Finite Group Databasebeta

← C22⋊C4×Dic47⋊C4 #26137696

Subgroups — C22⋊C4×Dic47⋊C4 #26137696

Order 12032.

2574 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic47⋊C4C211yesmaximal, characteristic
2C2×#15688981C211yesmaximal, characteristic
3C2×C4×Dic47⋊C4C212yesmaximal, complemented
4C2×C22⋊C4×Dic47C211yesmaximal, characteristic
5C2×C22⋊C4×Dic47C211yesmaximal, characteristic
6#20241621C212yesmaximal, complemented
7#20241619C212yesmaximal, complemented
8Dic47⋊#95C212yesmaximal, complemented
9#20241611C211yesmaximal, characteristic
10#20241610C211yesmaximal, characteristic
11C2×C4×C22⋊C4×C47C211yesmaximal, characteristic
12C24×Dic47C2211yescharacteristic
13C24×Dic47C2211yescharacteristic
14C22×Dic47⋊C4—28no—
15C22×Dic47⋊C4C418yescomplemented
16C22×Dic47⋊C4C2211yescharacteristic
17C22×Dic47⋊C4C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2212yes—
20C22×Dic47⋊C4C2211yescharacteristic
21C22×C22⋊Dic47C2211yescharacteristic
22C22×C22⋊Dic47C2211yescharacteristic
23C22×C4×Dic47C2212yes—
24C22×C4×Dic47C2212yes—
25#15688981C418yescomplemented
26C4×Dic47⋊C4—28no—
27C22⋊C4×Dic47—24no—
28C22⋊C4×Dic47C418yescomplemented
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C24×C4×C47C2211yescharacteristic
37C22×C22⋊C4×C47C2211yescharacteristic
38C22×C22⋊C4×C47C2211yescharacteristic
39C22×C42×C47C2212yes—
40C4×C22⋊C4×C47—24no—
41C2×#95×C47C2212yes—
42C23×Dic47—24no—
43C23×Dic47—24no—
44C23×Dic47—22no—
45C23×Dic47—22no—
46C23×Dic47—24no—
47C23×Dic47—42no—
48C23×Dic47C2×C414yes—
49C23×Dic47C2×C414yes—
50C23×Dic47C2×C414yes—
51C23×Dic47C2×C414yes—
52C23×Dic47C2312yes—
53C23×Dic47C2312yes—
54C23×Dic47C2311yescharacteristic
55C23×Dic47C2311yescharacteristic
56C23×Dic47C2311yescharacteristic
57C23×Dic47C2311yescharacteristic
58C2×Dic47⋊C4—24no—
59C2×Dic47⋊C4—24no—
60C2×Dic47⋊C4—24no—
61C2×Dic47⋊C4—24no—
62C2×Dic47⋊C4—24no—
63C2×Dic47⋊C4—232no—
64C2×Dic47⋊C4C2×C414yes—
65C2×Dic47⋊C4C2×C414yes—
66C2×Dic47⋊C4C2×C414yes—
67C2×Dic47⋊C4C2×C414yes—
68C2×Dic47⋊C4C2×C418yescomplemented
69C2×Dic47⋊C4D418yes—
70C2×C22⋊Dic47—22no—
71C2×C22⋊Dic47—22no—
72C2×C22⋊Dic47—22no—
73C2×C22⋊Dic47—22no—
74C2×C22⋊Dic47C2×C414yes—
75C2×C22⋊Dic47C2×C414yes—
76C2×C4×Dic47—24no—
77C2×C4×Dic47—24no—
78C2×C4×Dic47—24no—
79C2×C4×Dic47—24no—
80C2×C4×Dic47—42no—
81C2×C4×Dic47C2×C418yescomplemented
82C47⋊#95—24no—
83C47⋊#95—24no—
84C47⋊#95—24no—
85C47⋊#95—42no—
86C47⋊#95—42no—
87C47⋊#95C2×C418yescomplemented
88C47⋊#95C2×C418yescomplemented
89C25×C47C2311yescharacteristic
90C23×C4×C47—22no—
91C23×C4×C47—22no—
92C23×C4×C47—24no—
93C23×C4×C47—42no—
94C23×C4×C47C2×C414yes—
95C23×C4×C47C2312yes—
96C23×C4×C47C2311yescharacteristic
