Finite Group Databasebeta

← #26231963

Subgroups — #26231963

Order 12032.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#10625329C211yesmaximal, characteristic, complemented
2C2×#15689140C211yesmaximal, characteristic, complemented
3C22×#13093951C211yesmaximal, characteristic, complemented
4#20245833C211yesmaximal, characteristic, complemented
5#20244308C211yesmaximal, characteristic, complemented
6#20244221C211yesmaximal, characteristic, complemented
7#20243837C211yesmaximal, characteristic, complemented
8#20243832C211yesmaximal, characteristic, complemented
9#20243691C211yesmaximal, characteristic, complemented
10#20243691C211yesmaximal, characteristic, complemented
11#20243408C211yesmaximal, characteristic, complemented
12#20243332C211yesmaximal, characteristic, complemented
13#20243332C211yesmaximal, characteristic, complemented
14#20243198C211yesmaximal, characteristic, complemented
15D4×#41×C47C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic, complemented
17C22×#10625329C2211yescharacteristic, complemented
18C2×#13093983C2211yescharacteristic, complemented
19C22×C4×Dic47C2211yescharacteristic, complemented
20#15689201—21no—
21#15689195—21no—
22#15689195—21no—
23D4×C47⋊C8—21no—
24#15689147C2211yescharacteristic, complemented
25#15689140—24no—
26C2×#13093951—24no—
27C2×#13093951C2211yescharacteristic
28C2×#13093951C2211yescharacteristic
29C2×#13093951C2211yescharacteristic
30C2×#13093951C2211yescharacteristic
31C2×#13093951C2211yescharacteristic, complemented
32C2×#13093951C2211yescharacteristic, complemented
33C2×#13093951C2211yescharacteristic, complemented
34C2×#13093951C2211yescharacteristic, complemented
35C2×#13093951C2211yescharacteristic, complemented
36C2×#13093951C2211yescharacteristic, complemented
37C2×#13093951C2211yescharacteristic, complemented
38C2×#13093951C2211yescharacteristic, complemented
39#15689087C2211yescharacteristic, complemented
40#15689087C2211yescharacteristic, complemented
41C4×#10625329C2211yescharacteristic, complemented
42#15689016—21no—
43#15689009—21no—
44#15689003—21no—
45#15688998—21no—
46C4×C4⋊Dic47C2211yescharacteristic, complemented
47C4×C22⋊Dic47C2211yescharacteristic, complemented
48C4×C22⋊Dic47C2211yescharacteristic, complemented
49#15688969C2211yescharacteristic, complemented
50#15688882C2211yescharacteristic, complemented
51#15688882C2211yescharacteristic, complemented
52#15688882C2211yescharacteristic, complemented
53#15688882C2211yescharacteristic, complemented
54C22×#41×C47C2211yescharacteristic
55C22×#41×C47C2211yescharacteristic
56C47×#550C411yescharacteristic, complemented
57D4×Q8×C47C411yescharacteristic, complemented
58C47×#548C411yescharacteristic, complemented
59C47×#548C411yescharacteristic, complemented
60C47×#547—21no—
61C47×#547C411yescharacteristic, complemented
62C47×#546—21no—
63C47×#546—21no—
64C47×#546C411yescharacteristic, complemented
65C47×#546C411yescharacteristic, complemented
66D42×C47—21no—
67D42×C47C411yescharacteristic, complemented
68C47×#532—21no—
69C47×#532C2211yescharacteristic
70C47×#525—21no—
71C47×#525—21no—
72C47×#525C2211yescharacteristic
73C47×#525C2211yescharacteristic
74C4×#41×C47C2211yescharacteristic
75C2×C4×D4×C47—21no—
76C2×C4×D4×C47C2211yescharacteristic
77C23×Dic47—21no—
78C2×#10625329—21no—
79C2×#10625329—21no—
80C2×#10625329—22no—
81C2×#10625329—22no—
82C2×#10625329—41no—
83C2×#10625329—41no—
84C2×#10625329C2311yescharacteristic
85C2×#10625329C2311yescharacteristic
86C2×#10625329C2311yescharacteristic
87C2×#10625329C2311yescharacteristic
88C22×C47⋊C8—21no—
89C22×C47⋊C8—21no—
90#13093983—22no—
91#13093983—41no—
92C2×C4⋊Dic47—21no—
93C2×C4⋊Dic47—21no—
94C2×C22⋊Dic47—21no—
95C2×C22⋊Dic47—21no—
96C2×C22⋊Dic47—21no—
97C2×C4×Dic47—22no—
98C2×C4×Dic47—21no—
99C2×C4×Dic47—41no—
100C2×C4×Dic47C2311yescharacteristic
