Finite Group Databasebeta

← #26232598

Subgroups — #26232598

Order 12032.

1258 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×#15689819C211yesmaximal, characteristic
2D4×C4⋊Dic47C211yesmaximal, characteristic, complemented
3#20244357C211yesmaximal, characteristic, complemented
4#20244343C211yesmaximal, characteristic, complemented
5#20243826C211yesmaximal, characteristic, complemented
6#20243816C211yesmaximal, characteristic, complemented
7#20243703C211yesmaximal, characteristic, complemented
8#20243703C211yesmaximal, characteristic, complemented
9#20243484C211yesmaximal, characteristic, complemented
10#20243479C211yesmaximal, characteristic, complemented
11#20243389C211yesmaximal, characteristic, complemented
12#20243214C211yesmaximal, characteristic, complemented
13#20243108C211yesmaximal, characteristic, complemented
14C2×#15688886C211yesmaximal, characteristic, complemented
15C2×C47×#435C211yesmaximal, characteristic, complemented
16#15689819—24no—
17#15689819C418yescomplemented
18C2×#13094019—21no—
19C2×#13094016C2211yescharacteristic
20C2×#13094006—21no—
21C2×#13093998C2211yescharacteristic
22C2×#13093998C2211yescharacteristic
23C2×#13093996—21no—
24C2×C4×D188C2211yescharacteristic
25C2×D4×Dic47—21no—
26C2×(C22⋊D47)⋊C4—21no—
27C2×#13093983C2211yescharacteristic
28C22×C4⋊Dic47C2211yescharacteristic
29C22×C4⋊Dic47C2211yescharacteristic
30C22×C4⋊Dic47C2211yescharacteristic
31C2×#13093946C2211yescharacteristic
32C2×#13093946C2211yescharacteristic
33C2×#13093946C2211yescharacteristic
34C2×#13093946C2211yescharacteristic
35#15689022—21no—
36#15688998—21no—
37#15688998—21no—
38#15688993C2211yescharacteristic
39#15688983C2211yescharacteristic
40#15688983C2211yescharacteristic
41C4×C4⋊Dic47C2211yescharacteristic
42#15688886C2211yescharacteristic
43#15688886C2211yescharacteristic
44#15688886C2211yescharacteristic
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688886C2211yescharacteristic
51#15688886C2211yescharacteristic
52#15688886C2211yescharacteristic
53#15688886C2211yescharacteristic
54C22×M16×C47C2211yescharacteristic
55C23×C8×C47C2211yescharacteristic
56C2×C4×D4×C47C2211yescharacteristic
57C47×#435—24no—
58C2×C4⋊C8×C47C2211yescharacteristic
59C2×C22⋊C8×C47C2211yescharacteristic
60C2×C22⋊C8×C47C2211yescharacteristic
61C2×#97×C47C2211yescharacteristic
62C22×D188C2311yescharacteristic
63C22×C22⋊D47—21no—
64C22×C22⋊D47—21no—
65C23×Dic47—21no—
66C23×Dic47—21no—
67C23×Dic47—21no—
68C22×C4×D47—21no—
69#13094019—28no—
70#13094016—22no—
71#13094016C2×C414yescomplemented
72#13094006—28no—
73#13093998—22no—
74#13093998—22no—
75#13093998C2×C414yescomplemented
76#13093998C2×C414yescomplemented
77#13093996—28no—
78C4×D188—22no—
79C4×D188C2×C414yescomplemented
80D4×Dic47—44no—
81(C22⋊D47)⋊C4—28no—
