Finite Group Databasebeta

← #26221426

Subgroups — #26221426

Order 12032.

1150 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689184C211yesmaximal, characteristic, complemented
2#20245744C211yesmaximal, characteristic, complemented
3#20244341C211yesmaximal, characteristic, complemented
4#20244337C211yesmaximal, characteristic, complemented
5#20244321C211yesmaximal, characteristic, complemented
6#20244321C211yesmaximal, characteristic, complemented
7#20243711C211yesmaximal, characteristic
8#20243706C211yesmaximal, characteristic
9#20243701C211yesmaximal, characteristic, complemented
10#20243696C211yesmaximal, characteristic, complemented
11#20243218C211yesmaximal, characteristic, complemented
12#20243213C211yesmaximal, characteristic, complemented
13C4×#13093948C211yesmaximal, characteristic, complemented
14C4×#13093945C211yesmaximal, characteristic, complemented
15C2×C47×#542C211yesmaximal, characteristic
16C2×#13093983C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18#15689184—24no—
19C2×C4⋊(C47⋊C8)C2211yescharacteristic
20C2×C4⋊(C47⋊C8)C2211yescharacteristic
21C2×#13093948C2211yescharacteristic
22C2×#13093948C2211yescharacteristic
23C2×#13093948C2211yescharacteristic
24C2×#13093948C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×#13093945C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×C22⋊(C47⋊C8)C2211yescharacteristic
31C2×#13093935C2211yescharacteristic
32C2×C4×C47⋊C8C2211yescharacteristic
33C4⋊C4×Dic47—21no—
34C4⋊C4×Dic47—21no—
35C4×C4⋊Dic47C2211yescharacteristic
36C4×C4⋊Dic47C2211yescharacteristic
37C4×C4⋊Dic47C2211yescharacteristic
38C4×C4⋊Dic47C2211yescharacteristic
39C22⋊C4×Dic47—21no—
40C22⋊C4×Dic47—21no—
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49C47×#542—24no—
50C47×#542C418yescomplemented
51C2×C4⋊Q8×C47C2211yescharacteristic
52C2×#126×C47—21no—
53C2×#124×C47—21no—
54C2×#124×C47C2211yescharacteristic
55C2×#123×C47—21no—
56C2×C22⋊Q8×C47—21no—
57C2×C22⋊Q8×C47C2211yescharacteristic
58C2×#121×C47C2211yescharacteristic
59C2×C4×Q8×C47C2211yescharacteristic
60C2×C4×D4×C47C2211yescharacteristic
61C2×#117×C47C2211yescharacteristic
62C23×Dic47—21no—
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67#13093983—22no—
68#13093983—22no—
69C2×C4⋊Dic47—21no—
70C2×C4⋊Dic47—22no—
71C2×C4⋊Dic47—22no—
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C22⋊Dic47—21no—
77C2×C4×Dic47—21no—
78C2×C4×Dic47—21no—
79C2×C4×Dic47—21no—
80C2×C4×Dic47—21no—
81C2×C4×Dic47—21no—
82C4⋊(C47⋊C8)—22no—
83C4⋊(C47⋊C8)—22no—
84#13093948—22no—
85#13093948—22no—
86#13093948—22no—
87#13093948—22no—
88#13093945—22no—
89#13093945—22no—
90#13093945—22no—
91#13093945—22no—
92C22⋊(C47⋊C8)—22no—
93C22⋊(C47⋊C8)—22no—
94#13093935—22no—
95C4×C47⋊C8—22no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C22×Q8×C47—21no—
101C22×Q8×C47C2311yescharacteristic
102C22×D4×C47—21no—
103C22×D4×C47C2311yescharacteristic
104C23×C4×C47—21no—
105C23×C4×C47C2311yescharacteristic
106C4⋊Q8×C47—22no—
107C4⋊Q8×C47C2×C414yescomplemented