101C2×C4×Dic47C2311yescharacteristic
102C2×C4×Dic47C2311yescharacteristic
103C2×C4×Dic47C2311yescharacteristic
104C4⋊(C47⋊C8)—21no—
105C4⋊(C47⋊C8)—21no—
106#13093951—22no—
107#13093951—22no—
108#13093951—22no—
109#13093951—22no—
110#13093951—22no—
111#13093951—22no—
112#13093951—22no—
113#13093951—41no—
114#13093951—41no—
115#13093951—41no—
116#13093951—41no—
117#13093951D414yescomplemented
118C22⋊(C47⋊C8)—21no—
119C22⋊(C47⋊C8)—21no—
120C22⋊(C47⋊C8)—21no—
121C22⋊(C47⋊C8)—21no—
122#13093935—21no—
123C4×C47⋊C8—21no—
124C47⋊#95—21no—
125C47⋊#95—21no—
126C47⋊#95—21no—
127C47⋊#95—21no—
128C47⋊#95—21no—
129C2×#41×C47—21no—
130C2×#41×C47—21no—
131C2×#41×C47—21no—
132C2×#41×C47—21no—
133C2×#41×C47—22no—
134C2×#41×C47—22no—
135C2×#41×C47—22no—
136C2×#41×C47—22no—
137C2×#41×C47—41no—
138C2×#41×C47—41no—
139C2×#41×C47—41no—
140C2×#41×C47—41no—
141C2×#41×C47C2×C411yescharacteristic
142C2×#41×C47C2×C411yescharacteristic
143C2×#41×C47C2×C411yescharacteristic, complemented
144C2×#41×C47C2×C411yescharacteristic, complemented
145C2×#41×C47C2311yescharacteristic
146C2×#41×C47C2311yescharacteristic
147C2×#41×C47C2311yescharacteristic
148C22×Q8×C47C2×C411yescharacteristic
149C22×Q8×C47C2×C411yescharacteristic, complemented
150C22×D4×C47—21no—
151C22×D4×C47—21no—
152C22×D4×C47—21no—
153C22×D4×C47C2×C411yescharacteristic
154C22×D4×C47C2×C411yescharacteristic, complemented
155C22×D4×C47D411yescharacteristic
156C23×C4×C47—21no—
157C23×C4×C47—21no—
158C23×C4×C47C2311yescharacteristic
159C23×C4×C47C2311yescharacteristic
160C4⋊Q8×C47—21no—
161C4⋊Q8×C47C2×C411yescharacteristic, complemented
162#127×C47—21no—
163#127×C47C2×C411yescharacteristic, complemented
164#124×C47—21no—
165#124×C47—21no—
166#124×C47C2×C411yescharacteristic, complemented
167#124×C47C2×C411yescharacteristic, complemented
168#123×C47—21no—
169#123×C47—21no—
170#123×C47—21no—
171#123×C47—21no—
172#123×C47—21no—
173#123×C47—21no—
174C22⋊Q8×C47—21no—
175C22⋊Q8×C47—21no—
176C22⋊Q8×C47—21no—
177C22⋊Q8×C47—21no—
178C22⋊Q8×C47C2×C411yescharacteristic
179C22⋊Q8×C47C2×C411yescharacteristic
180C22⋊Q8×C47C2×C411yescharacteristic, complemented
181C22⋊Q8×C47C2×C411yescharacteristic, complemented
182#121×C47—21no—
183#121×C47—21no—
184#121×C47—21no—
185#121×C47—21no—
186#121×C47—21no—
187#121×C47—21no—
188#121×C47—21no—
189#121×C47—21no—
190#121×C47—21no—
191#121×C47—21no—
192#121×C47C2×C411yescharacteristic
193#121×C47C2×C411yescharacteristic
194#121×C47C2×C411yescharacteristic, complemented
195#121×C47C2×C411yescharacteristic, complemented
196#120×C47—21no—
197#120×C47—21no—
198#120×C47—21no—
199#120×C47—21no—
200#120×C47—21no—
201#120×C47—21no—
202C4×Q8×C47C2×C411yescharacteristic, complemented
203C4×Q8×C47C2×C411yescharacteristic, complemented
204C4×D4×C47—21no—
205C4×D4×C47—21no—
206C4×D4×C47—21no—
207C4×D4×C47—21no—
208C4×D4×C47—21no—
209C4×D4×C47—21no—
210C4×D4×C47—21no—
211C4×D4×C47—21no—
212C4×D4×C47—21no—
213C4×D4×C47—21no—
214C4×D4×C47—21no—
215C4×D4×C47—21no—
216C4×D4×C47C2×C411yescharacteristic
217C4×D4×C47C2×C411yescharacteristic
218C4×D4×C47C2×C411yescharacteristic
219C4×D4×C47C2×C411yescharacteristic
220C4×D4×C47C2×C411yescharacteristic, complemented
221C4×D4×C47C2×C411yescharacteristic, complemented
222C4×D4×C47D411yescharacteristic
223C4×D4×C47D411yescharacteristic
224C4×D4×C47D411yescharacteristic
225C4×D4×C47D411yescharacteristic
226#117×C47—21no—
227#117×C47C2311yescharacteristic
228C2×C4⋊C4×C47—21no—
229C2×C4⋊C4×C47D411yescharacteristic
230C2×C22⋊C4×C47—21no—
231C2×C22⋊C4×C47—21no—
232C2×C22⋊C4×C47D411yescharacteristic
233C2×C22⋊C4×C47D411yescharacteristic
234C2×C42×C47—21no—
235C2×C42×C47C2311yescharacteristic
236C24×C47—21no—
237C24×C47—21no—
238C24×C47C2×D411yescharacteristic
239C24×C47C2×D411yescharacteristic
240#41×C47—21no—
241#41×C47—21no—
