Finite Group Databasebeta

← #26183803

Subgroups — #26183803

Order 12032.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252423C211yesmaximal, characteristic, complemented
2#20246021C211yesmaximal, characteristic, complemented
3#20241965C211yesmaximal, characteristic, complemented
4#20241956C211yesmaximal, characteristic, complemented
5#20241948C211yesmaximal, characteristic, complemented
6#20241944C211yesmaximal, characteristic, complemented
7#20241935C211yesmaximal, characteristic, complemented
8#20241931C211yesmaximal, characteristic, complemented
9#20241926C211yesmaximal, characteristic, complemented
10#20241917C211yesmaximal, characteristic, complemented
11#20241904C211yesmaximal, characteristic, complemented
12#20241892C211yesmaximal, characteristic, complemented
13#20241879C211yesmaximal, characteristic, complemented
14C2×#15688857C211yesmaximal, characteristic, complemented
15C47×#3519C211yesmaximal, characteristic
16#15689201—21no—
17#15689195—21no—
18#15689195—21no—
19D4×C47⋊C8—21no—
20#15689180C2211yescharacteristic, complemented
21#15689176C2211yescharacteristic, complemented
22#15689087C2211yescharacteristic, complemented
23#15689087C2211yescharacteristic, complemented
24C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
25C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
26#15689016—21no—
27#15689009—21no—
28#15689003—21no—
29#15688998—21no—
30#15688991C2211yescharacteristic, complemented
31#15688989C2211yescharacteristic, complemented
32#15688986C2211yescharacteristic, complemented
33#15688983C2211yescharacteristic, complemented
34C4×C22⋊Dic47C2211yescharacteristic, complemented
35C2×C47⋊#95C2211yescharacteristic, complemented
36#15688860C2211yescharacteristic, complemented
37#15688860C2211yescharacteristic, complemented
38#15688860C2211yescharacteristic, complemented
39#15688860C2211yescharacteristic, complemented
40#15688857C2211yescharacteristic
41#15688857C2211yescharacteristic
42#15688857C2211yescharacteristic
43#15688857C2211yescharacteristic
44#15688857C2211yescharacteristic, complemented
45#15688857C2211yescharacteristic, complemented
46#15688857C2211yescharacteristic, complemented
47#15688857C2211yescharacteristic, complemented
48#15688857C2211yescharacteristic, complemented
49#15688857C2211yescharacteristic, complemented
50#15688857C2211yescharacteristic, complemented
51#15688857C2211yescharacteristic, complemented
52C47×#555C411yescharacteristic, complemented
53C47×#554C411yescharacteristic, complemented
54C47×#553—21no—
55C47×#553C411yescharacteristic, complemented
56C47×#553C411yescharacteristic, complemented
57C47×#550C411yescharacteristic, complemented
58C47×#546—21no—
59C47×#546—21no—
60C47×#546C411yescharacteristic, complemented
61C47×#546C411yescharacteristic, complemented
62D42×C47—21no—
63D42×C47C411yescharacteristic, complemented
64C47×#540—21no—
65C47×#538—21no—
66C47×#538—21no—
67C47×#532C2211yescharacteristic
68C47×#529C2211yescharacteristic
69C47×#525C2211yescharacteristic
70C47×#525C2211yescharacteristic
71C2×#121×C47C2211yescharacteristic
72C2×#121×C47C2211yescharacteristic
