Finite Group Databasebeta

← #26233645

Subgroups — #26233645

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#20252042C211yesmaximal, characteristic, complemented
2#20251907C211yesmaximal, characteristic
3#20244102C211yesmaximal, characteristic, complemented
4#20244095C211yesmaximal, characteristic, complemented
5#20244033C211yesmaximal, characteristic, complemented
6#20244033C211yesmaximal, characteristic, complemented
7#20243663C211yesmaximal, characteristic, complemented
8#20243663C211yesmaximal, characteristic, complemented
9#20243485C211yesmaximal, characteristic, complemented
10#20243428C211yesmaximal, characteristic, complemented
11#20243332C211yesmaximal, characteristic
12#20243230C211yesmaximal, characteristic, complemented
13#20243223C211yesmaximal, characteristic, complemented
14#20243174C211yesmaximal, characteristic, complemented
15C47×#2880C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C2×#13093983C2211yescharacteristic
18#15689181—21no—
19#15689181—21no—
20#15689177—21no—
21#15689173—21no—
22C2×#13093959C2211yescharacteristic, complemented
23C2×#13093959C2211yescharacteristic, complemented
24#15689149C2211yescharacteristic, complemented
25#15689149C2211yescharacteristic, complemented
26C2×#13093951C2211yescharacteristic
27C2×#13093951C2211yescharacteristic
28C2×#13093951C2211yescharacteristic
29C2×#13093951C2211yescharacteristic
30#15689132C411yescharacteristic, complemented
31#15689132C411yescharacteristic, complemented
32#15689128C411yescharacteristic, complemented
33#15689128C411yescharacteristic, complemented
34#15689124C411yescharacteristic, complemented
35#15689124C411yescharacteristic, complemented
36#15689124C411yescharacteristic, complemented
37#15689124C411yescharacteristic, complemented
38#15689119C2211yescharacteristic
39#15689119C2211yescharacteristic
40#15689119C2211yescharacteristic
41#15689119C2211yescharacteristic
42#15689087C2211yescharacteristic
43#15689078C2211yescharacteristic, complemented
44#15689078C2211yescharacteristic, complemented
45C2×#13093934C2211yescharacteristic, complemented
46C2×C8×Dic47C2211yescharacteristic, complemented
47C4×C22⋊Dic47C2211yescharacteristic
48#15688887C2211yescharacteristic, complemented
49#15688887C2211yescharacteristic, complemented
50#15688884C2211yescharacteristic, complemented
51#15688884C2211yescharacteristic, complemented
52#15688884C2211yescharacteristic, complemented
53#15688884C2211yescharacteristic, complemented
54#15688877C2211yescharacteristic, complemented
55#15688877C2211yescharacteristic, complemented
56C22×#41×C47C2211yescharacteristic
57C2×#131×C47C2211yescharacteristic
58C2×#131×C47C2211yescharacteristic
59C47×#408—21no—
60C47×#408—21no—
61C47×#408C2211yescharacteristic
62C47×#408C2211yescharacteristic
63C47×#407—21no—
64C47×#407C2211yescharacteristic
65C2×C22⋊C8×C47—21no—
66C2×C22⋊C8×C47C2211yescharacteristic
67C2×#10625329—41no—
68C2×#10625329—41no—
69C2×#10625329C2×C411yescharacteristic
70C2×#10625329C2×C411yescharacteristic
71C2×#10625329C2×C411yescharacteristic
72C2×#10625329C2×C411yescharacteristic
73C2×#10625329C2311yescharacteristic
74C2×#10625329C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77#13093983—21no—
78#13093983—21no—
