Finite Group Databasebeta

← #26138898

Subgroups — #26138898

Order 12032.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689016C211yesmaximal, characteristic
2C2×C22⋊C4×Dic47C211yesmaximal, characteristic
3#20241647C211yesmaximal, characteristic, complemented
4#20241644C211yesmaximal, characteristic, complemented
5#20241631C211yesmaximal, characteristic
6#20241631C211yesmaximal, characteristic
7#20241621C211yesmaximal, characteristic, complemented
8#20241619C211yesmaximal, characteristic, complemented
9#20241617C211yesmaximal, characteristic, complemented
10Dic47⋊#95C211yesmaximal, characteristic, complemented
11#20241614C211yesmaximal, characteristic, complemented
12#20241610C211yesmaximal, characteristic
13#20241610C211yesmaximal, characteristic
14C4×C47⋊#95C211yesmaximal, characteristic, complemented
15C2×C47×#388C211yesmaximal, characteristic
16C24×Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2211yescharacteristic
20C22×C22⋊Dic47C2211yescharacteristic
21C22×C22⋊Dic47C2211yescharacteristic
22C22×C22⋊Dic47C2211yescharacteristic
23C22×C4×Dic47C2211yescharacteristic
24C22×C4×Dic47C2211yescharacteristic
25C22×C4×Dic47C2211yescharacteristic
26#15689016—24no—
27C22⋊C4×Dic47C418yescomplemented
28C2×C47⋊#95C2211yescharacteristic
29C2×C47⋊#95C2211yescharacteristic
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2211yescharacteristic
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
46C22×C4⋊C4×C47C2211yescharacteristic
47C22×C22⋊C4×C47C2211yescharacteristic
48C22×C22⋊C4×C47C2211yescharacteristic
49C22×C22⋊C4×C47C2211yescharacteristic
50C22×C42×C47C2211yescharacteristic
51C47×#388—24no—
52C2×#95×C47C2211yescharacteristic
53C2×#95×C47C2211yescharacteristic
54C23×Dic47—22no—
55C23×Dic47—22no—
56C23×Dic47—41no—
57C23×Dic47—41no—
58C23×Dic47—41no—
59C23×Dic47—41no—
60C23×Dic47C2×C414yes—
61C23×Dic47C2311yescharacteristic
62C23×Dic47C2311yescharacteristic
63C23×Dic47C2311yescharacteristic
64C23×Dic47C2311yescharacteristic
65C23×Dic47C2311yescharacteristic
66C23×Dic47C2311yescharacteristic
67C23×Dic47C2311yescharacteristic
68C23×Dic47C2311yescharacteristic
69C2×C4⋊Dic47—22no—
70C2×C4⋊Dic47—22no—
71C2×C4⋊Dic47—41no—
72C2×Dic47⋊C4—22no—
73C2×Dic47⋊C4—22no—
74C2×Dic47⋊C4—22no—
75C2×Dic47⋊C4—22no—
76C2×Dic47⋊C4—41no—
77C2×Dic47⋊C4—41no—
78C2×C22⋊Dic47—22no—
79C2×C22⋊Dic47—22no—
80C2×C22⋊Dic47—22no—
81C2×C22⋊Dic47—22no—
82C2×C22⋊Dic47—22no—
83C2×C22⋊Dic47—22no—
84C2×C22⋊Dic47—41no—
85C2×C22⋊Dic47—41no—
86C2×C22⋊Dic47C2×C414yes—
87C2×C4×Dic47—22no—
88C2×C4×Dic47—22no—
89C2×C4×Dic47—41no—
90C2×C4×Dic47—41no—
91C2×C4×Dic47—41no—
92C2×C4×Dic47—41no—
93C2×C4×Dic47—41no—
94C2×C4×Dic47C2×C414yes—
95C2×C4×Dic47C2×C414yes—
96C47⋊#95—22no—
97C47⋊#95—22no—
98C47⋊#95—22no—
99C47⋊#95—22no—
100C47⋊#95—22no—
101C47⋊#95—22no—
102C47⋊#95—22no—
103C47⋊#95—22no—
104C47⋊#95—22no—
105C47⋊#95—22no—
106C47⋊#95—41no—
107C47⋊#95—41no—
108C47⋊#95—41no—
