Finite Group Databasebeta

← #26137787

Subgroups — #26137787

Order 12032.

2298 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688996C211yesmaximal, characteristic
2C2×#15688995C211yesmaximal, characteristic
3C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic47C211yesmaximal, characteristic
5C2×C22⋊C4×Dic47C211yesmaximal, characteristic
6C22×C47⋊#95C211yesmaximal, characteristic
7#20241621C211yesmaximal, characteristic, complemented
8#20241621C211yesmaximal, characteristic, complemented
9#20241619C211yesmaximal, characteristic, complemented
10#20241619C211yesmaximal, characteristic, complemented
11Dic47⋊#95C211yesmaximal, characteristic, complemented
12#20241614C211yesmaximal, characteristic, complemented
13#20241610C211yesmaximal, characteristic
14C4×C47⋊#95C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C47C211yesmaximal, characteristic
16C24×Dic47C2211yescharacteristic
17C24×Dic47C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2211yescharacteristic
20C22×Dic47⋊C4C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×C22⋊Dic47C2211yescharacteristic
23C22×C22⋊Dic47C2211yescharacteristic
24C22×C4×Dic47C2211yescharacteristic
25C22×C4×Dic47C2211yescharacteristic
26C22×C4×Dic47C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28#15688996C418yescomplemented
29#15688995C418yescomplemented
30C4×Dic47⋊C4—24no—
31C22⋊C4×Dic47—24no—
32C22⋊C4×Dic47C418yescomplemented
33C2×C47⋊#95—24no—
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
46C2×C47⋊#95C2211yescharacteristic
47C2×C47⋊#95C2211yescharacteristic
48C2×C47⋊#95C2211yescharacteristic
49C2×C47⋊#95C2211yescharacteristic
50C24×C4×C47C2211yescharacteristic
51C22×C22⋊C4×C47C2211yescharacteristic
52C22×C22⋊C4×C47C2211yescharacteristic
53C22×C42×C47C2211yescharacteristic
54C22×C42×C47C2211yescharacteristic
55C4×C22⋊C4×C47—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×Dic47—22no—
65C23×Dic47—22no—
66C23×Dic47—41no—
67C23×Dic47—41no—
68C23×Dic47—41no—
69C23×Dic47—41no—
70C23×Dic47C2×C414yes—
71C23×Dic47C2×C414yes—
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C2×Dic47⋊C4—22no—
81C2×Dic47⋊C4—22no—
82C2×Dic47⋊C4—22no—
83C2×Dic47⋊C4—22no—
84C2×Dic47⋊C4—41no—
85C2×Dic47⋊C4—41no—
86C2×Dic47⋊C4—41no—
87C2×Dic47⋊C4—41no—
88C2×Dic47⋊C4C2×C414yescomplemented
89C2×Dic47⋊C4C2×C414yescomplemented
90C2×Dic47⋊C4C2×C414yescomplemented
91C2×Dic47⋊C4C2×C414yescomplemented
92C2×C22⋊Dic47—22no—
93C2×C22⋊Dic47—22no—
94C2×C22⋊Dic47C2×C414yes—
95C2×C22⋊Dic47C2×C414yes—
96C2×C22⋊Dic47C2×C414yes—
97C2×C22⋊Dic47C2×C414yes—
98C2×C4×Dic47—22no—
99C2×C4×Dic47—22no—
100C2×C4×Dic47—22no—
101C2×C4×Dic47—22no—
102C2×C4×Dic47—22no—
103C2×C4×Dic47—22no—
104C2×C4×Dic47—41no—
105C2×C4×Dic47—41no—
106C2×C4×Dic47—41no—
107C2×C4×Dic47—41no—
108C2×C4×Dic47C2×C414yescomplemented
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×C414yescomplemented
120C47⋊#95C2×C414yescomplemented
121C47⋊#95C2×C414yescomplemented
