Finite Group Databasebeta

← #26183807

Subgroups — #26183807

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#20257420C211yesmaximal, characteristic
2#20246021C211yesmaximal, characteristic, complemented
3#20241966C211yesmaximal, characteristic, complemented
4#20241957C211yesmaximal, characteristic, complemented
5#20241949C211yesmaximal, characteristic, complemented
6#20241945C211yesmaximal, characteristic, complemented
7#20241936C211yesmaximal, characteristic, complemented
8#20241932C211yesmaximal, characteristic, complemented
9#20241927C211yesmaximal, characteristic, complemented
10#20241918C211yesmaximal, characteristic, complemented
11#20241905C211yesmaximal, characteristic, complemented
12#20241893C211yesmaximal, characteristic, complemented
13#20241880C211yesmaximal, characteristic, complemented
14C2×#15688858C211yesmaximal, characteristic, complemented
15C47×#2974C211yesmaximal, characteristic, complemented
16#15689838C411yescharacteristic, complemented
17#15689830C411yescharacteristic, complemented
18#15689821—21no—
19#15689819C411yescharacteristic, complemented
20#15689819C411yescharacteristic, complemented
21#15689794C411yescharacteristic, complemented
22#15689769C411yescharacteristic, complemented
23#15689769C411yescharacteristic, complemented
24#15689763—21no—
25#15689763—21no—
26D4×D188C411yescharacteristic, complemented
27D4×C22⋊D47—21no—
28#15689724—21no—
29#15689706—21no—
30#15689706—21no—
31#15689673C2211yescharacteristic
32#15689657C2211yescharacteristic
33#15689634C2211yescharacteristic
34#15689634C2211yescharacteristic
35C2×#13093998C2211yescharacteristic
36C2×#13093998C2211yescharacteristic
37#15689595—21no—
38#15689016—21no—
39#15689009—21no—
40#15689003—21no—
41#15688998—21no—
42#15688991C2211yescharacteristic, complemented
43#15688989C2211yescharacteristic, complemented
44#15688986C2211yescharacteristic, complemented
45#15688983C2211yescharacteristic, complemented
46C4×C22⋊Dic47C2211yescharacteristic, complemented
47C2×C47⋊#95C2211yescharacteristic, complemented
48#15688861C2211yescharacteristic, complemented
49#15688861C2211yescharacteristic, complemented
50#15688861C2211yescharacteristic, complemented
51#15688861C2211yescharacteristic, complemented
52#15688858C2211yescharacteristic
53#15688858C2211yescharacteristic
54#15688858C2211yescharacteristic
55#15688858C2211yescharacteristic
56#15688858C2211yescharacteristic, complemented
57#15688858C2211yescharacteristic, complemented
58#15688858C2211yescharacteristic, complemented
59#15688858C2211yescharacteristic, complemented
60#15688858C2211yescharacteristic, complemented
61#15688858C2211yescharacteristic, complemented
62#15688858C2211yescharacteristic, complemented
63#15688858C2211yescharacteristic, complemented
64C2×C4×D4×C47C2211yescharacteristic
65C47×#436—21no—
66C47×#435—21no—
67C47×#435—21no—
68C8×D4×C47—21no—
69C47×#432C2211yescharacteristic, complemented