73C47×#518—21no—
74C2×C4×D4×C47C2211yescharacteristic
75C23×Dic47—21no—
76C2×#10625329—21no—
77C2×#10625329—21no—
78C22×C47⋊C8—21no—
79C22×C47⋊C8—21no—
80C2×C4⋊Dic47—21no—
81C2×C4⋊Dic47—21no—
82C2×C22⋊Dic47—21no—
83C2×C22⋊Dic47—21no—
84C2×C22⋊Dic47—21no—
85C2×C4×Dic47—21no—
86C4⋊(C47⋊C8)—21no—
87C4⋊(C47⋊C8)—21no—
88C22⋊(C47⋊C8)—21no—
89C22⋊(C47⋊C8)—21no—
90C22⋊(C47⋊C8)—21no—
91C22⋊(C47⋊C8)—21no—
92C22⋊(C47⋊C8)C2311yescharacteristic
93C22⋊(C47⋊C8)C2311yescharacteristic
94C22⋊(C47⋊C8)C2311yescharacteristic
95C22⋊(C47⋊C8)C2311yescharacteristic
96#13093935—21no—
97C4×C47⋊C8—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C47⋊#95C2311yescharacteristic
104C47⋊#95C2311yescharacteristic
105C47⋊#95C2311yescharacteristic
106C47⋊#95C2311yescharacteristic
107C2×#41×C47—21no—
108C2×#41×C47C2×C411yescharacteristic
109C2×#41×C47C2×C411yescharacteristic, complemented
110C22×D4×C47—21no—
111C22×D4×C47—21no—
112C22×D4×C47—21no—
113C22×D4×C47C2×C411yescharacteristic
114C22×D4×C47C2×C411yescharacteristic, complemented
115C22×D4×C47D411yescharacteristic
116C23×C4×C47C2311yescharacteristic
117C23×C4×C47C2311yescharacteristic
118C4⋊Q8×C47C2×C411yescharacteristic, complemented
119#127×C47—21no—
120#127×C47C2×C411yescharacteristic, complemented
121#126×C47—21no—
122#126×C47—21no—
123#126×C47—21no—
124#125×C47—21no—
125#125×C47C2×C411yescharacteristic, complemented
126#124×C47—21no—
127#124×C47—21no—
128#124×C47—21no—
129#124×C47C2×C411yescharacteristic, complemented
130#123×C47—21no—
131#123×C47—21no—
132#123×C47—21no—
133#123×C47—21no—
134#123×C47—21no—
135#123×C47—21no—
136#123×C47—21no—
137C22⋊Q8×C47—21no—
138C22⋊Q8×C47—21no—
139C22⋊Q8×C47C2×C411yescharacteristic
140C22⋊Q8×C47C2×C411yescharacteristic, complemented
141C22⋊Q8×C47C2311yescharacteristic
142#121×C47—21no—
143#121×C47—21no—
144#121×C47—21no—
145#121×C47—21no—
146#121×C47—21no—
147#121×C47—21no—
148#121×C47—21no—
149#121×C47—21no—
150#121×C47—21no—
151#121×C47—21no—
152#121×C47—21no—
153#121×C47—21no—
154#121×C47—21no—
155#121×C47C2×C411yescharacteristic
156#121×C47C2×C411yescharacteristic
157#121×C47C2×C411yescharacteristic
158#121×C47C2×C411yescharacteristic, complemented
159#121×C47C2×C411yescharacteristic, complemented
160#121×C47C2×C411yescharacteristic, complemented
161#121×C47C2311yescharacteristic
162#121×C47C2311yescharacteristic
163#121×C47C2311yescharacteristic
164#120×C47—21no—
165#120×C47—21no—
166#120×C47—21no—
167#120×C47—21no—
168#120×C47—21no—
169#120×C47—21no—
170C4×Q8×C47C2×C411yescharacteristic, complemented
171C4×D4×C47—21no—
172C4×D4×C47—21no—
173C4×D4×C47—21no—
174C4×D4×C47—21no—
175C4×D4×C47—21no—
176C4×D4×C47—21no—
177C4×D4×C47—21no—
178C4×D4×C47—21no—
179C4×D4×C47—21no—
180C4×D4×C47—21no—
181C4×D4×C47C2×C411yescharacteristic
182C4×D4×C47C2×C411yescharacteristic
183C4×D4×C47C2×C411yescharacteristic
184C4×D4×C47C2×C411yescharacteristic
185C4×D4×C47C2×C411yescharacteristic, complemented
186C4×D4×C47C2×C411yescharacteristic, complemented
187C4×D4×C47C2×C411yescharacteristic, complemented
188C4×D4×C47D411yescharacteristic
189C4×D4×C47D411yescharacteristic
