Finite Group Databasebeta

← C2×#20253335 #27084083

Subgroups — C2×#20253335 #27084083

Order 12032.

2326 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D47C211yesmaximal, characteristic
2C2×#117×D47C211yesmaximal, characteristic
3#20253335C2116yesmaximal, direct product factor
4C2×#15689460C211yesmaximal, characteristic, complemented
5C2×#15689457C211yesmaximal, characteristic, complemented
6C2×#15689465C211yesmaximal, characteristic, complemented
7C2×#15689464C211yesmaximal, characteristic, complemented
8C2×#15689461C211yesmaximal, characteristic, complemented
9C2×#15689455C211yesmaximal, characteristic, complemented
10C2×#15689452C211yesmaximal, characteristic, complemented
11C2×#15689164C211yesmaximal, characteristic, complemented
12C2×#15689162C211yesmaximal, characteristic, complemented
13C2×#15689130C211yesmaximal, characteristic, complemented
14C2×#15689130C211yesmaximal, characteristic, complemented
15C2×#15689085C211yesmaximal, characteristic
16C2×C47×#485C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C22×#10625324C2211yescharacteristic
21C2×#13094004C2211yescharacteristic
22C2×#13094003C2211yescharacteristic
23C2×#13094002—21no—
24C2×#13094001—21no—
25C2×#13094000C2211yescharacteristic
26C22⋊Q8×D47—24no—
27C22⋊Q8×D47C2218yes—
28C2×#13093983C2211yescharacteristic
29C2×#13093982C2211yescharacteristic
30C2×#13093982C2211yescharacteristic
31C2×#13093981—21no—
32C2×#13093980—21no—
33#117×D47—24no—
34#117×D47C2218yes—
35C2×C4⋊C4×D47—21no—
36C2×C4⋊C4×D47C2211yescharacteristic
37C2×C4⋊C4×D47C2211yescharacteristic
38C2×C4⋊C4×D47C2211yescharacteristic
39C2×C22⋊C4×D47—21no—
40C2×C22⋊C4×D47—21no—
41C2×C42×D47—21no—
42#15689465C2218yescomplemented
43#15689464C2218yescomplemented
44#15689461C2218yescomplemented
45#15689460C2218yescomplemented
46#15689457C2218yescomplemented
47#15689455C2218yescomplemented
48#15689452C2218yescomplemented
49#15689164C2218yescomplemented
50#15689162C2218yescomplemented
51C2×#13093958C2211yescharacteristic, complemented
52C2×#13093957C2211yescharacteristic, complemented
53C2×#13093957C2211yescharacteristic, complemented
54C2×#13093956C2211yescharacteristic, complemented
55C2×#13093955C2211yescharacteristic, complemented
56C2×#13093955C2211yescharacteristic, complemented
57#15689130C2218yescomplemented
58#15689130C2218yescomplemented
59C2×#13093949C2211yescharacteristic, complemented
60C2×#13093949C2211yescharacteristic, complemented
61C2×#13093948C2211yescharacteristic, complemented
62C2×#13093948C2211yescharacteristic, complemented
63C2×#13093947C2211yescharacteristic, complemented
64C2×#13093947C2211yescharacteristic, complemented
65#15689085C2218yes—
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic
69C2×C22⋊Q8×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic
71C47×#485C2218yescomplemented
72C2×#107×C47C2211yescharacteristic, complemented
73C2×#106×C47C2211yescharacteristic, complemented
74C2×#103×C47C2211yescharacteristic, complemented
75C2×#103×C47C2211yescharacteristic, complemented
76C2×C22⋊C8×C47C2211yescharacteristic
77C24×D47D411yescharacteristic
78C22×Dic94—21no—
79C22×Dic94C2311yescharacteristic
80C2×Q8×D47—22no—
