Finite Group Databasebeta

← #26233164

Subgroups — #26233164

Order 12032.

1118 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×#15689254C211yesmaximal, characteristic, complemented
2#20246345C211yesmaximal, characteristic, complemented
3#20244321C211yesmaximal, characteristic, complemented
4#20244321C211yesmaximal, characteristic, complemented
5#20244316C211yesmaximal, characteristic
6#20244213C211yesmaximal, characteristic
7#20244205C211yesmaximal, characteristic, complemented
8#20244200C211yesmaximal, characteristic, complemented
9#20243403C211yesmaximal, characteristic, complemented
10#20243398C211yesmaximal, characteristic, complemented
11#20243388C211yesmaximal, characteristic, complemented
12#20243218C211yesmaximal, characteristic, complemented
13#20243213C211yesmaximal, characteristic, complemented
14C4×#13093945C211yesmaximal, characteristic, complemented
15C2×C47×#559C211yesmaximal, characteristic
16#15689254—24no—
17C2×C4⋊(C47⋊C8)C2211yescharacteristic
18C2×C4⋊(C47⋊C8)C2211yescharacteristic
19C2×C4⋊(C47⋊C8)C2211yescharacteristic
20C2×#13093948C2211yescharacteristic
21C2×#13093948C2211yescharacteristic
22C2×#13093948C2211yescharacteristic
23C2×#13093948C2211yescharacteristic
24C2×#13093945C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×#13093945C2211yescharacteristic
29C2×#13093945C2211yescharacteristic
30C2×#13093945C2211yescharacteristic
31C2×#13093945C2211yescharacteristic
32C2×#13093935C2211yescharacteristic
33C2×#13093935C2211yescharacteristic
34C2×C4×C47⋊C8C2211yescharacteristic
35#15689030—21no—
36#15689009—21no—
37#15689009—21no—
38#15688993C2211yescharacteristic
39#15688989C2211yescharacteristic
40#15688989C2211yescharacteristic
41C4⋊C4×Dic47—21no—
42C4×C4⋊Dic47C2211yescharacteristic
43C4×C4⋊Dic47C2211yescharacteristic
44C4×C4⋊Dic47C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49C47×#559—24no—
50C47×#559C418yescomplemented
51C2×#127×C47C2211yescharacteristic
52C2×#124×C47—21no—
53C2×#124×C47C2211yescharacteristic
54C2×#124×C47C2211yescharacteristic
55C2×#123×C47—21no—
56C2×#123×C47—21no—
57C2×C4×Q8×C47C2211yescharacteristic
58C2×C4×Q8×C47C2211yescharacteristic
59C2×C4×D4×C47—21no—
60C2×C4×D4×C47C2211yescharacteristic
61C2×C4×D4×C47C2211yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C2×C4⋊Dic47—21no—
67C2×C4⋊Dic47—21no—
68C2×C4⋊Dic47C2311yescharacteristic
69C2×C4⋊Dic47C2311yescharacteristic
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4×Dic47—21no—
73C2×C4×Dic47—21no—
74C2×C4×Dic47—21no—
75C4⋊(C47⋊C8)—22no—
76C4⋊(C47⋊C8)—22no—
77C4⋊(C47⋊C8)—22no—
78#13093948—22no—
79#13093948—22no—
80#13093948—41no—
81#13093948—41no—
82#13093945—22no—
83#13093945—22no—
84#13093945—22no—
85#13093945—22no—
86#13093945—41no—
87#13093945—41no—
88#13093945—41no—
89#13093945—41no—
90#13093935—22no—
91#13093935—22no—
92C4×C47⋊C8—22no—
93C47⋊#95—21no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C22×Q8×C47D411yescharacteristic
101C22×Q8×C47C2311yescharacteristic
102C22×D4×C47—21no—
103C22×D4×C47—21no—
104C22×D4×C47C2311yescharacteristic
105C22×D4×C47C2311yescharacteristic
106C23×C4×C47—21no—
107C23×C4×C47—21no—
108#127×C47—22no—
109#127×C47C2×C414yes—
110#124×C47—28no—
111#124×C47—22no—
112#124×C47—22no—
113#124×C47C2×C414yes—
114#124×C47C2×C414yes—
115#123×C47—28no—
116#123×C47—28no—
117C4×Q8×C47—22no—
118C4×Q8×C47C2×C414yes—
119C4×Q8×C47C2×C414yes—
120C4×Q8×C47D414yes—
121C4×D4×C47—28no—
122C4×D4×C47—22no—
123C4×D4×C47—22no—
124C4×D4×C47C2×C414yes—