190C4×D4×C47D411yescharacteristic
191C4×D4×C47D411yescharacteristic
192#117×C47—21no—
193#117×C47—21no—
194#117×C47C2×C411yescharacteristic
195#117×C47C2×C411yescharacteristic, complemented
196C2×C4⋊C4×C47C2×C411yescharacteristic
197C2×C4⋊C4×C47C2×C411yescharacteristic, complemented
198C2×C4⋊C4×C47D411yescharacteristic
199C2×C22⋊C4×C47—21no—
200C2×C22⋊C4×C47—21no—
201C2×C22⋊C4×C47—21no—
202C2×C22⋊C4×C47—21no—
203C2×C22⋊C4×C47D411yescharacteristic
204C2×C22⋊C4×C47D411yescharacteristic
205C2×C42×C47C2311yescharacteristic
206C24×C47—21no—
207C24×C47—21no—
208C24×C47C2×D411yescharacteristic
209C24×C47C2×D411yescharacteristic
210#41×C47—81no—
211#41×C47—81no—
212#41×C47—81no—
213#41×C47—81no—
214C2×Q8×C47—21no—
215C2×Q8×C47C22×C411yescharacteristic
216C2×D4×C47—21no—
217C2×D4×C47—21no—
218C2×D4×C47—21no—
219C2×D4×C47—21no—
220C2×D4×C47—21no—
221C2×D4×C47—21no—
222C2×D4×C47—21no—
223C2×D4×C47—21no—
224C2×D4×C47—21no—
225C2×D4×C47—21no—
226C2×D4×C47—21no—
227C2×D4×C47—21no—
228C2×D4×C47—21no—
229C2×D4×C47—21no—
230C2×D4×C47—21no—
231C2×D4×C47—42no—
232C2×D4×C47—44no—
233C2×D4×C47—81no—
234C2×D4×C47—81no—
235C2×D4×C47—81no—
236C2×D4×C47—81no—
237C2×D4×C47—81no—
238C2×D4×C47—81no—
239C2×D4×C47C22⋊C411yescharacteristic
240C2×D4×C47C22⋊C411yescharacteristic
241C2×D4×C47C22⋊C411yescharacteristic
242C2×D4×C47C22⋊C411yescharacteristic
243C2×D4×C47C22×C411yescharacteristic
244C2×D4×C47C22×C411yescharacteristic
245C2×D4×C47C22×C411yescharacteristic
246C22×C4×C47—21no—
247C22×C4×C47—21no—
248C22×C4×C47—21no—
249C22×C4×C47—21no—
250C22×C4×C47—21no—
251C22×C4×C47—21no—
252C22×C4×C47—21no—
253C22×C4×C47—81no—
254C22×C4×C47—81no—
255C22×C4×C47C22×C411yescharacteristic
256C22×C4×C47C22×C411yescharacteristic
257C22×C4×C47C22×C411yescharacteristic
258C22×C4×C47C22×C411yescharacteristic
259C22×C4×C47C2×D411yescharacteristic
260C22×C4×C47C2×D411yescharacteristic
261C22×C4×C47C2×D411yescharacteristic
262C22×C4×C47C2×D411yescharacteristic
263C22×C4×C47C2×D411yescharacteristic
264C22×C4×C47C2×D411yescharacteristic
265C22×C4×C47C2×D411yescharacteristic
266C22×C4×C47C2×D411yescharacteristic
267C22×C4×C47C2411yescharacteristic
268C22×Dic47—21no—
269C22×Dic47—21no—
270C22×Dic47—21no—
271C22×Dic47—21no—
272C22×Dic47—42no—
273C22×Dic47—81no—
274C22×Dic47—81no—
275C4⋊C4×C47—21no—
276C4⋊C4×C47—21no—
277C4⋊C4×C47—21no—
278C4⋊C4×C47—21no—
279C4⋊C4×C47—21no—
280C4⋊C4×C47—21no—
281C4⋊C4×C47—21no—
282C4⋊C4×C47—21no—
283C4⋊C4×C47—21no—
284C4⋊C4×C47C22⋊C411yescharacteristic
285C4⋊C4×C47C22⋊C411yescharacteristic
286C4⋊C4×C47C22⋊C411yescharacteristic
287C4⋊C4×C47C22⋊C411yescharacteristic
288C4⋊C4×C47C22×C411yescharacteristic
289C4⋊C4×C47C22×C411yescharacteristic
290C4⋊C4×C47C22×C411yescharacteristic
291C4⋊C4×C47C22×C411yescharacteristic
292C22⋊C4×C47—21no—
293C22⋊C4×C47—21no—
294C22⋊C4×C47—21no—
295C22⋊C4×C47—21no—
296C22⋊C4×C47—21no—
297C22⋊C4×C47—21no—
298C22⋊C4×C47—21no—
299C22⋊C4×C47—21no—
300C22⋊C4×C47—21no—
301C22⋊C4×C47—21no—
302C22⋊C4×C47—21no—
303C22⋊C4×C47—21no—
304C22⋊C4×C47—21no—
305C22⋊C4×C47—21no—
306C22⋊C4×C47—21no—
307C22⋊C4×C47—21no—
