Finite Group Databasebeta

← C2×#20253306 #27084050

Subgroups — C2×#20253306 #27084050

Order 12032.

2378 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689636C211yesmaximal, characteristic
2C2×#117×D47C211yesmaximal, characteristic, complemented
3#20253306C2116yesmaximal, direct product factor
4C2×#15689457C211yesmaximal, characteristic, complemented
5C2×#15689443C211yesmaximal, characteristic, complemented
6C2×#15689461C211yesmaximal, characteristic, complemented
7C2×#15689448C211yesmaximal, characteristic, complemented
8C2×#15689447C211yesmaximal, characteristic, complemented
9C2×#15689452C211yesmaximal, characteristic, complemented
10C2×#15689438C211yesmaximal, characteristic, complemented
11C2×#15689160C211yesmaximal, characteristic, complemented
12C2×#15689158C211yesmaximal, characteristic, complemented
13C2×#15689118C211yesmaximal, characteristic, complemented
14C2×#15689118C211yesmaximal, characteristic, complemented
15C2×C22⋊C8×D47C211yesmaximal, characteristic, complemented
16C2×C47×#485C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21#15689636—24no—
22#15689636C2218yes—
23C2×#13094009—21no—
24C2×#13094000C2211yescharacteristic
25C2×#13093999C2211yescharacteristic
26C2×#13093998C2211yescharacteristic
27C2×#13093994—21no—
28C2×#13093986—21no—
29C2×(C22⋊D47)⋊C4—21no—
30C2×#13093983C2211yescharacteristic
31C2×#13093982C2211yescharacteristic
32C2×#13093982C2211yescharacteristic
33C2×#13093982C2211yescharacteristic
34C2×#13093981—21no—
35C2×#13093980—21no—
36#117×D47—24no—
37#117×D47C2218yescomplemented
38C2×C4⋊C4×D47C2211yescharacteristic
39C2×C4⋊C4×D47C2211yescharacteristic
40C2×C22⋊C4×D47—21no—
41C2×C42×D47—21no—
42#15689461C2218yescomplemented
43#15689457C2218yescomplemented
44#15689452C2218yescomplemented
45#15689448C2218yescomplemented
46#15689447C2218yescomplemented
47#15689443C2218yescomplemented
48#15689438C2218yescomplemented
49#15689160C2218yescomplemented
50#15689158C2218yescomplemented
51C2×#13093958C2211yescharacteristic, complemented
52C2×#13093957C2211yescharacteristic, complemented
53C2×#13093957C2211yescharacteristic, complemented
54C2×#13093956C2211yescharacteristic, complemented
55C2×#13093955C2211yescharacteristic, complemented
56C2×#13093955C2211yescharacteristic, complemented
57#15689118C2218yescomplemented
58#15689118C2218yescomplemented
59C2×#13093948C2211yescharacteristic, complemented
60C2×#13093948C2211yescharacteristic, complemented
61C2×#13093946C2211yescharacteristic, complemented
62C2×#13093946C2211yescharacteristic, complemented
63C2×#13093944C2211yescharacteristic, complemented
64C2×#13093944C2211yescharacteristic, complemented
65C2×C22⋊(C47⋊C8)C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C22⋊C8×D47C2218yescomplemented
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
78C2×#10625354—22no—
79C2×#10625354—24no—
80C2×#10625354—24no—
81C2×#10625354C2314yes—
82C22×D188—21no—
83C22×D188—21no—
84C22×D188C2311yescharacteristic
