Finite Group Databasebeta

← #26233320

Subgroups — #26233320

Order 12032.

990 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689181C211yesmaximal, characteristic, complemented
2C2×#15689090C211yesmaximal, characteristic
3#20245879C211yesmaximal, characteristic
4#20244004C211yesmaximal, characteristic, complemented
5#20243998C211yesmaximal, characteristic, complemented
6#20243998C211yesmaximal, characteristic, complemented
7#20243997C211yesmaximal, characteristic, complemented
8#20243570C211yesmaximal, characteristic, complemented
9#20243565C211yesmaximal, characteristic, complemented
10#20243457C211yesmaximal, characteristic, complemented
11#20243366C211yesmaximal, characteristic, complemented
12#20243174C211yesmaximal, characteristic, complemented
13#20243167C211yesmaximal, characteristic, complemented
14#20243152C211yesmaximal, characteristic, complemented
15C47×#1780C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19C22×C4×Dic47C2211yescharacteristic
20#15689181—24no—
21C2×Dic47⋊C8C2211yescharacteristic
22C2×Dic47⋊C8C2211yescharacteristic
23C2×Dic47⋊C8C2211yescharacteristic
24C2×Dic47⋊C8C2211yescharacteristic
25#15689090—24no—
26C2×C22⋊(C47⋊C8)C2211yescharacteristic
27C2×C22⋊(C47⋊C8)C2211yescharacteristic
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×#13093934C2211yescharacteristic
31C2×#13093934C2211yescharacteristic
32C2×#13093934C2211yescharacteristic
33C2×C8×Dic47C2211yescharacteristic
34#15689030C411yescharacteristic
35#15689030C411yescharacteristic
36#15689026C411yescharacteristic
37#15689026C411yescharacteristic
38#15689003C411yescharacteristic
39#15689003C411yescharacteristic
40#15689003C411yescharacteristic
41#15689003C411yescharacteristic
42C4×C22⋊Dic47C2211yescharacteristic
43C4×C22⋊Dic47C2211yescharacteristic
44C4×C22⋊Dic47C2211yescharacteristic
45C4×C22⋊Dic47C2211yescharacteristic
46#15688877C2211yescharacteristic
47#15688877C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54C22×#41×C47C2211yescharacteristic
55C2×C22⋊C8×C47C2211yescharacteristic
56C2×C22⋊C8×C47C2211yescharacteristic
57C2×C22⋊C8×C47C2211yescharacteristic
58C2×C22⋊C8×C47C2211yescharacteristic
59C2×C22⋊C8×C47C2211yescharacteristic
60C2×C22⋊C8×C47C2211yescharacteristic
61C23×Dic47C2×C411yescharacteristic
62C23×Dic47C2×C411yescharacteristic
63C2×#10625329—22no—
64C2×#10625329—22no—
65C2×#10625329—41no—
66C22×C47⋊C8—22no—
67C22×C47⋊C8—22no—
68C22×C47⋊C8—41no—
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73#13093983—22no—
74#13093983—22no—
75C2×C4⋊Dic47C2×C411yescharacteristic
76C2×C4⋊Dic47C2×C411yescharacteristic
77C2×C22⋊Dic47C2×C411yescharacteristic
78C2×C22⋊Dic47C2×C411yescharacteristic
79C2×C22⋊Dic47C2×C411yescharacteristic
80C2×C22⋊Dic47C2×C411yescharacteristic
81C2×C22⋊Dic47C2×C411yescharacteristic
82C2×C22⋊Dic47C2×C411yescharacteristic
83C2×C22⋊Dic47C2×C411yescharacteristic
84C2×C22⋊Dic47C2×C411yescharacteristic
85C2×C22⋊Dic47C2×C411yescharacteristic
86C2×C22⋊Dic47C2×C411yescharacteristic
87C2×C4×Dic47—41no—
88C2×C4×Dic47—41no—
89C2×C4×Dic47C2×C411yescharacteristic
