Finite Group Databasebeta

← #26137694

Subgroups — #26137694

Order 12032.

2574 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D47C211yesmaximal, characteristic
2C2×#15688980C211yesmaximal, characteristic
3C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
6C2×#15688970C212yesmaximal
7#20241619C212yesmaximal, complemented
8#20241619C212yesmaximal, complemented
9#20241617C211yesmaximal, characteristic, complemented
10(C2×D47)⋊#95C212yesmaximal
11C47×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D47C2212yes—
13C23×C4×D47C2211yescharacteristic
14C22×C4⋊Dic47C2211yescharacteristic
15C22×C4⋊Dic47C2211yescharacteristic
16C22×Dic47⋊C4C2212yes—
17C2×C4⋊C4×D47—24no—
18C2×C4⋊C4×D47—24no—
19C2×C4⋊C4×D47C418yescomplemented
20C22×(C2×D47)⋊C4C2211yescharacteristic
21C22×(C2×D47)⋊C4C2212yes—
22C22×(C2×D47)⋊C4C2211yescharacteristic
23C22×C4×Dic47C2212yes—
24C22×C4×Dic47C2212yes—
25C22×C4×Dic47C2211yescharacteristic
26#15688980C418yescomplemented
27C4⋊C4×Dic47—24no—
28C4×C4⋊Dic47—24no—
29C4×(C2×D47)⋊C4C418yescomplemented
30#15688970—28no—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2211yescharacteristic
36C2×C47⋊#95C2211yescharacteristic
37C2×C47⋊#95C2212yes—
38C22×C4⋊C4×C47C2211yescharacteristic
39C22×C4⋊C4×C47C2211yescharacteristic
40C22×C42×C47C2211yescharacteristic
41C2×#95×C47C2212yes—
42C2×#95×C47C2212yes—
43C24×D47C2311yescharacteristic
44C23×Dic47C2311yescharacteristic
45C23×Dic47C2312yes—
46C23×Dic47C2311yescharacteristic
47C23×Dic47C2312yes—
48C23×Dic47C2311yescharacteristic
49C22×C4×D47—22no—
50C22×C4×D47—22no—
51C22×C4×D47—22no—
52C22×C4×D47—22no—
53C22×C4×D47—24no—
54C22×C4×D47—24no—
55C22×C4×D47—24no—
56C22×C4×D47—24no—
57C22×C4×D47—42no—
58C22×C4×D47—42no—
59C22×C4×D47C2×C418yes—
60C22×C4×D47C2×C414yes—
61C22×C4×D47C2×C414yes—
62C22×C4×D47C2×C414yes—
63C2×C4⋊Dic47—22no—
64C2×C4⋊Dic47—22no—
65C2×C4⋊Dic47C2×C414yes—
66C2×C4⋊Dic47C2×C414yescomplemented
67C2×C4⋊Dic47D414yes—
68C2×C4⋊Dic47D414yes—
69C2×Dic47⋊C4—24no—
70C2×Dic47⋊C4—24no—
71C2×Dic47⋊C4C2×C418yes—
72C4⋊C4×D47—232no—
73C2×(C2×D47)⋊C4—24no—
74C2×(C2×D47)⋊C4—22no—
75C2×(C2×D47)⋊C4—22no—
76C2×(C2×D47)⋊C4—24no—
77C2×(C2×D47)⋊C4C2×C414yes—
78C2×(C2×D47)⋊C4C2×C418yes—
79C2×(C2×D47)⋊C4C2×C414yes—
80C2×(C2×D47)⋊C4D414yes—
81C2×(C2×D47)⋊C4Q814yes—
82C2×C4×Dic47—22no—
83C2×C4×Dic47—22no—
84C2×C4×Dic47—24no—
85C2×C4×Dic47—24no—
86C2×C4×Dic47—24no—
87C2×C4×Dic47—24no—
88C2×C4×Dic47—42no—
89C2×C4×Dic47—42no—
90C2×C4×Dic47C2×C414yescomplemented
91C47⋊#95—24no—
92C47⋊#95—24no—
93C47⋊#95—24no—
94C47⋊#95—42no—
95C47⋊#95C2×C414yescomplemented
96C47⋊#95C2×C414yescomplemented
97C47⋊#95C2×C418yescomplemented
98C23×C4×C47C2311yescharacteristic
99C23×C4×C47C2312yes—