242#41×C47—22no—
243#41×C47—22no—
244#41×C47—22no—
245#41×C47—22no—
246#41×C47—21no—
247#41×C47—21no—
248#41×C47—21no—
249#41×C47—21no—
250#41×C47—21no—
251#41×C47—21no—
252#41×C47—21no—
253#41×C47—21no—
254#41×C47—42no—
255#41×C47—42no—
256#41×C47—42no—
257#41×C47—42no—
258#41×C47—41no—
259#41×C47—41no—
260#41×C47—41no—
261#41×C47—41no—
262#41×C47—42no—
263#41×C47—42no—
264#41×C47—42no—
265#41×C47—42no—
266#41×C47C2×D412yes—
267#41×C47#4112yes—
268C2×Q8×C47—21no—
269C2×Q8×C47—21no—
270C2×Q8×C47—22no—
271C2×Q8×C47—22no—
272C2×Q8×C47—41no—
273C2×Q8×C47—41no—
274C2×Q8×C47C22×C411yescharacteristic
275C2×Q8×C47C22×C411yescharacteristic
276C2×Q8×C47C22×C411yescharacteristic
277C2×D4×C47—21no—
278C2×D4×C47—22no—
279C2×D4×C47—22no—
280C2×D4×C47—21no—
281C2×D4×C47—21no—
282C2×D4×C47—21no—
283C2×D4×C47—21no—
284C2×D4×C47—21no—
285C2×D4×C47—21no—
286C2×D4×C47—21no—
287C2×D4×C47—21no—
288C2×D4×C47—21no—
289C2×D4×C47—21no—
290C2×D4×C47—21no—
291C2×D4×C47—21no—
292C2×D4×C47—21no—
293C2×D4×C47—21no—
294C2×D4×C47—41no—
295C2×D4×C47—41no—
296C2×D4×C47—42no—
297C2×D4×C47—42no—
298C2×D4×C47—42no—
299C2×D4×C47—42no—
300C2×D4×C47—42no—
301C2×D4×C47—44no—
302C2×D4×C47C22⋊C411yescharacteristic
303C2×D4×C47C22⋊C411yescharacteristic
304C2×D4×C47C22⋊C411yescharacteristic
305C2×D4×C47C22⋊C411yescharacteristic
306C2×D4×C47C22×C411yescharacteristic
307C2×D4×C47C22×C411yescharacteristic
308C2×D4×C47C22×C411yescharacteristic
309C22×C4×C47—21no—
310C22×C4×C47—21no—
311C22×C4×C47—21no—
312C22×C4×C47—21no—
313C22×C4×C47—21no—
314C22×C4×C47—21no—
315C22×C4×C47—21no—
316C22×C4×C47—21no—
317C22×C4×C47—21no—
318C22×C4×C47—21no—
319C22×C4×C47—21no—
320C22×C4×C47—21no—
321C22×C4×C47—21no—
322C22×C4×C47—21no—
323C22×C4×C47—21no—
324C22×C4×C47—21no—
325C22×C4×C47—21no—
326C22×C4×C47—21no—
327C22×C4×C47—21no—
328C22×C4×C47—42no—
329C22×C4×C47—42no—
330C22×C4×C47—42no—
331C22×C4×C47—42no—
332C22×C4×C47C22×C411yescharacteristic
333C22×C4×C47C22×C411yescharacteristic
334C22×C4×C47C22×C411yescharacteristic
335C22×C4×C47C22×C411yescharacteristic
336C22×C4×C47C2×D411yescharacteristic
337C22×C4×C47C2×D411yescharacteristic
338C22×C4×C47C2×D411yescharacteristic
339C22×C4×C47C2×D411yescharacteristic
340C22×C4×C47C2×D411yescharacteristic
341C22×C4×C47C2×D411yescharacteristic
342C22×C4×C47C2×D411yescharacteristic
343C22×C4×C47C2×D411yescharacteristic
344C22×C4×C47C2411yescharacteristic
345C22×Dic47—21no—
346C22×Dic47—21no—
347C22×Dic47—21no—
348C22×Dic47—21no—
349C22×Dic47—42no—
350C22×Dic47—42no—
351C22×Dic47—42no—
352C4⋊C4×C47—21no—
353C4⋊C4×C47—21no—
354C4⋊C4×C47—21no—
355C4⋊C4×C47—21no—
356C4⋊C4×C47—21no—
357C4⋊C4×C47—21no—
358C4⋊C4×C47—21no—
359C4⋊C4×C47—21no—
360C4⋊C4×C47C22⋊C411yescharacteristic
361C4⋊C4×C47C22⋊C411yescharacteristic
362C4⋊C4×C47C22⋊C411yescharacteristic
363C4⋊C4×C47C22⋊C411yescharacteristic
364C4⋊C4×C47C22×C411yescharacteristic
365C4⋊C4×C47C22×C411yescharacteristic
366C22⋊C4×C47—21no—
367C22⋊C4×C47—21no—
368C22⋊C4×C47—21no—
369C22⋊C4×C47—21no—
370C22⋊C4×C47—21no—
371C22⋊C4×C47—21no—
372C22⋊C4×C47—21no—
373C22⋊C4×C47—21no—
374C22⋊C4×C47—21no—
375C22⋊C4×C47—21no—
376C22⋊C4×C47—21no—
377C22⋊C4×C47—21no—
378C22⋊C4×C47—21no—
379C22⋊C4×C47—21no—
380C22⋊C4×C47—21no—
381C22⋊C4×C47C22⋊C411yescharacteristic
382C22⋊C4×C47C22⋊C411yescharacteristic
383C22⋊C4×C47C22⋊C411yescharacteristic
384C22⋊C4×C47C22⋊C411yescharacteristic
385C22⋊C4×C47C22⋊C411yescharacteristic
386C22⋊C4×C47C22⋊C411yescharacteristic
387C22⋊C4×C47C22⋊C411yescharacteristic
388C22⋊C4×C47C22⋊C411yescharacteristic
389C42×C47—21no—
390C42×C47—21no—
391C42×C47—21no—
392C42×C47C22×C411yescharacteristic
393C42×C47C22×C411yescharacteristic
394C42×C47C2×D411yescharacteristic
395C42×C47C2×D411yescharacteristic
396C22⋊Dic47—42no—
397C22⋊Dic47—42no—
398C22⋊Dic47—42no—
399C4⋊Dic47—42no—
400C4⋊Dic47—42no—
