Finite Group Databasebeta

← #26137809

Subgroups — #26137809

Order 12032.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689014C211yesmaximal, characteristic
2C2×#15689012C211yesmaximal, characteristic
3C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
4C2×#15688970C211yesmaximal, characteristic
5C2×#15688969C211yesmaximal, characteristic, complemented
6#20241626C211yesmaximal, characteristic
7#20241624C211yesmaximal, characteristic
8#20241621C211yesmaximal, characteristic, complemented
9#20241619C211yesmaximal, characteristic, complemented
10Dic47⋊#95C211yesmaximal, characteristic, complemented
11#20241613C211yesmaximal, characteristic, complemented
12(C2×D47)⋊#95C211yesmaximal, characteristic
13C4×C47⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic47C211yesmaximal, characteristic, complemented
15C4×#95×C47C211yesmaximal, characteristic, complemented
16C23×C4×D47C2211yescharacteristic
17C22×Dic47⋊C4C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×(C2×D47)⋊C4C2211yescharacteristic
20C22×(C2×D47)⋊C4C2211yescharacteristic
21C22×(C2×D47)⋊C4C2211yescharacteristic
22C22×(C2×D47)⋊C4C2211yescharacteristic
23C22×(C2×D47)⋊C4C2211yescharacteristic
24C22×(C2×D47)⋊C4C2211yescharacteristic
25C22×C4×Dic47C2211yescharacteristic
26C22×C4×Dic47C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28C22×C4×Dic47C2211yescharacteristic
29C22×C4×Dic47C2211yescharacteristic
30#15689014C418yescomplemented
31#15689012C418yescomplemented
32C4×(C2×D47)⋊C4—24no—
33#15688970C418yescomplemented
34#15688969—24no—
35C2×C47⋊#95C2211yescharacteristic
36C2×C47⋊#95C2211yescharacteristic
37C2×C47⋊#95C2211yescharacteristic
38C2×C47⋊#95C2211yescharacteristic
39C2×C47⋊#95C2211yescharacteristic
40C2×C47⋊#95C2211yescharacteristic
41C2×C47⋊#95C2211yescharacteristic
42C2×C47⋊#95C2211yescharacteristic
43C2×C47⋊#95C2211yescharacteristic
44C2×C47⋊#95C2211yescharacteristic
45C2×C47⋊#95C2211yescharacteristic
46C2×C47⋊#95C2211yescharacteristic
47C2×C47⋊#95C2211yescharacteristic
48C2×C47⋊#95C2211yescharacteristic
49C22×C42×C47C2211yescharacteristic
50C22×C42×C47C2211yescharacteristic
51C22×C42×C47C2211yescharacteristic
52C2×#95×C47C2211yescharacteristic
53C2×#95×C47C2211yescharacteristic
54C2×#95×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C24×D47C2311yescharacteristic
57C23×Dic47C2311yescharacteristic
58C23×Dic47C2311yescharacteristic
59C23×Dic47C2311yescharacteristic
60C23×Dic47C2311yescharacteristic
61C23×Dic47C2311yescharacteristic
62C23×Dic47C2311yescharacteristic
63C23×Dic47C2311yescharacteristic
64C22×C4×D47—22no—
65C22×C4×D47—22no—
66C22×C4×D47—22no—
67C22×C4×D47—22no—
68C22×C4×D47—41no—
69C22×C4×D47—41no—
70C22×C4×D47C2×C414yes—
71C2×Dic47⋊C4—41no—
72C2×Dic47⋊C4—41no—
73C2×Dic47⋊C4—41no—
74C2×Dic47⋊C4—41no—
75C2×Dic47⋊C4C2×C414yescomplemented
76C2×Dic47⋊C4C2×C414yescomplemented
77C2×(C2×D47)⋊C4—22no—
78C2×(C2×D47)⋊C4—22no—
79C2×(C2×D47)⋊C4—22no—
80C2×(C2×D47)⋊C4—22no—
81C2×(C2×D47)⋊C4—22no—
82C2×(C2×D47)⋊C4—22no—
