Finite Group Databasebeta

← #26139074

Subgroups — #26139074

Order 12032.

2266 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic47C211yesmaximal, characteristic, complemented
2C2×#15689030C211yesmaximal, characteristic, complemented
3C2×#15688983C211yesmaximal, characteristic
4C2×C4×C22⋊Dic47C211yesmaximal, characteristic
5#20241641C212yesmaximal, complemented
6#20241633C212yesmaximal
7#20241625C212yesmaximal
8#20241620C212yesmaximal, complemented
9#20241617C211yesmaximal, characteristic, complemented
10#20241617C211yesmaximal, characteristic, complemented
11C22×C22⋊Q8×C47C211yesmaximal, characteristic
12C2×Q8×Dic47—24no—
13C2×Q8×Dic47—24no—
14C2×Q8×Dic47—24no—
15C22×C4⋊Dic47C2211yescharacteristic
16C22×C4⋊Dic47C2212yes—
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C22⋊Dic47C2211yescharacteristic
19C22×C22⋊Dic47C2212yes—
20C22×C22⋊Dic47C2211yescharacteristic
21C22×C4×Dic47C2212yes—
22C22×C4×Dic47C2211yescharacteristic
23C22×C4×Dic47C2211yescharacteristic
24#15689030—24no—
25#15688983—24no—
26C4×C22⋊Dic47—24no—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C23×Q8×C47C2211yescharacteristic
37C24×C4×C47C2211yescharacteristic
38C2×C22⋊Q8×C47—24no—
39C2×C22⋊Q8×C47—24no—
40C2×C22⋊Q8×C47C418yescomplemented
41C22×C4⋊C4×C47C2211yescharacteristic
42C22×C4⋊C4×C47C2212yes—
43C22×C22⋊C4×C47C2212yes—
44C23×Dic47C2312yes—
45C23×Dic47C2312yes—
46C23×Dic47C2311yescharacteristic
47C23×Dic47C2311yescharacteristic
48C23×Dic47C2311yescharacteristic
49C23×Dic47C2311yescharacteristic
50Q8×Dic47—232no—
51C2×C4⋊Dic47—24no—
52C2×C4⋊Dic47—22no—
53C2×C4⋊Dic47—22no—
54C2×C4⋊Dic47—24no—
55C2×C4⋊Dic47—24no—
56C2×C4⋊Dic47—22no—
57C2×C4⋊Dic47—22no—
58C2×C4⋊Dic47—22no—
59C2×C4⋊Dic47D414yes—
60C2×C22⋊Dic47—22no—
61C2×C22⋊Dic47—22no—
62C2×C22⋊Dic47—22no—
63C2×C22⋊Dic47—22no—
64C2×C22⋊Dic47—22no—
65C2×C22⋊Dic47—24no—
66C2×C22⋊Dic47—24no—
67C2×C22⋊Dic47—42no—
68C2×C22⋊Dic47Q814yescomplemented
69C2×C4×Dic47—24no—
70C2×C4×Dic47—22no—
71C2×C4×Dic47—22no—
72C2×C4×Dic47—24no—
73C2×C4×Dic47—24no—
74C2×C4×Dic47—22no—
75C2×C4×Dic47—22no—
76C2×C4×Dic47—22no—
77C2×C4×Dic47D414yes—
78C47⋊#95—24no—
79C47⋊#95—24no—
80C47⋊#95—22no—
81C47⋊#95—22no—
82C47⋊#95—24no—
83C47⋊#95—24no—
84C47⋊#95—24no—
85C47⋊#95—42no—
86C47⋊#95—42no—
87C25×C47C2311yescharacteristic
88C22×Q8×C47—22no—
89C22×Q8×C47—22no—
90C22×Q8×C47—22no—
91C22×Q8×C47—22no—
92C22×Q8×C47C2×C414yes—
93C22×Q8×C47D414yes—
94C22×Q8×C47D414yes—
95C23×C4×C47—22no—
96C23×C4×C47—22no—
97C23×C4×C47—22no—
98C23×C4×C47—22no—
99C23×C4×C47—22no—
100C23×C4×C47—22no—
101C23×C4×C47C2×C414yes—
102C23×C4×C47C2312yes—
103C23×C4×C47C2311yescharacteristic
104C23×C4×C47C2312yes—
105C23×C4×C47C2311yescharacteristic
106C22⋊Q8×C47—232no—
107C2×C4⋊C4×C47—22no—
108C2×C4⋊C4×C47—22no—
109C2×C4⋊C4×C47—24no—
110C2×C4⋊C4×C47—24no—
111C2×C4⋊C4×C47C2×C414yes—
112C2×C4⋊C4×C47C2×C418yes—
113C2×C22⋊C4×C47—24no—