401C4×Dic47—21no—
402C4×Dic47—21no—
403C4×Dic47—21no—
404C4×Dic47—21no—
405C4×Dic47—21no—
406C4×Dic47—21no—
407C4×Dic47—21no—
408C4×Dic47—42no—
409C4×Dic47C2×D412yescomplemented
410#10625329—21no—
411#10625329—21no—
412#10625329—21no—
413#10625329—21no—
414#10625329—21no—
415#10625329—21no—
416#10625329—21no—
417#10625329—42no—
418#10625329—42no—
419#10625329C2×D412yescomplemented
420C2×C47⋊C8—21no—
421C2×C47⋊C8—21no—
422C2×C47⋊C8—21no—
423C2×C47⋊C8—21no—
424C2×C47⋊C8—42no—
425C2×C47⋊C8—42no—
426C23×C47—21no—
427C23×C47—21no—
428C23×C47—21no—
429C23×C47—22no—
430C23×C47—21no—
431C23×C47—21no—
432C23×C47—21no—
433C23×C47—21no—
434C23×C47—41no—
435C23×C47—41no—
436C23×C47—41no—
437C23×C47—42no—
438C23×C47—42no—
439C23×C47—42no—
440C23×C47—42no—
441C23×C47—81no—
442C23×C47—81no—
443C23×C47C2×C22⋊C411yescharacteristic
444C23×C47C2×C22⋊C411yescharacteristic
445C23×C47C2×C22⋊C411yescharacteristic
446C23×C47C2×C22⋊C411yescharacteristic
447C23×C47C22×D411yescharacteristic
448Q8×C47—21no—
449Q8×C47—21no—
450Q8×C47—21no—
451Q8×C47—21no—
452Q8×C47—21no—
453Q8×C47—42no—
454Q8×C47—42no—
455Q8×C47C4×D412yes—
456D4×C47—22no—
457D4×C47—22no—
458D4×C47—22no—
459D4×C47—22no—
460D4×C47—21no—
461D4×C47—21no—
462D4×C47—21no—
463D4×C47—21no—
464D4×C47—21no—
465D4×C47—41no—
466D4×C47—41no—
467D4×C47—42no—
468D4×C47—42no—
469D4×C47—42no—
470D4×C47—42no—
471D4×C47—42no—
472D4×C47—42no—
473D4×C47—42no—
474D4×C47—42no—
475D4×C47—41no—
476D4×C47—41no—
477D4×C47—41no—
478D4×C47—41no—
479D4×C47—42no—
480D4×C47—81no—
481D4×C47—81no—
482D4×C47—81no—
483D4×C47C4×D412yes—
484C2×C4×C47—21no—
485C2×C4×C47—21no—
486C2×C4×C47—21no—
487C2×C4×C47—21no—
488C2×C4×C47—21no—
489C2×C4×C47—21no—
490C2×C4×C47—21no—
491C2×C4×C47—21no—
492C2×C4×C47—21no—
493C2×C4×C47—21no—
494C2×C4×C47—21no—
495C2×C4×C47—21no—
496C2×C4×C47—21no—
497C2×C4×C47—21no—
498C2×C4×C47—21no—
499C2×C4×C47—21no—
500C2×C4×C47—21no—
501C2×C4×C47—22no—
502C2×C4×C47—21no—
503C2×C4×C47—21no—
504C2×C4×C47—21no—
505C2×C4×C47—21no—
506C2×C4×C47—22no—
507C2×C4×C47—21no—
508C2×C4×C47—21no—
509C2×C4×C47—21no—
510C2×C4×C47—21no—
511C2×C4×C47—41no—
512C2×C4×C47—41no—
513C2×C4×C47—42no—
514C2×C4×C47—42no—
515C2×C4×C47—42no—
516C2×C4×C47—42no—
517C2×C4×C47—42no—
518C2×C4×C47—42no—
519C2×C4×C47—42no—
520C2×C4×C47—41no—
521C2×C4×C47—41no—
522C2×C4×C47—41no—
523C2×C4×C47—41no—
524C2×C4×C47—81no—
525C2×C4×C47C2×C22⋊C411yescharacteristic
526C2×C4×C47C2×C22⋊C411yescharacteristic
527C2×C4×C47C2×C22⋊C411yescharacteristic
528C2×C4×C47C2×C22⋊C411yescharacteristic
529C2×C4×C47C2×C22⋊C411yescharacteristic
530C2×C4×C47C2×C22⋊C411yescharacteristic
531C2×C4×C47C2×C22⋊C411yescharacteristic
532C2×C4×C47C2×C22⋊C411yescharacteristic
533C2×C4×C47C23×C411yescharacteristic
534C2×C4×C47C22×D411yescharacteristic
535C2×C4×C47C22×D411yescharacteristic
536C2×C4×C47C2×#4111yescharacteristic
537C2×C4×C47H(5,𝔽2)11yescharacteristic
538C2×C4×C47H(5,𝔽2)11yescharacteristic
539C2×Dic47—22no—
540C2×Dic47—22no—
541C2×Dic47—41no—
542C2×Dic47—41no—
543C2×Dic47—41no—
544C2×Dic47—48no—
545C2×Dic47—41no—
546C2×Dic47—41no—
547C2×Dic47—41no—
548C2×Dic47—41no—
549C2×Dic47—41no—
550C2×Dic47—41no—
551C2×Dic47—41no—
552C47⋊C8—22no—
553C47⋊C8—41no—
554C47⋊C8—41no—
555C47⋊C8—41no—
556#22434—471nomaximal, Sylow
557C22×C47—21no—
558C22×C47—21no—
559C22×C47—21no—
560C22×C47—21no—
561C22×C47—21no—
562C22×C47—21no—
563C22×C47—21no—
564C22×C47—22no—
565C22×C47—21no—
566C22×C47—21no—
567C22×C47—21no—
568C22×C47—21no—
569C22×C47—21no—
570C22×C47—21no—
571C22×C47—42no—
572C22×C47—42no—
573C22×C47—41no—
574C22×C47—41no—
575C22×C47—41no—
576C22×C47—41no—
577C22×C47—41no—
578C22×C47—41no—
579C22×C47—41no—
580C22×C47—41no—
581C22×C47—81no—
582C22×C47—81no—
583C22×C47—84no—
584C22×C47—84no—
585C22×C47#42112yescomplemented
586C22×C47C22×C22⋊C411yescharacteristic