70C47×#431C2211yescharacteristic, complemented
71C47×#407C2211yescharacteristic, complemented
72C47×#407C2211yescharacteristic, complemented
73C2×C22⋊C8×C47C2211yescharacteristic, complemented
74C2×C22⋊C8×C47C2211yescharacteristic, complemented
75C2×#10625350—21no—
76C2×#10625350C2×C411yescharacteristic
77C2×#10625350C2×C411yescharacteristic, complemented
78C22×D188C2×C411yescharacteristic
79C22×D188C2×C411yescharacteristic, complemented
80C22×C22⋊D47—21no—
81C22×C22⋊D47—21no—
82C2×D4×D47—21no—
83C23×Dic47—21no—
84#13094024C2×C411yescharacteristic, complemented
85#13094021C2×C411yescharacteristic, complemented
86#13094020—21no—
87#13094019—21no—
88#13094019—21no—
89#13094018—21no—
90#13094016C2×C411yescharacteristic, complemented
91#13094015—21no—
92#13094012—21no—
93#13094012C2×C411yescharacteristic, complemented
94#13094010—21no—
95#13094010—21no—
96#13094009—21no—
97#13094009—21no—
98#13094007—21no—
99#13094007—21no—
100#13094007—21no—
101#13094006—21no—
102#13094006—21no—
103#13094003C2×C411yescharacteristic
104#13094003C2×C411yescharacteristic, complemented
105#13094003C2311yescharacteristic
106#13094001—21no—
107#13094001—21no—
108#13093999—21no—
109#13093998—21no—
110#13093998—21no—
111#13093998—21no—
112#13093998—21no—
113#13093998—21no—
114#13093998C2×C411yescharacteristic
115#13093998C2×C411yescharacteristic
116#13093998C2×C411yescharacteristic
117#13093998C2×C411yescharacteristic, complemented
118#13093998C2×C411yescharacteristic, complemented
119#13093998C2×C411yescharacteristic, complemented
120#13093998C2311yescharacteristic
121#13093998C2311yescharacteristic
122#13093998C2311yescharacteristic
123#13093997—21no—
124#13093997—21no—
125#13093997—21no—
126#13093997—21no—
127#13093996—21no—
128#13093996—21no—
129#13093995—21no—
130#13093994—21no—
131#13093994—21no—
132#13093993—21no—
133#13093993—21no—
134#13093992—21no—
135#13093992—21no—
136C4×Dic94C2×C411yescharacteristic, complemented
137C4×D188—21no—
138C4×D188C2×C411yescharacteristic, complemented
139C4×D188C2×C411yescharacteristic, complemented
140C4×D188C2×C411yescharacteristic, complemented
141D4×Dic47—21no—
142#13093986—21no—
143C4×C22⋊D47—21no—
144C4×C22⋊D47—21no—
145C4×C22⋊D47—21no—
146C4×C22⋊D47—21no—
147C4×C22⋊D47—21no—
148(C22⋊D47)⋊C4—21no—
149(C22⋊D47)⋊C4—21no—
150#13093983C2×C411yescharacteristic
151#13093983C2×C411yescharacteristic, complemented
152#13093982—21no—
153#13093981—21no—
154C2×C4⋊Dic47—21no—
155C2×C4⋊Dic47—21no—
156C2×C4⋊Dic47C2×C411yescharacteristic
157C2×C4⋊Dic47C2×C411yescharacteristic, complemented
158C2×C22⋊Dic47—21no—
159C2×C22⋊Dic47—21no—
160C2×C22⋊Dic47—21no—
161C2×(C2×D47)⋊C4—21no—
162C2×(C2×D47)⋊C4—21no—
163C22⋊C4×D47—21no—
164C22⋊C4×D47—21no—
165C2×C4×Dic47—21no—
166C47⋊#95—21no—
167C47⋊#95—21no—
168C47⋊#95—21no—
169C47⋊#95—21no—
170C47⋊#95—21no—
171C47⋊#95C2311yescharacteristic
172C47⋊#95C2311yescharacteristic
173C47⋊#95C2311yescharacteristic
174C47⋊#95C2311yescharacteristic