114C2×C22⋊C4×C47—24no—
115C2×C22⋊C4×C47C2×C418yes—
116C24×C47—21no—
117C24×C47—21no—
118C24×C47—21no—
119C24×C47—21no—
120C24×C47—21no—
121C24×C47—21no—
122C24×C47—21no—
123C24×C47—21no—
124C24×C47—21no—
125C24×C47—21no—
126C24×C47—21no—
127C24×C47—21no—
128C24×C47C22×C412yes—
129C24×C47C2×Q812yes—
130C24×C47#4112yes—
131C24×C47C2411yescharacteristic
132C2×Q8×C47—28no—
133C2×Q8×C47—28no—
134C2×Q8×C47—28no—
135C2×Q8×C47—28no—
136C2×Q8×C47—28no—
137C2×Q8×C47—28no—
138C2×Q8×C47C22⋊C4116yescomplemented
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—28no—
156C22×C4×C47—28no—
157C22×C4×C47—28no—
158C22×C4×C47—44no—
159C22×C4×C47—44no—
160C22×C4×C47—44no—
161C22×C4×C47—44no—
162C22×C4×C47C22×C414yes—
163C22×C4×C47C22×C412yes—
164C22×C4×C47C22×C414yes—
165C22×C4×C47C22×C412yes—
166C22×C4×C47C2×D414yes—
167C22×C4×C47C2×D414yes—
168C22×C4×C47C2×D412yes—
169C22×C4×C47C2×D412yes—
170C22×C4×C47C2×D412yes—
171C22×C4×C47C2×D412yes—
172C22×C4×C47#4112yes—
173C22×C4×C47#4112yes—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—21no—
179C22×Dic47—21no—
180C22×Dic47—21no—
181C22×Dic47—21no—
182C22×Dic47—22no—
183C22×Dic47—21no—
184C22×Dic47—22no—
185C22×Dic47—21no—
186C22×Dic47—22no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C22×Dic47—21no—
190C22×Dic47—21no—
191C22×Dic47—21no—
192C22×Dic47—21no—
193C22×Dic47—22no—
194C22×Dic47—21no—
195C22×Dic47—21no—
196C22×Dic47—22no—
197C22×Dic47—21no—
198C22×Dic47—22no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47C2×D414yes—
210C22×Dic47C2×D412yes—
211C22×Dic47C2×D412yes—
212C22×Dic47C2×Q812yes—
213C22×Dic47C2×Q812yes—
214C22×Dic47#4112yes—
215C22×Dic47#4112yes—
216C4⋊C4×C47—28no—
217C4⋊C4×C47—216no—
218C22⋊C4×C47—216no—
219C22⋊Dic47—28no—
220C22⋊Dic47—28no—
221C22⋊Dic47—48no—
222C4⋊Dic47—216no—
223C4⋊Dic47—28no—
224C4⋊Dic47—44no—
225C4×Dic47—216no—
226C4×Dic47—28no—
227C4×Dic47—44no—
228C23×C47—22no—
229C23×C47—22no—
230C23×C47—22no—
231C23×C47—22no—
232C23×C47—22no—
233C23×C47—22no—
234C23×C47—22no—
235C23×C47—22no—
236C23×C47—22no—
237C23×C47—22no—
238C23×C47—22no—
239C23×C47—22no—
240C23×C47—22no—
241C23×C47—22no—
242C23×C47—22no—
243C23×C47—22no—
244C23×C47—22no—
245C23×C47—22no—
246C23×C47—41no—
247C23×C47—41no—
248C23×C47—41no—
249C23×C47—41no—
250C23×C47—41no—
251C23×C47—41no—
252C23×C47—41no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47C4×Q814yescomplemented
263C23×C47C23×C411yescharacteristic
264C23×C47C22×D411yescharacteristic
265C23×C47C22×D411yescharacteristic
266C23×C47C22×D411yescharacteristic
267C23×C47C22×D411yescharacteristic
268C23×C47C22×Q811yescharacteristic
269C23×C47C2×#4111yescharacteristic
270C23×C47C2×#4111yescharacteristic
271C23×C47C2×#4111yescharacteristic
272C23×C47C2×#4111yescharacteristic
273C23×C47C2×#4111yescharacteristic
274C23×C47H(5,𝔽2)11yescharacteristic
275C23×C472−1+411yescharacteristic
276C23×C472−1+411yescharacteristic
