Finite Group Databasebeta

← #26226080

Subgroups — #26226080

Order 12032.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic
2C2×#15688983C211yesmaximal, characteristic, complemented
3#20244373C212yesmaximal, complemented
4#20244224C212yesmaximal, complemented
5#20243839C214yesmaximal, complemented
6#20243373C214yesmaximal, complemented
7C47×#2280C211yesmaximal, characteristic, complemented
8C22×#10625350C411yescharacteristic, complemented
9#15689634—21no—
10#15689634—21no—
11#15689634—21no—
12#15689634—21no—
13#15689634—21no—
14#15689634—21no—
15#15689634—21no—
16#15689634—21no—
17C2×#13094007C412yescomplemented
18C2×#13094003C411yescharacteristic, complemented
19C2×#13094003C2211yescharacteristic
20C2×#13093998C411yescharacteristic, complemented
21C2×#13093998C2211yescharacteristic
22C2×#13093993C2212yes—
23C2×C4×C22⋊D47C412yescomplemented
24C2×C4×C22⋊D47C2212yes—
25C2×#13093983C411yescharacteristic, complemented
26C22×C4⋊Dic47—21no—
27C22×C22⋊Dic47C2212yes—
28C2×#13093938C2218yes—
29#15688983—21no—
30#15688983—21no—
31#15688983C2212yes—
32#15688983C2212yes—
33C2×C47⋊#95—21no—
34#15688889C2218yes—
35C24×C4×C47C2211yescharacteristic
36C2×#117×C47—21no—
37C47×#381—21no—
38C47×#380—21no—
39C47×#380C2212yes—
40C47×#379C2212yes—
41C4×C22⋊C4×C47—21no—
42C4×C22⋊C4×C47C2212yes—
43C2×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350—21no—
47C2×#10625350—44no—
48C22×Dic94C2×C411yescharacteristic, complemented
49C22×D188C2×C411yescharacteristic, complemented
50C22×C22⋊D47C2×C412yes—
51C22×C22⋊D47C2×C412yes—
52C22×C22⋊D47C2312yes—
53C23×Dic47—22no—
54C22×C4×D47C2×C412yescomplemented
55#13094007—22no—
56#13094007—22no—
57#13094007—22no—
58#13094007—22no—
59#13094003—21no—
60#13094003—21no—
61#13094003—21no—
62#13094003—21no—
63#13094003—21no—
64#13094003—21no—
65#13094003—21no—
66#13094003—21no—
67#13093998—21no—
68#13093998—21no—
69#13093998—21no—
70#13093998—21no—
71#13093998—21no—
72#13093998—21no—
73#13093998—21no—
74#13093998—21no—
75#13093993—22no—
76#13093993—22no—
77#13093993—22no—
78#13093993—22no—
79C4×C22⋊D47—22no—
80C4×C22⋊D47—22no—
81C4×C22⋊D47—22no—
82C4×C22⋊D47—22no—
83C4×C22⋊D47—22no—
84C4×C22⋊D47—22no—
85C4×C22⋊D47—22no—
86C4×C22⋊D47—22no—
87#13093983—21no—
88#13093983—21no—
89#13093983—21no—
90#13093983—21no—
91C2×C4⋊Dic47—22no—
92C2×C4⋊Dic47—22no—
93C2×C4⋊Dic47—44no—
94C2×C4⋊Dic47C2×C411yescharacteristic, complemented
95C2×C4⋊Dic47C2×C411yescharacteristic, complemented
96C2×Dic47⋊C4C2×C412yescomplemented
97C2×Dic47⋊C4C2×C412yescomplemented
98C2×C22⋊Dic47—22no—
99C2×C22⋊Dic47—44no—
100C2×C22⋊Dic47C2×C412yes—
101C2×C22⋊Dic47C2×C412yes—
102C2×C22⋊Dic47C2314yes—
103C2×C22⋊Dic47C2312yes—
104C2×(C2×D47)⋊C4C2×C412yescomplemented
105C2×(C2×D47)⋊C4C2×C412yescomplemented
106C2×C4×Dic47C2×C412yescomplemented
107#13093938—48no—
108C47⋊#95—22no—
109C47⋊#95—22no—
