Finite Group Databasebeta

← C2×#20253374 #27084136

Subgroups — C2×#20253374 #27084136

Order 12032.

2234 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689703C211yesmaximal, characteristic
2C2×#15689603C211yesmaximal, characteristic, complemented
3#20253374C2116yesmaximal, direct product factor
4C2×#15689443C211yesmaximal, characteristic, complemented
5C2×#15689442C211yesmaximal, characteristic, complemented
6C2×#15689462C211yesmaximal, characteristic, complemented
7C2×#15689450C211yesmaximal, characteristic, complemented
8C2×#15689447C211yesmaximal, characteristic, complemented
9C2×#15689452C211yesmaximal, characteristic, complemented
10C2×#15689451C211yesmaximal, characteristic, complemented
11C2×#15689164C211yesmaximal, characteristic, complemented
12C2×#106×D47C211yesmaximal, characteristic, complemented
13C2×#15689123C211yesmaximal, characteristic, complemented
14C2×#15689118C211yesmaximal, characteristic, complemented
15C2×#15689088C211yesmaximal, characteristic, complemented
16C2×C47×#485C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625350C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21#15689703—24no—
22#15689703C2218yes—
23C2×#13094002—21no—
24C2×#13094000C2211yescharacteristic
25C2×#13093999—21no—
26C2×#13093999C2211yescharacteristic
27C2×#13093998C2211yescharacteristic
28C2×#13093997—21no—
29C2×#13093997—21no—
30#15689603—24no—
31#15689603C2218yescomplemented
32C2×C4×Dic94—21no—
33C2×C4×D188—21no—
34C2×(C22⋊D47)⋊C4—21no—
35C2×(C22⋊D47)⋊C4—21no—
36C2×#13093982C2211yescharacteristic
37C2×#13093982C2211yescharacteristic
38C22×C4⋊Dic47C2211yescharacteristic
39C2×C4⋊C4×D47C2211yescharacteristic
40C2×C4⋊C4×D47C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42#15689462C2218yescomplemented
43#15689452C2218yescomplemented
44#15689451C2218yescomplemented
45#15689450C2218yescomplemented
46#15689447C2218yescomplemented
47#15689443C2218yescomplemented
48#15689442C2218yescomplemented
49#15689164C2218yescomplemented
50C2×#13093957C2211yescharacteristic
51C2×#13093956C2211yescharacteristic
52C2×#13093956C2211yescharacteristic
53C2×#13093955C2211yescharacteristic
54C2×#13093955C2211yescharacteristic
55C2×#13093955C2211yescharacteristic
56#106×D47C2218yescomplemented
57#15689123C2218yescomplemented
58#15689118C2218yescomplemented
59C2×#13093948C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093946C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65#15689088C2218yescomplemented
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
73C2×#106×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C2×#10625354—22no—
78C2×#10625354—24no—
79C2×#10625354—24no—
80C2×#10625354C2314yes—
81C2×#10625350—24no—
82C2×#10625350—24no—
83C2×#10625350D414yes—
84C2×#10625350C2314yes—
85C22×Dic94D411yescharacteristic
86C22×D188—21no—
87C22×D188—21no—