277C23×C472−1+411yescharacteristic
278Q8×C47—232no—
279C2×C4×C47—24no—
280C2×C4×C47—24no—
281C2×C4×C47—24no—
282C2×C4×C47—24no—
283C2×C4×C47—24no—
284C2×C4×C47—24no—
285C2×C4×C47—24no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—24no—
290C2×C4×C47—24no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47—416no—
300C2×C4×C47C2×C22⋊C418yes—
301C2×C4×C47C2×C22⋊C414yes—
302C2×C4×C47C4×D414yes—
303C2×C4×C47C4×D414yes—
304C2×C4×C47#12014yes—
305C2×C4×C47#12114yes—
306C2×C4×C47#12114yes—
307C2×C4×C47#12314yes—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
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—22no—
320C2×Dic47—24no—
321C2×Dic47—24no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—41no—
327C2×Dic47—41no—
328C2×Dic47—42no—
329C2×Dic47—41no—
330C2×Dic47—42no—
331C2×Dic47—41no—
332C2×Dic47—41no—
333C2×Dic47—41no—
334C2×Dic47—41no—
335C2×Dic47—42no—
336C2×Dic47—41no—
337C2×Dic47—42no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340C2×Dic47—41no—
341C2×Dic47—41no—
342C2×Dic47—42no—
343C2×Dic47—42no—
344C2×Dic47—42no—
345C2×Dic47—42no—
346C2×Dic47—42no—
347C2×Dic47—42no—
348C2×Dic47—42no—
349C2×Dic47C22⋊Q814yescomplemented
350#13969—471nomaximal, Sylow
351C22×C47—24no—
352C22×C47—24no—
353C22×C47—24no—
354C22×C47—42no—
355C22×C47—42no—
356C22×C47—42no—
357C22×C47—42no—
358C22×C47—42no—
359C22×C47—42no—
360C22×C47—42no—
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—42no—
364C22×C47—42no—
365C22×C47—42no—
366C22×C47C22×C22⋊C411yescharacteristic
367C22×C47C2×C4×D411yescharacteristic
368C22×C47C2×C4×D411yescharacteristic
369C22×C47C2×C4×Q811yescharacteristic
370C22×C47C4×#4111yescharacteristic
371C22×C47#51911yescharacteristic
372C22×C47#52011yescharacteristic
373C22×C47C2×#12011yescharacteristic
374C22×C47C2×#12111yescharacteristic
375C22×C47C2×#12111yescharacteristic
376C22×C47C2×C22⋊Q811yescharacteristic
377C22×C47C2×#12311yescharacteristic
378C22×C47#52511yescharacteristic
379C22×C47#52911yescharacteristic
380C22×C47#53311yescharacteristic
381C22×C47#53611yescharacteristic
382C22×C47#53711yescharacteristic
383C22×C47#54111yescharacteristic
384C22×C47#54211yescharacteristic
385C22×C47#54611yescharacteristic
386C22×C47#54711yescharacteristic
387C22×C47#54811yescharacteristic
388C22×C47#54811yescharacteristic
389C22×C47#54811yescharacteristic
390C22×C47#54811yescharacteristic
391C22×C47#54811yescharacteristic
392C22×C47D4×Q811yescharacteristic
393C22×C47D4×Q811yescharacteristic
394C22×C47D4×Q811yescharacteristic
395C22×C47#55011yescharacteristic
396C22×C47#55011yescharacteristic
397C22×C47#55211yescharacteristic
398C22×C47#55211yescharacteristic
399C22×C47#55411yescharacteristic
400C22×C47#55611yescharacteristic
401C4×C47—28no—
402C4×C47—44no—
403C4×C47—42no—
404C4×C47#38618yes—
405Dic47—24no—
406Dic47—42no—
407Dic47—44no—
408Dic47—42no—
409Dic47—42no—
410Dic47—82no—
