Finite Group Databasebeta

← #26238822

Subgroups — #26238822

Order 12032.

892 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252966C211yesmaximal, characteristic
2C2×#15689238C211yesmaximal, characteristic, complemented
3#20252109C211yesmaximal, characteristic, complemented
4C22×#13093959C211yesmaximal, characteristic, complemented
5#20244275C211yesmaximal, characteristic, complemented
6#20244133C211yesmaximal, characteristic, complemented
7#20244036C211yesmaximal, characteristic, complemented
8#20244033C211yesmaximal, characteristic, complemented
9#20243691C211yesmaximal, characteristic, complemented
10#20243690C211yesmaximal, characteristic, complemented
11#20243663C211yesmaximal, characteristic, complemented
12#20243662C211yesmaximal, characteristic, complemented
13#20243268C211yesmaximal, characteristic, complemented
14#20243162C211yesmaximal, characteristic, complemented
15C47×#2933C211yesmaximal, characteristic, complemented
16C2×#13094044C2211yescharacteristic
17C2×#13094030C2211yescharacteristic
18C22×#10625329C2211yescharacteristic
19C23×C47⋊C8C2211yescharacteristic
20#15689634C2211yescharacteristic
21#15689362C411yescharacteristic, complemented
22#15689362C411yescharacteristic, complemented
23#15689357C411yescharacteristic, complemented
24#15689357C411yescharacteristic, complemented
25#15689354C411yescharacteristic, complemented
26#15689354C411yescharacteristic, complemented
27#15689350C411yescharacteristic, complemented
28#15689350C411yescharacteristic, complemented
29#15689238—24no—
30#15689198—21no—
31#15689197—21no—
32#15689191—21no—
33(C22⋊D47)⋊C8—21no—
34C2×#13093959—24no—
35C2×#13093959C2211yescharacteristic
36C2×#13093959C2211yescharacteristic
37C2×#13093959C2211yescharacteristic
38C2×#13093959C2211yescharacteristic
39#15689159C2211yescharacteristic
40#15689149C2211yescharacteristic
41C2×#13093951C2211yescharacteristic
42C2×#13093951C2211yescharacteristic
43C2×#13093950C2211yescharacteristic
44C2×#13093950C2211yescharacteristic
45#15689119C2211yescharacteristic
46#15689117C2211yescharacteristic
47#15689089C2211yescharacteristic
48#15689078C2211yescharacteristic
49C2×C8×Dic47C2211yescharacteristic
50C2×C8×Dic47C2211yescharacteristic
51C4×C22⋊Dic47C2211yescharacteristic
52#15688884C2211yescharacteristic
53#15688884C2211yescharacteristic
54#15688882C2211yescharacteristic
55#15688882C2211yescharacteristic
56#15688877C2211yescharacteristic
57#15688877C2211yescharacteristic
58C2×#131×C47C2211yescharacteristic
59C22×M16×C47C2211yescharacteristic
60C47×#525C2211yescharacteristic
61C47×#436—21no—
62C47×#435—21no—
63C47×#435—21no—
64C8×D4×C47—21no—
65C47×#424C2211yescharacteristic
66C47×#408C2211yescharacteristic
67C2×C22⋊C8×C47C2211yescharacteristic
68C47×#405C2211yescharacteristic
69C2×#10625350C2311yescharacteristic
70#13094044—22no—
71#13094044—22no—
72C2×#10625337C2×C411yescharacteristic
73C2×#10625335C2×C411yescharacteristic
74C2×#10625336C2×C411yescharacteristic
75C2×#10625334C2×C411yescharacteristic
