Finite Group Databasebeta

← #26140081

Subgroups — #26140081

Order 12032.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689030C211yesmaximal, characteristic, complemented
2C2×#15688998C211yesmaximal, characteristic
3C2×C22⋊C4×Dic47C211yesmaximal, characteristic
4C22×C47⋊#95C211yesmaximal, characteristic
5#20241659C211yesmaximal, characteristic, complemented
6#20241656C211yesmaximal, characteristic, complemented
7#20241641C211yesmaximal, characteristic, complemented
8#20241641C211yesmaximal, characteristic, complemented
9#20241620C211yesmaximal, characteristic, complemented
10#20241620C211yesmaximal, characteristic, complemented
11#20241617C211yesmaximal, characteristic, complemented
12#20241611C211yesmaximal, characteristic
13#20241610C211yesmaximal, characteristic
14#20241610C211yesmaximal, characteristic
15C22×C22⋊Q8×C47C211yesmaximal, characteristic
16C24×Dic47C2211yescharacteristic
17C24×Dic47C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20C22×C22⋊Dic47C2211yescharacteristic
21C22×C22⋊Dic47C2211yescharacteristic
22C22×C4×Dic47C2211yescharacteristic
23C22×C4×Dic47C2211yescharacteristic
24#15689030—24no—
25#15688998—24no—
26C22⋊C4×Dic47—24no—
27C2×C47⋊#95—24no—
28C2×C47⋊#95C2211yescharacteristic
29C2×C47⋊#95C2211yescharacteristic
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2211yescharacteristic
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
48C23×Q8×C47C2211yescharacteristic
49C24×C4×C47C2211yescharacteristic
50C2×C22⋊Q8×C47—24no—
51C2×C22⋊Q8×C47—24no—
52C2×C22⋊Q8×C47C418yescomplemented
53C22×C4⋊C4×C47C2211yescharacteristic
54C22×C4⋊C4×C47C2211yescharacteristic
55C22×C4⋊C4×C47C2211yescharacteristic
56C22×C22⋊C4×C47C2211yescharacteristic
57C22×C22⋊C4×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—22no—
67C23×Dic47—41no—
68C23×Dic47—41no—
69C23×Dic47—41no—
70C23×Dic47—41no—
71C23×Dic47Q814yescomplemented
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C2×C4⋊Dic47—22no—
81C2×C4⋊Dic47—22no—
82C2×C4⋊Dic47—22no—
83C2×C4⋊Dic47—22no—
84C2×C4⋊Dic47—41no—
85C2×C4⋊Dic47—41no—
86C2×C22⋊Dic47—22no—
87C2×C22⋊Dic47—22no—
88C2×C22⋊Dic47—22no—
89C2×C22⋊Dic47—22no—
90C2×C22⋊Dic47—22no—
91C2×C22⋊Dic47Q814yescomplemented
92C2×C4×Dic47—22no—
93C2×C4×Dic47—22no—
94C2×C4×Dic47—22no—
95C2×C4×Dic47—22no—
96C2×C4×Dic47—41no—
97C2×C4×Dic47—41no—
98C47⋊#95—22no—
99C47⋊#95—22no—
100C47⋊#95—22no—
101C47⋊#95—22no—
102C47⋊#95—22no—
103C47⋊#95—22no—
104C47⋊#95—22no—
105C47⋊#95—22no—
106C47⋊#95—22no—
107C47⋊#95—22no—
108C47⋊#95—22no—
109C47⋊#95—22no—
110C47⋊#95—22no—
111C47⋊#95—41no—
112C47⋊#95—41no—
113C47⋊#95—41no—
114C47⋊#95—41no—
115C47⋊#95—41no—
116C47⋊#95—41no—
117C47⋊#95D414yes—
118C25×C47C2311yescharacteristic
119C22×Q8×C47—22no—
120C22×Q8×C47—22no—
121C22×Q8×C47—22no—
122C22×Q8×C47—22no—