82#13093983—22no—
83#13093983C2×C414yescomplemented
84C2×C4⋊Dic47—22no—
85C2×C4⋊Dic47—21no—
86C2×C4⋊Dic47—22no—
87C2×C4⋊Dic47—22no—
88C2×C4⋊Dic47—21no—
89C2×C4⋊Dic47—21no—
90C2×C4⋊Dic47—21no—
91C2×C4⋊Dic47—21no—
92C2×C4⋊Dic47—41no—
93C2×C4⋊Dic47—41no—
94C2×C4⋊Dic47C2×C414yescomplemented
95C2×C4⋊Dic47C2311yescharacteristic
96C2×C4⋊Dic47C2311yescharacteristic
97C2×C4⋊Dic47C2311yescharacteristic
98C2×C4⋊Dic47C2311yescharacteristic
99C2×C4⋊Dic47C2311yescharacteristic
100C2×C4⋊Dic47C2311yescharacteristic
101C2×C4⋊Dic47C2311yescharacteristic
102C2×Dic47⋊C4—21no—
103C2×Dic47⋊C4—21no—
104C2×C22⋊Dic47—21no—
105C2×C22⋊Dic47—21no—
106C2×C22⋊Dic47—21no—
107C2×(C2×D47)⋊C4—21no—
108C2×(C2×D47)⋊C4—21no—
109C2×(C2×D47)⋊C4—21no—
110C2×C4×Dic47—21no—
111C2×C4×Dic47—21no—
112#13093946—22no—
113#13093946—22no—
114#13093946—41no—
115#13093946—41no—
116C47⋊#95—21no—
117C47⋊#95—21no—
118C47⋊#95—21no—
119C22×D4×C47D411yescharacteristic
120C23×C4×C47C2311yescharacteristic
121C23×C4×C47C2311yescharacteristic
122C2×M16×C47—22no—
123C2×M16×C47—22no—
124C2×M16×C47—41no—
125C22×C8×C47—22no—
126C22×C8×C47—22no—
127C22×C8×C47—41no—
128C22×C8×C47C2311yescharacteristic
129C22×C8×C47C2311yescharacteristic
130C22×C8×C47C2311yescharacteristic
131C22×C8×C47C2311yescharacteristic
132C4×D4×C47C2×C414yes—
133C4×D4×C47D414yes—
134C2×C4⋊C4×C47D411yescharacteristic
135C2×C22⋊C4×C47D411yescharacteristic
136C2×C22⋊C4×C47D411yescharacteristic
137C2×C42×C47C2311yescharacteristic
138C4⋊C8×C47—22no—
139C22⋊C8×C47—22no—
140C22⋊C8×C47—22no—
141#97×C47—22no—
142C24×C47C2×D411yescharacteristic
143C24×C47C2×D411yescharacteristic
144C23×D47—21no—
145C2×D4×C47—22no—
146C2×D4×C47—22no—
147C2×D4×C47C22⋊C414yes—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47C22×C412yes—
157C22×C4×C47C22×C412yes—
158C22×C4×C47C2×D411yescharacteristic
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2×D411yescharacteristic
161C22×C4×C47C2×D411yescharacteristic
162C22×C4×C47C2×D412yes—
163C22×C4×C47C2×D412yes—
164C22×C4×C47C2411yescharacteristic
165C2×C22⋊D47—24no—
166C2×C22⋊D47—24no—
167C2×C22⋊D47—42no—
168C2×C22⋊D47—42no—
169C2×C22⋊D47—81no—
170C2×C22⋊D47—81no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—24no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—21no—
179C22×Dic47—42no—
180C22×Dic47—42no—
181C22×Dic47—42no—
182C22×Dic47—42no—
183C22×Dic47—81no—
184C22×Dic47—81no—
185C22×Dic47—81no—
186C22×Dic47—81no—
187C2×D188—21no—
188C2×D188—21no—
189C2×D188—21no—
190C2×D188—21no—
191C2×D188—21no—
192C2×D188C22×C412yes—
193C2×C4×D47—24no—
194C2×C4×D47—81no—
195C2×C4×D47—81no—
196M16×C47—44no—
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—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—44no—
209C2×C8×C47#4112yes—
210C4⋊C4×C47C22⋊C414yes—