122C47⋊#95C2×C414yescomplemented
123C47⋊#95C2×C414yescomplemented
124C47⋊#95C2×C414yescomplemented
125C47⋊#95D414yes—
126C25×C47C2311yescharacteristic
127C23×C4×C47—22no—
128C23×C4×C47—22no—
129C23×C4×C47—22no—
130C23×C4×C47—22no—
131C23×C4×C47—41no—
132C23×C4×C47—41no—
133C23×C4×C47C2×C414yes—
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2311yescharacteristic
139C23×C4×C47C2311yescharacteristic
140C2×C22⋊C4×C47—22no—
141C2×C22⋊C4×C47—22no—
142C2×C22⋊C4×C47C2×C414yes—
143C2×C22⋊C4×C47C2×C414yes—
144C2×C22⋊C4×C47D414yes—
145C2×C22⋊C4×C47Q814yes—
146C2×C42×C47—22no—
147C2×C42×C47—22no—
148C2×C42×C47—22no—
149C2×C42×C47—22no—
150C2×C42×C47—41no—
151C2×C42×C47—41no—
152#95×C47—22no—
153#95×C47—22no—
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×C47C22×C412yes—
164C24×C47C22×C412yes—
165C24×C47C2×D412yes—
166C24×C47C2×Q812yes—
167C24×C47#4112yes—
168C24×C47#4112yes—
169C24×C47C2411yescharacteristic
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—28no—
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×C47—21no—
201C22×C4×C47—28no—
202C22×C4×C47—44no—
203C22×C4×C47—44no—
204C22×C4×C47—44no—
205C22×C4×C47—44no—
206C22×C4×C47—44no—
207C22×C4×C47C22×C412yes—
208C22×C4×C47C22×C412yes—
209C22×C4×C47C22×C412yes—
210C22×C4×C47C22×C412yes—
211C22×C4×C47C22×C412yes—
212C22×C4×C47C22×C412yes—
213C22×C4×C47C2×D412yes—
214C22×C4×C47C2×D412yes—
215C22×C4×C47C2×D412yes—
216C22×C4×C47C2×Q812yes—
217C22×C4×C47C2×Q812yes—
218C22×C4×C47#4112yes—
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—28no—
236C22×Dic47—28no—
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×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—21no—
254C22×Dic47—21no—
255C22×Dic47—21no—
256C22×Dic47—21no—
257C22×Dic47—21no—
258C22×Dic47—21no—
259C22×Dic47—21no—
260C22×Dic47—21no—
261C22×Dic47—28no—
262C22×Dic47—28no—
263C22×Dic47—44no—
264C22×Dic47—44no—
265C22×Dic47—44no—
266C22×Dic47—44no—
267C22×Dic47—44no—
268C22×Dic47—44no—
269C22×Dic47—44no—
270C22×Dic47—44no—
271C22×Dic47—44no—
272C22×Dic47—44no—
273C22×Dic47C22×C412yes—
274C22×Dic47C22×C412yes—
275C22×Dic47C22×C412yes—
276C22×Dic47C22×C412yes—
277C22×Dic47C22×C412yes—
278C22×Dic47C22×C412yes—
279C22×Dic47C22×C412yes—
280C22×Dic47C22×C412yes—
281C22×Dic47C22×C412yes—
282C22×Dic47C22×C412yes—
283C22×Dic47C22×C412yes—
284C22×Dic47C22×C412yes—
285C22×Dic47C2×D412yes—
286C22×Dic47C2×D412yes—
287C22×Dic47#4112yes—
288C22×Dic47#4112yes—
289C22⋊C4×C47—28no—
290C22⋊C4×C47C4⋊C4116yescomplemented
291C42×C47—44no—
292C42×C47—44no—
293C22⋊Dic47—28no—
294C22⋊Dic47C42116yescomplemented
295Dic47⋊C4—28no—
296Dic47⋊C4—28no—
297Dic47⋊C4—44no—
298Dic47⋊C4—44no—
299C4×Dic47—28no—
300C4×Dic47—44no—
301C4×Dic47—44no—
302C4×Dic47—44no—
303C23×C47—22no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47—22no—
311C23×C47—22no—
312C23×C47—22no—
313C23×C47—22no—
314C23×C47—22no—
315C23×C47—22no—
316C23×C47—22no—
317C23×C47—22no—
318C23×C47—22no—