587C22×C47D4211yescharacteristic
588C22×C47#54611yescharacteristic
589C4×C47—21no—
590C4×C47—21no—
591C4×C47—21no—
592C4×C47—21no—
593C4×C47—22no—
594C4×C47—21no—
595C4×C47—21no—
596C4×C47—21no—
597C4×C47—21no—
598C4×C47—41no—
599C4×C47—41no—
600C4×C47—41no—
601C4×C47—41no—
602C4×C47C2×C4×D411yescharacteristic
603C4×C47#51811yescharacteristic
604C4×C47D4211yescharacteristic
605C4×C47#54611yescharacteristic
606Dic47—42no—
607Dic47—42no—
608Dic47—81no—
609Dic47—81no—
610D4×#41D4711yescharacteristic
611D4×M16—471no—
612C2×#421—471no—
613C22×#104—471no—
614#2290—471no—
615#1980—471no—
616#1963—471no—
617#1897—471no—
618#1896—471no—
619#1871—471no—
620#1871—471no—
621#1806—471no—
622#1789—471no—
623#1789—471no—
624#1759—471no—
625C2×C47—21no—
626C2×C47—21no—
627C2×C47—22no—
628C2×C47—41no—
629C2×C47—41no—
630C2×C47—41no—
631C2×C47—42no—
632C2×C47—81no—
633C2×C47—81no—
634C2×C47D4×C22⋊C411yescharacteristic
635C2×C47C2×#42111yescharacteristic
636C2×C47#290111yescharacteristic
637C22×#41C2×D4711yescharacteristic
638C22×#41C2×D4711yescharacteristic
639C22×M16—471no—
640C22×M16—471no—
641#550Dic4711yescharacteristic, complemented
642D4×Q8Dic4711yescharacteristic, complemented
643#548Dic4711yescharacteristic, complemented
644#548Dic4711yescharacteristic, complemented
645#547—21no—
646#547Dic4711yescharacteristic, complemented
647#546—21no—
648#546—21no—
649#546Dic4711yescharacteristic, complemented
650#546Dic4711yescharacteristic, complemented
651D42—21no—
652D42Dic4711yescharacteristic, complemented
653#532—21no—
654#532C2×D4711yescharacteristic
655#525—21no—
656#525—21no—
657#525C2×D4711yescharacteristic
658#525C2×D4711yescharacteristic
659C4×#41C2×D4711yescharacteristic
660C2×C4×D4—21no—
661C2×C4×D4C2×D4711yescharacteristic
662C2×#117—471no—
663C22×C42—471no—
664#436—941no—
665#435—941no—
666#435—941no—
667C8×D4—941no—
668#423—471no—
669#421—944no—
670C2×#104—471no—
671C2×#104—471no—
672C2×#104—471no—
673C2×#104—471no—
674C2×#104—471no—
675C2×#104—471no—
676C2×#104—471no—
677C2×#104—471no—
678C2×#104—471no—
679C2×#104—471no—
680C2×#104—471no—
681C2×#104—471no—
682C2×#104—944no—
683#407—471no—
684#407—471no—
685C4×M16—471no—
686#388—941no—
687#387—941no—
688#386—941no—
689#385—941no—
690C4×C4⋊C4—471no—
691C4×C22⋊C4—471no—
692C4×C22⋊C4—471no—
693#376—471no—
694#339—471no—
695#339—471no—
696#339—471no—
697#339—471no—
698C47#2243411yescharacteristic, complemented, Sylow
699C2×#41—21no—
700C2×#41—21no—
701C2×#41—21no—
702C2×#41—21no—
703C2×#41—22no—
704C2×#41—22no—
705C2×#41—22no—
706C2×#41—22no—
707C2×#41—41no—
708C2×#41—41no—
709C2×#41—41no—
710C2×#41—41no—
711C2×#41C2×Dic4711yescharacteristic
712C2×#41C2×Dic4711yescharacteristic
713C2×#41C2×Dic4711yescharacteristic, complemented
714C2×#41C2×Dic4711yescharacteristic, complemented
715C2×#41C22×D4711yescharacteristic
716C2×#41C22×D4711yescharacteristic
717C2×#41C22×D4711yescharacteristic
718C22×Q8C2×Dic4711yescharacteristic
719C22×Q8C2×Dic4711yescharacteristic, complemented
720C22×D4—21no—
721C22×D4—21no—
722C22×D4—21no—
723C22×D4C2×Dic4711yescharacteristic
724C22×D4C2×Dic4711yescharacteristic, complemented
725C22×D4C22⋊D4711yescharacteristic
726C23×C4—21no—
727C23×C4—21no—
728C23×C4—941no—
729C23×C4C22×D4711yescharacteristic
730C23×C4C22×D4711yescharacteristic
731C2×M16—471no—
732C2×M16—471no—
733C2×M16—471no—
734C2×M16—471no—
735C2×M16—941no—
736C2×M16—941no—
737C2×M16—942no—
738C2×M16—942no—
739C2×M16—1881no—
740C2×M16—1881no—
741C22×C8—941no—
742C22×C8—941no—
743C4⋊Q8—21no—
744C4⋊Q8C2×Dic4711yescharacteristic, complemented
745#127—21no—
746#127C2×Dic4711yescharacteristic, complemented
747#124—21no—
748#124—21no—
749#124C2×Dic4711yescharacteristic, complemented
750#124C2×Dic4711yescharacteristic, complemented
751#123—21no—
752#123—21no—
753#123—21no—
754#123—21no—
