Finite Group Databasebeta

← #26222042

Subgroups — #26222042

Order 12032.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689285C211yesmaximal, characteristic
2C2×#15689228C211yesmaximal, characteristic, complemented
3C2×C4×#10625335C211yesmaximal, characteristic, complemented
4#20246070C211yesmaximal, characteristic, complemented
5#20243729C211yesmaximal, characteristic, complemented
6#20243722C211yesmaximal, characteristic, complemented
7#20243695C211yesmaximal, characteristic, complemented
8#20243656C211yesmaximal, characteristic, complemented
9#20243649C211yesmaximal, characteristic, complemented
10#20243581C211yesmaximal, characteristic, complemented
11#20243328C211yesmaximal, characteristic
12#20243213C211yesmaximal, characteristic, complemented
13C4×#13093948C211yesmaximal, characteristic, complemented
14#20243154C211yesmaximal, characteristic, complemented
15C2×C47×#520C211yesmaximal, characteristic
16C22×#10625337C2211yescharacteristic
17C22×#10625335C2211yescharacteristic
18C2×#13094003C2211yescharacteristic
19C2×C4×Dic94C2211yescharacteristic
20#15689285C418yescomplemented
21#15689228—24no—
22C4×#10625335—24no—
23C2×#13093955C2211yescharacteristic
24C2×#13093955C2211yescharacteristic
25C2×#13093948C2211yescharacteristic
26C2×#13093948C2211yescharacteristic
27C2×#13093948C2211yescharacteristic
28C2×#13093947C2211yescharacteristic
29C2×#13093947C2211yescharacteristic
30C2×#13093945C2211yescharacteristic
31C2×#13093945C2211yescharacteristic
32C2×#13093945C2211yescharacteristic
33C2×C22⋊(C47⋊C8)C2211yescharacteristic
34C2×C22⋊(C47⋊C8)C2211yescharacteristic
35C2×#13093935C2211yescharacteristic
36C2×C4×C47⋊C8C2211yescharacteristic
37#15689029C2211yescharacteristic
38#15689021C2211yescharacteristic
39#15689018—21no—
40#15689017—21no—
41#15689011—21no—
42#15689004—21no—
43#15688983C2211yescharacteristic
44C4×C4⋊Dic47C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688878C2211yescharacteristic
50#15688878C2211yescharacteristic
51C22×#41×C47C2211yescharacteristic
52C47×#520—24no—
53C47×#520—24no—
54C2×C4×Q8×C47C2211yescharacteristic
55C2×C4×Q8×C47C2211yescharacteristic
56C2×C4×D4×C47—21no—
57C2×C4×D4×C47—21no—
58C2×C4×D4×C47C2211yescharacteristic
59C2×C4×D4×C47C2211yescharacteristic
60C2×#117×C47—21no—
61C2×#117×C47C2211yescharacteristic
62C22×C4⋊C4×C47—21no—
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×Dic94C2311yescharacteristic
65C2×#10625337—22no—
66C2×#10625337—22no—
67C2×#10625337C2×C414yescomplemented
68C2×#10625335—22no—
69C2×#10625335—22no—
70C2×#10625335C2×C414yescomplemented
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75#13094003—22no—
76#13094003C2×C414yescomplemented
77C4×Dic94—22no—
78C4×Dic94—22no—
79C2×C4⋊Dic47C2311yescharacteristic
80C2×C4⋊Dic47C2311yescharacteristic
81C2×C4⋊Dic47C2311yescharacteristic
82C2×Dic47⋊C4—21no—
83C2×Dic47⋊C4—21no—
84C2×Dic47⋊C4—21no—
85C2×C22⋊Dic47—21no—
86C2×C22⋊Dic47—21no—
87C2×C4×Dic47—21no—
88C2×C4×Dic47—21no—
89#13093955—22no—
90#13093955—22no—
91#13093948—22no—
92#13093948—22no—