76#13094030—22no—
77#13094030—41no—
78C2×#10625329—21no—
79C2×#10625329—22no—
80C2×#10625329—41no—
81C2×#10625329C2311yescharacteristic
82C2×#10625329C2311yescharacteristic
83C2×#10625324—21no—
84C22×C47⋊C8—22no—
85C22×C47⋊C8—22no—
86C22×C47⋊C8—21no—
87C22×C47⋊C8C2×C411yescharacteristic
88C22×C47⋊C8C2×C411yescharacteristic
89C22×C47⋊C8C2×C411yescharacteristic
90C22×C47⋊C8C2×C411yescharacteristic
91C22×C47⋊C8C2311yescharacteristic
92C22×C47⋊C8C2311yescharacteristic
93C2×C8×D47—21no—
94#13094007—21no—
95#13094003C2×C411yescharacteristic
96#13094003C2×C411yescharacteristic
97#13093998C2×C411yescharacteristic
98#13093998C2×C411yescharacteristic
99#13093993—21no—
100C4×C22⋊D47—21no—
101C4×C22⋊D47—21no—
102#13093983C2311yescharacteristic
103C2×C22⋊Dic47—21no—
104C2×C4×Dic47C2311yescharacteristic
105C2×C4×Dic47C2311yescharacteristic
106#13093959—22no—
107#13093959—22no—
108#13093959—22no—
109#13093959D414yescomplemented
110#13093957C2×C411yescharacteristic
111#13093957C2×C411yescharacteristic
112#13093955C2×C411yescharacteristic
113#13093955C2×C411yescharacteristic
114Dic47⋊C8—21no—
115Dic47⋊C8—21no—
116#13093951—22no—
117#13093951—41no—
118#13093950—22no—
119#13093950—41no—
120#13093948C2×C411yescharacteristic
121#13093948C2×C411yescharacteristic
122#13093947C2×C411yescharacteristic
123#13093947C2×C411yescharacteristic
124#13093945C2×C411yescharacteristic
125#13093945C2×C411yescharacteristic
126#13093944C2×C411yescharacteristic
127#13093944C2×C411yescharacteristic
128(C2×D47)⋊C8—21no—
129(C2×D47)⋊C8—21no—
130#13093934—21no—
131C8×Dic47—21no—
132C8×Dic47—22no—
133C8×Dic47—22no—
134C47⋊#95—21no—
135C2×#41×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137#131×C47—22no—
138#131×C47—41no—
139C2×M16×C47—21no—
140C2×M16×C47—21no—
141C2×M16×C47—22no—
142C2×M16×C47—41no—
143C2×M16×C47C2311yescharacteristic
144C2×M16×C47C2311yescharacteristic
145C22×C8×C47—21no—
146C22×C8×C47—21no—
147C22×C8×C47C2311yescharacteristic
148C22×C8×C47C2311yescharacteristic
149#123×C47—21no—
150C22⋊Q8×C47C2×C411yescharacteristic
151C22⋊Q8×C47C2×C411yescharacteristic
152#121×C47C2×C411yescharacteristic
153#121×C47C2×C411yescharacteristic
154#120×C47—21no—
155C4×D4×C47—21no—
156C4×D4×C47—21no—
157#117×C47C2311yescharacteristic
158C4⋊C8×C47—21no—
159C4⋊C8×C47—21no—
160C22⋊C8×C47—21no—
161C22⋊C8×C47—21no—
162C22⋊C8×C47D411yescharacteristic
163C22⋊C8×C47D411yescharacteristic
164C22⋊C8×C47D411yescharacteristic
165C22⋊C8×C47D411yescharacteristic
166#97×C47—21no—
167C4×C8×C47—21no—
168C24×C47#4111yescharacteristic
169#41×C47—21no—
170#41×C47—21no—
171#41×C47—21no—
172#41×C47—21no—
173C2×Q8×C47C22×C411yescharacteristic
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47C22×C411yescharacteristic
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47C22×C411yescharacteristic
184C22×C4×C47C22×C411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47#4111yescharacteristic
188C22×C4×C47C2411yescharacteristic
189C2×C22⋊D47—21no—