108#126×C47—28no—
109#124×C47—28no—
110#124×C47—22no—
111#124×C47C2×C414yescomplemented
112#123×C47—28no—
113C22⋊Q8×C47—22no—
114C22⋊Q8×C47—28no—
115C22⋊Q8×C47C2×C414yes—
116#121×C47—22no—
117#121×C47C2×C414yes—
118C4×Q8×C47—22no—
119C4×Q8×C47C2×C414yescomplemented
120C4×D4×C47—22no—
121C4×D4×C47C2×C414yescomplemented
122#117×C47C2×C414yes—
123#117×C47D414yes—
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47—21no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47D411yescharacteristic
128C2×C4⋊C4×C47D411yescharacteristic
129C2×C4⋊C4×C47C2311yescharacteristic
130C2×C4⋊C4×C47C2311yescharacteristic
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134C2×C22⋊C4×C47—21no—
135C2×C22⋊C4×C47—21no—
136C2×C22⋊C4×C47D411yescharacteristic
137C2×C22⋊C4×C47D411yescharacteristic
138C2×C42×C47—21no—
139C2×C42×C47C2311yescharacteristic
140C2×C42×C47C2311yescharacteristic
141C24×C47—21no—
142C24×C47C2×D411yescharacteristic
143C2×Q8×C47—24no—
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—81no—
150C2×Q8×C47—81no—
151C2×Q8×C47C22×C412yes—
152C2×D4×C47—24no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—81no—
159C2×D4×C47—81no—
160C2×D4×C47C22×C412yes—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—24no—
169C22×C4×C47—81no—
170C22×C4×C47—81no—
171C22×C4×C47C22×C412yes—
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47C2×D411yescharacteristic
174C22×C4×C47C2×D411yescharacteristic
175C22×C4×C47C2×D411yescharacteristic
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47C2×D412yes—
178C22×C4×C47C2411yescharacteristic
179C22×Dic47—21no—
180C22×Dic47—21no—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—24no—
184C22×Dic47—81no—
185C22×Dic47—81no—
186C4⋊C4×C47—24no—
187C4⋊C4×C47—24no—
188C4⋊C4×C47—24no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47C22⋊C414yes—
192C4⋊C4×C47C22⋊C414yes—
193C4⋊C4×C47C22×C412yes—
194C4⋊C4×C47C22×C412yes—
195C22⋊C4×C47—24no—
196C22⋊C4×C47—24no—
197C22⋊C4×C47—24no—
198C22⋊C4×C47—24no—
199C22⋊C4×C47—24no—
200C22⋊C4×C47C22⋊C414yes—
201C22⋊C4×C47C22⋊C414yes—
202C42×C47—24no—
203C42×C47C22×C412yes—
204C42×C47C22×C412yes—
205C42×C47C2×D412yes—
206C42×C47C2×D412yes—
207C22⋊Dic47—24no—
208C4⋊Dic47—24no—
209C4⋊Dic47—21no—
210C4⋊Dic47—21no—
211C4⋊Dic47—21no—
212C4⋊Dic47—21no—
213C4⋊Dic47#4112yes—
214C4⋊Dic47#4112yes—
215C4⋊Dic47#4112yes—
216C4⋊Dic47#4112yes—
217C4×Dic47—24no—
218C4×Dic47—81no—
219C4×Dic47—81no—
220C4×Dic47—81no—
221C4×Dic47—81no—
222C2×C47⋊C8—21no—
223C2×C47⋊C8—21no—
224C2×C47⋊C8—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C23×C47—21no—
235C23×C47—21no—
236C23×C47—21no—
237C23×C47—21no—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47—22no—
241C23×C47—41no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47—41no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47C2×C22⋊C412yes—
248C23×C47C22×D411yescharacteristic
249Q8×C47—22no—
250Q8×C47—22no—
251Q8×C47—41no—
252Q8×C47—41no—
253Q8×C47—84no—
254D4×C47—22no—
255D4×C47—22no—
256D4×C47—41no—
257D4×C47—41no—