100C23×C4×C47C2312yes—
101C23×C4×C47C2311yescharacteristic
102C23×C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47—22no—
104C2×C4⋊C4×C47—22no—
105C2×C4⋊C4×C47—22no—
106C2×C4⋊C4×C47—22no—
107C2×C4⋊C4×C47C2×C414yes—
108C2×C4⋊C4×C47C2×C414yescomplemented
109C2×C42×C47—22no—
110C2×C42×C47—22no—
111C2×C42×C47C2×C414yescomplemented
112#95×C47—24no—
113#95×C47—42no—
114C24×C47C2411yescharacteristic
115C23×D47—21no—
116C23×D47—21no—
117C23×D47—21no—
118C23×D47—21no—
119C23×D47—21no—
120C23×D47—21no—
121C23×D47—21no—
122C23×D47—21no—
123C23×D47C22×C412yes—
124C23×D47C22×C412yes—
125C23×D47C22×C412yes—
126C23×D47C2×D412yes—
127C23×D47C2×Q812yes—
128C23×D47#4112yes—
129C23×D47#4112yes—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
140C22×C4×C47—21no—
141C22×C4×C47—22no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—21no—
150C22×C4×C47—22no—
151C22×C4×C47—21no—
152C22×C4×C47C22×C412yes—
153C22×C4×C47C22×C414yes—
154C22×C4×C47C22×C414yes—
155C22×C4×C47C22×C412yes—
156C22×C4×C47C22×C412yes—
157C22×C4×C47C22×C412yes—
158C22×C4×C47C22×C412yes—
159C22×C4×C47C2×D412yes—
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2×D412yes—
162C22×C4×C47C2×Q812yes—
163C22×C4×C47#4112yes—
164C22×C4×C47#4112yes—
165C22×Dic47—21no—
166C22×Dic47—22no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—22no—
173C22×Dic47—21no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—21no—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—21no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—21no—
189C22×Dic47C22×C412yes—
190C22×Dic47C22×C414yes—
191C22×Dic47C22×C412yes—
192C22×Dic47C22×C412yes—
193C22×Dic47C22×C412yes—
194C22×Dic47C22×C414yes—
195C22×Dic47C22×C412yes—
196C22×Dic47C2×D414yes—
197C22×Dic47C2×D414yes—
198C22×Dic47C2×D412yes—
199C22×Dic47C2×Q812yes—
200C2×C4×D47—28no—
201C2×C4×D47—28no—
202C2×C4×D47—28no—
203C2×C4×D47—28no—
204C2×C4×D47—28no—
205C2×C4×D47—28no—
206C2×C4×D47—216no—
207C2×C4×D47—216no—
208C2×C4×D47—48no—
209C2×C4×D47—48no—
210C2×C4×D47—48no—
211C2×C4×D47—48no—
212C2×C4×D47—48no—
213C2×C4×D47C42116yescomplemented
214C4⋊C4×C47—28no—
215C4⋊C4×C47—28no—
216C42×C47—28no—
217(C2×D47)⋊C4—28no—
218(C2×D47)⋊C4—216no—
219(C2×D47)⋊C4C4⋊C4116yescomplemented
220C4⋊Dic47—28no—
221C4⋊Dic47C22⋊C4116yescomplemented
222Dic47⋊C4—216no—
223C4×Dic47—28no—
224C4×Dic47—48no—
225C4×Dic47—48no—
226C23×C47C23×C411yescharacteristic
227C23×C47C23×C411yescharacteristic
228C23×C47C23×C411yescharacteristic
229C23×C47C22×D411yescharacteristic
230C23×C47C22×D411yescharacteristic
231C23×C47C22×D411yescharacteristic
232C23×C47C22×Q811yescharacteristic
233C23×C47C2×#4111yescharacteristic
234C23×C47C2×#4111yescharacteristic