83C2×(C2×D47)⋊C4—41no—
84C2×(C2×D47)⋊C4—41no—
85C2×(C2×D47)⋊C4—41no—
86C2×(C2×D47)⋊C4—41no—
87C2×(C2×D47)⋊C4C2×C414yes—
88C2×(C2×D47)⋊C4C2×C414yes—
89C2×(C2×D47)⋊C4C2×C414yes—
90C2×(C2×D47)⋊C4C2×C414yes—
91C2×(C2×D47)⋊C4C2×C414yes—
92C2×(C2×D47)⋊C4C2×C414yes—
93C2×(C2×D47)⋊C4C2×C414yes—
94C2×(C2×D47)⋊C4C2×C414yes—
95C2×C4×Dic47—22no—
96C2×C4×Dic47—22no—
97C2×C4×Dic47—22no—
98C2×C4×Dic47—22no—
99C2×C4×Dic47—22no—
100C2×C4×Dic47—22no—
101C2×C4×Dic47—22no—
102C2×C4×Dic47—22no—
103C2×C4×Dic47—41no—
104C2×C4×Dic47—41no—
105C2×C4×Dic47—41no—
106C2×C4×Dic47—41no—
107C2×C4×Dic47C2×C414yes—
108C2×C4×Dic47C2×C414yes—
109C2×C4×Dic47C2×C414yescomplemented
110C47⋊#95—22no—
111C47⋊#95—22no—
112C47⋊#95—22no—
113C47⋊#95—22no—
114C47⋊#95—22no—
115C47⋊#95—22no—
116C47⋊#95—22no—
117C47⋊#95—41no—
118C47⋊#95—41no—
119C47⋊#95C2×C414yes—
120C47⋊#95C2×C414yescomplemented
121C47⋊#95C2×C414yescomplemented
122C47⋊#95C2×C414yescomplemented
123C47⋊#95D414yes—
124C23×C4×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C2×C42×C47—22no—
132C2×C42×C47—22no—
133C2×C42×C47—22no—
134C2×C42×C47—22no—
135C2×C42×C47—22no—
136C2×C42×C47—22no—
137C2×C42×C47—41no—
138C2×C42×C47—41no—
139C2×C42×C47C2×C414yescomplemented
140#95×C47—22no—
141#95×C47—22no—
142#95×C47C2×C414yes—
143#95×C47C2×C414yescomplemented
144C24×C47C2411yescharacteristic
145C23×D47—21no—
146C23×D47—21no—
147C23×D47—21no—
148C23×D47—21no—
149C23×D47—21no—
150C23×D47—21no—
151C23×D47—21no—
152C23×D47—21no—
153C23×D47—21no—
154C23×D47—21no—
155C23×D47—21no—
156C23×D47—21no—
157C23×D47C22×C412yes—
158C23×D47C22×C412yes—
159C23×D47C22×C412yes—
160C22×C4×C47—21no—
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—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47C22×C412yes—
195C22×C4×C47C22×C412yes—
196C22×C4×C47C22×C412yes—
197C22×C4×C47C22×C412yes—
198C22×C4×C47C22×C412yes—
199C22×C4×C47C22×C412yes—
200C22×C4×C47C22×C412yes—
201C22×C4×C47C22×C412yes—
202C22×C4×C47C22×C412yes—
203C22×C4×C47C2×D412yes—
204C22×C4×C47#4112yes—
205C22×C4×C47#4112yes—
206C22×C4×C47#4112yes—
207C22×C4×C47#4112yes—
208C22×C4×C47#4112yes—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—21no—
219C22×Dic47—21no—
220C22×Dic47—21no—
221C22×Dic47—21no—
222C22×Dic47—21no—
223C22×Dic47—21no—
224C22×Dic47—21no—
225C22×Dic47—21no—
226C22×Dic47—21no—
227C22×Dic47—21no—
228C22×Dic47—21no—
229C22×Dic47—21no—
230C22×Dic47—21no—
231C22×Dic47—21no—
232C22×Dic47—21no—
233C22×Dic47—21no—
234C22×Dic47—21no—
235C22×Dic47—21no—
236C22×Dic47—21no—
237C22×Dic47—21no—
238C22×Dic47—21no—
239C22×Dic47—21no—
240C22×Dic47—21no—
241C22×Dic47—21no—
242C22×Dic47—21no—
243C22×Dic47—21no—
244C22×Dic47—21no—
245C22×Dic47C22×C412yes—
246C22×Dic47C22×C412yes—
247C22×Dic47C22×C412yes—
248C22×Dic47C22×C412yes—
249C22×Dic47C22×C412yes—
250C22×Dic47C22×C412yes—
251C22×Dic47C22×C412yes—
252C22×Dic47C22×C412yes—
253C22×Dic47C22×C412yes—
254C22×Dic47C2×D412yes—
255C22×Dic47C2×D412yes—
256C22×Dic47#4112yes—
257C22×Dic47#4112yes—
258C2×C4×D47—28no—
