Finite Group Databasebeta

← #26233650

Subgroups — #26233650

Order 12032.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251905C211yesmaximal, characteristic
2#20251834C211yesmaximal, characteristic
3#20244098C211yesmaximal, characteristic, complemented
4#20244091C211yesmaximal, characteristic, complemented
5#20244036C211yesmaximal, characteristic, complemented
6#20244036C211yesmaximal, characteristic, complemented
7#20243662C211yesmaximal, characteristic, complemented
8#20243662C211yesmaximal, characteristic, complemented
9#20243487C211yesmaximal, characteristic, complemented
10#20243428C211yesmaximal, characteristic, complemented
11#20243331C211yesmaximal, characteristic
12#20243234C211yesmaximal, characteristic, complemented
13#20243227C211yesmaximal, characteristic, complemented
14#20243174C211yesmaximal, characteristic, complemented
15C47×#2924C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17C2×#13094030C2211yescharacteristic
18C2×#13094030C2211yescharacteristic
19C22×#10625329C2211yescharacteristic
20C2×#13093959C2211yescharacteristic, complemented
21C2×#13093959C2211yescharacteristic, complemented
22C2×#13093950C2211yescharacteristic
23C2×#13093950C2211yescharacteristic
24C2×#13093950C2211yescharacteristic
25C2×#13093950C2211yescharacteristic
26#15689131C411yescharacteristic, complemented
27#15689131C411yescharacteristic, complemented
28#15689127C411yescharacteristic, complemented
29#15689127C411yescharacteristic, complemented
30#15689122C411yescharacteristic, complemented
31#15689122C411yescharacteristic, complemented
32#15689122C411yescharacteristic, complemented
33#15689122C411yescharacteristic, complemented
34#15689117C2211yescharacteristic
35#15689117C2211yescharacteristic
36#15689117C2211yescharacteristic
37#15689117C2211yescharacteristic
38#15689089C2211yescharacteristic
39#15689089C2211yescharacteristic
40#15689088—21no—
41#15689088—21no—
42#15689087C2211yescharacteristic
43#15689085—21no—
44C22⋊C8×D47—21no—
45C2×#13093934C2211yescharacteristic, complemented
46C2×C8×Dic47C2211yescharacteristic, complemented
47C4×C22⋊Dic47C2211yescharacteristic
48#15688887C2211yescharacteristic, complemented
49#15688887C2211yescharacteristic, complemented
50#15688882C2211yescharacteristic, complemented
51#15688882C2211yescharacteristic, complemented
52#15688882C2211yescharacteristic, complemented
53#15688882C2211yescharacteristic, complemented
54#15688877C2211yescharacteristic, complemented
55#15688877C2211yescharacteristic, complemented
56C2×#117×C47C2211yescharacteristic
57C47×#433—21no—
58C47×#433—21no—
59C47×#432—21no—
60C47×#431—21no—
61C47×#424C2211yescharacteristic, complemented
62C47×#424C2211yescharacteristic, complemented
63C47×#407C2211yescharacteristic
64C2×C22⋊C8×C47C2211yescharacteristic
65C47×#405C2211yescharacteristic, complemented
66C47×#405C2211yescharacteristic, complemented
67C2×#10625350—21no—
68C2×#10625350—21no—
69C2×#10625350—22no—
70C2×#10625350—22no—
71C2×#10625350—41no—
72C2×#10625350—41no—
73C2×#10625350C2×C411yescharacteristic
74C2×#10625350C2×C411yescharacteristic
75C2×#10625350C2311yescharacteristic
76C2×#10625350C2311yescharacteristic