90C2×C4×Dic47C2×C411yescharacteristic
91C2×C4×Dic47C2311yescharacteristic
92C2×C4×Dic47C2311yescharacteristic
93C2×C4×Dic47C2311yescharacteristic
94C2×C4×Dic47C2311yescharacteristic
95Dic47⋊C8—22no—
96Dic47⋊C8—22no—
97Dic47⋊C8—41no—
98Dic47⋊C8—41no—
99C22⋊(C47⋊C8)—22no—
100C22⋊(C47⋊C8)—22no—
101C22⋊(C47⋊C8)—22no—
102C22⋊(C47⋊C8)D414yes—
103#13093934—22no—
104#13093934—41no—
105#13093934—41no—
106C8×Dic47—22no—
107C47⋊#95C2×C411yescharacteristic
108C47⋊#95C2×C411yescharacteristic
109C47⋊#95C2×C411yescharacteristic
110C47⋊#95C2×C411yescharacteristic
111C47⋊#95C2×C411yescharacteristic
112C47⋊#95C2×C411yescharacteristic
113C47⋊#95C2×C411yescharacteristic
114C47⋊#95C2×C411yescharacteristic
115C2×#41×C47—22no—
116C2×#41×C47—22no—
117C2×#41×C47—22no—
118C2×#41×C47—22no—
119C2×#41×C47—41no—
120C2×#41×C47—41no—
121C22×Q8×C47C2×C411yescharacteristic
122C22×D4×C47C2×C411yescharacteristic
123C22×D4×C47C2×C411yescharacteristic
124C22×D4×C47C2×C411yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C22×C8×C47C2311yescharacteristic
129C22×C8×C47C2311yescharacteristic
130C22×C8×C47C2311yescharacteristic
131C22×C8×C47C2311yescharacteristic
132C22⋊C8×C47—22no—
133C22⋊C8×C47—22no—
134C22⋊C8×C47—22no—
135C22⋊C8×C47—22no—
136C22⋊C8×C47—41no—
137C22⋊C8×C47—41no—
138C24×C47C22×C411yescharacteristic
139C24×C47C22×C411yescharacteristic
140C24×C47C22×C411yescharacteristic
141#41×C47—44no—
142#41×C47—44no—
143#41×C47—44no—
144#41×C47—44no—
145C2×Q8×C47—22no—
146C2×Q8×C47—22no—
147C2×Q8×C47—41no—
148C2×D4×C47—22no—
149C2×D4×C47—22no—
150C2×D4×C47—22no—
151C2×D4×C47—22no—
152C2×D4×C47—22no—
153C2×D4×C47—22no—
154C2×D4×C47—41no—
155C2×D4×C47—41no—
156C2×D4×C47—41no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—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×C47—21no—
171C22×C4×C47C22×C411yescharacteristic
172C22×C4×C47C22×C411yescharacteristic
173C22×C4×C47C22×C411yescharacteristic
174C22×C4×C47C2×D412yes—
175C22×C4×C47#4112yes—
176C22×C4×C47#4112yes—
177C22×C4×C47#4112yes—
178C22×C4×C47C2411yescharacteristic
179C22×Dic47—22no—
180C22×Dic47—41no—
181C22×Dic47—41no—
182C22×Dic47—41no—
183C22×Dic47—41no—
184C22×Dic47—41no—
185C22×Dic47C22×C411yescharacteristic
186C22×Dic47C22×C411yescharacteristic
187C22×Dic47C22×C411yescharacteristic
188C22×Dic47C22×C411yescharacteristic
189C22×Dic47C22×C411yescharacteristic
190C22×Dic47C22×C411yescharacteristic
191C22×Dic47C22×C411yescharacteristic
192C22×Dic47C22×C411yescharacteristic
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C22⋊Dic47—22no—
206C22⋊Dic47—22no—
207C22⋊Dic47—22no—
208C22⋊Dic47—22no—
209C22⋊Dic47—41no—
210C22⋊Dic47—41no—
211C22⋊Dic47—41no—
212C22⋊Dic47—41no—
213C22⋊Dic47—41no—
214C22⋊Dic47—41no—
215C4⋊Dic47—22no—
216C4⋊Dic47—22no—
217C4×Dic47—21no—
218C4×Dic47—21no—
219C4×Dic47—21no—
220C4×Dic47—21no—
221C4×Dic47—21no—
222C4×Dic47—21no—
223C4×Dic47—21no—
224C4×Dic47—21no—
225C4×Dic47—41no—
226C4×Dic47—41no—
227#10625329—44no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C2×C47⋊C8—21no—
238C2×C47⋊C8—44no—
