Finite Group Databasebeta

← C4⋊C4×Dic47⋊C4 #26137715

Subgroups — C4⋊C4×Dic47⋊C4 #26137715

Order 12032.

1838 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688992C211yesmaximal, characteristic
2C2×C4⋊C4×Dic47C211yesmaximal, characteristic
3C2×C4⋊C4×Dic47C211yesmaximal, characteristic
4C2×C4×Dic47⋊C4C212yesmaximal
5C2×C4×Dic47⋊C4C211yesmaximal, characteristic
6#20241621C212yesmaximal
7#20241619C212yesmaximal
8#20241618C211yesmaximal, characteristic
9#20241617C211yesmaximal, characteristic
10Dic47⋊#95C212yesmaximal
11C2×C4×C4⋊C4×C47C211yesmaximal, characteristic
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2211yescharacteristic
14C22×Dic47⋊C4C2212yes—
15C22×Dic47⋊C4C2211yescharacteristic
16C22×Dic47⋊C4C2212yes—
17C22×Dic47⋊C4C2211yescharacteristic
18C22×C4×Dic47C2212yes—
19C22×C4×Dic47C2212yes—
20C22×C4×Dic47C2211yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22#15688992C418yescomplemented
23C4⋊C4×Dic47—24no—
24C4⋊C4×Dic47C418yescomplemented
25C4×Dic47⋊C4—28no—
26C4×Dic47⋊C4C418yescomplemented
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2211yescharacteristic
35C22×C4⋊C4×C47C2211yescharacteristic
36C22×C4⋊C4×C47C2211yescharacteristic
37C22×C42×C47C2212yes—
38C22×C42×C47C2211yescharacteristic
39C4×C4⋊C4×C47—24no—
40C2×#95×C47C2212yes—
41C23×Dic47C2311yescharacteristic
42C23×Dic47C2312yes—
43C23×Dic47C2312yes—
44C23×Dic47C2311yescharacteristic
45C23×Dic47C2311yescharacteristic
46C23×Dic47C2311yescharacteristic
47C2×C4⋊Dic47—22no—
48C2×C4⋊Dic47—22no—
49C2×C4⋊Dic47—22no—
50C2×C4⋊Dic47—22no—
51C2×C4⋊Dic47C2×C414yes—
52C2×C4⋊Dic47C2×C414yes—
53C2×Dic47⋊C4—24no—
54C2×Dic47⋊C4—22no—
55C2×Dic47⋊C4—22no—
56C2×Dic47⋊C4—24no—
57C2×Dic47⋊C4—42no—
58C2×Dic47⋊C4—42no—
59C2×Dic47⋊C4C2×C414yes—
60C2×Dic47⋊C4C2×C418yes—
61C2×Dic47⋊C4C2×C418yes—
62C2×Dic47⋊C4C2×C414yes—
63C2×Dic47⋊C4D414yes—
64C2×Dic47⋊C4Q814yes—
65C2×C4×Dic47—22no—
66C2×C4×Dic47—22no—
67C2×C4×Dic47—24no—
68C2×C4×Dic47—24no—
69C2×C4×Dic47—24no—
70C2×C4×Dic47—24no—
71C2×C4×Dic47—42no—
72C2×C4×Dic47C2×C414yes—
73C2×C4×Dic47C2×C418yes—
74C2×C4×Dic47C2×C414yes—
75C2×C4×Dic47C2×C414yes—
76C2×C4×Dic47C2×C414yes—
77C47⋊#95—24no—
78C47⋊#95—24no—
79C47⋊#95—24no—
80C47⋊#95—42no—
81C47⋊#95—42no—
82C47⋊#95C2×C414yes—
83C47⋊#95C2×C414yes—
84C47⋊#95C2×C418yes—
85C23×C4×C47C2311yescharacteristic
86C23×C4×C47C2312yes—
87C23×C4×C47C2311yescharacteristic
88C23×C4×C47C2312yes—
89C23×C4×C47C2311yescharacteristic
90C2×C4⋊C4×C47—22no—
91C2×C4⋊C4×C47—22no—
92C2×C4⋊C4×C47C2×C414yes—
93C2×C4⋊C4×C47C2×C414yes—
94C2×C4⋊C4×C47D414yes—
95C2×C4⋊C4×C47Q814yes—
96C2×C42×C47—22no—
97C2×C42×C47—22no—
98C2×C42×C47—24no—
99C2×C42×C47—24no—
100C2×C42×C47—42no—
101C2×C42×C47C2×C414yes—
102#95×C47—24no—
