Finite Group Databasebeta

← #26232620

Subgroups — #26232620

Order 12032.

1390 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689777C211yesmaximal, characteristic
2C2×#15689195C211yesmaximal, characteristic, complemented
3#20244360C211yesmaximal, characteristic, complemented
4#20244336C211yesmaximal, characteristic, complemented
5#20243824C211yesmaximal, characteristic, complemented
6#20243814C211yesmaximal, characteristic, complemented
7#20243710C211yesmaximal, characteristic, complemented
8#20243705C211yesmaximal, characteristic, complemented
9#20243476C211yesmaximal, characteristic, complemented
10#20243472C211yesmaximal, characteristic, complemented
11#20243395C211yesmaximal, characteristic, complemented
12#20243216C211yesmaximal, characteristic, complemented
13#20243109C211yesmaximal, characteristic, complemented
14C2×#15688885C211yesmaximal, characteristic, complemented
15C47×#2352C211yesmaximal, characteristic, complemented
16C22×#10625352—21no—
17C22×#10625329C2211yescharacteristic
18C23×C47⋊C8C2211yescharacteristic
19#15689777—24no—
20#15689777C418yescomplemented
21C2×#13094024C2211yescharacteristic
22C2×#13094008—21no—
23C2×#13094008—21no—
24C2×#13094004—21no—
25C2×#13093998C2211yescharacteristic
26C2×#13093998C2211yescharacteristic
27C2×C4×D188C2211yescharacteristic
28C22×C4⋊Dic47C2211yescharacteristic
29C22×C4⋊Dic47C2211yescharacteristic
30#15689195—24no—
31C2×C4⋊(C47⋊C8)C2211yescharacteristic
32C2×#13093944C2211yescharacteristic
33C2×#13093944C2211yescharacteristic
34C2×#13093944C2211yescharacteristic
35C2×#13093944C2211yescharacteristic
36C2×C22⋊(C47⋊C8)C2211yescharacteristic
37C2×C22⋊(C47⋊C8)C2211yescharacteristic
38C2×#13093935C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51C2×C4×D4×C47C2211yescharacteristic
52C2×#117×C47C2211yescharacteristic
53C22×C4⋊C4×C47C2211yescharacteristic
54C47×#388—21no—
55C47×#387—21no—
56C47×#386—21no—
57C47×#382C2211yescharacteristic
58C47×#380C2211yescharacteristic
59C47×#380C2211yescharacteristic
60C4×C4⋊C4×C47C2211yescharacteristic
61C4×C22⋊C4×C47—21no—
62C2×#10625352—28no—
63C2×#10625352—44no—
64C2×#10625352—44no—
65C22×Dic94—21no—
66C22×D188C2311yescharacteristic
67C22×C22⋊D47—21no—
68C22×C22⋊D47—21no—
69C23×Dic47—21no—
70C23×Dic47—21no—
71C22×C4×D47—21no—
72C2×#10625329—22no—
73C2×#10625329—22no—
74C2×#10625329—41no—
75C22×C47⋊C8—22no—
76C22×C47⋊C8—22no—
77C22×C47⋊C8—41no—
78C22×C47⋊C8C2311yescharacteristic
79C22×C47⋊C8C2311yescharacteristic
80C22×C47⋊C8C2311yescharacteristic
81C22×C47⋊C8C2311yescharacteristic
82#13094024—22no—
83#13094024C2×C414yescomplemented
84#13094008—28no—
85#13094008—28no—
86#13094004—28no—
87#13093998—22no—
88#13093998—22no—
89#13093998C2×C414yes—
90#13093998C2×C414yescomplemented
91C4×D188—22no—
92C4×D188C2×C414yescomplemented
93C2×C4⋊Dic47—22no—
94C2×C4⋊Dic47—22no—
95C2×C4⋊Dic47—21no—
96C2×C4⋊Dic47—21no—
97C2×C4⋊Dic47—21no—
98C2×C4⋊Dic47C2×C414yes—
99C2×C4⋊Dic47C2×C414yescomplemented
100C2×C4⋊Dic47C2311yescharacteristic
101C2×C4⋊Dic47C2311yescharacteristic
102C2×C4⋊Dic47C2311yescharacteristic
103C2×(C2×D47)⋊C4—21no—
104C2×(C2×D47)⋊C4—21no—
105C2×(C2×D47)⋊C4—21no—
106C4⋊(C47⋊C8)—22no—
107#13093944—22no—
108#13093944—22no—