319C23×C47—22no—
320C23×C47—22no—
321C23×C47—22no—
322C23×C47—22no—
323C23×C47—22no—
324C23×C47—22no—
325C23×C47—22no—
326C23×C47—22no—
327C23×C47—22no—
328C23×C47—22no—
329C23×C47—22no—
330C23×C47—22no—
331C23×C47C2×C4214yes—
332C23×C47C2×C4⋊C414yes—
333C23×C47#11714yes—
334C23×C47C4×D414yes—
335C23×C47C4×D414yes—
336C23×C47C4×Q814yes—
337C23×C47C4×Q814yes—
338C23×C47C23×C411yescharacteristic
339C23×C47C23×C411yescharacteristic
340C23×C47C23×C411yescharacteristic
341C23×C47C22×D411yescharacteristic
342C23×C47C22×D411yescharacteristic
343C23×C47C22×Q811yescharacteristic
344C23×C47C2×#4111yescharacteristic
345C23×C47C2×#4111yescharacteristic
346C23×C47C2×#4111yescharacteristic
347C23×C47C2×#4111yescharacteristic
348C23×C47C2×#4111yescharacteristic
349C23×C47H(5,𝔽2)11yescharacteristic
350C23×C47H(5,𝔽2)11yescharacteristic
351C23×C47H(5,𝔽2)11yescharacteristic
352C23×C472−1+411yescharacteristic
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—22no—
365C2×C4×C47—22no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—22no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—22no—
376C2×C4×C47—22no—
377C2×C4×C47—22no—
378C2×C4×C47—22no—
379C2×C4×C47—22no—
380C2×C4×C47—416no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—41no—
388C2×C4×C47—41no—
389C2×C4×C47—41no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—41no—
393C2×C4×C47C2×C4⋊C414yes—
394C2×C4×C47C2×C4⋊C414yes—
395C2×C4×C47C4×D414yes—
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—22no—
411C2×Dic47—22no—
412C2×Dic47—22no—
413C2×Dic47—22no—
414C2×Dic47—22no—
415C2×Dic47—22no—
416C2×Dic47—22no—
417C2×Dic47—22no—
418C2×Dic47—22no—
419C2×Dic47—22no—
420C2×Dic47—22no—
421C2×Dic47—22no—
422C2×Dic47—22no—
423C2×Dic47—22no—
424C2×Dic47—22no—
425C2×Dic47—22no—
426C2×Dic47—22no—
427C2×Dic47—22no—
428C2×Dic47—22no—
429C2×Dic47—22no—
430C2×Dic47—22no—
431C2×Dic47—22no—
432C2×Dic47—416no—
433C2×Dic47—416no—
434C2×Dic47—41no—
435C2×Dic47—41no—
436C2×Dic47—41no—
437C2×Dic47—41no—
438C2×Dic47—41no—
439C2×Dic47—41no—
440C2×Dic47—41no—
441C2×Dic47—41no—
442C2×Dic47—41no—
443C2×Dic47—41no—
444C2×Dic47—41no—
445C2×Dic47—41no—
446C2×Dic47—41no—
447C2×Dic47—41no—
448C2×Dic47—41no—
449C2×Dic47—41no—
450C2×Dic47C2×C4214yes—
451C2×Dic47C2×C4214yes—
452C2×Dic47C4×D414yes—
453C2×Dic47C4×D414yes—
454#13814—471nomaximal, Sylow
455C22×C47—24no—
456C22×C47—24no—
457C22×C47—24no—
458C22×C47—24no—
459C22×C47—24no—
460C22×C47—24no—
461C22×C47—24no—
462C22×C47—24no—
463C22×C47—24no—
464C22×C47—24no—
465C22×C47—24no—
466C22×C47—24no—
467C22×C47—24no—
468C22×C47—24no—
469C22×C47C4×C4⋊C418yescomplemented
470C22×C47C22×C4211yescharacteristic
471C22×C47C22×C4⋊C411yescharacteristic
472C22×C47C2×#11711yescharacteristic
473C22×C47C2×C4×D411yescharacteristic
474C22×C47C2×C4×D411yescharacteristic
475C22×C47C2×C4×D411yescharacteristic
476C22×C47C2×C4×D411yescharacteristic
477C22×C47C2×C4×D411yescharacteristic
478C22×C47C2×C4×Q811yescharacteristic