235C23×C47C2×#4111yescharacteristic
236C23×C47C2×#4111yescharacteristic
237C23×C47H(5,𝔽2)11yescharacteristic
238C23×C47H(5,𝔽2)11yescharacteristic
239C23×C472−1+411yescharacteristic
240C23×C472−1+411yescharacteristic
241C22×D47—22no—
242C22×D47—22no—
243C22×D47—22no—
244C22×D47—22no—
245C22×D47—22no—
246C22×D47—22no—
247C22×D47—22no—
248C22×D47—22no—
249C22×D47—22no—
250C22×D47—22no—
251C22×D47—22no—
252C22×D47—22no—
253C22×D47—22no—
254C22×D47—22no—
255C22×D47—22no—
256C22×D47—22no—
257C22×D47—22no—
258C22×D47—22no—
259C22×D47—22no—
260C22×D47—22no—
261C22×D47—22no—
262C22×D47—22no—
263C22×D47—22no—
264C22×D47—22no—
265C22×D47—22no—
266C22×D47—22no—
267C22×D47—22no—
268C22×D47—22no—
269C22×D47C2×C4214yes—
270C22×D47C2×C4⋊C414yes—
271C22×D47#11714yes—
272C22×D47C4×D414yes—
273C22×D47C4×D414yes—
274C22×D47C4×Q814yes—
275C22×D47C4×Q814yes—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—24no—
283C2×C4×C47—22no—
284C2×C4×C47—24no—
285C2×C4×C47—22no—
286C2×C4×C47—24no—
287C2×C4×C47—24no—
288C2×C4×C47—24no—
289C2×C4×C47—24no—
290C2×C4×C47—22no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—41no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—42no—
303C2×C4×C47C2×C4214yes—
304C2×C4×C47C2×C22⋊C414yes—
305C2×C4×C47C2×C4⋊C414yescomplemented
306C2×C4×C47#11714yes—
307C2×C4×C47C4×D414yes—
308C2×C4×C47C4×D414yes—
309C2×C4×C47C4×D414yes—
310C2×C4×C47C4×D414yes—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—24no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—24no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—24no—
323C2×Dic47—24no—
324C2×Dic47—24no—
325C2×Dic47—24no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—24no—
332C2×Dic47—24no—
333C2×Dic47—22no—
334C2×Dic47—24no—
335C2×Dic47—42no—
336C2×Dic47—41no—
337C2×Dic47—42no—
338C2×Dic47—41no—
339C2×Dic47—42no—
340C2×Dic47—41no—
341C2×Dic47—41no—
342C2×Dic47—42no—
343C2×Dic47C2×C4214yes—
344C2×Dic47C2×C22⋊C418yes—
345C2×Dic47C2×C4⋊C414yescomplemented
346C4×D47—232no—
347C4×D47—432no—
348C22⋊C4×C4⋊C4—471nomaximal, Sylow
349C22×C47C22×C4211yescharacteristic
350C22×C47C22×C22⋊C411yescharacteristic
351C22×C47C22×C4⋊C411yescharacteristic
352C22×C47C2×#11711yescharacteristic
353C22×C47C2×#11711yescharacteristic
354C22×C47C2×C4×D411yescharacteristic
355C22×C47C2×C4×D411yescharacteristic
356C22×C47C2×C4×D411yescharacteristic
357C22×C47C2×C4×D411yescharacteristic
358C22×C47C2×C4×D411yescharacteristic
359C22×C47C2×C4×D411yescharacteristic
360C22×C47C2×C4×Q811yescharacteristic
361C22×C47C2×C4×Q811yescharacteristic
362C22×C47#51811yescharacteristic
363C22×C47#51911yescharacteristic
364C22×C47#52011yescharacteristic
365C22×C47#52011yescharacteristic