109C47⋊#95—41no—
110C47⋊#95—41no—
111C47⋊#95—41no—
112C47⋊#95C2×C414yes—
113C47⋊#95C2×C414yes—
114C25×C47C2311yescharacteristic
115C23×C4×C47C2311yescharacteristic
116C23×C4×C47C2311yescharacteristic
117C23×C4×C47C2311yescharacteristic
118C23×C4×C47C2311yescharacteristic
119C23×C4×C47C2311yescharacteristic
120C23×C4×C47C2311yescharacteristic
121C2×C4⋊C4×C47—22no—
122C2×C4⋊C4×C47—22no—
123C2×C4⋊C4×C47—41no—
124C2×C22⋊C4×C47—22no—
125C2×C22⋊C4×C47—22no—
126C2×C22⋊C4×C47—22no—
127C2×C22⋊C4×C47—22no—
128C2×C22⋊C4×C47—41no—
129C2×C22⋊C4×C47—41no—
130C2×C22⋊C4×C47C2×C414yes—
131C2×C22⋊C4×C47D414yes—
132C2×C22⋊C4×C47Q814yes—
133C2×C42×C47—22no—
134C2×C42×C47—22no—
135C2×C42×C47—41no—
136#95×C47—22no—
137#95×C47—22no—
138C24×C47—21no—
139C24×C47—21no—
140C24×C47—21no—
141C24×C47—21no—
142C24×C47—21no—
143C24×C47—21no—
144C24×C47—21no—
145C24×C47—21no—
146C24×C47—21no—
147C24×C47—21no—
148C24×C47—21no—
149C24×C47—21no—
150C24×C47C22×C412yes—
151C24×C47C2×D412yes—
152C24×C47C2×Q812yes—
153C24×C47C2411yescharacteristic
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
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×C47C22×C412yes—
189C22×C4×C47C22×C412yes—
190C22×C4×C47C2×D412yes—
191C22×C4×C47C2×D412yes—
192C22×C4×C47C2×Q812yes—
193C22×C4×C47C2×Q812yes—
194C22×C4×C47#4112yes—
195C22×C4×C47#4112yes—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
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—28no—
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—44no—
244C22×Dic47—44no—
245C22×Dic47—44no—
246C22×Dic47—44no—
247C22×Dic47—44no—
248C22×Dic47—44no—
249C22×Dic47C22×C412yes—
250C22×Dic47C22×C412yes—
251C22×Dic47C22×C412yes—
252C22×Dic47C22×C412yes—
253C22×Dic47#4112yes—
254C22×Dic47#4112yes—
255C22×Dic47#4112yes—
256C22×Dic47#4112yes—
257C22×Dic47#4112yes—
258C22×Dic47#4112yes—
259C4⋊C4×C47—44no—
260C22⋊C4×C47—44no—
261C22⋊C4×C47—44no—
262C22⋊C4×C47C4⋊C4116yescomplemented
263C42×C47—44no—
264C22⋊Dic47—28no—
265C22⋊Dic47—44no—
266C22⋊Dic47—44no—
267C4⋊Dic47—44no—
268Dic47⋊C4—44no—
269Dic47⋊C4—44no—
270C4×Dic47—44no—
271C4×Dic47—44no—
272C4×Dic47—44no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47—22no—
281C23×C47—22no—
282C23×C47—22no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—22no—
287C23×C47—22no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—41no—
298C23×C47—41no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47C2×C4⋊C414yes—
308C23×C47C23×C411yescharacteristic
309C23×C47C22×D411yescharacteristic
310C23×C47C22×Q811yescharacteristic
311C23×C47C2×#4111yescharacteristic
312C23×C47C2×#4111yescharacteristic
313C23×C47C2×#4111yescharacteristic
314C23×C47C2×#4111yescharacteristic
315C23×C47C2×#4111yescharacteristic
316C23×C47C2×#4111yescharacteristic
317C23×C47C2×#4111yescharacteristic
318C23×C47C2×#4111yescharacteristic
319C23×C47H(5,𝔽2)11yescharacteristic
320C23×C47H(5,𝔽2)11yescharacteristic