103C24×C47C2411yescharacteristic
104C22×C4×C47—21no—
105C22×C4×C47—22no—
106C22×C4×C47—21no—
107C22×C4×C47—22no—
108C22×C4×C47—21no—
109C22×C4×C47—22no—
110C22×C4×C47—22no—
111C22×C4×C47—21no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—21no—
115C22×C4×C47—21no—
116C22×C4×C47—22no—
117C22×C4×C47—21no—
118C22×C4×C47—21no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—21no—
122C22×C4×C47—22no—
123C22×C4×C47—21no—
124C22×C4×C47C22×C412yes—
125C22×C4×C47C22×C414yes—
126C22×C4×C47C22×C412yes—
127C22×C4×C47C22×C414yes—
128C22×C4×C47C22×C412yes—
129C22×C4×C47C22×C412yes—
130C22×C4×C47C22×C412yes—
131C22×C4×C47C2×D412yes—
132C22×C4×C47C2×D414yes—
133C22×C4×C47C2×D412yes—
134C22×C4×C47C2×Q814yes—
135C22×C4×C47C2×Q812yes—
136C22×C4×C47C2×Q812yes—
137C22×C4×C47#4112yes—
138C22×C4×C47#4112yes—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47—21no—
145C22×Dic47—21no—
146C22×Dic47—21no—
147C22×Dic47—22no—
148C22×Dic47—21no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47—21no—
153C22×Dic47—21no—
154C22×Dic47—21no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—21no—
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—22no—
163C22×Dic47—21no—
164C22×Dic47—22no—
165C22×Dic47C22×C412yes—
166C22×Dic47C22×C414yes—
167C22×Dic47C22×C414yes—
168C22×Dic47C22×C412yes—
169C22×Dic47C22×C412yes—
170C22×Dic47C22×C412yes—
171C22×Dic47C22×C412yes—
172C22×Dic47C22×C412yes—
173C22×Dic47C22×C412yes—
174C22×Dic47C22×C412yes—
175C22×Dic47C2×D412yes—
176C22×Dic47C2×D412yes—
177C22×Dic47C2×Q812yes—
178C22×Dic47C2×Q812yes—
179C22×Dic47#4112yes—
180C22×Dic47#4112yes—
181C4⋊C4×C47—28no—
182C4⋊C4×C47C4⋊C4116yescomplemented
183C42×C47—28no—
184C42×C47—48no—
185C4⋊Dic47—28no—
186C4⋊Dic47—28no—
187Dic47⋊C4—28no—
188Dic47⋊C4—216no—
189Dic47⋊C4—48no—
190Dic47⋊C4C4⋊C4116yesdirect product factor
191C4×Dic47—28no—
192C4×Dic47—216no—
193C4×Dic47—48no—
194C4×Dic47C42116yescomplemented
195C23×C47C23×C411yescharacteristic
196C23×C47C23×C411yescharacteristic
197C23×C47C23×C411yescharacteristic
198C23×C47C22×D411yescharacteristic
199C23×C47C22×D411yescharacteristic
200C23×C47C22×Q811yescharacteristic
201C23×C47C22×Q811yescharacteristic
202C23×C47C2×#4111yescharacteristic
203C23×C47C2×#4111yescharacteristic
204C23×C47C2×#4111yescharacteristic
205C23×C47C2×#4111yescharacteristic
206C23×C47H(5,𝔽2)11yescharacteristic
207C23×C47H(5,𝔽2)11yescharacteristic
208C23×C472−1+411yescharacteristic
209C23×C472−1+411yescharacteristic
210C2×C4×C47—24no—
211C2×C4×C47—22no—
212C2×C4×C47—24no—
213C2×C4×C47—22no—
214C2×C4×C47—24no—
215C2×C4×C47—22no—
216C2×C4×C47—24no—
217C2×C4×C47—22no—
218C2×C4×C47—22no—
219C2×C4×C47—24no—
220C2×C4×C47—22no—
221C2×C4×C47—24no—
222C2×C4×C47—22no—
223C2×C4×C47—24no—