88C22×D188D411yescharacteristic
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—21no—
91C22×C22⋊D47D411yescharacteristic
92C22×C22⋊D47D411yescharacteristic
93C23×Dic47—21no—
94C22×C4×D47—21no—
95C22×C4×D47—21no—
96C22×C4×D47—21no—
97C22×C4×D47—21no—
98C22×C4×D47C2311yescharacteristic
99C22×C4×D47C2311yescharacteristic
100C2×#10625324—24no—
101C2×#10625324C2314yes—
102C22×C47⋊C8C2311yescharacteristic
103C22×C47⋊C8C2311yescharacteristic
104C2×C8×D47—24no—
105C2×C8×D47C2314yes—
106#13094002—28no—
107#13094000—22no—
108#13094000C2314yes—
109#13093999—28no—
110#13093999—22no—
111#13093999C2314yes—
112#13093998—22no—
113#13093998C2314yes—
114#13093997—28no—
115#13093997—28no—
116C4×Dic94—28no—
117C4×D188—28no—
118(C22⋊D47)⋊C4—28no—
119(C22⋊D47)⋊C4—28no—
120#13093982—22no—
121#13093982—22no—
122#13093982C2314yes—
123#13093982C2314yes—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47—22no—
126C2×C4⋊Dic47C2311yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×C4⋊Dic47C2314yes—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C4⋊C4×D47—22no—
135C4⋊C4×D47—22no—
136C4⋊C4×D47—22no—
137C4⋊C4×D47C2314yes—
138C4⋊C4×D47C2314yes—
139C4⋊C4×D47C2314yes—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47—21no—
147#13093957C2314yes—
148#13093956C2314yes—
149#13093956C2314yes—
150#13093955C2314yes—
151#13093955C2314yes—
152#13093955C2314yes—
153#13093948C2314yes—
154#13093948C2314yes—
155#13093946C2314yes—
156#13093946C2314yes—
157#13093944C2314yes—
158#13093944C2314yes—
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×C47C2314yes—
178#106×C47C2314yes—
179#103×C47C2314yes—
180#103×C47C2314yes—
181C22⋊C8×C47C2314yes—
182C24×C47C2×D411yescharacteristic
183C23×D47—21no—
184C23×D47C2×D411yescharacteristic
185C23×D47C2×D411yescharacteristic
186C2×Q8×C47—21no—
187C2×Q8×C47—22no—
188C2×Q8×C47—22no—
189C2×Q8×C47C2412yes—
190C22×C4×C47—22no—
191C22×C4×C47—22no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D412yes—
198C22×C4×C47C2412yes—
199C22×C4×C47C2411yescharacteristic
200C2×C22⋊D47—24no—
201C2×C22⋊D47—24no—
202C2×C22⋊D47—24no—
203C2×C22⋊D47—82no—
204C2×C22⋊D47C2×D414yes—
205C2×C22⋊D47C2×D414yes—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—24no—
210C22×Dic47—82no—
211C22×Dic47C2×D411yescharacteristic
212C22×Dic47C2×D411yescharacteristic
213#10625354—28no—
214#10625354—28no—
215#10625354—48no—
216#10625350—216no—
217#10625350—28no—
218#10625350—28no—
219C2×D188—24no—
220C2×D188—22no—
221C2×D188—22no—
222C2×D188—24no—
223C2×D188—21no—
224C2×D188—24no—
225C2×D188—44no—
226C2×D188—82no—
227C2×D188C2×D414yes—
228C2×D188C2412yes—
229C2×C4×D47—22no—
230C2×C4×D47—22no—
231C2×C4×D47—24no—
232C2×C4×D47—24no—
233C2×C4×D47—24no—
234C2×C4×D47—24no—
235C2×C4×D47—44no—
236C2×C4×D47—82no—
237C2×C4×D47—82no—
238C2×C4×D47—82no—
239C2×C4×D47C2×D412yes—
240C2×C4×D47C2×D412yes—
241C2×C4×D47#4114yes—