239C2×C47⋊C8C2×D412yes—
240C2×C47⋊C8C2×D412yes—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—21no—
260C23×C47#11712yes—
261C23×C47C4×D412yes—
262C23×C47C23×C411yescharacteristic
263Q8×C47—44no—
264D4×C47—44no—
265D4×C47—44no—
266D4×C47—44no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47#11712yes—
287C2×C4×C47C4×D412yes—
288C2×C4×C47C22×D411yescharacteristic
289C2×C4×C47C2×#4111yescharacteristic
290C2×C4×C47C2×#4111yescharacteristic
291C2×C4×C47C2×#4111yescharacteristic
292C2×C4×C47H(5,𝔽2)11yescharacteristic
293C2×C4×C47H(5,𝔽2)11yescharacteristic
294C2×Dic47—21no—
295C2×Dic47—21no—
296C2×Dic47—21no—
297C2×Dic47—21no—
298C2×Dic47—21no—
299C2×Dic47—21no—
300C2×Dic47—21no—
301C2×Dic47—21no—
302C2×Dic47—21no—
303C2×Dic47—21no—
304C2×Dic47—21no—
305C2×Dic47—21no—
306C2×Dic47—21no—
307C2×Dic47—21no—
308C2×Dic47—21no—
309C2×Dic47—21no—
310C2×Dic47—21no—
311C2×Dic47—21no—
312C2×Dic47—21no—
313C2×Dic47—21no—
314C2×Dic47—21no—
315C2×Dic47—21no—
316C2×Dic47—21no—
317C2×Dic47—44no—
318C2×Dic47—44no—
319C2×Dic47#13112yes—
320C8×C47—41no—
321C8×C47—41no—
322C8×C47—41no—
323C8×C47—41no—
324C47⋊C8—22no—
325C47⋊C8—22no—
326C47⋊C8—41no—
327C47⋊C8—41no—
328#22561—471nomaximal, Sylow
329C22×C47—22no—
330C22×C47—22no—
331C22×C47—22no—
332C22×C47—22no—
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—41no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47—41no—
350C22×C47C2×#11711yescharacteristic
351C22×C47C2×C4×D411yescharacteristic
352C22×C47#51811yescharacteristic
353C22×C47C2×#13111yescharacteristic
354C22×C47#56811yescharacteristic
355C22×C47#56811yescharacteristic
356C22×C47#56811yescharacteristic
357C4×C47—22no—
358C4×C47—22no—
359C4×C47—41no—
360C4×C47#54611yescharacteristic
361C4×C47#54611yescharacteristic
362C4×C47#55111yescharacteristic
363C4×C47#55111yescharacteristic
364Dic47—22no—
365Dic47—41no—
366Dic47—41no—
367Dic47—41no—
368Dic47—41no—
369Dic47—41no—
370Dic47—41no—
371Dic47—41no—
372C2×#433—471no—
373C2×#408—471no—
374#2297—471no—
375#1924—471no—
376#1924—471no—
377#1924—471no—
378#1923—471no—
379#1851—471no—
380#1850—471no—
381#1818—471no—
382#1797—471no—
383#1780D4711yescharacteristic
384#1753—471no—
385#1752—471no—
386#1749—471no—
387C2×C47—42no—
388C2×C47—42no—
389C2×C47—81no—
390C2×C47#234211yescharacteristic
391C2×C47#292311yescharacteristic
392C2×C47#292511yescharacteristic
393C2×C47#293211yescharacteristic
394C2×C47#293511yescharacteristic
395C2×C47#297611yescharacteristic
396C2×C47#297811yescharacteristic
397C22×#41C2×D4711yescharacteristic
398C22×M16—471no—
399C23×C8—471no—
400C2×#117—471no—
401C22×C42—471no—
402#433—944no—
403C2×C4⋊C8—471no—
404C2×C4⋊C8—471no—
405C2×C4⋊C8—471no—
406C2×C4⋊C8—471no—
407#408—944no—
408C2×C22⋊C8—471no—
409C2×C22⋊C8—471no—
410C2×C22⋊C8—471no—
411C2×C22⋊C8—471no—
412C2×C22⋊C8C2×D4711yescharacteristic
413C2×C22⋊C8C2×D4711yescharacteristic
414C2×C22⋊C8C2×D4711yescharacteristic
415C2×C22⋊C8C2×D4711yescharacteristic
416C2×C22⋊C8C2×D4711yescharacteristic
417C2×C22⋊C8C2×D4711yescharacteristic
418C2×#97—471no—
419C2×#97—471no—