125C4×D4×C47C2×C414yes—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47D411yescharacteristic
128C2×C4⋊C4×C47D411yescharacteristic
129C2×C4⋊C4×C47D411yescharacteristic
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×C47—21no—
137C2×C42×C47—21no—
138C2×C42×C47C2311yescharacteristic
139C2×C42×C47C2311yescharacteristic
140C2×C42×C47C2311yescharacteristic
141C24×C47—21no—
142C24×C47—21no—
143C2×Q8×C47—21no—
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—41no—
149C2×Q8×C47—41no—
150C2×Q8×C47C22⋊C414yes—
151C2×Q8×C47C22×C412yes—
152C2×D4×C47—24no—
153C2×D4×C47—24no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47—42no—
165C2×D4×C47—42no—
166C2×D4×C47—81no—
167C2×D4×C47—81no—
168C2×D4×C47C22×C412yes—
169C2×D4×C47C22×C412yes—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—24no—
173C22×C4×C47—24no—
174C22×C4×C47—81no—
175C22×C4×C47—81no—
176C22×C4×C47—81no—
177C22×C4×C47—81no—
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2411yescharacteristic
185C22×Dic47—21no—
186C22×Dic47—21no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C4⋊C4×C47—24no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47C22⋊C414yes—
192C4⋊C4×C47C22⋊C414yes—
193C4⋊C4×C47C22⋊C414yes—
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×C47—24no—
201C42×C47—24no—
202C42×C47C22×C412yes—
203C42×C47C22×C412yes—
204C42×C47C22×C412yes—
205C42×C47C2×D412yes—
206C42×C47C2×D412yes—
207C42×C47C2×D412yes—
208C4⋊Dic47—21no—
209C4⋊Dic47—21no—
210C4⋊Dic47—21no—
211C4⋊Dic47—21no—
212C4⋊Dic47—21no—
213C4⋊Dic47—21no—
214C4⋊Dic47—21no—
215C4⋊Dic47—42no—
216C4⋊Dic47—81no—
217C4⋊Dic47#4112yes—
218C4×Dic47—42no—
219C4×Dic47—81no—
220C4×Dic47—81no—
221C2×C47⋊C8—21no—
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#4112yes—
233C23×C47—22no—
234C23×C47—22no—
235C23×C47—41no—
236C23×C47—41no—
237C23×C47—41no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47—41no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47—41no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47C22×D411yescharacteristic
248Q8×C47—22no—
249Q8×C47—22no—
250Q8×C47—44no—
251Q8×C47—41no—
252Q8×C47—41no—
253D4×C47—22no—
254D4×C47—22no—
255D4×C47—22no—
256D4×C47—22no—
257D4×C47—48no—
258D4×C47—41no—
259D4×C47—41no—
260D4×C47—41no—
261D4×C47—41no—
262D4×C47—84no—
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—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—84no—
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×C47C2×C22⋊C412yes—
289C2×C4×C47C23×C411yescharacteristic
290C2×C4×C47C22×D411yescharacteristic
291C2×C4×C47C2×#4111yescharacteristic
292C2×C4×C47C2×#4111yescharacteristic
293C2×C4×C47H(5,𝔽2)11yescharacteristic
294C2×C4×C472−1+411yescharacteristic
295C2×Dic47—22no—
296C2×Dic47—41no—
297C2×Dic47—41no—
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—41no—
307C47⋊C8—22no—
308C47⋊C8—41no—
309C47⋊C8—41no—
310C47⋊C8—41no—
311#22549—471nomaximal, Sylow
312C22×C47—42no—
313C22×C47—42no—
314C22×C47—42no—
315C22×C47—42no—
316C22×C47—42no—
317C22×C47—42no—
318C22×C47—81no—
319C22×C47—81no—
320C22×C47—81no—
321C22×C47—81no—
322C22×C47—81no—
323C22×C47—81no—
324C22×C47—81no—
325C22×C47—81no—
326C22×C47C22×C22⋊C411yescharacteristic
327C22×C47#54811yescharacteristic
328C22×C47#55011yescharacteristic
329C22×C47#57511yescharacteristic
330C22×C47#57511yescharacteristic
331C22×C47#57611yescharacteristic
332C22×C47#57711yescharacteristic
333C4×C47—22no—
334C4×C47—22no—
335C4×C47—22no—
336C4×C47—22no—
337C4×C47—22no—
338C4×C47—22no—
339C4×C47—42no—
340C4×C47—42no—
341C4×C47C4×#4111yescharacteristic
