Finite Group Databasebeta

← #26138226

Subgroups — #26138226

Order 12032.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689016C211yesmaximal, characteristic
2C2×#15688992C211yesmaximal, characteristic, complemented
3C2×#15688981C211yesmaximal, characteristic
4C2×#15688981C211yesmaximal, characteristic
5C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×Dic47C211yesmaximal, characteristic
7#20241647C211yesmaximal, characteristic, complemented
8#20241644C211yesmaximal, characteristic, complemented
9#20241631C211yesmaximal, characteristic
10#20241631C211yesmaximal, characteristic
11#20241621C211yesmaximal, characteristic, complemented
12#20241619C211yesmaximal, characteristic, complemented
13Dic47⋊#95C211yesmaximal, characteristic, complemented
14Dic47⋊#95C211yesmaximal, characteristic, complemented
15C2×C47×#388C211yesmaximal, characteristic
16C24×Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2211yescharacteristic
20C22×Dic47⋊C4C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×Dic47⋊C4C2211yescharacteristic
24C22×C22⋊Dic47C2211yescharacteristic
25C22×C22⋊Dic47C2211yescharacteristic
26C22×C22⋊Dic47C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28C22×C4×Dic47C2211yescharacteristic
29C22×C4×Dic47C2211yescharacteristic
30#15689016—24no—
31#15688992—24no—
32#15688981—24no—
33#15688981—24no—
34C4×Dic47⋊C4—24no—
35C22⋊C4×Dic47C418yescomplemented
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
49C2×C47⋊#95C2211yescharacteristic
50C22×C4⋊C4×C47C2211yescharacteristic
51C22×C22⋊C4×C47C2211yescharacteristic
52C22×C22⋊C4×C47C2211yescharacteristic
53C22×C22⋊C4×C47C2211yescharacteristic
54C22×C42×C47C2211yescharacteristic
55C47×#388—24no—
56C2×#95×C47C2211yescharacteristic
57C2×#95×C47C2211yescharacteristic
58C23×Dic47—22no—
59C23×Dic47—22no—
60C23×Dic47—22no—
61C23×Dic47—22no—
62C23×Dic47—22no—
63C23×Dic47—22no—
64C23×Dic47C2×C414yes—
65C23×Dic47C2311yescharacteristic
66C23×Dic47C2311yescharacteristic
67C23×Dic47C2311yescharacteristic
68C23×Dic47C2311yescharacteristic
69C23×Dic47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C2×C4⋊Dic47—22no—
74C2×C4⋊Dic47—22no—
75C2×C4⋊Dic47—41no—
76C2×Dic47⋊C4—22no—
77C2×Dic47⋊C4—22no—
78C2×Dic47⋊C4—22no—
79C2×Dic47⋊C4—22no—
80C2×Dic47⋊C4—22no—
81C2×Dic47⋊C4—22no—
82C2×Dic47⋊C4—22no—
83C2×Dic47⋊C4—22no—
84C2×Dic47⋊C4—22no—
85C2×Dic47⋊C4—22no—
86C2×Dic47⋊C4—22no—
87C2×Dic47⋊C4—22no—
88C2×Dic47⋊C4—22no—
89C2×Dic47⋊C4—22no—
90C2×Dic47⋊C4—41no—
91C2×Dic47⋊C4—41no—
92C2×Dic47⋊C4D414yes—
93C2×Dic47⋊C4D414yes—
94C2×C22⋊Dic47—22no—
95C2×C22⋊Dic47—22no—
96C2×C22⋊Dic47—22no—
97C2×C22⋊Dic47—22no—
98C2×C22⋊Dic47—22no—
99C2×C22⋊Dic47—22no—
100C2×C22⋊Dic47—41no—
101C2×C22⋊Dic47—41no—
102C2×C22⋊Dic47C2×C414yes—
103C2×C4×Dic47—22no—
104C2×C4×Dic47—22no—
105C2×C4×Dic47—22no—
106C2×C4×Dic47—22no—
107C2×C4×Dic47—22no—
108C2×C4×Dic47—22no—
109C2×C4×Dic47—41no—
110C2×C4×Dic47C2×C414yes—
111C2×C4×Dic47C2×C414yes—
112C47⋊#95—22no—
113C47⋊#95—22no—
114C47⋊#95—22no—
115C47⋊#95—22no—
116C47⋊#95—22no—
117C47⋊#95—22no—
118C47⋊#95—22no—