81C2×Q8×D47—24no—
82C2×Q8×D47—24no—
83C2×Q8×D47C2314yes—
84C23×Dic47D411yescharacteristic
85C22×C4×D47—24no—
86C22×C4×D47—24no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47—21no—
90C22×C4×D47—21no—
91C22×C4×D47D411yescharacteristic
92C22×C4×D47D411yescharacteristic
93C22×C4×D47D414yes—
94C22×C4×D47C2311yescharacteristic
95C22×C4×D47C2314yes—
96C22×C4×D47C2311yescharacteristic
97C2×#10625324—24no—
98C2×#10625324—24no—
99C2×#10625324C2314yes—
100C2×#10625324C2314yes—
101C22×C47⋊C8C2311yescharacteristic
102C22×C47⋊C8C2311yescharacteristic
103#13094004—22no—
104#13094004C2314yes—
105#13094003—22no—
106#13094003C2314yes—
107#13094002—28no—
108#13094001—28no—
109#13094000—22no—
110#13094000C2314yes—
111#13093983—22no—
112#13093983C2314yes—
113#13093982—22no—
114#13093982—22no—
115#13093982C2314yes—
116#13093982C2314yes—
117#13093981—28no—
118#13093980—28no—
119C2×C4⋊Dic47—21no—
120C2×C4⋊Dic47C2311yescharacteristic
121C2×C4⋊Dic47C2311yescharacteristic
122C2×C4⋊Dic47C2311yescharacteristic
123C2×Dic47⋊C4—21no—
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C4⋊C4×D47—28no—
129C4⋊C4×D47—22no—
130C4⋊C4×D47—22no—
131C4⋊C4×D47—22no—
132C4⋊C4×D47C2314yes—
133C4⋊C4×D47C2314yes—
134C4⋊C4×D47C2314yes—
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C22⋊C4×D47—28no—
142C22⋊C4×D47—28no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C42×D47—28no—
147#13093958C2314yescomplemented
148#13093957C2314yescomplemented
149#13093957C2314yescomplemented
150#13093956C2314yescomplemented
151#13093955C2314yescomplemented
152#13093955C2314yescomplemented
153#13093949C2314yescomplemented
154#13093949C2314yescomplemented
155#13093948C2314yescomplemented
156#13093948C2314yescomplemented
157#13093947C2314yescomplemented
158#13093947C2314yescomplemented
159C22⋊(C47⋊C8)C2314yes—
160(C2×D47)⋊C8C2314yes—
161(C2×D47)⋊C8C2314yes—
162C22×Q8×C47C2311yescharacteristic
163C23×C4×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C22⋊Q8×C47—22no—
167C22⋊Q8×C47C2314yes—
168#117×C47—22no—
169#117×C47C2314yes—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176C2×C42×C47—21no—
177#107×C47C2314yescomplemented
178#106×C47C2314yescomplemented
179#103×C47C2314yescomplemented
180#103×C47C2314yescomplemented
181C22⋊C8×C47C2314yes—
182C24×C47C2×D411yescharacteristic
183C23×D47—24no—
184C23×D47—24no—
185C23×D47—42no—
186C23×D47C2×D414yes—
187C23×D47C2×D411yescharacteristic
188C23×D47C2×D411yescharacteristic
189C2×Q8×C47—21no—
190C2×Q8×C47—22no—
191C2×Q8×C47—22no—
192C2×Q8×C47C2412yes—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D412yes—
201C22×C4×C47C2412yes—
202C22×C4×C47C2411yescharacteristic
203C22×Dic47—24no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47C2×D411yescharacteristic
209C22×Dic47C2×D414yes—
210C22×Dic47C2×D411yescharacteristic
211Q8×D47—28no—
212Q8×D47—28no—
213Q8×D47—48no—
214C2×C4×D47—24no—
215C2×C4×D47—22no—
216C2×C4×D47—22no—
217C2×C4×D47—24no—
218C2×C4×D47—216no—
219C2×C4×D47—28no—
220C2×C4×D47—28no—
221C2×C4×D47—24no—
222C2×C4×D47—24no—
223C2×C4×D47—24no—
224C2×C4×D47—24no—
225C2×C4×D47—44no—
226C2×C4×D47—44no—
227C2×C4×D47—44no—
228C2×C4×D47—44no—