175C22×D4×C47D411yescharacteristic
176C23×C4×C47C2311yescharacteristic
177C23×C4×C47C2311yescharacteristic
178C2×M16×C47—21no—
179C2×M16×C47—21no—
180C22×C8×C47—21no—
181C22×C8×C47—21no—
182C4×D4×C47C2×C411yescharacteristic
183C4×D4×C47C2×C411yescharacteristic
184C4×D4×C47C2×C411yescharacteristic
185C4×D4×C47C2×C411yescharacteristic
186C4×D4×C47D411yescharacteristic
187C4×D4×C47D411yescharacteristic
188C4×D4×C47D411yescharacteristic
189C4×D4×C47D411yescharacteristic
190C2×C4⋊C4×C47D411yescharacteristic
191C2×C22⋊C4×C47D411yescharacteristic
192C2×C22⋊C4×C47D411yescharacteristic
193C2×C42×C47C2311yescharacteristic
194C4⋊C8×C47—21no—
195C4⋊C8×C47—21no—
196C22⋊C8×C47—21no—
197C22⋊C8×C47—21no—
198C22⋊C8×C47—21no—
199C22⋊C8×C47—21no—
200C22⋊C8×C47C2311yescharacteristic
201C22⋊C8×C47C2311yescharacteristic
202C22⋊C8×C47C2311yescharacteristic
203C22⋊C8×C47C2311yescharacteristic
204#97×C47—21no—
205C4×C8×C47—21no—
206C24×C47C2×D411yescharacteristic
207C24×C47C2×D411yescharacteristic
208C23×D47—21no—
209C23×D47—21no—
210C2×D4×C47—42no—
211C2×D4×C47C22⋊C411yescharacteristic
212C2×D4×C47C22⋊C411yescharacteristic
213C2×D4×C47C22⋊C411yescharacteristic
214C2×D4×C47C22⋊C411yescharacteristic
215C22×C4×C47—81no—
216C22×C4×C47—81no—
217C22×C4×C47C22×C411yescharacteristic
218C22×C4×C47C22×C411yescharacteristic
219C22×C4×C47C22×C411yescharacteristic
220C22×C4×C47C22×C411yescharacteristic
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2×D411yescharacteristic
226C22×C4×C47C2×D411yescharacteristic
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2411yescharacteristic
230C2×C22⋊D47—21no—
231C2×C22⋊D47—21no—
232C2×C22⋊D47—21no—
233C2×C22⋊D47—21no—
234C2×C22⋊D47—21no—
235C2×C22⋊D47—21no—
236C2×C22⋊D47—21no—
237C2×C22⋊D47—21no—
238C2×C22⋊D47—21no—
239C2×C22⋊D47—21no—
240C2×C22⋊D47—21no—
241C2×C22⋊D47—81no—
242C2×C22⋊D47—81no—
243C2×C22⋊D47—81no—
244C2×C22⋊D47—81no—
245C22×Dic47—21no—
246C22×Dic47—21no—
247C22×Dic47—21no—
248C22×Dic47—21no—
249C22×Dic47—21no—
250C22×Dic47—21no—
251C22×Dic47—42no—
252C22×Dic47—81no—
253C22×Dic47—81no—
254D4×D47—44no—
255#10625350—81no—
256#10625350—81no—
257#10625350—81no—
258#10625350—81no—
259C2×D188—21no—
260C2×D188—21no—
261C2×D188—21no—
262C2×D188—21no—
263C2×D188—81no—
264C2×D188—81no—
265C2×D188C22×C411yescharacteristic
266C2×D188C22×C411yescharacteristic
267C2×D188C22×C411yescharacteristic
268C2×C4×D47—21no—
269C2×C4×D47—21no—
270C2×C4×D47—21no—
271C2×C4×D47—21no—
272C2×C4×D47—21no—
273C2×Dic94—21no—
274C2×Dic94C22×C411yescharacteristic
275M16×C47—81no—
276M16×C47—81no—
277C2×C8×C47—21no—
278C2×C8×C47—21no—
279C2×C8×C47—21no—
280C2×C8×C47—21no—
281C2×C8×C47—81no—
282C2×C8×C47—81no—
283C4⋊C4×C47C22⋊C411yescharacteristic
284C4⋊C4×C47C22⋊C411yescharacteristic
285C4⋊C4×C47C22⋊C411yescharacteristic
286C4⋊C4×C47C22⋊C411yescharacteristic
287C22⋊C4×C47C22⋊C411yescharacteristic
288C22⋊C4×C47C22⋊C411yescharacteristic
289C22⋊C4×C47C22⋊C411yescharacteristic
