Finite Group Databasebeta

← #26221422

Subgroups — #26221422

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×#15689744C211yesmaximal, characteristic
2C2×#15689184C211yesmaximal, characteristic, complemented
3#20244340C211yesmaximal, characteristic, complemented
4#20244336C211yesmaximal, characteristic, complemented
5#20244320C211yesmaximal, characteristic, complemented
6#20244320C211yesmaximal, characteristic, complemented
7#20243710C211yesmaximal, characteristic
8#20243705C211yesmaximal, characteristic
9#20243700C211yesmaximal, characteristic, complemented
10#20243695C211yesmaximal, characteristic, complemented
11#20243221C211yesmaximal, characteristic, complemented
12#20243216C211yesmaximal, characteristic, complemented
13C4×#13093947C211yesmaximal, characteristic, complemented
14C4×#13093944C211yesmaximal, characteristic, complemented
15C47×#2274C211yesmaximal, characteristic, complemented
16#15689744—24no—
17#15689744C418yescomplemented
18C2×#13094024C2211yescharacteristic
19C2×#13094019—21no—
20C2×#13094012C2211yescharacteristic
21C2×#13094010—21no—
22C2×#13094006—21no—
23C2×#13094003C2211yescharacteristic
24C2×#13094002—21no—
25C2×#13093998C2211yescharacteristic
26C2×C4×Dic94C2211yescharacteristic
27C2×C4×D188C2211yescharacteristic
28#15689184—24no—
29C2×C4⋊(C47⋊C8)C2211yescharacteristic
30C2×C4⋊(C47⋊C8)C2211yescharacteristic
31C2×#13093947C2211yescharacteristic
32C2×#13093947C2211yescharacteristic
33C2×#13093947C2211yescharacteristic
34C2×#13093947C2211yescharacteristic
35C2×#13093944C2211yescharacteristic
36C2×#13093944C2211yescharacteristic
37C2×#13093944C2211yescharacteristic
38C2×#13093944C2211yescharacteristic
39C2×C22⋊(C47⋊C8)C2211yescharacteristic
40C2×C22⋊(C47⋊C8)C2211yescharacteristic
41C2×#13093935C2211yescharacteristic
42C2×C4×C47⋊C8C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51C2×#117×C47C2211yescharacteristic
52C2×#117×C47C2211yescharacteristic
53C22×C4⋊C4×C47C2211yescharacteristic
54C4×C4⋊C4×C47—21no—
55C4×C4⋊C4×C47—21no—
56C4×C4⋊C4×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C4×C4⋊C4×C47C2211yescharacteristic
60C4×C22⋊C4×C47—21no—
61C4×C22⋊C4×C47—21no—
62C22×Dic94—21no—
63C22×Dic94C2311yescharacteristic
64C22×D188C2311yescharacteristic
65C22×C22⋊D47—21no—
66C22×C4×D47—21no—
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71#13094024—22no—
72#13094024C2×C414yescomplemented
73#13094019—28no—
74#13094012—22no—
75#13094012C2×C414yescomplemented
76#13094010—28no—
77#13094006—28no—
78#13094003—22no—
79#13094003C2×C414yes—
80#13094002—28no—
81#13093998—22no—
82#13093998C2×C414yes—
83C4×Dic94—22no—
84C4×Dic94C2×C414yescomplemented
85C4×D188—22no—
86C4×D188C2×C414yescomplemented
87C2×C4⋊Dic47—21no—
88C2×C4⋊Dic47C2311yescharacteristic
89C2×C4⋊Dic47C2311yescharacteristic
90C2×Dic47⋊C4—21no—
91C2×Dic47⋊C4—21no—
92C2×C22⋊Dic47—21no—
93C2×(C2×D47)⋊C4—21no—
94C2×(C2×D47)⋊C4—21no—
95C2×(C2×D47)⋊C4—21no—
96C2×(C2×D47)⋊C4—21no—
97C2×C4×Dic47—21no—
98C4⋊(C47⋊C8)—22no—
99C4⋊(C47⋊C8)—22no—
100#13093947—22no—
101#13093947—22no—
102#13093947—22no—
103#13093947—22no—
104#13093944—22no—
105#13093944—22no—
106#13093944—22no—
107#13093944—22no—
108C22⋊(C47⋊C8)—22no—
109C22⋊(C47⋊C8)—22no—
110#13093935—22no—
111C4×C47⋊C8—22no—
112C23×C4×C47—21no—
113C23×C4×C47C2311yescharacteristic
114#117×C47—22no—
115#117×C47—22no—
116#117×C47C2×C414yes—
117#117×C47D414yes—
118C2×C4⋊C4×C47—21no—
119C2×C4⋊C4×C47—22no—
120C2×C4⋊C4×C47—22no—
121C2×C4⋊C4×C47D411yescharacteristic