93#13093948C2×C414yescomplemented
94#13093947—22no—
95#13093947—22no—
96#13093945—22no—
97#13093945—22no—
98#13093945C2×C414yescomplemented
99C22⋊(C47⋊C8)—22no—
100C22⋊(C47⋊C8)C2×C414yescomplemented
101#13093935—22no—
102C4×C47⋊C8—22no—
103C47⋊#95—21no—
104C47⋊#95—21no—
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C2×#41×C47—22no—
109C2×#41×C47—22no—
110C2×#41×C47—22no—
111C2×#41×C47—22no—
112C2×#41×C47—22no—
113C2×#41×C47C2×C414yes—
114C22×Q8×C47C2311yescharacteristic
115C22×D4×C47—21no—
116C22×D4×C47C2311yescharacteristic
117C23×C4×C47—21no—
118C23×C4×C47—21no—
119C23×C4×C47—21no—
120C23×C4×C47—21no—
121C23×C4×C47C2311yescharacteristic
122C4×Q8×C47—22no—
123C4×Q8×C47—22no—
124C4×Q8×C47—22no—
125C4×Q8×C47D414yes—
126C4×D4×C47—28no—
127C4×D4×C47—28no—
128C4×D4×C47—22no—
129C4×D4×C47—22no—
130C4×D4×C47—22no—
131C4×D4×C47D414yes—
132#117×C47—28no—
133#117×C47—22no—
134#117×C47—22no—
135C2×C4⋊C4×C47—28no—
136C2×C4⋊C4×C47—21no—
137C2×C4⋊C4×C47—21no—
138C2×C4⋊C4×C47—21no—
139C2×C4⋊C4×C47—22no—
140C2×C4⋊C4×C47—22no—
141C2×C4⋊C4×C47D411yescharacteristic
142C2×C4⋊C4×C47D411yescharacteristic
143C2×C4⋊C4×C47C2311yescharacteristic
144C2×C4⋊C4×C47C2311yescharacteristic
145C2×C22⋊C4×C47—21no—
146C2×C22⋊C4×C47—21no—
147C2×C22⋊C4×C47D411yescharacteristic
148C2×C22⋊C4×C47D411yescharacteristic
149C2×C42×C47—21no—
150C2×C42×C47—21no—
151C2×C42×C47C2311yescharacteristic
152C2×C42×C47C2311yescharacteristic
153C24×C47—21no—
154C24×C47C2×D411yescharacteristic
155#41×C47—28no—
156#41×C47—28no—
157#41×C47—28no—
158#41×C47—28no—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47—21no—
162C2×Q8×C47C22×C412yes—
163C2×Q8×C47C2×D412yes—
164C2×Q8×C47#4112yes—
165C2×D4×C47—24no—
166C2×D4×C47—24no—
167C2×D4×C47—24no—
168C2×D4×C47—21no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47C22×C412yes—
172C2×D4×C47C2×D412yes—
173C2×D4×C47#4112yes—
174C22×C4×C47—24no—
175C22×C4×C47—24no—
176C22×C4×C47—21no—
177C22×C4×C47—24no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—24no—
185C22×C4×C47—24no—
186C22×C4×C47—24no—
187C22×C4×C47—81no—
188C22×C4×C47—81no—
189C22×C4×C47—81no—
190C22×C4×C47—81no—
191C22×C4×C47—81no—
192C22×C4×C47—81no—
193C22×C4×C47C22×C412yes—
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47#4112yes—
200C22×C4×C47C2411yescharacteristic
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C2×Dic94—21no—
206C2×Dic94—21no—
207C2×Dic94—21no—
208C2×Dic94—21no—
209C2×Dic94—21no—
210C2×Dic94C22×C412yes—
211C4⋊C4×C47—24no—
212C4⋊C4×C47—24no—
213C4⋊C4×C47—22no—
214C4⋊C4×C47—24no—
215C4⋊C4×C47—22no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47C2×D412yes—
219C4⋊C4×C47C2×D412yes—
220C22⋊C4×C47—24no—
221C22⋊C4×C47—24no—
222C22⋊C4×C47—22no—
223C22⋊C4×C47—22no—
224C42×C47—24no—
225C42×C47—24no—
226C42×C47—21no—
227C42×C47—21no—
228C42×C47C2×D412yes—
229C42×C47C2×D412yes—
230C22⋊Dic47—24no—
231C22⋊Dic47—81no—
232#10625337—28no—
233#10625335—28no—
234C4⋊Dic47—21no—
235C4⋊Dic47—21no—
236C4⋊Dic47—21no—
237C4⋊Dic47—21no—
238C4⋊Dic47—21no—
239C4⋊Dic47C22×C412yes—
240Dic47⋊C4—24no—
