescharacteristic
416C23×Q8C2×D7111yescharacteristic
417C22×Q16—711no—
418C22×Q16—711no—
419C22×SD16—711no—
420C22×M16—711no—
421C23×C8—711no—
422#554—718no—
423#554—1424no—
424#548—24no—
425#548C2×D7118yes—
426C2×C4⋊Q8—711no—
427C2×#125—1421no—
428C2×#124—21no—
429C2×#124C2×D7111yescharacteristic
430C2×C22⋊Q8—21no—
431C2×C22⋊Q8—711no—
432C2×C22⋊Q8—711no—
433C2×C22⋊Q8—1421no—
434C2×C22⋊Q8—1421no—
435C2×C22⋊Q8C2×D7111yescharacteristic
436C2×#121—21no—
437C2×#121C2×D7111yescharacteristic
438C2×C4×Q8—711no—
439C2×C4×Q8C2×D7111yescharacteristic
440C2×C4×D4—21no—
441C2×C4×D4—1421no—
442C2×C4×D4C2×D7111yescharacteristic
443C22×C4⋊C4—711no—
444C22×C4⋊C4—711no—
445#489—718no—
446#483—718no—
447#481—718no—
448#475—718no—
449#470—718no—
450#465—718no—
451#464—718no—
452#452—718no—
453#451—718no—
454#441—718no—
455#435—718no—
456C2×#106—711no—
457C2×#106—711no—
458C2×#106—711no—
459C2×C4⋊C8—711no—
460#417—718no—
461C2×#103—711no—
462C2×#103—711no—
463C2×#103—711no—
464C2×#103—711no—
465C2×#103—711no—
466C2×#103—711no—
467C2×#103—718no—
468C2×#103—711no—
469C2×#102—711no—
470C2×#102—711no—
471C2×#102—711no—
472C2×C22⋊C8—711no—
473C2×C22⋊C8—711no—
474C2×#97—711no—
475C2×#41—22no—
476C2×#41—24no—
477C2×#41—42no—
478C2×#41C22×D7114yes—
479C22×Q8—21no—
480C22×Q8—22no—
481C22×Q8—24no—
482C22×Q8—42no—
483C22×Q8—711no—
484C22×Q8—1421no—
485C22×Q8C22×D7111yescharacteristic
486C22×Q8C22×D7114yes—
487C22×Q8C22×D7111yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4C22⋊D7111yescharacteristic
491C22×D4C22×D7111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—1421no—
495C23×C4—1421no—
496C23×C4C22×D7111yescharacteristic
497C23×C4C22×D7111yescharacteristic
498C2×Q16—2842no—
499C2×Q16—714no—
500C2×Q16—714no—
501C2×Q16—1424no—
502C2×SD16—2842no—
503C2×SD16—714no—
504C2×M16—2842no—
505C2×M16—714no—
506C22×C8—2842no—
507C22×C8—714no—
508C22×C8—711no—
509C22×C8—711no—
510C22×C8—711no—
511C22×C8—711no—
512C4⋊Q8—714no—
513C4⋊Q8—1422no—
514#125—1428no—
515#124—28no—
516#124—22no—
517#124C22×D7114yes—
518C22⋊Q8—22no—
519C22⋊Q8—28no—
520C22⋊Q8—714no—
521C22⋊Q8—714no—
522C22⋊Q8—1422no—
523C22⋊Q8—1422no—
524C22⋊Q8—1428no—
525C22⋊Q8—1428no—
526C22⋊Q8C22×D7114yes—
527#121—28no—
528#121—22no—
529#121C22×D7114yes—
530C4×Q8—22no—
531C4×Q8—714no—
532C4×Q8—1422no—
533C4×Q8C22×D7114yes—
534C4×D4—28no—
535C4×D4—1428no—
536C4×D4C22⋊D7114yes—
537C4×D4C22×D7114yes—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—711no—
541C2×C4⋊C4—711no—
542C2×C4⋊C4—711no—
543C2×C4⋊C4—714no—
544C2×C4⋊C4—714no—
545C2×C4⋊C4—1421no—
546C2×C4⋊C4—1421no—
547C2×C4⋊C4—1422no—
548C2×C4⋊C4—1422no—
549C2×C4⋊C4—1421no—
550C2×C4⋊C4—1421no—
551C2×C4⋊C4—1421no—
552C2×C4⋊C4—1421no—
553C2×C4⋊C4C22⋊D7111yescharacteristic
554C2×C4⋊C4C22×D7111yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—1421no—
560C2×C22⋊C4—1421no—
561C2×C22⋊C4C22⋊D7111yescharacteristic
562C2×C22⋊C4C22⋊D7111yescharacteristic
563C2×C42—21no—
564C2×C42—1421no—
565C2×C42C22×D7111yescharacteristic
566#106—714no—
567#106—714no—
568#106—714no—
569C4⋊C8—714no—
570#103—714no—
571#103—714no—
572#103—714no—
573#103—714no—
574#103—714no—
575#103—714no—
576#103—714no—
577#102—714no—
578#102—714no—
579#102—714no—
580C22⋊C8—714no—
581C22⋊C8—714no—
582#97—714no—
583C24—21no—
584C24C2×C22⋊D7111yescharacteristic
585C24C2×C22⋊D7111yescharacteristic
586#41—28no—
587#41—44no—
588#41—48no—
589C2×Q8—21no—
590C2×Q8—24no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—28no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—44no—
597C2×Q8—44no—
598C2×Q8—48no—
599C2×Q8—5682no—
600C2×Q8—712no—
601C2×Q8—1422no—
602C2×Q8—1422no—
603C2×Q8—1421no—
604C2×Q8—1424no—
605C2×Q8#1176586414yes—
606C2×Q8C23×D7112yes—
607C2×Q8C23×D7112yes—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4C2×C22⋊D7114yes—
617C2×D4C23×D7112yes—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—24no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—5682no—
630C22×C4—5682no—
631C22×C4—1421no—
632C22×C4—1421no—
633C22×C4—1421no—