258D4×C47—84no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—84no—
283C2×C4×C47C2×C22⋊C412yes—
284C2×C4×C47C2×C22⋊C412yes—
285C2×C4×C47C2×C22⋊C412yes—
286C2×C4×C47C2×C22⋊C412yes—
287C2×C4×C47C2×C22⋊C412yes—
288C2×C4×C47C23×C411yescharacteristic
289C2×C4×C47C22×D411yescharacteristic
290C2×C4×C47C2×#4111yescharacteristic
291C2×C4×C47C2×#4111yescharacteristic
292C2×C4×C47C2×#4111yescharacteristic
293C2×C4×C47C2×#4111yescharacteristic
294C2×Dic47—22no—
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—41no—
299C2×Dic47—41no—
300C2×Dic47—41no—
301C2×Dic47—41no—
302C2×Dic47—41no—
303C2×Dic47—41no—
304C2×Dic47—41no—
305C2×Dic47—41no—
306C2×Dic47—84no—
307C47⋊C8—41no—
308C47⋊C8—41no—
309C47⋊C8—41no—
310C47⋊C8—41no—
311#21397—471nomaximal, Sylow
312C22×C47—22no—
313C22×C47—22no—
314C22×C47—22no—
315C22×C47—41no—
316C22×C47—41no—
317C22×C47—41no—
318C22×C47—41no—
319C22×C47—42no—
320C22×C47—42no—
321C22×C47—42no—
322C22×C47—81no—
323C22×C47—81no—
324C22×C47—81no—
325C22×C47—81no—
326C22×C47C22×C22⋊C411yescharacteristic
327C22×C47#52511yescharacteristic
328C22×C47#52511yescharacteristic
329C22×C47#57611yescharacteristic
330C22×C47#57711yescharacteristic
331C22×C47#57711yescharacteristic
332C22×C47#57811yescharacteristic
333C4×C47—22no—
334C4×C47—22no—
335C4×C47—22no—
336C4×C47—22no—
337C4×C47—22no—
338C4×C47—42no—
339C4×C47—42no—
340C4×C47—42no—
341C4×C47C4×#4111yescharacteristic
342C4×C47C4×#4111yescharacteristic
343C4×C47#53211yescharacteristic
344C4×C47#53211yescharacteristic
345Dic47—42no—
346Dic47—42no—
347Dic47—42no—
348Dic47—42no—
349C2×#542D4711yescharacteristic
350C2×#433—471no—
351#2274—471no—
352#1988—471no—
353#1987—471no—
354#1983—471no—
355#1983—471no—
356#1875—471no—
357#1874—471no—
358#1873—471no—
359#1872—471no—
360#1763—471no—
361#1762—471no—
362C4×#103—471no—
363C4×#102—471no—
364C2×C47—42no—
365C2×C47—82no—
366C2×C47#229711yescharacteristic
367C2×C47#289711yescharacteristic
368C2×C47#289811yescharacteristic
369C2×C47#311811yescharacteristic
370C2×C47#312111yescharacteristic
371C2×C47#312411yescharacteristic
372C2×C47#312511yescharacteristic
373#542—24no—
374#542Dic4718yescomplemented
375C2×C4⋊Q8C2×D4711yescharacteristic
376C2×#126—21no—
377C2×#124—21no—
378C2×#124C2×D4711yescharacteristic
379C2×#123—21no—
380C2×C22⋊Q8—21no—
381C2×C22⋊Q8C2×D4711yescharacteristic
382C2×#121C2×D4711yescharacteristic
383C2×C4×Q8C2×D4711yescharacteristic
384C2×C4×D4C2×D4711yescharacteristic
385C2×#117—471no—
386C2×#117C2×D4711yescharacteristic
387C22×C4⋊C4—471no—
388#433—944no—
389C2×C4⋊C8—471no—
390C2×C4⋊C8—471no—
391C2×#103—471no—
392C2×#103—471no—
393C2×#103—471no—
394C2×#103—471no—
395C2×#102—471no—
396C2×#102—471no—
397C2×#102—471no—
398C2×#102—471no—
399C2×C22⋊C8—471no—
400C2×C22⋊C8—471no—
401C2×#97—471no—
402C2×C4×C8—471no—
403C4×C4⋊C4—471no—
404C4×C4⋊C4—471no—
405C4×C4⋊C4—471no—
406C4×C4⋊C4—471no—
407C4×C4⋊C4—941no—
408C4×C4⋊C4—941no—
409C4×C22⋊C4—941no—
410C4×C22⋊C4—941no—
411#340—471no—
412#340—471no—
413#340—471no—