241Dic47⋊C4—42no—
242Dic47⋊C4—81no—
243C4×Dic47—42no—
244C4×Dic47—81no—
245C2×C47⋊C8—21no—
246C2×C47⋊C8—21no—
247C2×C47⋊C8—21no—
248C2×C47⋊C8—21no—
249C2×C47⋊C8—21no—
250C2×C47⋊C8—21no—
251C2×C47⋊C8—21no—
252C2×C47⋊C8—21no—
253C2×C47⋊C8—21no—
254C2×C47⋊C8—21no—
255C2×C47⋊C8C22×C412yes—
256C2×C47⋊C8C22×C412yes—
257C23×C47—22no—
258C23×C47—21no—
259C23×C47—22no—
260C23×C47—21no—
261C23×C47—22no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47C4×D412yes—
271C23×C47C22×D411yescharacteristic
272Q8×C47—22no—
273Q8×C47—22no—
274Q8×C47—22no—
275Q8×C47C4×D414yes—
276D4×C47—216no—
277D4×C47—22no—
278D4×C47—22no—
279D4×C47—22no—
280D4×C47C4×D414yes—
281C2×C4×C47—216no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—22no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—84no—
308C2×C4×C47—84no—
309C2×C4×C47—84no—
310C2×C4×C47C4×D412yes—
311C2×C4×C47#12012yes—
312C2×C4×C47#12012yes—
313C2×C4×C47C23×C411yescharacteristic
314C2×C4×C47C22×D411yescharacteristic
315C2×C4×C47C22×D411yescharacteristic
316C2×C4×C47C2×#4111yescharacteristic
317C2×C4×C47C2×#4111yescharacteristic
318C2×C4×C47C2×#4111yescharacteristic
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323C2×Dic47—41no—
324C2×Dic47—41no—
325C2×Dic47—41no—
326C2×Dic47—41no—
327C2×Dic47—41no—
328C2×Dic47—41no—
329C2×Dic47—41no—
330C2×Dic47—41no—
331Dic94—22no—
332Dic94—22no—
333Dic94—41no—
334Dic94—41no—
335C47⋊C8—22no—
336C47⋊C8—22no—
337C47⋊C8—41no—
338C47⋊C8—41no—
339#21461—471nomaximal, Sylow
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—24no—
344C22×C47—41no—
345C22×C47—42no—
346C22×C47—41no—
347C22×C47—42no—
348C22×C47—42no—
349C22×C47—42no—
350C22×C47—41no—
351C22×C47—42no—
352C22×C47—41no—
353C22×C47—42no—
354C22×C47C2×C4×D411yescharacteristic
355C22×C47C2×#12011yescharacteristic
356C22×C47#52511yescharacteristic
357C22×C47#57711yescharacteristic
358C22×C47#57711yescharacteristic
359C22×C47#57711yescharacteristic
360C22×C47#57811yescharacteristic
361C4×C47—22no—
362C4×C47—22no—
363C4×C47—22no—
364C4×C47—24no—
365C4×C47—41no—
366C4×C47—42no—
367C4×C47—42no—
368C4×C47—41no—
369C4×C47C2×C4×D411yescharacteristic
370C4×C47C2×C4×D411yescharacteristic
371C4×C47#52511yescharacteristic
372C4×C47#52511yescharacteristic
373Dic47—42no—
374Dic47—42no—
375Dic47—81no—
376Dic47—81no—
377C2×#520D4711yescharacteristic
378C2×#452—471no—
379C2×#441—471no—
380C2×C4×SD16—471no—
381#2323—471no—
382#1878—471no—
383#1877—471no—
384#1872—471no—
385#1865—471no—
386#1864—471no—
387#1853—471no—
388#1788—471no—
389#1762—471no—
390C4×#103—471no—
391#1750—471no—
392C2×C47—42no—
393C2×C47—44no—
394C2×C47C4×#12011yescharacteristic
395C2×C47#294711yescharacteristic
396C2×C47#295211yescharacteristic
397C2×C47#300911yescharacteristic
398C2×C47#301311yescharacteristic
399C2×C47#312011yescharacteristic
400C2×C47#312511yescharacteristic
401C22×#41C2×D4711yescharacteristic
402C22×Q16—471no—
403C22×SD16—471no—
404C2×C22⋊Q8—471no—
405#520—24no—
406#520—24no—
407C2×C4×Q8—471no—
408C2×C4×Q8C2×D4711yescharacteristic
409C2×C4×Q8C2×D4711yescharacteristic