97C23×C4×C47C2311yescharacteristic
98C23×C4×C47C2312yes—
99C2×C22⋊C4×C47—22no—
100C2×C22⋊C4×C47—22no—
101C2×C22⋊C4×C47C2×C414yes—
102C2×C22⋊C4×C47C2×C414yes—
103C2×C22⋊C4×C47D414yes—
104C2×C22⋊C4×C47Q814yes—
105C2×C42×C47—24no—
106C2×C42×C47—24no—
107C2×C42×C47—42no—
108#95×C47—24no—
109C24×C47—22no—
110C24×C47—22no—
111C24×C47—22no—
112C24×C47—22no—
113C24×C47C22×C412yes—
114C24×C47C22×C412yes—
115C24×C47C22×C412yes—
116C24×C47C2×D412yes—
117C24×C47C2×Q812yes—
118C24×C47#4112yes—
119C24×C47#4112yes—
120C24×C47C2411yescharacteristic
121C22×C4×C47—21no—
122C22×C4×C47—22no—
123C22×C4×C47—21no—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—28no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—21no—
133C22×C4×C47—22no—
134C22×C4×C47—21no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—28no—
140C22×C4×C47—44no—
141C22×C4×C47—48no—
142C22×C4×C47—48no—
143C22×C4×C47C22×C414yes—
144C22×C4×C47C22×C412yes—
145C22×C4×C47C22×C412yes—
146C22×C4×C47C22×C414yes—
147C22×C4×C47C2×D414yes—
148C22×C4×C47C2×D414yes—
149C22×C4×C47C2×Q814yes—
150C22×Dic47—21no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—21no—
154C22×Dic47—22no—
155C22×Dic47—28no—
156C22×Dic47—28no—
157C22×Dic47—216no—
158C22×Dic47—216no—
159C22×Dic47—28no—
160C22×Dic47—22no—
161C22×Dic47—21no—
162C22×Dic47—22no—
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—21no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—28no—
177C22×Dic47—44no—
178C22×Dic47—48no—
179C22×Dic47—48no—
180C22×Dic47C42116yescomplemented
181C22×Dic47C22×C414yes—
182C22×Dic47C22×C414yes—
183C22×Dic47C22×C412yes—
184C22×Dic47C22×C412yes—
185C22×Dic47C22×C412yes—
186C22×Dic47C22×C412yes—
187C22×Dic47C22×C412yes—
188C22×Dic47C22×C412yes—
189C22×Dic47C22×C412yes—
190C22×Dic47C22×C412yes—
191C22×Dic47C2×D414yes—
192C22×Dic47C2×D414yes—
193C22×Dic47#4114yes—
194C22⋊C4×C47—28no—
195C22⋊C4×C47C4⋊C4116yescomplemented
196C42×C47—48no—
197C22⋊Dic47—28no—
198C22⋊Dic47—28no—
199Dic47⋊C4—28no—
200Dic47⋊C4—28no—
201Dic47⋊C4—28no—
202Dic47⋊C4—216no—
203Dic47⋊C4C22⋊C4116yesdirect product factor
204C4×Dic47—216no—
205C4×Dic47—48no—
206C23×C47—22no—
207C23×C47—22no—
208C23×C47—24no—
209C23×C47—24no—
210C23×C47—22no—
211C23×C47—22no—
212C23×C47—24no—
213C23×C47—24no—
214C23×C47—24no—
215C23×C47—24no—
216C23×C47—24no—
217C23×C47—24no—
218C23×C47—24no—
219C23×C47—24no—
220C23×C47—24no—
221C23×C47—24no—
222C23×C47C2×C4214yes—
223C23×C47C2×C4⋊C414yes—
224C23×C47#11714yes—
225C23×C47C4×D414yes—
226C23×C47C4×D414yes—
227C23×C47C4×Q814yes—
228C23×C47C4×Q814yes—
229C23×C47C23×C411yescharacteristic
230C23×C47C23×C411yescharacteristic