414#340—471no—
415#340—471no—
416#340—471no—
417#340—471no—
418#340—471no—
419C47#2139711yescharacteristic, complemented, Sylow
420C22×Q8—21no—
421C22×Q8C22×D4711yescharacteristic
422C22×D4—21no—
423C22×D4C22×D4711yescharacteristic
424C23×C4—21no—
425C23×C4—941no—
426C23×C4C22×D4711yescharacteristic
427C22×C8—471no—
428C22×C8—471no—
429C22×C8—471no—
430C22×C8—471no—
431C4⋊Q8—22no—
432C4⋊Q8C2×Dic4714yescomplemented
433#126—28no—
434#124—28no—
435#124—22no—
436#124C2×Dic4714yescomplemented
437#123—28no—
438C22⋊Q8—22no—
439C22⋊Q8—28no—
440C22⋊Q8C2×Dic4714yes—
441#121—22no—
442#121C2×Dic4714yes—
443C4×Q8—22no—
444C4×Q8C2×Dic4714yescomplemented
445C4×D4—22no—
446C4×D4C2×Dic4714yescomplemented
447#117—942no—
448#117—942no—
449#117C2×Dic4714yes—
450#117C22⋊D4714yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—471no—
455C2×C4⋊C4—471no—
456C2×C4⋊C4—471no—
457C2×C4⋊C4—471no—
458C2×C4⋊C4—942no—
459C2×C4⋊C4—942no—
460C2×C4⋊C4—941no—
461C2×C4⋊C4C22⋊D4711yescharacteristic
462C2×C4⋊C4C22⋊D4711yescharacteristic
463C2×C4⋊C4C22×D4711yescharacteristic
464C2×C4⋊C4C22×D4711yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—941no—
471C2×C22⋊C4C22⋊D4711yescharacteristic
472C2×C22⋊C4C22⋊D4711yescharacteristic
473C2×C42—21no—
474C2×C42—941no—
475C2×C42—941no—
476C2×C42—941no—
477C2×C42—941no—
478C2×C42—941no—
479C2×C42C22×D4711yescharacteristic
480C2×C42C22×D4711yescharacteristic
481C4⋊C8—942no—
482C4⋊C8—942no—
483#103—942no—
484#103—942no—
485#103—942no—
486#103—942no—
487#102—942no—
488#102—942no—
489#102—942no—
490#102—942no—
491C22⋊C8—942no—
492C22⋊C8—942no—
493#97—942no—
494C4×C8—942no—
495#95—941no—
496#95—941no—
497#95—941no—
498#95—941no—
499C24—21no—
500C24C2×C22⋊D4711yescharacteristic
501C2×Q8—24no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—81no—
508C2×Q8—81no—
509C2×Q8C22×Dic4712yes—
510C2×D4—24no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—81no—
517C2×D4—81no—
518C2×D4C22×Dic4712yes—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—24no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4—944no—
530C22×C4—941no—
531C22×C4—941no—
532C22×C4—941no—
533C22×C4—941no—
534C22×C4—3761no—
535C22×C4—3761no—
536C22×C4C22×Dic4712yes—
537C22×C4C2×C22⋊D4711yescharacteristic
538C22×C4C2×C22⋊D4711yescharacteristic
539C22×C4C2×C22⋊D4711yescharacteristic
540C22×C4C2×C22⋊D4711yescharacteristic
541C22×C4C2×C22⋊D4711yescharacteristic
542C22×C4C2×C22⋊D4712yes—
543C22×C4C23×D4711yescharacteristic
544C2×C8—941no—
545C2×C8—941no—
546C2×C8—941no—
547C2×C8—941no—
548C2×C8—941no—
549C2×C8—941no—
550C2×C8—941no—
551C2×C8—941no—
552C2×C8—941no—
553C2×C8—941no—
554C2×C8—941no—
555C2×C8—941no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—472no—
562C4⋊C4—472no—
563C4⋊C4—472no—
564C4⋊C4—472no—
565C4⋊C4—944no—
566C4⋊C4—941no—
567C4⋊C4—941no—
568C4⋊C4—941no—
569C4⋊C4—941no—
570C4⋊C4C22⋊Dic4714yes—
571C4⋊C4C22⋊Dic4714yes—
572C4⋊C4C22×Dic4712yes—
573C4⋊C4C22×Dic4712yes—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—944no—