755#123—21no—
756#123—21no—
757C22⋊Q8—21no—
758C22⋊Q8—21no—
759C22⋊Q8—21no—
760C22⋊Q8—21no—
761C22⋊Q8C2×Dic4711yescharacteristic
762C22⋊Q8C2×Dic4711yescharacteristic
763C22⋊Q8C2×Dic4711yescharacteristic, complemented
764C22⋊Q8C2×Dic4711yescharacteristic, complemented
765#121—21no—
766#121—21no—
767#121—21no—
768#121—21no—
769#121—21no—
770#121—21no—
771#121—21no—
772#121—21no—
773#121—21no—
774#121—21no—
775#121C2×Dic4711yescharacteristic
776#121C2×Dic4711yescharacteristic
777#121C2×Dic4711yescharacteristic, complemented
778#121C2×Dic4711yescharacteristic, complemented
779#120—21no—
780#120—21no—
781#120—21no—
782#120—21no—
783#120—21no—
784#120—21no—
785C4×Q8C2×Dic4711yescharacteristic, complemented
786C4×Q8C2×Dic4711yescharacteristic, complemented
787C4×D4—21no—
788C4×D4—21no—
789C4×D4—21no—
790C4×D4—21no—
791C4×D4—21no—
792C4×D4—21no—
793C4×D4—21no—
794C4×D4—21no—
795C4×D4—21no—
796C4×D4—21no—
797C4×D4—21no—
798C4×D4—21no—
799C4×D4C2×Dic4711yescharacteristic
800C4×D4C2×Dic4711yescharacteristic
801C4×D4C2×Dic4711yescharacteristic
802C4×D4C2×Dic4711yescharacteristic
803C4×D4C2×Dic4711yescharacteristic, complemented
804C4×D4C2×Dic4711yescharacteristic, complemented
805C4×D4C22⋊D4711yescharacteristic
806C4×D4C22⋊D4711yescharacteristic
807C4×D4C22⋊D4711yescharacteristic
808C4×D4C22⋊D4711yescharacteristic
809#117—21no—
810#117—942no—
811#117—1881no—
812#117C22×D4711yescharacteristic
813C2×C4⋊C4—21no—
814C2×C4⋊C4—941no—
815C2×C4⋊C4—941no—
816C2×C4⋊C4C22⋊D4711yescharacteristic
817C2×C22⋊C4—21no—
818C2×C22⋊C4—21no—
819C2×C22⋊C4—941no—
820C2×C22⋊C4—941no—
821C2×C22⋊C4—941no—
822C2×C22⋊C4C22⋊D4711yescharacteristic
823C2×C22⋊C4C22⋊D4711yescharacteristic
824C2×C42—21no—
825C2×C42—471no—
826C2×C42—471no—
827C2×C42—471no—
828C2×C42—471no—
829C2×C42—942no—
830C2×C42—941no—
831C2×C42—1881no—
832C2×C42C22×D4711yescharacteristic
833C4⋊C8—941no—
834C4⋊C8—941no—
835#104—474no—
836#104—942no—
837#104—942no—
838#104—942no—
839#104—942no—
840#104—942no—
841#104—942no—
842#104—942no—
843#104—1881no—
844#104—1881no—
845#104—1881no—
846#104—1881no—
847C22⋊C8—941no—
848C22⋊C8—941no—
849C22⋊C8—941no—
850C22⋊C8—941no—
851#97—941no—
852C4×C8—941no—
853#95—941no—
854#95—941no—
855#95—941no—
856#95—941no—
857#95—941no—
858C24—21no—
859C24—21no—
860C24C2×C22⋊D4711yescharacteristic
861C24C2×C22⋊D4711yescharacteristic
862#41—21no—
863#41—21no—
864#41—22no—
865#41—22no—
866#41—22no—
867#41—22no—
868#41—21no—
869#41—21no—
870#41—21no—
871#41—21no—
872#41—21no—
873#41—21no—
874#41—21no—
875#41—21no—
876#41—42no—
877#41—42no—
878#41—42no—
879#41—42no—
880#41—41no—
881#41—41no—
882#41—41no—
883#41—41no—
884#41—42no—
885#41—42no—
886#41—42no—
887#41—42no—
888#41D4×D4712yes—
889#41#1062535212yes—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—22no—
893C2×Q8—22no—
894C2×Q8—41no—
895C2×Q8—41no—
896C2×Q8C22×Dic4711yescharacteristic
897C2×Q8C22×Dic4711yescharacteristic
898C2×Q8C22×Dic4711yescharacteristic
899C2×D4—21no—
900C2×D4—22no—
901C2×D4—22no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—41no—
917C2×D4—41no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—44no—
924C2×D4C22⋊Dic4711yescharacteristic
925C2×D4C22⋊Dic4711yescharacteristic
926C2×D4C22⋊Dic4711yescharacteristic
927C2×D4C22⋊Dic4711yescharacteristic
928C2×D4C22×Dic4711yescharacteristic
929C2×D4C22×Dic4711yescharacteristic
930C2×D4C22×Dic4711yescharacteristic
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—941no—
955C22×C4—941no—
956C22×C4—941no—
957C22×C4—941no—
958C22×C4—1882no—
959C22×C4—1882no—
960C22×C4—1882no—
961C22×C4C22×Dic4711yescharacteristic
962C22×C4C22×Dic4711yescharacteristic
963C22×C4C22×Dic4711yescharacteristic
964C22×C4C22×Dic4711yescharacteristic
965C22×C4C2×C22⋊D4711yescharacteristic
966C22×C4C2×C22⋊D4711yescharacteristic