242C2×C4×D47#4114yes—
243C2×C4×D47C2412yes—
244C2×C4×D47C2412yes—
245C2×Dic94—24no—
246C2×Dic94C2×D414yes—
247C2×C8×C47—22no—
248C2×C8×C47—22no—
249C2×C8×C47C2412yes—
250C2×C8×C47C2412yes—
251C4⋊C4×C47—24no—
252C4⋊C4×C47—21no—
253C4⋊C4×C47—21no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47C2412yes—
256C4⋊C4×C47C2412yes—
257C4⋊C4×C47C2412yes—
258C22⋊C4×C47—24no—
259C22⋊C4×C47—24no—
260C42×C47—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4—24no—
264(C2×D47)⋊C4—24no—
265(C2×D47)⋊C4—24no—
266C4⋊Dic47—21no—
267C4⋊Dic47—21no—
268C4⋊Dic47—21no—
269C4⋊Dic47—24no—
270C4⋊Dic47C2412yes—
271C4⋊Dic47C2412yes—
272C4⋊Dic47C2412yes—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277C4×Dic47—24no—
278C4×Dic47—24no—
279C2×C47⋊C8—22no—
280C2×C47⋊C8—22no—
281C2×C47⋊C8C2412yes—
282C2×C47⋊C8C2412yes—
283#10625324—28no—
284C8×D47—28no—
285C23×C47—22no—
286C23×C47—22no—
287C23×C47—22no—
288C23×C47C22×D412yes—
289C23×C47C22×D411yescharacteristic
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—22no—
293C22×D47—22no—
294C22×D47—22no—
295C22×D47—22no—
296C22×D47—42no—
297C22×D47—42no—
298C22×D47—42no—
299C22×D47#12314yes—
300C22×D47C22×D412yes—
301C22×D47C22×D412yes—
302Q8×C47—22no—
303Q8×C47—22no—
304Q8×C47—42no—
305C2×C4×C47—22no—
306C2×C4×C47—24no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—42no—
314C2×C4×C47—42no—
315C2×C4×C47—42no—
316C2×C4×C47—42no—
317C2×C4×C47C22×D412yes—
318C2×C4×C47C22×D411yescharacteristic
319C2×C4×C47C2×#4112yes—
320C2×C4×C47C2×#4112yes—
321C2×C4×C47C2511yescharacteristic
322C22⋊D47—28no—
323C22⋊D47—28no—
324C22⋊D47—84no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47—84no—
333C2×Dic47#12314yes—
334C2×Dic47C22×D412yes—
335C2×Dic47C22×D412yes—
336D188—28no—
337D188—22no—
338D188—22no—
339D188—48no—
340D188—42no—
341D188—84no—
342C4×D47—24no—
343C4×D47—22no—
344C4×D47—22no—
345C4×D47—48no—
346C4×D47—84no—
347C4×D47—84no—
348C4×D47—84no—
349C4×D47#12318yes—
350C4×D47C2×#4114yes—
351C4×D47C2×#4114yes—
352Dic94—28no—
353C8×C47—22no—
354C8×C47—22no—
355C47⋊C8—22no—
356C47⋊C8—22no—
357C2×#3099—471nomaximal, Sylow
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—22no—
361C22×C47—44no—
362C22×C47C2×#12312yes—
363C22×C47#57712yes—
364C22×C47#57712yes—
365C22×C47C23×D411yescharacteristic
366C2×D47—28no—
367C2×D47—22no—
368C2×D47—22no—
369C2×D47—22no—
370C2×D47—22no—
371C2×D47—22no—
372C2×D47—44no—
373C2×D47—42no—
374C2×D47—42no—
375C2×D47—42no—
376C2×D47—84no—
377C2×D47C2×#12314yes—
378C4×C47—22no—
379C4×C47—42no—
380C4×C47—42no—
381C4×C47—42no—
382C4×C47—42no—
383C4×C47C2×#12312yes—
384C4×C47C22×#4111yescharacteristic
385C4×C47C22×#4111yescharacteristic
386Dic47—22no—
387Dic47—42no—
388Dic47—42no—
389Dic47—42no—
390Dic47C2×#12314yes—
391C2×#537—471no—
392C2×#520—471no—
393#3099—4716no—
394C2×#481—471no—
395C2×#481—471no—
396C2×#485—471no—