229C2×C4×D47C2×D414yes—
230C2×C4×D47C2×D414yes—
231C2×C4×D47C2×D412yes—
232C2×C4×D47C2×D412yes—
233C2×C4×D47#4114yes—
234C2×C4×D47#4114yes—
235C2×C4×D47C2412yes—
236C2×C4×D47C2412yes—
237C2×Dic94—22no—
238C2×Dic94—22no—
239C2×Dic94—21no—
240C2×Dic94—24no—
241C2×Dic94—44no—
242C2×Dic94C2412yes—
243C2×C8×C47—22no—
244C2×C8×C47—22no—
245C2×C8×C47C2412yes—
246C2×C8×C47C2412yes—
247C4⋊C4×C47—24no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47C2412yes—
252C4⋊C4×C47C2412yes—
253C4⋊C4×C47C2412yes—
254C22⋊C4×C47—24no—
255C22⋊C4×C47—24no—
256C42×C47—24no—
257C22⋊Dic47—24no—
258C22⋊Dic47—24no—
259(C2×D47)⋊C4—24no—
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263C4⋊Dic47—21no—
264C4⋊Dic47—21no—
265C4⋊Dic47—21no—
266C4⋊Dic47—24no—
267C4⋊Dic47C2412yes—
268C4⋊Dic47C2412yes—
269C4⋊Dic47C2412yes—
270Dic47⋊C4—24no—
271Dic47⋊C4—24no—
272Dic47⋊C4—24no—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275C4×Dic47—24no—
276C4×Dic47—24no—
277C4×Dic47—24no—
278C2×C47⋊C8—22no—
279C2×C47⋊C8—22no—
280C2×C47⋊C8C2412yes—
281C2×C47⋊C8C2412yes—
282#10625324—28no—
283#10625324—28no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—22no—
287C23×C47C22×D412yes—
288C23×C47C22×D411yescharacteristic
289C22×D47—22no—
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—22no—
293C22×D47—28no—
294C22×D47—28no—
295C22×D47—44no—
296C22×D47—416no—
297C22×D47#12314yes—
298C22×D47#13714yes—
299C22×D47C22×D412yes—
300C22×D47C22×D412yes—
301Q8×C47—22no—
302Q8×C47—22no—
303Q8×C47—42no—
304C2×C4×C47—22no—
305C2×C4×C47—24no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—42no—
313C2×C4×C47—42no—
314C2×C4×C47—42no—
315C2×C4×C47—42no—
316C2×C4×C47C22×D412yes—
317C2×C4×C47C22×D411yescharacteristic
318C2×C4×C47C2×#4112yes—
319C2×C4×C47C2×#4112yes—
320C2×C4×C47C2511yescharacteristic
321C2×Dic47—22no—
322C2×Dic47—28no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47#12314yes—
332C2×Dic47C22×D412yes—
333C2×Dic47C22×D412yes—
334C4×D47—28no—
335C4×D47—24no—
336C4×D47—22no—
337C4×D47—22no—
338C4×D47—28no—
339C4×D47—48no—
340C4×D47—48no—
341C4×D47—48no—
342C4×D47—48no—
343C4×D47#12318yes—
344C4×D47C2×#4114yes—
345C4×D47C2×#4114yes—
346Dic94—22no—
347Dic94—22no—
348Dic94—42no—
349Dic94—48no—
350C8×C47—22no—
351C8×C47—22no—
352C47⋊C8—22no—
353C47⋊C8—22no—
354C2×#3095—471nomaximal, Sylow
355C22×C47—22no—
356C22×C47—22no—
357C22×C47—22no—
358C22×C47—44no—
359C22×C47C2×#12312yes—
360C22×C47C2×#13712yes—
361C22×C47#57512yes—
362C22×C47C23×D411yescharacteristic
363C2×D47—28no—
364C2×D47—28no—
365C2×D47—22no—
366C2×D47—22no—
367C2×D47—22no—
368C2×D47—22no—
369C2×D47—416no—
370C2×D47C2×#12314yes—
371C2×D47C2×#13714yes—
372C4×C47—22no—
373C4×C47—42no—
374C4×C47—42no—
375C4×C47—42no—
376C4×C47—42no—
377C4×C47C2×#12312yes—
378C4×C47C22×#4111yescharacteristic
379C4×C47C22×#4111yescharacteristic
380Dic47—22no—
381Dic47—42no—
382Dic47—42no—
383Dic47—42no—
384Dic47—42no—
385Dic47C2×#12314yes—
386C22×C22⋊Q8—471no—
387C22×#117—471no—
388#3095—4716no—
389C2×#484—471no—
390C2×#484—471no—
391C2×#485—471no—
392C2×#485—471no—
393C2×#485—471no—
394C2×#485D4711yescharacteristic, complemented
395C2×#483—471no—
396C2×#483—471no—