123C22×Q8×C47—41no—
124C22×Q8×C47—41no—
125C22×Q8×C47C2×C414yescomplemented
126C23×C4×C47—22no—
127C23×C4×C47—22no—
128C23×C4×C47—22no—
129C23×C4×C47—22no—
130C23×C4×C47—41no—
131C23×C4×C47—41no—
132C23×C4×C47C2×C414yes—
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2311yescharacteristic
139C22⋊Q8×C47—232no—
140C2×C4⋊C4×C47—22no—
141C2×C4⋊C4×C47—22no—
142C2×C4⋊C4×C47—22no—
143C2×C4⋊C4×C47—22no—
144C2×C4⋊C4×C47—22no—
145C2×C4⋊C4×C47—22no—
146C2×C4⋊C4×C47C2×C414yescomplemented
147C2×C4⋊C4×C47C2×C414yescomplemented
148C2×C4⋊C4×C47C2×C414yescomplemented
149C2×C22⋊C4×C47—22no—
150C2×C22⋊C4×C47—22no—
151C2×C22⋊C4×C47C2×C414yes—
152C2×C22⋊C4×C47C2×C414yes—
153C2×C22⋊C4×C47D414yes—
154C2×C22⋊C4×C47D414yes—
155C24×C47—21no—
156C24×C47—21no—
157C24×C47—21no—
158C24×C47—21no—
159C24×C47—21no—
160C24×C47—21no—
161C24×C47—21no—
162C24×C47—21no—
163C24×C47C22×C412yes—
164C24×C47C2×D412yes—
165C24×C47C2×D412yes—
166C24×C47C2×Q812yes—
167C24×C47C2×Q812yes—
168C24×C47#4112yes—
169C24×C47#4112yes—
170C24×C47C2411yescharacteristic
171C2×Q8×C47—28no—
172C2×Q8×C47—28no—
173C2×Q8×C47—44no—
174C2×Q8×C47—44no—
175C2×Q8×C47—44no—
176C2×Q8×C47—44no—
177C2×Q8×C47—44no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
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—28no—
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—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—28no—
210C22×C4×C47—44no—
211C22×C4×C47—44no—
212C22×C4×C47—44no—
213C22×C4×C47—44no—
214C22×C4×C47—44no—
215C22×C4×C47C22×C412yes—
216C22×C4×C47C22×C412yes—
217C22×C4×C47C22×C412yes—
218C22×C4×C47C22×C412yes—
219C22×C4×C47C22×C412yes—
220C22×C4×C47C22×C412yes—
221C22×C4×C47C2×D412yes—
222C22×C4×C47C2×D412yes—
223C22×C4×C47C2×D412yes—
224C22×C4×C47C2×D412yes—
225C22×C4×C47C2×D412yes—
226C22×C4×C47#4112yes—
227C22×Dic47—21no—
228C22×Dic47—21no—
229C22×Dic47—21no—
230C22×Dic47—21no—
231C22×Dic47—28no—
232C22×Dic47—28no—
233C22×Dic47—21no—
234C22×Dic47—21no—
235C22×Dic47—21no—
236C22×Dic47—21no—
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—21no—
262C22×Dic47—21no—
263C22×Dic47—28no—
264C22×Dic47—21no—
265C22×Dic47—21no—
266C22×Dic47—21no—
267C22×Dic47—21no—
268C22×Dic47—21no—
269C22×Dic47—21no—
270C22×Dic47—21no—
271C22×Dic47—21no—
272C22×Dic47—21no—
273C22×Dic47—21no—
274C22×Dic47—21no—
275C22×Dic47—21no—
276C22×Dic47—21no—
277C22×Dic47—21no—
278C22×Dic47—44no—
279C22×Dic47—44no—
280C22×Dic47—44no—
281C22×Dic47—44no—
282C22×Dic47—44no—
283C22×Dic47—44no—
284C22×Dic47—44no—
285C22×Dic47—44no—
286C22×Dic47—44no—
287C22×Dic47—44no—
288C22×Dic47—44no—
289C22×Dic47C2×D412yes—
290C22×Dic47C2×D412yes—
291C22×Dic47C2×Q812yes—
292C22×Dic47C2×Q812yes—
293C22×Dic47C2×Q812yes—
294C22×Dic47C2×Q812yes—
295C22×Dic47#4112yes—
296C22×Dic47#4112yes—
297C4⋊C4×C47—28no—
