Finite Group Databasebeta

← #26234819

Subgroups — #26234819

Order 12032.

944 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689195C211yesmaximal, characteristic
2#20245833C211yesmaximal, characteristic
3#20244109C211yesmaximal, characteristic, complemented
4#20244106C211yesmaximal, characteristic, complemented
5#20243570C211yesmaximal, characteristic, complemented
6#20243566C211yesmaximal, characteristic, complemented
7#20243566C211yesmaximal, characteristic, complemented
8#20243565C211yesmaximal, characteristic, complemented
9#20243507C211yesmaximal, characteristic, complemented
10#20243370C211yesmaximal, characteristic, complemented
11#20243366C211yesmaximal, characteristic, complemented
12#20243246C211yesmaximal, characteristic, complemented
13#20243084C211yesmaximal, characteristic, complemented
14C2×#15688877C211yesmaximal, characteristic, complemented
15C2×C8×D4×C47C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19C22×C4×Dic47C2211yescharacteristic
20#15689195—24no—
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×Dic47⋊C8C2211yescharacteristic
23C2×Dic47⋊C8C2211yescharacteristic
24C2×Dic47⋊C8C2211yescharacteristic
25C2×Dic47⋊C8C2211yescharacteristic
26C2×Dic47⋊C8C2211yescharacteristic
27C2×Dic47⋊C8C2211yescharacteristic
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×#13093935C2211yescharacteristic
31#15689016C411yescharacteristic
32#15689016C411yescharacteristic
33#15689009C411yescharacteristic
34#15689009C411yescharacteristic
35#15689003C411yescharacteristic
36#15689003C411yescharacteristic
37#15688998C411yescharacteristic
38#15688998C411yescharacteristic
39C4×C4⋊Dic47C2211yescharacteristic
40C4×C22⋊Dic47C2211yescharacteristic
41C4×C22⋊Dic47C2211yescharacteristic
42#15688969C2211yescharacteristic
43#15688877C2211yescharacteristic
44#15688877C2211yescharacteristic
45#15688877C2211yescharacteristic
46#15688877C2211yescharacteristic
47#15688877C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53C23×C8×C47C2211yescharacteristic
54C23×C8×C47C2211yescharacteristic
55C2×C4×D4×C47C2211yescharacteristic
56C8×D4×C47—24no—
57C2×C4⋊C8×C47C2211yescharacteristic
58C2×C22⋊C8×C47C2211yescharacteristic
59C2×C22⋊C8×C47C2211yescharacteristic
60C2×C4×C8×C47C2211yescharacteristic
61C23×Dic47C2×C411yescharacteristic
62C23×Dic47C2×C411yescharacteristic
63C2×#10625329—22no—
64C2×#10625329—22no—
65C2×#10625329—41no—
66C22×C47⋊C8—22no—
67C22×C47⋊C8—22no—
68C22×C47⋊C8—41no—
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73#13093983—41no—
74#13093983—41no—
75C2×C4⋊Dic47C2×C411yescharacteristic
76C2×C4⋊Dic47C2×C411yescharacteristic
