Finite Group Databasebeta

← C2×#20253300 #27084044

Subgroups — C2×#20253300 #27084044

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×#15689633C211yesmaximal, characteristic
2C2×#117×D47C211yesmaximal, characteristic, complemented
3#20253300C2116yesmaximal, direct product factor
4C2×#15689460C211yesmaximal, characteristic, complemented
5C2×#15689440C211yesmaximal, characteristic, complemented
6C2×#15689465C211yesmaximal, characteristic, complemented
7C2×#15689464C211yesmaximal, characteristic, complemented
8C2×#15689444C211yesmaximal, characteristic, complemented
9C2×#15689455C211yesmaximal, characteristic, complemented
10C2×#15689435C211yesmaximal, characteristic, complemented
11C2×#15689160C211yesmaximal, characteristic, complemented
12C2×#15689158C211yesmaximal, characteristic, complemented
13C2×#15689116C211yesmaximal, characteristic, complemented
14C2×#15689116C211yesmaximal, characteristic, complemented
15C2×C22⋊C8×D47C211yesmaximal, characteristic, complemented
16C2×C47×#482C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21#15689633—24no—
22#15689633C2218yes—
23C2×#13094006—21no—
24C2×#13094004C2211yescharacteristic
25C2×#13094003C2211yescharacteristic
26C2×#13093995C2211yescharacteristic
27C2×#13093992—21no—
28C2×D4×Dic47—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#15689465C2218yescomplemented
43#15689464C2218yescomplemented
44#15689460C2218yescomplemented
45#15689455C2218yescomplemented
46#15689444C2218yescomplemented
47#15689440C2218yescomplemented
48#15689435C2218yescomplemented
49#15689160C2218yescomplemented
50#15689158C2218yescomplemented
51C2×#13093958C2211yescharacteristic, complemented
52C2×#13093957C2211yescharacteristic, complemented
53C2×#13093957C2211yescharacteristic, complemented
54C2×#13093956C2211yescharacteristic, complemented
55C2×#13093955C2211yescharacteristic, complemented
56C2×#13093955C2211yescharacteristic, complemented
57#15689116C2218yescomplemented
58#15689116C2218yescomplemented
59C2×#13093949C2211yescharacteristic, complemented
60C2×#13093949C2211yescharacteristic, complemented
61C2×#13093947C2211yescharacteristic, complemented
62C2×#13093947C2211yescharacteristic, complemented
63C2×#13093945C2211yescharacteristic, complemented
64C2×#13093945C2211yescharacteristic, complemented
65C2×C22⋊(C47⋊C8)C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C22⋊C8×D47C2218yescomplemented
69C2×#121×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic
71C47×#482C2218yescomplemented
72C2×#107×C47C2211yescharacteristic, complemented
73C2×#106×C47C2211yescharacteristic, complemented
74C2×#102×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic, complemented
76C2×C22⋊C8×C47C2211yescharacteristic
77C24×D47D411yescharacteristic
78C2×#10625352—22no—
79C2×#10625352—24no—
80C2×#10625352—24no—
81C2×#10625352C2314yes—
82C22×Dic94C2311yescharacteristic
83C22×C22⋊D47—21no—
84C22×C22⋊D47—21no—
85C23×Dic47—21no—
86C23×Dic47D411yescharacteristic
87C22×C4×D47—24no—
88C22×C4×D47—24no—
89C22×C4×D47—21no—
90C22×C4×D47—21no—
91C22×C4×D47D411yescharacteristic
92C22×C4×D47D414yes—
93C22×C4×D47D411yescharacteristic
94C22×C4×D47C2311yescharacteristic
95C22×C4×D47C2314yes—
96C22×C4×D47C2311yescharacteristic
97C22×C47⋊C8C2311yescharacteristic
98C22×C47⋊C8C2311yescharacteristic
99C2×C8×D47—24no—
100C2×C8×D47—24no—
101C2×C8×D47C2314yes—
102C2×C8×D47C2314yes—
103#13094006—28no—
104#13094004—22no—
105#13094004C2314yes—
106#13094003—22no—
107#13094003C2314yes—
108#13093995—22no—
109#13093995C2314yes—
110#13093992—28no—
111D4×Dic47—28no—
112(C22⋊D47)⋊C4—28no—
113#13093983—22no—
114#13093983C2314yes—
115#13093982—22no—
116#13093982—22no—
117#13093982—22no—
118#13093982C2314yes—