110C25×C47C2311yescharacteristic
111C23×C4×C47—44no—
112C23×C4×C47C2×C411yescharacteristic
113C23×C4×C47C2×C411yescharacteristic
114C23×C4×C47C2×C411yescharacteristic
115C23×C4×C47C2×C411yescharacteristic
116C23×C4×C47D411yescharacteristic
117C23×C4×C47D411yescharacteristic
118C23×C4×C47D411yescharacteristic
119C23×C4×C47D411yescharacteristic
120C23×C4×C47D411yescharacteristic
121C23×C4×C47D411yescharacteristic
122C23×C4×C47D411yescharacteristic
123C23×C4×C47D411yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126#117×C47—44no—
127C2×C4⋊C4×C47—22no—
128C2×C22⋊C4×C47—22no—
129C2×C22⋊C4×C47—22no—
130C2×C22⋊C4×C47C2314yes—
131C2×C42×C47—22no—
132#95×C47—22no—
133#95×C47—22no—
134C24×C47—22no—
135C24×C47—22no—
136C24×C47—42no—
137C24×C47—42no—
138C24×C47C22×C411yescharacteristic
139C24×C47C22×C411yescharacteristic
140C24×C47C2×D411yescharacteristic
141C24×C47C2×D411yescharacteristic
142C24×C47C2×D411yescharacteristic
143C24×C47C2×D411yescharacteristic
144C24×C47C2411yescharacteristic
145C23×D47C22×C412yes—
146C22×C4×C47—24no—
147C22×C4×C47—24no—
148C22×C4×C47—24no—
149C22×C4×C47—24no—
150C22×C4×C47—42no—
151C22×C4×C47—42no—
152C22×C4×C47—42no—
153C22×C4×C47—42no—
154C22×C4×C47—42no—
155C22×C4×C47—42no—
156C22×C4×C47—42no—
157C22×C4×C47—42no—
158C22×C4×C47—42no—
159C22×C4×C47—42no—
160C22×C4×C47—42no—
161C22×C4×C47C22⋊C411yescharacteristic
162C22×C4×C47C22⋊C411yescharacteristic
163C22×C4×C47C22⋊C411yescharacteristic
164C22×C4×C47C22⋊C411yescharacteristic
165C22×C4×C47C22⋊C411yescharacteristic
166C22×C4×C47C22⋊C411yescharacteristic
167C22×C4×C47C22⋊C411yescharacteristic
168C22×C4×C47C22⋊C411yescharacteristic
169C22×C4×C47C22⋊C411yescharacteristic
170C22×C4×C47C22⋊C411yescharacteristic
171C22×C4×C47C22⋊C411yescharacteristic
172C22×C4×C47C22⋊C411yescharacteristic
173C22×C4×C47C22⋊C411yescharacteristic
174C22×C4×C47C22⋊C411yescharacteristic
175C22×C4×C47C22⋊C411yescharacteristic
176C22×C4×C47C22⋊C411yescharacteristic
177C22×C4×C47C22×C411yescharacteristic
178C22×C4×C47C22×C411yescharacteristic
179C22×C4×C47C22×C411yescharacteristic
180C22×C4×C47C22×C411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C2×C22⋊D47—22no—
190C2×C22⋊D47—22no—
191C2×C22⋊D47—22no—
192C2×C22⋊D47—22no—
193C2×C22⋊D47—22no—
194C2×C22⋊D47—22no—
195C2×C22⋊D47—24no—
196C2×C22⋊D47—24no—
197C2×C22⋊D47—44no—
198C2×C22⋊D47—44no—
199C22×Dic47—24no—
200C22×Dic47—44no—
201C22×Dic47—44no—
202C22×Dic47—44no—
203C22×Dic47C22×C412yes—
204C22×Dic47C22×C412yes—
205C22×Dic47C22×C412yes—
206#10625350—44no—
207#10625350—44no—
208#10625350—44no—
209#10625350—44no—
210C2×D188—21no—
211C2×D188—21no—
212C2×D188—42no—
213C2×C4×D47—22no—
214C2×C4×D47—22no—
215C2×C4×D47—44no—
216C2×Dic94—21no—
217C2×Dic94—21no—
218C2×Dic94—42no—
219C4⋊C4×C47—44no—
220C22⋊C4×C47—24no—
221C22⋊C4×C47—24no—
222C22⋊C4×C47—44no—
223C22⋊C4×C47—44no—