190C2×C22⋊D47—21no—
191C2×C22⋊D47—21no—
192C22×Dic47—21no—
193C22×Dic47—21no—
194#10625350—21no—
195#10625350—21no—
196#10625350—21no—
197#10625350—21no—
198C2×D188C22×C411yescharacteristic
199C2×C4×D47—21no—
200C2×Dic94C22×C411yescharacteristic
201M16×C47—21no—
202M16×C47—21no—
203M16×C47—21no—
204M16×C47—42no—
205M16×C47—42no—
206M16×C47C2×D412yes—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47—42no—
214C2×C8×C47—42no—
215C2×C8×C47C2×D411yescharacteristic
216C2×C8×C47C2×D411yescharacteristic
217C2×C8×C47C2×D411yescharacteristic
218C2×C8×C47C2×D411yescharacteristic
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47C22×C411yescharacteristic
222C4⋊C4×C47C22×C411yescharacteristic
223C22⋊C4×C47—21no—
224C22⋊C4×C47—21no—
225C22⋊C4×C47—21no—
226C22⋊C4×C47—21no—
227C22⋊C4×C47—21no—
228C42×C47—21no—
229C22⋊Dic47—24no—
230C22⋊Dic47—21no—
231C22⋊Dic47—21no—
232C22⋊Dic47—21no—
233#10625337—22no—
234#10625336—22no—
235#10625335—22no—
236#10625334—22no—
237(C2×D47)⋊C4—21no—
238(C2×D47)⋊C4—21no—
239C4⋊Dic47C22×C411yescharacteristic
240C4⋊Dic47C22×C411yescharacteristic
241Dic47⋊C4—21no—
242Dic47⋊C4—21no—
243C4×Dic47—21no—
244C4×Dic47—21no—
245C4×Dic47—21no—
246C4×Dic47—21no—
247C4×Dic47—21no—
248#10625329—21no—
249#10625329—21no—
250#10625329—21no—
251#10625329—42no—
252#10625329C2×D412yes—
253C2×C47⋊C8—21no—
254C2×C47⋊C8—21no—
255C2×C47⋊C8—21no—
256C2×C47⋊C8—22no—
257C2×C47⋊C8—22no—
258C2×C47⋊C8—22no—
259C2×C47⋊C8—22no—
260C2×C47⋊C8—21no—
261C2×C47⋊C8—42no—
262C2×C47⋊C8C22×C411yescharacteristic
263C2×C47⋊C8C22×C411yescharacteristic
264C2×C47⋊C8C22×C411yescharacteristic
265C2×C47⋊C8C22×C411yescharacteristic
266C2×C47⋊C8C2×D412yes—
267C2×C47⋊C8#4112yes—
268#10625324—42no—
269C8×D47—42no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—22no—
273C23×C47—21no—
274C23×C47—41no—
275C23×C47C4×D411yescharacteristic
276C23×C47C4×D411yescharacteristic
277C23×C47C2×#4111yescharacteristic
278C22×D47—21no—
279Q8×C47—21no—
280Q8×C47—21no—
281D4×C47—21no—
282D4×C47—21no—
283D4×C47—41no—
284D4×C47—41no—
285D4×C47—42no—
286D4×C47—81no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47C4×D411yescharacteristic
303C2×C4×C47C4×D411yescharacteristic
304C2×C4×C47C23×C411yescharacteristic
305C2×C4×C47C22×D411yescharacteristic
306C2×C4×C47C22×D411yescharacteristic
307C2×C4×C47C2×#4111yescharacteristic
308C2×C4×C47H(5,𝔽2)11yescharacteristic
309C2×C4×C472−1+411yescharacteristic
310C22⋊D47—41no—
311C22⋊D47—41no—
312C22⋊D47—42no—
313C22⋊D47—81no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—21no—
317C2×Dic47—21no—
318C2×Dic47—21no—
319C2×Dic47—41no—
320C2×Dic47—41no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323D188—21no—
324D188—21no—
325C4×D47—41no—
326C4×D47—41no—
327Dic94—21no—
328Dic94—21no—
329C8×C47—21no—
330C8×C47—21no—
331C8×C47—22no—
332C8×C47—21no—
333C8×C47—21no—
334C8×C47—41no—
335C47⋊C8—21no—
336C47⋊C8—21no—
337C47⋊C8—22no—
338C47⋊C8—41no—
339C47⋊C8C4×D412yes—
340C47⋊C8C4×D412yes—