479C22×C47C2×C4×Q811yescharacteristic
480C22×C47C4×#4111yescharacteristic
481C22×C47C4×#4111yescharacteristic
482C22×C47C4×#4111yescharacteristic
483C22×C47#51811yescharacteristic
484C22×C47#51811yescharacteristic
485C22×C47#51811yescharacteristic
486C22×C47#52011yescharacteristic
487C22×C47#52011yescharacteristic
488C22×C47#52011yescharacteristic
489C22×C47D4211yescharacteristic
490C22×C47#54611yescharacteristic
491C22×C47#54611yescharacteristic
492C22×C47#54611yescharacteristic
493C22×C47#54611yescharacteristic
494C22×C47#54711yescharacteristic
495C22×C47D4×Q811yescharacteristic
496C22×C47#55111yescharacteristic
497C22×C47#55111yescharacteristic
498C22×C47#55111yescharacteristic
499C22×C47#55111yescharacteristic
500C22×C47#55211yescharacteristic
501C22×C47#55211yescharacteristic
502C22×C47#55411yescharacteristic
503C22×C47#55411yescharacteristic
504C22×C47#55411yescharacteristic
505C4×C47—24no—
506C4×C47—24no—
507C4×C47—24no—
508C4×C47—42no—
509C4×C47—42no—
510C4×C47—42no—
511Dic47—24no—
512Dic47—24no—
513Dic47—24no—
514Dic47—24no—
515Dic47—42no—
516Dic47—42no—
517Dic47—42no—
518Dic47—42no—
519C2×#385—471no—
520C2×#385—471no—
521C2×C4×C4⋊C4—471no—
522C2×C4×C22⋊C4—471no—
523C2×C4×C22⋊C4—471no—
524C2×C4×C22⋊C4D4711yescharacteristic
525C22×#95—471no—
526#1436—471no—
527#1436—471no—
528#1436—471no—
529#1436—471no—
530C4⋊#95—471no—
531#1434—471no—
532C22⋊#95—471no—
533C4×#95—471no—
534C2×C47—28no—
535C2×C47C2×C4×C4⋊C411yescharacteristic
536C2×C47C42×D411yescharacteristic
537C2×C47#227511yescharacteristic
538C2×C47#234211yescharacteristic
539C2×C47#234311yescharacteristic
540C2×C47D4×C4⋊C411yescharacteristic
541C2×C47#234911yescharacteristic
542C2×C47#235811yescharacteristic
543C2×C47#235811yescharacteristic
544C2×C47#235911yescharacteristic
545C2×C47#235911yescharacteristic
546C2×C47#236011yescharacteristic
547C2×C47#236011yescharacteristic
548C2×C47#236811yescharacteristic
549C2×C47#236811yescharacteristic
550C24×C4—471no—
551C24×C4—471no—
552C24×C4C2×D4711yescharacteristic
553C22×C4⋊C4—471no—
554C22×C4⋊C4—471no—
555C22×C4⋊C4—471no—
556C22×C4⋊C4—471no—
557C22×C22⋊C4—471no—
558C22×C22⋊C4—471no—
559C22×C22⋊C4C2×D4711yescharacteristic
560C22×C22⋊C4C2×D4711yescharacteristic
561C22×C42—471no—
562C22×C42—471no—
563C22×C42—471no—
564C22×C42—471no—
565C22×C42C2×D4711yescharacteristic
566C22×C42C2×D4711yescharacteristic
567#385—478no—
568#385—478no—
569C4×C4⋊C4—944no—
570C4×C22⋊C4—24no—
571C4×C22⋊C4—478no—
572C4×C22⋊C4—944no—
573C2×#95—471no—
574C2×#95—471no—
575C2×#95—471no—
576C2×#95—471no—
577C2×#95—471no—
578C2×#95—471no—
579C2×#95—471no—
580C2×#95—471no—
581C2×#95—471no—
582C2×#95—471no—
583C2×#95—471no—
584C2×#95—471no—
585C2×#95—471no—
586C2×#95—471no—
587C2×#95—471no—
588C2×#95—471no—
589C2×#95—944no—
590C2×#95C2×D4711yescharacteristic
591C2×#95C2×D4711yescharacteristic
592C47#1381411yescharacteristic, complemented, Sylow
593C25C22×D4711yescharacteristic