259C2×C4×D47—28no—
260C2×C4×D47—44no—
261C2×C4×D47—44no—
262C2×C4×D47—44no—
263C2×C4×D47—44no—
264C2×C4×D47—44no—
265C42×C47—28no—
266C42×C47—44no—
267C42×C47—44no—
268(C2×D47)⋊C4—28no—
269(C2×D47)⋊C4—28no—
270(C2×D47)⋊C4—28no—
271(C2×D47)⋊C4—44no—
272(C2×D47)⋊C4—44no—
273(C2×D47)⋊C4C42116yescomplemented
274Dic47⋊C4—44no—
275Dic47⋊C4—44no—
276C4×Dic47—28no—
277C4×Dic47—28no—
278C4×Dic47—44no—
279C4×Dic47—44no—
280C4×Dic47—44no—
281C23×C47C23×C411yescharacteristic
282C23×C47C23×C411yescharacteristic
283C23×C47C23×C411yescharacteristic
284C23×C47C22×D411yescharacteristic
285C23×C47C2×#4111yescharacteristic
286C23×C47C2×#4111yescharacteristic
287C23×C47C2×#4111yescharacteristic
288C23×C47C2×#4111yescharacteristic
289C23×C47C2×#4111yescharacteristic
290C23×C47C2×#4111yescharacteristic
291C23×C47C2×#4111yescharacteristic
292C23×C47H(5,𝔽2)11yescharacteristic
293C23×C47H(5,𝔽2)11yescharacteristic
294C23×C47H(5,𝔽2)11yescharacteristic
295C23×C472−1+411yescharacteristic
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—22no—
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—22no—
308C22×D47—22no—
309C22×D47—22no—
310C22×D47—22no—
311C22×D47—22no—
312C22×D47—22no—
313C22×D47—22no—
314C22×D47—41no—
315C22×D47—41no—
316C22×D47—41no—
317C22×D47—41no—
318C22×D47—41no—
319C22×D47—41no—
320C22×D47—41no—
321C22×D47—41no—
322C22×D47—41no—
323C22×D47—41no—
324C22×D47—41no—
325C22×D47—41no—
326C22×D47—41no—
327C22×D47—41no—
328C22×D47—41no—
329C22×D47—41no—
330C22×D47C2×C4214yes—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—41no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47C2×C4214yes—
377C2×C4×C47#11714yes—
378C2×C4×C47#11714yes—
379C2×C4×C47C4×D414yes—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—22no—
383C2×Dic47—22no—
384C2×Dic47—22no—
385C2×Dic47—22no—
386C2×Dic47—22no—
387C2×Dic47—22no—
388C2×Dic47—22no—
389C2×Dic47—22no—
390C2×Dic47—22no—
391C2×Dic47—22no—
392C2×Dic47—22no—
393C2×Dic47—22no—
394C2×Dic47—22no—
395C2×Dic47—22no—
396C2×Dic47—22no—
397C2×Dic47—22no—
398C2×Dic47—22no—
399C2×Dic47—22no—
400C2×Dic47—22no—
401C2×Dic47—22no—
402C2×Dic47—22no—
403C2×Dic47—22no—
404C2×Dic47—22no—
405C2×Dic47—22no—
406C2×Dic47—22no—
407C2×Dic47—22no—
408C2×Dic47—22no—
409C2×Dic47—22no—
410C2×Dic47—41no—
411C2×Dic47—41no—
412C2×Dic47—41no—
413C2×Dic47—41no—
414C2×Dic47—41no—
415C2×Dic47—41no—
416C2×Dic47—41no—
417C2×Dic47—41no—
418C2×Dic47—41no—
419C2×Dic47—41no—
420C2×Dic47—41no—
421C2×Dic47—41no—
422C2×Dic47—41no—
423C2×Dic47—41no—
424C2×Dic47—41no—
425C2×Dic47—41no—
426C2×Dic47C2×C4214yes—
427C2×Dic47C4×D414yes—
428C2×Dic47C4×D414yes—
429C4×D47—416no—
430#13816—471nomaximal, Sylow
431C22×C47C22×C4211yescharacteristic
432C22×C47C2×#11711yescharacteristic
433C22×C47C2×#11711yescharacteristic
434C22×C47C2×C4×D411yescharacteristic
435C22×C47C2×C4×D411yescharacteristic
436C22×C47C2×C4×D411yescharacteristic
437C22×C47C4×#4111yescharacteristic
438C22×C47C4×#4111yescharacteristic
439C22×C47C4×#4111yescharacteristic