366C22×C47#52011yescharacteristic
367C22×C47#52011yescharacteristic
368C22×C47D4211yescharacteristic
369C22×C47D4211yescharacteristic
370C22×C47#54611yescharacteristic
371C22×C47#54611yescharacteristic
372C22×C47#54711yescharacteristic
373C22×C47#54711yescharacteristic
374C22×C47#54811yescharacteristic
375C22×C47#54811yescharacteristic
376C22×C47D4×Q811yescharacteristic
377C22×C47D4×Q811yescharacteristic
378C22×C47#55211yescharacteristic
379C22×C47#55211yescharacteristic
380C22×C47#55311yescharacteristic
381C22×C47#55311yescharacteristic
382C22×C47#55411yescharacteristic
383C22×C47#55411yescharacteristic
384C2×D47—24no—
385C2×D47—24no—
386C2×D47—24no—
387C2×D47—24no—
388C2×D47—24no—
389C2×D47—24no—
390C2×D47—24no—
391C2×D47—24no—
392C2×D47—24no—
393C2×D47—24no—
394C2×D47—24no—
395C2×D47—24no—
396C2×D47—24no—
397C2×D47—24no—
398C2×D47C4×C4⋊C418yescomplemented
399C4×C47—24no—
400C4×C47—44no—
401C4×C47—42no—
402C4×C47—44no—
403C4×C47C4×C22⋊C418yescomplemented
404Dic47—28no—
405Dic47—24no—
406Dic47—24no—
407Dic47—42no—
408Dic47—44no—
409C23×C4⋊C4—471no—
410C2×#380—471no—
411C2×C4×C4⋊C4—471no—
412C2×C4×C4⋊C4—471no—
413C2×C4×C22⋊C4—471no—
414C2×C4×C22⋊C4—472no—
415#1436—472no—
416#1436—472no—
417C4⋊#95—471no—
418C4⋊#95D4711yescharacteristic, complemented
419C22⋊#95—472no—
420C2×C47C2×C4×C22⋊C411yescharacteristic
421C2×C47C2×C4×C4⋊C411yescharacteristic
422C2×C47#227411yescharacteristic
423C2×C47D4×C22⋊C411yescharacteristic
424C2×C47Q8×C22⋊C411yescharacteristic
425C2×C47#234411yescharacteristic
426C2×C47#234511yescharacteristic
427C2×C47D4×C4⋊C411yescharacteristic
428C2×C47D4×C4⋊C411yescharacteristic
429C2×C47#235211yescharacteristic
430C2×C47#235211yescharacteristic
431C2×C47#236011yescharacteristic
432C2×C47#236011yescharacteristic
433C2×C47#236111yescharacteristic
434C2×C47#236111yescharacteristic
435D47—28no—
436C24×C4—471no—
437C24×C4—472no—
438C22×C4⋊C4—471no—
439C22×C4⋊C4—472no—
440C22×C4⋊C4—471no—
441C22×C4⋊C4—478no—
442C22×C4⋊C4—944no—
443C22×C4⋊C4—944no—
444C22×C4⋊C4C2×D4711yescharacteristic
445C22×C4⋊C4C2×D4711yescharacteristic
446C22×C22⋊C4—471no—
447C22×C22⋊C4—471no—
448C22×C22⋊C4—472no—
449C22×C42—471no—
450C22×C42—472no—
451C22×C42—472no—
452C22×C42C2×D4711yescharacteristic
453#380—478no—
454C4×C4⋊C4—944no—
455C4×C4⋊C4—944no—
456C4×C22⋊C4—478no—
457C4×C22⋊C4—948no—
458C2×#95—471no—
459C2×#95—471no—
460C2×#95—472no—
461C2×#95—472no—
462C2×#95—472no—
463C2×#95—472no—
464C2×#95—472no—
465C2×#95C2×D4712yes—
466C2×#95C2×D4712yes—
467C47C22⋊C4×C4⋊C411yescharacteristic, complemented, Sylow
468C25—471no—
469C23×C4—471no—
470C23×C4—471no—
471C23×C4—472no—
472C23×C4—474no—
473C23×C4—474no—
474C23×C4—474no—
475C23×C4—472no—
476C23×C4—471no—