224C42×C47—44no—
225C22⋊Dic47—22no—
226C22⋊Dic47—22no—
227C22⋊Dic47—22no—
228C22⋊Dic47—22no—
229C22⋊Dic47—22no—
230C22⋊Dic47—22no—
231C22⋊Dic47—28no—
232C22⋊Dic47—44no—
233(C2×D47)⋊C4—22no—
234(C2×D47)⋊C4—22no—
235(C2×D47)⋊C4—22no—
236(C2×D47)⋊C4—22no—
237C4⋊Dic47—21no—
238C4⋊Dic47—21no—
239C4⋊Dic47—21no—
240C4⋊Dic47—21no—
241C4⋊Dic47—44no—
242C4⋊Dic47—44no—
243Dic47⋊C4—22no—
244Dic47⋊C4—22no—
245Dic47⋊C4—22no—
246Dic47⋊C4—22no—
247C4×Dic47—22no—
248C4×Dic47—22no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—22no—
252C23×C47—22no—
253C23×C47—22no—
254C23×C47—22no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—22no—
258C23×C47—22no—
259C23×C47—22no—
260C23×C47—22no—
261C23×C47—22no—
262C23×C47—22no—
263C23×C47—41no—
264C23×C47—41no—
265C23×C47—41no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47—48no—
272C23×C47—48no—
273C23×C47C2×C22⋊C411yescharacteristic
274C23×C47C2×C22⋊C411yescharacteristic
275C23×C47C2×C22⋊C411yescharacteristic
276C23×C47C2×C22⋊C411yescharacteristic
277C23×C47C23×C411yescharacteristic
278C23×C47C22×D411yescharacteristic
279C23×C47C22×D411yescharacteristic
280C23×C47H(5,𝔽2)12yes—
281C23×C472−1+412yes—
282C22×D47—22no—
283C22×D47—24no—
284C22×D47—42no—
285C22×D47—42no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—44no—
314C2×C4×C47—44no—
315C2×C4×C47—44no—
316C2×C4×C47#9914yescomplemented
317C2×C4×C47C2×C22⋊C411yescharacteristic
318C2×C4×C47C2×C22⋊C411yescharacteristic
319C2×C4×C47C2×C22⋊C411yescharacteristic
320C2×C4×C47C2×C22⋊C411yescharacteristic
321C2×C4×C47C2×C22⋊C411yescharacteristic
322C2×C4×C47C2×C22⋊C411yescharacteristic
323C2×C4×C47C2×C22⋊C411yescharacteristic
324C2×C4×C47C2×C22⋊C411yescharacteristic
325C22⋊D47—44no—
326C22⋊D47—44no—
327C22⋊D47—42no—
328C22⋊D47—42no—
329C22⋊D47—44no—
330C22⋊D47—44no—
331C22⋊D47—44no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—24no—
336C2×Dic47—42no—
337C2×Dic47—42no—
338C2×Dic47—44no—
339C2×Dic47—44no—
340C2×Dic47—44no—
341C2×Dic47—88no—
342D188—42no—
343D188—42no—
344C4×D47—44no—
345C4×D47—44no—
346Dic94—42no—
347Dic94—42no—
348#21874—471nomaximal, Sylow
349C22×C47—24no—
350C22×C47—24no—
351C22×C47—21no—
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—21no—
361C22×C47—21no—
362C22×C47—21no—
363C22×C47—21no—
364C22×C47—21no—
365C22×C47—21no—
366C22×C47—21no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47—44no—
370C22×C47—44no—
371C22×C47—44no—
372C22×C47—44no—
373C22×C47—42no—
374C22×C47—42no—
375C22×C47C2×#9912yes—
376C22×C47#41012yes—
377C22×C47C22×C22⋊C411yescharacteristic
378C22×C47#52012yes—
379C22×C47#53511yescharacteristic
380C22×C47#53611yescharacteristic
381C22×C47#53712yes—
382C2×D47—42no—
383C2×D47—42no—
384C2×D47—42no—
385C2×D47—84no—
386C4×C47—21no—
387C4×C47—21no—
388C4×C47—21no—
389C4×C47—21no—
390C4×C47—21no—
391C4×C47—21no—