298C4⋊C4×C47—28no—
299C4⋊C4×C47—28no—
300C22⋊C4×C47—28no—
301C22⋊C4×C47C22⋊C4116yes—
302C22⋊Dic47—28no—
303C22⋊Dic47—44no—
304C4⋊Dic47—44no—
305C4⋊Dic47—44no—
306C4×Dic47—44no—
307C4×Dic47—44no—
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×C47—22no—
332C23×C47—22no—
333C23×C47—22no—
334C23×C47—22no—
335C23×C47—22no—
336C23×C47C2×C22⋊C414yes—
337C23×C47C4×Q814yes—
338C23×C47C4×Q814yes—
339C23×C47C22⋊Q814yes—
340C23×C47C22⋊Q814yes—
341C23×C47#12414yes—
342C23×C47C4⋊Q814yes—
343C23×C47C23×C411yescharacteristic
344C23×C47C22×D411yescharacteristic
345C23×C47C22×D411yescharacteristic
346C23×C47C22×D411yescharacteristic
347C23×C47C22×Q811yescharacteristic
348C23×C47C22×Q811yescharacteristic
349C23×C47C2×#4111yescharacteristic
350C23×C47C2×#4111yescharacteristic
351C23×C47C2×#4111yescharacteristic
352C23×C47C2×#4111yescharacteristic
353C23×C47C2×#4111yescharacteristic
354C23×C47H(5,𝔽2)11yescharacteristic
355C23×C47H(5,𝔽2)11yescharacteristic
356C23×C47H(5,𝔽2)11yescharacteristic
357C23×C472−1+411yescharacteristic
358Q8×C47—416no—
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—22no—
381C2×C4×C47—22no—
382C2×C4×C47—22no—
383C2×C4×C47—22no—
384C2×C4×C47—22no—
385C2×C4×C47—22no—
386C2×C4×C47—416no—
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×C47—41no—
394C2×C4×C47—41no—
395C2×C4×C47—41no—
396C2×C4×C47—41no—
397C2×C4×C47—41no—
398C2×C4×C47—41no—
399C2×C4×C47C2×C22⋊C414yes—
400C2×C4×C47C2×C22⋊C414yes—
401C2×C4×C47C4×D414yes—
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—416no—
424C2×Dic47—416no—
425C2×Dic47—41no—
426C2×Dic47—41no—
427C2×Dic47—41no—
428C2×Dic47—41no—
429C2×Dic47—41no—
430C2×Dic47—41no—
431C2×Dic47—41no—
432C2×Dic47—41no—
433C2×Dic47—41no—
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×Dic47—41no—
451C2×Dic47—41no—
452C2×Dic47—41no—
453C2×Dic47—41no—
454C2×Dic47—41no—
455C2×Dic47—41no—
456C2×Dic47—41no—
457C2×Dic47—41no—
458C2×Dic47—41no—
459C2×Dic47C22⋊Q814yescomplemented
460#14052—471nomaximal, Sylow
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×C47—24no—
470C22×C47—24no—
471C22×C47—24no—
472C22×C47—24no—
473C22×C47—24no—
474C22×C47—24no—
475C22×C47#39118yescomplemented
476C22×C47C22×C22⋊C411yescharacteristic
477C22×C47C2×C4×D411yescharacteristic
478C22×C47C2×C4×Q811yescharacteristic
479C22×C47C2×C4×Q811yescharacteristic
480C22×C47C4×#4111yescharacteristic
481C22×C47#51811yescharacteristic
482C22×C47#52011yescharacteristic
483C22×C47C2×C22⋊Q811yescharacteristic
484C22×C47C2×C22⋊Q811yescharacteristic
485C22×C47C2×C22⋊Q811yescharacteristic
486C22×C47#52511yescharacteristic
487C22×C47C2×#12411yescharacteristic
488C22×C47#52911yescharacteristic
489C22×C47C2×C4⋊Q811yescharacteristic
490C22×C47#53311yescharacteristic
491C22×C47#53811yescharacteristic
492C22×C47#53911yescharacteristic