231C23×C47C23×C411yescharacteristic
232C23×C47C22×D412yes—
233C23×C47C22×D411yescharacteristic
234C23×C47C22×Q811yescharacteristic
235C23×C47C2×#4112yes—
236C23×C47C2×#4111yescharacteristic
237C23×C47C2×#4111yescharacteristic
238C23×C47H(5,𝔽2)12yes—
239C23×C472−1+412yes—
240C2×C4×C47—24no—
241C2×C4×C47—22no—
242C2×C4×C47—22no—
243C2×C4×C47—24no—
244C2×C4×C47—24no—
245C2×C4×C47—24no—
246C2×C4×C47—24no—
247C2×C4×C47—24no—
248C2×C4×C47—24no—
249C2×C4×C47—24no—
250C2×C4×C47—22no—
251C2×C4×C47—24no—
252C2×C4×C47—24no—
253C2×C4×C47—22no—
254C2×C4×C47—22no—
255C2×C4×C47—24no—
256C2×C4×C47—416no—
257C2×C4×C47—42no—
258C2×C4×C47—42no—
259C2×C4×C47—42no—
260C2×C4×C47—42no—
261C2×C4×C47—42no—
262C2×C4×C47—42no—
263C2×C4×C47C2×C22⋊C414yes—
264C2×C4×C47C2×C4⋊C418yescomplemented
265C2×Dic47—22no—
266C2×Dic47—22no—
267C2×Dic47—24no—
268C2×Dic47—24no—
269C2×Dic47—22no—
270C2×Dic47—22no—
271C2×Dic47—24no—
272C2×Dic47—24no—
273C2×Dic47—232no—
274C2×Dic47—22no—
275C2×Dic47—24no—
276C2×Dic47—24no—
277C2×Dic47—24no—
278C2×Dic47—24no—
279C2×Dic47—22no—
280C2×Dic47—22no—
281C2×Dic47—24no—
282C2×Dic47—24no—
283C2×Dic47—416no—
284C2×Dic47—42no—
285C2×Dic47—42no—
286C2×Dic47—42no—
287C2×Dic47—42no—
288C2×Dic47—42no—
289C2×Dic47—42no—
290C2×Dic47—42no—
291C2×Dic47—42no—
292C2×Dic47—42no—
293C2×Dic47—42no—
294C2×Dic47C2×C4214yes—
295C2×Dic47C2×C4214yes—
296C2×Dic47C2×C22⋊C414yes—
297C2×Dic47C2×C22⋊C414yes—
298C2×Dic47#11714yes—
299C2×Dic47C4×D418yes—
300C2×Dic47C4×D418yes—
301C22⋊C4×C4⋊C4—471nomaximal, Sylow
302C22×C47—24no—
303C22×C47—24no—
304C22×C47—24no—
305C22×C47—24no—
306C22×C47—28no—
307C22×C47—28no—
308C22×C47—28no—
309C22×C47—28no—
310C22×C47—24no—
311C22×C47—24no—
312C22×C47C4×C4⋊C418yescomplemented
313C22×C47C22×C4211yescharacteristic
314C22×C47C22×C22⋊C411yescharacteristic
315C22×C47C22×C4⋊C411yescharacteristic
316C22×C47C2×#11711yescharacteristic
317C22×C47C2×#11711yescharacteristic
318C22×C47C2×C4×D412yes—
319C22×C47C2×C4×D412yes—
320C22×C47C2×C4×D411yescharacteristic
321C22×C47C2×C4×D411yescharacteristic
322C22×C47C2×C4×Q811yescharacteristic
323C22×C47C2×C4×Q811yescharacteristic
324C22×C47#51811yescharacteristic
325C22×C47#51911yescharacteristic
326C22×C47#52012yes—
327C22×C47#52012yes—
328C22×C47D4212yes—
329C22×C47#54612yes—
330C22×C47#54712yes—
331C22×C47#54812yes—
332C22×C47D4×Q812yes—
333C22×C47#55212yes—
334C22×C47#55312yes—
335C22×C47#55412yes—
336C4×C47—24no—
337C4×C47—28no—
338C4×C47—42no—
339C4×C47—44no—
340Dic47—24no—
341Dic47—24no—
342Dic47—42no—
343Dic47—44no—
344Dic47—44no—
345Dic47C4×C22⋊C418yescomplemented
346C23×C4⋊C4—471no—
347C2×#380—471no—
348C2×C4×C4⋊C4—472no—
349C2×C4×C22⋊C4—471no—