77C22×Dic94C2×C411yescharacteristic
78C22×D188C2×C411yescharacteristic
79C22×C22⋊D47—21no—
80C22×C4×D47—21no—
81#13094030—22no—
82#13094030—22no—
83#13094030—41no—
84#13094030—41no—
85C2×#10625329—41no—
86C2×#10625329—41no—
87C2×#10625329C2×C411yescharacteristic
88C2×#10625329C2×C411yescharacteristic
89C2×#10625329C2×C411yescharacteristic
90C2×#10625329C2×C411yescharacteristic
91C2×#10625329C2311yescharacteristic
92C2×#10625329C2311yescharacteristic
93C2×#10625324—21no—
94C2×#10625324—21no—
95C22×C47⋊C8C2311yescharacteristic
96C22×C47⋊C8C2311yescharacteristic
97C2×C8×D47—21no—
98C2×C8×D47—21no—
99C2×C22⋊Dic47—21no—
100C2×C4×Dic47C2311yescharacteristic
101C2×C4×Dic47C2311yescharacteristic
102#13093959—41no—
103#13093959—41no—
104#13093950—22no—
105#13093950—22no—
106#13093950—41no—
107#13093950—41no—
108#13093947C2×C411yescharacteristic
109#13093947C2×C411yescharacteristic
110#13093947C2×C411yescharacteristic
111#13093947C2×C411yescharacteristic
112#13093947C2×C411yescharacteristic
113#13093947C2×C411yescharacteristic
114#13093947C2×C411yescharacteristic
115#13093947C2×C411yescharacteristic
116#13093944C2×C411yescharacteristic
117#13093944C2×C411yescharacteristic
118#13093944C2×C411yescharacteristic
119#13093944C2×C411yescharacteristic
120#13093944C2×C411yescharacteristic
121#13093944C2×C411yescharacteristic
122#13093944C2×C411yescharacteristic
123#13093944C2×C411yescharacteristic
124C22⋊(C47⋊C8)—21no—
125C22⋊(C47⋊C8)—21no—
126(C2×D47)⋊C8—21no—
127(C2×D47)⋊C8—21no—
128(C2×D47)⋊C8—21no—
129(C2×D47)⋊C8—21no—
130#13093934—41no—
131C8×Dic47—41no—
132C47⋊#95—21no—
133C23×C4×C47C2311yescharacteristic
134C2×M16×C47C2311yescharacteristic
135C2×M16×C47C2311yescharacteristic
136C22×C8×C47C2311yescharacteristic
137C22×C8×C47C2311yescharacteristic
138#117×C47—21no—
139#117×C47—21no—
140#117×C47C2×C411yescharacteristic
141#117×C47C2×C411yescharacteristic
142#117×C47C2311yescharacteristic
143#117×C47C2311yescharacteristic
144C2×C4⋊C4×C47C2×C411yescharacteristic
145C2×C4⋊C4×C47C2×C411yescharacteristic
146C2×C22⋊C4×C47—21no—
147C2×C42×C47—21no—
148C4⋊C8×C47—21no—
149C4⋊C8×C47—21no—
150C4⋊C8×C47—21no—
151C4⋊C8×C47—21no—
152C22⋊C8×C47—21no—
153C22⋊C8×C47—21no—
154C22⋊C8×C47D411yescharacteristic
155C22⋊C8×C47D411yescharacteristic
156C22⋊C8×C47D411yescharacteristic
157C22⋊C8×C47D411yescharacteristic
158#97×C47—21no—
159#97×C47—21no—
160C4×C8×C47—21no—
161C4×C8×C47—21no—
162C24×C47#4111yescharacteristic
163C23×D47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47C22×C411yescharacteristic
171C22×C4×C47C22×C411yescharacteristic
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47C2×D411yescharacteristic
174C22×C4×C47#4111yescharacteristic
175C22×C4×C47C2411yescharacteristic
176C2×C22⋊D47—21no—
177C2×C22⋊D47—21no—
178C2×C22⋊D47—21no—
179C2×C22⋊D47—21no—
180C2×C22⋊D47—42no—
181C2×C22⋊D47—42no—
182C22×Dic47—21no—
183C22×Dic47—21no—
184C22×Dic47—21no—
185#10625350—21no—
186#10625350—21no—
187#10625350—21no—
188#10625350—21no—
189#10625350—21no—
190#10625350—21no—
191#10625350—22no—
192#10625350—22no—
193#10625350—41no—
194#10625350—41no—
195#10625350—42no—
196#10625350—42no—