79#13093983C2×C411yescharacteristic
80#13093983C2×C411yescharacteristic
81#13093983C2311yescharacteristic
82#13093983C2311yescharacteristic
83C2×C4⋊Dic47C2×C411yescharacteristic
84C2×C4⋊Dic47C2×C411yescharacteristic
85C2×C22⋊Dic47—21no—
86C2×C22⋊Dic47—21no—
87C2×C4×Dic47—21no—
88C2×C4×Dic47C2311yescharacteristic
89C2×C4×Dic47C2311yescharacteristic
90#13093959—41no—
91#13093959—41no—
92Dic47⋊C8—21no—
93Dic47⋊C8—21no—
94Dic47⋊C8—21no—
95Dic47⋊C8—21no—
96#13093951—22no—
97#13093951—22no—
98#13093951—41no—
99#13093951—41no—
100#13093948C2×C411yescharacteristic
101#13093948C2×C411yescharacteristic
102#13093948C2×C411yescharacteristic
103#13093948C2×C411yescharacteristic
104#13093948C2×C411yescharacteristic
105#13093948C2×C411yescharacteristic
106#13093948C2×C411yescharacteristic
107#13093948C2×C411yescharacteristic
108#13093945C2×C411yescharacteristic
109#13093945C2×C411yescharacteristic
110#13093945C2×C411yescharacteristic
111#13093945C2×C411yescharacteristic
112#13093945C2×C411yescharacteristic
113#13093945C2×C411yescharacteristic
114#13093945C2×C411yescharacteristic
115#13093945C2×C411yescharacteristic
116C22⋊(C47⋊C8)—21no—
117C22⋊(C47⋊C8)—21no—
118#13093934—21no—
119#13093934—21no—
120#13093934—41no—
121C8×Dic47—21no—
122C8×Dic47—21no—
123C8×Dic47—41no—
124C47⋊#95—21no—
125C2×#41×C47—21no—
126C2×#41×C47—21no—
127C2×#41×C47—22no—
128C2×#41×C47—22no—
129C2×#41×C47—41no—
130C2×#41×C47—41no—
131C2×#41×C47C2×C411yescharacteristic
132C2×#41×C47C2×C411yescharacteristic
133C2×#41×C47C2311yescharacteristic
134C2×#41×C47C2311yescharacteristic
135C22×Q8×C47C2×C411yescharacteristic
136C22×D4×C47—21no—
137C22×D4×C47C2×C411yescharacteristic
138C23×C4×C47—21no—
139C23×C4×C47C2311yescharacteristic
140#131×C47—22no—
141#131×C47—22no—
142#131×C47—41no—
143#131×C47—41no—
144C2×M16×C47—21no—
145C2×M16×C47—21no—
146C2×M16×C47C2311yescharacteristic
147C2×M16×C47C2311yescharacteristic
148C22×C8×C47—21no—
149C22×C8×C47—21no—
150C22×C8×C47C2311yescharacteristic
151C22×C8×C47C2311yescharacteristic
152C22⋊C8×C47—21no—
153C22⋊C8×C47—21no—
154C22⋊C8×C47—21no—
155C22⋊C8×C47—21no—
156C22⋊C8×C47—21no—
157C22⋊C8×C47—21no—
158C22⋊C8×C47D411yescharacteristic
159C22⋊C8×C47D411yescharacteristic
160C22⋊C8×C47D411yescharacteristic
161C22⋊C8×C47D411yescharacteristic
162C24×C47—21no—
163C24×C47#4111yescharacteristic
164#41×C47—21no—
165#41×C47—21no—
166#41×C47—22no—
167#41×C47—22no—
168#41×C47—21no—
169#41×C47—21no—
170#41×C47—21no—
171#41×C47—21no—
172#41×C47—42no—
173#41×C47—42no—
174#41×C47—41no—
175#41×C47—41no—
176#41×C47—42no—
177#41×C47—42no—
178#41×C47#4112yes—
179#41×C47#4112yes—
180C2×Q8×C47—21no—
181C2×Q8×C47—22no—
182C2×Q8×C47—41no—
183C2×Q8×C47C22×C411yescharacteristic
184C2×Q8×C47C22×C411yescharacteristic
185C2×D4×C47—21no—
186C2×D4×C47—22no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—21no—
190C2×D4×C47—21no—
191C2×D4×C47—41no—
192C2×D4×C47—42no—
193C2×D4×C47—42no—
194C2×D4×C47C22×C411yescharacteristic
195C2×D4×C47C22×C411yescharacteristic
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—42no—
206C22×C4×C47—42no—
207C22×C4×C47C22×C411yescharacteristic
208C22×C4×C47C22×C411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47#4111yescharacteristic