411C22×C22⋊Q8D4711yescharacteristic
412C22×C4×Q8—471no—
413C2×#391—471no—
414C2×#380—471no—
415C2×C4×C22⋊C4—471no—
416#1441—472no—
417#1439—472no—
418#1437—472no—
419#1436—472no—
420C4⋊#95—471no—
421C4⋊#95—471no—
422C2×C47—44no—
423C2×C47C2×#38611yescharacteristic
424C2×C47C4×C22⋊Q811yescharacteristic
425C2×C47#232311yescharacteristic
426C2×C47Q8×C22⋊C411yescharacteristic
427C2×C47#234111yescharacteristic
428C2×C47#236011yescharacteristic
429C2×C47#236211yescharacteristic
430C2×C47#240711yescharacteristic
431C2×C47#240911yescharacteristic
432C2×C47#242111yescharacteristic
433C2×C47#242311yescharacteristic
434C2×C47#242611yescharacteristic
435C2×C47#242911yescharacteristic
436C2×C47#253611yescharacteristic
437C2×C47#253811yescharacteristic
438C23×Q8C2×D4711yescharacteristic
439C24×C4C2×D4711yescharacteristic
440C2×C22⋊Q8—24no—
441C2×C22⋊Q8—24no—
442C2×C22⋊Q8Dic4718yescomplemented
443C2×C4×Q8—944no—
444C2×C4×Q8—944no—
445C2×C4×Q8—944no—
446C22×C4⋊C4—471no—
447C22×C4⋊C4—472no—
448C22×C4⋊C4—471no—
449C22×C4⋊C4C2×D4711yescharacteristic
450C22×C4⋊C4C2×D4712yes—
451C22×C22⋊C4—471no—
452C22×C22⋊C4—471no—
453C22×C22⋊C4—472no—
454C22×C22⋊C4C2×D4712yes—
455C22×C42—471no—
456C22×C42—472no—
457C22×C42—471no—
458#391—944no—
459#380—944no—
460C4×C22⋊C4—944no—
461C2×#95—472no—
462C2×#95—472no—
463C2×#95—471no—
464C2×#95—472no—
465C2×#95—472no—
466C2×#95—472no—
467C2×#95—471no—
468C2×#95—472no—
469C2×#95—472no—
470C47#1396911yescharacteristic, complemented, Sylow
471C25C22×D4711yescharacteristic
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—22no—
475C22×Q8—22no—
476C22×Q8C2×Dic4714yes—
477C22×Q8C22⋊D4714yes—
478C22×Q8C22⋊D4714yes—
479C23×C4—22no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—22no—
485C23×C4—471no—
486C23×C4—471no—
487C23×C4—472no—
488C23×C4—471no—
489C23×C4—471no—
490C23×C4—472no—
491C23×C4C2×Dic4714yes—
492C23×C4C22×D4712yes—
493C23×C4C22×D4711yescharacteristic
494C23×C4C22×D4712yes—
495C23×C4C22×D4711yescharacteristic
496C22⋊Q8—232no—
497C4×Q8—9432no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—24no—
502C2×C4⋊C4—474no—
503C2×C4⋊C4—944no—
504C2×C4⋊C4—944no—
505C2×C4⋊C4—942no—
506C2×C4⋊C4—944no—
507C2×C4⋊C4—942no—
508C2×C4⋊C4—942no—
509C2×C4⋊C4—942no—
510C2×C4⋊C4—942no—
511C2×C4⋊C4C2×Dic4714yes—
512C2×C4⋊C4C2×Dic4718yes—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—474no—
516C2×C22⋊C4—942no—
517C2×C22⋊C4—942no—
518C2×C22⋊C4—942no—
519C2×C22⋊C4—942no—
520C2×C22⋊C4—942no—
521C2×C22⋊C4—944no—
522C2×C22⋊C4—944no—
523C2×C22⋊C4—1882no—
524C2×C22⋊C4C2×Dic4718yes—
525C2×C42—474no—
526C2×C42—944no—
527C2×C42—944no—
528C2×C42—942no—
529C2×C42—944no—
530C2×C42—942no—
531C2×C42—942no—
532C2×C42—942no—
533C2×C42—942no—
534#95—944no—
535#95—944no—
536#95—942no—
537#95—942no—
538#95—944no—
539#95—944no—
540#95—944no—
541#95—1882no—
542#95—1882no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—21no—