392C4×C47—84no—
393C4×C47C2×#9912yes—
394C4×C47C2×#9912yes—
395Dic47—42no—
396Dic47—42no—
397Dic47—42no—
398Dic47—84no—
399C2×#525—471no—
400#2280D4711yescharacteristic, complemented
401C2×#380—471no—
402#1996—472no—
403#1964—472no—
404#1898—474no—
405#1799—474no—
406C2×C47—21no—
407C2×C47—22no—
408C2×C47—22no—
409C2×C47—21no—
410C2×C47—22no—
411C2×C47—22no—
412C2×C47—41no—
413C2×C47—41no—
414C2×C47#231111yescharacteristic
415C2×C47C22×#9911yescharacteristic
416C2×C47C2×#41011yescharacteristic
417D47—82no—
418C22×#41—471no—
419C24×C4C2×D4711yescharacteristic
420#525—941no—
421#525—941no—
422#525—941no—
423#525—941no—
424#525—941no—
425#525—941no—
426#525—941no—
427#525—941no—
428C2×#123—472no—
429C2×C22⋊Q8—471no—
430C2×C22⋊Q8—471no—
431C2×#121—471no—
432C2×#121—471no—
433C2×#120—472no—
434C2×C4×D4—472no—
435C2×C4×D4—472no—
436C2×#117—21no—
437C2×#117—471no—
438C22×C4⋊C4—941no—
439C22×C22⋊C4—472no—
440C2×#99—478no—
441#381—21no—
442#380—21no—
443#380—472no—
444#380—472no—
445#380—941no—
446#380—941no—
447#380C2×D4712yes—
448#379C2×D4712yes—
449C4×C22⋊C4—21no—
450C4×C22⋊C4C2×D4712yes—
451C2×#95—941no—
452#342—478no—
453C47#2187411yescharacteristic, complemented, Sylow
454C25C22×D4711yescharacteristic
455C2×#41—941no—
456C2×#41—941no—
457C2×#41—941no—
458C2×#41—941no—
459C2×#41—1884no—
460C22×Q8—471no—
461C22×D4—472no—
462C22×D4—472no—
463C22×D4—472no—
464C22×D4—471no—
465C23×C4—44no—
466C23×C4—472no—
467C23×C4—942no—
468C23×C4C4×D4711yescharacteristic
469C23×C4C4×D4711yescharacteristic
470C23×C4C4×D4711yescharacteristic
471C23×C4C4×D4711yescharacteristic
472C23×C4D18811yescharacteristic
473C23×C4D18811yescharacteristic
474C23×C4D18811yescharacteristic
475C23×C4D18811yescharacteristic
476C23×C4C22⋊D4711yescharacteristic
477C23×C4C22⋊D4711yescharacteristic
478C23×C4C22⋊D4711yescharacteristic
479C23×C4C22⋊D4711yescharacteristic
480C23×C4C22×D4711yescharacteristic
481C23×C4C22×D4711yescharacteristic
482#123—942no—
483#123—942no—
484#123—942no—
485#123—942no—
486C22⋊Q8—941no—
487C22⋊Q8—941no—
488C22⋊Q8—941no—
489C22⋊Q8—941no—
490C22⋊Q8—941no—
491C22⋊Q8—941no—
492C22⋊Q8—941no—
493C22⋊Q8—941no—
494#121—941no—
495#121—941no—
496#121—941no—
497#121—941no—
498#121—941no—
499#121—941no—
500#121—941no—
501#121—941no—
502#120—942no—
503#120—942no—
504#120—942no—
505#120—942no—
506C4×D4—942no—
507C4×D4—942no—
508C4×D4—942no—
509C4×D4—942no—
510C4×D4—942no—
511C4×D4—942no—
512C4×D4—942no—
513C4×D4—942no—
514#117—44no—
515#117—941no—
516#117—941no—
517#117—941no—
518#117—941no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—472no—
523C2×C4⋊C4—472no—
524C2×C4⋊C4—942no—
525C2×C4⋊C4—942no—
526C2×C4⋊C4—1884no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—472no—
530C2×C22⋊C4—472no—
531C2×C22⋊C4—472no—
532C2×C22⋊C4—472no—
533C2×C22⋊C4—472no—
534C2×C22⋊C4—474no—
535C2×C22⋊C4—942no—