77C2×C4⋊Dic47C2×C411yescharacteristic
78C2×C4⋊Dic47C2×C411yescharacteristic
79C2×C22⋊Dic47C2×C411yescharacteristic
80C2×C22⋊Dic47C2×C411yescharacteristic
81C2×C22⋊Dic47C2×C411yescharacteristic
82C2×C22⋊Dic47C2×C411yescharacteristic
83C2×C22⋊Dic47C2×C411yescharacteristic
84C2×C22⋊Dic47C2×C411yescharacteristic
85C2×C4×Dic47—41no—
86C2×C4×Dic47—41no—
87C2×C4×Dic47C2×C411yescharacteristic
88C2×C4×Dic47C2×C411yescharacteristic
89C2×C4×Dic47C2311yescharacteristic
90C2×C4×Dic47C2311yescharacteristic
91C2×C4×Dic47C2311yescharacteristic
92C2×C4×Dic47C2311yescharacteristic
93C4⋊(C47⋊C8)—22no—
94Dic47⋊C8—22no—
95Dic47⋊C8—22no—
96Dic47⋊C8—41no—
97Dic47⋊C8—41no—
98Dic47⋊C8—41no—
99Dic47⋊C8—41no—
100C22⋊(C47⋊C8)—22no—
101C22⋊(C47⋊C8)—22no—
102#13093935—22no—
103C47⋊#95C2×C411yescharacteristic
104C47⋊#95C2×C411yescharacteristic
105C47⋊#95C2×C411yescharacteristic
106C47⋊#95C2×C411yescharacteristic
107C47⋊#95C2×C411yescharacteristic
108C47⋊#95C2×C411yescharacteristic
109C47⋊#95C2×C411yescharacteristic
110C47⋊#95C2×C411yescharacteristic
111C47⋊#95C2×C411yescharacteristic
112C47⋊#95C2×C411yescharacteristic
113C22×D4×C47C2×C411yescharacteristic
114C23×C4×C47C2311yescharacteristic
115C23×C4×C47C2311yescharacteristic
116C22×C8×C47—22no—
117C22×C8×C47—22no—
118C22×C8×C47—22no—
119C22×C8×C47—22no—
120C22×C8×C47—41no—
121C22×C8×C47—41no—
122C22×C8×C47C2311yescharacteristic
123C22×C8×C47C2311yescharacteristic
124C22×C8×C47C2311yescharacteristic
125C22×C8×C47C2311yescharacteristic
126C4×D4×C47D414yes—
127C4×D4×C47Q814yes—
128C2×C4⋊C4×C47C2×C411yescharacteristic
129C2×C22⋊C4×C47C2×C411yescharacteristic
130C2×C22⋊C4×C47C2×C411yescharacteristic
131C2×C42×C47C2311yescharacteristic
132C4⋊C8×C47—22no—
133C22⋊C8×C47—22no—
134C22⋊C8×C47—22no—
135C4×C8×C47—22no—
136C24×C47C22×C411yescharacteristic
137C24×C47C22×C411yescharacteristic
138C2×D4×C47—22no—
139C2×D4×C47—22no—
140C2×D4×C47C4⋊C414yes—
141C22×C4×C47—21no—
142C22×C4×C47—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×C47C22×C411yescharacteristic
150C22×C4×C47C22×C411yescharacteristic
151C22×C4×C47C22×C411yescharacteristic
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C2×D412yes—
154C22×C4×C47C2×D412yes—
155C22×C4×C47C2×Q812yes—
156C22×C4×C47C2×Q812yes—
157C22×C4×C47C2411yescharacteristic
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47—22no—
161C22×Dic47—41no—
162C22×Dic47—41no—
163C22×Dic47—41no—
164C22×Dic47C22×C411yescharacteristic
165C22×Dic47C22×C411yescharacteristic
166C22×Dic47C22×C411yescharacteristic
167C22×Dic47C22×C411yescharacteristic
168C22×Dic47C22×C411yescharacteristic
169C22×Dic47C22×C411yescharacteristic
170C22×Dic47C22×C411yescharacteristic