85C22×C22⋊D47—21no—
86C23×Dic47D411yescharacteristic
87C22×C4×D47—24no—
88C22×C4×D47—24no—
89C22×C4×D47—21no—
90C22×C4×D47—21no—
91C22×C4×D47—21no—
92C22×C4×D47D411yescharacteristic
93C22×C4×D47D414yes—
94C22×C4×D47D411yescharacteristic
95C22×C4×D47C2311yescharacteristic
96C22×C4×D47C2314yes—
97C22×C4×D47C2311yescharacteristic
98C22×C47⋊C8C2311yescharacteristic
99C22×C47⋊C8C2311yescharacteristic
100C2×C8×D47—24no—
101C2×C8×D47—24no—
102C2×C8×D47C2314yes—
103C2×C8×D47C2314yes—
104#13094009—28no—
105#13094000—22no—
106#13094000C2314yes—
107#13093999—22no—
108#13093999C2314yes—
109#13093998—22no—
110#13093998C2314yes—
111#13093994—28no—
112#13093986—28no—
113(C22⋊D47)⋊C4—28no—
114#13093983—22no—
115#13093983C2314yes—
116#13093982—22no—
117#13093982—22no—
118#13093982—22no—
119#13093982C2314yes—
120#13093982C2314yes—
121#13093982C2314yes—
122#13093981—28no—
123#13093980—28no—
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C4⋊C4×D47—22no—
131C4⋊C4×D47—22no—
132C4⋊C4×D47C2314yes—
133C4⋊C4×D47C2314yes—
134C2×C22⋊Dic47—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—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—
142C2×C4×Dic47—21no—
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#13093948C2314yescomplemented
154#13093948C2314yescomplemented
155#13093946C2314yescomplemented
156#13093946C2314yescomplemented
157#13093944C2314yescomplemented
158#13093944C2314yescomplemented
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—21no—
186C23×D47—42no—
187C23×D47C2×D414yes—
188C23×D47C2×D411yescharacteristic
189C23×D47C2×D411yescharacteristic
190C2×Q8×C47—21no—
191C2×Q8×C47—22no—
192C2×Q8×C47—22no—
193C2×Q8×C47C2412yes—
194C22×C4×C47—22no—
195C22×C4×C47—22no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D412yes—
202C22×C4×C47C2412yes—
203C22×C4×C47C2411yescharacteristic
204C2×C22⋊D47—24no—
205C2×C22⋊D47—44no—
206C22×Dic47—24no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47C2×D411yescharacteristic
211C22×Dic47C2×D414yes—
212C22×Dic47C2×D411yescharacteristic
213#10625354—28no—
214#10625354—28no—
215#10625354—48no—
216C2×D188—22no—
217C2×D188—22no—
218C2×D188—24no—
219C2×D188—24no—
220C2×D188—21no—
221C2×D188—44no—
222C2×D188—44no—
223C2×D188C2412yes—
224C2×C4×D47—24no—
225C2×C4×D47—22no—
226C2×C4×D47—22no—
227C2×C4×D47—24no—
228C2×C4×D47—216no—
229C2×C4×D47—28no—
230C2×C4×D47—28no—
231C2×C4×D47—24no—
232C2×C4×D47—24no—
233C2×C4×D47—24no—
234C2×C4×D47—44no—
235C2×C4×D47—44no—
236C2×C4×D47—44no—
237C2×C4×D47C2×D414yes—
238C2×C4×D47C2×D412yes—
239C2×C4×D47C2×D414yes—
240C2×C4×D47C2×D412yes—
241C2×C4×D47#4114yes—
242C2×C4×D47#4114yes—
243C2×C4×D47C2412yes—
244C2×C4×D47C2412yes—
245C2×C8×C47—22no—
246C2×C8×C47—22no—
247C2×C8×C47C2412yes—
248C2×C8×C47C2412yes—
249C4⋊C4×C47—24no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47—21no—
252C4⋊C4×C47—21no—
253C4⋊C4×C47C2412yes—
254C4⋊C4×C47C2412yes—
255C4⋊C4×C47C2412yes—
256C22⋊C4×C47—24no—