122C2×C4⋊C4×C47D411yescharacteristic
123C2×C4⋊C4×C47C2311yescharacteristic
124C2×C4⋊C4×C47C2311yescharacteristic
125C2×C4⋊C4×C47C2311yescharacteristic
126C2×C4⋊C4×C47C2311yescharacteristic
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47D411yescharacteristic
129C2×C22⋊C4×C47D411yescharacteristic
130C2×C42×C47—21no—
131C2×C42×C47—21no—
132C2×C42×C47—21no—
133C2×C42×C47—21no—
134C2×C42×C47—21no—
135C2×C42×C47C2311yescharacteristic
136C2×C42×C47C2311yescharacteristic
137#95×C47—21no—
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141C24×C47C2×D411yescharacteristic
142C23×D47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—24no—
152C22×C4×C47—81no—
153C22×C4×C47—81no—
154C22×C4×C47C22×C412yes—
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47C2×D411yescharacteristic
158C22×C4×C47C2×D411yescharacteristic
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2411yescharacteristic
162C2×C22⋊D47—24no—
163C2×C22⋊D47—81no—
164C2×C22⋊D47—81no—
165C22×Dic47—21no—
166C22×Dic47—21no—
167C22×Dic47—21no—
168C2×D188—21no—
169C2×D188—21no—
170C2×D188—21no—
171C2×D188—21no—
172C2×D188—21no—
173C2×D188C22×C412yes—
174C2×C4×D47—24no—
175C2×C4×D47—81no—
176C2×C4×D47—81no—
177C2×Dic94—21no—
178C2×Dic94—21no—
179C2×Dic94—21no—
180C2×Dic94—21no—
181C2×Dic94—21no—
182C2×Dic94—24no—
183C2×Dic94—81no—
184C2×Dic94—81no—
185C2×Dic94C22×C412yes—
186C4⋊C4×C47—24no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47C22⋊C414yes—
192C4⋊C4×C47C22⋊C414yes—
193C4⋊C4×C47#4112yes—
194C4⋊C4×C47#4112yes—
195C4⋊C4×C47#4112yes—
196C4⋊C4×C47#4112yes—
197C22⋊C4×C47—24no—
198C22⋊C4×C47C22⋊C414yes—
199C22⋊C4×C47C22⋊C414yes—
200C42×C47—24no—
201C42×C47—81no—
202C42×C47—81no—
203C42×C47—81no—
204C42×C47—81no—
205C42×C47C22×C412yes—
206C42×C47C22×C412yes—
207C42×C47C2×D412yes—
208C42×C47C2×D412yes—
209C22⋊Dic47—24no—
210(C2×D47)⋊C4—24no—
211(C2×D47)⋊C4—24no—
212(C2×D47)⋊C4—24no—
213(C2×D47)⋊C4—24no—
214C4⋊Dic47—24no—
215C4⋊Dic47—21no—
216C4⋊Dic47—21no—
217C4⋊Dic47C22×C412yes—
218C4⋊Dic47C22×C412yes—
219Dic47⋊C4—24no—
220Dic47⋊C4—24no—
221C4×Dic47—24no—
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×C47C2×C22⋊C412yes—
241C23×C47C22×D411yescharacteristic
242C22×D47—22no—
243C22×D47—41no—
244C22×D47—41no—
245C22×D47—41no—
246C22×D47—41no—
247C22×D47—41no—
248C22×D47—41no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—41no—
268C2×C4×C47—41no—
269C2×C4×C47—41no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—41no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—84no—
276C2×C4×C47C2×C22⋊C412yes—
277C2×C4×C47C2×C22⋊C412yes—
278C2×C4×C47C2×C22⋊C412yes—
279C2×C4×C47C2×C22⋊C412yes—
280C2×C4×C47C2×C22⋊C412yes—
281C2×C4×C47C23×C411yescharacteristic
282C2×C4×C47C22×D411yescharacteristic
283C2×C4×C47C2×#4111yescharacteristic
284C2×C4×C47C2×#4111yescharacteristic
285C2×C4×C47C2×#4111yescharacteristic
286C2×C4×C47C2×#4111yescharacteristic
287C22⋊D47—84no—
288C2×Dic47—22no—
289C2×Dic47—22no—
290C2×Dic47—22no—
291C2×Dic47—41no—
292C2×Dic47—41no—
293C2×Dic47—41no—
294C2×Dic47—41no—
295C2×Dic47—41no—
296C2×Dic47—41no—
297D188—22no—
298D188—22no—
299D188—41no—
300D188—41no—
301C4×D47—84no—
302Dic94—22no—
303Dic94—22no—
304Dic94—41no—
305Dic94—41no—
306Dic94—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×C47C22×C22⋊C411yescharacteristic
320C22×C47#52511yescharacteristic
321C22×C47#52511yescharacteristic
322C22×C47#57611yescharacteristic
323C22×C47#57711yescharacteristic
324C22×C47#57711yescharacteristic
325C22×C47#57811yescharacteristic