341#23018—471nomaximal, Sylow
342C22×C47—21no—
343C22×C47—21no—
344C22×C47—21no—
345C22×C47—21no—
346C22×C47—21no—
347C22×C47—21no—
348C22×C47—21no—
349C22×C47—42no—
350C22×C47—42no—
351C22×C47—41no—
352C22×C47—41no—
353C22×C47—41no—
354C22×C47#44312yescomplemented
355C22×C47C2×C4×D411yescharacteristic
356C22×C47#54811yescharacteristic
357C22×C47#55311yescharacteristic
358C2×D47—41no—
359C2×D47—41no—
360C2×D47—41no—
361C4×C47—21no—
362C4×C47—21no—
363C4×C47—41no—
364C4×C47—41no—
365C4×C47—41no—
366C4×C47C2×C4×D411yescharacteristic
367C4×C47#52011yescharacteristic
368C4×C47D4211yescharacteristic
369C4×C47#54711yescharacteristic
370Dic47—42no—
371Dic47—42no—
372Dic47—41no—
373Dic47—41no—
374Dic47—41no—
375#3050—471no—
376C2×#443—471no—
377#2933—471no—
378#2933D4711yescharacteristic, complemented
379C22×#108—471no—
380#1974—471no—
381#1945—471no—
382#1929—471no—
383#1929—471no—
384#1871—471no—
385#1871—471no—
386#1866—471no—
387#1866—471no—
388#1772—471no—
389C8×C22⋊C4—471no—
390C2×C47—21no—
391C2×C47—21no—
392C2×C47—22no—
393C2×C47—41no—
394C2×C47—81no—
395C2×C47#236111yescharacteristic
396C2×C47C2×#44311yescharacteristic
397C2×C47#295711yescharacteristic
398D47—81no—
399C2×#135—471no—
400C2×#131—471no—
401C2×#131C2×D4711yescharacteristic
402C22×M16—471no—
403C22×M16C2×D4711yescharacteristic
404C23×C8—471no—
405#525—471no—
406#525C2×D4711yescharacteristic
407#467—471no—
408#467—471no—
409#466—471no—
410#466—471no—
411#465—471no—
412#465—471no—
413#465—471no—
414#465—471no—
415#443—944no—
416#436—21no—
417#436—941no—
418#435—21no—
419#435—21no—
420#435—941no—
421#435—941no—
422C8×D4—21no—
423C8×D4—941no—
424C2×#108—471no—
425C2×#108—471no—
426C2×#108—471no—
427C2×#108—471no—
428C2×#108—944no—
429#427—471no—
430#424—471no—
431#424C2×D4711yescharacteristic
432C2×#104—471no—
433C2×#104—471no—
434C2×#104—471no—
435C2×#104—471no—
436#416—471no—
437#416—471no—
438#408—471no—
439#408C2×D4711yescharacteristic
440C2×C22⋊C8C2×D4711yescharacteristic
441#405—471no—
442#405C2×D4711yescharacteristic
443C2×C4×C8—471no—
444C2×C4×C8—471no—
445C4×C22⋊C4—471no—
446#339—471no—
447#339—471no—
448#339—471no—
449#339—471no—
450#336—471no—
451#336—471no—
452C47#2301811yescharacteristic, complemented, Sylow
453C2×#41—471no—
454C2×#41C22×D4711yescharacteristic
455C23×C4C22×D4711yescharacteristic
456#135—942no—
457#135—942no—
458C2×Q16—471no—
459C2×SD16—471no—
460C2×SD16—471no—
461C2×D8—471no—
462#131—22no—
463#131—41no—
464#131—942no—
465#131—1881no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—22no—
469C2×M16—41no—
470C2×M16—471no—
471C2×M16—471no—
472C2×M16—941no—
473C2×M16—941no—
474C2×M16—942no—
475C2×M16—1881no—
476C2×M16C22×D4711yescharacteristic
477C2×M16C22×D4711yescharacteristic
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—471no—
481C22×C8—471no—
482C22×C8—471no—
483C22×C8—471no—
484C22×C8—471no—
485C22×C8—471no—
486C22×C8—942no—
487C22×C8—942no—
488C22×C8—941no—
489C22×C8—941no—
490C22×C8C22×D4711yescharacteristic