290C22⋊C4×C47C22⋊C411yescharacteristic
291C22⋊C4×C47C22⋊C411yescharacteristic
292C22⋊C4×C47C22⋊C411yescharacteristic
293C22⋊C4×C47C22⋊C411yescharacteristic
294C22⋊C4×C47C22⋊C411yescharacteristic
295C42×C47C22×C411yescharacteristic
296C42×C47C22×C411yescharacteristic
297C42×C47C2×D411yescharacteristic
298C42×C47C2×D411yescharacteristic
299C22⋊Dic47—21no—
300C22⋊Dic47—21no—
301C22⋊Dic47—21no—
302C22⋊Dic47—21no—
303C22⋊Dic47—21no—
304C22⋊Dic47—42no—
305C22⋊Dic47—81no—
306C22⋊Dic47—81no—
307(C2×D47)⋊C4—21no—
308(C2×D47)⋊C4—21no—
309(C2×D47)⋊C4—21no—
310(C2×D47)⋊C4—21no—
311(C2×D47)⋊C4—21no—
312(C2×D47)⋊C4—21no—
313(C2×D47)⋊C4—21no—
314(C2×D47)⋊C4—21no—
315(C2×D47)⋊C4—21no—
316(C2×D47)⋊C4—21no—
317(C2×D47)⋊C4—21no—
318(C2×D47)⋊C4—21no—
319(C2×D47)⋊C4—21no—
320(C2×D47)⋊C4—21no—
321C4⋊Dic47—21no—
322C4⋊Dic47—21no—
323C4⋊Dic47—21no—
324C4⋊Dic47—81no—
325C4⋊Dic47—81no—
326C4⋊Dic47C22×C411yescharacteristic
327C4⋊Dic47C22×C411yescharacteristic
328C4⋊Dic47C22×C411yescharacteristic
329C4⋊Dic47C22×C411yescharacteristic
330Dic47⋊C4—21no—
331Dic47⋊C4—21no—
332Dic47⋊C4—21no—
333Dic47⋊C4—21no—
334Dic47⋊C4—21no—
335Dic47⋊C4—21no—
336C4×Dic47—21no—
337C4×Dic47—21no—
338C4×Dic47—21no—
339C4×Dic47—81no—
340C23×C47—21no—
341C23×C47—21no—
342C23×C47—22no—
343C23×C47—21no—
344C23×C47—21no—
345C23×C47—41no—
346C23×C47—41no—
347C23×C47—41no—
348C23×C47C2×C22⋊C411yescharacteristic
349C23×C47C2×C22⋊C411yescharacteristic
350C23×C47C2×C22⋊C411yescharacteristic
351C23×C47C2×C22⋊C411yescharacteristic
352C23×C47C22×D411yescharacteristic
353C22×D47—21no—
354C22×D47—21no—
355C22×D47—21no—
356C22×D47—42no—
357C22×D47—42no—
358C22×D47—81no—
359C22×D47—81no—
360C22×D47—81no—
361C22×D47—81no—
362D4×C47—22no—
363D4×C47—22no—
364D4×C47—41no—
365D4×C47—41no—
366C2×C4×C47—21no—
367C2×C4×C47—21no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47C2×C22⋊C411yescharacteristic
381C2×C4×C47C2×C22⋊C411yescharacteristic
382C2×C4×C47C2×C22⋊C411yescharacteristic
383C2×C4×C47C2×C22⋊C411yescharacteristic
384C2×C4×C47C2×C22⋊C411yescharacteristic
385C2×C4×C47C2×C22⋊C411yescharacteristic
386C2×C4×C47C2×C22⋊C411yescharacteristic
387C2×C4×C47C2×C22⋊C411yescharacteristic
388C2×C4×C47C23×C411yescharacteristic
389C2×C4×C47C22×D411yescharacteristic
390C22⋊D47—42no—
391C22⋊D47—41no—
392C22⋊D47—41no—
393C22⋊D47—41no—
394C22⋊D47—41no—
395C22⋊D47—41no—
396C22⋊D47—41no—
397C22⋊D47—42no—
398C22⋊D47—81no—
399C22⋊D47—81no—
400C22⋊D47—81no—
401C22⋊D47—81no—
402C22⋊D47—81no—
403C22⋊D47—81no—
404C2×Dic47—21no—
405C2×Dic47—21no—
406C2×Dic47—21no—
407C2×Dic47—21no—
408C2×Dic47—21no—
409C2×Dic47—41no—
410C2×Dic47—41no—
411C2×Dic47—41no—
412C2×Dic47—41no—
413C2×Dic47—41no—
414C2×Dic47—41no—
415C2×Dic47—41no—
416C2×Dic47—41no—
417C2×Dic47—41no—
418C2×Dic47—41no—
419C2×Dic47—41no—
420C2×Dic47—41no—
421C2×Dic47—81no—
422C2×Dic47—81no—
423C2×Dic47—84no—
424D188—41no—
425D188—41no—
426D188—41no—
427D188—42no—
428D188—81no—