326C2×D47—42no—
327C2×D47—42no—
328C2×D47—42no—
329C2×D47—81no—
330C2×D47—81no—
331C2×D47—81no—
332C2×D47—81no—
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×C47—42no—
342C4×C47C4×#4111yescharacteristic
343C4×C47C4×#4111yescharacteristic
344C4×C47#53211yescharacteristic
345C4×C47#53211yescharacteristic
346Dic47—42no—
347Dic47—42no—
348Dic47—42no—
349C2×#542—471no—
350C2×#433—471no—
351#2274D4711yescharacteristic, complemented
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#229711yescharacteristic
366C2×C47#289711yescharacteristic
367C2×C47#289811yescharacteristic
368C2×C47#311811yescharacteristic
369C2×C47#312111yescharacteristic
370C2×C47#312411yescharacteristic
371C2×C47#312511yescharacteristic
372D47—82no—
373#542—478no—
374#542—944no—
375C2×C4⋊Q8—471no—
376C2×#126—941no—
377C2×#124—471no—
378C2×#124—941no—
379C2×#123—941no—
380C2×C22⋊Q8—471no—
381C2×C22⋊Q8—941no—
382C2×#121—471no—
383C2×C4×Q8—471no—
384C2×C4×D4—471no—
385C2×#117C2×D4711yescharacteristic
386C2×#117C2×D4711yescharacteristic
387C22×C4⋊C4C2×D4711yescharacteristic
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—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4C2×D4711yescharacteristic
406C4×C4⋊C4C2×D4711yescharacteristic
407C4×C4⋊C4C2×D4711yescharacteristic
408C4×C4⋊C4C2×D4711yescharacteristic
409C4×C22⋊C4—21no—
410C4×C22⋊C4—21no—
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—471no—
421C22×Q8—941no—
422C22×D4—471no—
423C22×D4—941no—
424C23×C4—21no—
425C23×C4—941no—
426C23×C4C22×D4711yescharacteristic
427C22×C8—471no—
428C22×C8—471no—
429C22×C8—471no—
430C22×C8—471no—
431C4⋊Q8—474no—
432C4⋊Q8—942no—
433#126—948no—
434#124—474no—
435#124—948no—
436#124—942no—
437#123—948no—
438C22⋊Q8—474no—
439C22⋊Q8—942no—
440C22⋊Q8—948no—
441#121—474no—
442#121—942no—
443C4×Q8—474no—
444C4×Q8—942no—
445C4×D4—474no—
446C4×D4—942no—
447#117—22no—
448#117—22no—
449#117C4×D4714yes—
450#117D18814yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—471no—
455C2×C4⋊C4—471no—
456C2×C4⋊C4—941no—
457C2×C4⋊C4—941no—
458C2×C4⋊C4—941no—
459C2×C4⋊C4C22⋊D4711yescharacteristic
460C2×C4⋊C4C22⋊D4711yescharacteristic
461C2×C4⋊C4C22×D4711yescharacteristic
462C2×C4⋊C4C22×D4711yescharacteristic
463C2×C4⋊C4C22×D4711yescharacteristic
464C2×C4⋊C4C22×D4711yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—941no—
467C2×C22⋊C4—941no—
468C2×C22⋊C4—941no—
469C2×C22⋊C4—941no—
470C2×C22⋊C4—941no—
471C2×C22⋊C4C22⋊D4711yescharacteristic
472C2×C22⋊C4C22⋊D4711yescharacteristic
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—21no—
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—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499C24—941no—
500C24C2×C22⋊D4711yescharacteristic
501C2×Q8—472no—
502C2×Q8—944no—
503C2×Q8—941no—
504C2×Q8—941no—
505C2×Q8—941no—
506C2×Q8—941no—
507C2×Q8—941no—
508C2×Q8—3761no—
509C2×Q8—3761no—
510C2×D4—472no—
511C2×D4—944no—
512C2×D4—941no—
513C2×D4—941no—
514C2×D4—941no—
515C2×D4—941no—
516C2×D4—941no—
517C2×D4—3761no—
518C2×D4—3761no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—24no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—941no—
531C22×C4—941no—
532C22×C4—941no—
533C22×C4—944no—
534C22×C4—3761no—
535C22×C4—3761no—
536C22×C4C2×C4×D4712yes—
537C22×C4C2×D18812yes—
538C22×C4C2×C22⋊D4711yescharacteristic
539C22×C4C2×C22⋊D4711yescharacteristic
540C22×C4C2×C22⋊D4711yescharacteristic
541C22×C4C2×C22⋊D4711yescharacteristic
542C22×C4C2×C22⋊D4711yescharacteristic