224C2×C4×C47—22no—
225C2×C4×C47—24no—
226C2×C4×C47—24no—
227C2×C4×C47—22no—
228C2×C4×C47—42no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—42no—
232C2×C4×C47—42no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—42no—
236C2×C4×C47C2×C4214yes—
237C2×C4×C47C2×C4⋊C414yes—
238C2×C4×C47C2×C4⋊C418yes—
239C2×C4×C47C2×C4⋊C414yes—
240C2×C4×C47#11714yes—
241C2×C4×C47C4×D414yes—
242C2×C4×C47C4×D414yes—
243C2×C4×C47C4×Q814yes—
244C2×C4×C47C4×Q814yes—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—22no—
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—22no—
253C2×Dic47—22no—
254C2×Dic47—22no—
255C2×Dic47—22no—
256C2×Dic47—22no—
257C2×Dic47—22no—
258C2×Dic47—24no—
259C2×Dic47—24no—
260C2×Dic47—22no—
261C2×Dic47—24no—
262C2×Dic47—24no—
263C2×Dic47—24no—
264C2×Dic47—22no—
265C2×Dic47—24no—
266C2×Dic47—42no—
267C2×Dic47—41no—
268C2×Dic47—42no—
269C2×Dic47—41no—
270C2×Dic47—42no—
271C2×Dic47—42no—
272C2×Dic47—42no—
273C2×Dic47—41no—
274C2×Dic47—42no—
275C2×Dic47—41no—
276C2×Dic47—42no—
277C2×Dic47—42no—
278C2×Dic47C2×C4214yes—
279C2×Dic47C2×C4214yes—
280C2×Dic47C2×C4⋊C414yes—
281C2×Dic47C2×C4⋊C414yes—
282C2×Dic47#11714yes—
283C2×Dic47C4×D414yes—
284C2×Dic47C4×D414yes—
285C2×Dic47C4×Q814yes—
286C2×Dic47C4×Q814yes—
287C4⋊C42—471nomaximal, Sylow
288C22×C47C22×C4211yescharacteristic
289C22×C47C22×C4⋊C411yescharacteristic
290C22×C47C22×C4⋊C411yescharacteristic
291C22×C47C2×#11711yescharacteristic
292C22×C47C2×#11711yescharacteristic
293C22×C47C2×C4×D411yescharacteristic
294C22×C47C2×C4×D411yescharacteristic
295C22×C47C2×C4×D411yescharacteristic
296C22×C47C2×C4×D411yescharacteristic
297C22×C47C2×C4×Q811yescharacteristic
298C22×C47C2×C4×Q811yescharacteristic
299C22×C47C2×C4×Q811yescharacteristic
300C22×C47C2×C4×Q811yescharacteristic
301C22×C47#51811yescharacteristic
302C22×C47#51911yescharacteristic
303C22×C47#52011yescharacteristic
304C22×C47#52011yescharacteristic
305C22×C47#52011yescharacteristic
306C22×C47#52011yescharacteristic
307C22×C47D4211yescharacteristic
308C22×C47#54711yescharacteristic
309C22×C47#54711yescharacteristic
310C22×C47D4×Q811yescharacteristic
311C22×C47D4×Q811yescharacteristic
312C22×C47#55011yescharacteristic
313C22×C47#55011yescharacteristic
314C22×C47#55411yescharacteristic
315C22×C47#55411yescharacteristic
316C22×C47#55511yescharacteristic
317C22×C47#55611yescharacteristic
318C22×C47#55611yescharacteristic
319C22×C47#55711yescharacteristic
320C22×C47#55711yescharacteristic
321C22×C47Q8211yescharacteristic
322C22×C47#55911yescharacteristic
323C4×C47—28no—
324C4×C47—24no—
325C4×C47—42no—
326C4×C47—44no—
327C4×C47C4×C4⋊C418yescomplemented
328Dic47—24no—
329Dic47—24no—
330Dic47—44no—
331Dic47—42no—
332Dic47—44no—
333Dic47C4×C4⋊C418yescomplemented