477C23×C4—478no—
478C23×C4—944no—
479C23×C4—944no—
480C23×C4—944no—
481C23×C4—944no—
482C23×C4—942no—
483C23×C4—942no—
484C23×C4—942no—
485C23×C4—942no—
486C23×C4—1882no—
487C23×C4—1882no—
488C23×C4C22×D4712yes—
489C23×C4C22×D4711yescharacteristic
490C23×C4C22×D4712yes—
491C23×C4C22×D4711yescharacteristic
492C23×C4C22×D4711yescharacteristic
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—474no—
498C2×C4⋊C4—474no—
499C2×C4⋊C4—474no—
500C2×C4⋊C4—478no—
501C2×C4⋊C4—474no—
502C2×C4⋊C4—9432no—
503C2×C4⋊C4—944no—
504C2×C4⋊C4—944no—
505C2×C4⋊C4—942no—
506C2×C4⋊C4—942no—
507C2×C4⋊C4C4×D4714yes—
508C2×C4⋊C4C4×D4714yescomplemented
509C2×C22⋊C4—474no—
510C2×C22⋊C4—474no—
511C2×C22⋊C4—474no—
512C2×C22⋊C4—474no—
513C2×C22⋊C4—478no—
514C2×C22⋊C4—942no—
515C2×C22⋊C4—944no—
516C2×C22⋊C4—942no—
517C2×C22⋊C4—944no—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—474no—
521C2×C42—942no—
522C2×C42—942no—
523C2×C42—944no—
524C2×C42—944no—
525C2×C42—944no—
526C2×C42—944no—
527C2×C42—1882no—
528C2×C42—1882no—
529C2×C42C4×D4714yescomplemented
530#95—24no—
531#95—42no—
532#95—474no—
533#95—474no—
534#95—478no—
535#95—944no—
536#95—944no—
537#95—944no—
538#95—1882no—
539C24—472no—
540C24—472no—
541C24—472no—
542C24—472no—
543C24—472no—
544C24—472no—
545C24—472no—
546C24—941no—
547C24—941no—
548C24—941no—
549C24—941no—
550C24—941no—
551C24—941no—
552C24—941no—
553C24—941no—
554C24C23×D4711yescharacteristic
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—472no—
578C22×C4—472no—
579C22×C4—472no—
580C22×C4—472no—
581C22×C4—474no—
582C22×C4—472no—
583C22×C4—474no—
584C22×C4—474no—
585C22×C4—472no—
586C22×C4—4716no—
587C22×C4—472no—
588C22×C4—474no—
589C22×C4—9416no—
590C22×C4—9416no—
591C22×C4—941no—
592C22×C4—942no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4—942no—
596C22×C4—941no—
597C22×C4—941no—
598C22×C4—941no—
599C22×C4—941no—
600C22×C4—942no—
601C22×C4—942no—
602C22×C4—941no—
603C22×C4—948no—
604C22×C4—948no—
605C22×C4—948no—
606C22×C4—948no—
607C22×C4—948no—
608C22×C4—948no—
609C22×C4—941no—
610C22×C4—942no—
611C22×C4—942no—
612C22×C4—941no—
613C22×C4—941no—
614C22×C4—942no—
615C22×C4—941no—
616C22×C4—942no—
617C22×C4—941no—
618C22×C4—942no—
619C22×C4—941no—
620C22×C4—942no—
621C22×C4—1888no—
622C22×C4—1888no—
623C22×C4—1888no—
624C22×C4—1888no—
625C22×C4—1888no—
626C22×C4C2×C4×D4712yes—
627C22×C4C2×C4×D4714yes—
628C22×C4C2×C4×D4714yes—
629C22×C4C2×C4×D4712yes—
630C22×C4C2×C4×D4712yes—
631C22×C4C2×C4×D4712yes—
632C22×C4C2×C4×D4712yes—
633C22×C4D4×D4712yes—
634C22×C4D4×D4712yes—
635C22×C4D4×D4712yes—
636C22×C4#1062535212yes—
637C22×C4Q8×D4712yes—
638C22×C4#1062535412yes—
639C4⋊C4—28no—
640C4⋊C4—28no—
641C4⋊C4—4716no—