211C22⋊C4×C47C22⋊C414yes—
212C22⋊C4×C47C22⋊C414yes—
213C42×C47C22×C412yes—
214C42×C47C2×D412yes—
215C22⋊Dic47—24no—
216C22⋊Dic47—42no—
217C22⋊Dic47—42no—
218(C2×D47)⋊C4—24no—
219(C2×D47)⋊C4—24no—
220(C2×D47)⋊C4—24no—
221C4⋊Dic47—24no—
222C4⋊Dic47—21no—
223C4⋊Dic47—21no—
224C4⋊Dic47—21no—
225C4⋊Dic47—21no—
226C4⋊Dic47—21no—
227C4⋊Dic47—21no—
228C4⋊Dic47—21no—
229C4⋊Dic47—21no—
230C4⋊Dic47—21no—
231C4⋊Dic47—21no—
232C4⋊Dic47—42no—
233C4⋊Dic47—42no—
234C4⋊Dic47—42no—
235C4⋊Dic47—81no—
236C4⋊Dic47C22×C412yes—
237C4⋊Dic47C22×C412yes—
238C4⋊Dic47C22×C412yes—
239C4⋊Dic47#4112yes—
240Dic47⋊C4—24no—
241Dic47⋊C4—24no—
242C4×Dic47—24no—
243C4×Dic47—42no—
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×C47C2×C22⋊C412yes—
255C23×C47C2×C22⋊C412yes—
256C23×C47AGL(1,ℤ/8)12yes—
257C23×C47#13712yes—
258C23×C47C22×D411yescharacteristic
259C22×D47—22no—
260C22×D47—41no—
261C22×D47—41no—
262C22×D47—41no—
263C22×D47—41no—
264C22×D47—41no—
265C22×D47—41no—
266D4×C47—28no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47C2×C22⋊C412yes—
284C2×C4×C47C2×C22⋊C412yes—
285C2×C4×C47C2×C22⋊C412yes—
286C2×C4×C47C2×C22⋊C412yes—
287C2×C4×C47C23×C411yescharacteristic
288C2×C4×C47C22×D411yescharacteristic
289C2×C4×C47C2×#4111yescharacteristic
290C2×C4×C47C2×#4111yescharacteristic
291C2×C4×C47H(5,𝔽2)11yescharacteristic
292C2×C4×C472−1+411yescharacteristic
293C22⋊D47—48no—
294C22⋊D47—84no—
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—22no—
299C2×Dic47—41no—
300C2×Dic47—41no—
301C2×Dic47—41no—
302C2×Dic47—41no—
303C2×Dic47—41no—
304C2×Dic47—41no—
305C2×Dic47—41no—
306C2×Dic47—41no—
307C2×Dic47—41no—
308C2×Dic47—41no—
309C2×Dic47—41no—
310C2×Dic47—41no—
311C2×Dic47—41no—
312C2×Dic47—41no—
313C2×Dic47—41no—
314C2×Dic47—41no—
315C2×Dic47—41no—
316C2×Dic47—84no—
317C2×Dic47—84no—
318C2×Dic47—84no—
319D188—22no—
320D188—22no—
321D188—41no—
322D188—41no—
323C4×D47—84no—
324C8×C47—22no—
325C8×C47—41no—
326C8×C47—41no—
327C8×C47—41no—
328#22493—471nomaximal, Sylow
329C22×C47—22no—
330C22×C47—22no—
331C22×C47—22no—
332C22×C47—22no—
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—22no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47#41714yes—
343C22×C47C22×C22⋊C411yescharacteristic
344C22×C47#54611yescharacteristic
345C22×C47#54711yescharacteristic
346C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C47C2×#13711yescharacteristic
348C22×C47#57611yescharacteristic
349C22×C47#57711yescharacteristic
350C2×D47—42no—
351C2×D47—42no—
352C2×D47—42no—
353C2×D47—81no—
354C2×D47—81no—
355C2×D47—81no—
356C2×D47—81no—
357C4×C47—22no—
358C4×C47—22no—
359C4×C47—22no—
360C4×C47—22no—
361C4×C47C4×#4111yescharacteristic
362C4×C47#52011yescharacteristic
363C4×C47#54611yescharacteristic
364C4×C47#54711yescharacteristic
365Dic47—42no—