440C22×C47C4×#4111yescharacteristic
441C22×C47C4×#4111yescharacteristic
442C22×C47C4×#4111yescharacteristic
443C22×C47C4×#4111yescharacteristic
444C22×C47#51811yescharacteristic
445C22×C47#51811yescharacteristic
446C22×C47#51811yescharacteristic
447C22×C47#52011yescharacteristic
448C22×C47#52011yescharacteristic
449C22×C47#52011yescharacteristic
450C22×C47#54611yescharacteristic
451C22×C47#54611yescharacteristic
452C22×C47#54711yescharacteristic
453C22×C47#55011yescharacteristic
454C22×C47#55111yescharacteristic
455C22×C47#55111yescharacteristic
456C22×C47#55111yescharacteristic
457C22×C47#55111yescharacteristic
458C22×C47#55211yescharacteristic
459C22×C47#55211yescharacteristic
460C22×C47#55311yescharacteristic
461C22×C47#55311yescharacteristic
462C22×C47#55511yescharacteristic
463C22×C47#55511yescharacteristic
464C22×C47#55511yescharacteristic
465C22×C47#55611yescharacteristic
466C2×D47—24no—
467C2×D47—24no—
468C2×D47—24no—
469C2×D47—42no—
470C2×D47—42no—
471C2×D47—42no—
472C2×D47—42no—
473C2×D47—42no—
474C2×D47—42no—
475C2×D47—42no—
476C2×D47—42no—
477C2×D47—42no—
478C2×D47—42no—
479C2×D47—42no—
480C2×D47—42no—
481C4×C47—24no—
482C4×C47—24no—
483C4×C47—24no—
484C4×C47—24no—
485C4×C47—42no—
486C4×C47—42no—
487C4×C47—42no—
488Dic47—24no—
489Dic47—24no—
490Dic47—24no—
491Dic47—42no—
492Dic47—42no—
493Dic47—42no—
494Dic47—42no—
495C2×#388—471no—
496C2×#388—471no—
497C2×C4×C22⋊C4—471no—
498C2×C4×C22⋊C4—471no—
499C2×#376—471no—
500#1437—471no—
501#1437—471no—
502#1436—471no—
503#1436—471no—
504C4⋊#95—471no—
505#1434—471no—
506C22⋊#95—471no—
507C4×#95—471no—
508C4×#95—471no—
509C4×#95D4711yescharacteristic, complemented
510C2×C47C4×#11711yescharacteristic
511C2×C47C42×D411yescharacteristic
512C2×C47#227511yescharacteristic
513C2×C47#234211yescharacteristic
514C2×C47#234611yescharacteristic
515C2×C47#235311yescharacteristic
516C2×C47#235411yescharacteristic
517C2×C47#235911yescharacteristic
518C2×C47#235911yescharacteristic
519C2×C47#236311yescharacteristic
520C2×C47#236311yescharacteristic
521C2×C47#237211yescharacteristic
522C2×C47#237211yescharacteristic
523C2×C47#237311yescharacteristic
524C2×C47#237311yescharacteristic
525D47—44no—
526C24×C4—471no—
527C22×C4⋊C4—471no—
528C22×C4⋊C4—471no—
529C22×C22⋊C4—471no—
530C22×C22⋊C4—471no—
531C22×C22⋊C4—471no—
532C22×C22⋊C4—471no—
533C22×C22⋊C4—471no—
534C22×C22⋊C4—471no—
535C22×C42—471no—
536C22×C42—471no—
537C22×C42—471no—
538C22×C42—471no—
539C22×C42—471no—
540C22×C42C2×D4711yescharacteristic
541C22×C42C2×D4711yescharacteristic
542C22×C42C2×D4711yescharacteristic
543#388—478no—
544#388—478no—
545C4×C22⋊C4—478no—
546C4×C22⋊C4—944no—
547#376—944no—
548C2×#95—471no—
549C2×#95—471no—
550C2×#95—471no—
551C2×#95—471no—
552C2×#95—471no—
553C2×#95—471no—
554C2×#95—471no—
555C2×#95—471no—
556C2×#95—471no—
557C2×#95—471no—
558C2×#95—471no—
559C2×#95—471no—
560C2×#95—471no—
561C2×#95—471no—
562C2×#95C2×D4711yescharacteristic
563C2×#95C2×D4711yescharacteristic
564C2×#95C2×D4711yescharacteristic