493C22×C47#54311yescharacteristic
494C22×C47#54411yescharacteristic
495C22×C47D4211yescharacteristic
496C22×C47D4211yescharacteristic
497C22×C47#54611yescharacteristic
498C22×C47#54611yescharacteristic
499C22×C47#54611yescharacteristic
500C22×C47#54611yescharacteristic
501C22×C47#54611yescharacteristic
502C22×C47#54711yescharacteristic
503C22×C47#54711yescharacteristic
504C22×C47D4×Q811yescharacteristic
505C22×C47#55111yescharacteristic
506C22×C47#55111yescharacteristic
507C22×C47#55211yescharacteristic
508C22×C47#55411yescharacteristic
509C22×C47#55411yescharacteristic
510C22×C47#55411yescharacteristic
511C4×C47—24no—
512C4×C47—24no—
513C4×C47—24no—
514C4×C47—42no—
515C4×C47—42no—
516C4×C47—42no—
517Dic47—24no—
518Dic47—42no—
519Dic47—42no—
520Dic47—42no—
521Dic47—42no—
522Dic47—42no—
523Dic47—81no—
524Dic47—81no—
525C22×C22⋊Q8D4711yescharacteristic
526C2×#391—471no—
527C2×#385—471no—
528C2×C4×C22⋊C4—471no—
529C22×#95—471no—
530#1446—471no—
531#1445—471no—
532#1441—471no—
533#1441—471no—
534#1436—471no—
535#1436—471no—
536C4⋊#95—471no—
537C22⋊#95—471no—
538C22⋊#95—471no—
539C22⋊#95—471no—
540C2×C47—28no—
541C2×C47C2×#39111yescharacteristic
542C2×C47C4×C22⋊Q811yescharacteristic
543C2×C47#232911yescharacteristic
544C2×C47D4×C22⋊C411yescharacteristic
545C2×C47#233911yescharacteristic
546C2×C47#236011yescharacteristic
547C2×C47#236811yescharacteristic
548C2×C47#243711yescharacteristic
549C2×C47#243811yescharacteristic
550C2×C47#244011yescharacteristic
551C2×C47#244911yescharacteristic
552C2×C47#245011yescharacteristic
553C2×C47#247211yescharacteristic
554C2×C47#248811yescharacteristic
555C2×C47#254911yescharacteristic
556C23×Q8C2×D4711yescharacteristic
557C24×C4—471no—
558C24×C4—471no—
559C24×C4C2×D4711yescharacteristic
560C2×C22⋊Q8—24no—
561C2×C22⋊Q8—24no—
562C2×C22⋊Q8Dic4718yescomplemented
563C22×C4⋊C4—471no—
564C22×C4⋊C4—471no—
565C22×C4⋊C4C2×D4711yescharacteristic
566C22×C4⋊C4C2×D4711yescharacteristic
567C22×C4⋊C4C2×D4711yescharacteristic
568C22×C22⋊C4—471no—
569C22×C22⋊C4—471no—
570C22×C22⋊C4C2×D4711yescharacteristic
571C22×C22⋊C4C2×D4711yescharacteristic
572C22×C42—471no—
573C22×C42—471no—
574#391—944no—
575#385—944no—
576C4×C22⋊C4—944no—
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—471no—
590C2×#95—471no—
591C2×#95—471no—
592C2×#95—471no—
593C2×#95—471no—
594C2×#95—471no—
595C2×#95—471no—
596C2×#95—471no—
597C2×#95—944no—
598C47#1405211yescharacteristic, complemented, Sylow
599C25C22×D4711yescharacteristic
600C22×Q8—22no—
601C22×Q8—22no—
602C22×Q8—22no—
603C22×Q8—22no—
604C22×Q8—41no—
605C22×Q8—41no—
606C22×Q8C2×Dic4714yescomplemented
607C23×C4—22no—
608C23×C4—22no—
609C23×C4—22no—
610C23×C4—22no—
611C23×C4—41no—
612C23×C4—41no—
613C23×C4—471no—
614C23×C4—471no—
615C23×C4—471no—
616C23×C4—471no—