429D188—81no—
430D188—81no—
431C4×D47—42no—
432C4×D47—81no—
433C4×D47—81no—
434C4×D47—81no—
435C4×D47—81no—
436Dic94—41no—
437Dic94—81no—
438C8×C47—41no—
439C8×C47—41no—
440C8×C47—41no—
441C8×C47—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—81no—
459C22×C47—81no—
460C22×C47#42112yes—
461C22×C47C22×C22⋊C411yescharacteristic
462C22×C47#57611yescharacteristic
463C22×C47#57711yescharacteristic
464C2×D47—41no—
465C2×D47—41no—
466C2×D47—41no—
467C2×D47—41no—
468C2×D47—41no—
469C2×D47—41no—
470C2×D47—41no—
471C2×D47—41no—
472C2×D47—41no—
473C2×D47—162no—
474C2×D47—162no—
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—
485Dic47—41no—
486Dic47—41no—
487Dic47—41no—
488Dic47—41no—
489Dic47—41no—
490Dic47—81no—
491Dic47—81no—
492Dic47—81no—
493Dic47—81no—
494#3519—471no—
495#2974D4711yescharacteristic, complemented
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#288311yescharacteristic
516C2×C47#289711yescharacteristic
517C2×C47C2×#42111yescharacteristic
518D47—81no—
519D47—81no—
520D47—81no—
521#555—471no—
522#554—471no—
523#553—471no—
524#553—471no—
525#553—941no—
526#550—471no—
527#546—471no—
528#546—471no—
529#546—941no—
530#546—941no—
531D42—471no—
532D42—941no—
533#540—941no—
534#538—941no—
535#538—941no—
536#532—471no—
537#529—471no—
538#525—471no—
539#525—471no—
540C2×#121—471no—
541C2×#121—471no—
542#518—941no—
543C2×C4×D4C2×D4711yescharacteristic
544#436—21no—
545#435—21no—
546#435—21no—
547C8×D4—21no—
548#432C2×D4711yescharacteristic, complemented
549#431C2×D4711yescharacteristic, complemented
550#407C2×D4711yescharacteristic, complemented
551#407C2×D4711yescharacteristic, complemented
552C2×C22⋊C8C2×D4711yescharacteristic, complemented
553C2×C22⋊C8C2×D4711yescharacteristic, complemented
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—471no—
582C2×#41—471no—
583C2×#41—941no—
584C22×D4—471no—
585C22×D4—471no—
586C22×D4—941no—
587C22×D4—941no—
588C22×D4—941no—
589C22×D4D18811yescharacteristic
590C23×C4—941no—
591C23×C4C22×D4711yescharacteristic
592C23×C4C22×D4711yescharacteristic
593C2×M16—21no—
594C2×M16—21no—
595C22×C8—21no—
596C22×C8—21no—
597C4⋊Q8—471no—
598#127—471no—
599#127—941no—
600#126—941no—
601#126—941no—
602#126—941no—
603#125—471no—
604#125—941no—
605#124—471no—
606#124—941no—
607#124—941no—
608#124—941no—
609#123—941no—
610#123—941no—
611#123—941no—
612#123—941no—
613#123—941no—
614#123—941no—
615#123—941no—
616C22⋊Q8—471no—
617C22⋊Q8—471no—
618C22⋊Q8—471no—
619C22⋊Q8—941no—
620C22⋊Q8—941no—
621#121—471no—
622#121—471no—
623#121—471no—
624#121—471no—
625#121—471no—
626#121—471no—
627#121—471no—
628#121—471no—
629#121—471no—
630#121—941no—
631#121—941no—
632#121—941no—
633#121—941no—
634#121—941no—
635#121—941no—
636#121—941no—
637#121—941no—
638#121—941no—
639#121—941no—
640#121—941no—
641#121—941no—
642#121—941no—
643#120—941no—
644#120—941no—
645#120—941no—
646#120—941no—
647#120—941no—
648#120—941no—
649C4×Q8—471no—