109#13093944—41no—
110#13093944—41no—
111C22⋊(C47⋊C8)—22no—
112C22⋊(C47⋊C8)—22no—
113#13093935—22no—
114C22×D4×C47D411yescharacteristic
115C23×C4×C47—21no—
116C23×C4×C47C2311yescharacteristic
117C23×C4×C47C2311yescharacteristic
118C4×D4×C47C2×C414yes—
119C4×D4×C47D414yes—
120#117×C47—22no—
121#117×C47—41no—
122C2×C4⋊C4×C47—22no—
123C2×C4⋊C4×C47—21no—
124C2×C4⋊C4×C47—41no—
125C2×C4⋊C4×C47D411yescharacteristic
126C2×C4⋊C4×C47C2311yescharacteristic
127C2×C4⋊C4×C47C2311yescharacteristic
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C4⋊C4×C47C2311yescharacteristic
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47D411yescharacteristic
134C2×C22⋊C4×C47D411yescharacteristic
135C2×C42×C47—21no—
136C2×C42×C47—21no—
137C2×C42×C47C2311yescharacteristic
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47—21no—
142#95×C47—21no—
143C24×C47C2×D411yescharacteristic
144C24×C47C2×D411yescharacteristic
145C23×D47—21no—
146C2×D4×C47—22no—
147C2×D4×C47—22no—
148C2×D4×C47C22⋊C414yes—
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×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—42no—
162C22×C4×C47—42no—
163C22×C4×C47—81no—
164C22×C4×C47C22×C412yes—
165C22×C4×C47C22×C412yes—
166C22×C4×C47C2×D411yescharacteristic
167C22×C4×C47C2×D411yescharacteristic
168C22×C4×C47C2×D411yescharacteristic
169C22×C4×C47C2×D411yescharacteristic
170C22×C4×C47C2×D412yes—
171C22×C4×C47C2×D412yes—
172C22×C4×C47C2411yescharacteristic
173C2×C22⋊D47—24no—
174C2×C22⋊D47—24no—
175C2×C22⋊D47—42no—
176C2×C22⋊D47—42no—
177C2×C22⋊D47—42no—
178C2×C22⋊D47—42no—
179C22×Dic47—24no—
180C22×Dic47—24no—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—21no—
184C22×Dic47—42no—
185C22×Dic47—42no—
186C22×Dic47—42no—
187C22×Dic47—42no—
188#10625352—432no—
189C2×D188—21no—
190C2×D188—21no—
191C2×D188—21no—
192C2×D188—21no—
193C2×D188—21no—
194C2×D188C22×C412yes—
195C2×C4×D47—24no—
196C2×C4×D47—42no—
197C2×C4×D47—42no—
198C2×Dic94—24no—
199C2×Dic94—42no—
200C2×Dic94—42no—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—21no—
203C4⋊C4×C47—21no—
204C4⋊C4×C47—21no—
205C4⋊C4×C47—21no—
206C4⋊C4×C47—21no—
207C4⋊C4×C47—21no—
208C4⋊C4×C47—42no—
209C4⋊C4×C47C22⋊C414yes—
210C4⋊C4×C47#4112yescomplemented
211C22⋊C4×C47—42no—
212C22⋊C4×C47—42no—
213C22⋊C4×C47—81no—
214C22⋊C4×C47C22⋊C414yes—
215C22⋊C4×C47C22⋊C414yes—
216C42×C47—42no—
217C42×C47—81no—
218C42×C47C22×C412yes—
219C42×C47C2×D412yes—
220(C2×D47)⋊C4—24no—
221(C2×D47)⋊C4—24no—
222(C2×D47)⋊C4—24no—
223C4⋊Dic47—24no—
224C4⋊Dic47—24no—
225C4⋊Dic47—24no—
226C4⋊Dic47—21no—
227C4⋊Dic47—21no—
228C4⋊Dic47—21no—
229C4⋊Dic47C22×C412yes—
230C4⋊Dic47C22×C412yes—
231C4⋊Dic47C22×C412yes—
232#10625329—44no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C2×C47⋊C8—21no—
238C2×C47⋊C8—21no—
239C2×C47⋊C8—21no—
240C2×C47⋊C8—21no—
241C2×C47⋊C8—21no—
242C2×C47⋊C8—21no—
243C2×C47⋊C8—21no—
244C2×C47⋊C8—44no—
245C2×C47⋊C8#4112yescomplemented
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×C47C2×C22⋊C412yes—
257C23×C47C2×C22⋊C412yes—
258C23×C47AGL(1,ℤ/8)12yes—
259C23×C47AGL(1,ℤ/8)12yes—
260C23×C47C22×D411yescharacteristic
261C22×D47—22no—
262C22×D47—41no—
263C22×D47—41no—
264C22×D47—41no—
265C22×D47—41no—