397C2×#485D4711yescharacteristic, complemented
398C2×#482—471no—
399C2×#482—471no—
400C2×#483—471no—
401C2×#483—471no—
402C2×#428—471no—
403C22×#106—471no—
404C2×#417—471no—
405C2×#416—471no—
406C2×#408—471no—
407C2×C47—42no—
408C2×C47#309914yescomplemented
409C2×C47C22×#12311yescharacteristic
410C2×C47C2×#57711yescharacteristic
411C2×C47C2×#57711yescharacteristic
412D47—24no—
413D47—42no—
414D47—82no—
415C22×#41—471no—
416C22×#41—471no—
417C22×M16—471no—
418C23×C8—471no—
419#537—478no—
420#537—944no—
421C2×C22⋊Q8—471no—
422C2×C22⋊Q8—941no—
423C2×C22⋊Q8C2×D4711yescharacteristic
424C2×#121—471no—
425C2×#121—471no—
426C2×#121—941no—
427C2×#121—941no—
428C2×#121—941no—
429#520—478no—
430#520—944no—
431C2×C4×Q8—941no—
432C2×C4×D4—941no—
433C2×C4×D4—941no—
434C2×C4×D4—941no—
435C2×#117—471no—
436C2×#117—471no—
437C2×#117C2×D4711yescharacteristic
438C22×C4⋊C4—471no—
439C22×C4⋊C4—471no—
440C22×C4⋊C4—471no—
441C22×C4⋊C4—471no—
442#485—478no—
443#485C2×D4718yescomplemented
444#483—478no—
445#483—478no—
446#482—478no—
447#482—478no—
448#481—478no—
449#481—478no—
450#428—478no—
451C2×#107—471no—
452C2×#107C2×D4711yescharacteristic
453C2×#106—471no—
454C2×#106—471no—
455C2×#106—471no—
456C2×#106—471no—
457C2×#106—471no—
458C2×#106—478no—
459C2×#106C2×D4711yescharacteristic
460#417—478no—
461#416—478no—
462C2×#103—471no—
463C2×#103—471no—
464C2×#103C2×D4711yescharacteristic
465C2×#103C2×D4711yescharacteristic
466C2×#102—471no—
467C2×#102—471no—
468C2×#102—471no—
469C2×#102—471no—
470#408—478no—
471C2×C22⋊C8—471no—
472C2×C22⋊C8—471no—
473C2×C22⋊C8—471no—
474C2×C22⋊C8C2×D4711yescharacteristic
475C47C2×#309911yescharacteristic, complemented, Sylow
476C2×#41—474no—
477C2×#41—474no—
478C2×#41—474no—
479C2×#41—944no—
480C2×#41—944no—
481C2×#41—942no—
482C2×#41—944no—
483C2×#41—944no—
484C22×Q8—471no—
485C22×Q8C22×D4711yescharacteristic
486C22×D4—471no—
487C22×D4—471no—
488C22×D4—471no—
489C22×D4—471no—
490C22×D4—941no—
491C22×D4—941no—
492C22×D4—941no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—941no—
496C23×C4—941no—
497C23×C4—941no—
498C23×C4—941no—
499C23×C4—941no—
500C23×C4C22×D4711yescharacteristic
501C2×M16—474no—
502C2×M16—944no—
503C22×C8—471no—
504C22×C8—471no—
505C22×C8—474no—
506C22×C8—944no—
507C22×C8C22×D4711yescharacteristic
508C22×C8C22×D4711yescharacteristic
509C22⋊Q8—22no—
510C22⋊Q8—474no—
511C22⋊Q8—948no—
512C22⋊Q8—942no—
513C22⋊Q8C22×D4714yes—
514#121—474no—
515#121—474no—
516#121—948no—
517#121—948no—
518#121—942no—
519#121—948no—
520#121—942no—
521C4×Q8—948no—
522C4×D4—948no—
523C4×D4—948no—
524C4×D4—948no—
525#117—22no—
526#117—474no—
527#117—474no—
528#117—942no—
529#117—942no—
530#117C22×D4714yes—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—471no—
533C2×C4⋊C4—471no—
534C2×C4⋊C4—474no—
535C2×C4⋊C4—471no—
536C2×C4⋊C4—474no—
537C2×C4⋊C4—474no—