119C47⋊#95—22no—
120C47⋊#95—22no—
121C47⋊#95—22no—
122C47⋊#95—41no—
123C47⋊#95—41no—
124C47⋊#95C2×C414yes—
125C47⋊#95C2×C414yes—
126C25×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C2×C4⋊C4×C47—22no—
134C2×C4⋊C4×C47—22no—
135C2×C4⋊C4×C47—41no—
136C2×C22⋊C4×C47—22no—
137C2×C22⋊C4×C47—22no—
138C2×C22⋊C4×C47—22no—
139C2×C22⋊C4×C47—22no—
140C2×C22⋊C4×C47—41no—
141C2×C22⋊C4×C47—41no—
142C2×C22⋊C4×C47C2×C414yes—
143C2×C22⋊C4×C47D414yes—
144C2×C22⋊C4×C47Q814yes—
145C2×C42×C47—22no—
146C2×C42×C47—22no—
147C2×C42×C47—41no—
148#95×C47—22no—
149#95×C47—22no—
150C24×C47—21no—
151C24×C47—21no—
152C24×C47—21no—
153C24×C47—21no—
154C24×C47—21no—
155C24×C47—21no—
156C24×C47—21no—
157C24×C47—21no—
158C24×C47—21no—
159C24×C47—21no—
160C24×C47—21no—
161C24×C47—21no—
162C24×C47C22×C412yes—
163C24×C47C2×D412yes—
164C24×C47C2×Q812yes—
165C24×C47C2411yescharacteristic
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×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47C22×C412yes—
201C22×C4×C47C22×C412yes—
202C22×C4×C47C2×D412yes—
203C22×C4×C47C2×D412yes—
204C22×C4×C47C2×D412yes—
205C22×C4×C47C2×D412yes—
206C22×C4×C47C2×Q812yes—
207C22×C4×C47C2×Q812yes—
208C22×Dic47—21no—
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—28no—
237C22×Dic47—28no—
238C22×Dic47—28no—
239C22×Dic47—21no—
240C22×Dic47—21no—
241C22×Dic47—21no—
242C22×Dic47—21no—
243C22×Dic47—21no—
244C22×Dic47—21no—
245C22×Dic47—21no—
246C22×Dic47—21no—
247C22×Dic47—21no—
248C22×Dic47—21no—
249C22×Dic47—21no—
250C22×Dic47—21no—
251C22×Dic47—21no—
252C22×Dic47—21no—
253C22×Dic47—44no—
254C22×Dic47—44no—
255C22×Dic47—44no—
256C22×Dic47—44no—
257C22×Dic47C22×C412yes—
258C22×Dic47C22×C412yes—
259C22×Dic47C22×C412yes—
260C22×Dic47C22×C412yes—
261C22×Dic47C2×D412yes—
262C22×Dic47C2×D412yes—
263C22×Dic47C2×D412yes—
264C22×Dic47C2×D412yes—
265C22×Dic47#4112yes—
266C22×Dic47#4112yes—
267C22×Dic47#4112yes—
268C22×Dic47#4112yes—
269C22×Dic47#4112yes—
270C22×Dic47#4112yes—
271C4⋊C4×C47—44no—
272C22⋊C4×C47—44no—
273C22⋊C4×C47—44no—
274C22⋊C4×C47C4⋊C4116yescomplemented
275C42×C47—44no—
276C22⋊Dic47—28no—
277C22⋊Dic47—44no—
278C22⋊Dic47—44no—
279C4⋊Dic47—44no—
280Dic47⋊C4—28no—
281Dic47⋊C4—28no—
282Dic47⋊C4—44no—
283Dic47⋊C4—44no—
284Dic47⋊C4—44no—
285Dic47⋊C4—44no—
286C4×Dic47—28no—
287C4×Dic47—28no—
288C4×Dic47—44no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—22no—
300C23×C47—22no—
301C23×C47—22no—
302C23×C47—22no—
303C23×C47—22no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—41no—
308C23×C47—41no—
309C23×C47—41no—
310C23×C47—41no—
311C23×C47—41no—
312C23×C47—41no—
313C23×C47—41no—
314C23×C47—41no—
315C23×C47—41no—
316C23×C47—41no—
317C23×C47—41no—
318C23×C47—41no—
319C23×C47—41no—
320C23×C47—41no—
321C23×C47—41no—
322C23×C47—41no—
323C23×C47C2×C4⋊C414yes—
324C23×C47C23×C411yescharacteristic
325C23×C47C22×D411yescharacteristic
326C23×C47C22×D411yescharacteristic
327C23×C47C22×D411yescharacteristic
328C23×C47C22×Q811yescharacteristic
329C23×C47C2×#4111yescharacteristic
330C23×C47C2×#4111yescharacteristic