420C2×#97—471no—
421C2×C4×C8—471no—
422#391—471no—
423#391—471no—
424#390—471no—
425#390—471no—
426#386—471no—
427#386—471no—
428#386—471no—
429#386—471no—
430C4×C22⋊C4—471no—
431C4×C22⋊C4—471no—
432C4×C22⋊C4—471no—
433C4×C22⋊C4—471no—
434#336—471no—
435#336—471no—
436#336—471no—
437#336—471no—
438#336—471no—
439#336—471no—
440#336—471no—
441#336—471no—
442C47#2256111yescharacteristic, complemented, Sylow
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—41no—
448C2×#41—41no—
449C22×Q8C4×D4711yescharacteristic
450C22×D4C4×D4711yescharacteristic
451C22×D4C4×D4711yescharacteristic
452C22×D4C4×D4711yescharacteristic
453C23×C4—471no—
454C23×C4—471no—
455C23×C4C22×D4711yescharacteristic
456C23×C4C22×D4711yescharacteristic
457C23×C4C22×D4711yescharacteristic
458C2×M16—942no—
459C2×M16—942no—
460C2×M16—1881no—
461C22×C8—471no—
462C22×C8—471no—
463C22×C8—471no—
464C22×C8—471no—
465C22×C8—942no—
466C22×C8—942no—
467C22×C8—1881no—
468C22×C8C22×D4711yescharacteristic
469C22×C8C22×D4711yescharacteristic
470C22×C8C22×D4711yescharacteristic
471C22×C8C22×D4711yescharacteristic
472#117—942no—
473#117—942no—
474C2×C4⋊C4—471no—
475C2×C4⋊C4—471no—
476C2×C22⋊C4—471no—
477C2×C22⋊C4—471no—
478C2×C22⋊C4—471no—
479C2×C22⋊C4—471no—
480C2×C22⋊C4—471no—
481C2×C22⋊C4—471no—
482C2×C22⋊C4—471no—
483C2×C22⋊C4—471no—
484C2×C22⋊C4—471no—
485C2×C22⋊C4—471no—
486C2×C42—471no—
487C2×C42—471no—
488C2×C42—471no—
489C2×C42—471no—
490C2×C42—471no—
491C2×C42—471no—
492C2×C42—1881no—
493C2×C42—1881no—
494C4⋊C8—942no—
495C4⋊C8—942no—
496C4⋊C8—1881no—
497C4⋊C8—1881no—
498C22⋊C8—22no—
499C22⋊C8—22no—
500C22⋊C8—22no—
501C22⋊C8—22no—
502C22⋊C8—41no—
503C22⋊C8—41no—
504C22⋊C8—474no—
505C22⋊C8—942no—
506C22⋊C8—942no—
507C22⋊C8—942no—
508#97—942no—
509#97—1881no—
510#97—1881no—
511C4×C8—942no—
512#95—471no—
513#95—471no—
514#95—471no—
515#95—471no—
516#95—471no—
517#95—471no—
518#95—471no—
519#95—471no—
520C24C2×C4×D4711yescharacteristic
521C24C2×C4×D4711yescharacteristic
522C24C2×C4×D4711yescharacteristic
523#41—44no—
524#41—44no—
525#41—44no—
526#41—44no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—41no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—41no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—471no—
554C22×C4—471no—
555C22×C4—471no—
556C22×C4—471no—
557C22×C4—471no—
558C22×C4—471no—
559C22×C4—471no—
560C22×C4—471no—
561C22×C4—942no—
562C22×C4—1881no—
563C22×C4—1881no—
564C22×C4—1881no—
565C22×C4—1881no—
566C22×C4—1881no—
567C22×C4C2×C4×D4711yescharacteristic
568C22×C4C2×C4×D4711yescharacteristic
569C22×C4C2×C4×D4711yescharacteristic
570C22×C4D4×D4712yes—
571C22×C4#1062535212yes—
572C22×C4#1062535212yes—
573C22×C4#1062535212yes—
574C22×C4C23×D4711yescharacteristic
575M16—1884no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—472no—
589C2×C8—472no—
590C2×C8—941no—
591C2×C8—941no—
592C2×C8—941no—
593C2×C8—941no—
594C2×C8—941no—
595C2×C8—941no—
596C2×C8—941no—
597C2×C8—941no—
598C2×C8—941no—
599C2×C8—941no—
600C2×C8—1884no—
601C4⋊C4—942no—
602C4⋊C4—942no—
603C22⋊C4—942no—
604C22⋊C4—942no—