171C22×Dic47C22×C411yescharacteristic
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47—21no—
182C2×C8×C47—21no—
183C2×C8×C47—44no—
184C2×C8×C47—44no—
185C2×C8×C47#4112yes—
186C4⋊C4×C47C4⋊C414yes—
187C22⋊C4×C47C4⋊C414yes—
188C22⋊C4×C47C4⋊C414yes—
189C42×C47C2×D412yes—
190C42×C47C2×Q812yes—
191C22⋊Dic47—22no—
192C22⋊Dic47—22no—
193C22⋊Dic47—22no—
194C22⋊Dic47—41no—
195C22⋊Dic47—41no—
196C22⋊Dic47—41no—
197C4⋊Dic47—22no—
198C4⋊Dic47—41no—
199C4⋊Dic47—41no—
200C4⋊Dic47—41no—
201C4×Dic47—21no—
202C4×Dic47—21no—
203C4×Dic47—21no—
204C4×Dic47—21no—
205C4×Dic47—21no—
206C4×Dic47—21no—
207C4×Dic47—21no—
208C4×Dic47—21no—
209C4×Dic47—41no—
210C4×Dic47—41no—
211#10625329—44no—
212C2×C47⋊C8—21no—
213C2×C47⋊C8—21no—
214C2×C47⋊C8—21no—
215C2×C47⋊C8—21no—
216C2×C47⋊C8—21no—
217C2×C47⋊C8—21no—
218C2×C47⋊C8—21no—
219C2×C47⋊C8—21no—
220C2×C47⋊C8—21no—
221C2×C47⋊C8—21no—
222C2×C47⋊C8—21no—
223C2×C47⋊C8—44no—
224C2×C47⋊C8#4112yes—
225C23×C47—21no—
226C23×C47—21no—
227C23×C47—21no—
228C23×C47—21no—
229C23×C47—21no—
230C23×C47—21no—
231C23×C47—21no—
232C23×C47—21no—
233C23×C47—21no—
234C23×C47—21no—
235C23×C47C2×C4⋊C412yes—
236C23×C47C2×C4⋊C412yes—
237C23×C47#13112yes—
238C23×C47#13112yes—
239C23×C47C23×C411yescharacteristic
240D4×C47—28no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—21no—
246C2×C4×C47—21no—
247C2×C4×C47—21no—
248C2×C4×C47—21no—
249C2×C4×C47—22no—
250C2×C4×C47—22no—
251C2×C4×C47—22no—
252C2×C4×C47—22no—
253C2×C4×C47—22no—
254C2×C4×C47—22no—
255C2×C4×C47—22no—
256C2×C4×C47—22no—
257C2×C4×C47C2×C4⋊C412yes—
258C2×C4×C47C2×C4⋊C412yes—
259C2×C4×C47C2×C4⋊C412yes—
260C2×C4×C47C2×C4⋊C412yes—
261C2×C4×C47C22×D411yescharacteristic
262C2×C4×C47C22×Q811yescharacteristic
263C2×C4×C47C2×#4111yescharacteristic
264C2×C4×C47C2×#4111yescharacteristic
265C2×C4×C47H(5,𝔽2)11yescharacteristic
266C2×C4×C47H(5,𝔽2)11yescharacteristic
267C2×Dic47—21no—
268C2×Dic47—21no—
269C2×Dic47—21no—
270C2×Dic47—21no—
271C2×Dic47—21no—
272C2×Dic47—21no—
273C2×Dic47—21no—
274C2×Dic47—21no—
275C2×Dic47—21no—
276C2×Dic47—21no—
277C2×Dic47—21no—
278C2×Dic47—21no—
279C2×Dic47—21no—
280C2×Dic47—21no—
281C2×Dic47—21no—
282C2×Dic47—21no—
283C2×Dic47—21no—
284C2×Dic47—21no—
285C2×Dic47—21no—
286C2×Dic47—21no—
287C2×Dic47—21no—
288C2×Dic47—21no—
289C2×Dic47—21no—
290C2×Dic47—44no—
291C2×Dic47—44no—
292C2×Dic47#13112yes—
293C8×C47—22no—
294C8×C47—41no—
295C8×C47—41no—
296C8×C47—41no—
297C47⋊C8—22no—
298C47⋊C8—41no—
299C47⋊C8—41no—
300C47⋊C8—41no—
301#22697—471nomaximal, Sylow
302C22×C47—22no—
303C22×C47—22no—
304C22×C47—22no—
305C22×C47—22no—
306C22×C47—22no—
307C22×C47—22no—
308C22×C47—22no—