555C24Q8×D4712yes—
556C24#1062535412yes—
557C24C22×Dic4712yes—
558C24C23×D4711yescharacteristic
559C2×Q8—28no—
560C2×Q8—28no—
561C2×Q8—28no—
562C2×Q8—28no—
563C2×Q8—28no—
564C2×Q8—28no—
565C2×Q8C22⋊Dic47116yescomplemented
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—472no—
590C22×C4—472no—
591C22×C4—472no—
592C22×C4—472no—
593C22×C4—474no—
594C22×C4—472no—
595C22×C4—472no—
596C22×C4—941no—
597C22×C4—941no—
598C22×C4—941no—
599C22×C4—941no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—942no—
604C22×C4—941no—
605C22×C4—941no—
606C22×C4—942no—
607C22×C4—941no—
608C22×C4—942no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—941no—
612C22×C4—941no—
613C22×C4—942no—
614C22×C4—941no—
615C22×C4—941no—
616C22×C4—941no—
617C22×C4—941no—
618C22×C4—942no—
619C22×C4—941no—
620C22×C4—942no—
621C22×C4—941no—
622C22×C4—941no—
623C22×C4—941no—
624C22×C4—942no—
625C22×C4—942no—
626C22×C4—942no—
627C22×C4—942no—
628C22×C4—942no—
629C22×C4—942no—
630C22×C4—942no—
631C22×C4D4×D4712yes—
632C22×C4D4×D4712yes—
633C22×C4#1062535212yes—
634C22×C4#1062535212yes—
635C22×C4C22×Dic4714yes—
636C22×C4C22×Dic4712yes—
637C22×C4C22×Dic4714yes—
638C22×C4C22×Dic4712yes—
639C22×C4C2×C22⋊D4714yes—
640C22×C4C2×C22⋊D4714yes—
641C22×C4C2×C22⋊D4712yes—
642C22×C4C2×C22⋊D4712yes—
643C4⋊C4—28no—
644C4⋊C4—216no—
645C4⋊C4—9416no—
646C4⋊C4—948no—
647C4⋊C4—1884no—
648C22⋊C4—216no—
649C22⋊C4—948no—
650C22⋊C4—948no—
651C22⋊C4—1888no—
652C42—9416no—
653C42—948no—
654C42—1884no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23Q8×Dic4714yescomplemented
690C23C23×Dic4711yescharacteristic
691C23C2×D4×D4711yescharacteristic
692C23C2×D4×D4711yescharacteristic
693C23C22×C22⋊D4711yescharacteristic
694C23C22×C22⋊D4711yescharacteristic
695C23C2×Q8×D4711yescharacteristic
696C23#41×D4711yescharacteristic
697C23#41×D4711yescharacteristic
698C23C2×#1062535211yescharacteristic
699C23C2×#1062535211yescharacteristic
700C23C2×#1062535411yescharacteristic
701C23#1309407011yescharacteristic
702C23#1309407111yescharacteristic
703C23#1309407211yescharacteristic
704C23#1309407211yescharacteristic
705Q8—232no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—416no—
727C2×C4—474no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—944no—
735C2×C4—944no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—944no—
741C2×C4—942no—
742C2×C4—942no—
743C2×C4—942no—
744C2×C4—942no—
745C2×C4—942no—
746C2×C4—1882no—
747C2×C4—1882no—
748C2×C4—1882no—
749C2×C4—1882no—
750C2×C4—1882no—
751C2×C4—1882no—
752C2×C4—1882no—
753C2×C4—1881no—
754C2×C4—1881no—
755C2×C4—1882no—
756C2×C4—1881no—
757C2×C4—1881no—
758C2×C4—1882no—
759C2×C4—1881no—
760C2×C4—1881no—
761C2×C4—1881no—
762C2×C4—1881no—
763C2×C4—1881no—
764C2×C4—1881no—
765C2×C4—1882no—
766C2×C4—1881no—
767C2×C4—1882no—
768C2×C4—1881no—
769C2×C4C2×C22⋊Dic4718yes—
770C2×C4C2×C22⋊Dic4714yes—
771C2×C4D4×Dic4714yes—