257C22⋊C4×C47—24no—
258C42×C47—24no—
259C22⋊Dic47—24no—
260(C2×D47)⋊C4—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⋊Dic47C2412yes—
270C4⋊Dic47C2412yes—
271C4⋊Dic47C2412yes—
272Dic47⋊C4—24no—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275C4×Dic47—24no—
276C4×Dic47—24no—
277C4×Dic47—24no—
278C4×Dic47—24no—
279C2×C47⋊C8—22no—
280C2×C47⋊C8—22no—
281C2×C47⋊C8C2412yes—
282C2×C47⋊C8C2412yes—
283C8×D47—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—28no—
295C22×D47—28no—
296C22×D47—22no—
297C22×D47—44no—
298C22×D47—416no—
299C22×D47—42no—
300C22×D47—42no—
301C22×D47—42no—
302C22×D47#12314yes—
303C22×D47#13514yes—
304C22×D47C22×D412yes—
305C22×D47C22×D412yes—
306Q8×C47—22no—
307Q8×C47—22no—
308Q8×C47—42no—
309C2×C4×C47—22no—
310C2×C4×C47—24no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—42no—
318C2×C4×C47—42no—
319C2×C4×C47—42no—
320C2×C4×C47—42no—
321C2×C4×C47C22×D412yes—
322C2×C4×C47C22×D411yescharacteristic
323C2×C4×C47C2×#4112yes—
324C2×C4×C47C2×#4112yes—
325C2×C4×C47C2511yescharacteristic
326C22⋊D47—48no—
327C2×Dic47—22no—
328C2×Dic47—28no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—42no—
333C2×Dic47—42no—
334C2×Dic47—42no—
335C2×Dic47#12314yes—
336C2×Dic47C22×D412yes—
337C2×Dic47C22×D412yes—
338D188—22no—
339D188—22no—
340D188—48no—
341D188—48no—
342D188—42no—
343C4×D47—28no—
344C4×D47—24no—
345C4×D47—22no—
346C4×D47—22no—
347C4×D47—28no—
348C4×D47—48no—
349C4×D47—48no—
350C4×D47—48no—
351C4×D47#12318yes—
352C4×D47C2×#4114yes—
353C4×D47C2×#4114yes—
354C8×C47—22no—
355C8×C47—22no—
356C47⋊C8—22no—
357C47⋊C8—22no—
358C2×#3091—471nomaximal, Sylow
359C22×C47—22no—
360C22×C47—22no—
361C22×C47—22no—
362C22×C47—44no—
363C22×C47C2×#12312yes—
364C22×C47C2×#13512yes—
365C22×C47#57512yes—
366C22×C47C23×D411yescharacteristic
367C2×D47—28no—
368C2×D47—28no—
369C2×D47—22no—
370C2×D47—22no—
371C2×D47—22no—
372C2×D47—22no—
373C2×D47—416no—
374C2×D47—42no—
375C2×D47—42no—
376C2×D47—42no—
377C2×D47—84no—
378C2×D47C2×#12314yes—
379C2×D47C2×#13514yes—
380C4×C47—22no—
381C4×C47—42no—
382C4×C47—42no—
383C4×C47—42no—
384C4×C47—42no—
385C4×C47C2×#12312yes—
386C4×C47C22×#4111yescharacteristic
387C4×C47C22×#4111yescharacteristic
388Dic47—22no—
389Dic47—42no—
390Dic47—42no—
391Dic47—42no—
392Dic47C2×#12314yes—
393C2×#525—471no—
394C22×#117—471no—
395#3091—4716no—
396C2×#484—471no—
397C2×#481—471no—
398C2×#485—471no—
399C2×#485D4711yescharacteristic, complemented
400C2×#482—471no—
401C2×#482—471no—
402C2×#483—471no—
403C2×#480—471no—
404C2×#427—471no—
405C2×#427—471no—
406C2×#416—471no—
407C2×#416—471no—
408C22×C22⋊C8—471no—
409C2×C47—42no—
410C2×C47#309114yescomplemented
411C2×C47C22×#12311yescharacteristic
412C2×C47C22×#13511yescharacteristic
413C2×C47C2×#57511yescharacteristic
414D47—24no—
415D47—24no—
416D47—82no—
417C22×#41—471no—
418C24×C4—471no—
419C23×C8—471no—
420C23×C8—471no—
421#525—478no—
422#525—944no—
423C2×#123—941no—
424C2×C22⋊Q8—471no—