212C22×C4×C47C2411yescharacteristic
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217M16×C47—21no—
218M16×C47—21no—
219M16×C47—21no—
220M16×C47—21no—
221M16×C47—42no—
222M16×C47—42no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—42no—
230C2×C8×C47—42no—
231C2×C8×C47C2×D411yescharacteristic
232C2×C8×C47C2×D411yescharacteristic
233C2×C8×C47C2×D411yescharacteristic
234C2×C8×C47C2×D411yescharacteristic
235C22⋊Dic47—21no—
236C22⋊Dic47—21no—
237C22⋊Dic47—21no—
238C22⋊Dic47—21no—
239C22⋊Dic47—42no—
240C4⋊Dic47—21no—
241C4⋊Dic47—21no—
242C4⋊Dic47C22×C411yescharacteristic
243C4⋊Dic47C22×C411yescharacteristic
244C4⋊Dic47C22×C411yescharacteristic
245C4⋊Dic47C22×C411yescharacteristic
246C4×Dic47—21no—
247C4×Dic47—21no—
248C4×Dic47—21no—
249C4×Dic47—21no—
250C4×Dic47—21no—
251C4×Dic47—21no—
252C4×Dic47—21no—
253C4×Dic47—21no—
254#10625329—21no—
255#10625329—21no—
256#10625329—21no—
257#10625329—21no—
258#10625329—41no—
259#10625329—41no—
260#10625329—41no—
261#10625329—41no—
262C2×C47⋊C8—21no—
263C2×C47⋊C8—21no—
264C2×C47⋊C8—21no—
265C2×C47⋊C8—21no—
266C2×C47⋊C8—21no—
267C2×C47⋊C8—21no—
268C2×C47⋊C8C22×C411yescharacteristic
269C2×C47⋊C8C22×C411yescharacteristic
270C2×C47⋊C8C22×C411yescharacteristic
271C2×C47⋊C8C22×C411yescharacteristic
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—21no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—42no—
279C23×C47—42no—
280C23×C47—81no—
281C23×C47C4×D411yescharacteristic
282C23×C47C4×D411yescharacteristic
283C23×C47C2×#4111yescharacteristic
284Q8×C47—21no—
285Q8×C47—21no—
286Q8×C47—21no—
287Q8×C47—42no—
288Q8×C47#11712yes—
289D4×C47—22no—
290D4×C47—22no—
291D4×C47—21no—
292D4×C47—21no—
293D4×C47—21no—
294D4×C47—42no—
295D4×C47—42no—
296D4×C47—42no—
297D4×C47—41no—
298D4×C47—41no—
299D4×C47#11712yes—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—42no—
315C2×C4×C47—42no—
316C2×C4×C47—42no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47C4×D411yescharacteristic
320C2×C4×C47C4×D411yescharacteristic
321C2×C4×C47C23×C411yescharacteristic
322C2×C4×C47C22×D411yescharacteristic
323C2×C4×C47C2×#4111yescharacteristic
324C2×C4×C47C2×#4111yescharacteristic
325C2×C4×C47H(5,𝔽2)11yescharacteristic
326C2×C4×C47H(5,𝔽2)11yescharacteristic
327C2×Dic47—22no—
328C2×Dic47—21no—
329C2×Dic47—21no—
330C2×Dic47—21no—
331C2×Dic47—21no—
332C2×Dic47—41no—
333C2×Dic47—42no—
334C2×Dic47—41no—
335C2×Dic47—41no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—81no—
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—22no—
357C22×C47—21no—
358C22×C47—21no—
359C22×C47—21no—
360C22×C47—21no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—41no—
366C22×C47—81no—
367C22×C47—81no—
368C22×C47—84no—
369C22×C47C2×C4×D411yescharacteristic
370C22×C47#55111yescharacteristic
371C22×C47#55111yescharacteristic
372C4×C47—21no—
373C4×C47—21no—
374C4×C47—22no—
375C4×C47—41no—
376C4×C47C2×#11711yescharacteristic
377C4×C47#51811yescharacteristic
378C4×C47#54611yescharacteristic
379C4×C47#54611yescharacteristic
380Dic47—42no—
381Dic47—41no—
382Dic47—41no—
383Dic47—41no—
384Dic47—41no—
385Dic47—81no—
386#2924—471no—
387#2896—471no—
388#2880D4711yescharacteristic
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—42no—
406C2×C47—81no—