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—41no—
599C23×C4—41no—
600C23×C4—471no—
601C23×C4—471no—
602C23×C4—471no—
603C23×C4—471no—
604C23×C4—471no—
605C23×C4—471no—
606C23×C4—471no—
607C23×C4—471no—
608C23×C4—474no—
609C23×C4—474no—
610C23×C4—942no—
611C23×C4—942no—
612C23×C4—942no—
613C23×C4—942no—
614C23×C4—942no—
615C23×C4—942no—
616C23×C4—942no—
617C23×C4—942no—
618C23×C4—1881no—
619C23×C4—1881no—
620C23×C4—1881no—
621C23×C4—1881no—
622C23×C4C4×D4714yes—
623C23×C4C22×D4711yescharacteristic
624C23×C4C22×D4711yescharacteristic
625C23×C4C22×D4711yescharacteristic
626C23×C4C22×D4711yescharacteristic
627C23×C4C22×D4711yescharacteristic
628C23×C4C22×D4711yescharacteristic
629C2×C4⋊C4—474no—
630C2×C4⋊C4—474no—
631C2×C4⋊C4—474no—
632C2×C4⋊C4—474no—
633C2×C4⋊C4—942no—
634C2×C4⋊C4—942no—
635C2×C4⋊C4—942no—
636C2×C4⋊C4—942no—
637C2×C4⋊C4—1881no—
638C2×C4⋊C4—1881no—
639C2×C4⋊C4—1881no—
640C2×C4⋊C4—1881no—
641C2×C22⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—474no—
644C2×C22⋊C4—474no—
645C2×C22⋊C4—474no—
646C2×C22⋊C4—474no—
647C2×C22⋊C4—942no—
648C2×C22⋊C4—942no—
649C2×C22⋊C4Dic9414yes—
650C2×C22⋊C4C4×D4714yes—
651C2×C22⋊C4C4×D4714yes—
652C2×C22⋊C4C22⋊D4714yes—
653C2×C42—22no—
654C2×C42—22no—
655C2×C42—22no—
656C2×C42—22no—
657C2×C42—41no—
658C2×C42—41no—
659C2×C42—474no—
660C2×C42—474no—
661C2×C42—942no—
662C2×C42—942no—
663C2×C42—942no—
664C2×C42—942no—
665C2×C42—942no—
666C2×C42—942no—
667C2×C42—1881no—
668C2×C42—1881no—
669C2×C42—1881no—
670C2×C42—1881no—
671#95—22no—
672#95—22no—
673#95—474no—
674#95—474no—
675#95—474no—
676#95—474no—
677#95—474no—
678#95—474no—
679#95—474no—
680#95—942no—
681#95—942no—
682#95—942no—
683#95—942no—
684#95—942no—
685#95—942no—
686#95—942no—
687#95—1881no—
688#95—1881no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C2×Dic9412yes—
698C24C2×C4×D4712yes—
699C24C2×C4×D4712yes—
700C24C2×C4×D4712yes—
701C24#1062535012yes—
702C24#1062535012yes—
703C24C2×C22⋊D4712yes—
704C24C23×D4711yescharacteristic
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—28no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—28no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—472no—
743C22×C4—472no—
744C22×C4—472no—
745C22×C4—472no—
746C22×C4—472no—
747C22×C4—472no—
748C22×C4—472no—
749C22×C4—472no—
750C22×C4—472no—
751C22×C4—472no—
752C22×C4—472no—
753C22×C4—472no—
754C22×C4—472no—
755C22×C4—472no—
756C22×C4—472no—
757C22×C4—472no—
758C22×C4—948no—
759C22×C4—948no—
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—948no—
777C22×C4—948no—
778C22×C4—941no—
779C22×C4—941no—
780C22×C4—941no—
781C22×C4—941no—
782C22×C4—941no—
783C22×C4—941no—
784C22×C4—941no—
785C22×C4—941no—
786C22×C4—941no—
787C22×C4—941no—
788C22×C4—941no—
789C22×C4—941no—
790C22×C4—941no—
791C22×C4—941no—
792C22×C4—941no—
793C22×C4—941no—
794C22×C4—941no—
795C22×C4—941no—
796C22×C4—941no—
797C22×C4—941no—
798C22×C4—941no—
799C22×C4—941no—
800C22×C4—941no—
801C22×C4—941no—