491C22×C8C22×D4711yescharacteristic
492#123—21no—
493#123—941no—
494C22⋊Q8—471no—
495C22⋊Q8—471no—
496C22⋊Q8C4×D4711yescharacteristic
497C22⋊Q8C4×D4711yescharacteristic
498#121—471no—
499#121—471no—
500#121C4×D4711yescharacteristic
501#121C4×D4711yescharacteristic
502#120—21no—
503#120—941no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—941no—
507C4×D4—941no—
508#117—471no—
509#117C22×D4711yescharacteristic
510C2×C22⋊C4—941no—
511C2×C42—471no—
512C2×C42—471no—
513#108—474no—
514#108—942no—
515#108—942no—
516#108—942no—
517#107—471no—
518#107—471no—
519#106—471no—
520#106—471no—
521C4⋊C8—21no—
522C4⋊C8—21no—
523C4⋊C8—941no—
524C4⋊C8—941no—
525#104—942no—
526#104—942no—
527#104—1881no—
528#104—1881no—
529#103—471no—
530#103—471no—
531#103—471no—
532#103—471no—
533#102—471no—
534#102—471no—
535#102—471no—
536#102—471no—
537C22⋊C8—21no—
538C22⋊C8—21no—
539C22⋊C8—941no—
540C22⋊C8—941no—
541C22⋊C8C22⋊D4711yescharacteristic
542C22⋊C8C22⋊D4711yescharacteristic
543C22⋊C8C22⋊D4711yescharacteristic
544C22⋊C8C22⋊D4711yescharacteristic
545#97—21no—
546#97—941no—
547C4×C8—21no—
548C4×C8—942no—
549C4×C8—942no—
550C4×C8—941no—
551#95—941no—
552C24#1062535011yescharacteristic
553#41—21no—
554#41—21no—
555#41—21no—
556#41—21no—
557#41—941no—
558#41—941no—
559#41—941no—
560#41—941no—
561C2×Q8—471no—
562C2×Q8C2×C4×D4711yescharacteristic
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—471no—
567C2×D4—941no—
568C2×D4—941no—
569C2×D4—941no—
570C2×D4C2×C4×D4711yescharacteristic
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—941no—
577C22×C4—941no—
578C22×C4—941no—
579C22×C4C2×C4×D4711yescharacteristic
580C22×C4C2×C4×D4711yescharacteristic
581C22×C4#1062535011yescharacteristic
582C22×C4C2×C22⋊D4711yescharacteristic
583C22×C4C2×C22⋊D4711yescharacteristic
584C22×C4C23×D4711yescharacteristic
585Q16—942no—
586SD16—942no—
587SD16—942no—
588D8—942no—
589M16—21no—
590M16—21no—
591M16—21no—
592M16—42no—
593M16—42no—
594M16—472no—
595M16—941no—
596M16—941no—
597M16—941no—
598M16—1882no—
599M16—1882no—
600M16D4×D4712yes—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—42no—
608C2×C8—42no—
609C2×C8—471no—
610C2×C8—471no—
611C2×C8—472no—
612C2×C8—472no—
613C2×C8—471no—
614C2×C8—471no—
615C2×C8—942no—
616C2×C8—942no—
617C2×C8—942no—
618C2×C8—942no—
619C2×C8—941no—
620C2×C8—941no—
621C2×C8—941no—
622C2×C8—941no—
623C2×C8—1882no—
624C2×C8—1882no—
625C2×C8C2×C22⋊D4711yescharacteristic
626C2×C8C2×C22⋊D4711yescharacteristic
627C2×C8C2×C22⋊D4711yescharacteristic
628C2×C8C2×C22⋊D4711yescharacteristic
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—471no—
632C4⋊C4—471no—
633C4⋊C4—941no—
634C4⋊C4—941no—
635C4⋊C4C2×C4×D4711yescharacteristic
636C4⋊C4C2×C4×D4711yescharacteristic
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—944no—
643C22⋊C4—941no—
644C22⋊C4—941no—
645C22⋊C4—941no—
646C22⋊C4—941no—
647C22⋊C4—941no—
648C42—21no—
649C42—941no—
650C42—941no—
651C42—941no—
652C42—941no—
653C42—941no—