197#10625350—42no—
198#10625350—42no—
199#10625350#4112yes—
200#10625350#4112yes—
201C2×D188—22no—
202C2×D188—21no—
203C2×D188—41no—
204C2×D188C22×C411yescharacteristic
205C2×D188C22×C411yescharacteristic
206C2×C4×D47—21no—
207C2×C4×D47—21no—
208C2×C4×D47—21no—
209C2×C4×D47—21no—
210C2×C4×D47—42no—
211C2×C4×D47—42no—
212C2×Dic94—22no—
213C2×Dic94—21no—
214C2×Dic94—41no—
215C2×Dic94C22×C411yescharacteristic
216C2×Dic94C22×C411yescharacteristic
217M16×C47—21no—
218M16×C47—21no—
219M16×C47—21no—
220M16×C47—21no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
226C2×C8×C47—21no—
227C2×C8×C47C2×D411yescharacteristic
228C2×C8×C47C2×D411yescharacteristic
229C2×C8×C47C2×D411yescharacteristic
230C2×C8×C47C2×D411yescharacteristic
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47C22×C411yescharacteristic
234C4⋊C4×C47C22×C411yescharacteristic
235C4⋊C4×C47C22×C411yescharacteristic
236C4⋊C4×C47C22×C411yescharacteristic
237C22⋊C4×C47—21no—
238C22⋊C4×C47—21no—
239C22⋊C4×C47—21no—
240C22⋊C4×C47—21no—
241C42×C47—21no—
242C42×C47—21no—
243C42×C47—21no—
244C42×C47—21no—
245C22⋊Dic47—42no—
246C4×Dic47—21no—
247C4×Dic47—21no—
248C4×Dic47—21no—
249C4×Dic47—21no—
250#10625329—21no—
251#10625329—21no—
252#10625329—21no—
253#10625329—21no—
254#10625329—41no—
255#10625329—41no—
256#10625329—41no—
257#10625329—41no—
258C2×C47⋊C8—21no—
259C2×C47⋊C8—21no—
260C2×C47⋊C8—21no—
261C2×C47⋊C8—21no—
262C2×C47⋊C8—21no—
263C2×C47⋊C8—21no—
264C2×C47⋊C8C22×C411yescharacteristic
265C2×C47⋊C8C22×C411yescharacteristic
266C2×C47⋊C8C22×C411yescharacteristic
267C2×C47⋊C8C22×C411yescharacteristic
268#10625324—42no—
269#10625324—42no—
270C8×D47—42no—
271C8×D47—42no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47C4×D411yescharacteristic
277C23×C47C4×D411yescharacteristic
278C23×C47C2×#4111yescharacteristic
279C22×D47—21no—
280C22×D47—21no—
281C22×D47—42no—
282C22×D47—42no—
283C22×D47—81no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
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—42no—
299C2×C4×C47—81no—
300C2×C4×C47C4×D411yescharacteristic
301C2×C4×C47C4×D411yescharacteristic
302C2×C4×C47C23×C411yescharacteristic
303C2×C4×C47C22×D411yescharacteristic
304C2×C4×C47C2×#4111yescharacteristic
305C2×C4×C47C2×#4111yescharacteristic
306C2×C4×C47H(5,𝔽2)11yescharacteristic
307C2×C4×C47H(5,𝔽2)11yescharacteristic
308C22⋊D47—22no—
309C22⋊D47—22no—
310C22⋊D47—42no—
311C22⋊D47—42no—
312C22⋊D47—41no—
313C22⋊D47—41no—
314C2×Dic47—21no—
315C2×Dic47—22no—
316C2×Dic47—21no—
317C2×Dic47—42no—
318C2×Dic47—41no—
319C2×Dic47—41no—
320C2×Dic47—41no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323D188—21no—
324D188—21no—
325D188—21no—
326D188—42no—
327D188#11712yes—
328C4×D47—22no—
329C4×D47—22no—
330C4×D47—42no—
331C4×D47—42no—
332C4×D47—41no—
333C4×D47—41no—
334Dic94—21no—
335Dic94—21no—
336Dic94—21no—
337Dic94—42no—
338Dic94#11712yes—
339C8×C47—21no—
340C8×C47—21no—
341C8×C47—21no—
342C8×C47—21no—
343C8×C47—41no—
344C8×C47—41no—
345C47⋊C8—21no—
346C47⋊C8—21no—
347C47⋊C8—21no—
348C47⋊C8—21no—
349C47⋊C8—41no—
350C47⋊C8—41no—
351#22588—471nomaximal, Sylow
352C22×C47—21no—
353C22×C47—21no—