309C22×C47—22no—
310C22×C47—22no—
311C22×C47—41no—
312C22×C47—41no—
313C22×C47—41no—
314C22×C47—41no—
315C22×C47#42414yes—
316C22×C47C22×C4⋊C411yescharacteristic
317C22×C47C4×#4111yescharacteristic
318C22×C47#51811yescharacteristic
319C22×C47C2×#13111yescharacteristic
320C22×C47C2×#13111yescharacteristic
321C22×C47C2×#13111yescharacteristic
322C22×C47#56811yescharacteristic
323C4×C47—22no—
324C4×C47—22no—
325C4×C47—22no—
326C4×C47—22no—
327C4×C47#54611yescharacteristic
328C4×C47#54611yescharacteristic
329C4×C47#55411yescharacteristic
330C4×C47#55411yescharacteristic
331Dic47—22no—
332Dic47—41no—
333Dic47—41no—
334Dic47—41no—
335Dic47—41no—
336Dic47—41no—
337Dic47—41no—
338Dic47—41no—
339C2×#435—471no—
340C2×C8×D4D4711yescharacteristic
341#2290—471no—
342#1940—471no—
343#1939—471no—
344#1851—471no—
345#1850—471no—
346#1850—471no—
347#1850—471no—
348#1832—471no—
349#1798—471no—
350#1797—471no—
351#1768—471no—
352#1729—471no—
353C2×#336—471no—
354C2×C47—24no—
355C2×C47—42no—
356C2×C47#234911yescharacteristic
357C2×C47C2×#42411yescharacteristic
358C2×C47#290611yescharacteristic
359C2×C47#296611yescharacteristic
360C2×C47#296811yescharacteristic
361C2×C47#297611yescharacteristic
362C2×C47#297711yescharacteristic
363C22×M16—471no—
364C23×C8—471no—
365C23×C8C2×D4711yescharacteristic
366C23×C8C2×D4711yescharacteristic
367C2×C4×D4C2×D4711yescharacteristic
368C2×#117—471no—
369C22×C42—471no—
370#435—944no—
371C8×D4—24no—
372C2×C4⋊C8—471no—
373C2×C4⋊C8—471no—
374C2×C4⋊C8—471no—
375C2×C4⋊C8—471no—
376C2×C4⋊C8—471no—
377C2×C4⋊C8—471no—
378C2×C4⋊C8—471no—
379C2×C4⋊C8C2×D4711yescharacteristic
380C2×C22⋊C8—471no—
381C2×C22⋊C8—471no—
382C2×C22⋊C8C2×D4711yescharacteristic
383C2×C22⋊C8C2×D4711yescharacteristic
384C2×#97—471no—
385C2×C4×C8C2×D4711yescharacteristic
386#388—471no—
387#388—471no—
388#387—471no—
389#387—471no—
390#386—471no—
391#386—471no—
392#385—471no—
393#385—471no—
394C4×C4⋊C4—471no—
395C4×C22⋊C4—471no—
396C4×C22⋊C4—471no—
397#376—471no—
398#336—471no—
399#336—471no—
400#336—471no—
401#336—471no—
402#336—471no—
403#336—471no—
404#336—471no—
405#336—471no—
406#336—471no—
407#336—471no—
408C47#2269711yescharacteristic, complemented, Sylow
409C22×D4C4×D4711yescharacteristic
410C23×C4—471no—
411C23×C4—471no—
412C23×C4C22×D4711yescharacteristic
413C23×C4C22×D4711yescharacteristic
414C2×M16—942no—
415C2×M16—942no—
416C2×M16—1881no—
417C22×C8—22no—
418C22×C8—22no—
419C22×C8—22no—
420C22×C8—22no—
421C22×C8—41no—
422C22×C8—41no—
423C22×C8—471no—
424C22×C8—471no—
425C22×C8—471no—
426C22×C8—471no—
427C22×C8—942no—
428C22×C8—942no—
429C22×C8—1881no—
430C22×C8C22×D4711yescharacteristic