308C22⋊C4×C47—21no—
309C22⋊C4×C47—21no—
310C22⋊C4×C47—21no—
311C22⋊C4×C47C22⋊C411yescharacteristic
312C22⋊C4×C47C22⋊C411yescharacteristic
313C22⋊C4×C47C22⋊C411yescharacteristic
314C22⋊C4×C47C22⋊C411yescharacteristic
315C22⋊C4×C47C22⋊C411yescharacteristic
316C22⋊C4×C47C22⋊C411yescharacteristic
317C22⋊C4×C47C22⋊C411yescharacteristic
318C22⋊C4×C47C22⋊C411yescharacteristic
319C42×C47—21no—
320C42×C47—21no—
321C42×C47—21no—
322C42×C47C22×C411yescharacteristic
323C42×C47C22×C411yescharacteristic
324C42×C47C2×D411yescharacteristic
325C42×C47C2×D411yescharacteristic
326C22⋊Dic47—42no—
327C22⋊Dic47—81no—
328C22⋊Dic47—81no—
329C4⋊Dic47—81no—
330C4⋊Dic47—81no—
331C4×Dic47—81no—
332#10625329—81no—
333#10625329—81no—
334C2×C47⋊C8—21no—
335C2×C47⋊C8—21no—
336C2×C47⋊C8—21no—
337C2×C47⋊C8—21no—
338C2×C47⋊C8—81no—
339C2×C47⋊C8—81no—
340C23×C47—21no—
341C23×C47—21no—
342C23×C47—22no—
343C23×C47—21no—
344C23×C47—21no—
345C23×C47—21no—
346C23×C47—21no—
347C23×C47—21no—
348C23×C47—41no—
349C23×C47—41no—
350C23×C47—41no—
351C23×C47—42no—
352C23×C47—42no—
353C23×C47—81no—
354C23×C47—81no—
355C23×C47—81no—
356C23×C47—81no—
357C23×C47C2×C22⋊C411yescharacteristic
358C23×C47C2×C22⋊C411yescharacteristic
359C23×C47C2×C22⋊C411yescharacteristic
360C23×C47C2×C22⋊C411yescharacteristic
361C23×C47C22×D411yescharacteristic
362Q8×C47—41no—
363Q8×C47—81no—
364D4×C47—22no—
365D4×C47—22no—
366D4×C47—41no—
367D4×C47—41no—
368D4×C47—41no—
369D4×C47—41no—
370D4×C47—41no—
371D4×C47—42no—
372D4×C47—42no—
373D4×C47—41no—
374D4×C47—41no—
375D4×C47—41no—
376D4×C47—41no—
377D4×C47—41no—
378D4×C47—41no—
379D4×C47—42no—
380D4×C47—81no—
381D4×C47—81no—
382D4×C47—81no—
383D4×C47—81no—
384D4×C47—81no—
385D4×C47—81no—
386D4×C47—81no—
387D4×C47—81no—
388D4×C47—81no—
389C2×C4×C47—21no—
390C2×C4×C47—21no—
391C2×C4×C47—21no—
392C2×C4×C47—21no—
393C2×C4×C47—21no—
394C2×C4×C47—21no—
395C2×C4×C47—21no—
396C2×C4×C47—41no—
397C2×C4×C47—41no—
398C2×C4×C47—41no—
399C2×C4×C47—41no—
400C2×C4×C47—41no—
401C2×C4×C47—41no—
402C2×C4×C47—41no—
403C2×C4×C47—41no—
404C2×C4×C47—41no—
405C2×C4×C47—41no—
406C2×C4×C47—41no—
407C2×C4×C47—41no—
408C2×C4×C47—42no—
409C2×C4×C47—81no—
410C2×C4×C47—81no—
411C2×C4×C47—81no—
412C2×C4×C47—81no—
413C2×C4×C47—81no—
414C2×C4×C47—81no—
415C2×C4×C47C2×C22⋊C411yescharacteristic
416C2×C4×C47C2×C22⋊C411yescharacteristic
417C2×C4×C47C2×C22⋊C411yescharacteristic
418C2×C4×C47C2×C22⋊C411yescharacteristic
419C2×C4×C47C2×C22⋊C411yescharacteristic
420C2×C4×C47C2×C22⋊C411yescharacteristic
421C2×C4×C47C2×C22⋊C411yescharacteristic
422C2×C4×C47C2×C22⋊C411yescharacteristic
423C2×C4×C47C23×C411yescharacteristic
424C2×C4×C47C22×D411yescharacteristic
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—84no—
438C47⋊C8—41no—
439C47⋊C8—41no—
440C47⋊C8—41no—
441C47⋊C8—41no—
442#17597—471nomaximal, Sylow
443C22×C47—21no—
444C22×C47—21no—
445C22×C47—21no—
446C22×C47—21no—
447C22×C47—21no—
448C22×C47—21no—
449C22×C47—21no—
450C22×C47—21no—
451C22×C47—21no—
452C22×C47—21no—
453C22×C47—21no—
454C22×C47—21no—
455C22×C47—21no—
456C22×C47—42no—
457C22×C47—42no—
458C22×C47—41no—