407C2×C47#234211yescharacteristic
408C2×C47#295511yescharacteristic
409C2×C47#295611yescharacteristic
410C22×#41C2×D4711yescharacteristic
411C2×#131C2×D4711yescharacteristic
412C2×#131C2×D4711yescharacteristic
413C22×M16—471no—
414C2×#117—471no—
415#433—941no—
416#433—941no—
417#432—941no—
418#431—941no—
419C2×#108—471no—
420C2×#108—471no—
421#424—471no—
422#424—471no—
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—21no—
440#408—21no—
441#408C2×D4711yescharacteristic
442#408C2×D4711yescharacteristic
443#407—21no—
444#407—471no—
445#407C2×D4711yescharacteristic
446C2×C22⋊C8—21no—
447C2×C22⋊C8C2×D4711yescharacteristic
448#405—471no—
449#405—471no—
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—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C4×D4711yescharacteristic
469C2×#41C4×D4711yescharacteristic
470C2×#41C22×D4711yescharacteristic
471C2×#41C22×D4711yescharacteristic
472C22×Q8C4×D4711yescharacteristic
473C22×D4—21no—
474C22×D4C4×D4711yescharacteristic
475C23×C4—21no—
476C23×C4C22×D4711yescharacteristic
477#131—22no—
478#131—22no—
479#131—41no—
480#131—41no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—471no—
484C2×M16—471no—
485C2×M16—471no—
486C2×M16—471no—
487C2×M16—471no—
488C2×M16—471no—
489C2×M16—1881no—
490C2×M16—1881no—
491C2×M16C22×D4711yescharacteristic
492C2×M16C22×D4711yescharacteristic
493C22×C8—21no—
494C22×C8—21no—
495C22×C8—471no—
496C22×C8—471no—
497C22×C8C22×D4711yescharacteristic
498C22×C8C22×D4711yescharacteristic
499#117—471no—
500#117—471no—
501#117—471no—
502#117—471no—
503#117—941no—
504#117—941no—
505C2×C4⋊C4—471no—
506C2×C4⋊C4—471no—
507C2×C22⋊C4—941no—
508C2×C22⋊C4—941no—
509C2×C42—471no—
510C2×C42—471no—
511C2×C42—941no—
512#108—1881no—
513#108—1881no—
514C4⋊C8—941no—
515C4⋊C8—941no—
516C4⋊C8—941no—
517C4⋊C8—941no—
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—21no—
541C22⋊C8—21no—
542C22⋊C8—21no—
543C22⋊C8—21no—
544C22⋊C8—941no—
545C22⋊C8—941no—
546C22⋊C8C22⋊D4711yescharacteristic
547C22⋊C8C22⋊D4711yescharacteristic
548C22⋊C8C22⋊D4711yescharacteristic
549C22⋊C8C22⋊D4711yescharacteristic
550#97—941no—
551#97—941no—
552#97—1881no—
553C4×C8—941no—
554C4×C8—941no—
555C4×C8—1881no—
556#95—941no—
557C24—21no—
558C24#1062535011yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#1062535212yes—
574#41#1062535212yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C2×C4×D4711yescharacteristic
579C2×Q8C2×C4×D4711yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C2×C4×D4711yescharacteristic
590C2×D4C2×C4×D4711yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—941no—
603C22×C4—941no—
604C22×C4—941no—
605C22×C4—941no—
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—42no—
617M16—42no—
618M16—941no—
619M16—941no—
620M16—941no—
621M16—941no—
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—42no—
633C2×C8—42no—
634C2×C8—471no—
635C2×C8—471no—
636C2×C8—471no—
637C2×C8—471no—
638C2×C8—941no—
639C2×C8—941no—
640C2×C8—941no—
641C2×C8—941no—
642C2×C8—941no—
643C2×C8—941no—
644C2×C8C2×C22⋊D4711yescharacteristic
645C2×C8C2×C22⋊D4711yescharacteristic
646C2×C8C2×C22⋊D4711yescharacteristic
647C2×C8C2×C22⋊D4711yescharacteristic
648C4⋊C4—471no—
649C4⋊C4—471no—
650C4⋊C4—471no—