565C2×#95C2×D4711yescharacteristic
566C47#1381611yescharacteristic, complemented, Sylow
567C25—471no—
568C23×C4—471no—
569C23×C4—471no—
570C23×C4—471no—
571C23×C4—471no—
572C23×C4—471no—
573C23×C4—471no—
574C23×C4—471no—
575C23×C4—474no—
576C23×C4—942no—
577C23×C4—942no—
578C23×C4—942no—
579C23×C4—942no—
580C23×C4—1881no—
581C23×C4—1881no—
582C23×C4C22×D4711yescharacteristic
583C23×C4C22×D4711yescharacteristic
584C23×C4C22×D4711yescharacteristic
585C23×C4C22×D4711yescharacteristic
586C23×C4C22×D4711yescharacteristic
587C23×C4C22×D4711yescharacteristic
588C23×C4C22×D4711yescharacteristic
589C2×C4⋊C4—474no—
590C2×C4⋊C4—474no—
591C2×C4⋊C4—1881no—
592C2×C4⋊C4—1881no—
593C2×C4⋊C4—1881no—
594C2×C4⋊C4—1881no—
595C2×C22⋊C4—474no—
596C2×C22⋊C4—474no—
597C2×C22⋊C4—474no—
598C2×C22⋊C4—474no—
599C2×C22⋊C4—474no—
600C2×C22⋊C4—474no—
601C2×C22⋊C4—474no—
602C2×C22⋊C4—474no—
603C2×C22⋊C4—942no—
604C2×C22⋊C4—942no—
605C2×C22⋊C4—942no—
606C2×C22⋊C4—942no—
607C2×C22⋊C4—942no—
608C2×C22⋊C4—942no—
609C2×C22⋊C4—1881no—
610C2×C22⋊C4—1881no—
611C2×C22⋊C4—1881no—
612C2×C22⋊C4—1881no—
613C2×C42—22no—
614C2×C42—22no—
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618C2×C42—22no—
619C2×C42—41no—
620C2×C42—41no—
621C2×C42—474no—
622C2×C42—474no—
623C2×C42—474no—
624C2×C42—942no—
625C2×C42—942no—
626C2×C42—942no—
627C2×C42—942no—
628C2×C42—942no—
629C2×C42—942no—
630C2×C42—942no—
631C2×C42—942no—
632C2×C42—1881no—
633C2×C42—1881no—
634C2×C42—1881no—
635C2×C42—1881no—
636C2×C42C4×D4714yescomplemented
637#95—22no—
638#95—22no—
639#95—474no—
640#95—474no—
641#95—474no—
642#95—474no—
643#95—474no—
644#95—942no—
645#95—942no—
646#95—942no—
647#95—942no—
648#95—942no—
649#95—942no—
650#95—942no—
651#95—1881no—
652#95—1881no—
653#95C4×D4714yes—
654#95C4×D4714yescomplemented
655C24—472no—
656C24—472no—
657C24—472no—
658C24—941no—
659C24—941no—
660C24—941no—
661C24—941no—
662C24—941no—
663C24—941no—
664C24—941no—
665C24—941no—
666C24—941no—
667C24—941no—
668C24—941no—
669C24—941no—
670C24C23×D4711yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—472no—
706C22×C4—472no—
707C22×C4—472no—
708C22×C4—472no—
709C22×C4—472no—
710C22×C4—472no—
711C22×C4—472no—
712C22×C4—472no—
713C22×C4—472no—
714C22×C4—472no—
715C22×C4—472no—
716C22×C4—472no—
717C22×C4—472no—
718C22×C4—948no—
719C22×C4—941no—
720C22×C4—941no—
721C22×C4—941no—
722C22×C4—941no—
723C22×C4—941no—
724C22×C4—941no—
725C22×C4—941no—
726C22×C4—941no—
727C22×C4—941no—
728C22×C4—941no—
729C22×C4—941no—
730C22×C4—941no—
731C22×C4—941no—
732C22×C4—941no—
733C22×C4—941no—
734C22×C4—941no—
735C22×C4—941no—
736C22×C4—941no—
737C22×C4—941no—
738C22×C4—941no—
739C22×C4—941no—
740C22×C4—941no—
741C22×C4—941no—
742C22×C4—941no—
743C22×C4—941no—
744C22×C4—941no—
745C22×C4—941no—
746C22×C4—941no—
747C22×C4—941no—
748C22×C4—941no—
749C22×C4—941no—
750C22×C4—941no—
751C22×C4—941no—
752C22×C4—941no—
753C22×C4—941no—
754C22×C4—941no—
755C22×C4—948no—
756C22×C4—1884no—
757C22×C4—1884no—
758C22×C4—1884no—