350C2×C4×C22⋊C4—471no—
351C2×C4×C22⋊C4D4711yescharacteristic
352#1436—472no—
353#1436—472no—
354C4⋊#95—472no—
355C22⋊#95—471no—
356C22⋊#95—471no—
357C2×C47—28no—
358C2×C47C2×C4×C22⋊C411yescharacteristic
359C2×C47C2×C4×C4⋊C411yescharacteristic
360C2×C47#227411yescharacteristic
361C2×C47D4×C22⋊C411yescharacteristic
362C2×C47Q8×C22⋊C411yescharacteristic
363C2×C47#234411yescharacteristic
364C2×C47#234511yescharacteristic
365C2×C47D4×C4⋊C412yes—
366C2×C47#235212yes—
367C2×C47#236012yes—
368C2×C47#236112yes—
369C24×C4—471no—
370C24×C4—471no—
371C24×C4C2×D4711yescharacteristic
372C22×C4⋊C4—471no—
373C22×C4⋊C4—478no—
374C22×C4⋊C4—471no—
375C22×C4⋊C4—471no—
376C22×C4⋊C4—471no—
377C22×C4⋊C4—472no—
378C22×C4⋊C4—948no—
379C22×C22⋊C4—471no—
380C22×C22⋊C4—471no—
381C22×C22⋊C4C2×D4711yescharacteristic
382C22×C22⋊C4C2×D4711yescharacteristic
383C22×C42—472no—
384C22×C42—472no—
385C22×C42C2×D4712yes—
386#380—478no—
387C4×C4⋊C4—948no—
388C4×C22⋊C4—24no—
389C4×C22⋊C4—478no—
390C4×C22⋊C4—944no—
391C2×#95—472no—
392C2×#95—472no—
393C2×#95—472no—
394C2×#95—472no—
395C2×#95—472no—
396C2×#95—472no—
397C2×#95—472no—
398C2×#95C2×D4712yes—
399C47C22⋊C4×C4⋊C411yescharacteristic, complemented, Sylow
400C25C22×D4711yescharacteristic
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—24no—
404C23×C4—42no—
405C23×C4—471no—
406C23×C4—474no—
407C23×C4—474no—
408C23×C4—474no—
409C23×C4—471no—
410C23×C4—471no—
411C23×C4—472no—
412C23×C4—472no—
413C23×C4—471no—
414C23×C4—474no—
415C23×C4—944no—
416C23×C4—944no—
417C23×C4—944no—
418C23×C4—942no—
419C23×C4—942no—
420C23×C4—1882no—
421C23×C4C4×D4714yes—
422C23×C4C22×D4712yes—
423C23×C4C22×D4711yescharacteristic
424C23×C4C22×D4712yes—
425C23×C4C22×D4711yescharacteristic
426C2×C4⋊C4—474no—
427C2×C4⋊C4—478no—
428C2×C4⋊C4—474no—
429C2×C4⋊C4—474no—
430C2×C4⋊C4—474no—
431C2×C4⋊C4—478no—
432C2×C4⋊C4—9432no—
433C2×C4⋊C4—944no—
434C2×C4⋊C4—944no—
435C2×C4⋊C4—944no—
436C2×C4⋊C4—944no—
437C2×C4⋊C4—944no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—474no—
441C2×C22⋊C4—474no—
442C2×C22⋊C4—942no—
443C2×C22⋊C4—942no—
444C2×C22⋊C4—942no—
445C2×C22⋊C4—942no—
446C2×C22⋊C4Dic9414yes—
447C2×C22⋊C4C4×D4714yes—
448C2×C22⋊C4C4×D4714yes—
449C2×C22⋊C4C22⋊D4714yes—
450C2×C42—24no—
451C2×C42—24no—
452C2×C42—42no—
453C2×C42—478no—
454C2×C42—944no—
455C2×C42—944no—
456C2×C42—944no—
457C2×C42—944no—
458C2×C42—1882no—
459#95—24no—
460#95—478no—
461#95—478no—
462#95—944no—
463#95—944no—
464#95—944no—
465#95—1882no—
466#95—1882no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24C2×Dic9412yes—
472C24C2×C4×D4712yes—
473C24C2×C4×D4712yes—
474C24C2×C4×D4712yes—
475C24#1062535012yes—