119#13093982C2314yes—
120#13093982C2314yes—
121#13093981—28no—
122#13093980—28no—
123C2×C4⋊Dic47—21no—
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×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—
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#13093949C2314yescomplemented
154#13093949C2314yescomplemented
155#13093947C2314yescomplemented
156#13093947C2314yescomplemented
157#13093945C2314yescomplemented
158#13093945C2314yescomplemented
159C22⋊(C47⋊C8)C2314yes—
160(C2×D47)⋊C8C2314yes—
161(C2×D47)⋊C8C2314yes—
162C22×D4×C47—21no—
163C22×D4×C47C2311yescharacteristic
164C23×C4×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167#121×C47—22no—
168#121×C47C2314yes—
169#117×C47—22no—
170#117×C47C2314yes—
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#102×C47C2314yescomplemented
180#102×C47C2314yescomplemented
181C22⋊C8×C47C2314yes—
182C24×C47—21no—
183C24×C47C2×D411yescharacteristic
184C23×D47—24no—
185C23×D47—24no—
186C23×D47—42no—
187C23×D47C2×D414yes—
188C23×D47C2×D411yescharacteristic
189C23×D47C2×D411yescharacteristic
190C2×D4×C47—24no—
191C2×D4×C47—21no—
192C2×D4×C47—22no—
193C2×D4×C47—22no—
194C2×D4×C47—44no—
195C2×D4×C47C2412yes—
196C22×C4×C47—22no—
197C22×C4×C47—22no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D412yes—
203C22×C4×C47C2412yes—
204C22×C4×C47C2411yescharacteristic
205C2×C22⋊D47—24no—
206C2×C22⋊D47—24no—
207C2×C22⋊D47—44no—
208C2×C22⋊D47—44no—
209C22×Dic47—24no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—24no—
215C22×Dic47—44no—
216C22×Dic47C2×D411yescharacteristic
217C22×Dic47C2×D414yes—
218C22×Dic47C2×D411yescharacteristic
219#10625352—28no—
220#10625352—28no—
221#10625352—48no—
222C2×C4×D47—24no—
223C2×C4×D47—22no—
224C2×C4×D47—22no—
225C2×C4×D47—24no—
226C2×C4×D47—216no—
227C2×C4×D47—28no—
228C2×C4×D47—28no—
229C2×C4×D47—24no—
230C2×C4×D47—24no—
231C2×C4×D47—44no—
232C2×C4×D47—44no—
233C2×C4×D47C2×D414yes—
234C2×C4×D47C2×D412yes—
235C2×C4×D47C2×D414yes—
236C2×C4×D47C2×D412yes—
237C2×C4×D47#4114yes—
238C2×C4×D47#4114yes—
239C2×C4×D47C2412yes—
240C2×C4×D47C2412yes—
241C2×Dic94—22no—
242C2×Dic94—22no—
243C2×Dic94—21no—
244C2×Dic94C2412yes—
245C2×C8×C47—22no—
246C2×C8×C47—22no—
247C2×C8×C47C2412yes—
248C2×C8×C47C2412yes—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47—21no—
252C4⋊C4×C47C2412yes—
253C4⋊C4×C47C2412yes—
254C4⋊C4×C47C2412yes—
255C22⋊C4×C47—24no—
256C22⋊C4×C47—24no—
257C42×C47—24no—
258C22⋊Dic47—24no—
259C22⋊Dic47—24no—
260C22⋊Dic47—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4—24no—
264(C2×D47)⋊C4—24no—
265C4⋊Dic47—21no—
266C4⋊Dic47—21no—
267C4⋊Dic47—21no—
268C4⋊Dic47—24no—
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×C47—22no—
289C23×C47—42no—
290C23×C47—42no—
291C23×C47—42no—
292C23×C47C22×D412yes—
293C23×C47C22×D411yescharacteristic
294C22×D47—22no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—28no—
299C22×D47—28no—
300C22×D47—44no—
301C22×D47—416no—
302C22×D47#12314yes—
303C22×D47#13514yes—
304C22×D47C22×D412yes—
305C22×D47C22×D412yes—
306D4×C47—22no—
307D4×C47—22no—
308D4×C47—48no—
309D4×C47—42no—
310C2×C4×C47—22no—
311C2×C4×C47—24no—
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×C47C22×D412yes—
321C2×C4×C47C22×D411yescharacteristic
322C2×C4×C47C2×#4112yes—
323C2×C4×C47C2×#4112yes—
324C2×C4×C47C2511yescharacteristic
325C22⋊D47—48no—
326C22⋊D47—48no—
327C2×Dic47—22no—
328C2×Dic47—28no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—42no—
334C2×Dic47—42no—
335C2×Dic47—42no—
336C2×Dic47—42no—
337C2×Dic47—48no—
338C2×Dic47#12314yes—
339C2×Dic47C22×D412yes—
340C2×Dic47C22×D412yes—
341C4×D47—28no—
342C4×D47—24no—
343C4×D47—22no—
344C4×D47—22no—
345C4×D47—28no—
346C4×D47—48no—
347C4×D47—48no—