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—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—472no—
562C4⋊C4—472no—
563C4⋊C4—944no—
564C4⋊C4—944no—
565C4⋊C4—944no—
566C4⋊C4—941no—
567C4⋊C4—941no—
568C4⋊C4(C2×D47)⋊C414yes—
569C4⋊C4(C2×D47)⋊C414yes—
570C4⋊C4#1062535012yes—
571C4⋊C4#1062535012yes—
572C4⋊C4#1062535012yes—
573C4⋊C4#1062535012yes—
574C22⋊C4—24no—
575C22⋊C4—944no—
576C22⋊C4—944no—
577C22⋊C4—944no—
578C22⋊C4—944no—
579C22⋊C4—944no—
580C22⋊C4(C2×D47)⋊C414yes—
581C22⋊C4(C2×D47)⋊C414yes—
582C42—24no—
583C42—81no—
584C42—81no—
585C42—81no—
586C42—81no—
587C42—944no—
588C42C2×C4×D4712yes—
589C42C2×C4×D4712yes—
590C42C2×D18812yes—
591C42C2×D18812yes—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—942no—
599C23—1881no—
600C23—1881no—
601C23—1881no—
602C23—1881no—
603C23—1881no—
604C23—1881no—
605C23C2×(C2×D47)⋊C412yes—
606C23C22×C22⋊D4711yescharacteristic
607Q8—942no—
608Q8—942no—
609Q8—3764no—
610Q8—1881no—
611Q8—1881no—
612D4—942no—
613D4—942no—
614D4—3764no—
615D4—1881no—
616D4—1881no—
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—22no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—84no—
644C2×C4—942no—
645C2×C4—942no—
646C2×C4—942no—
647C2×C4—3764no—
648C2×C4—1881no—
649C2×C4—1881no—
650C2×C4—1881no—
651C2×C4—1881no—
652C2×C4—1881no—
653C2×C4—1881no—
654C2×C4C2×(C2×D47)⋊C412yes—
655C2×C4C2×(C2×D47)⋊C412yes—
656C2×C4C2×(C2×D47)⋊C412yes—
657C2×C4C2×(C2×D47)⋊C412yes—
658C2×C4C2×(C2×D47)⋊C412yes—
659C2×C4C22×C4×D4711yescharacteristic
660C2×C4C22×D18811yescharacteristic
661C2×C4C2×#1062535011yescharacteristic
662C2×C4C2×#1062535011yescharacteristic
663C2×C4C2×#1062535011yescharacteristic
664C2×C4C2×#1062535011yescharacteristic
665C8—1881no—
666C8—1881no—
667C8—1881no—
668C8—1881no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—3761no—
677C22—3761no—
678C22—3761no—
679C22—3761no—
680C22—1882no—
681C22—1882no—
682C22—1882no—
683C22C22×(C2×D47)⋊C411yescharacteristic
684C22#1568963411yescharacteristic
685C22#1568963411yescharacteristic
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—42no—
699C4—1882no—
700C4—1882no—
701C4—1882no—
702C4C4×#1062535011yescharacteristic
703C4C4×#1062535011yescharacteristic
704C4#1568967311yescharacteristic
705C4#1568967311yescharacteristic
706C2—42no—
707C2—3762no—
708C2#2024587811yescharacteristic
709C2#2025191111yescharacteristic
710C2#2025191811yescharacteristic
711C2#2025357211yescharacteristic
712C2#2025361711yescharacteristic
713C2#2025365011yescharacteristic
714C2#2025366511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2274C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
cosocleC22×C4×C47C24
hypercenter#2274D47
hypocenterC47#21397
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. C2×#15689184C2semidirect
3. #20244340C2semidirect
4. #20244336C2semidirect
5. #20244320C2semidirect
6. #20244320C2semidirect
9. #20243700C2semidirect
10. #20243695C2semidirect
11. #20243221C2semidirect
12. #20243216C2semidirect
13. C4×#13093947C2semidirect
14. C4×#13093944C2semidirect
15. C47×#2274C2semidirect
17. #15689744C4semidirect
72. #13094024C2×C4semidirect
75. #13094012C2×C4semidirect
84. C4×Dic94C2×C4semidirect
86. C4×D188C2×C4semidirect
351. #2274D47semidirect
419. C47#21397semidirect

Maximal subgroups

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

subgroupindex
C2×#156897442
C2×#156891842
#202443402
#202443362
#202443202
#202437102
#202437052
#202437002
#202436952
#202432212
#202432162
C4×#130939472
C4×#130939442
C47×#22742
#2139747