331C23×C47C2×#4111yescharacteristic
332C23×C47C2×#4111yescharacteristic
333C23×C47C2×#4111yescharacteristic
334C23×C47C2×#4111yescharacteristic
335C23×C47H(5,𝔽2)11yescharacteristic
336C23×C47H(5,𝔽2)11yescharacteristic
337C23×C472−1+411yescharacteristic
338C23×C472−1+411yescharacteristic
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—41no—
358C2×C4×C47—41no—
359C2×C4×C47—41no—
360C2×C4×C47—41no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
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×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—41no—
379C2×C4×C47C2×C4⋊C414yes—
380C2×C4×C47C2×C4⋊C414yes—
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—41no—
400C2×Dic47—41no—
401C2×Dic47—41no—
402C2×Dic47—41no—
403C2×Dic47—41no—
404C2×Dic47—41no—
405C2×Dic47—41no—
406C2×Dic47—41no—
407C2×Dic47—41no—
408C2×Dic47—41no—
409C2×Dic47—41no—
410C2×Dic47—41no—
411C2×Dic47—41no—
412C2×Dic47—41no—
413C2×Dic47—41no—
414C2×Dic47—41no—
415C2×Dic47—416no—
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×Dic47—41no—
427C2×Dic47—41no—
428C2×Dic47—41no—
429C2×Dic47—41no—
430C2×Dic47#11714yes—
431C2×Dic47#11714yes—
432C2×Dic47C4×D414yes—
433C2×Dic47C4×D414yes—
434C2×Dic47#12114yes—
435C2×Dic47#12314yes—
436C2×Dic47#12414yes—
437C2×Dic47#12614yes—
438#13876—471nomaximal, Sylow
439C22×C47—24no—
440C22×C47—24no—
441C22×C47—24no—
442C22×C47—42no—
443C22×C47—42no—
444C22×C47—42no—
445C22×C47—42no—
446C22×C47—42no—
447C22×C47—42no—
448C22×C47—42no—
449C22×C47—42no—
450C22×C47—42no—
451C22×C47—42no—
452C22×C47—42no—
453C22×C47—42no—
454C22×C47C22×C4⋊C411yescharacteristic
455C22×C47C2×#11711yescharacteristic
456C22×C47C2×#11711yescharacteristic
457C22×C47C2×C4×D411yescharacteristic
458C22×C47C2×C4×D411yescharacteristic
459C22×C47#52011yescharacteristic
460C22×C47#52011yescharacteristic
461C22×C47C2×#12111yescharacteristic
462C22×C47C2×#12311yescharacteristic
463C22×C47C2×#12411yescharacteristic
464C22×C47C2×#12611yescharacteristic
465C22×C47#53211yescharacteristic
466C22×C47#53211yescharacteristic
467C22×C47#53311yescharacteristic
468C22×C47#53311yescharacteristic
469C22×C47#54011yescharacteristic
470C22×C47#54111yescharacteristic
471C22×C47#54211yescharacteristic
472C22×C47#54211yescharacteristic
473C22×C47D4211yescharacteristic
474C22×C47D4211yescharacteristic
475C22×C47#54611yescharacteristic
476C22×C47#54711yescharacteristic
477C22×C47#54711yescharacteristic
478C22×C47#54711yescharacteristic
479C22×C47#54811yescharacteristic
480C22×C47D4×Q811yescharacteristic
481C22×C47D4×Q811yescharacteristic
482C22×C47#55011yescharacteristic
483C22×C47#55211yescharacteristic
484C22×C47#55311yescharacteristic
485C22×C47#55411yescharacteristic
486C22×C47#55411yescharacteristic
487C22×C47#55511yescharacteristic
488C22×C47#55611yescharacteristic
489C4×C47—24no—
490C4×C47—24no—
491C4×C47—42no—
492C4×C47—42no—
493C4×C47—81no—
494C4×C47—81no—
495Dic47—24no—
496Dic47—42no—
497Dic47—42no—
498Dic47—42no—
499Dic47—42no—
500Dic47—81no—
501Dic47—81no—
502Dic47#38818yescomplemented
503C2×#388—471no—