348C4×D47#12318yes—
349C4×D47C2×#4114yes—
350C4×D47C2×#4114yes—
351Dic94—22no—
352Dic94—22no—
353Dic94—42no—
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×C47—42no—
364C22×C47—42no—
365C22×C47—42no—
366C22×C47—84no—
367C22×C47C2×#12312yes—
368C22×C47C2×#13512yes—
369C22×C47#57512yes—
370C22×C47C23×D411yescharacteristic
371C2×D47—28no—
372C2×D47—28no—
373C2×D47—22no—
374C2×D47—22no—
375C2×D47—22no—
376C2×D47—22no—
377C2×D47—416no—
378C2×D47C2×#12314yes—
379C2×D47C2×#13514yes—
380C4×C47—22no—
381C4×C47—42no—
382C4×C47—42no—
383C4×C47—42no—
384C4×C47C2×#12312yes—
385C4×C47C22×#4111yescharacteristic
386C4×C47C22×#4111yescharacteristic
387Dic47—22no—
388Dic47—42no—
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×#485—471no—
400C2×#482—471no—
401C2×#482D4711yescharacteristic, complemented
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—82no—
411C2×C47#309114yescomplemented
412C2×C47C22×#12311yescharacteristic
413C2×C47C22×#13511yescharacteristic
414C2×C47C2×#57511yescharacteristic
415D47—24no—
416D47—24no—
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⋊Q8—471no—
426C2×#121—471no—
427C2×#121C2×D4711yescharacteristic
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#485—478no—
446#484—478no—
447#483—478no—
448#482—478no—
449#482C2×D4718yescomplemented
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×#103—471no—
467C2×#103—471no—
468C2×#102—471no—
469C2×#102—471no—
470C2×#102C2×D4711yescharacteristic, complemented
471C2×#102C2×D4711yescharacteristic, complemented
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×Q8—471no—
484C22×D4—21no—
485C22×D4—941no—
486C22×D4—941no—
487C22×D4C22×D4711yescharacteristic
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—474no—
511C22⋊Q8—474no—
512C22⋊Q8—942no—
513C22⋊Q8—942no—
514#121—22no—
515#121—474no—
516#121—942no—
517#121C22×D4714yes—
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—471no—
534C2×C4⋊C4—471no—
535C2×C4⋊C4—471no—
536C2×C4⋊C4—474no—
537C2×C4⋊C4—474no—
538C2×C4⋊C4—942no—
539C2×C4⋊C4—942no—
540C2×C4⋊C4—941no—
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#103—474no—
574#103—474no—
575#102—474no—
576#102—474no—
577#102C22×D4714yescomplemented
578#102C22×D4714yescomplemented
579C22⋊C8—474no—
580C22⋊C8—474no—
581C22⋊C8—474no—
582C22⋊C8C22×D4714yes—
583C24—21no—
584C24—471no—
585C24—471no—
586C24—474no—
587C24—944no—
588C24—944no—
589C24—1882no—
590C24D4×D4711yescharacteristic
591#41—948no—
592#41—948no—
593#41—1888no—
594C2×Q8—472no—
595C2×Q8—941no—
596C2×Q8—942no—
597C2×Q8—942no—
598C2×D4—24no—
599C2×D4—21no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—44no—
603C2×D4—944no—
604C2×D4—944no—
605C2×D4—1884no—
606C2×D4—1884no—
607C2×D4C23×D4712yes—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—471no—
614C22×C4—472no—
615C22×C4—474no—
616C22×C4—474no—
617C22×C4—472no—
618C22×C4—474no—
619C22×C4—471no—
620C22×C4—474no—
621C22×C4—472no—
622C22×C4—474no—
623C22×C4—472no—
624C22×C4—944no—
625C22×C4—9416no—
626C22×C4—948no—
627C22×C4—948no—
628C22×C4—944no—
629C22×C4—944no—
630C22×C4—944no—
631C22×C4—944no—
632C22×C4—944no—
633C22×C4—942no—
634C22×C4—942no—
635C22×C4—941no—
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—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—472no—
660C4⋊C4—472no—
661C4⋊C4—472no—
662C4⋊C4—944no—
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—22no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—474no—
694C23—474no—
695C23—472no—
696C23—472no—
697C23—948no—
698C23—948no—
699C23—942no—
700C23—942no—
701C23—942no—
702C23—942no—
703C23—1884no—
704C23—18816no—
705C23C2×D4×D4712yes—
706C23C2×D4×D4711yescharacteristic
707Q8—942no—
708Q8—942no—