397C2×#428—471no—
398C2×#428—471no—
399C2×#419—471no—
400C2×#419—471no—
401C2×#407—471no—
402C2×C47—42no—
403C2×C47#309514yescomplemented
404C2×C47C22×#12311yescharacteristic
405C2×C47C22×#13711yescharacteristic
406C2×C47C2×#57511yescharacteristic
407D47—24no—
408D47—24no—
409C23×Q8—471no—
410C24×C4—471no—
411C22×M16—471no—
412C22×M16—471no—
413C2×C22⋊Q8—471no—
414C2×C22⋊Q8—471no—
415C2×C22⋊Q8—478no—
416C2×C22⋊Q8—471no—
417C2×C22⋊Q8—941no—
418C2×C22⋊Q8—941no—
419C2×C22⋊Q8—944no—
420C2×C22⋊Q8C2×D4711yescharacteristic
421C2×#117—471no—
422C2×#117—478no—
423C2×#117—471no—
424C2×#117—471no—
425C2×#117—941no—
426C2×#117—941no—
427C2×#117—944no—
428C2×#117C2×D4711yescharacteristic
429C22×C4⋊C4—471no—
430C22×C4⋊C4—471no—
431C22×C4⋊C4—471no—
432C22×C4⋊C4—941no—
433C22×C22⋊C4—941no—
434C22×C22⋊C4—941no—
435C22×C42—941no—
436#485—478no—
437#485—478no—
438#485—478no—
439#485C2×D4718yescomplemented
440#484—478no—
441#484—478no—
442#483—478no—
443#483—478no—
444#428—478no—
445#428—478no—
446C2×#107—471no—
447C2×#107—471no—
448C2×#107—471no—
449C2×#107C2×D4711yescharacteristic, complemented
450C2×#106—471no—
451C2×#106—471no—
452C2×#106—471no—
453C2×#106C2×D4711yescharacteristic, complemented
454#419—478no—
455#419—478no—
456C2×#103—471no—
457C2×#103—471no—
458C2×#103—471no—
459C2×#103—471no—
460C2×#103—471no—
461C2×#103—471no—
462C2×#103C2×D4711yescharacteristic, complemented
463C2×#103C2×D4711yescharacteristic, complemented
464#407—478no—
465C2×C22⋊C8—471no—
466C2×C22⋊C8—471no—
467C2×C22⋊C8—471no—
468C2×C22⋊C8C2×D4711yescharacteristic
469C47C2×#309511yescharacteristic, complemented, Sylow
470C25—471no—
471C22×Q8—474no—
472C22×Q8—471no—
473C22×Q8—941no—
474C22×Q8—942no—
475C22×Q8—944no—
476C22×Q8—944no—
477C22×Q8C22×D4711yescharacteristic
478C23×C4—471no—
479C23×C4—471no—
480C23×C4—471no—
481C23×C4—474no—
482C23×C4—471no—
483C23×C4—471no—
484C23×C4—474no—
485C23×C4—944no—
486C23×C4—944no—
487C23×C4—941no—
488C23×C4—941no—
489C23×C4—941no—
490C23×C4—941no—
491C23×C4C22×D4711yescharacteristic
492C2×M16—474no—
493C2×M16—474no—
494C2×M16—944no—
495C2×M16—944no—
496C22×C8—471no—
497C22×C8—471no—
498C22×C8C22×D4711yescharacteristic
499C22×C8C22×D4711yescharacteristic
500C22⋊Q8—22no—
501C22⋊Q8—474no—
502C22⋊Q8—474no—
503C22⋊Q8—474no—
504C22⋊Q8—948no—
505C22⋊Q8—948no—
506C22⋊Q8—942no—
507C22⋊Q8—942no—
508C22⋊Q8—942no—
509C22⋊Q8C22×D4714yes—
510#117—22no—
511#117—474no—
512#117—474no—
513#117—474no—
514#117—948no—
515#117—948no—
516#117—942no—
517#117—942no—
518#117—942no—
519#117C22×D4714yes—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—471no—
523C2×C4⋊C4—471no—
524C2×C4⋊C4—474no—
525C2×C4⋊C4—474no—
526C2×C4⋊C4—474no—
527C2×C4⋊C4—942no—
528C2×C4⋊C4—942no—
529C2×C4⋊C4—942no—
530C2×C4⋊C4—948no—
531C2×C4⋊C4—941no—
532C2×C4⋊C4—941no—
533C2×C4⋊C4—941no—
534C2×C4⋊C4—941no—
535C2×C4⋊C4—941no—
536C2×C4⋊C4—941no—
537C2×C4⋊C4C22×D4711yescharacteristic
538C2×C4⋊C4C22×D4711yescharacteristic
539C2×C4⋊C4C22×D4711yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—948no—
543C2×C22⋊C4—948no—
544C2×C22⋊C4—941no—
545C2×C22⋊C4—941no—
546C2×C22⋊C4—941no—
547C2×C22⋊C4—941no—
548C2×C22⋊C4—941no—