536C2×C22⋊C4—1884no—
537C2×C22⋊C4C22×D4714yes—
538C2×C42—22no—
539C2×C42—472no—
540#99—1888no—
541#95—22no—
542#95—22no—
543#95—942no—
544#95—942no—
545C24—22no—
546C24—22no—
547C24—42no—
548C24—42no—
549C24—472no—
550C24C2×C4×D4711yescharacteristic
551C24C2×C4×D4711yescharacteristic
552C24C2×D18811yescharacteristic
553C24C2×D18811yescharacteristic
554C24C2×C22⋊D4711yescharacteristic
555C24C2×C22⋊D4711yescharacteristic
556C24C23×D4711yescharacteristic
557#41—1884no—
558#41—1884no—
559#41—1884no—
560#41—1884no—
561C2×Q8—941no—
562C2×Q8—941no—
563C2×Q8—1882no—
564C2×D4—942no—
565C2×D4—942no—
566C2×D4—942no—
567C2×D4—942no—
568C2×D4—942no—
569C2×D4—942no—
570C2×D4—944no—
571C2×D4—944no—
572C2×D4—941no—
573C2×D4—941no—
574C2×D4—1882no—
575C2×D4—1884no—
576C2×D4—1884no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—472no—
593C22×C4—472no—
594C22×C4—472no—
595C22×C4—942no—
596C22×C4—942no—
597C22×C4—944no—
598C22×C4—1884no—
599C22×C4—1884no—
600C22×C4—1884no—
601C22×C4—1884no—
602C22×C4(C2×D47)⋊C411yescharacteristic
603C22×C4(C2×D47)⋊C411yescharacteristic
604C22×C4(C2×D47)⋊C411yescharacteristic
605C22×C4(C2×D47)⋊C411yescharacteristic
606C22×C4(C2×D47)⋊C411yescharacteristic
607C22×C4(C2×D47)⋊C411yescharacteristic
608C22×C4(C2×D47)⋊C411yescharacteristic
609C22×C4(C2×D47)⋊C411yescharacteristic
610C22×C4(C2×D47)⋊C411yescharacteristic
611C22×C4(C2×D47)⋊C411yescharacteristic
612C22×C4(C2×D47)⋊C411yescharacteristic
613C22×C4(C2×D47)⋊C411yescharacteristic
614C22×C4(C2×D47)⋊C411yescharacteristic
615C22×C4(C2×D47)⋊C411yescharacteristic
616C22×C4(C2×D47)⋊C411yescharacteristic
617C22×C4(C2×D47)⋊C411yescharacteristic
618C22×C4C2×C4×D4711yescharacteristic
619C22×C4C2×C4×D4711yescharacteristic
620C22×C4C2×C4×D4711yescharacteristic
621C22×C4C2×C4×D4711yescharacteristic
622C22×C4C2×D18811yescharacteristic
623C22×C4C2×D18811yescharacteristic
624C22×C4C2×D18811yescharacteristic
625C22×C4C2×D18811yescharacteristic
626C22×C4C2×C22⋊D4711yescharacteristic
627C22×C4C2×C22⋊D4711yescharacteristic
628C22×C4C2×C22⋊D4711yescharacteristic
629C22×C4C2×C22⋊D4711yescharacteristic
630C4⋊C4—44no—
631C4⋊C4—942no—
632C4⋊C4—942no—
633C4⋊C4—942no—
634C4⋊C4—942no—
635C4⋊C4—941no—
636C4⋊C4—941no—
637C4⋊C4—941no—
638C4⋊C4—941no—
639C4⋊C4—1884no—
640C4⋊C4—1884no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—942no—
646C22⋊C4—942no—
647C22⋊C4—942no—
648C22⋊C4—942no—
649C22⋊C4—942no—
650C22⋊C4—942no—
651C22⋊C4—942no—
652C22⋊C4—942no—
653C22⋊C4—942no—
654C22⋊C4—942no—
655C22⋊C4—948no—
656C22⋊C4—1884no—
657C42—44no—
658C42—942no—
659C42—942no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—21no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—22no—
673C23—22no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—48no—
683C23—48no—
684C23—944no—
685C23—942no—
686C23—1882no—
687C23—1882no—