617C23×C4—471no—
618C23×C4—471no—
619C23×C4—474no—
620C23×C4—471no—
621C23×C4—471no—
622C23×C4—942no—
623C23×C4—942no—
624C23×C4—942no—
625C23×C4—942no—
626C23×C4—942no—
627C23×C4—942no—
628C23×C4—942no—
629C23×C4—942no—
630C23×C4—942no—
631C23×C4—1881no—
632C23×C4—1881no—
633C23×C4—1881no—
634C23×C4—1881no—
635C23×C4C2×Dic4714yes—
636C23×C4C22×D4711yescharacteristic
637C23×C4C22×D4711yescharacteristic
638C23×C4C22×D4711yescharacteristic
639C23×C4C22×D4711yescharacteristic
640C23×C4C22×D4711yescharacteristic
641C23×C4C22×D4711yescharacteristic
642C22⋊Q8—232no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—942no—
650C2×C4⋊C4—942no—
651C2×C4⋊C4—942no—
652C2×C4⋊C4—942no—
653C2×C4⋊C4—1881no—
654C2×C4⋊C4—1881no—
655C2×C4⋊C4C2×Dic4714yescomplemented
656C2×C4⋊C4C2×Dic4714yescomplemented
657C2×C4⋊C4C2×Dic4714yescomplemented
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—474no—
661C2×C22⋊C4—942no—
662C2×C22⋊C4—942no—
663C2×C22⋊C4—942no—
664C2×C22⋊C4—942no—
665C2×C22⋊C4—942no—
666C2×C22⋊C4C2×Dic4714yes—
667C2×C22⋊C4C2×Dic4714yes—
668C2×C22⋊C4C22⋊D4714yes—
669C2×C22⋊C4C22⋊D4714yes—
670C2×C42—942no—
671C2×C42—942no—
672C2×C42—942no—
673C2×C42—942no—
674C2×C42—1881no—
675C2×C42—1881no—
676#95—474no—
677#95—942no—
678#95—942no—
679#95—942no—
680#95—942no—
681#95—942no—
682#95—942no—
683#95—942no—
684#95—942no—
685#95—942no—
686#95—942no—
687#95—942no—
688#95—942no—
689#95—942no—
690#95—1881no—
691#95—1881no—
692#95—1881no—
693#95—1881no—
694#95—1881no—
695#95—1881no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24Q8×D4712yes—
705C24Q8×D4712yes—
706C24#1062535412yes—
707C24#1062535412yes—
708C24C22×Dic4712yes—
709C24C2×C22⋊D4712yes—
710C24C2×C22⋊D4712yes—
711C24C23×D4711yescharacteristic
712C2×Q8—28no—
713C2×Q8—28no—
714C2×Q8—44no—
715C2×Q8—44no—
716C2×Q8—44no—
717C2×Q8—44no—
718C2×Q8—44no—
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—28no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—28no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—472no—
757C22×C4—472no—
758C22×C4—472no—
759C22×C4—472no—
760C22×C4—472no—
761C22×C4—472no—
762C22×C4—472no—
763C22×C4—472no—
764C22×C4—948no—
765C22×C4—941no—
766C22×C4—941no—
767C22×C4—941no—
768C22×C4—941no—
769C22×C4—948no—
770C22×C4—948no—
771C22×C4—941no—
772C22×C4—941no—
773C22×C4—941no—
774C22×C4—941no—
775C22×C4—941no—
776C22×C4—941no—
777C22×C4—941no—
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—941no—
803C22×C4—941no—
804C22×C4—941no—
805C22×C4—941no—
806C22×C4—941no—
807C22×C4—941no—
808C22×C4—941no—
809C22×C4—941no—
810C22×C4—941no—
811C22×C4—941no—
812C22×C4—941no—
813C22×C4—941no—
814C22×C4—941no—
815C22×C4—1884no—
816C22×C4—1884no—
817C22×C4—1884no—
818C22×C4—1884no—
819C22×C4—1884no—
820C22×C4—1884no—
821C22×C4—1884no—