334C2×#384—471no—
335C2×C4×C4⋊C4—471no—
336C2×C4×C4⋊C4—472no—
337C2×C4×C4⋊C4—471no—
338C2×C4×C4⋊C4—471no—
339C2×C4×C4⋊C4D4711yescharacteristic
340#1436—472no—
341#1436—472no—
342C4⋊#95—471no—
343C4⋊#95—472no—
344C4⋊#95—471no—
345C2×C47C2×C4×C4⋊C411yescharacteristic
346C2×C47C2×C4×C4⋊C411yescharacteristic
347C2×C47#227411yescharacteristic
348C2×C47D4×C4⋊C411yescharacteristic
349C2×C47D4×C4⋊C411yescharacteristic
350C2×C47Q8×C4⋊C411yescharacteristic
351C2×C47Q8×C4⋊C411yescharacteristic
352C2×C47#235411yescharacteristic
353C2×C47#235411yescharacteristic
354C2×C47#235511yescharacteristic
355C2×C47#235511yescharacteristic
356C2×C47#236511yescharacteristic
357C2×C47#236511yescharacteristic
358C2×C47#236611yescharacteristic
359C2×C47#236911yescharacteristic
360C22×C4⋊C4—471no—
361C22×C4⋊C4—471no—
362C22×C4⋊C4—472no—
363C22×C4⋊C4—471no—
364C22×C4⋊C4—471no—
365C22×C4⋊C4—472no—
366C22×C4⋊C4C2×D4711yescharacteristic
367C22×C4⋊C4C2×D4711yescharacteristic
368C22×C42—471no—
369C22×C42—472no—
370C22×C42—471no—
371C22×C42—472no—
372C22×C42C2×D4712yes—
373C22×C42C2×D4711yescharacteristic
374#384—478no—
375C4×C4⋊C4—24no—
376C4×C4⋊C4—478no—
377C4×C4⋊C4—478no—
378C4×C4⋊C4—948no—
379C4×C4⋊C4—944no—
380C2×#95—471no—
381C2×#95—472no—
382C2×#95—471no—
383C2×#95—472no—
384C2×#95—472no—
385C2×#95—472no—
386C2×#95—472no—
387C2×#95—472no—
388C2×#95C2×D4712yes—
389C47C4⋊C4211yescharacteristic, complemented, Sylow
390C23×C4—471no—
391C23×C4—471no—
392C23×C4—471no—
393C23×C4—472no—
394C23×C4—472no—
395C23×C4—471no—
396C23×C4C22×D4712yes—
397C23×C4C22×D4711yescharacteristic
398C23×C4C22×D4712yes—
399C23×C4C22×D4711yescharacteristic
400C23×C4C22×D4711yescharacteristic
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—474no—
404C2×C4⋊C4—474no—
405C2×C4⋊C4—474no—
406C2×C4⋊C4—474no—
407C2×C4⋊C4—478no—
408C2×C4⋊C4—474no—
409C2×C4⋊C4—474no—
410C2×C4⋊C4—478no—
411C2×C4⋊C4—942no—
412C2×C4⋊C4—942no—
413C2×C4⋊C4—944no—
414C2×C4⋊C4—944no—
415C2×C4⋊C4—942no—
416C2×C4⋊C4—942no—
417C2×C4⋊C4—942no—
418C2×C4⋊C4—942no—
419C2×C4⋊C4—1882no—
420C2×C4⋊C4—1882no—
421C2×C4⋊C4Dic9414yes—
422C2×C4⋊C4C4×D4714yes—
423C2×C4⋊C4C4×D4714yes—
424C2×C4⋊C4C22⋊D4714yes—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—24no—
428C2×C42—24no—
429C2×C42—42no—
430C2×C42—474no—
431C2×C42—474no—
432C2×C42—474no—
433C2×C42—478no—
434C2×C42—474no—
435C2×C42—944no—
436C2×C42—944no—
437C2×C42—942no—
438C2×C42—942no—
439C2×C42—944no—
440C2×C42—944no—
441C2×C42—1882no—
442C2×C42C4×D4714yes—
443#95—24no—
444#95—474no—
445#95—474no—
446#95—478no—
447#95—944no—
448#95—944no—
449#95—944no—
450#95—1882no—
451#95—1882no—
452C24C23×D4711yescharacteristic
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—472no—