549C2×C22⋊C4—941no—
550C2×C42—21no—
551C2×C42—948no—
552C2×C42—941no—
553C2×C42—941no—
554C2×C42—941no—
555#107—474no—
556#107—474no—
557#107—474no—
558#107C22×D4714yescomplemented
559#106—474no—
560#106—474no—
561#106—474no—
562#106C22×D4714yescomplemented
563#103—474no—
564#103—474no—
565#103—474no—
566#103—474no—
567#103—474no—
568#103—474no—
569#103C22×D4714yescomplemented
570#103C22×D4714yescomplemented
571C22⋊C8—474no—
572C22⋊C8—474no—
573C22⋊C8—474no—
574C22⋊C8C22×D4714yes—
575C24—471no—
576C24—471no—
577C24—474no—
578C24—944no—
579C24—944no—
580C24—1882no—
581C24D4×D4711yescharacteristic
582C2×Q8—21no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—472no—
586C2×Q8—944no—
587C2×Q8—948no—
588C2×Q8—948no—
589C2×Q8—941no—
590C2×Q8—942no—
591C2×Q8—942no—
592C2×Q8—1884no—
593C2×Q8—1888no—
594C2×Q8C23×D4712yes—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—471no—
602C22×C4—472no—
603C22×C4—474no—
604C22×C4—474no—
605C22×C4—472no—
606C22×C4—474no—
607C22×C4—471no—
608C22×C4—474no—
609C22×C4—474no—
610C22×C4—472no—
611C22×C4—472no—
612C22×C4—944no—
613C22×C4—9416no—
614C22×C4—948no—
615C22×C4—948no—
616C22×C4—944no—
617C22×C4—944no—
618C22×C4—944no—
619C22×C4—944no—
620C22×C4—944no—
621C22×C4—944no—
622C22×C4—942no—
623C22×C4—942no—
624C22×C4—941no—
625C22×C4—941no—
626C22×C4—941no—
627C22×C4—941no—
628C22×C4—1884no—
629C22×C4—1884no—
630C22×C4—1884no—
631C22×C4—1884no—
632C22×C4D4×D4712yes—
633C22×C4D4×D4711yescharacteristic
634C22×C4C23×D4712yes—
635C22×C4C23×D4711yescharacteristic
636M16—948no—
637M16—948no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—472no—
641C2×C8—472no—
642C2×C8—942no—
643C2×C8—942no—
644C2×C8C23×D4712yes—
645C2×C8C23×D4712yes—
646C4⋊C4—24no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—472no—
651C4⋊C4—472no—
652C4⋊C4—472no—
653C4⋊C4—944no—
654C4⋊C4—944no—
655C4⋊C4—944no—
656C4⋊C4—944no—
657C4⋊C4—944no—
658C4⋊C4—944no—
659C4⋊C4—941no—
660C4⋊C4—941no—
661C4⋊C4—941no—
662C4⋊C4C23×D4712yes—
663C4⋊C4C23×D4712yes—
664C4⋊C4C23×D4712yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—944no—
668C22⋊C4—944no—
669C22⋊C4—944no—
670C22⋊C4—944no—
671C22⋊C4—944no—
672C22⋊C4—944no—
673C42—24no—
674C42—944no—
675C42—944no—
676C42—944no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—474no—
681C23—474no—
682C23—472no—
683C23—472no—
684C23—948no—
685C23—948no—
686C23—942no—
687C23—942no—
688C23—942no—
689C23—942no—
690C23—1884no—
691C23—18816no—
692C23C2×D4×D4712yes—
693C23C2×D4×D4711yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—42no—
697Q8—942no—
698Q8—942no—
699Q8—1888no—
700Q8—1882no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—474no—
714C2×C4—472no—
715C2×C4—478no—
716C2×C4—474no—
717C2×C4—474no—
718C2×C4—472no—
719C2×C4—948no—
720C2×C4—948no—
721C2×C4—948no—
722C2×C4—942no—
723C2×C4—944no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—1888no—
731C2×C4—1888no—
732C2×C4—1888no—
733C2×C4—1888no—
734C2×C4—1882no—
735C2×C4—1882no—
736C2×C4—1882no—
737C2×C4—1882no—
738C2×C4C2×D4×D4712yes—
739C2×C4C2×D4×D4711yescharacteristic
740C2×C4#41×D4712yes—
741C2×C4#41×D4712yes—
742C2×C4C24×D4711yescharacteristic
743C8—22no—