538C2×C4⋊C4—474no—
539C2×C4⋊C4—942no—
540C2×C4⋊C4—942no—
541C2×C4⋊C4—942no—
542C2×C4⋊C4—941no—
543C2×C4⋊C4—941no—
544C2×C4⋊C4—941no—
545C2×C4⋊C4—941no—
546C2×C4⋊C4—941no—
547C2×C4⋊C4—942no—
548C2×C4⋊C4C22×D4711yescharacteristic
549C2×C4⋊C4C22×D4711yescharacteristic
550C2×C4⋊C4C22×D4711yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—941no—
554C2×C22⋊C4—941no—
555C2×C22⋊C4—941no—
556C2×C22⋊C4—941no—
557C2×C22⋊C4—941no—
558C2×C42—21no—
559C2×C42—941no—
560C2×C42—941no—
561#107—474no—
562#107C22×D4714yes—
563#106—474no—
564#106—474no—
565#106—474no—
566#106—474no—
567#106—474no—
568#106C22×D4714yes—
569#103—474no—
570#103—474no—
571#103C22×D4714yes—
572#103C22×D4714yes—
573#102—474no—
574#102—474no—
575#102—474no—
576#102—474no—
577C22⋊C8—474no—
578C22⋊C8—474no—
579C22⋊C8—474no—
580C22⋊C8C22×D4714yes—
581C24—471no—
582C24—471no—
583C24—941no—
584C24D4×D4711yescharacteristic
585#41—9416no—
586#41—948no—
587#41—948no—
588#41—948no—
589#41—948no—
590#41—1888no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—474no—
595C2×Q8—944no—
596C2×Q8C23×D4712yes—
597C2×D4—474no—
598C2×D4—474no—
599C2×D4—474no—
600C2×D4—472no—
601C2×D4—944no—
602C2×D4—944no—
603C2×D4—944no—
604C2×D4—944no—
605C2×D4—944no—
606C2×D4—944no—
607C2×D4—941no—
608C2×D4—942no—
609C2×D4—942no—
610C2×D4—3762no—
611C2×D4—3762no—
612C2×D4—1884no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—471no—
620C22×C4—472no—
621C22×C4—474no—
622C22×C4—474no—
623C22×C4—472no—
624C22×C4—471no—
625C22×C4—472no—
626C22×C4—472no—
627C22×C4—944no—
628C22×C4—944no—
629C22×C4—944no—
630C22×C4—944no—
631C22×C4—942no—
632C22×C4—942no—
633C22×C4—944no—
634C22×C4—941no—
635C22×C4—941no—
636C22×C4—941no—
637C22×C4—3762no—
638C22×C4—3762no—
639C22×C4—3762no—
640C22×C4—3762no—
641C22×C4—1884no—
642C22×C4D4×D4712yes—
643C22×C4D4×D4711yescharacteristic
644C22×C4C23×D4712yes—
645C22×C4C23×D4711yescharacteristic
646M16—948no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—472no—
650C2×C8—472no—
651C2×C8—948no—
652C2×C8—942no—
653C2×C8—942no—
654C2×C8C23×D4712yes—
655C2×C8C23×D4712yes—
656C4⋊C4—24no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—472no—
661C4⋊C4—472no—
662C4⋊C4—472no—
663C4⋊C4—944no—
664C4⋊C4—944no—
665C4⋊C4—944no—
666C4⋊C4—944no—
667C4⋊C4—941no—
668C4⋊C4—941no—
669C4⋊C4—944no—
670C4⋊C4—941no—
671C4⋊C4C23×D4712yes—
672C4⋊C4C23×D4712yes—
673C4⋊C4C23×D4712yes—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—944no—
677C22⋊C4—944no—
678C22⋊C4—944no—
679C22⋊C4—944no—
680C22⋊C4—944no—
681C42—24no—
682C42—944no—
683C42—944no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—474no—
688C23—472no—
689C23—472no—
690C23—942no—
691C23—942no—
692C23—942no—
693C23—942no—
694C23—942no—
695C23—942no—
696C23—1882no—
697C23—1882no—
698C23—1882no—
699C23C2×D4×D4712yes—
700C23C2×D4×D4711yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—42no—