459C22×C47—41no—
460C22×C47—41no—
461C22×C47—41no—
462C22×C47—41no—
463C22×C47—41no—
464C22×C47—41no—
465C22×C47—41no—
466C22×C47—41no—
467C22×C47—81no—
468C22×C47—81no—
469C22×C47—162no—
470C22×C47—162no—
471C22×C47#42112yes—
472C22×C47C22×C22⋊C411yescharacteristic
473C22×C47#57611yescharacteristic
474C22×C47#57711yescharacteristic
475C4×C47—21no—
476C4×C47—21no—
477C4×C47—21no—
478C4×C47—21no—
479C4×C47—21no—
480C4×C47—21no—
481C4×C47—21no—
482C4×C47—21no—
483C4×C47—21no—
484C4×C47—21no—
485C4×C47—41no—
486C4×C47—41no—
487C4×C47—41no—
488C4×C47—41no—
489C4×C47—41no—
490Dic47—81no—
491Dic47—81no—
492Dic47—81no—
493Dic47—81no—
494#3519D4711yescharacteristic
495#2974—471no—
496#2318—471no—
497#1521—471no—
498#1519—471no—
499#1517—471no—
500#1516—471no—
501#1514—471no—
502#1513—471no—
503#1512—471no—
504#1510—471no—
505#1507—471no—
506#1504—471no—
507#1501—471no—
508C2×#327—471no—
509C2×C47—21no—
510C2×C47—21no—
511C2×C47—22no—
512C2×C47—41no—
513C2×C47—41no—
514C2×C47—41no—
515C2×C47—81no—
516C2×C47—81no—
517C2×C47—81no—
518C2×C47#288311yescharacteristic
519C2×C47#289711yescharacteristic
520C2×C47C2×#42111yescharacteristic
521#555Dic4711yescharacteristic, complemented
522#554Dic4711yescharacteristic, complemented
523#553—21no—
524#553Dic4711yescharacteristic, complemented
525#553Dic4711yescharacteristic, complemented
526#550Dic4711yescharacteristic, complemented
527#546—21no—
528#546—21no—
529#546Dic4711yescharacteristic, complemented
530#546Dic4711yescharacteristic, complemented
531D42—21no—
532D42Dic4711yescharacteristic, complemented
533#540—21no—
534#538—21no—
535#538—21no—
536#532C2×D4711yescharacteristic
537#529C2×D4711yescharacteristic
538#525C2×D4711yescharacteristic
539#525C2×D4711yescharacteristic
540C2×#121C2×D4711yescharacteristic
541C2×#121C2×D4711yescharacteristic
542#518—21no—
543C2×C4×D4C2×D4711yescharacteristic
544#436—941no—
545#435—941no—
546#435—941no—
547C8×D4—941no—
548#432—471no—
549#431—471no—
550#407—471no—
551#407—471no—
552C2×C22⋊C8—471no—
553C2×C22⋊C8—471no—
554#388—941no—
555#387—941no—
556#386—941no—
557#385—941no—
558#383—471no—
559#382—471no—
560#381—471no—
561#380—471no—
562C4×C22⋊C4—471no—
563C2×#95—471no—
564#328—471no—
565#328—471no—
566#328—471no—
567#328—471no—
568#327—471no—
569#327—471no—
570#327—471no—
571#327—471no—
572#327—471no—
573#327—471no—
574#327—471no—
575#327—471no—
576#327—471no—
577#327—471no—
578#327—471no—
579#327—471no—
580C47#1759711yescharacteristic, complemented, Sylow
581C2×#41—21no—
582C2×#41C2×Dic4711yescharacteristic
583C2×#41C2×Dic4711yescharacteristic, complemented
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4C2×Dic4711yescharacteristic
588C22×D4C2×Dic4711yescharacteristic, complemented
589C22×D4C22⋊D4711yescharacteristic
590C23×C4—941no—
591C23×C4C22×D4711yescharacteristic
592C23×C4C22×D4711yescharacteristic
593C2×M16—941no—
594C2×M16—941no—
595C22×C8—941no—
596C22×C8—941no—
597C4⋊Q8C2×Dic4711yescharacteristic, complemented
598#127—21no—
599#127C2×Dic4711yescharacteristic, complemented
600#126—21no—
601#126—21no—
602#126—21no—
603#125—21no—