431C22×C8C22×D4711yescharacteristic
432C22×C8C22×D4711yescharacteristic
433C22×C8C22×D4711yescharacteristic
434C4×D4Dic9414yes—
435C4×D4C22⋊D4714yes—
436#117—1881no—
437#117—1881no—
438C2×C4⋊C4—471no—
439C2×C4⋊C4—471no—
440C2×C4⋊C4—471no—
441C2×C4⋊C4—471no—
442C2×C4⋊C4C4×D4711yescharacteristic
443C2×C22⋊C4—471no—
444C2×C22⋊C4—471no—
445C2×C22⋊C4—471no—
446C2×C22⋊C4—471no—
447C2×C22⋊C4—471no—
448C2×C22⋊C4—471no—
449C2×C22⋊C4C4×D4711yescharacteristic
450C2×C22⋊C4C4×D4711yescharacteristic
451C2×C42—471no—
452C2×C42—471no—
453C2×C42—471no—
454C2×C42—471no—
455C2×C42—471no—
456C2×C42—471no—
457C2×C42—1881no—
458C2×C42—1881no—
459C2×C42C22×D4711yescharacteristic
460C4⋊C8—22no—
461C4⋊C8—942no—
462C4⋊C8—942no—
463C4⋊C8—942no—
464C4⋊C8—1881no—
465C4⋊C8—1881no—
466C4⋊C8—1881no—
467C4⋊C8—1881no—
468C22⋊C8—22no—
469C22⋊C8—22no—
470C22⋊C8—942no—
471C22⋊C8—942no—
472#97—942no—
473C4×C8—22no—
474#95—471no—
475#95—471no—
476#95—471no—
477#95—471no—
478#95—471no—
479#95—471no—
480#95—471no—
481#95—471no—
482#95—471no—
483#95—471no—
484C24C2×C4×D4711yescharacteristic
485C24C2×C4×D4711yescharacteristic
486C2×D4—22no—
487C2×D4—22no—
488C2×D4Dic47⋊C414yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—471no—
498C22×C4—471no—
499C22×C4—471no—
500C22×C4—471no—
501C22×C4—471no—
502C22×C4—471no—
503C22×C4—471no—
504C22×C4—471no—
505C22×C4—942no—
506C22×C4—942no—
507C22×C4—942no—
508C22×C4—1881no—
509C22×C4—1881no—
510C22×C4—1881no—
511C22×C4C2×Dic9412yes—
512C22×C4C2×Dic9412yes—
513C22×C4C2×C4×D4711yescharacteristic
514C22×C4C2×C4×D4711yescharacteristic
515C22×C4C2×C4×D4711yescharacteristic
516C22×C4C2×C4×D4711yescharacteristic
517C22×C4C2×C22⋊D4712yes—
518C22×C4C2×C22⋊D4712yes—
519C22×C4C23×D4711yescharacteristic
520M16—1884no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—44no—
533C2×C8—44no—
534C2×C8—472no—
535C2×C8—941no—
536C2×C8—941no—
537C2×C8—941no—
538C2×C8—941no—
539C2×C8—941no—
540C2×C8—941no—
541C2×C8—941no—
542C2×C8—941no—
543C2×C8—941no—
544C2×C8—941no—
545C2×C8—941no—
546C2×C8—1884no—
547C2×C8#1062535212yes—
548C4⋊C4—942no—
549C4⋊C4—1881no—
550C4⋊C4—1881no—
551C4⋊C4—1881no—
552C4⋊C4Dic47⋊C414yes—
553C22⋊C4—942no—
554C22⋊C4—942no—
555C22⋊C4—942no—
556C22⋊C4—1881no—
557C22⋊C4—1881no—
558C22⋊C4—1881no—
559C22⋊C4Dic47⋊C414yes—
560C22⋊C4Dic47⋊C414yes—
561C42—941no—
562C42—941no—
563C42—941no—
564C42—941no—
565C42—941no—
566C42—941no—
567C42—941no—
568C42—941no—
569C42—1881no—
570C42—1881no—
571C42C2×Dic9412yes—
572C42C2×C22⋊D4712yes—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23C2×Dic47⋊C412yes—
584C23C2×Dic47⋊C412yes—
585C23#1309403012yes—
586C23#1309403012yes—