651C4⋊C4—471no—
652C4⋊C4—941no—
653C4⋊C4—941no—
654C22⋊C4—941no—
655C22⋊C4—941no—
656C22⋊C4—941no—
657C22⋊C4—941no—
658C22⋊C4—1882no—
659C42—941no—
660C42—941no—
661C42—941no—
662C42—941no—
663C42—941no—
664C42—941no—
665C42—941no—
666C42—941no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23C4×C22⋊D4711yescharacteristic
677C23C4×C22⋊D4711yescharacteristic
678C23C2×#1062535011yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#1309398012yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#1309398012yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
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—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—942no—
715C2×C4—941no—
716C2×C4—941no—
717C2×C4—941no—
718C2×C4—941no—
719C2×C4—3761no—
720C2×C4—1881no—
721C2×C4—1881no—
722C2×C4—1881no—
723C2×C4—1881no—
724C2×C4—1882no—
725C2×C4—1881no—
726C2×C4C4×C22⋊D4711yescharacteristic
727C2×C4C4×C22⋊D4711yescharacteristic
728C2×C4C22×C4×D4711yescharacteristic
729C2×C4C22×C22⋊D4711yescharacteristic
730C2×C4C2×#1062535211yescharacteristic
731C2×C4C2×#1062535211yescharacteristic
732C2×C4#1309406911yescharacteristic
733C2×C4#1309406911yescharacteristic
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—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×C4×C22⋊D4711yescharacteristic
764C22#1568979911yescharacteristic
765C22#1568979911yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—41no—
770C4—3761no—
771C4—1882no—
772C4—1881no—
773C4—1881no—
774C4—1881no—
775C4—1881no—
776C4C2×#1309398011yescharacteristic
777C4#1568959611yescharacteristic
778C4#1568976711yescharacteristic
779C4#1568976711yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#2024623311yescharacteristic
787C2#2025228911yescharacteristic
788C2#2025229511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2880C2
socleC22×C47C2×C4×D4
prime radicalC22×#41×C47C22
cosocleC22×C4×C47C24
hypercenter#2880D47
hypocenterC47#22588
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
1. #20252042C2semidirect
3. #20244102C2semidirect
4. #20244095C2semidirect
5. #20244033C2semidirect
6. #20244033C2semidirect
7. #20243663C2semidirect
8. #20243663C2semidirect
9. #20243485C2semidirect
10. #20243428C2semidirect
12. #20243230C2semidirect
13. #20243223C2semidirect
14. #20243174C2semidirect
22. C2×#13093959C22semidirect
23. C2×#13093959C22semidirect
24. #15689149C22semidirect
25. #15689149C22semidirect
30. #15689132C4semidirect
31. #15689132C4semidirect
32. #15689128C4semidirect
33. #15689128C4semidirect
34. #15689124C4semidirect
35. #15689124C4semidirect
36. #15689124C4semidirect
37. #15689124C4semidirect
43. #15689078C22semidirect
44. #15689078C22semidirect
45. C2×#13093934C22semidirect
46. C2×C8×Dic47C22semidirect
48. #15688887C22semidirect
49. #15688887C22semidirect
50. #15688884C22semidirect
51. #15688884C22semidirect
52. #15688884C22semidirect
53. #15688884C22semidirect
54. #15688877C22semidirect
55. #15688877C22semidirect
461. C47#22588semidirect

Maximal subgroups

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

subgroupindex
#202520422
#202519072
#202441022
#202440952
#202440332
#202436632
#202434852
#202434282
#202433322
#202432302
#202432232
#202431742
C47×#28802
#2258847