802C22×C4—1884no—
803C22×C4—1884no—
804C22×C4—1884no—
805C22×C4—1884no—
806C22×C4—1884no—
807C22×C4—1884no—
808C22×C4—1884no—
809C22×C4—1884no—
810C22×C4—1884no—
811C22×C4—1884no—
812C22×C4C2×Dic9412yes—
813C22×C4C2×Dic9412yes—
814C22×C4C2×C4×D4712yes—
815C22×C4C2×C4×D4712yes—
816C22×C4C2×C4×D4712yes—
817C22×C4C2×C4×D4712yes—
818C22×C4C2×C4×D4712yes—
819C22×C4C2×C4×D4712yes—
820C22×C4D4×D4712yes—
821C22×C4#1062535212yes—
822C22×C4C2×C22⋊D4712yes—
823C22×C4C2×C22⋊D4712yes—
824C4⋊C4—948no—
825C4⋊C4—948no—
826C4⋊C4—1884no—
827C4⋊C4—1884no—
828C22⋊C4—28no—
829C22⋊C4—4716no—
830C22⋊C4—948no—
831C22⋊C4Dic47⋊C4116yescomplemented
832C42—44no—
833C42—44no—
834C42—948no—
835C42—1884no—
836C42—1884no—
837C42—1884no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23C42×D4714yes—
867C23C2×Dic47⋊C414yes—
868C23#1309398114yes—
869C23C4×C22⋊D4714yes—
870C23C4×C22⋊D4714yes—
871C23C4×Dic9414yes—
872C23C4×Dic9414yes—
873C23C22×C4×D4711yescharacteristic
874C23C22×C4×D4711yescharacteristic
875C23C22×C4×D4711yescharacteristic
876C23C2×D4×D4711yescharacteristic
877C23C22×C22⋊D4711yescharacteristic
878C23C22×Dic9411yescharacteristic
879C23#41×D4711yescharacteristic
880C23#41×D4711yescharacteristic
881C23C2×#1062535211yescharacteristic
882C23C2×#1062535011yescharacteristic
883C23C2×#1062535011yescharacteristic
884C23#1309406911yescharacteristic
885C23#1309406911yescharacteristic
886C23#1309407011yescharacteristic
887C23#1309407111yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—416no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—474no—
929C2×C4—474no—
930C2×C4—474no—
931C2×C4—474no—
932C2×C4—942no—
933C2×C4—942no—
934C2×C4—942no—
935C2×C4—942no—
936C2×C4—942no—
937C2×C4—942no—
938C2×C4—942no—
939C2×C4—942no—
940C2×C4—942no—
941C2×C4—942no—
942C2×C4—942no—
943C2×C4—942no—
944C2×C4—942no—
945C2×C4—942no—
946C2×C4—942no—
947C2×C4—942no—
948C2×C4—942no—
949C2×C4—942no—
950C2×C4—942no—
951C2×C4—942no—
952C2×C4—942no—
953C2×C4—942no—
954C2×C4—942no—
955C2×C4—942no—
956C2×C4—942no—
957C2×C4—942no—
958C2×C4—942no—
959C2×C4—942no—
960C2×C4—942no—
961C2×C4—942no—
962C2×C4—942no—
963C2×C4—942no—
964C2×C4—942no—
965C2×C4—942no—
966C2×C4—942no—
967C2×C4—942no—
968C2×C4—18816no—
969C2×C4—18816no—
970C2×C4—1881no—
971C2×C4—1881no—
972C2×C4—1881no—
973C2×C4—1881no—
974C2×C4—1881no—
975C2×C4—1881no—
976C2×C4—1881no—
977C2×C4—1881no—
978C2×C4—1881no—
979C2×C4—1881no—
980C2×C4—1881no—
981C2×C4—1881no—
982C2×C4—1881no—
983C2×C4—1881no—
984C2×C4—1881no—
985C2×C4—1881no—
986C2×C4C2×Dic47⋊C414yes—
987C2×C4C2×Dic47⋊C414yes—
988C2×C4(C22⋊D47)⋊C414yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22C4×Dic47⋊C418yescomplemented
1004C22C2×C42×D4711yescharacteristic
1005C22C22×Dic47⋊C411yescharacteristic
1006C22C2×#1309398111yescharacteristic
1007C22C4×D4×D4711yescharacteristic
1008C22C4×D4×D4711yescharacteristic
1009C22C2×(C22⋊D47)⋊C411yescharacteristic
1010C22C2×C4×C22⋊D4711yescharacteristic