604#125C2×Dic4711yescharacteristic, complemented
605#124—21no—
606#124—21no—
607#124—21no—
608#124C2×Dic4711yescharacteristic, complemented
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8C2×Dic4711yescharacteristic
619C22⋊Q8C2×Dic4711yescharacteristic, complemented
620C22⋊Q8C22×D4711yescharacteristic
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121C2×Dic4711yescharacteristic
635#121C2×Dic4711yescharacteristic
636#121C2×Dic4711yescharacteristic
637#121C2×Dic4711yescharacteristic, complemented
638#121C2×Dic4711yescharacteristic, complemented
639#121C2×Dic4711yescharacteristic, complemented
640#121C22×D4711yescharacteristic
641#121C22×D4711yescharacteristic
642#121C22×D4711yescharacteristic
643#120—21no—
644#120—21no—
645#120—21no—
646#120—21no—
647#120—21no—
648#120—21no—
649C4×Q8C2×Dic4711yescharacteristic, complemented
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4C2×Dic4711yescharacteristic
661C4×D4C2×Dic4711yescharacteristic
662C4×D4C2×Dic4711yescharacteristic
663C4×D4C2×Dic4711yescharacteristic
664C4×D4C2×Dic4711yescharacteristic, complemented
665C4×D4C2×Dic4711yescharacteristic, complemented
666C4×D4C2×Dic4711yescharacteristic, complemented
667C4×D4C22⋊D4711yescharacteristic
668C4×D4C22⋊D4711yescharacteristic
669C4×D4C22⋊D4711yescharacteristic
670C4×D4C22⋊D4711yescharacteristic
671#117—21no—
672#117—21no—
673#117C2×Dic4711yescharacteristic
674#117C2×Dic4711yescharacteristic, complemented
675C2×C4⋊C4—941no—
676C2×C4⋊C4—941no—
677C2×C4⋊C4C2×Dic4711yescharacteristic
678C2×C4⋊C4C2×Dic4711yescharacteristic, complemented
679C2×C4⋊C4C22⋊D4711yescharacteristic
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—941no—
685C2×C22⋊C4—941no—
686C2×C22⋊C4—941no—
687C2×C22⋊C4C22⋊D4711yescharacteristic
688C2×C22⋊C4C22⋊D4711yescharacteristic
689C2×C42—941no—
690C2×C42C22×D4711yescharacteristic
691C4⋊C8—941no—
692C4⋊C8—941no—
693C22⋊C8—471no—
694C22⋊C8—471no—
695C22⋊C8—471no—
696C22⋊C8—471no—
697C22⋊C8—941no—
698C22⋊C8—941no—
699C22⋊C8—941no—
700C22⋊C8—941no—
701#97—941no—
702C4×C8—941no—
703#95—471no—
704#95—471no—
705#95—471no—
706#95—471no—
707#95—941no—
708#95—941no—
709#95—941no—
710#95—941no—
711#95—941no—
712C24—21no—
713C24—21no—
714C24C2×C22⋊D4711yescharacteristic
715C24C2×C22⋊D4711yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719#41—81no—
720C2×Q8—21no—
721C2×Q8C22×Dic4711yescharacteristic
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—42no—
738C2×D4—44no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4—81no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4C22⋊Dic4711yescharacteristic
746C2×D4C22⋊Dic4711yescharacteristic
747C2×D4C22⋊Dic4711yescharacteristic
748C2×D4C22⋊Dic4711yescharacteristic
749C2×D4C22×Dic4711yescharacteristic
750C2×D4C22×Dic4711yescharacteristic
751C2×D4C22×Dic4711yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—81no—
760C22×C4—81no—
761C22×C4—941no—
762C22×C4—941no—
763C22×C4—941no—
764C22×C4—941no—
765C22×C4—3761no—
766C22×C4—3761no—
767C22×C4—1882no—
768C22×C4C22×Dic4711yescharacteristic
769C22×C4C22×Dic4711yescharacteristic
770C22×C4C22×Dic4711yescharacteristic