321C23×C47H(5,𝔽2)11yescharacteristic
322C23×C47H(5,𝔽2)11yescharacteristic
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
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—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47—41no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
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×C47C2×C4⋊C414yes—
364C2×C4×C47C2×C4⋊C414yes—
365C2×Dic47—22no—
366C2×Dic47—22no—
367C2×Dic47—22no—
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—22no—
371C2×Dic47—22no—
372C2×Dic47—22no—
373C2×Dic47—22no—
374C2×Dic47—22no—
375C2×Dic47—22no—
376C2×Dic47—22no—
377C2×Dic47—22no—
378C2×Dic47—22no—
379C2×Dic47—22no—
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—416no—
390C2×Dic47—41no—
391C2×Dic47—41no—
392C2×Dic47—41no—
393C2×Dic47—41no—
394C2×Dic47—41no—
395C2×Dic47—41no—
396C2×Dic47—41no—
397C2×Dic47—41no—
398C2×Dic47—41no—
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—41no—
416C2×Dic47—41no—
417C2×Dic47—41no—
418C2×Dic47—41no—
419C2×Dic47—41no—
420C2×Dic47#11714yes—
421C2×Dic47#11714yes—
422#13948—471nomaximal, Sylow
423C22×C47—24no—
424C22×C47—24no—
425C22×C47—24no—
426C22×C47—42no—
427C22×C47—42no—
428C22×C47—42no—
429C22×C47—42no—
430C22×C47—42no—
431C22×C47—42no—
432C22×C47—42no—
433C22×C47—42no—
434C22×C47—42no—
435C22×C47—42no—
436C22×C47—42no—
437C22×C47—42no—
438C22×C47C22×C4⋊C411yescharacteristic
439C22×C47C2×#11711yescharacteristic
440C22×C47C2×#11711yescharacteristic
441C22×C47C4×#4111yescharacteristic
442C22×C47C4×#4111yescharacteristic
443C22×C47#51811yescharacteristic
444C22×C47#51811yescharacteristic
445C22×C47#52911yescharacteristic
446C22×C47#52911yescharacteristic
447C22×C47#52911yescharacteristic
448C22×C47#52911yescharacteristic
449C22×C47#53211yescharacteristic
450C22×C47#53211yescharacteristic
451C22×C47#53311yescharacteristic
452C22×C47#53311yescharacteristic
453C22×C47#53811yescharacteristic
454C22×C47#53811yescharacteristic
455C22×C47#53811yescharacteristic
456C22×C47#53811yescharacteristic
457C22×C47#54611yescharacteristic
458C22×C47#54611yescharacteristic
459C22×C47#54611yescharacteristic
460C22×C47#54611yescharacteristic
461C22×C47#55111yescharacteristic
462C22×C47#55111yescharacteristic
463C22×C47#55311yescharacteristic
464C22×C47#55311yescharacteristic
465C22×C47#55311yescharacteristic
466C22×C47#55311yescharacteristic
467C22×C47#55411yescharacteristic
468C22×C47#55411yescharacteristic
469C22×C47#55411yescharacteristic
470C22×C47#55411yescharacteristic
471C22×C47#55911yescharacteristic
472C22×C47#55911yescharacteristic
473C4×C47—24no—
474C4×C47—24no—
475C4×C47—42no—
476C4×C47—42no—
477C4×C47—81no—
478C4×C47—81no—
479Dic47—24no—
480Dic47—24no—
481Dic47—42no—
482Dic47—42no—
483Dic47—42no—
484Dic47—42no—
485Dic47—81no—
486Dic47—81no—
487C2×#388—471no—
488C2×#388D4711yescharacteristic
489C2×C4×C22⋊C4—471no—
490#1442—471no—
491#1442—471no—