822C22×C4—1884no—
823C22×C4—1884no—
824C22×C4—1884no—
825C22×C4—1884no—
826C22×C4D4×D4712yes—
827C22×C4#1062535212yes—
828C22×C4C22×Dic4712yes—
829C22×C4C22×Dic4712yes—
830C22×C4C22×Dic4712yes—
831C22×C4C22×Dic4712yes—
832C22×C4C22×Dic4712yes—
833C22×C4C22×Dic4712yes—
834C22×C4C2×C22⋊D4712yes—
835C22×C4C2×C22⋊D4712yes—
836C22×C4C2×C22⋊D4712yes—
837C22×C4C2×C22⋊D4712yes—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—1884no—
842C4⋊C4—1884no—
843C22⋊C4—28no—
844C22⋊C4—948no—
845C22⋊C4—1884no—
846C22⋊C4C22⋊Dic47116yes—
847C42—1884no—
848C42—1884no—
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—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23C2×C22⋊Dic4714yes—
878C23Q8×Dic4714yes—
879C23Q8×Dic4714yes—
880C23#1309400014yes—
881C23#1309400014yes—
882C23#1309401314yes—
883C23#1309402214yes—
884C23C23×Dic4711yescharacteristic
885C23C2×D4×D4711yescharacteristic
886C23C22×C22⋊D4711yescharacteristic
887C23C22×C22⋊D4711yescharacteristic
888C23C2×Q8×D4711yescharacteristic
889C23C2×Q8×D4711yescharacteristic
890C23#41×D4711yescharacteristic
891C23#41×D4711yescharacteristic
892C23C2×#1062535211yescharacteristic
893C23C2×#1062535411yescharacteristic
894C23C2×#1062535411yescharacteristic
895C23#1309406911yescharacteristic
896C23#1309406911yescharacteristic
897C23#1309407011yescharacteristic
898C23#1309407111yescharacteristic
899Q8—416no—
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—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—416no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—474no—
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—18816no—
963C2×C4—1881no—
964C2×C4—1881no—
965C2×C4—1881no—
966C2×C4—1881no—
967C2×C4—1881no—
968C2×C4—1881no—
969C2×C4—1881no—
970C2×C4—1881no—
971C2×C4—1881no—
972C2×C4—1881no—
973C2×C4—1881no—
974C2×C4—1881no—
975C2×C4—1881no—
976C2×C4—1881no—
977C2×C4—18816no—
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×C4—1881no—
987C2×C4—1881no—
988C2×C4—1881no—
989C2×C4—1881no—
990C2×C4—1881no—
991C2×C4—1881no—
992C2×C4—1881no—
993C2×C4—1881no—
994C2×C4—1881no—
995C2×C4—1881no—
996C2×C4—1881no—
997C2×C4—1881no—
998C2×C4C2×C22⋊Dic4714yes—
999C2×C4C2×C22⋊Dic4714yes—
1000C2×C4D4×Dic4714yes—
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—24no—
1005C22—24no—
1006C22—24no—
1007C22—24no—
1008C22—24no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22#1568903018yescomplemented
1016C22C22×C22⋊Dic4711yescharacteristic
1017C22C2×D4×Dic4711yescharacteristic
1018C22C2×Q8×Dic4711yescharacteristic
1019C22C2×Q8×Dic4711yescharacteristic
1020C22#41×Dic4711yescharacteristic
1021C22#1568959811yescharacteristic
1022C22#1568960611yescharacteristic
1023C22C22⋊Q8×D4711yescharacteristic
1024C22C2×#1309400011yescharacteristic
1025C22C2×#1309400011yescharacteristic