504C2×#388D4711yescharacteristic
505C2×#384—471no—
506C2×#380—471no—
507C2×#380—471no—
508C2×C4×C4⋊C4—471no—
509C2×C4×C22⋊C4—471no—
510#1442—471no—
511#1442—471no—
512#1439—471no—
513#1439—471no—
514#1436—471no—
515#1436—471no—
516C4⋊#95—471no—
517C4⋊#95—471no—
518C2×C47—44no—
519C2×C47#228511yescharacteristic
520C2×C47C2×#38811yescharacteristic
521C2×C47#231411yescharacteristic
522C2×C47D4×C4⋊C411yescharacteristic
523C2×C47D4×C4⋊C411yescharacteristic
524C2×C47#235211yescharacteristic
525C2×C47#235411yescharacteristic
526C2×C47#242211yescharacteristic
527C2×C47#242311yescharacteristic
528C2×C47#242811yescharacteristic
529C2×C47#242911yescharacteristic
530C2×C47#249111yescharacteristic
531C2×C47#249211yescharacteristic
532C2×C47#249611yescharacteristic
533C2×C47#249711yescharacteristic
534C24×C4—471no—
535C22×C4⋊C4—471no—
536C22×C4⋊C4—471no—
537C22×C4⋊C4—471no—
538C22×C4⋊C4—471no—
539C22×C4⋊C4—471no—
540C22×C4⋊C4—471no—
541C22×C4⋊C4—471no—
542C22×C4⋊C4C2×D4711yescharacteristic
543C22×C22⋊C4—471no—
544C22×C22⋊C4—471no—
545C22×C22⋊C4—471no—
546C22×C22⋊C4C2×D4711yescharacteristic
547C22×C22⋊C4C2×D4711yescharacteristic
548C22×C22⋊C4C2×D4711yescharacteristic
549C22×C42—471no—
550C22×C42—471no—
551C22×C42—471no—
552C22×C42C2×D4711yescharacteristic
553#388—24no—
554#388—944no—
555#384—944no—
556#380—944no—
557#380—944no—
558C4×C4⋊C4—944no—
559C4×C22⋊C4—478no—
560C2×#95—471no—
561C2×#95—471no—
562C2×#95—471no—
563C2×#95—471no—
564C2×#95—471no—
565C2×#95—471no—
566C2×#95—471no—
567C2×#95—471no—
568C2×#95—471no—
569C2×#95—471no—
570C2×#95—471no—
571C2×#95—471no—
572C2×#95—471no—
573C2×#95—471no—
574C2×#95C2×D4711yescharacteristic
575C2×#95C2×D4711yescharacteristic
576C47#1387611yescharacteristic, complemented, Sylow
577C25C22×D4711yescharacteristic
578C23×C4—471no—
579C23×C4—471no—
580C23×C4—474no—
581C23×C4—471no—
582C23×C4—471no—
583C23×C4—471no—
584C23×C4—471no—
585C23×C4—471no—
586C23×C4—471no—
587C23×C4—942no—
588C23×C4—942no—
589C23×C4—942no—
590C23×C4—942no—
591C23×C4—942no—
592C23×C4—942no—
593C23×C4C22×D4711yescharacteristic
594C23×C4C22×D4711yescharacteristic
595C23×C4C22×D4711yescharacteristic
596C23×C4C22×D4711yescharacteristic
597C23×C4C22×D4711yescharacteristic
598C23×C4C22×D4711yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—474no—
603C2×C4⋊C4—474no—
604C2×C4⋊C4—942no—
605C2×C4⋊C4—942no—
606C2×C4⋊C4—942no—
607C2×C4⋊C4—942no—
608C2×C4⋊C4—942no—
609C2×C4⋊C4—942no—
610C2×C4⋊C4—942no—
611C2×C4⋊C4—942no—
612C2×C4⋊C4—942no—
613C2×C4⋊C4—942no—
614C2×C4⋊C4—942no—
615C2×C4⋊C4—942no—
616C2×C4⋊C4—942no—
617C2×C4⋊C4—942no—
618C2×C4⋊C4—942no—
619C2×C4⋊C4—942no—
620C2×C4⋊C4—1881no—
621C2×C4⋊C4—1881no—
622C2×C4⋊C4—1881no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—41no—
628C2×C22⋊C4—41no—
629C2×C22⋊C4—474no—
630C2×C22⋊C4—942no—
631C2×C22⋊C4—942no—
632C2×C22⋊C4—942no—
633C2×C22⋊C4—942no—
634C2×C22⋊C4—942no—
635C2×C22⋊C4—942no—
636C2×C22⋊C4—1881no—
637C2×C22⋊C4—1881no—
638C2×C22⋊C4Dic9414yes—
639C2×C22⋊C4C4×D4714yes—
640C2×C22⋊C4C22⋊D4714yes—
641C2×C42—22no—
642C2×C42—22no—