650C4×D4—471no—
651C4×D4—471no—
652C4×D4—471no—
653C4×D4—941no—
654C4×D4—941no—
655C4×D4—941no—
656C4×D4—941no—
657C4×D4—941no—
658C4×D4—941no—
659C4×D4—941no—
660C4×D4—941no—
661C4×D4—941no—
662C4×D4—941no—
663C4×D4C4×D4711yescharacteristic
664C4×D4C4×D4711yescharacteristic
665C4×D4C4×D4711yescharacteristic
666C4×D4C4×D4711yescharacteristic
667C4×D4C22⋊D4711yescharacteristic
668C4×D4C22⋊D4711yescharacteristic
669C4×D4C22⋊D4711yescharacteristic
670C4×D4C22⋊D4711yescharacteristic
671#117—471no—
672#117—471no—
673#117—941no—
674#117—941no—
675C2×C4⋊C4—471no—
676C2×C4⋊C4—471no—
677C2×C4⋊C4—941no—
678C2×C4⋊C4—941no—
679C2×C4⋊C4D18811yescharacteristic
680C2×C22⋊C4—941no—
681C2×C22⋊C4—941no—
682C2×C22⋊C4—941no—
683C2×C22⋊C4—941no—
684C2×C22⋊C4—941no—
685C2×C22⋊C4—941no—
686C2×C22⋊C4—941no—
687C2×C22⋊C4D18811yescharacteristic
688C2×C22⋊C4D18811yescharacteristic
689C2×C42—941no—
690C2×C42C22×D4711yescharacteristic
691C4⋊C8—21no—
692C4⋊C8—21no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696C22⋊C8—21no—
697C22⋊C8C22×D4711yescharacteristic
698C22⋊C8C22×D4711yescharacteristic
699C22⋊C8C22×D4711yescharacteristic
700C22⋊C8C22×D4711yescharacteristic
701#97—21no—
702C4×C8—21no—
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—941no—
713C24—941no—
714C24C2×D18811yescharacteristic
715C24C2×D18811yescharacteristic
716#41—3761no—
717#41—3761no—
718#41—3761no—
719#41—3761no—
720C2×Q8—471no—
721C2×Q8—941no—
722C2×D4—42no—
723C2×D4—471no—
724C2×D4—471no—
725C2×D4—471no—
726C2×D4—941no—
727C2×D4—941no—
728C2×D4—941no—
729C2×D4—941no—
730C2×D4—941no—
731C2×D4—941no—
732C2×D4—941no—
733C2×D4—941no—
734C2×D4—941no—
735C2×D4—941no—
736C2×D4—941no—
737C2×D4—941no—
738C2×D4—941no—
739C2×D4—941no—
740C2×D4—941no—
741C2×D4—3761no—
742C2×D4—3761no—
743C2×D4—3761no—
744C2×D4—3761no—
745C2×D4—3761no—
746C2×D4—3761no—
747C2×D4—1884no—
748C2×D4(C2×D47)⋊C411yescharacteristic
749C2×D4(C2×D47)⋊C411yescharacteristic
750C2×D4(C2×D47)⋊C411yescharacteristic
751C2×D4(C2×D47)⋊C411yescharacteristic
752C22×C4—81no—
753C22×C4—81no—
754C22×C4—941no—
755C22×C4—941no—
756C22×C4—941no—
757C22×C4—941no—
758C22×C4—941no—
759C22×C4—941no—
760C22×C4—941no—
761C22×C4—941no—
762C22×C4—941no—
763C22×C4—941no—
764C22×C4—941no—
765C22×C4—3761no—
766C22×C4—3761no—
767C22×C4—1882no—
768C22×C4C2×C4×D4711yescharacteristic
769C22×C4C2×C4×D4711yescharacteristic
770C22×C4C2×C4×D4711yescharacteristic
771C22×C4C2×C4×D4711yescharacteristic
772C22×C4C2×D18811yescharacteristic
773C22×C4C2×D18811yescharacteristic
774C22×C4C2×D18811yescharacteristic
775C22×C4C2×D18811yescharacteristic
776C22×C4C2×C22⋊D4711yescharacteristic
777C22×C4C2×C22⋊D4711yescharacteristic
778C22×C4C2×C22⋊D4711yescharacteristic
779C22×C4C2×C22⋊D4711yescharacteristic
780C22×C4C23×D4711yescharacteristic
781M16—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C2×C8—81no—
789C4⋊C4—471no—
790C4⋊C4—471no—
791C4⋊C4—471no—
792C4⋊C4—471no—
793C4⋊C4—941no—