474C22×C4—472no—
475C22×C4—472no—
476C22×C4—472no—
477C22×C4—472no—
478C22×C4—472no—
479C22×C4—472no—
480C22×C4—472no—
481C22×C4—472no—
482C22×C4—472no—
483C22×C4—472no—
484C22×C4—472no—
485C22×C4—472no—
486C22×C4—472no—
487C22×C4—474no—
488C22×C4—474no—
489C22×C4—941no—
490C22×C4—941no—
491C22×C4—941no—
492C22×C4—941no—
493C22×C4—941no—
494C22×C4—941no—
495C22×C4—941no—
496C22×C4—941no—
497C22×C4—942no—
498C22×C4—942no—
499C22×C4—941no—
500C22×C4—942no—
501C22×C4—942no—
502C22×C4—941no—
503C22×C4—941no—
504C22×C4—942no—
505C22×C4—941no—
506C22×C4—942no—
507C22×C4—942no—
508C22×C4—942no—
509C22×C4—942no—
510C22×C4—941no—
511C22×C4—942no—
512C22×C4—942no—
513C22×C4—941no—
514C22×C4—942no—
515C22×C4C2×Dic9414yes—
516C22×C4C2×Dic9412yes—
517C22×C4C2×C4×D4712yes—
518C22×C4C2×C4×D4714yes—
519C22×C4C2×C4×D4712yes—
520C22×C4C2×C4×D4714yes—
521C22×C4C2×C4×D4712yes—
522C22×C4C2×C4×D4712yes—
523C22×C4C2×C4×D4712yes—
524C22×C4#1062535012yes—
525C22×C4#1062535012yes—
526C22×C4D4×D4712yes—
527C22×C4Q8×D4712yes—
528C22×C4C2×C22⋊D4714yes—
529C22×C4C2×C22⋊D4712yes—
530C4⋊C4—28no—
531C4⋊C4—4716no—
532C4⋊C4—948no—
533C4⋊C4—9416no—
534C4⋊C4—948no—
535C4⋊C4—948no—
536C4⋊C4—1888no—
537C4⋊C4Dic47⋊C4116yesdirect product factor
538C42—28no—
539C42—48no—
540C42—4716no—
541C42—9416no—
542C42—948no—
543C42—1888no—
544C23C22×C4×D4711yescharacteristic
545C23C22×C4×D4711yescharacteristic
546C23C22×C4×D4711yescharacteristic
547C23C2×D4×D4711yescharacteristic
548C23C22×C22⋊D4711yescharacteristic
549C23C2×Q8×D4711yescharacteristic
550C23C22×Dic9411yescharacteristic
551C23#41×D4711yescharacteristic
552C23#41×D4711yescharacteristic
553C23C2×#1062535011yescharacteristic
554C23C2×#1062535011yescharacteristic
555C23#1309406911yescharacteristic
556C23#1309407011yescharacteristic
557C23#1309407111yescharacteristic
558C23#1309407211yescharacteristic
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—474no—
586C2×C4—474no—
587C2×C4—474no—
588C2×C4—474no—
589C2×C4—474no—
590C2×C4—474no—
591C2×C4—474no—
592C2×C4—474no—
593C2×C4—474no—
594C2×C4—942no—
595C2×C4—942no—
596C2×C4—942no—
597C2×C4—942no—
598C2×C4—942no—
599C2×C4—942no—
600C2×C4—942no—
601C2×C4—942no—
602C2×C4—942no—
603C2×C4—942no—
604C2×C4—942no—
605C2×C4—942no—
606C2×C4—942no—
607C2×C4—944no—
608C2×C4—944no—
609C2×C4—944no—
610C2×C4—942no—
611C2×C4—944no—
612C2×C4—944no—
613C2×C4—942no—
614C2×C4—944no—
615C2×C4—1882no—
616C2×C4—1881no—
617C2×C4—1882no—
618C2×C4—1881no—
619C2×C4—1882no—
620C2×C4—1882no—
621C2×C4—1882no—
622C2×C4—1882no—
623C2×C4—1881no—
624C2×C4—1881no—
625C2×C4—1882no—
626C2×C4—1882no—
627C2×C4C42×D4714yes—
628C2×C4C4⋊C4×D4714yes—
629C2×C4C2×Dic47⋊C418yes—
630C2×C4C2×Dic47⋊C414yes—
631C2×C4#1309398114yes—