654C23—22no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—41no—
659C23—941no—
660C23C4×C22⋊D4711yescharacteristic
661C23C4×C22⋊D4711yescharacteristic
662C23C2×#1062535011yescharacteristic
663Q8—21no—
664Q8—21no—
665Q8—941no—
666Q8—941no—
667D4—21no—
668D4—21no—
669D4—42no—
670D4—41no—
671D4—41no—
672D4—81no—
673D4—941no—
674D4—941no—
675D4—3761no—
676D4—1882no—
677D4—1881no—
678D4—1881no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—941no—
697C2×C4—941no—
698C2×C4—941no—
699C2×C4—1881no—
700C2×C4—1881no—
701C2×C4—1881no—
702C2×C4—1881no—
703C2×C4—1881no—
704C2×C4—1881no—
705C2×C4C4×C22⋊D4711yescharacteristic
706C2×C4C4×C22⋊D4711yescharacteristic
707C2×C4C22×C4×D4711yescharacteristic
708C2×C4C2×D4×D4711yescharacteristic
709C2×C4C22×C22⋊D4711yescharacteristic
710C2×C4#41×D4711yescharacteristic
711C2×C4#1309406911yescharacteristic
712C2×C4#1309407111yescharacteristic
713C8—21no—
714C8—21no—
715C8—22no—
716C8—21no—
717C8—21no—
718C8—41no—
719C8—472no—
720C8—472no—
721C8—942no—
722C8—941no—
723C8—941no—
724C8—1881no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—1881no—
738C22—1881no—
739C22—1881no—
740C22#1568923812yescomplemented
741C22C2×C4×C22⋊D4711yescharacteristic
742C22#1568978211yescharacteristic
743C22#1568982211yescharacteristic
744C4—21no—
745C4—21no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—1882no—
750C4—1882no—
751C4—1881no—
752C4—1881no—
753C4—1881no—
754C4C4×D4×D4711yescharacteristic
755C4#1568960211yescharacteristic
756C4D4×C22⋊D4711yescharacteristic
757C4#1568977211yescharacteristic
758C2—21no—
759C2—21no—
760C2—22no—
761C2—41no—
762C2—81no—
763C2—3761no—
764C2#2024640511yescharacteristic
765C2C2×#1568923811yescharacteristic
766C2#2025230311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2933C2
socleC22×C47C2×C4×D4
prime radical#20252966C2
cosocleC22×C4×C47C24
hypercenter#2933D47
hypocenterC47#23018
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2933

Complements

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

NH ≅ G/Ntype
2. C2×#15689238C2semidirect
3. #20252109C2semidirect
4. C22×#13093959C2semidirect
5. #20244275C2semidirect
6. #20244133C2semidirect
7. #20244036C2semidirect
8. #20244033C2semidirect
9. #20243691C2semidirect
10. #20243690C2semidirect
11. #20243663C2semidirect
12. #20243662C2semidirect
13. #20243268C2semidirect
14. #20243162C2semidirect
15. C47×#2933C2semidirect
21. #15689362C4semidirect
22. #15689362C4semidirect
23. #15689357C4semidirect
24. #15689357C4semidirect
25. #15689354C4semidirect
26. #15689354C4semidirect
27. #15689350C4semidirect
28. #15689350C4semidirect
109. #13093959D4semidirect
354. C22×C47#443semidirect
378. #2933D47semidirect
452. C47#23018semidirect
740. C22#15689238semidirect

Maximal subgroups

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

subgroupindex
#202529662
C2×#156892382
#202521092
C22×#130939592
#202442752
#202441332
#202440362
#202440332
#202436912
#202436902
#202436632
#202436622
#202432682
#202431622
C47×#29332
#2301847