476C24#1062535012yes—
477C24C2×C22⋊D4712yes—
478C24C23×D4711yescharacteristic
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—28no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—28no—
498C22×C4—44no—
499C22×C4—48no—
500C22×C4—48no—
501C22×C4—472no—
502C22×C4—472no—
503C22×C4—472no—
504C22×C4—474no—
505C22×C4—474no—
506C22×C4—4716no—
507C22×C4—472no—
508C22×C4—472no—
509C22×C4—472no—
510C22×C4—472no—
511C22×C4—474no—
512C22×C4—474no—
513C22×C4—474no—
514C22×C4—472no—
515C22×C4—948no—
516C22×C4—948no—
517C22×C4—9416no—
518C22×C4—9416no—
519C22×C4—948no—
520C22×C4—942no—
521C22×C4—941no—
522C22×C4—942no—
523C22×C4—941no—
524C22×C4—942no—
525C22×C4—948no—
526C22×C4—942no—
527C22×C4—942no—
528C22×C4—942no—
529C22×C4—941no—
530C22×C4—942no—
531C22×C4—942no—
532C22×C4—942no—
533C22×C4—942no—
534C22×C4—942no—
535C22×C4—942no—
536C22×C4—941no—
537C22×C4—942no—
538C22×C4—942no—
539C22×C4—942no—
540C22×C4—942no—
541C22×C4—942no—
542C22×C4—1884no—
543C22×C4—1888no—
544C22×C4—1888no—
545C22×C4C2×Dic9414yes—
546C22×C4C2×C4×D4714yes—
547C22×C4C2×C4×D4712yes—
548C22×C4C2×C4×D4712yes—
549C22×C4C2×C4×D4714yes—
550C22×C4D4×D4714yes—
551C22×C4C2×C22⋊D4714yes—
552C4⋊C4—4716no—
553C4⋊C4—9416no—
554C4⋊C4—948no—
555C4⋊C4—948no—
556C4⋊C4—948no—
557C22⋊C4—28no—
558C22⋊C4—948no—
559C22⋊C4—948no—
560C22⋊C4Dic47⋊C4116yesdirect product factor
561C42—48no—
562C42—9416no—
563C42—1888no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—22no—
572C23—22no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—22no—
577C23—22no—
578C23—24no—
579C23—24no—
580C23C42×D4714yes—
581C23C2×Dic47⋊C414yes—
582C23#1309398114yes—
583C23C4×C22⋊D4714yes—
584C23C4×C22⋊D4714yes—
585C23C4×Dic9414yes—
586C23C4×Dic9414yes—
587C23C22×C4×D4711yescharacteristic
588C23C22×C4×D4711yescharacteristic
589C23C22×C4×D4711yescharacteristic
590C23C2×D4×D4712yes—
591C23C22×C22⋊D4711yescharacteristic
592C23C22×Dic9411yescharacteristic
593C23#41×D4712yes—
594C23C2×#1062535011yescharacteristic
595C23C2×#1062535011yescharacteristic
596C23#1309406912yes—
597C23#1309407112yes—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—22no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—24no—
614C2×C4—416no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—474no—
622C2×C4—474no—
623C2×C4—474no—
624C2×C4—478no—
625C2×C4—478no—
626C2×C4—474no—
627C2×C4—474no—
628C2×C4—9432no—
629C2×C4—944no—
630C2×C4—944no—
631C2×C4—942no—
632C2×C4—942no—
633C2×C4—944no—
634C2×C4—944no—
635C2×C4—942no—
636C2×C4—942no—
637C2×C4—942no—
638C2×C4—944no—
639C2×C4—944no—
640C2×C4—944no—
641C2×C4—944no—
642C2×C4—942no—
643C2×C4—942no—
644C2×C4—944no—