366Dic47—42no—
367Dic47—42no—
368Dic47—42no—
369Dic47—81no—
370Dic47—81no—
371Dic47—81no—
372C2×#553—471no—
373C2×#435D4711yescharacteristic, complemented
374D4×C4⋊C4—471no—
375#1992—471no—
376#1989—471no—
377#1895—471no—
378#1893—471no—
379#1874—471no—
380#1874—471no—
381#1825—471no—
382#1824—471no—
383#1802—471no—
384#1762—471no—
385#1736—471no—
386C2×#340—471no—
387C2×C47—24no—
388C2×C47—42no—
389C2×C47#233911yescharacteristic
390C2×C47C2×#41711yescharacteristic
391C2×C47#289711yescharacteristic
392C2×C47#331811yescharacteristic
393C2×C47#332011yescharacteristic
394C2×C47#334511yescharacteristic
395C2×C47#334611yescharacteristic
396D47—82no—
397C22×M16C2×D4711yescharacteristic
398C23×C8C2×D4711yescharacteristic
399#553—478no—
400#553—944no—
401C2×#126—941no—
402C2×#125—471no—
403C2×#123—941no—
404C2×#121—471no—
405C2×#121—471no—
406C2×#121—941no—
407C2×C4×D4—471no—
408C2×C4×D4—941no—
409C2×C4×D4—941no—
410C2×C4×D4C2×D4711yescharacteristic
411C2×#117—471no—
412C22×C4⋊C4—471no—
413C22×C4⋊C4—471no—
414C22×C4⋊C4—471no—
415#435—24no—
416C2×C4⋊C8C2×D4711yescharacteristic
417C2×#102—471no—
418C2×#102—471no—
419C2×#102—471no—
420C2×#102—471no—
421C2×C22⋊C8C2×D4711yescharacteristic
422C2×C22⋊C8C2×D4711yescharacteristic
423C2×#97C2×D4711yescharacteristic
424#389—941no—
425#385—941no—
426#385—941no—
427#384—471no—
428#380—471no—
429#380—471no—
430C4×C4⋊C4—471no—
431#340—471no—
432#340—471no—
433#340—471no—
434#340—471no—
435#340—471no—
436#340—471no—
437#340—471no—
438#340—471no—
439#340—471no—
440#340—471no—
441#340—471no—
442#340—471no—
443C47#2249311yescharacteristic, complemented, Sylow
444C22×D4—471no—
445C22×D4—941no—
446C22×D4—941no—
447C22×D4D18811yescharacteristic
448C23×C4—941no—
449C23×C4—941no—
450C23×C4—941no—
451C23×C4—941no—
452C23×C4C22×D4711yescharacteristic
453C23×C4C22×D4711yescharacteristic
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—41no—
457C22×C8—22no—
458C22×C8—22no—
459C22×C8—41no—
460C22×C8C22×D4711yescharacteristic
461C22×C8C22×D4711yescharacteristic
462C22×C8C22×D4711yescharacteristic
463C22×C8C22×D4711yescharacteristic
464#126—948no—
465#125—474no—
466#125—942no—
467#123—948no—
468#121—474no—
469#121—474no—
470#121—948no—
471#121—942no—
472#121—942no—
473C4×D4—474no—
474C4×D4—948no—
475C4×D4—942no—
476C4×D4—1884no—
477C4×D4C4×D4714yes—
478C4×D4C22⋊D4714yes—
479#117—474no—
480#117—942no—
481C2×C4⋊C4—474no—
482C2×C4⋊C4—471no—
483C2×C4⋊C4—471no—
484C2×C4⋊C4—471no—
485C2×C4⋊C4—471no—
486C2×C4⋊C4—471no—
487C2×C4⋊C4—471no—
488C2×C4⋊C4—471no—
489C2×C4⋊C4—942no—
490C2×C4⋊C4—942no—
491C2×C4⋊C4—941no—
492C2×C4⋊C4—941no—
493C2×C4⋊C4—941no—
494C2×C4⋊C4—942no—
495C2×C4⋊C4—941no—
496C2×C4⋊C4—941no—
497C2×C4⋊C4—941no—
498C2×C4⋊C4—941no—
499C2×C4⋊C4—1881no—
500C2×C4⋊C4—1881no—