634C22×C4—1421no—
635C22×C4—1424no—
636C22×C4—1424no—
637C22×C4C2×C22⋊D7112yes—
638C22×C4C2×C22⋊D7112yes—
639C22×C4C2×C22⋊D7111yescharacteristic
640C22×C4C2×C22⋊D7111yescharacteristic
641C22×C4C2×C22⋊D7111yescharacteristic
642C22×C4C2×C22⋊D7111yescharacteristic
643C22×C4C23×D7112yes—
644C22×C4C23×D7112yes—
645C22×C4C23×D7111yescharacteristic
646Q16—2844no—
647Q16—1428no—
648SD16—2844no—
649M16—2844no—
650C2×C8—2844no—
651C2×C8—712no—
652C2×C8—712no—
653C2×C8—712no—
654C2×C8—712no—
655C2×C8—1422no—
656C2×C8—1422no—
657C2×C8—1422no—
658C2×C8—1422no—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—712no—
663C4⋊C4—712no—
664C4⋊C4—712no—
665C4⋊C4—1424no—
666C4⋊C4—1424no—
667C4⋊C4—1424no—
668C4⋊C4—1421no—
669C4⋊C4—1424no—
670C4⋊C4—1424no—
671C4⋊C4—1421no—
672C4⋊C4—1421no—
673C4⋊C4—1424no—
674C4⋊C4C2×C22⋊D7114yes—
675C4⋊C4C23×D7112yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—1424no—
681C22⋊C4—1424no—
682C22⋊C4C2×C22⋊D7114yes—
683C22⋊C4C2×C22⋊D7114yes—
684C42—24no—
685C42—1424no—
686C42C2×C22⋊D7112yes—
687C42C23×D7112yes—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23#1455615814yes—
698C23C22×C22⋊D7112yes—
699C23C22×C22⋊D7112yes—
700C23C22×C22⋊D7111yescharacteristic
701Q8—22no—
702Q8—24no—
703Q8—22no—
704Q8—22no—
705Q8—48no—
706Q8—42no—
707Q8—2842no—
708Q8—5684no—
709Q8—1422no—
710Q8—1422no—
711Q8C2×#1176586414yes—
712D4—28no—
713D4—22no—
714D4—22no—
715D4—48no—
716D4—48no—
717D4—42no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—48no—
733C2×C4—48no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—2842no—
737C2×C4—2842no—
738C2×C4—2842no—
739C2×C4—2842no—
740C2×C4—5684no—
741C2×C4—5684no—
742C2×C4—1422no—
743C2×C4—1422no—
744C2×C4—1422no—
745C2×C4—1422no—
746C2×C4C22×C22⋊D7112yes—
747C2×C4C22×C22⋊D7112yes—
748C2×C4C22×C22⋊D7112yes—
749C2×C4C22×C22⋊D7112yes—
750C2×C4C22×C22⋊D7111yescharacteristic
751C2×C4C2×#1176586412yes—
752C2×C4#1455617312yes—
753C2×C4C24×D7111yescharacteristic
754C8—1422no—
755C8—1422no—
756C8—1422no—
757C8—1422no—
758C22—28no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22#1798664312yes—
770C22C2×#1455615814yes—
771C22C2×#1455615812yes—
772C22#1798680712yes—
773C22C23×C22⋊D7111yescharacteristic
774C4—22no—
775C4—22no—
776C4—24no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—2842no—
782C4—2842no—
783C4—2842no—
784C4—2842no—
785C4#1798664312yes—
786C4C22×#1176586411yescharacteristic
787C4C2×#1455617311yescharacteristic
788C2—24no—
789C2—42no—
790C2—82no—
791C2#2260045114yesdirect product factor
792C2C2×#1798664311yescharacteristic
793C2C22×#1455615811yescharacteristic
794C2C2×#1798680711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
Fitting, prime radicalC2×#548×C71C2
socleC23×C71C22×D4
hypercenterC2×#548D71
hypocenterC71C2×#3316
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#17986706C2semidirect
2. #22600451C2direct (N × H)
3. C2×#17986358C2semidirect
4. C2×#17986315C2semidirect
5. C2×#17986327C2semidirect
6. C2×#17986284C2semidirect
7. C2×#17986255C2semidirect
8. C2×#17986226C2semidirect
9. C2×#17986218C2semidirect
10. C2×#17986161C2semidirect
11. C2×#17986155C2semidirect
12. C2×#17986104C2semidirect
13. C2×#17986071C2semidirect
14. C2×#17986000C2semidirect
15. C22×#14556052C2semidirect
23. #17986706C22semidirect
34. #17986358C22semidirect
35. #17986327C22semidirect
36. #17986315C22semidirect
37. #17986284C22semidirect
38. #17986255C22semidirect
39. #17986226C22semidirect
40. #17986218C22semidirect
41. #17986161C22semidirect
42. #17986155C22semidirect
43. #17986104C22semidirect
44. #17986071C22semidirect
49. #17986000C22semidirect
56. C2×#14556052C22semidirect
394. C2×C71#3316semidirect
414. C71C2×#3316semidirect
791. C2#22600451direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867062
#226004512
C2×#179863582
C2×#179863152
C2×#179863272
C2×#179862842
C2×#179862552
C2×#179862262
C2×#179862182
C2×#179861612
C2×#179861552
C2×#179861042
C2×#179860712
C2×#179860002
C22×#145560522
C2×#548×C712
C2×#331671