642C4⋊C4—9416no—
643C4⋊C4—948no—
644C22⋊C4—4716no—
645C22⋊C4—948no—
646C22⋊C4—9416no—
647C42—28no—
648C42—948no—
649C42—1888no—
650C42—1888no—
651C23—474no—
652C23—474no—
653C23—474no—
654C23—474no—
655C23—474no—
656C23—474no—
657C23—474no—
658C23—942no—
659C23—942no—
660C23—942no—
661C23—942no—
662C23—942no—
663C23—942no—
664C23—942no—
665C23—942no—
666C23—942no—
667C23—942no—
668C23—942no—
669C23—942no—
670C23—942no—
671C23—942no—
672C23—942no—
673C23—942no—
674C23—942no—
675C23—942no—
676C23—942no—
677C23—942no—
678C23—942no—
679C23—942no—
680C23—942no—
681C23—942no—
682C23—942no—
683C23—942no—
684C23—942no—
685C23—942no—
686C23C22×C4×D4711yescharacteristic
687C23C22×C4×D4711yescharacteristic
688C23C22×C4×D4711yescharacteristic
689C23C2×D4×D4711yescharacteristic
690C23C2×D4×D4711yescharacteristic
691C23C2×D4×D4711yescharacteristic
692C23C2×Q8×D4711yescharacteristic
693C23#41×D4711yescharacteristic
694C23#41×D4711yescharacteristic
695C23C2×#1062535211yescharacteristic
696C23C2×#1062535411yescharacteristic
697C23#1309406911yescharacteristic
698C23#1309407011yescharacteristic
699C23#1309407111yescharacteristic
700C23#1309407211yescharacteristic
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—474no—
729C2×C4—478no—
730C2×C4—474no—
731C2×C4—944no—
732C2×C4—942no—
733C2×C4—944no—
734C2×C4—944no—
735C2×C4—944no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—944no—
742C2×C4—942no—
743C2×C4—942no—
744C2×C4—942no—
745C2×C4—942no—
746C2×C4—942no—
747C2×C4—944no—
748C2×C4—942no—
749C2×C4—9432no—
750C2×C4—942no—
751C2×C4—944no—
752C2×C4—942no—
753C2×C4—944no—
754C2×C4—942no—
755C2×C4—944no—
756C2×C4—18832no—
757C2×C4—1882no—
758C2×C4—1881no—
759C2×C4—1882no—
760C2×C4—1881no—
761C2×C4—1882no—
762C2×C4—1881no—
763C2×C4—1881no—
764C2×C4—1882no—
765C2×C4C42×D4714yes—
766C2×C4C22⋊C4×D4714yes—
767C2×C4C4⋊C4×D4714yescomplemented
768C2×C4#1309398214yes—
769C2×C4(C22⋊D47)⋊C414yes—
770C2×C4(C22⋊D47)⋊C414yes—
771C2×C4#1309398614yes—
772C2×C4#1309398614yes—
773C22—478no—
774C22—944no—
775C22—944no—
776C22—944no—
777C22—944no—
778C22—944no—
779C22—944no—
780C22—944no—
781C22—944no—
782C22—944no—
783C22—944no—
784C22—944no—
785C22—944no—
786C22—944no—
787C22—944no—
788C22C2×C42×D4711yescharacteristic
789C22C2×C22⋊C4×D4711yescharacteristic
790C22C2×C4⋊C4×D4711yescharacteristic
791C22#117×D4711yescharacteristic
792C22C2×#1309398211yescharacteristic
793C22C4×D4×D4711yescharacteristic
794C22C4×D4×D4711yescharacteristic
795C22C2×(C22⋊D47)⋊C411yescharacteristic
796C22C2×(C22⋊D47)⋊C411yescharacteristic
797C22C2×#1309398611yescharacteristic
798C22C2×#1309398611yescharacteristic
799C22C4×Q8×D4711yescharacteristic
800C22C4×Q8×D4711yescharacteristic