354C22×C47—21no—
355C22×C47—21no—
356C22×C47—21no—
357C22×C47—21no—
358C22×C47—21no—
359C22×C47—21no—
360C22×C47—81no—
361C22×C47—81no—
362C22×C47C2×C4×D411yescharacteristic
363C22×C47#55111yescharacteristic
364C22×C47#55111yescharacteristic
365C2×D47—22no—
366C2×D47—41no—
367C2×D47—41no—
368C2×D47—41no—
369C2×D47—41no—
370C2×D47—41no—
371C2×D47—84no—
372C4×C47—21no—
373C4×C47—21no—
374C4×C47—41no—
375C4×C47—41no—
376C4×C47—41no—
377C4×C47—41no—
378C4×C47C2×#11711yescharacteristic
379C4×C47#51811yescharacteristic
380C4×C47#54611yescharacteristic
381C4×C47#54611yescharacteristic
382Dic47—22no—
383Dic47—42no—
384Dic47—41no—
385Dic47—81no—
386#2924D4711yescharacteristic, complemented
387#2896—471no—
388#2880—471no—
389#1938—471no—
390#1937—471no—
391#1929—471no—
392#1929—471no—
393#1866—471no—
394#1866—471no—
395#1826—471no—
396#1811—471no—
397#1789—471no—
398#1765—471no—
399#1764—471no—
400#1753—471no—
401C2×C47—21no—
402C2×C47—21no—
403C2×C47—41no—
404C2×C47—41no—
405C2×C47#234211yescharacteristic
406C2×C47#295511yescharacteristic
407C2×C47#295611yescharacteristic
408D47—42no—
409D47—81no—
410C22×#41—471no—
411C2×#131—471no—
412C2×#131—471no—
413C22×M16—471no—
414C2×#117C2×D4711yescharacteristic
415#433—21no—
416#433—21no—
417#432—21no—
418#431—21no—
419C2×#108—471no—
420C2×#108—471no—
421#424C2×D4711yescharacteristic, complemented
422#424C2×D4711yescharacteristic, complemented
423C2×#104—471no—
424C2×#104—471no—
425C2×#104—471no—
426C2×#104—471no—
427#419—471no—
428#419—471no—
429#418—471no—
430#418—471no—
431#417—471no—
432#417—471no—
433#417—471no—
434#417—471no—
435#416—471no—
436#416—471no—
437#416—471no—
438#416—471no—
439#408—471no—
440#408—471no—
441#408—941no—
442#408—941no—
443#407—471no—
444#407—941no—
445#407C2×D4711yescharacteristic
446C2×C22⋊C8—941no—
447C2×C22⋊C8C2×D4711yescharacteristic
448#405C2×D4711yescharacteristic, complemented
449#405C2×D4711yescharacteristic, complemented
450C2×#97—471no—
451C2×C4×C8—471no—
452C4×C22⋊C4—471no—
453#341—471no—
454#341—471no—
455#339—471no—
456#339—471no—
457#339—471no—
458#339—471no—
459#336—471no—
460#336—471no—
461C47#2258811yescharacteristic, complemented, Sylow
462C2×#41—471no—
463C2×#41—471no—
464C2×#41—471no—
465C2×#41—471no—
466C2×#41—942no—
467C2×#41—942no—
468C2×#41—941no—
469C2×#41—941no—
470C2×#41—1881no—
471C2×#41—1881no—
472C22×Q8—471no—
473C22×D4—471no—
474C22×D4—941no—
475C23×C4—941no—
476C23×C4C22×D4711yescharacteristic
477#131—942no—
478#131—942no—
479#131—1881no—
480#131—1881no—
481C2×M16—471no—
482C2×M16—471no—
483C2×M16—471no—
484C2×M16—471no—
485C2×M16—471no—
486C2×M16—471no—
487C2×M16—941no—
488C2×M16—941no—
489C2×M16—1881no—
490C2×M16—1881no—
491C2×M16C22×D4711yescharacteristic
492C2×M16C22×D4711yescharacteristic
493C22×C8—471no—
494C22×C8—471no—
495C22×C8—941no—
496C22×C8—941no—
497C22×C8C22×D4711yescharacteristic
498C22×C8C22×D4711yescharacteristic
499#117—21no—
500#117—21no—
501#117C4×D4711yescharacteristic
502#117C4×D4711yescharacteristic
503#117C22×D4711yescharacteristic
504#117C22×D4711yescharacteristic
505C2×C4⋊C4C4×D4711yescharacteristic
506C2×C4⋊C4C4×D4711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—941no—