632C2×C4C4×C22⋊D4714yes—
633C2×C4C4×C22⋊D4714yes—
634C2×C4C4×Dic9414yes—
635C2×C4C4×Dic9414yes—
636C22C2×C42×D4711yescharacteristic
637C22C2×C4⋊C4×D4711yescharacteristic
638C22C22×Dic47⋊C411yescharacteristic
639C22#117×D4711yescharacteristic
640C22C2×#1309398111yescharacteristic
641C22C4×D4×D4711yescharacteristic
642C22C4×D4×D4711yescharacteristic
643C22C2×C4×C22⋊D4711yescharacteristic
644C22C2×C4×C22⋊D4711yescharacteristic
645C22C4×Q8×D4711yescharacteristic
646C22C4×Q8×D4711yescharacteristic
647C22C2×C4×Dic9411yescharacteristic
648C22C2×C4×Dic9411yescharacteristic
649C22#1568959511yescharacteristic
650C22#1568959911yescharacteristic
651C22#1568960211yescharacteristic
652C22#1568960311yescharacteristic
653C22#1568960411yescharacteristic
654C22#1568960511yescharacteristic
655C22D4×C22⋊D4711yescharacteristic
656C22#1568977211yescharacteristic
657C22#1568977411yescharacteristic
658C22Q8×C22⋊D4711yescharacteristic
659C22D4×Dic9411yescharacteristic
660C22#1568979211yescharacteristic
661C22#1568979411yescharacteristic
662C22#1568982811yescharacteristic
663C22#1568983211yescharacteristic
664C22#1568983611yescharacteristic
665C22#1568984111yescharacteristic
666C22#1568984511yescharacteristic
667C22#1568984911yescharacteristic
668C22#1568985111yescharacteristic
669C22Q8×Dic9411yescharacteristic
670C22#1568985611yescharacteristic
671C4—28no—
672C4—24no—
673C4—42no—
674C4—44no—
675C4—478no—
676C4—944no—
677C4—944no—
678C4—1884no—
679C4—1882no—
680C4—1884no—
681C4C4×Dic47⋊C418yescomplemented
682C2C4×C4⋊C4×D4711yescharacteristic
683C2C2×C4×Dic47⋊C411yescharacteristic
684C2#2024574211yescharacteristic
685C2D4×Dic47⋊C411yescharacteristic
686C2C4⋊C4×C22⋊D4711yescharacteristic
687C2Q8×Dic47⋊C411yescharacteristic
688C2C4⋊C4×Dic9411yescharacteristic
689C2#2024633311yescharacteristic
690C2#2024633811yescharacteristic
691C2#2024634111yescharacteristic
692C2#2024634611yescharacteristic
693C2#2024644211yescharacteristic
694C2#2024644711yescharacteristic
695C2#2024645011yescharacteristic
696C2#2024647511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC2×C4×C4⋊C4×C47C2
socle, prime radical, cosocleC24×C47C24
hypercenterC2×C4×C4⋊C4D47
hypocenterC47C4⋊C42
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
22. #15688992C4semidirect
24. C4⋊C4×Dic47C4semidirect
26. C4×Dic47⋊C4C4semidirect
182. C4⋊C4×C47C4⋊C4semidirect
190. Dic47⋊C4C4⋊C4direct (N × H)
194. C4×Dic47C42semidirect
327. C4×C47C4×C4⋊C4semidirect
333. Dic47C4×C4⋊C4semidirect
389. C47C4⋊C42semidirect
537. C4⋊C4Dic47⋊C4direct (N × H)
681. C4C4×Dic47⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#156889922
C2×C4⋊C4×Dic472
C2×C4×Dic47⋊C42
#202416212
#202416192
#202416182
#202416172
Dic47⋊#952
C2×C4×C4⋊C4×C472
C4⋊C4247