425C2×C22⋊Q8C2×D4711yescharacteristic
426C2×#121—471no—
427C2×#121—471no—
428C2×#120—941no—
429C2×C4×D4—941no—
430C2×C4×D4—941no—
431C2×#117—471no—
432C2×#117—478no—
433C2×#117—471no—
434C2×#117—471no—
435C2×#117—471no—
436C2×#117—941no—
437C2×#117—941no—
438C2×#117—944no—
439C2×#117C2×D4711yescharacteristic
440C22×C4⋊C4—471no—
441C22×C4⋊C4—471no—
442C22×C22⋊C4—941no—
443C22×C42—941no—
444#485—478no—
445#485C2×D4718yescomplemented
446#484—478no—
447#483—478no—
448#482—478no—
449#482—478no—
450#481—478no—
451#480—478no—
452#427—478no—
453#427—478no—
454C2×#107—471no—
455C2×#107—471no—
456C2×#107—471no—
457C2×#107C2×D4711yescharacteristic, complemented
458C2×#106—471no—
459C2×#106—471no—
460C2×#106—471no—
461C2×#106C2×D4711yescharacteristic, complemented
462#416—478no—
463#416—478no—
464C2×#103—471no—
465C2×#103—471no—
466C2×#103C2×D4711yescharacteristic, complemented
467C2×#103C2×D4711yescharacteristic, complemented
468C2×#102—471no—
469C2×#102—471no—
470C2×#102—471no—
471C2×#102—471no—
472C2×C22⋊C8—471no—
473C2×C22⋊C8—471no—
474C2×C22⋊C8—471no—
475C2×C22⋊C8—478no—
476C2×C22⋊C8C2×D4711yescharacteristic
477C47C2×#309111yescharacteristic, complemented, Sylow
478C25—471no—
479C2×#41—474no—
480C2×#41—942no—
481C2×#41—944no—
482C2×#41—944no—
483C22×Q8C22×D4711yescharacteristic
484C22×D4—471no—
485C22×D4—941no—
486C22×D4—941no—
487C22×D4—941no—
488C23×C4—471no—
489C23×C4—471no—
490C23×C4—471no—
491C23×C4—474no—
492C23×C4—471no—
493C23×C4—471no—
494C23×C4—474no—
495C23×C4—944no—
496C23×C4—944no—
497C23×C4—941no—
498C23×C4—941no—
499C23×C4—941no—
500C23×C4C22×D4711yescharacteristic
501C22×C8—471no—
502C22×C8—471no—
503C22×C8—474no—
504C22×C8—474no—
505C22×C8—944no—
506C22×C8—944no—
507C22×C8C22×D4711yescharacteristic
508C22×C8C22×D4711yescharacteristic
509#123—948no—
510C22⋊Q8—22no—
511C22⋊Q8—474no—
512C22⋊Q8—942no—
513C22⋊Q8C22×D4714yes—
514#121—474no—
515#121—474no—
516#121—942no—
517#121—942no—
518#120—948no—
519C4×D4—948no—
520C4×D4—948no—
521#117—22no—
522#117—474no—
523#117—474no—
524#117—474no—
525#117—474no—
526#117—948no—
527#117—948no—
528#117—942no—
529#117—942no—
530#117—942no—
531#117—942no—
532#117C22×D4714yes—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—471no—
535C2×C4⋊C4—471no—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—474no—
538C2×C4⋊C4—474no—
539C2×C4⋊C4—942no—
540C2×C4⋊C4—942no—
541C2×C4⋊C4—941no—
542C2×C4⋊C4—941no—
543C2×C4⋊C4—941no—
544C2×C4⋊C4C22×D4711yescharacteristic
545C2×C4⋊C4C22×D4711yescharacteristic
546C2×C4⋊C4C22×D4711yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—948no—
550C2×C22⋊C4—941no—
551C2×C22⋊C4—941no—
552C2×C22⋊C4—941no—
553C2×C22⋊C4—941no—
554C2×C22⋊C4—941no—
555C2×C22⋊C4—941no—
556C2×C22⋊C4—941no—
557C2×C42—21no—
558C2×C42—948no—
559C2×C42—941no—
560C2×C42—941no—
561C2×C42—941no—
562C2×C42—941no—
563#107—474no—
564#107—474no—
565#107—474no—
566#107C22×D4714yescomplemented
567#106—474no—
568#106—474no—
569#106—474no—