645C2×C4—944no—
646C2×C4—18816no—
647C2×C4—1882no—
648C2×C4—1882no—
649C2×C4—1882no—
650C2×C4—1882no—
651C2×C4—1882no—
652C2×C4—1882no—
653C2×C4—1882no—
654C2×C4—1882no—
655C2×C4—1882no—
656C2×C4—1882no—
657C2×C4C22⋊C4×D4714yes—
658C2×C4C2×Dic47⋊C418yescomplemented
659C22—28no—
660C22—28no—
661C22—28no—
662C22—28no—
663C22—24no—
664C22—24no—
665C22—24no—
666C22—24no—
667C22—24no—
668C22—24no—
669C22C4×Dic47⋊C418yescomplemented
670C22C2×C42×D4711yescharacteristic
671C22C2×C22⋊C4×D4711yescharacteristic
672C22C22×Dic47⋊C411yescharacteristic
673C22#117×D4711yescharacteristic
674C22C2×#1309398111yescharacteristic
675C22C4×D4×D4712yes—
676C22C4×D4×D4712yes—
677C22C2×C4×C22⋊D4711yescharacteristic
678C22C2×C4×C22⋊D4711yescharacteristic
679C22C2×C4×Dic9411yescharacteristic
680C22C2×C4×Dic9411yescharacteristic
681C22#1568959611yescharacteristic
682C22#1568960011yescharacteristic
683C22#1568960212yes—
684C22#1568960212yes—
685C22D4×C22⋊D4712yes—
686C22#1568976312yes—
687C22#1568977212yes—
688C22#1568978212yes—
689C22D4×Dic9412yes—
690C22#1568980612yes—
691C22#1568982212yes—
692C22#1568983212yes—
693C4—28no—
694C4—24no—
695C4—44no—
696C4—42no—
697C4—478no—
698C4—944no—
699C4—944no—
700C4—1884no—
701C4—1884no—
702C4—1882no—
703C2—28no—
704C2C4×C22⋊C4×D4711yescharacteristic
705C2C2×C4×Dic47⋊C411yescharacteristic
706C2#2024574311yescharacteristic
707C2C22⋊C4×C22⋊D4711yescharacteristic
708C2C22⋊C4×Dic9411yescharacteristic
709C2#2024625811yescharacteristic
710C2#2024626611yescharacteristic
711C2D4×Dic47⋊C412yes—
712C2#2024631112yes—
713C2#2024639412yes—
714C2#2024640512yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC2×C4×C22⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×C4×C22⋊C4D47
hypocenterC47C22⋊C4×C4⋊C4
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
6. #20241621C2semidirect
7. #20241619C2semidirect
8. Dic47⋊#95C2semidirect
15. C22×Dic47⋊C4C4semidirect
25. #15688981C4semidirect
28. C22⋊C4×Dic47C4semidirect
68. C2×Dic47⋊C4C2×C4semidirect
81. C2×C4×Dic47C2×C4semidirect
87. C47⋊#95C2×C4semidirect
88. C47⋊#95C2×C4semidirect
180. C22×Dic47C42semidirect
195. C22⋊C4×C47C4⋊C4semidirect
203. Dic47⋊C4C22⋊C4direct (N × H)
264. C2×C4×C47C2×C4⋊C4semidirect
312. C22×C47C4×C4⋊C4semidirect
345. Dic47C4×C22⋊C4semidirect
399. C47C22⋊C4×C4⋊C4semidirect
560. C22⋊C4Dic47⋊C4direct (N × H)
658. C2×C4C2×Dic47⋊C4semidirect
669. C22C4×Dic47⋊C4semidirect

Maximal subgroups

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

subgroupindex
C23×Dic47⋊C42
C2×#156889812
C2×C4×Dic47⋊C42
C2×C22⋊C4×Dic472
#202416212
#202416192
Dic47⋊#952
#202416112
#202416102
C2×C4×C22⋊C4×C472
C22⋊C4×C4⋊C447