587C23C22×C4×D4711yescharacteristic
588D4—28no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—472no—
606C2×C4—941no—
607C2×C4—941no—
608C2×C4—941no—
609C2×C4—941no—
610C2×C4—941no—
611C2×C4—941no—
612C2×C4—941no—
613C2×C4—941no—
614C2×C4—941no—
615C2×C4—941no—
616C2×C4—941no—
617C2×C4—941no—
618C2×C4—941no—
619C2×C4—941no—
620C2×C4—941no—
621C2×C4—941no—
622C2×C4—941no—
623C2×C4—941no—
624C2×C4—941no—
625C2×C4—941no—
626C2×C4—941no—
627C2×C4—941no—
628C2×C4—941no—
629C2×C4—1884no—
630C2×C4—1884no—
631C2×C4C2×Dic47⋊C412yes—
632C2×C4C2×Dic47⋊C412yes—
633C2×C4C2×Dic47⋊C412yes—
634C2×C4C2×Dic47⋊C412yes—
635C2×C4C22×C22⋊D4711yescharacteristic
636C2×C4C22×Dic9411yescharacteristic
637C2×C4#41×D4711yescharacteristic
638C2×C4C2×#1062535211yescharacteristic
639C2×C4#1309406911yescharacteristic
640C2×C4#1309407011yescharacteristic
641C8—22no—
642C8—41no—
643C8—41no—
644C8—41no—
645C8—942no—
646C8—1881no—
647C8—1881no—
648C8—1881no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22#1568914914yes—
663C22C22×Dic47⋊C411yescharacteristic
664C22C4×#1062535211yescharacteristic
665C22#1568959511yescharacteristic
666C22#131×D4711yescharacteristic
667C22C2×#1309403011yescharacteristic
668C22C2×#1309403011yescharacteristic
669C22#1568988811yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—22no—
674C4—942no—
675C4—1881no—
676C4—1881no—
677C4—1881no—
678C4—1881no—
679C4—1881no—
680C4—1881no—
681C4—1881no—
682C4#1568976111yescharacteristic
683C4#1568976711yescharacteristic
684C4#1568983011yescharacteristic
685C4#1568983211yescharacteristic
686C2—24no—
687C2—42no—
688C2#2024629311yescharacteristic
689C2C2×#1568914911yescharacteristic
690C2#2025195411yescharacteristic
691C2#2025235611yescharacteristic
692C2#2025237611yescharacteristic
693C2#2025243011yescharacteristic
694C2#2025244111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC2×C8×D4×C47C2
prime radicalC22×D4×C47C2×C4
cosocleC22×C4×C47C24
hypercenterC2×C8×D4D47
hypocenterC47#22697
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
3. #20244109C2semidirect
4. #20244106C2semidirect
5. #20243570C2semidirect
6. #20243566C2semidirect
7. #20243566C2semidirect
8. #20243565C2semidirect
9. #20243507C2semidirect
10. #20243370C2semidirect
11. #20243366C2semidirect
12. #20243246C2semidirect
13. #20243084C2semidirect
14. C2×#15688877C2semidirect
408. C47#22697semidirect

Maximal subgroups

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

subgroupindex
C2×#156891952
#202458332
#202441092
#202441062
#202435702
#202435662
#202435652
#202435072
#202433702
#202433662
#202432462
#202430842
C2×#156888772
C2×C8×D4×C472
#2269747