492#1439—471no—
493#1439—471no—
494#1436—471no—
495#1436—471no—
496C4⋊#95—471no—
497C4⋊#95—471no—
498#1434—471no—
499C22⋊#95—471no—
500C22⋊#95—471no—
501C4×#95—471no—
502C2×C47—44no—
503C2×C47#228511yescharacteristic
504C2×C47#229811yescharacteristic
505C2×C47#231211yescharacteristic
506C2×C47#234911yescharacteristic
507C2×C47#234911yescharacteristic
508C2×C47#235311yescharacteristic
509C2×C47#235711yescharacteristic
510C2×C47#255711yescharacteristic
511C2×C47#255711yescharacteristic
512C2×C47#255911yescharacteristic
513C2×C47#255911yescharacteristic
514C2×C47#258711yescharacteristic
515C2×C47#258711yescharacteristic
516C2×C47#258911yescharacteristic
517C2×C47#258911yescharacteristic
518C24×C4—471no—
519C22×C4⋊C4—471no—
520C22×C4⋊C4—471no—
521C22×C4⋊C4—471no—
522C22×C4⋊C4C2×D4711yescharacteristic
523C22×C22⋊C4—471no—
524C22×C22⋊C4—471no—
525C22×C22⋊C4—471no—
526C22×C22⋊C4C2×D4711yescharacteristic
527C22×C22⋊C4C2×D4711yescharacteristic
528C22×C22⋊C4C2×D4711yescharacteristic
529C22×C42—471no—
530C22×C42—471no—
531C22×C42—471no—
532C22×C42C2×D4711yescharacteristic
533#388—24no—
534#388—944no—
535C4×C22⋊C4—478no—
536C2×#95—471no—
537C2×#95—471no—
538C2×#95—471no—
539C2×#95—471no—
540C2×#95—471no—
541C2×#95—471no—
542C2×#95—471no—
543C2×#95—471no—
544C2×#95—471no—
545C2×#95—471no—
546C2×#95—471no—
547C2×#95—471no—
548C2×#95—471no—
549C2×#95—471no—
550C2×#95—471no—
551C2×#95—471no—
552C2×#95—471no—
553C2×#95—471no—
554C2×#95C2×D4711yescharacteristic
555C2×#95C2×D4711yescharacteristic
556C47#1394811yescharacteristic, complemented, Sylow
557C25C22×D4711yescharacteristic
558C23×C4—471no—
559C23×C4—471no—
560C23×C4—471no—
561C23×C4—471no—
562C23×C4—471no—
563C23×C4—471no—
564C23×C4—474no—
565C23×C4—471no—
566C23×C4—471no—
567C23×C4—942no—
568C23×C4—942no—
569C23×C4—1881no—
570C23×C4—1881no—
571C23×C4—1881no—
572C23×C4—1881no—
573C23×C4C22×D4711yescharacteristic
574C23×C4C22×D4711yescharacteristic
575C23×C4C22×D4711yescharacteristic
576C23×C4C22×D4711yescharacteristic
577C23×C4C22×D4711yescharacteristic
578C23×C4C22×D4711yescharacteristic
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4—942no—
583C2×C4⋊C4—942no—
584C2×C4⋊C4—942no—
585C2×C4⋊C4—942no—
586C2×C4⋊C4—942no—
587C2×C4⋊C4—942no—
588C2×C4⋊C4—1881no—
589C2×C4⋊C4—1881no—
590C2×C4⋊C4—1881no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—41no—
596C2×C22⋊C4—41no—
597C2×C22⋊C4—474no—
598C2×C22⋊C4—942no—
599C2×C22⋊C4—942no—
600C2×C22⋊C4—942no—
601C2×C22⋊C4—942no—
602C2×C22⋊C4—942no—
603C2×C22⋊C4—942no—
604C2×C22⋊C4—1881no—
605C2×C22⋊C4—1881no—
606C2×C22⋊C4Dic9414yes—
607C2×C22⋊C4C4×D4714yes—
608C2×C22⋊C4C22⋊D4714yes—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—41no—
612C2×C42—474no—
613C2×C42—474no—
614C2×C42—942no—
615C2×C42—942no—
616C2×C42—1881no—
617C2×C42—1881no—
618C2×C42—1881no—
619C2×C42—1881no—
620C2×C42—1881no—
621#95—22no—
622#95—22no—
623#95—474no—
624#95—474no—