771C22×C4C22×Dic4711yescharacteristic
772C22×C4C2×C22⋊D4711yescharacteristic
773C22×C4C2×C22⋊D4711yescharacteristic
774C22×C4C2×C22⋊D4711yescharacteristic
775C22×C4C2×C22⋊D4711yescharacteristic
776C22×C4C2×C22⋊D4711yescharacteristic
777C22×C4C2×C22⋊D4711yescharacteristic
778C22×C4C2×C22⋊D4711yescharacteristic
779C22×C4C2×C22⋊D4711yescharacteristic
780C22×C4C23×D4711yescharacteristic
781M16—3761no—
782M16—3761no—
783C2×C8—941no—
784C2×C8—941no—
785C2×C8—941no—
786C2×C8—941no—
787C2×C8—3761no—
788C2×C8—3761no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—3761no—
799C4⋊C4—3761no—
800C4⋊C4C22⋊Dic4711yescharacteristic
801C4⋊C4C22⋊Dic4711yescharacteristic
802C4⋊C4C22⋊Dic4711yescharacteristic
803C4⋊C4C22⋊Dic4711yescharacteristic
804C4⋊C4C22×Dic4711yescharacteristic
805C4⋊C4C22×Dic4711yescharacteristic
806C4⋊C4C22×Dic4711yescharacteristic
807C4⋊C4C22×Dic4711yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—3761no—
828C22⋊C4—3761no—
829C22⋊C4—1882no—
830C22⋊C4C22⋊Dic4711yescharacteristic
831C22⋊C4C22⋊Dic4711yescharacteristic
832C22⋊C4C22⋊Dic4711yescharacteristic
833C22⋊C4C22⋊Dic4711yescharacteristic
834C22⋊C4C22⋊Dic4711yescharacteristic
835C22⋊C4C22⋊Dic4711yescharacteristic
836C22⋊C4C22⋊Dic4711yescharacteristic
837C22⋊C4C22⋊Dic4711yescharacteristic
838C42—21no—
839C42—21no—
840C42—21no—
841C42—3761no—
842C42C22×Dic4711yescharacteristic
843C42C22×Dic4711yescharacteristic
844C42C2×C22⋊D4711yescharacteristic
845C42C2×C22⋊D4711yescharacteristic
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—81no—
860C23—81no—
861C23—81no—
862C23—81no—
863C23C2×C22⋊Dic4711yescharacteristic
864C23C2×C22⋊Dic4711yescharacteristic
865C23C2×C22⋊Dic4711yescharacteristic
866C23C2×C22⋊Dic4711yescharacteristic
867C23C22×C22⋊D4711yescharacteristic
868Q8—41no—
869Q8—81no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—42no—
878D4—42no—
879D4—42no—
880D4—41no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—81no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—42no—
915C2×C4—81no—
916C2×C4—81no—
917C2×C4—81no—
918C2×C4—81no—
919C2×C4—81no—
920C2×C4—81no—
921C2×C4—3764no—
922C2×C4—1881no—
923C2×C4—1881no—
924C2×C4—1881no—
925C2×C4—1881no—
926C2×C4—1881no—
927C2×C4—1881no—
928C2×C4—1881no—
929C2×C4—1881no—
930C2×C4—1881no—
931C2×C4—1881no—
932C2×C4—1881no—
933C2×C4—1881no—
934C2×C4C2×C22⋊Dic4711yescharacteristic
935C2×C4C2×C22⋊Dic4711yescharacteristic
936C2×C4C2×C22⋊Dic4711yescharacteristic
937C2×C4C2×C22⋊Dic4711yescharacteristic
938C2×C4C2×C22⋊Dic4711yescharacteristic
939C2×C4C2×C22⋊Dic4711yescharacteristic
940C2×C4C2×C22⋊Dic4711yescharacteristic
941C2×C4C2×C22⋊Dic4711yescharacteristic
942C2×C4C23×Dic4711yescharacteristic
943C2×C4C22×C22⋊D4711yescharacteristic
944C8—1881no—
945C8—1881no—
946C8—1881no—
947C8—1881no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—81no—
973C22—81no—
974C22—162no—
975C22—162no—
976C22#1568914012yes—
977C22C22×C22⋊Dic4711yescharacteristic
978C22#1568992611yescharacteristic
979C22#1568993411yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—3761no—
996C4—3761no—
997C4—3761no—