709Q8—1882no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—42no—
714D4—1888no—
715D4—1888no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
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—948no—
733C2×C4—948no—
734C2×C4—948no—
735C2×C4—942no—
736C2×C4—944no—
737C2×C4—942no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—942no—
743C2×C4—1888no—
744C2×C4—1888no—
745C2×C4—1888no—
746C2×C4—1882no—
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—42no—
764C22—42no—
765C22—42no—
766C22—84no—
767C22—474no—
768C22—474no—
769C22—942no—
770C22—942no—
771C22—942no—
772C22—942no—
773C22—948no—
774C22—948no—
775C22—18816no—
776C22#123×D4712yes—
777C22#135×D4712yes—
778C22#1568991912yes—
779C22C22×D4×D4711yescharacteristic
780C4—22no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—474no—
785C4—942no—
786C4—1882no—
787C4—1882no—
788C4—1882no—
789C4—1882no—
790C4#123×D4712yes—
791C4C2×#41×D4711yescharacteristic
792C4C2×#41×D4711yescharacteristic
793C2—42no—
794C2—82no—
795C2—944no—
796C2—944no—
797C2#2025330014yesdirect product factor
798C2C2×#123×D4711yescharacteristic
799C2C2×#135×D4711yescharacteristic
800C2C2×#1568991911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#482C2
socleC23×C47C22×D4
prime radicalC2×#15689633C2
hypercenterC2×#482D47
hypocenterC47C2×#3091
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
2. C2×#117×D47C2semidirect
3. #20253300C2direct (N × H)
4. C2×#15689460C2semidirect
5. C2×#15689440C2semidirect
6. C2×#15689465C2semidirect
7. C2×#15689464C2semidirect
8. C2×#15689444C2semidirect
9. C2×#15689455C2semidirect
10. C2×#15689435C2semidirect
11. C2×#15689160C2semidirect
12. C2×#15689158C2semidirect
13. C2×#15689116C2semidirect
14. C2×#15689116C2semidirect
15. C2×C22⋊C8×D47C2semidirect
16. C2×C47×#482C2semidirect
37. #117×D47C22semidirect
42. #15689465C22semidirect
43. #15689464C22semidirect
44. #15689460C22semidirect
45. #15689455C22semidirect
46. #15689444C22semidirect
47. #15689440C22semidirect
48. #15689435C22semidirect
49. #15689160C22semidirect
50. #15689158C22semidirect
51. C2×#13093958C22semidirect
52. C2×#13093957C22semidirect
53. C2×#13093957C22semidirect
54. C2×#13093956C22semidirect
55. C2×#13093955C22semidirect
56. C2×#13093955C22semidirect
57. #15689116C22semidirect
58. #15689116C22semidirect
59. C2×#13093949C22semidirect
60. C2×#13093949C22semidirect
61. C2×#13093947C22semidirect
62. C2×#13093947C22semidirect
63. C2×#13093945C22semidirect
64. C2×#13093945C22semidirect
68. C22⋊C8×D47C22semidirect
71. C47×#482C22semidirect
72. C2×#107×C47C22semidirect
73. C2×#106×C47C22semidirect
74. C2×#102×C47C22semidirect
75. C2×#102×C47C22semidirect
147. #13093958C23semidirect
148. #13093957C23semidirect
149. #13093957C23semidirect
150. #13093956C23semidirect
151. #13093955C23semidirect
152. #13093955C23semidirect
153. #13093949C23semidirect
154. #13093949C23semidirect
155. #13093947C23semidirect
156. #13093947C23semidirect
157. #13093945C23semidirect
158. #13093945C23semidirect
177. #107×C47C23semidirect
178. #106×C47C23semidirect
179. #102×C47C23semidirect
180. #102×C47C23semidirect
401. C2×#482D47semidirect
411. C2×C47#3091semidirect
449. #482C2×D47semidirect
457. C2×#107C2×D47semidirect
461. C2×#106C2×D47semidirect
470. C2×#102C2×D47semidirect
471. C2×#102C2×D47semidirect
477. C47C2×#3091semidirect
566. #107C22×D47semidirect
570. #106C22×D47semidirect
577. #102C22×D47semidirect
578. #102C22×D47semidirect
797. C2#20253300direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896332
C2×#117×D472
#202533002
C2×#156894602
C2×#156894402
C2×#156894652
C2×#156894642
C2×#156894442
C2×#156894552
C2×#156894352
C2×#156891602
C2×#156891582
C2×#156891162
C2×C22⋊C8×D472
C2×C47×#4822
C2×#309147