759C22×C4—1884no—
760C22×C4—1884no—
761C22×C4C2×C4×D4712yes—
762C22×C4C2×C4×D4712yes—
763C22×C4C2×C4×D4712yes—
764C22×C4C2×C4×D4712yes—
765C22×C4C2×C4×D4712yes—
766C22×C4C2×C4×D4712yes—
767C22×C4C2×C4×D4712yes—
768C22×C4C2×C4×D4712yes—
769C22×C4C2×C4×D4712yes—
770C22×C4#1062535012yes—
771C22×C4#1062535012yes—
772C22×C4#1062535012yes—
773C22×C4#1062535012yes—
774C22×C4D4×D4712yes—
775C22×C4#1062535212yes—
776C4⋊C4—1884no—
777C4⋊C4—1884no—
778C22⋊C4—4716no—
779C22⋊C4—948no—
780C22⋊C4—948no—
781C22⋊C4—948no—
782C22⋊C4—1884no—
783C22⋊C4—1884no—
784C42—28no—
785C42—44no—
786C42—44no—
787C42—948no—
788C42—948no—
789C42—1884no—
790C42—1884no—
791C42—1884no—
792C23—474no—
793C23—942no—
794C23—942no—
795C23—942no—
796C23—942no—
797C23—942no—
798C23—942no—
799C23—942no—
800C23—942no—
801C23—942no—
802C23—942no—
803C23—942no—
804C23—942no—
805C23—942no—
806C23—942no—
807C23—942no—
808C23—942no—
809C23—942no—
810C23—942no—
811C23—1881no—
812C23—1881no—
813C23—1881no—
814C23—1881no—
815C23—1881no—
816C23—1881no—
817C23—1881no—
818C23—1881no—
819C23—1881no—
820C23—1881no—
821C23—1881no—
822C23—1881no—
823C23—1881no—
824C23—1881no—
825C23—1881no—
826C23—1881no—
827C23C22×C4×D4711yescharacteristic
828C23C22×C4×D4711yescharacteristic
829C23C22×C4×D4711yescharacteristic
830C23C2×D4×D4711yescharacteristic
831C23#41×D4711yescharacteristic
832C23#41×D4711yescharacteristic
833C23C2×#1062535211yescharacteristic
834C23C2×#1062535011yescharacteristic
835C23C2×#1062535011yescharacteristic
836C23C2×#1062535011yescharacteristic
837C23C2×#1062535011yescharacteristic
838C23#1309406911yescharacteristic
839C23#1309407011yescharacteristic
840C23#1309407011yescharacteristic
841C23#1309407211yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—474no—
888C2×C4—474no—
889C2×C4—474no—
890C2×C4—942no—
891C2×C4—942no—
892C2×C4—942no—
893C2×C4—942no—
894C2×C4—942no—
895C2×C4—942no—
896C2×C4—942no—
897C2×C4—942no—
898C2×C4—942no—
899C2×C4—942no—
900C2×C4—942no—
901C2×C4—942no—
902C2×C4—942no—
903C2×C4—942no—
904C2×C4—942no—
905C2×C4—942no—
906C2×C4—942no—
907C2×C4—942no—
908C2×C4—942no—
909C2×C4—942no—
910C2×C4—942no—
911C2×C4—942no—
912C2×C4—942no—
913C2×C4—942no—
914C2×C4—942no—
915C2×C4—942no—
916C2×C4—942no—
917C2×C4—942no—
918C2×C4—942no—
919C2×C4—942no—
920C2×C4—18816no—
921C2×C4—1881no—
922C2×C4—1881no—
923C2×C4—1881no—
924C2×C4—1881no—
925C2×C4—1881no—
926C2×C4—1881no—
927C2×C4—1881no—
928C2×C4—1881no—
929C2×C4—1881no—
930C2×C4—1881no—
931C2×C4—1881no—
932C2×C4—1881no—
933C2×C4—1881no—
934C2×C4—1881no—
935C2×C4—1881no—
936C2×C4—1881no—
937C2×C4C42×D4714yes—
938C2×C4#1309398114yes—
939C2×C4#1309398114yes—
940C2×C4(C22⋊D47)⋊C414yes—
941C22—944no—
942C22—944no—
943C22—944no—
944C22—1882no—
945C22—1882no—
946C22—1882no—
947C22—1882no—
948C22—1882no—
949C22—1882no—
950C22—1882no—
951C22—1882no—
952C22—1882no—
953C22—1882no—
954C22—1882no—
955C22—1882no—
956C22C2×C42×D4711yescharacteristic
957C22C2×#1309398111yescharacteristic
958C22C2×#1309398111yescharacteristic