625#95—942no—
626#95—942no—
627#95—942no—
628#95—942no—
629#95—942no—
630#95—942no—
631#95—942no—
632#95—942no—
633#95—942no—
634#95—942no—
635#95—1881no—
636#95—1881no—
637#95—1881no—
638#95—1881no—
639#95—1881no—
640#95—1881no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C2×Dic9412yes—
654C24C2×C4×D4712yes—
655C24C2×C22⋊D4712yes—
656C24C23×D4711yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
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—472no—
692C22×C4—472no—
693C22×C4—472no—
694C22×C4—472no—
695C22×C4—472no—
696C22×C4—472no—
697C22×C4—472no—
698C22×C4—472no—
699C22×C4—472no—
700C22×C4—472no—
701C22×C4—948no—
702C22×C4—941no—
703C22×C4—941no—
704C22×C4—941no—
705C22×C4—941no—
706C22×C4—941no—
707C22×C4—941no—
708C22×C4—941no—
709C22×C4—941no—
710C22×C4—941no—
711C22×C4—941no—
712C22×C4—941no—
713C22×C4—941no—
714C22×C4—941no—
715C22×C4—941no—
716C22×C4—941no—
717C22×C4—941no—
718C22×C4—941no—
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—1884no—
749C22×C4—1884no—
750C22×C4—1884no—
751C22×C4—1884no—
752C22×C4—1884no—
753C22×C4—1884no—
754C22×C4C2×Dic9412yes—
755C22×C4C2×Dic9412yes—
756C22×C4C2×C4×D4712yes—
757C22×C4C2×C4×D4712yes—
758C22×C4#1062535212yes—
759C22×C4#1062535212yes—
760C22×C4C2×C22⋊D4712yes—
761C22×C4C2×C22⋊D4712yes—
762C4⋊C4—44no—
763C4⋊C4—1884no—
764C4⋊C4—1884no—
765C4⋊C4—1884no—
766C22⋊C4—44no—
767C22⋊C4—44no—
768C22⋊C4—948no—
769C22⋊C4—1884no—
770C22⋊C4—1884no—
771C22⋊C4Dic47⋊C4116yescomplemented
772C42—44no—
773C42—1884no—
774C42—1884no—
775C42—1884no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×Dic47⋊C414yes—
811C23C22×C4×D4711yescharacteristic
812C23C22×C22⋊D4711yescharacteristic
813C23C22×Dic9411yescharacteristic
814C23#41×D4711yescharacteristic
815C23#41×D4711yescharacteristic
816C23#41×D4711yescharacteristic
817C23#41×D4711yescharacteristic
818C23#41×D4711yescharacteristic
819C23#41×D4711yescharacteristic
820C23C2×#1062535211yescharacteristic
821C23C2×#1062535211yescharacteristic
822C23#1309406911yescharacteristic
823C23#1309406911yescharacteristic
824C23#1309407011yescharacteristic
825C23#1309407011yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—474no—
867C2×C4—474no—
868C2×C4—942no—
869C2×C4—942no—
870C2×C4—942no—
871C2×C4—942no—
872C2×C4—942no—
873C2×C4—942no—
874C2×C4—942no—
875C2×C4—942no—
876C2×C4—942no—
877C2×C4—942no—
878C2×C4—942no—
879C2×C4—942no—
880C2×C4—942no—
881C2×C4—942no—
882C2×C4—942no—
883C2×C4—942no—
884C2×C4—942no—
885C2×C4—942no—
886C2×C4—942no—
887C2×C4—942no—
888C2×C4—942no—
889C2×C4—942no—
890C2×C4—942no—
891C2×C4—942no—
892C2×C4—18816no—
893C2×C4—1881no—
894C2×C4—1881no—
895C2×C4—1881no—
896C2×C4—1881no—
897C2×C4—1881no—
898C2×C4—1881no—
899C2×C4—1881no—
900C2×C4—1881no—
901C2×C4—1881no—
902C2×C4—1881no—
903C2×C4—1881no—
904C2×C4—1881no—
905C2×C4—1881no—
906C2×C4—1881no—
907C2×C4—1881no—
908C2×C4—1881no—
909C2×C4—1881no—
910C2×C4—1881no—