509C2×C42—21no—
510C2×C42—471no—
511C2×C42—471no—
512#108—1881no—
513#108—1881no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517C4⋊C8—21no—
518#104—942no—
519#104—942no—
520#104—1881no—
521#104—1881no—
522#103—471no—
523#103—471no—
524#103—471no—
525#103—471no—
526#103—471no—
527#103—471no—
528#103—471no—
529#103—471no—
530#102—471no—
531#102—471no—
532#102—471no—
533#102—471no—
534#102—471no—
535#102—471no—
536#102—471no—
537#102—471no—
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—941no—
541C22⋊C8—941no—
542C22⋊C8—941no—
543C22⋊C8—941no—
544C22⋊C8—941no—
545C22⋊C8—941no—
546C22⋊C8C22⋊D4711yescharacteristic
547C22⋊C8C22⋊D4711yescharacteristic
548C22⋊C8C22⋊D4711yescharacteristic
549C22⋊C8C22⋊D4711yescharacteristic
550#97—21no—
551#97—21no—
552#97—1881no—
553C4×C8—21no—
554C4×C8—21no—
555C4×C8—1881no—
556#95—941no—
557C24—941no—
558C24#1062535011yescharacteristic
559#41—472no—
560#41—472no—
561#41—942no—
562#41—942no—
563#41—941no—
564#41—941no—
565#41—941no—
566#41—941no—
567#41—941no—
568#41—941no—
569#41—1882no—
570#41—1882no—
571#41—1881no—
572#41—1881no—
573#41—1882no—
574#41—1882no—
575C2×Q8—471no—
576C2×Q8—471no—
577C2×Q8—942no—
578C2×Q8—941no—
579C2×Q8—1881no—
580C2×D4—471no—
581C2×D4—471no—
582C2×D4—942no—
583C2×D4—941no—
584C2×D4—941no—
585C2×D4—941no—
586C2×D4—941no—
587C2×D4—941no—
588C2×D4—1881no—
589C2×D4—1882no—
590C2×D4—1882no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—941no—
598C22×C4—941no—
599C22×C4—941no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—941no—
604C22×C4—1882no—
605C22×C4—1882no—
606C22×C4C2×C4×D4711yescharacteristic
607C22×C4C2×C4×D4711yescharacteristic
608C22×C4#1062535011yescharacteristic
609C22×C4C2×C22⋊D4711yescharacteristic
610C22×C4C2×C22⋊D4711yescharacteristic
611C22×C4C23×D4711yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—941no—
617M16—941no—
618M16—941no—
619M16—941no—
620M16—1882no—
621M16—1882no—
622M16—1881no—
623M16—1881no—
624M16—1881no—
625M16—1881no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—471no—
633C2×C8—471no—
634C2×C8—471no—
635C2×C8—471no—
636C2×C8—941no—
637C2×C8—941no—
638C2×C8—941no—
639C2×C8—941no—
640C2×C8—941no—
641C2×C8—941no—
642C2×C8—1882no—
643C2×C8—1882no—
644C2×C8C2×C22⋊D4711yescharacteristic
645C2×C8C2×C22⋊D4711yescharacteristic
646C2×C8C2×C22⋊D4711yescharacteristic
647C2×C8C2×C22⋊D4711yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C2×C4×D4711yescharacteristic
651C4⋊C4C2×C4×D4711yescharacteristic
652C4⋊C4C2×C4×D4711yescharacteristic
653C4⋊C4C2×C4×D4711yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—1882no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—941no—
664C42—941no—
665C42—941no—
666C42—941no—
667C23—21no—
668C23—21no—
669C23—41no—
670C23—41no—
671C23—941no—
672C23—941no—
673C23—3761no—
674C23—1882no—
675C23—1882no—
676C23C4×C22⋊D4711yescharacteristic
677C23C4×C22⋊D4711yescharacteristic
678C23C2×#1062535011yescharacteristic
679Q8—472no—
680Q8—941no—
681Q8—941no—
682Q8—941no—
683Q8—1882no—
684D4—472no—
685D4—942no—
686D4—942no—
687D4—941no—
688D4—941no—
689D4—941no—
690D4—1882no—