967C22×C4C2×C22⋊D4711yescharacteristic
968C22×C4C2×C22⋊D4711yescharacteristic
969C22×C4C2×C22⋊D4711yescharacteristic
970C22×C4C2×C22⋊D4711yescharacteristic
971C22×C4C2×C22⋊D4711yescharacteristic
972C22×C4C2×C22⋊D4711yescharacteristic
973C22×C4C23×D4711yescharacteristic
974M16—472no—
975M16—941no—
976M16—941no—
977M16—941no—
978M16—941no—
979M16—941no—
980M16—941no—
981M16—941no—
982M16—1882no—
983M16—1882no—
984C2×C8—941no—
985C2×C8—941no—
986C2×C8—941no—
987C2×C8—941no—
988C2×C8—1882no—
989C2×C8—1882no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—1882no—
999C4⋊C4—1882no—
1000C4⋊C4C22⋊Dic4711yescharacteristic
1001C4⋊C4C22⋊Dic4711yescharacteristic
1002C4⋊C4C22⋊Dic4711yescharacteristic
1003C4⋊C4C22⋊Dic4711yescharacteristic
1004C4⋊C4C22×Dic4711yescharacteristic
1005C4⋊C4C22×Dic4711yescharacteristic
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—21no—
1009C22⋊C4—21no—
1010C22⋊C4—21no—
1011C22⋊C4—21no—
1012C22⋊C4—21no—
1013C22⋊C4—21no—
1014C22⋊C4—21no—
1015C22⋊C4—21no—
1016C22⋊C4—21no—
1017C22⋊C4—21no—
1018C22⋊C4—21no—
1019C22⋊C4—21no—
1020C22⋊C4—21no—
1021C22⋊C4—1882no—
1022C22⋊C4—1882no—
1023C22⋊C4—1882no—
1024C22⋊C4C22⋊Dic4711yescharacteristic
1025C22⋊C4C22⋊Dic4711yescharacteristic
1026C22⋊C4C22⋊Dic4711yescharacteristic
1027C22⋊C4C22⋊Dic4711yescharacteristic
1028C22⋊C4C22⋊Dic4711yescharacteristic
1029C22⋊C4C22⋊Dic4711yescharacteristic
1030C22⋊C4C22⋊Dic4711yescharacteristic
1031C22⋊C4C22⋊Dic4711yescharacteristic
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—472no—
1036C42—941no—
1037C42—941no—
1038C42—941no—
1039C42—941no—
1040C42—941no—
1041C42—941no—
1042C42—941no—
1043C42—1882no—
1044C42C22×Dic4711yescharacteristic
1045C42C22×Dic4711yescharacteristic
1046C42C2×C22⋊D4711yescharacteristic
1047C42C2×C22⋊D4711yescharacteristic
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—22no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—81no—
1064C23—81no—
1065C23C2×C22⋊Dic4711yescharacteristic
1066C23C2×C22⋊Dic4711yescharacteristic
1067C23C2×C22⋊Dic4711yescharacteristic
1068C23C2×C22⋊Dic4711yescharacteristic
1069C23C22×C22⋊D4711yescharacteristic
1070Q8—21no—
1071Q8—21no—
1072Q8—21no—
1073Q8—21no—
1074Q8—21no—
1075Q8—42no—
1076Q8—42no—
1077Q8D4×Dic4712yes—
1078D4—22no—
1079D4—22no—
1080D4—22no—
1081D4—22no—
1082D4—21no—
1083D4—21no—
1084D4—21no—
1085D4—21no—
1086D4—21no—
1087D4—41no—
1088D4—41no—
1089D4—42no—
1090D4—42no—
1091D4—42no—
1092D4—42no—
1093D4—42no—
1094D4—42no—
1095D4—42no—
1096D4—42no—
1097D4—41no—
1098D4—41no—
1099D4—41no—
1100D4—41no—
1101D4—42no—
1102D4—81no—
1103D4—81no—
1104D4—81no—
1105D4D4×Dic4712yes—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—22no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—81no—
1147C2×C4—942no—
1148C2×C4—942no—
1149C2×C4—1881no—
1150C2×C4—1881no—
1151C2×C4—1881no—
1152C2×C4—1881no—
1153C2×C4—1881no—
1154C2×C4—1881no—
1155C2×C4—1881no—
1156C2×C4—1881no—
1157C2×C4—1881no—
1158C2×C4—1888no—
1159C2×C4—1881no—
1160C2×C4C2×C22⋊Dic4711yescharacteristic
1161C2×C4C2×C22⋊Dic4711yescharacteristic
1162C2×C4C2×C22⋊Dic4711yescharacteristic
1163C2×C4C2×C22⋊Dic4711yescharacteristic
1164C2×C4C2×C22⋊Dic4711yescharacteristic
1165C2×C4C2×C22⋊Dic4711yescharacteristic
1166C2×C4C2×C22⋊Dic4711yescharacteristic
1167C2×C4C2×C22⋊Dic4711yescharacteristic
1168C2×C4C23×Dic4711yescharacteristic
1169C2×C4C2×D4×D4711yescharacteristic
1170C2×C4C22×C22⋊D4711yescharacteristic
1171C2×C4C2×#1062535211yescharacteristic
1172C2×C4#1309406911yescharacteristic
1173C2×C4#1309406911yescharacteristic
1174C8—942no—
1175C8—1881no—
1176C8—1881no—
1177C8—1881no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—21no—
1187C22—21no—
1188C22—21no—
1189C22—21no—
1190C22—21no—
1191C22—22no—
1192C22—42no—
1193C22—42no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—81no—
1203C22—81no—
1204C22—84no—