794C4⋊C4—941no—
795C4⋊C4—941no—
796C4⋊C4—941no—
797C4⋊C4—941no—
798C4⋊C4—941no—
799C4⋊C4—941no—
800C4⋊C4—941no—
801C4⋊C4—941no—
802C4⋊C4—3761no—
803C4⋊C4—3761no—
804C4⋊C4(C2×D47)⋊C411yescharacteristic
805C4⋊C4(C2×D47)⋊C411yescharacteristic
806C4⋊C4(C2×D47)⋊C411yescharacteristic
807C4⋊C4(C2×D47)⋊C411yescharacteristic
808C22⋊C4—941no—
809C22⋊C4—941no—
810C22⋊C4—941no—
811C22⋊C4—941no—
812C22⋊C4—941no—
813C22⋊C4—941no—
814C22⋊C4—941no—
815C22⋊C4—941no—
816C22⋊C4—941no—
817C22⋊C4—941no—
818C22⋊C4—941no—
819C22⋊C4—941no—
820C22⋊C4—941no—
821C22⋊C4—941no—
822C22⋊C4—941no—
823C22⋊C4—941no—
824C22⋊C4—941no—
825C22⋊C4—941no—
826C22⋊C4—941no—
827C22⋊C4—3761no—
828C22⋊C4—3761no—
829C22⋊C4—1882no—
830C22⋊C4(C2×D47)⋊C411yescharacteristic
831C22⋊C4(C2×D47)⋊C411yescharacteristic
832C22⋊C4(C2×D47)⋊C411yescharacteristic
833C22⋊C4(C2×D47)⋊C411yescharacteristic
834C22⋊C4(C2×D47)⋊C411yescharacteristic
835C22⋊C4(C2×D47)⋊C411yescharacteristic
836C22⋊C4(C2×D47)⋊C411yescharacteristic
837C22⋊C4(C2×D47)⋊C411yescharacteristic
838C42—941no—
839C42—941no—
840C42—941no—
841C42—3761no—
842C42C2×C4×D4711yescharacteristic
843C42C2×C4×D4711yescharacteristic
844C42C2×C22⋊D4711yescharacteristic
845C42C2×C22⋊D4711yescharacteristic
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—941no—
855C23—941no—
856C23—941no—
857C23—3761no—
858C23—3761no—
859C23—3761no—
860C23—3761no—
861C23—1882no—
862C23—1882no—
863C23C2×(C2×D47)⋊C411yescharacteristic
864C23C2×(C2×D47)⋊C411yescharacteristic
865C23C2×(C2×D47)⋊C411yescharacteristic
866C23C2×(C2×D47)⋊C411yescharacteristic
867C23C22×D18811yescharacteristic
868Q8—3761no—
869Q8—1881no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—3761no—
875D4—3761no—
876D4—3761no—
877D4—3761no—
878D4—3761no—
879D4—3761no—
880D4—3761no—
881D4—3761no—
882D4—3761no—
883D4—1881no—
884D4—1881no—
885D4—1881no—
886D4—1882no—
887D4—1882no—
888D4—1882no—
889D4—1881no—
890D4—1881no—
891D4—1881no—
892D4—1881no—
893D4—1881no—
894D4—1881no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—941no—
910C2×C4—941no—
911C2×C4—941no—
912C2×C4—941no—
913C2×C4—941no—
914C2×C4—3761no—
915C2×C4—3761no—
916C2×C4—3761no—
917C2×C4—3761no—
918C2×C4—3764no—
919C2×C4—3761no—
920C2×C4—3761no—
921C2×C4—1882no—
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×(C2×D47)⋊C411yescharacteristic
935C2×C4C2×(C2×D47)⋊C411yescharacteristic
936C2×C4C2×(C2×D47)⋊C411yescharacteristic
937C2×C4C2×(C2×D47)⋊C411yescharacteristic
938C2×C4C2×(C2×D47)⋊C411yescharacteristic
939C2×C4C2×(C2×D47)⋊C411yescharacteristic
940C2×C4C2×(C2×D47)⋊C411yescharacteristic
941C2×C4C2×(C2×D47)⋊C411yescharacteristic
942C2×C4C22×C4×D4711yescharacteristic
943C2×C4C22×C22⋊D4711yescharacteristic
944C8—41no—
945C8—41no—
946C8—41no—
947C8—41no—
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—81no—
964C22—81no—
965C22—1881no—
966C22—1881no—
967C22—1881no—
968C22—1881no—
969C22—1881no—
970C22—1881no—
971C22—1881no—
972C22—1881no—