998C4—3761no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—81no—
1006C2—81no—
1007C2—81no—
1008C2#2025184911yescharacteristic
1009C2#2025191411yescharacteristic
1010C2C2×#1568914011yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC47×#3519C2
socleC22×C47C22×C22⋊C4
cosocleC22×C4×C47C24
hypercenter#3519D47
hypocenterC47#17597
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3519

Complements

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

NH ≅ G/Ntype
1. #20252423C2semidirect
2. #20246021C2semidirect
3. #20241965C2semidirect
4. #20241956C2semidirect
5. #20241948C2semidirect
6. #20241944C2semidirect
7. #20241935C2semidirect
8. #20241931C2semidirect
9. #20241926C2semidirect
10. #20241917C2semidirect
11. #20241904C2semidirect
12. #20241892C2semidirect
13. #20241879C2semidirect
14. C2×#15688857C2semidirect
20. #15689180C22semidirect
21. #15689176C22semidirect
22. #15689087C22semidirect
23. #15689087C22semidirect
24. C2×C22⋊(C47⋊C8)C22semidirect
25. C2×C22⋊(C47⋊C8)C22semidirect
30. #15688991C22semidirect
31. #15688989C22semidirect
32. #15688986C22semidirect
33. #15688983C22semidirect
34. C4×C22⋊Dic47C22semidirect
35. C2×C47⋊#95C22semidirect
36. #15688860C22semidirect
37. #15688860C22semidirect
38. #15688860C22semidirect
39. #15688860C22semidirect
44. #15688857C22semidirect
45. #15688857C22semidirect
46. #15688857C22semidirect
47. #15688857C22semidirect
48. #15688857C22semidirect
49. #15688857C22semidirect
50. #15688857C22semidirect
51. #15688857C22semidirect
52. C47×#555C4semidirect
53. C47×#554C4semidirect
55. C47×#553C4semidirect
56. C47×#553C4semidirect
57. C47×#550C4semidirect
60. C47×#546C4semidirect
61. C47×#546C4semidirect
63. D42×C47C4semidirect
109. C2×#41×C47C2×C4semidirect
114. C22×D4×C47C2×C4semidirect
118. C4⋊Q8×C47C2×C4semidirect
120. #127×C47C2×C4semidirect
125. #125×C47C2×C4semidirect
129. #124×C47C2×C4semidirect
140. C22⋊Q8×C47C2×C4semidirect
158. #121×C47C2×C4semidirect
159. #121×C47C2×C4semidirect
160. #121×C47C2×C4semidirect
170. C4×Q8×C47C2×C4semidirect
185. C4×D4×C47C2×C4semidirect
186. C4×D4×C47C2×C4semidirect
187. C4×D4×C47C2×C4semidirect
195. #117×C47C2×C4semidirect
197. C2×C4⋊C4×C47C2×C4semidirect
521. #555Dic47semidirect
522. #554Dic47semidirect
524. #553Dic47semidirect
525. #553Dic47semidirect
526. #550Dic47semidirect
529. #546Dic47semidirect
530. #546Dic47semidirect
532. D42Dic47semidirect
580. C47#17597semidirect
583. C2×#41C2×Dic47semidirect
588. C22×D4C2×Dic47semidirect
597. C4⋊Q8C2×Dic47semidirect
599. #127C2×Dic47semidirect
604. #125C2×Dic47semidirect
608. #124C2×Dic47semidirect
619. C22⋊Q8C2×Dic47semidirect
637. #121C2×Dic47semidirect
638. #121C2×Dic47semidirect
639. #121C2×Dic47semidirect
649. C4×Q8C2×Dic47semidirect
664. C4×D4C2×Dic47semidirect
665. C4×D4C2×Dic47semidirect
666. C4×D4C2×Dic47semidirect
674. #117C2×Dic47semidirect
678. C2×C4⋊C4C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
#202524232
#202460212
#202419652
#202419562
#202419482
#202419442
#202419352
#202419312
#202419262
#202419172
#202419042
#202418922
#202418792
C2×#156888572
C47×#35192
#1759747