691D4—1882no—
692D4—1882no—
693D4—1881no—
694D4—1881no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—42no—
710C2×C4—81no—
711C2×C4—941no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—941no—
716C2×C4—1882no—
717C2×C4—1882no—
718C2×C4—1882no—
719C2×C4—1881no—
720C2×C4—1881no—
721C2×C4—1881no—
722C2×C4—1881no—
723C2×C4—1881no—
724C2×C4—1881no—
725C2×C4—1881no—
726C2×C4C4×C22⋊D4711yescharacteristic
727C2×C4C4×C22⋊D4711yescharacteristic
728C2×C4C22×C4×D4711yescharacteristic
729C2×C4C22×C22⋊D4711yescharacteristic
730C2×C4#41×D4711yescharacteristic
731C2×C4#41×D4711yescharacteristic
732C2×C4#1309407011yescharacteristic
733C2×C4#1309407011yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—41no—
739C8—41no—
740C8—941no—
741C8—941no—
742C8—941no—
743C8—941no—
744C8—1881no—
745C8—1881no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—81no—
755C22—81no—
756C22—942no—
757C22—3764no—
758C22—1881no—
759C22—1881no—
760C22—1881no—
761C22—1881no—
762C22—1881no—
763C22C2×C4×C22⋊D4711yescharacteristic
764C22#1568979711yescharacteristic
765C22#1568979711yescharacteristic
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—942no—
773C4—3761no—
774C4—1882no—
775C4—1881no—
776C4#117×D4711yescharacteristic
777C4#1568959711yescharacteristic
778C4#1568976111yescharacteristic
779C4#1568976111yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—3761no—
785C2—1882no—
786C2#2024623811yescharacteristic
787C2#2025228911yescharacteristic
788C2#2025229511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2924C2
socleC22×C47C2×C4×D4
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenter#2924D47
hypocenterC47#22588
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2924

Complements

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

NH ≅ G/Ntype
3. #20244098C2semidirect
4. #20244091C2semidirect
5. #20244036C2semidirect
6. #20244036C2semidirect
7. #20243662C2semidirect
8. #20243662C2semidirect
9. #20243487C2semidirect
10. #20243428C2semidirect
12. #20243234C2semidirect
13. #20243227C2semidirect
14. #20243174C2semidirect
15. C47×#2924C2semidirect
20. C2×#13093959C22semidirect
21. C2×#13093959C22semidirect
26. #15689131C4semidirect
27. #15689131C4semidirect
28. #15689127C4semidirect
29. #15689127C4semidirect
30. #15689122C4semidirect
31. #15689122C4semidirect
32. #15689122C4semidirect
33. #15689122C4semidirect
45. C2×#13093934C22semidirect
46. C2×C8×Dic47C22semidirect
48. #15688887C22semidirect
49. #15688887C22semidirect
50. #15688882C22semidirect
51. #15688882C22semidirect
52. #15688882C22semidirect
53. #15688882C22semidirect
54. #15688877C22semidirect
55. #15688877C22semidirect
61. C47×#424C22semidirect
62. C47×#424C22semidirect
65. C47×#405C22semidirect
66. C47×#405C22semidirect
386. #2924D47semidirect
421. #424C2×D47semidirect
422. #424C2×D47semidirect
448. #405C2×D47semidirect
449. #405C2×D47semidirect
461. C47#22588semidirect

Maximal subgroups

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

subgroupindex
#202519052
#202518342
#202440982
#202440912
#202440362
#202436622
#202434872
#202434282
#202433312
#202432342
#202432272
#202431742
C47×#29242
#2258847