973C22—1881no—
974C22—7522no—
975C22—7522no—
976C22#1568913912yes—
977C22C22×(C2×D47)⋊C411yescharacteristic
978C22#1568992811yescharacteristic
979C22#1568993511yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—3761no—
991C4—3761no—
992C4—3761no—
993C4—3761no—
994C4—1881no—
995C4—1881no—
996C4—1881no—
997C4—1881no—
998C4—1881no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—3761no—
1006C2—3761no—
1007C2—3761no—
1008C2#2025184811yescharacteristic
1009C2#2025191511yescharacteristic
1010C2C2×#1568913911yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2974C2
socleC22×C47C22×C22⋊C4
prime radical#20257420C2
cosocleC22×C4×C47C24
hypercenter#2974D47
hypocenterC47#17597
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #20246021C2semidirect
3. #20241966C2semidirect
4. #20241957C2semidirect
5. #20241949C2semidirect
6. #20241945C2semidirect
7. #20241936C2semidirect
8. #20241932C2semidirect
9. #20241927C2semidirect
10. #20241918C2semidirect
11. #20241905C2semidirect
12. #20241893C2semidirect
13. #20241880C2semidirect
14. C2×#15688858C2semidirect
15. C47×#2974C2semidirect
16. #15689838C4semidirect
17. #15689830C4semidirect
19. #15689819C4semidirect
20. #15689819C4semidirect
21. #15689794C4semidirect
22. #15689769C4semidirect
23. #15689769C4semidirect
26. D4×D188C4semidirect
42. #15688991C22semidirect
43. #15688989C22semidirect
44. #15688986C22semidirect
45. #15688983C22semidirect
46. C4×C22⋊Dic47C22semidirect
47. C2×C47⋊#95C22semidirect
48. #15688861C22semidirect
49. #15688861C22semidirect
50. #15688861C22semidirect
51. #15688861C22semidirect
56. #15688858C22semidirect
57. #15688858C22semidirect
58. #15688858C22semidirect
59. #15688858C22semidirect
60. #15688858C22semidirect
61. #15688858C22semidirect
62. #15688858C22semidirect
63. #15688858C22semidirect
69. C47×#432C22semidirect
70. C47×#431C22semidirect
71. C47×#407C22semidirect
72. C47×#407C22semidirect
73. C2×C22⋊C8×C47C22semidirect
74. C2×C22⋊C8×C47C22semidirect
77. C2×#10625350C2×C4semidirect
79. C22×D188C2×C4semidirect
84. #13094024C2×C4semidirect
85. #13094021C2×C4semidirect
90. #13094016C2×C4semidirect
93. #13094012C2×C4semidirect
104. #13094003C2×C4semidirect
117. #13093998C2×C4semidirect
118. #13093998C2×C4semidirect
119. #13093998C2×C4semidirect
136. C4×Dic94C2×C4semidirect
138. C4×D188C2×C4semidirect
139. C4×D188C2×C4semidirect
140. C4×D188C2×C4semidirect
151. #13093983C2×C4semidirect
157. C2×C4⋊Dic47C2×C4semidirect
495. #2974D47semidirect
548. #432C2×D47semidirect
549. #431C2×D47semidirect
550. #407C2×D47semidirect
551. #407C2×D47semidirect
552. C2×C22⋊C8C2×D47semidirect
553. C2×C22⋊C8C2×D47semidirect
580. C47#17597semidirect

Maximal subgroups

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

subgroupindex
#202574202
#202460212
#202419662
#202419572
#202419492
#202419452
#202419362
#202419322
#202419272
#202419182
#202419052
#202418932
#202418802
C2×#156888582
C47×#29742
#1759747