643C2×C42—41no—
644C2×C42—474no—
645C2×C42—474no—
646C2×C42—942no—
647C2×C42—942no—
648C2×C42—942no—
649C2×C42—942no—
650C2×C42—942no—
651C2×C42—942no—
652C2×C42—1881no—
653#95—22no—
654#95—22no—
655#95—474no—
656#95—474no—
657#95—942no—
658#95—942no—
659#95—942no—
660#95—942no—
661#95—942no—
662#95—942no—
663#95—942no—
664#95—942no—
665#95—942no—
666#95—942no—
667#95—1881no—
668#95—1881no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C2×Dic9412yes—
682C24C2×C4×D4712yes—
683C24C2×C22⋊D4712yes—
684C24C23×D4711yescharacteristic
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—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—472no—
720C22×C4—472no—
721C22×C4—472no—
722C22×C4—472no—
723C22×C4—472no—
724C22×C4—472no—
725C22×C4—472no—
726C22×C4—472no—
727C22×C4—472no—
728C22×C4—472no—
729C22×C4—472no—
730C22×C4—472no—
731C22×C4—472no—
732C22×C4—472no—
733C22×C4—948no—
734C22×C4—948no—
735C22×C4—948no—
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—941no—
756C22×C4—941no—
757C22×C4—941no—
758C22×C4—941no—
759C22×C4—941no—
760C22×C4—941no—
761C22×C4—941no—
762C22×C4—941no—
763C22×C4—941no—
764C22×C4—941no—
765C22×C4—941no—
766C22×C4—941no—
767C22×C4—941no—
768C22×C4—941no—
769C22×C4—941no—
770C22×C4—941no—
771C22×C4—941no—
772C22×C4—941no—
773C22×C4—941no—
774C22×C4—941no—
775C22×C4—941no—
776C22×C4—941no—
777C22×C4—941no—
778C22×C4—1884no—
779C22×C4—1884no—
780C22×C4—1884no—
781C22×C4—1884no—
782C22×C4C2×Dic9412yes—
783C22×C4C2×Dic9412yes—
784C22×C4C2×C4×D4712yes—
785C22×C4C2×C4×D4712yes—
786C22×C4D4×D4712yes—
787C22×C4D4×D4712yes—
788C22×C4C2×C22⋊D4712yes—
789C22×C4C2×C22⋊D4712yes—
790C4⋊C4—44no—
791C4⋊C4—948no—
792C4⋊C4—948no—
793C4⋊C4—1884no—
794C4⋊C4—1884no—
795C4⋊C4—1884no—
796C4⋊C4—1884no—
797C4⋊C4—1884no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C22⋊C4—948no—
801C22⋊C4—1884no—
802C22⋊C4—1884no—
803C22⋊C4Dic47⋊C4116yescomplemented
804C42—44no—
805C42—948no—
806C42—948no—
807C42—1884no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×Dic47⋊C414yes—
843C23C22×C4×D4711yescharacteristic
844C23C2×D4×D4711yescharacteristic
845C23C2×D4×D4711yescharacteristic
846C23C22×C22⋊D4711yescharacteristic
847C23C22×Dic9411yescharacteristic
848C23#41×D4711yescharacteristic
849C23#41×D4711yescharacteristic
850C23#41×D4711yescharacteristic
851C23#41×D4711yescharacteristic
852C23#41×D4711yescharacteristic
853C23#41×D4711yescharacteristic
854C23#1309406911yescharacteristic
855C23#1309406911yescharacteristic
856C23#1309407111yescharacteristic
857C23#1309407111yescharacteristic
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—22no—
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—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—474no—
899C2×C4—474no—
900C2×C4—474no—
901C2×C4—474no—
902C2×C4—474no—
903C2×C4—474no—
904C2×C4—474no—
905C2×C4—474no—
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—942no—
921C2×C4—942no—
922C2×C4—942no—
923C2×C4—942no—
924C2×C4—18816no—
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×C4—1881no—
938C2×C4—1881no—