342C4×C47#52011yescharacteristic
343C4×C47#54811yescharacteristic
344C4×C47#55011yescharacteristic
345Dic47—42no—
346Dic47—81no—
347Dic47—81no—
348Dic47—81no—
349C2×#559D4711yescharacteristic
350C2×#446—471no—
351#2355—471no—
352#1983—471no—
353#1983—471no—
354#1982—471no—
355#1961—471no—
356#1959—471no—
357#1958—471no—
358#1805—471no—
359#1804—471no—
360#1802—471no—
361#1763—471no—
362#1762—471no—
363C4×#102—471no—
364C2×C47—82no—
365C2×C47—82no—
366C2×C47#234111yescharacteristic
367C2×C47#289611yescharacteristic
368C2×C47#289711yescharacteristic
369C2×C47#337011yescharacteristic
370C2×C47#337111yescharacteristic
371C2×C47#340111yescharacteristic
372C2×C47#340311yescharacteristic
373#559—24no—
374#559Dic4718yescomplemented
375C2×#127C2×D4711yescharacteristic
376C2×#124—21no—
377C2×#124C2×D4711yescharacteristic
378C2×#124C2×D4711yescharacteristic
379C2×#123—21no—
380C2×#123—21no—
381C2×C4×Q8C2×D4711yescharacteristic
382C2×C4×Q8C2×D4711yescharacteristic
383C2×C4×D4—21no—
384C2×C4×D4C2×D4711yescharacteristic
385C2×C4×D4C2×D4711yescharacteristic
386#446—944no—
387C2×C4⋊C8—471no—
388C2×C4⋊C8—471no—
389C2×C4⋊C8—471no—
390C2×#103—471no—
391C2×#103—471no—
392C2×#103—471no—
393C2×#103—471no—
394C2×#102—471no—
395C2×#102—471no—
396C2×#102—471no—
397C2×#102—471no—
398C2×#102—471no—
399C2×#102—471no—
400C2×#102—471no—
401C2×#102—471no—
402C2×#97—471no—
403C2×#97—471no—
404C2×C4×C8—471no—
405#391—941no—
406#387—941no—
407#387—941no—
408#384—471no—
409#382—471no—
410#382—471no—
411C4×C4⋊C4—471no—
412C4×C4⋊C4—471no—
413C4×C4⋊C4—471no—
414C4×C4⋊C4—941no—
415#340—471no—
416#340—471no—
417#340—471no—
418#340—471no—
419C47#2254911yescharacteristic, complemented, Sylow
420C22×Q8C22⋊D4711yescharacteristic
421C22×Q8C22×D4711yescharacteristic
422C22×D4—21no—
423C22×D4—21no—
424C22×D4C22×D4711yescharacteristic
425C22×D4C22×D4711yescharacteristic
426C23×C4—21no—
427C23×C4—21no—
428C22×C8—471no—
429C22×C8—471no—
430C22×C8—471no—
431C22×C8—471no—
432#127—22no—
433#127C2×Dic4714yes—
434#124—28no—
435#124—22no—
436#124—22no—
437#124C2×Dic4714yes—
438#124C2×Dic4714yes—
439#123—28no—
440#123—28no—
441C4×Q8—22no—
442C4×Q8C2×Dic4714yes—
443C4×Q8C2×Dic4714yes—
444C4×Q8C22⋊D4714yes—
445C4×D4—28no—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4C2×Dic4714yes—
449C4×D4C2×Dic4714yes—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—471no—
452C2×C4⋊C4—471no—
453C2×C4⋊C4—471no—
454C2×C4⋊C4—471no—
455C2×C4⋊C4—941no—
456C2×C4⋊C4—941no—
457C2×C4⋊C4C22⋊D4711yescharacteristic
458C2×C4⋊C4C22⋊D4711yescharacteristic
459C2×C4⋊C4C22⋊D4711yescharacteristic
460C2×C4⋊C4C22×D4711yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C42—21no—
468C2×C42—941no—
469C2×C42—941no—
470C2×C42—941no—
471C2×C42C22×D4711yescharacteristic
472C2×C42C22×D4711yescharacteristic
473C2×C42C22×D4711yescharacteristic
474C4⋊C8—942no—
475C4⋊C8—942no—
476C4⋊C8—942no—
477#103—942no—
478#103—942no—
479#103—1881no—
480#103—1881no—
481#102—942no—
482#102—942no—
483#102—942no—
484#102—942no—
485#102—1881no—
486#102—1881no—
487#102—1881no—
488#102—1881no—
489#97—942no—
490#97—942no—
491C4×C8—942no—
492#95—941no—
493#95—941no—
494#95—941no—
495#95—941no—
496#95—941no—
497#95—941no—
498#95—941no—
499C24—21no—
500C24—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—41no—
507C2×Q8—41no—
508C2×Q8C22⋊Dic4714yes—
509C2×Q8C22×Dic4712yes—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—81no—
525C2×D4—81no—
526C2×D4C22×Dic4712yes—
527C2×D4C22×Dic4712yes—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4—941no—