266C22×D47—41no—
267C22×D47—41no—
268D4×C47—28no—
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—21no—
276C2×C4×C47—21no—
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×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—84no—
298C2×C4×C47C2×C22⋊C412yes—
299C2×C4×C47C2×C22⋊C412yes—
300C2×C4×C47C2×C22⋊C412yes—
301C2×C4×C47C2×C22⋊C412yes—
302C2×C4×C47C23×C411yescharacteristic
303C2×C4×C47C22×D411yescharacteristic
304C2×C4×C47C2×#4111yescharacteristic
305C2×C4×C47C2×#4111yescharacteristic
306C2×C4×C47H(5,𝔽2)11yescharacteristic
307C2×C4×C472−1+411yescharacteristic
308C22⋊D47—48no—
309C22⋊D47—48no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—48no—
314C2×Dic47—41no—
315C2×Dic47—41no—
316C2×Dic47—41no—
317C2×Dic47—41no—
318C2×Dic47—41no—
319C2×Dic47—41no—
320C2×Dic47—48no—
321D188—22no—
322D188—22no—
323D188—41no—
324D188—41no—
325C4×D47—48no—
326Dic94—48no—
327C47⋊C8—22no—
328C47⋊C8—41no—
329C47⋊C8—41no—
330C47⋊C8—41no—
331#22495—471nomaximal, Sylow
332C22×C47—22no—
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—22no—
338C22×C47—22no—
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47#41814yes—
346C22×C47C22×C22⋊C411yescharacteristic
347C22×C47#54611yescharacteristic
348C22×C47#54711yescharacteristic
349C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C47#57711yescharacteristic
352C22×C47#57811yescharacteristic
353C2×D47—42no—
354C2×D47—42no—
355C2×D47—42no—
356C2×D47—81no—
357C2×D47—81no—
358C2×D47—81no—
359C2×D47—81no—
360C4×C47—22no—
361C4×C47—22no—
362C4×C47—22no—
363C4×C47—22no—
364C4×C47—42no—
365C4×C47—81no—
366C4×C47—81no—
367C4×C47—81no—
368C4×C47C4×#4111yescharacteristic
369C4×C47#52011yescharacteristic
370C4×C47#54611yescharacteristic
371C4×C47#54711yescharacteristic
372Dic47—42no—
373Dic47—42no—
374Dic47—42no—
375C2×#547—471no—
376C2×#435—471no—
377#2352D4711yescharacteristic, complemented
378#1993—471no—
379#1987—471no—
380#1895—471no—
381#1893—471no—
382#1875—471no—
383#1874—471no—
384#1824—471no—
385#1823—471no—
386#1804—471no—
387#1762—471no—
388#1736—471no—
389C2×#340—471no—
390C2×C47—24no—
391C2×C47—42no—
392C2×C47#233911yescharacteristic
393C2×C47C2×#41811yescharacteristic
394C2×C47#289811yescharacteristic
395C2×C47#330611yescharacteristic
396C2×C47#330811yescharacteristic
397C2×C47#334311yescharacteristic
398C2×C47#334511yescharacteristic
399D47—82no—
400C22×#41—941no—
401C22×M16—471no—
402C23×C8—471no—
403#547—478no—
404#547—944no—
405C2×C4⋊Q8—471no—
406C2×#123—941no—
407C2×#123—941no—
408C2×C22⋊Q8—941no—
409C2×#121—471no—
410C2×#121—471no—
411C2×C4×D4—471no—
412C2×C4×D4C2×D4711yescharacteristic
413C2×#117C2×D4711yescharacteristic
414C22×C4⋊C4—471no—
415C22×C4⋊C4—471no—
416C22×C4⋊C4C2×D4711yescharacteristic
417#435—944no—
418C2×C4⋊C8—471no—
419C2×#102—471no—
420C2×#102—471no—
421C2×#102—471no—
422C2×#102—471no—
423C2×C22⋊C8—471no—
424C2×C22⋊C8—471no—
425C2×#97—471no—
426#388—21no—
427#387—21no—
428#386—21no—
429#382C2×D4711yescharacteristic
430#380C2×D4711yescharacteristic
431#380C2×D4711yescharacteristic
432C4×C4⋊C4C2×D4711yescharacteristic
433C4×C22⋊C4—21no—
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—
443#340—471no—
444#340—471no—
445#340—471no—