1026C22#1568963611yescharacteristic
1027C22C2×#1309401311yescharacteristic
1028C22#1568965911yescharacteristic
1029C22C2×#1309402211yescharacteristic
1030C22#1568967511yescharacteristic
1031C22#1568971311yescharacteristic
1032C22#1568972211yescharacteristic
1033C22#1568974811yescharacteristic
1034C22#1568975211yescharacteristic
1035C22D4×C22⋊D4711yescharacteristic
1036C22D4×C22⋊D4711yescharacteristic
1037C22#1568976111yescharacteristic
1038C22#1568976111yescharacteristic
1039C22#1568976411yescharacteristic
1040C22#1568976711yescharacteristic
1041C22#1568976711yescharacteristic
1042C22#1568977211yescharacteristic
1043C22#1568977211yescharacteristic
1044C22#1568978611yescharacteristic
1045C22#1568980011yescharacteristic
1046C22#1568980011yescharacteristic
1047C22#1568981511yescharacteristic
1048C22#1568982711yescharacteristic
1049C22#1568982711yescharacteristic
1050C22#1568983111yescharacteristic
1051C4—24no—
1052C4—24no—
1053C4—24no—
1054C4—42no—
1055C4—42no—
1056C4—42no—
1057C4—944no—
1058C4—3761no—
1059C4—3761no—
1060C4—1882no—
1061C4—1882no—
1062C4—1882no—
1063C4—1882no—
1064C4—1882no—
1065C2—28no—
1066C2C2×#1568903011yescharacteristic
1067C2C22⋊Q8×Dic4711yescharacteristic
1068C2#2024612311yescharacteristic
1069C2D4×C22⋊Dic4711yescharacteristic
1070C2#2024621811yescharacteristic
1071C2#2024639711yescharacteristic
1072C2#2024647311yescharacteristic
1073C2#2024705111yescharacteristic
1074C2#2024706011yescharacteristic
1075C2#2024708711yescharacteristic
1076C2#2024719311yescharacteristic
1077C2#2024720811yescharacteristic
1078C2#2024752111yescharacteristic
1079C2#2024772011yescharacteristic
1080C2#2024839611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC22×C22⋊Q8×C47C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC22×C22⋊Q8D47
hypocenterC47#14052
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#15689030C2semidirect
5. #20241659C2semidirect
6. #20241656C2semidirect
7. #20241641C2semidirect
8. #20241641C2semidirect
9. #20241620C2semidirect
10. #20241620C2semidirect
11. #20241617C2semidirect
52. C2×C22⋊Q8×C47C4semidirect
71. C23×Dic47Q8semidirect
91. C2×C22⋊Dic47Q8semidirect
125. C22×Q8×C47C2×C4semidirect
146. C2×C4⋊C4×C47C2×C4semidirect
147. C2×C4⋊C4×C47C2×C4semidirect
148. C2×C4⋊C4×C47C2×C4semidirect
459. C2×Dic47C22⋊Q8semidirect
475. C22×C47#391semidirect
562. C2×C22⋊Q8Dic47semidirect
598. C47#14052semidirect
606. C22×Q8C2×Dic47semidirect
655. C2×C4⋊C4C2×Dic47semidirect
656. C2×C4⋊C4C2×Dic47semidirect
657. C2×C4⋊C4C2×Dic47semidirect
1015. C22#15689030semidirect

Maximal subgroups

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

subgroupindex
C2×#156890302
C2×#156889982
C2×C22⋊C4×Dic472
C22×C47⋊#952
#202416592
#202416562
#202416412
#202416202
#202416172
#202416112
#202416102
C22×C22⋊Q8×C472
#1405247