501C2×C4⋊C4D18811yescharacteristic
502C2×C22⋊C4—941no—
503C2×C22⋊C4—941no—
504C2×C22⋊C4—941no—
505C2×C22⋊C4—941no—
506C2×C22⋊C4—941no—
507C2×C22⋊C4—941no—
508C2×C22⋊C4D18811yescharacteristic
509C2×C22⋊C4D18811yescharacteristic
510C2×C42—941no—
511C2×C42—941no—
512C2×C42C22×D4711yescharacteristic
513C4⋊C8—22no—
514#102—942no—
515#102—942no—
516#102—1881no—
517#102—1881no—
518C22⋊C8—22no—
519C22⋊C8—22no—
520#97—22no—
521#95—941no—
522#95—941no—
523#95—941no—
524C24—941no—
525C24C2×D18811yescharacteristic
526C24C2×D18811yescharacteristic
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—472no—
530C2×D4—944no—
531C2×D4—944no—
532C2×D4—941no—
533C2×D4—941no—
534C2×D4—941no—
535C2×D4—941no—
536C2×D4—941no—
537C2×D4—3761no—
538C2×D4—3761no—
539C2×D4—1882no—
540C2×D4—1882no—
541C2×D4(C2×D47)⋊C414yes—
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—944no—
551C22×C4—941no—
552C22×C4—941no—
553C22×C4—941no—
554C22×C4—941no—
555C22×C4—944no—
556C22×C4—941no—
557C22×C4—941no—
558C22×C4—941no—
559C22×C4—3761no—
560C22×C4—3761no—
561C22×C4—3761no—
562C22×C4—3761no—
563C22×C4—3761no—
564C22×C4—3761no—
565C22×C4—1882no—
566C22×C4—1882no—
567C22×C4—1882no—
568C22×C4—1882no—
569C22×C4C2×C4×D4712yes—
570C22×C4C2×C4×D4712yes—
571C22×C4C2×D18811yescharacteristic
572C22×C4C2×D18811yescharacteristic
573C22×C4C2×D18811yescharacteristic
574C22×C4C2×D18811yescharacteristic
575C22×C4C2×C22⋊D4712yes—
576C22×C4C2×C22⋊D4712yes—
577C22×C4C23×D4711yescharacteristic
578M16—44no—
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—21no—
589C2×C8—21no—
590C2×C8—44no—
591C2×C8#1062535212yes—
592C4⋊C4—472no—
593C4⋊C4—472no—
594C4⋊C4—472no—
595C4⋊C4—472no—
596C4⋊C4—944no—
597C4⋊C4—944no—
598C4⋊C4—944no—
599C4⋊C4—941no—
600C4⋊C4—941no—
601C4⋊C4—941no—
602C4⋊C4—941no—
603C4⋊C4—941no—
604C4⋊C4—941no—
605C4⋊C4—941no—
606C4⋊C4—941no—
607C4⋊C4—941no—
608C4⋊C4—941no—
609C4⋊C4—3761no—
610C4⋊C4—1882no—
611C4⋊C4—1882no—
612C4⋊C4—1882no—
613C4⋊C4(C2×D47)⋊C414yes—
614C22⋊C4—944no—
615C22⋊C4—944no—
616C22⋊C4—944no—
617C22⋊C4—944no—
618C22⋊C4—1882no—
619C22⋊C4—1882no—
620C22⋊C4(C2×D47)⋊C414yes—
621C22⋊C4(C2×D47)⋊C414yes—
622C42—944no—
623C42—1882no—
624C42C2×C4×D4712yes—
625C42C2×C22⋊D4712yes—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—942no—
637C23—1881no—
638C23—1881no—
639C23—1881no—
640C23—1881no—
641C23—1881no—
642C23—1881no—
643C23C2×(C2×D47)⋊C412yes—
644C23C2×(C2×D47)⋊C412yes—
645C23#1309405212yes—
646C23#1309405712yes—
647C23C22×D18811yescharacteristic
648D4—28no—
649D4—942no—
650D4—942no—
651D4—3764no—
652D4—1888no—
653D4—1881no—
654D4—1881no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—942no—
672C2×C4—942no—
673C2×C4—942no—
674C2×C4—942no—
675C2×C4—3764no—
676C2×C4—3764no—
677C2×C4—3764no—
678C2×C4—3764no—
679C2×C4—1881no—