570#106C22×D4714yescomplemented
571#103—474no—
572#103—474no—
573#103C22×D4714yescomplemented
574#103C22×D4714yescomplemented
575#102—474no—
576#102—474no—
577#102—474no—
578#102—474no—
579C22⋊C8—474no—
580C22⋊C8—474no—
581C22⋊C8—474no—
582C22⋊C8C22×D4714yes—
583C24—471no—
584C24—471no—
585C24—474no—
586C24—944no—
587C24—944no—
588C24—941no—
589C24—1882no—
590C24D4×D4711yescharacteristic
591#41—948no—
592#41—948no—
593#41—1888no—
594C2×Q8—21no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8C23×D4712yes—
598C2×D4—472no—
599C2×D4—944no—
600C2×D4—944no—
601C2×D4—944no—
602C2×D4—941no—
603C2×D4—942no—
604C2×D4—942no—
605C2×D4—1884no—
606C2×D4—1884no—
607C2×D4—1884no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—471no—
615C22×C4—472no—
616C22×C4—474no—
617C22×C4—474no—
618C22×C4—472no—
619C22×C4—474no—
620C22×C4—471no—
621C22×C4—474no—
622C22×C4—472no—
623C22×C4—474no—
624C22×C4—472no—
625C22×C4—944no—
626C22×C4—9416no—
627C22×C4—948no—
628C22×C4—948no—
629C22×C4—944no—
630C22×C4—944no—
631C22×C4—944no—
632C22×C4—944no—
633C22×C4—944no—
634C22×C4—942no—
635C22×C4—942no—
636C22×C4—941no—
637C22×C4—941no—
638C22×C4—941no—
639C22×C4—1884no—
640C22×C4—1884no—
641C22×C4—1884no—
642C22×C4D4×D4712yes—
643C22×C4D4×D4711yescharacteristic
644C22×C4C23×D4712yes—
645C22×C4C23×D4711yescharacteristic
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—472no—
649C2×C8—472no—
650C2×C8—948no—
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—941no—
667C4⋊C4—941no—
668C4⋊C4—941no—
669C4⋊C4C23×D4712yes—
670C4⋊C4C23×D4712yes—
671C4⋊C4C23×D4712yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—944no—
675C22⋊C4—944no—
676C22⋊C4—944no—
677C22⋊C4—944no—
678C22⋊C4—944no—
679C22⋊C4—944no—
680C22⋊C4—944no—
681C42—24no—
682C42—944no—
683C42—944no—
684C42—944no—
685C42—944no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—474no—
690C23—474no—
691C23—472no—
692C23—472no—
693C23—948no—
694C23—948no—
695C23—942no—
696C23—942no—
697C23—942no—
698C23—942no—
699C23—942no—
700C23—1884no—
701C23—18816no—
702C23—1882no—
703C23—1882no—
704C23—1882no—
705C23C2×D4×D4712yes—
706C23C2×D4×D4711yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—42no—
710D4—942no—
711D4—942no—
712D4—1888no—
713D4—1888no—
714D4—1888no—
715D4—1882no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—474no—
729C2×C4—472no—
730C2×C4—478no—
731C2×C4—474no—
732C2×C4—474no—
733C2×C4—472no—
734C2×C4—948no—
735C2×C4—948no—
736C2×C4—948no—
737C2×C4—942no—
738C2×C4—944no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—942no—
743C2×C4—942no—
744C2×C4—1888no—
745C2×C4—1888no—
746C2×C4—1888no—
747C2×C4—1882no—
748C2×C4—1882no—
749C2×C4—1882no—
750C2×C4C2×D4×D4712yes—
751C2×C4C2×D4×D4711yescharacteristic
752C2×C4#41×D4712yes—
753C2×C4#41×D4712yes—
754C2×C4C24×D4711yescharacteristic
755C8—22no—
756C8—22no—
757C8—942no—
758C8—942no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—44no—
763C22—474no—
764C22—474no—
765C22—942no—