446C47#2249511yescharacteristic, complemented, Sylow
447C2×#41—948no—
448C2×#41—1884no—
449C2×#41—1884no—
450C22×Q8—941no—
451C22×D4—471no—
452C22×D4—941no—
453C22×D4—941no—
454C22×D4C22⋊D4711yescharacteristic
455C23×C4—21no—
456C23×C4—941no—
457C23×C4—941no—
458C23×C4—941no—
459C23×C4C22×D4711yescharacteristic
460C23×C4C22×D4711yescharacteristic
461C2×M16—942no—
462C2×M16—942no—
463C2×M16—1881no—
464C22×C8—471no—
465C22×C8—471no—
466C22×C8—471no—
467C22×C8—471no—
468C22×C8—942no—
469C22×C8—942no—
470C22×C8—1881no—
471C4⋊Q8—474no—
472C4⋊Q8—942no—
473#123—948no—
474#123—948no—
475C22⋊Q8—948no—
476#121—474no—
477#121—474no—
478#121—942no—
479#121—942no—
480C4×D4—474no—
481C4×D4—942no—
482C4×D4C4×D4714yes—
483C4×D4D18814yes—
484#117—22no—
485#117—41no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—41no—
489C2×C4⋊C4—474no—
490C2×C4⋊C4—474no—
491C2×C4⋊C4—471no—
492C2×C4⋊C4—471no—
493C2×C4⋊C4—471no—
494C2×C4⋊C4—942no—
495C2×C4⋊C4—942no—
496C2×C4⋊C4—941no—
497C2×C4⋊C4—941no—
498C2×C4⋊C4—941no—
499C2×C4⋊C4C22⋊D4711yescharacteristic
500C2×C4⋊C4C22×D4711yescharacteristic
501C2×C4⋊C4C22×D4711yescharacteristic
502C2×C4⋊C4C22×D4711yescharacteristic
503C2×C4⋊C4C22×D4711yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—941no—
508C2×C22⋊C4—941no—
509C2×C22⋊C4—941no—
510C2×C22⋊C4C22⋊D4711yescharacteristic
511C2×C22⋊C4C22⋊D4711yescharacteristic
512C2×C42—21no—
513C2×C42—21no—
514C2×C42C22×D4711yescharacteristic
515C4⋊C8—942no—
516#102—942no—
517#102—942no—
518#102—1881no—
519#102—1881no—
520C22⋊C8—942no—
521C22⋊C8—942no—
522#97—942no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528C24—941no—
529C24C2×C22⋊D4711yescharacteristic
530C24C2×C22⋊D4711yescharacteristic
531#41—18832no—
532C2×Q8—944no—
533C2×Q8—1882no—
534C2×Q8—1882no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—472no—
538C2×D4—944no—
539C2×D4—944no—
540C2×D4—941no—
541C2×D4—941no—
542C2×D4—941no—
543C2×D4—941no—
544C2×D4—941no—
545C2×D4—1882no—
546C2×D4—1882no—
547C2×D4—1882no—
548C2×D4—1882no—
549C2×D4(C2×D47)⋊C414yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—81no—
565C22×C4—944no—
566C22×C4—944no—
567C22×C4—941no—
568C22×C4—941no—
569C22×C4—941no—
570C22×C4—944no—
571C22×C4—1882no—
572C22×C4—1882no—
573C22×C4—1882no—
574C22×C4—1882no—
575C22×C4—1882no—
576C22×C4—1882no—
577C22×C4C2×C4×D4712yes—
578C22×C4C2×C4×D4712yes—
579C22×C4C2×D18812yes—
580C22×C4C2×D18812yes—
581C22×C4C2×C22⋊D4711yescharacteristic
582C22×C4C2×C22⋊D4711yescharacteristic
583C22×C4C2×C22⋊D4711yescharacteristic
584C22×C4C2×C22⋊D4711yescharacteristic
585C22×C4C23×D4711yescharacteristic
586M16—1884no—
587C2×C8—472no—
588C2×C8—941no—
589C2×C8—941no—
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—1884no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—42no—
608C4⋊C4—472no—
609C4⋊C4—472no—
610C4⋊C4—472no—
611C4⋊C4—944no—
612C4⋊C4—944no—
613C4⋊C4—944no—
614C4⋊C4—941no—
615C4⋊C4—941no—
616C4⋊C4—941no—
617C4⋊C4(C2×D47)⋊C414yes—
618C4⋊C4#1062535212yescomplemented
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—81no—
622C22⋊C4—944no—
623C22⋊C4—944no—
624C22⋊C4—944no—
625C22⋊C4(C2×D47)⋊C414yes—
626C22⋊C4(C2×D47)⋊C414yes—
627C42—42no—
628C42—81no—