772C2×C4D4×Dic4714yes—
773C2×C4#1309399214yes—
774C2×C4#1309399614yes—
775C2×C4#1309399614yes—
776C2×C4#1309400514yes—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22C22×C22⋊Dic4711yescharacteristic
793C22C2×D4×Dic4711yescharacteristic
794C22C2×D4×Dic4711yescharacteristic
795C22C2×Q8×Dic4711yescharacteristic
796C22#41×Dic4711yescharacteristic
797C22#1568960111yescharacteristic
798C22#1568960611yescharacteristic
799C22C2×#1309399211yescharacteristic
800C22C2×#1309399611yescharacteristic
801C22C2×#1309399611yescharacteristic
802C22C22⋊Q8×D4711yescharacteristic
803C22C2×#1309400511yescharacteristic
804C22#1568963611yescharacteristic
805C22#1568965911yescharacteristic
806C22#1568967511yescharacteristic
807C22#1568969611yescharacteristic
808C22#1568970311yescharacteristic
809C22#1568973311yescharacteristic
810C22#1568974611yescharacteristic
811C22#1568976411yescharacteristic
812C22#1568977511yescharacteristic
813C22#1568978011yescharacteristic
814C22#1568978011yescharacteristic
815C22#1568978311yescharacteristic
816C22#1568978411yescharacteristic
817C22#1568978411yescharacteristic
818C22#1568978611yescharacteristic
819C22Q8×C22⋊D4711yescharacteristic
820C22Q8×C22⋊D4711yescharacteristic
821C22#1568979211yescharacteristic
822C22#1568979211yescharacteristic
823C22#1568980711yescharacteristic
824C22#1568981511yescharacteristic
825C22#1568983111yescharacteristic
826C22#1568984411yescharacteristic
827C4—28no—
828C4—42no—
829C4—44no—
830C4—944no—
831C4—3762no—
832C4—1884no—
833C4—1882no—
834C4—1882no—
835C4—1882no—
836C4#1568900318yes—
837C2—44no—
838C2C2×#1568900311yescharacteristic
839C2C22⋊Q8×Dic4711yescharacteristic
840C2#2024607211yescharacteristic
841C2Q8×C22⋊Dic4711yescharacteristic
842C2#2024622911yescharacteristic
843C2#2024639711yescharacteristic
844C2#2024641911yescharacteristic
845C2#2024673511yescharacteristic
846C2#2024674911yescharacteristic
847C2#2024688711yescharacteristic
848C2#2024690911yescharacteristic
849C2#2024695611yescharacteristic
850C2#2024698911yescharacteristic
851C2#2024829511yescharacteristic
852C2#2024830711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC22×C22⋊Q8×C47C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC22×C22⋊Q8D47
hypocenterC47#13969
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic47C2semidirect
2. C2×#15689030C2semidirect
5. #20241641C2semidirect
8. #20241620C2semidirect
9. #20241617C2semidirect
10. #20241617C2semidirect
40. C2×C22⋊Q8×C47C4semidirect
68. C2×C22⋊Dic47Q8semidirect
138. C2×Q8×C47C22⋊C4semidirect
262. C23×C47C4×Q8semidirect
349. C2×Dic47C22⋊Q8semidirect
442. C2×C22⋊Q8Dic47semidirect
470. C47#13969semidirect
565. C2×Q8C22⋊Dic47semidirect
689. C23Q8×Dic47semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic472
C2×#156890302
C2×#156889832
C2×C4×C22⋊Dic472
#202416412
#202416332
#202416252
#202416202
#202416172
C22×C22⋊Q8×C472
#1396947