766C22—942no—
767C22—942no—
768C22—942no—
769C22—948no—
770C22—948no—
771C22—3764no—
772C22—18816no—
773C22—1882no—
774C22—1882no—
775C22—1882no—
776C22#123×D4712yes—
777C22#135×D4712yes—
778C22#1568992212yes—
779C22C22×D4×D4711yescharacteristic
780C4—22no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—474no—
786C4—942no—
787C4—1882no—
788C4—1882no—
789C4—1882no—
790C4#123×D4712yes—
791C4C2×#41×D4711yescharacteristic
792C4C2×#41×D4711yescharacteristic
793C2—42no—
794C2—944no—
795C2—944no—
796C2—3762no—
797C2#2025330614yesdirect product factor
798C2C2×#123×D4711yescharacteristic
799C2C2×#135×D4711yescharacteristic
800C2C2×#1568992211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#485C2
socleC23×C47C22×D4
prime radicalC2×#15689636C2
hypercenterC2×#485D47
hypocenterC47C2×#3091
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×#117×D47C2semidirect
3. #20253306C2direct (N × H)
4. C2×#15689457C2semidirect
5. C2×#15689443C2semidirect
6. C2×#15689461C2semidirect
7. C2×#15689448C2semidirect
8. C2×#15689447C2semidirect
9. C2×#15689452C2semidirect
10. C2×#15689438C2semidirect
11. C2×#15689160C2semidirect
12. C2×#15689158C2semidirect
13. C2×#15689118C2semidirect
14. C2×#15689118C2semidirect
15. C2×C22⋊C8×D47C2semidirect
16. C2×C47×#485C2semidirect
37. #117×D47C22semidirect
42. #15689461C22semidirect
43. #15689457C22semidirect
44. #15689452C22semidirect
45. #15689448C22semidirect
46. #15689447C22semidirect
47. #15689443C22semidirect
48. #15689438C22semidirect
49. #15689160C22semidirect
50. #15689158C22semidirect
51. C2×#13093958C22semidirect
52. C2×#13093957C22semidirect
53. C2×#13093957C22semidirect
54. C2×#13093956C22semidirect
55. C2×#13093955C22semidirect
56. C2×#13093955C22semidirect
57. #15689118C22semidirect
58. #15689118C22semidirect
59. C2×#13093948C22semidirect
60. C2×#13093948C22semidirect
61. C2×#13093946C22semidirect
62. C2×#13093946C22semidirect
63. C2×#13093944C22semidirect
64. C2×#13093944C22semidirect
68. C22⋊C8×D47C22semidirect
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. #13093948C23semidirect
154. #13093948C23semidirect
155. #13093946C23semidirect
156. #13093946C23semidirect
157. #13093944C23semidirect
158. #13093944C23semidirect
177. #107×C47C23semidirect
178. #106×C47C23semidirect
179. #103×C47C23semidirect
180. #103×C47C23semidirect
399. C2×#485D47semidirect
410. C2×C47#3091semidirect
445. #485C2×D47semidirect
457. C2×#107C2×D47semidirect
461. C2×#106C2×D47semidirect
466. C2×#103C2×D47semidirect
467. C2×#103C2×D47semidirect
477. C47C2×#3091semidirect
566. #107C22×D47semidirect
570. #106C22×D47semidirect
573. #103C22×D47semidirect
574. #103C22×D47semidirect
797. C2#20253306direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896362
C2×#117×D472
#202533062
C2×#156894572
C2×#156894432
C2×#156894612
C2×#156894482
C2×#156894472
C2×#156894522
C2×#156894382
C2×#156891602
C2×#156891582
C2×#156891182
C2×C22⋊C8×D472
C2×C47×#4852
C2×#309147