629C42C2×C4×D4712yes—
630C42C2×D18812yes—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—942no—
642C23—1881no—
643C23—1881no—
644C23—1881no—
645C23—1881no—
646C23—1881no—
647C23—1881no—
648C23C2×(C2×D47)⋊C412yes—
649C23C2×(C2×D47)⋊C412yes—
650C23#1309404912yes—
651C23#1309404912yes—
652C23C22×C22⋊D4711yescharacteristic
653Q8—1888no—
654D4—28no—
655D4—942no—
656D4—942no—
657D4—1888no—
658D4—1888no—
659D4—1881no—
660D4—1881no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—84no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—1888no—
694C2×C4—1888no—
695C2×C4—1888no—
696C2×C4—1881no—
697C2×C4—1881no—
698C2×C4—1881no—
699C2×C4—1881no—
700C2×C4—1881no—
701C2×C4—1881no—
702C2×C4C2×(C2×D47)⋊C412yes—
703C2×C4C2×(C2×D47)⋊C412yes—
704C2×C4C2×(C2×D47)⋊C412yes—
705C2×C4C2×(C2×D47)⋊C412yes—
706C2×C4C22×C4×D4711yescharacteristic
707C2×C4C22×D18811yescharacteristic
708C2×C4#41×D4711yescharacteristic
709C2×C4C2×#1062535211yescharacteristic
710C2×C4#1309406911yescharacteristic
711C2×C4#1309407111yescharacteristic
712C8—942no—
713C8—1881no—
714C8—1881no—
715C8—1881no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—3761no—
730C22—3761no—
731C22—3761no—
732C22—3761no—
733C22—1882no—
734C22—1882no—
735C22—1882no—
736C22#1568912714yes—
737C22C22×(C2×D47)⋊C411yescharacteristic
738C22#1568976711yescharacteristic
739C22#1568977211yescharacteristic
740C22C2×#1309404911yescharacteristic
741C22C2×#1309404911yescharacteristic
742C22#1568993411yescharacteristic
743C22#1568993811yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—42no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4—1882no—
753C4—1882no—
754C4—1882no—
755C4C4×#1062535211yescharacteristic
756C4#1568960211yescharacteristic
757C4#1568976811yescharacteristic
758C4#1568977711yescharacteristic
759C2—24no—
760C2—42no—
761C2—3762no—
762C2#2024621311yescharacteristic
763C2C2×#1568912711yescharacteristic
764C2#2025191811yescharacteristic
765C2#2025534911yescharacteristic
766C2#2025537911yescharacteristic
767C2#2025582811yescharacteristic
768C2#2025585211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2352C2
socleC23×C47C22×D4
prime radicalC2×#15689777C2
cosocleC22×C4×C47C24
hypercenter#2352D47
hypocenterC47#22495
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#15689195C2semidirect
3. #20244360C2semidirect
4. #20244336C2semidirect
5. #20243824C2semidirect
6. #20243814C2semidirect
7. #20243710C2semidirect
8. #20243705C2semidirect
9. #20243476C2semidirect
10. #20243472C2semidirect
11. #20243395C2semidirect
12. #20243216C2semidirect
13. #20243109C2semidirect
14. C2×#15688885C2semidirect
15. C47×#2352C2semidirect
20. #15689777C4semidirect
83. #13094024C2×C4semidirect
90. #13093998C2×C4semidirect
92. C4×D188C2×C4semidirect
99. C2×C4⋊Dic47C2×C4semidirect
210. C4⋊C4×C47#41semidirect
245. C2×C47⋊C8#41semidirect
377. #2352D47semidirect
446. C47#22495semidirect
618. C4⋊C4#10625352semidirect

Maximal subgroups

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

subgroupindex
C2×#156897772
C2×#156891952
#202443602
#202443362
#202438242
#202438142
#202437102
#202437052
#202434762
#202434722
#202433952
#202432162
#202431092
C2×#156888852
C47×#23522
#2249547