537C22×C4—941no—
538C22×C4—941no—
539C22×C4—941no—
540C22×C4C2×C22⋊D4711yescharacteristic
541C22×C4C2×C22⋊D4711yescharacteristic
542C22×C4C2×C22⋊D4711yescharacteristic
543C22×C4C2×C22⋊D4711yescharacteristic
544C22×C4C2×C22⋊D4711yescharacteristic
545C22×C4C2×C22⋊D4711yescharacteristic
546C22×C4C23×D4711yescharacteristic
547C2×C8—472no—
548C2×C8—941no—
549C2×C8—941no—
550C2×C8—941no—
551C2×C8—941no—
552C2×C8—941no—
553C2×C8—941no—
554C2×C8—941no—
555C2×C8—941no—
556C2×C8—941no—
557C2×C8—941no—
558C2×C8—941no—
559C4⋊C4—24no—
560C4⋊C4—21no—
561C4⋊C4—472no—
562C4⋊C4—941no—
563C4⋊C4—941no—
564C4⋊C4—941no—
565C4⋊C4—941no—
566C4⋊C4—941no—
567C4⋊C4—941no—
568C4⋊C4—941no—
569C4⋊C4—3761no—
570C4⋊C4—1882no—
571C4⋊C4C22⋊Dic4714yes—
572C4⋊C4C22⋊Dic4714yes—
573C4⋊C4C22⋊Dic4714yes—
574C4⋊C4C22×Dic4712yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C42—24no—
582C42—3761no—
583C42—3761no—
584C42—1882no—
585C42C22×Dic4712yes—
586C42C22×Dic4712yes—
587C42C22×Dic4712yes—
588C42C2×C22⋊D4712yes—
589C42C2×C22⋊D4712yes—
590C42C2×C22⋊D4712yes—
591C23—22no—
592C23—22no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C22×C22⋊D4711yescharacteristic
606Q8—22no—
607Q8—22no—
608Q8—44no—
609Q8—41no—
610Q8—41no—
611D4—22no—
612D4—22no—
613D4—22no—
614D4—22no—
615D4—48no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—84no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—84no—
640C2×C4—84no—
641C2×C4—942no—
642C2×C4—1881no—
643C2×C4—1881no—
644C2×C4—1881no—
645C2×C4—1881no—
646C2×C4—1881no—
647C2×C4—1881no—
648C2×C4—1881no—
649C2×C4—1881no—
650C2×C4—1881no—
651C2×C4—1881no—
652C2×C4—1881no—
653C2×C4C2×C22⋊Dic4712yes—
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#1309407011yescharacteristic
664C2×C4#1309407111yescharacteristic
665C8—942no—
666C8—1881no—
667C8—1881no—
668C8—1881no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C22×C22⋊Dic4711yescharacteristic
684C22#1568978011yescharacteristic
685C22#1568979211yescharacteristic
686C22#1568992111yescharacteristic
687C22#1568992111yescharacteristic
688C22#1568992611yescharacteristic
689C22#1568993411yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—22no—
696C4—42no—
697C4—42no—
698C4—3761no—
699C4—3761no—
700C4—3761no—
701C4—1882no—
702C4#41×Dic4711yescharacteristic
703C4#1568960611yescharacteristic
704C4#1568978011yescharacteristic
705C4#1568979211yescharacteristic
706C2—82no—
707C2—82no—
708C2#2024622911yescharacteristic
709C2#2025190711yescharacteristic
710C2#2025191411yescharacteristic
711C2#2025613511yescharacteristic
712C2#2025615011yescharacteristic
713C2#2025644811yescharacteristic
714C2#2025647211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#559C2
socleC23×C47C22×D4
prime radicalC2×#127×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#559D47
hypocenterC47#22549
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#15689254C2semidirect
2. #20246345C2semidirect
3. #20244321C2semidirect
4. #20244321C2semidirect
7. #20244205C2semidirect
8. #20244200C2semidirect
9. #20243403C2semidirect
10. #20243398C2semidirect
11. #20243388C2semidirect
12. #20243218C2semidirect
13. #20243213C2semidirect
14. C4×#13093945C2semidirect
50. C47×#559C4semidirect
374. #559Dic47semidirect
419. C47#22549semidirect

Maximal subgroups

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

subgroupindex
C2×#156892542
#202463452
#202443212
#202443162
#202442132
#202442052
#202442002
#202434032
#202433982
#202433882
#202432182
#202432132
C4×#130939452
C2×C47×#5592
#2254947