688C23C2×(C2×D47)⋊C411yescharacteristic
689C23C2×(C2×D47)⋊C411yescharacteristic
690C23C2×(C2×D47)⋊C411yescharacteristic
691C23C2×(C2×D47)⋊C411yescharacteristic
692C23C22×C4×D4711yescharacteristic
693C23C22×C22⋊D4711yescharacteristic
694C23C22×D18811yescharacteristic
695C23#1309407012yes—
696C23#1309407112yes—
697Q8—1882no—
698Q8—1882no—
699D4—1882no—
700D4—1884no—
701D4—1884no—
702D4—1884no—
703D4—1884no—
704D4—1882no—
705D4—1882no—
706D4—1884no—
707D4—1882no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—944no—
742C2×C4—3768no—
743C2×C4—1884no—
744C2×C4—1884no—
745C2×C4—1884no—
746C2×C4—1884no—
747C2×C4—1884no—
748C2×C4—1882no—
749C2×C4—1882no—
750C2×C4#1309393814yescomplemented
751C2×C4C2×(C2×D47)⋊C411yescharacteristic
752C2×C4C2×(C2×D47)⋊C411yescharacteristic
753C2×C4C2×(C2×D47)⋊C411yescharacteristic
754C2×C4C2×(C2×D47)⋊C411yescharacteristic
755C2×C4C2×(C2×D47)⋊C411yescharacteristic
756C2×C4C2×(C2×D47)⋊C411yescharacteristic
757C2×C4C2×(C2×D47)⋊C411yescharacteristic
758C2×C4C2×(C2×D47)⋊C411yescharacteristic
759C22—24no—
760C22—24no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—3764no—
786C22—1882no—
787C22—1882no—
788C22—1882no—
789C22C2×#1309393812yes—
790C22#1568909612yes—
791C22C22×(C2×D47)⋊C411yescharacteristic
792C22#1568960312yes—
793C22#1568969211yescharacteristic
794C22#1568969911yescharacteristic
795C22#1568970112yes—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—84no—
803C4—3764no—
804C4—1882no—
805C4—1882no—
806C4—1882no—
807C4C2×#1309393812yes—
808C4C2×#1309393812yes—
809C2—22no—
810C2—21no—
811C2—22no—
812C2—22no—
813C2—21no—
814C2—22no—
815C2—41no—
816C2—41no—
817C2—3762no—
818C2#2024597611yescharacteristic
819C2C22×#1309393811yescharacteristic
820C2C2×#1568909611yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC47×#2280C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#15689634C2
cosocleC24×C47C24
hypercenter#2280D47
hypocenterC47#21874
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×#15688983C2semidirect
3. #20244373C2semidirect
4. #20244224C2semidirect
5. #20243839C2semidirect
6. #20243373C2semidirect
7. C47×#2280C2semidirect
8. C22×#10625350C4semidirect
17. C2×#13094007C4semidirect
18. C2×#13094003C4semidirect
20. C2×#13093998C4semidirect
23. C2×C4×C22⋊D47C4semidirect
25. C2×#13093983C4semidirect
48. C22×Dic94C2×C4semidirect
49. C22×D188C2×C4semidirect
54. C22×C4×D47C2×C4semidirect
94. C2×C4⋊Dic47C2×C4semidirect
95. C2×C4⋊Dic47C2×C4semidirect
96. C2×Dic47⋊C4C2×C4semidirect
97. C2×Dic47⋊C4C2×C4semidirect
104. C2×(C2×D47)⋊C4C2×C4semidirect
105. C2×(C2×D47)⋊C4C2×C4semidirect
106. C2×C4×Dic47C2×C4semidirect
316. C2×C4×C47#99semidirect
400. #2280D47semidirect
453. C47#21874semidirect
750. C2×C4#13093938semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
C2×#156889832
#202443732
#202442242
#202438392
#202433732
C47×#22802
#2187447