744C8—22no—
745C8—942no—
746C8—942no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—44no—
751C22—474no—
752C22—474no—
753C22—942no—
754C22—942no—
755C22—942no—
756C22—942no—
757C22—948no—
758C22—948no—
759C22—18816no—
760C22#123×D4712yes—
761C22#137×D4712yes—
762C22#1568992012yes—
763C22C22×D4×D4711yescharacteristic
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—474no—
770C4—942no—
771C4—1882no—
772C4—1882no—
773C4—1882no—
774C4—1882no—
775C4#123×D4712yes—
776C4C2×#41×D4711yescharacteristic
777C4C2×#41×D4711yescharacteristic
778C2—42no—
779C2—944no—
780C2—944no—
781C2#2025333514yesdirect product factor
782C2C2×#123×D4711yescharacteristic
783C2C2×#137×D4711yescharacteristic
784C2C2×#1568992011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#485C2
socleC23×C47C22×D4
prime radicalC24×D47D4
hypercenterC2×#485D47
hypocenterC47C2×#3095
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #20253335C2direct (N × H)
4. C2×#15689460C2semidirect
5. C2×#15689457C2semidirect
6. C2×#15689465C2semidirect
7. C2×#15689464C2semidirect
8. C2×#15689461C2semidirect
9. C2×#15689455C2semidirect
10. C2×#15689452C2semidirect
11. C2×#15689164C2semidirect
12. C2×#15689162C2semidirect
13. C2×#15689130C2semidirect
14. C2×#15689130C2semidirect
16. C2×C47×#485C2semidirect
42. #15689465C22semidirect
43. #15689464C22semidirect
44. #15689461C22semidirect
45. #15689460C22semidirect
46. #15689457C22semidirect
47. #15689455C22semidirect
48. #15689452C22semidirect
49. #15689164C22semidirect
50. #15689162C22semidirect
51. C2×#13093958C22semidirect
52. C2×#13093957C22semidirect
53. C2×#13093957C22semidirect
54. C2×#13093956C22semidirect
55. C2×#13093955C22semidirect
56. C2×#13093955C22semidirect
57. #15689130C22semidirect
58. #15689130C22semidirect
59. C2×#13093949C22semidirect
60. C2×#13093949C22semidirect
61. C2×#13093948C22semidirect
62. C2×#13093948C22semidirect
63. C2×#13093947C22semidirect
64. C2×#13093947C22semidirect
71. C47×#485C22semidirect
72. C2×#107×C47C22semidirect
73. C2×#106×C47C22semidirect
74. C2×#103×C47C22semidirect
75. C2×#103×C47C22semidirect
147. #13093958C23semidirect
148. #13093957C23semidirect
149. #13093957C23semidirect
150. #13093956C23semidirect
151. #13093955C23semidirect
152. #13093955C23semidirect
153. #13093949C23semidirect
154. #13093949C23semidirect
155. #13093948C23semidirect
156. #13093948C23semidirect
157. #13093947C23semidirect
158. #13093947C23semidirect
177. #107×C47C23semidirect
178. #106×C47C23semidirect
179. #103×C47C23semidirect
180. #103×C47C23semidirect
394. C2×#485D47semidirect
403. C2×C47#3095semidirect
439. #485C2×D47semidirect
449. C2×#107C2×D47semidirect
453. C2×#106C2×D47semidirect
462. C2×#103C2×D47semidirect
463. C2×#103C2×D47semidirect
469. C47C2×#3095semidirect
558. #107C22×D47semidirect
562. #106C22×D47semidirect
569. #103C22×D47semidirect
570. #103C22×D47semidirect
781. C2#20253335direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D472
C2×#117×D472
#202533352
C2×#156894602
C2×#156894572
C2×#156894652
C2×#156894642
C2×#156894612
C2×#156894552
C2×#156894522
C2×#156891642
C2×#156891622
C2×#156891302
C2×#156890852
C2×C47×#4852
C2×#309547