939C2×C4—1881no—
940C2×C4—1881no—
941C2×C4—1881no—
942C2×C4—1881no—
943C2×C4—1881no—
944C2×C4—1881no—
945C2×C4—1881no—
946C2×C4—1881no—
947C2×C4—1881no—
948C2×C4—1881no—
949C2×C4—1881no—
950C2×C4—1881no—
951C2×C4—1881no—
952C2×C4—1881no—
953C2×C4—1881no—
954C2×C4—1881no—
955C2×C4C2×Dic47⋊C414yes—
956C2×C4C2×Dic47⋊C414yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×Dic47⋊C411yescharacteristic
973C22#117×D4711yescharacteristic
974C22#117×D4711yescharacteristic
975C22C4×D4×D4711yescharacteristic
976C22C4×D4×D4711yescharacteristic
977C22#1568960211yescharacteristic
978C22#1568960211yescharacteristic
979C22#121×D4711yescharacteristic
980C22#123×D4711yescharacteristic
981C22#124×D4711yescharacteristic
982C22#126×D4711yescharacteristic
983C22#1568966911yescharacteristic
984C22#1568966911yescharacteristic
985C22#1568967611yescharacteristic
986C22#1568967611yescharacteristic
987C22#1568972311yescharacteristic
988C22#1568973011yescharacteristic
989C22#1568973711yescharacteristic
990C22#1568974111yescharacteristic
991C22D4×C22⋊D4711yescharacteristic
992C22D4×C22⋊D4711yescharacteristic
993C22#1568976211yescharacteristic
994C22#1568977111yescharacteristic
995C22#1568977211yescharacteristic
996C22#1568977211yescharacteristic
997C22#1568978111yescharacteristic
998C22D4×Dic9411yescharacteristic
999C22D4×Dic9411yescharacteristic
1000C22#1568979111yescharacteristic
1001C22#1568980911yescharacteristic
1002C22#1568981811yescharacteristic
1003C22#1568983211yescharacteristic
1004C22#1568983211yescharacteristic
1005C22#1568983511yescharacteristic
1006C22#1568984011yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—81no—
1012C4—81no—
1013C4—478no—
1014C4—944no—
1015C4—3761no—
1016C4—3761no—
1017C4—1882no—
1018C4—1882no—
1019C4—1882no—
1020C4—1882no—
1021C2—44no—
1022C2#2024579111yescharacteristic
1023C2#388×D4711yescharacteristic
1024C2#2024599211yescharacteristic
1025C2D4×Dic47⋊C411yescharacteristic
1026C2D4×Dic47⋊C411yescharacteristic
1027C2#2024631611yescharacteristic
1028C2#2024633411yescharacteristic
1029C2#2024689911yescharacteristic
1030C2#2024691011yescharacteristic
1031C2#2024697311yescharacteristic
1032C2#2024698411yescharacteristic
1033C2#2024774811yescharacteristic
1034C2#2024775911yescharacteristic
1035C2#2024780711yescharacteristic
1036C2#2024781811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#388C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#388D47
hypocenterC47#13876
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#15688992C2semidirect
5. C2×C4×Dic47⋊C4C2semidirect
7. #20241647C2semidirect
8. #20241644C2semidirect
11. #20241621C2semidirect
12. #20241619C2semidirect
13. Dic47⋊#95C2semidirect
14. Dic47⋊#95C2semidirect
35. C22⋊C4×Dic47C4semidirect
274. C22⋊C4×C47C4⋊C4semidirect
502. Dic47#388semidirect
576. C47#13876semidirect
803. C22⋊C4Dic47⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#156890162
C2×#156889922
C2×#156889812
C2×C4×Dic47⋊C42
C2×C22⋊C4×Dic472
#202416472
#202416442
#202416312
#202416212
#202416192
Dic47⋊#952
C2×C47×#3882
#1387647