704Q8—948no—
705D4—948no—
706D4—948no—
707D4—948no—
708D4—942no—
709D4—942no—
710D4—3764no—
711D4—3764no—
712D4—1888no—
713D4—1882no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—474no—
727C2×C4—472no—
728C2×C4—478no—
729C2×C4—474no—
730C2×C4—474no—
731C2×C4—472no—
732C2×C4—942no—
733C2×C4—944no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—942no—
739C2×C4—3764no—
740C2×C4—3764no—
741C2×C4—3764no—
742C2×C4—3764no—
743C2×C4—1888no—
744C2×C4—1882no—
745C2×C4—1882no—
746C2×C4—1882no—
747C2×C4C2×D4×D4712yes—
748C2×C4C2×D4×D4711yescharacteristic
749C2×C4#41×D4712yes—
750C2×C4#41×D4712yes—
751C2×C4C24×D4711yescharacteristic
752C8—22no—
753C8—22no—
754C8—942no—
755C8—942no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—474no—
761C22—942no—
762C22—942no—
763C22—948no—
764C22—942no—
765C22—942no—
766C22—942no—
767C22—3764no—
768C22—1882no—
769C22—1882no—
770C22—1882no—
771C22—1884no—
772C22#123×D4712yes—
773C22#1568993012yes—
774C22#1568993212yes—
775C22C22×D4×D4711yescharacteristic
776C4—22no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—474no—
782C4—942no—
783C4—1882no—
784C4—1882no—
785C4—1882no—
786C4#123×D4712yes—
787C4C2×#41×D4711yescharacteristic
788C4C2×#41×D4711yescharacteristic
789C2—42no—
790C2—944no—
791C2—3762no—
792C2—1882no—
793C2#2025337414yesdirect product factor
794C2C2×#123×D4711yescharacteristic
795C2C2×#1568993011yescharacteristic
796C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#485C2
socleC23×C47C22×D4
prime radicalC2×#15689703C2
hypercenterC2×#485D47
hypocenterC47C2×#3099
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
2. C2×#15689603C2semidirect
3. #20253374C2direct (N × H)
4. C2×#15689443C2semidirect
5. C2×#15689442C2semidirect
6. C2×#15689462C2semidirect
7. C2×#15689450C2semidirect
8. C2×#15689447C2semidirect
9. C2×#15689452C2semidirect
10. C2×#15689451C2semidirect
11. C2×#15689164C2semidirect
12. C2×#106×D47C2semidirect
13. C2×#15689123C2semidirect
14. C2×#15689118C2semidirect
15. C2×#15689088C2semidirect
16. C2×C47×#485C2semidirect
31. #15689603C22semidirect
42. #15689462C22semidirect
43. #15689452C22semidirect
44. #15689451C22semidirect
45. #15689450C22semidirect
46. #15689447C22semidirect
47. #15689443C22semidirect
48. #15689442C22semidirect
49. #15689164C22semidirect
56. #106×D47C22semidirect
57. #15689123C22semidirect
58. #15689118C22semidirect
65. #15689088C22semidirect
71. C47×#485C22semidirect
397. C2×#485D47semidirect
408. C2×C47#3099semidirect
443. #485C2×D47semidirect
475. C47C2×#3099semidirect
793. C2#20253374direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897032
C2×#156896032
#202533742
C2×#156894432
C2×#156894422
C2×#156894622
C2×#156894502
C2×#156894472
C2×#156894522
C2×#156894512
C2×#156891642
C2×#106×D472
C2×#156891232
C2×#156891182
C2×#156890882
C2×C47×#4852
C2×#309947