911C2×C4—1881no—
912C2×C4—1881no—
913C2×C4—1881no—
914C2×C4—1881no—
915C2×C4—1881no—
916C2×C4—1881no—
917C2×C4—1881no—
918C2×C4—1881no—
919C2×C4—1881no—
920C2×C4—1881no—
921C2×C4—1881no—
922C2×C4—1881no—
923C2×C4C2×Dic47⋊C414yes—
924C2×C4C2×Dic47⋊C414yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×Dic47⋊C411yescharacteristic
941C22#117×D4711yescharacteristic
942C22#117×D4711yescharacteristic
943C22C4×#1062535211yescharacteristic
944C22C4×#1062535211yescharacteristic
945C22#1568959511yescharacteristic
946C22#1568959511yescharacteristic
947C22#1568965011yescharacteristic
948C22#1568965211yescharacteristic
949C22#1568965411yescharacteristic
950C22#1568965611yescharacteristic
951C22#1568966911yescharacteristic
952C22#1568966911yescharacteristic
953C22#1568967611yescharacteristic
954C22#1568967611yescharacteristic
955C22#1568970511yescharacteristic
956C22#1568970711yescharacteristic
957C22#1568970911yescharacteristic
958C22#1568971211yescharacteristic
959C22#1568976111yescharacteristic
960C22#1568976111yescharacteristic
961C22#1568976711yescharacteristic
962C22#1568976711yescharacteristic
963C22#1568979611yescharacteristic
964C22#1568980311yescharacteristic
965C22#1568981611yescharacteristic
966C22#1568982011yescharacteristic
967C22#1568982411yescharacteristic
968C22#1568982411yescharacteristic
969C22#1568983011yescharacteristic
970C22#1568983011yescharacteristic
971C22#1568983211yescharacteristic
972C22#1568983211yescharacteristic
973C22#1568985511yescharacteristic
974C22#1568985711yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—81no—
980C4—81no—
981C4—944no—
982C4—944no—
983C4—3761no—
984C4—3761no—
985C4—1882no—
986C4—1882no—
987C4—1882no—
988C4—1882no—
989C2—44no—
990C2#2024579111yescharacteristic
991C2#2024588211yescharacteristic
992C2#2024598211yescharacteristic
993C2#2024629311yescharacteristic
994C2#2024629311yescharacteristic
995C2#2024632311yescharacteristic
996C2#2024635811yescharacteristic
997C2#2024848311yescharacteristic
998C2#2024848511yescharacteristic
999C2#2024851311yescharacteristic
1000C2#2024851511yescharacteristic
1001C2#2024880511yescharacteristic
1002C2#2024880711yescharacteristic
1003C2#2024883511yescharacteristic
1004C2#2024883711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#388C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#388D47
hypocenterC47#13948
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. #20241647C2semidirect
4. #20241644C2semidirect
7. #20241621C2semidirect
8. #20241619C2semidirect
9. #20241617C2semidirect
10. Dic47⋊#95C2semidirect
11. #20241614C2semidirect
14. C4×C47⋊#95C2semidirect
27. C22⋊C4×Dic47C4semidirect
262. C22⋊C4×C47C4⋊C4semidirect
556. C47#13948semidirect
771. 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×C22⋊C4×Dic472
#202416472
#202416442
#202416312
#202416212
#202416192
#202416172
Dic47⋊#952
#202416142
#202416102
C4×C47⋊#952
C2×C47×#3882
#1394847