801C22#1568959511yescharacteristic
802C22#1568959911yescharacteristic
803C22#1568960211yescharacteristic
804C22#1568960311yescharacteristic
805C22#1568960411yescharacteristic
806C22#1568960511yescharacteristic
807C22#1568975711yescharacteristic
808C22#1568975811yescharacteristic
809C22#1568976611yescharacteristic
810C22#1568977011yescharacteristic
811C22#1568977311yescharacteristic
812C22#1568977611yescharacteristic
813C22#1568978111yescharacteristic
814C22#1568978311yescharacteristic
815C22#1568978611yescharacteristic
816C22#1568978811yescharacteristic
817C22#1568980711yescharacteristic
818C22#1568981111yescharacteristic
819C22#1568982011yescharacteristic
820C22#1568982611yescharacteristic
821C22#1568983111yescharacteristic
822C22#1568983411yescharacteristic
823C4—24no—
824C4—42no—
825C4—44no—
826C4—44no—
827C4—944no—
828C4—948no—
829C4—944no—
830C4—1882no—
831C4—1884no—
832C4#1568897018yescomplemented
833C2—948no—
834C2C2×#1568897011yescharacteristic
835C2C4×C4⋊C4×D4711yescharacteristic
836C2#2024574211yescharacteristic
837C2#2024620911yescharacteristic
838C2#2024622211yescharacteristic
839C2#2024625611yescharacteristic
840C2#2024626411yescharacteristic
841C2#2024628411yescharacteristic
842C2#2024628811yescharacteristic
843C2#2024631011yescharacteristic
844C2#2024631411yescharacteristic
845C2#2024639211yescharacteristic
846C2#2024639811yescharacteristic
847C2#2024640311yescharacteristic
848C2#2024640911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC47×C4⋊#95C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenterC4⋊#95D47
hypocenterC47C22⋊C4×C4⋊C4
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic47C2semidirect
4. C2×C4×C4⋊Dic47C2semidirect
7. #20241619C2semidirect
8. #20241619C2semidirect
9. #20241617C2semidirect
11. C47×C4⋊#95C2semidirect
19. C2×C4⋊C4×D47C4semidirect
26. #15688980C4semidirect
29. C4×(C2×D47)⋊C4C4semidirect
66. C2×C4⋊Dic47C2×C4semidirect
90. C2×C4×Dic47C2×C4semidirect
95. C47⋊#95C2×C4semidirect
96. C47⋊#95C2×C4semidirect
97. C47⋊#95C2×C4semidirect
108. C2×C4⋊C4×C47C2×C4semidirect
111. C2×C42×C47C2×C4semidirect
213. C2×C4×D47C42semidirect
219. (C2×D47)⋊C4C4⋊C4semidirect
221. C4⋊Dic47C22⋊C4semidirect
305. C2×C4×C47C2×C4⋊C4semidirect
345. C2×Dic47C2×C4⋊C4semidirect
398. C2×D47C4×C4⋊C4semidirect
403. C4×C47C4×C22⋊C4semidirect
418. C4⋊#95D47semidirect
467. C47C22⋊C4×C4⋊C4semidirect
508. C2×C4⋊C4C4×D47semidirect
529. C2×C42C4×D47semidirect
767. C2×C4C4⋊C4×D47semidirect
832. C4#15688970semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D472
C2×#156889802
C2×C4⋊C4×Dic472
C2×C4×C4⋊Dic472
C2×C4×(C2×D47)⋊C42
C2×#156889702
#202416192
#202416172
(C2×D47)⋊#952
C47×C4⋊#952
C22⋊C4×C4⋊C447