1205C22—84no—
1206C22#1568914012yescomplemented
1207C22C22×C22⋊Dic4711yescharacteristic
1208C22D4×C22⋊D4711yescharacteristic
1209C22#1568976711yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—21no—
1213C4—21no—
1214C4—21no—
1215C4—21no—
1216C4—21no—
1217C4—21no—
1218C4—22no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—3761no—
1224C4—3761no—
1225C4—1882no—
1226C4—1882no—
1227C4C2×D4×Dic4711yescharacteristic
1228C4#1568959811yescharacteristic
1229C4D4×C22⋊D4711yescharacteristic
1230C4#1568976711yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—22no—
1234C2—41no—
1235C2—41no—
1236C2—41no—
1237C2—42no—
1238C2—81no—
1239C2—81no—
1240C2D4×C22⋊Dic4711yescharacteristic
1241C2C2×#1568914011yescharacteristic
1242C2#2025193511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalD4×#41×C47C2
socleC22×C47C22×C22⋊C4
cosocleC22×C4×C47C24
hypercenterD4×#41D47
hypocenterC47#22434
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. D4×#10625329C2semidirect
2. C2×#15689140C2semidirect
3. C22×#13093951C2semidirect
4. #20245833C2semidirect
5. #20244308C2semidirect
6. #20244221C2semidirect
7. #20243837C2semidirect
8. #20243832C2semidirect
9. #20243691C2semidirect
10. #20243691C2semidirect
11. #20243408C2semidirect
12. #20243332C2semidirect
13. #20243332C2semidirect
14. #20243198C2semidirect
16. C22×#10625329C22semidirect
17. C22×#10625329C22semidirect
18. C2×#13093983C22semidirect
19. C22×C4×Dic47C22semidirect
24. #15689147C22semidirect
31. C2×#13093951C22semidirect
32. C2×#13093951C22semidirect
33. C2×#13093951C22semidirect
34. C2×#13093951C22semidirect
35. C2×#13093951C22semidirect
36. C2×#13093951C22semidirect
37. C2×#13093951C22semidirect
38. C2×#13093951C22semidirect
39. #15689087C22semidirect
40. #15689087C22semidirect
41. C4×#10625329C22semidirect
46. C4×C4⋊Dic47C22semidirect
47. C4×C22⋊Dic47C22semidirect
48. C4×C22⋊Dic47C22semidirect
49. #15688969C22semidirect
50. #15688882C22semidirect
51. #15688882C22semidirect
52. #15688882C22semidirect
53. #15688882C22semidirect
56. C47×#550C4semidirect
57. D4×Q8×C47C4semidirect
58. C47×#548C4semidirect
59. C47×#548C4semidirect
61. C47×#547C4semidirect
64. C47×#546C4semidirect
65. C47×#546C4semidirect
67. D42×C47C4semidirect
117. #13093951D4semidirect
143. C2×#41×C47C2×C4semidirect
144. C2×#41×C47C2×C4semidirect
149. C22×Q8×C47C2×C4semidirect
154. C22×D4×C47C2×C4semidirect
161. C4⋊Q8×C47C2×C4semidirect
163. #127×C47C2×C4semidirect
166. #124×C47C2×C4semidirect
167. #124×C47C2×C4semidirect
180. C22⋊Q8×C47C2×C4semidirect
181. C22⋊Q8×C47C2×C4semidirect
194. #121×C47C2×C4semidirect
195. #121×C47C2×C4semidirect
202. C4×Q8×C47C2×C4semidirect
203. C4×Q8×C47C2×C4semidirect
220. C4×D4×C47C2×C4semidirect
221. C4×D4×C47C2×C4semidirect
409. C4×Dic47C2×D4semidirect
419. #10625329C2×D4semidirect
585. C22×C47#421semidirect
641. #550Dic47semidirect
642. D4×Q8Dic47semidirect
643. #548Dic47semidirect
644. #548Dic47semidirect
646. #547Dic47semidirect
649. #546Dic47semidirect
650. #546Dic47semidirect
652. D42Dic47semidirect
698. C47#22434semidirect
713. C2×#41C2×Dic47semidirect
714. C2×#41C2×Dic47semidirect
719. C22×Q8C2×Dic47semidirect
724. C22×D4C2×Dic47semidirect
744. C4⋊Q8C2×Dic47semidirect
746. #127C2×Dic47semidirect
749. #124C2×Dic47semidirect
750. #124C2×Dic47semidirect
763. C22⋊Q8C2×Dic47semidirect
764. C22⋊Q8C2×Dic47semidirect
777. #121C2×Dic47semidirect
778. #121C2×Dic47semidirect
785. C4×Q8C2×Dic47semidirect
786. C4×Q8C2×Dic47semidirect
803. C4×D4C2×Dic47semidirect
804. C4×D4C2×Dic47semidirect
1206. C22#15689140semidirect

Maximal subgroups

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

subgroupindex
D4×#106253292
C2×#156891402
C22×#130939512
#202458332
#202443082
#202442212
#202438372
#202438322
#202436912
#202434082
#202433322
#202431982
D4×#41×C472
#2243447