1011C22C2×C4×C22⋊D4711yescharacteristic
1012C22C2×C4×Dic9411yescharacteristic
1013C22C2×C4×Dic9411yescharacteristic
1014C22C4×#1062535211yescharacteristic
1015C22C4×#1062535211yescharacteristic
1016C22#1568959111yescharacteristic
1017C22#1568959511yescharacteristic
1018C22#1568959511yescharacteristic
1019C22#1568959611yescharacteristic
1020C22#1568960211yescharacteristic
1021C22#1568960211yescharacteristic
1022C22#1568960311yescharacteristic
1023C22D4×C22⋊D4711yescharacteristic
1024C22#1568976111yescharacteristic
1025C22#1568976311yescharacteristic
1026C22#1568976711yescharacteristic
1027C22#1568976911yescharacteristic
1028C22#1568977211yescharacteristic
1029C22D4×Dic9411yescharacteristic
1030C22#1568979711yescharacteristic
1031C22#1568979911yescharacteristic
1032C22#1568980211yescharacteristic
1033C22#1568980211yescharacteristic
1034C22#1568980611yescharacteristic
1035C22#1568981311yescharacteristic
1036C22#1568983011yescharacteristic
1037C22#1568983211yescharacteristic
1038C22#1568983211yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—944no—
1046C4—944no—
1047C4—944no—
1048C4—944no—
1049C4—1882no—
1050C4—1882no—
1051C4—1882no—
1052C4—1882no—
1053C2—28no—
1054C2C2×C4×Dic47⋊C411yescharacteristic
1055C2C4×(C22⋊D47)⋊C411yescharacteristic
1056C2#2024574711yescharacteristic
1057C2#2024623111yescharacteristic
1058C2#2024624211yescharacteristic
1059C2D4×Dic47⋊C411yescharacteristic
1060C2#2024629311yescharacteristic
1061C2#2024636511yescharacteristic
1062C2#2024636711yescharacteristic
1063C2#2024637411yescharacteristic
1064C2#2024638011yescharacteristic
1065C2#2024639111yescharacteristic
1066C2#2024639411yescharacteristic
1067C2#2024646611yescharacteristic
1068C2#2024647111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC2×C4×C22⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×C4×C22⋊C4D47
hypocenterC47#13814
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic47⋊C4C2semidirect
7. #20241621C2semidirect
8. #20241621C2semidirect
9. #20241619C2semidirect
10. #20241619C2semidirect
11. Dic47⋊#95C2semidirect
12. #20241614C2semidirect
14. C4×C47⋊#95C2semidirect
28. #15688996C4semidirect
29. #15688995C4semidirect
32. C22⋊C4×Dic47C4semidirect
88. C2×Dic47⋊C4C2×C4semidirect
89. C2×Dic47⋊C4C2×C4semidirect
90. C2×Dic47⋊C4C2×C4semidirect
91. C2×Dic47⋊C4C2×C4semidirect
108. C2×C4×Dic47C2×C4semidirect
109. C2×C4×Dic47C2×C4semidirect
119. C47⋊#95C2×C4semidirect
120. C47⋊#95C2×C4semidirect
121. C47⋊#95C2×C4semidirect
122. C47⋊#95C2×C4semidirect
123. C47⋊#95C2×C4semidirect
124. C47⋊#95C2×C4semidirect
290. C22⋊C4×C47C4⋊C4semidirect
294. C22⋊Dic47C42semidirect
469. C22×C47C4×C4⋊C4semidirect
592. C47#13814semidirect
831. C22⋊C4Dic47⋊C4semidirect
1003. C22C4×Dic47⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#156889962
C2×#156889952
C2×C4×Dic47⋊C42
C2×C22⋊C4×Dic472
C22×C47⋊#952
#202416212
#202416192
Dic47⋊#952
#202416142
#202416102
C4×C47⋊#952
C2×C4×C22⋊C4×C472
#1381447