605C22⋊C4—942no—
606C22⋊C4—942no—
607C22⋊C4—1881no—
608C22⋊C4—1881no—
609C22⋊C4—1881no—
610C22⋊C4—1881no—
611C22⋊C4—1881no—
612C22⋊C4—1881no—
613C42—941no—
614C42—941no—
615C42—941no—
616C42—941no—
617C42—941no—
618C42—941no—
619C42—941no—
620C42—941no—
621C42—1881no—
622C42—1881no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23#1309398012yes—
643C23(C22⋊D47)⋊C412yes—
644C23C22×C4×D4711yescharacteristic
645Q8—44no—
646D4—44no—
647D4—44no—
648D4—44no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—472no—
669C2×C4—941no—
670C2×C4—941no—
671C2×C4—941no—
672C2×C4—941no—
673C2×C4—941no—
674C2×C4—941no—
675C2×C4—941no—
676C2×C4—941no—
677C2×C4—941no—
678C2×C4—941no—
679C2×C4—941no—
680C2×C4—941no—
681C2×C4—941no—
682C2×C4—941no—
683C2×C4—941no—
684C2×C4—941no—
685C2×C4—941no—
686C2×C4—941no—
687C2×C4—941no—
688C2×C4—941no—
689C2×C4—941no—
690C2×C4—941no—
691C2×C4—941no—
692C2×C4—1884no—
693C2×C4—1884no—
694C2×C4#1309398012yes—
695C2×C4(C22⋊D47)⋊C412yes—
696C2×C4C2×D4×D4711yescharacteristic
697C2×C4C2×#1062535211yescharacteristic
698C2×C4C2×#1062535211yescharacteristic
699C2×C4C2×#1062535211yescharacteristic
700C2×C4#1309406911yescharacteristic
701C2×C4#1309406911yescharacteristic
702C8—41no—
703C8—41no—
704C8—41no—
705C8—41no—
706C8—942no—
707C8—942no—
708C8—1881no—
709C8—1881no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22C2×#1309398011yescharacteristic
732C22C2×(C22⋊D47)⋊C411yescharacteristic
733C22#1568959611yescharacteristic
734C22#131×D4711yescharacteristic
735C22#1568988811yescharacteristic
736C22#1568988811yescharacteristic
737C22#1568988811yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—942no—
742C4—1881no—
743C4—1881no—
744C4—1881no—
745C4—1881no—
746C4—1881no—
747C4—1881no—
748C4—1881no—
749C4#1568976011yescharacteristic
750C4#1568976011yescharacteristic
751C4#1568980411yescharacteristic
752C4#1568980411yescharacteristic
753C2—42no—
754C2—42no—
755C2—81no—
756C2#2024623911yescharacteristic
757C2#2025203511yescharacteristic
758C2#2025205011yescharacteristic
759C2#2025210311yescharacteristic
760C2#2025212811yescharacteristic
761C2#2025243111yescharacteristic
762C2#2025244611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1780C2
prime radicalC22×#41×C47C22
cosocleC22×C4×C47C24
hypercenter#1780D47
hypocenterC47#22561
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1780

Complements

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

NH ≅ G/Ntype
1. C2×#15689181C2semidirect
4. #20244004C2semidirect
5. #20243998C2semidirect
6. #20243998C2semidirect
7. #20243997C2semidirect
8. #20243570C2semidirect
9. #20243565C2semidirect
10. #20243457C2semidirect
11. #20243366C2semidirect
12. #20243174C2semidirect
13. #20243167C2semidirect
14. #20243152C2semidirect
442. C47#22561semidirect

Maximal subgroups

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

subgroupindex
C2×#156891812
C2×#156890902
#202458792
#202440042
#202439982
#202439972
#202435702
#202435652
#202434572
#202433662
#202431742
#202431672
#202431522
C47×#17802
#2256147