680C2×C4—1881no—
681C2×C4—1881no—
682C2×C4—1881no—
683C2×C4—1881no—
684C2×C4—1881no—
685C2×C4—1881no—
686C2×C4—1881no—
687C2×C4—1881no—
688C2×C4—1881no—
689C2×C4—1881no—
690C2×C4—1881no—
691C2×C4—1881no—
692C2×C4—1881no—
693C2×C4—1881no—
694C2×C4—1881no—
695C2×C4—1881no—
696C2×C4C2×(C2×D47)⋊C412yes—
697C2×C4C2×(C2×D47)⋊C412yes—
698C2×C4C2×(C2×D47)⋊C412yes—
699C2×C4C2×(C2×D47)⋊C412yes—
700C2×C4C22×C4×D4711yescharacteristic
701C2×C4C22×C22⋊D4711yescharacteristic
702C2×C4#41×D4711yescharacteristic
703C2×C4C2×#1062535211yescharacteristic
704C2×C4#1309406911yescharacteristic
705C2×C4#1309407111yescharacteristic
706C8—22no—
707C8—41no—
708C8—41no—
709C8—41no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—3761no—
724C22—3761no—
725C22—3761no—
726C22—3761no—
727C22—1882no—
728C22—1882no—
729C22—1882no—
730C22#1568912514yes—
731C22C22×(C2×D47)⋊C411yescharacteristic
732C22#1568976811yescharacteristic
733C22#1568977711yescharacteristic
734C22C2×#1309405211yescharacteristic
735C22C2×#1309405711yescharacteristic
736C22#1568992811yescharacteristic
737C22#1568993511yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—3761no—
743C4—3761no—
744C4—3761no—
745C4—1882no—
746C4—1882no—
747C4—1882no—
748C4—1882no—
749C4C4×#1062535211yescharacteristic
750C4#1568960211yescharacteristic
751C4#1568976711yescharacteristic
752C4#1568977211yescharacteristic
753C2—24no—
754C2—42no—
755C2—3762no—
756C2#2024621311yescharacteristic
757C2C2×#1568912511yescharacteristic
758C2#2025191511yescharacteristic
759C2#2025553111yescharacteristic
760C2#2025556111yescharacteristic
761C2#2025586011yescharacteristic
762C2#2025587511yescharacteristic
subgroupG/H
centerC23C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#435C2
socleC23×C47C22×D4
prime radicalC2×#15689819C2
cosocleC22×C4×C47C24
hypercenterC2×#435D47
hypocenterC47#22493
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. D4×C4⋊Dic47C2semidirect
3. #20244357C2semidirect
4. #20244343C2semidirect
5. #20243826C2semidirect
6. #20243816C2semidirect
7. #20243703C2semidirect
8. #20243703C2semidirect
9. #20243484C2semidirect
10. #20243479C2semidirect
11. #20243389C2semidirect
12. #20243214C2semidirect
13. #20243108C2semidirect
14. C2×#15688886C2semidirect
15. C2×C47×#435C2semidirect
17. #15689819C4semidirect
71. #13094016C2×C4semidirect
75. #13093998C2×C4semidirect
76. #13093998C2×C4semidirect
79. C4×D188C2×C4semidirect
83. #13093983C2×C4semidirect
94. C2×C4⋊Dic47C2×C4semidirect
373. C2×#435D47semidirect
443. C47#22493semidirect

Maximal subgroups

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

subgroupindex
C2×#156898192
D4×C4⋊Dic472
#202443572
#202443432
#202438262
#202438162
#202437032
#202434842
#202434792
#202433892
#202432142
#202431082
C2×#156888862
C2×C47×#4352
#2249347