959C22C4×D4×D4711yescharacteristic
960C22C4×D4×D4711yescharacteristic
961C22C2×(C22⋊D47)⋊C411yescharacteristic
962C22C4×#1062535211yescharacteristic
963C22C4×#1062535211yescharacteristic
964C22#1568959111yescharacteristic
965C22C4×#1062535011yescharacteristic
966C22C4×#1062535011yescharacteristic
967C22C4×#1062535011yescharacteristic
968C22C4×#1062535011yescharacteristic
969C22#1568959511yescharacteristic
970C22#1568959511yescharacteristic
971C22#1568959711yescharacteristic
972C22#1568960411yescharacteristic
973C22#1568960511yescharacteristic
974C22#1568960511yescharacteristic
975C22#1568976311yescharacteristic
976C22#1568976911yescharacteristic
977C22#1568977411yescharacteristic
978C22#1568979411yescharacteristic
979C22#1568979711yescharacteristic
980C22#1568979711yescharacteristic
981C22#1568979911yescharacteristic
982C22#1568980211yescharacteristic
983C22#1568980811yescharacteristic
984C22#1568981411yescharacteristic
985C22#1568981911yescharacteristic
986C22#1568982211yescharacteristic
987C22#1568983611yescharacteristic
988C22#1568983611yescharacteristic
989C22#1568983811yescharacteristic
990C22#1568984511yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—24no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—944no—
999C4—944no—
1000C4—944no—
1001C4—1882no—
1002C4—1882no—
1003C4—1882no—
1004C4—1882no—
1005C2—1884no—
1006C2C4×#1309398111yescharacteristic
1007C2C4×(C22⋊D47)⋊C411yescharacteristic
1008C2#2024574811yescharacteristic
1009C2#2024623111yescharacteristic
1010C2#2024626911yescharacteristic
1011C2#2024632211yescharacteristic
1012C2#2024633311yescharacteristic
1013C2#2024637611yescharacteristic
1014C2#2024638511yescharacteristic
1015C2#2024642411yescharacteristic
1016C2#2024642711yescharacteristic
1017C2#2024649611yescharacteristic
1018C2#2024649811yescharacteristic
1019C2#2024650411yescharacteristic
1020C2#2024651311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC4×#95×C47C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenterC4×#95D47
hypocenterC47#13816
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
5. C2×#15688969C2semidirect
8. #20241621C2semidirect
9. #20241619C2semidirect
10. Dic47⋊#95C2semidirect
11. #20241613C2semidirect
13. C4×C47⋊#95C2semidirect
14. #95×Dic47C2semidirect
15. C4×#95×C47C2semidirect
30. #15689014C4semidirect
31. #15689012C4semidirect
33. #15688970C4semidirect
75. C2×Dic47⋊C4C2×C4semidirect
76. C2×Dic47⋊C4C2×C4semidirect
109. C2×C4×Dic47C2×C4semidirect
120. C47⋊#95C2×C4semidirect
121. C47⋊#95C2×C4semidirect
122. C47⋊#95C2×C4semidirect
139. C2×C42×C47C2×C4semidirect
143. #95×C47C2×C4semidirect
273. (C2×D47)⋊C4C42semidirect
509. C4×#95D47semidirect
566. C47#13816semidirect
636. C2×C42C4×D47semidirect
654. #95C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156890142
C2×#156890122
C2×C4×(C2×D47)⋊C42
C2×#156889702
C2×#156889692
#202416262
#202416242
#202416212
#202416192
Dic47⋊#952
#202416132
(C2×D47)⋊#952
C4×C47⋊#952
#95×Dic472
C4×#95×C472
#1381647