580C22⋊C4C22⋊Dic4714yes—
581C22⋊C4C22⋊Dic4714yes—
582C42—24no—
583C42—944no—
584C42—3761no—
585C42—3761no—
586C42—3761no—
587C42—3761no—
588C42C22×Dic4712yes—
589C42C22×Dic4712yes—
590C42C2×C22⋊D4712yes—
591C42C2×C22⋊D4712yes—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—22no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C2×C22⋊Dic4712yes—
606C23C22×C22⋊D4711yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—84no—
612D4—22no—
613D4—22no—
614D4—41no—
615D4—41no—
616D4—84no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—84no—
641C2×C4—942no—
642C2×C4—942no—
643C2×C4—942no—
644C2×C4—942no—
645C2×C4—3764no—
646C2×C4—1881no—
647C2×C4—1881no—
648C2×C4—1881no—
649C2×C4—1881no—
650C2×C4—1881no—
651C2×C4—1881no—
652C2×C4—1881no—
653C2×C4—1881no—
654C2×C4C2×C22⋊Dic4712yes—
655C2×C4C2×C22⋊Dic4712yes—
656C2×C4C2×C22⋊Dic4712yes—
657C2×C4C2×C22⋊Dic4712yes—
658C2×C4C2×C22⋊Dic4712yes—
659C2×C4C23×Dic4711yescharacteristic
660C2×C4C22×C22⋊D4711yescharacteristic
661C2×C4#41×D4711yescharacteristic
662C2×C4#41×D4711yescharacteristic
663C2×C4#41×D4711yescharacteristic
664C2×C4#41×D4711yescharacteristic
665C8—1881no—
666C8—1881no—
667C8—1881no—
668C8—1881no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C22×C22⋊Dic4711yescharacteristic
684C22#1568963011yescharacteristic
685C22#1568963011yescharacteristic
686C22#1568992611yescharacteristic
687C22#1568993111yescharacteristic
688C22#1568993411yescharacteristic
689C22#1568993811yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—1882no—
699C4—1882no—
700C4—1882no—
701C4—1882no—
702C4#41×Dic4711yescharacteristic
703C4#41×Dic4711yescharacteristic
704C4#1568966911yescharacteristic
705C4#1568966911yescharacteristic
706C2—42no—
707C2—82no—
708C2#2024587911yescharacteristic
709C2#2025191411yescharacteristic
710C2#2025192111yescharacteristic
711C2#2025356611yescharacteristic
712C2#2025361111yescharacteristic
713C2#2025364411yescharacteristic
714C2#2025365911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#542C2
socleC23×C47C22×D4
prime radicalC2×#121×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#542D47
hypocenterC47#21397
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#15689184C2semidirect
2. #20245744C2semidirect
3. #20244341C2semidirect
4. #20244337C2semidirect
5. #20244321C2semidirect
6. #20244321C2semidirect
9. #20243701C2semidirect
10. #20243696C2semidirect
11. #20243218C2semidirect
12. #20243213C2semidirect
13. C4×#13093948C2semidirect
14. C4×#13093945C2semidirect
50. C47×#542C4semidirect
107. C4⋊Q8×C47C2×C4semidirect
111. #124×C47C2×C4semidirect
119. C4×Q8×C47C2×C4semidirect
121. C4×D4×C47C2×C4semidirect
374. #542Dic47semidirect
419. C47#21397semidirect
432. C4⋊Q8C2×Dic47semidirect
436. #124C2×Dic47semidirect
444. C4×Q8C2×Dic47semidirect
446. C4×D4C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156891842
#202457442
#202443412
#202443372
#202443212
#202437112
#202437062
#202437012
#202436962
#202432182
#202432132
C4×#130939482
C4×#130939452
C2×C47×#5422
#2139747