410C2×C4×D4—21no—
411C2×C4×D4—21no—
412C2×C4×D4C2×D4711yescharacteristic
413C2×C4×D4C2×D4711yescharacteristic
414C2×#117—21no—
415C2×#117C2×D4711yescharacteristic
416C22×C4⋊C4—21no—
417C22×C4⋊C4C2×D4711yescharacteristic
418#452—478no—
419#441—944no—
420C4×SD16—944no—
421C2×#106—471no—
422C2×#106—471no—
423C2×#103—471no—
424C2×#103—471no—
425C2×#103—471no—
426C2×#103—471no—
427C2×#103—471no—
428C2×#102—471no—
429C2×#102—471no—
430C2×#102—471no—
431C2×C22⋊C8—471no—
432C2×C22⋊C8—471no—
433C2×#97—471no—
434C2×C4×C8—471no—
435#391—471no—
436#389—471no—
437#389—941no—
438#388—941no—
439#388—941no—
440#387—941no—
441#380—471no—
442C4×C4⋊C4—471no—
443#340—471no—
444#340—471no—
445#340—471no—
446#340—471no—
447#336—471no—
448#336—471no—
449C47#2146111yescharacteristic, complemented, Sylow
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—22no—
455C2×#41C4×D4714yes—
456C22×Q8—471no—
457C22×Q8C22×D4711yescharacteristic
458C22×D4—21no—
459C22×D4C22×D4711yescharacteristic
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—21no—
463C23×C4—21no—
464C23×C4C22×D4711yescharacteristic
465C2×Q16—474no—
466C2×Q16—942no—
467C2×Q16—942no—
468C2×SD16—474no—
469C2×SD16—942no—
470C2×SD16—942no—
471C22×C8—471no—
472C22×C8—471no—
473C22×C8—471no—
474C22×C8—471no—
475C22⋊Q8—474no—
476C22⋊Q8—942no—
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—942no—
481C4×Q8—942no—
482C4×Q8C22⋊D4714yes—
483C4×D4—28no—
484C4×D4—28no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4C22⋊D4714yes—
489#117—28no—
490#117—22no—
491#117—22no—
492C2×C4⋊C4—28no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—471no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4C22⋊D4711yescharacteristic
505C2×C4⋊C4C22⋊D4711yescharacteristic
506C2×C4⋊C4C22×D4711yescharacteristic
507C2×C4⋊C4C22×D4711yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—941no—
511C2×C22⋊C4—941no—
512C2×C22⋊C4C22⋊D4711yescharacteristic
513C2×C22⋊C4C22⋊D4711yescharacteristic
514C2×C42—21no—
515C2×C42—21no—
516C2×C42—941no—
517C2×C42—941no—
518C2×C42C22×D4711yescharacteristic
519C2×C42C22×D4711yescharacteristic
520#106—942no—
521#106—942no—
522#103—474no—
523#103—942no—
524#103—942no—
525#103—942no—
526#103—942no—
527#102—474no—
528#102—942no—
529#102—942no—
530C22⋊C8—474no—
531C22⋊C8—942no—
532#97—942no—
533C4×C8—942no—
534#95—941no—
535#95—941no—
536#95—941no—
537#95—941no—
538#95—941no—
539C24—21no—
540C24C2×C22⋊D4711yescharacteristic
541#41—28no—
542#41—28no—
543#41—28no—
544#41—28no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—472no—
549C2×Q8—941no—
550C2×Q8—941no—
551C2×Q8—941no—
552C2×Q8—941no—
553C2×Q8—941no—
554C2×Q8C2×C4×D4712yes—
555C2×Q8#1062535012yes—
556C2×Q8C2×C22⋊D4712yes—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4C2×C4×D4712yes—
564C2×D4#1062535012yes—
565C2×D4C2×C22⋊D4712yes—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4—941no—
586C22×C4—941no—
587C22×C4—941no—
588C22×C4—941no—
589C22×C4C2×C4×D4712yes—
590C22×C4#1062535012yes—
591C22×C4C2×C22⋊D4711yescharacteristic
592C22×C4C2×C22⋊D4711yescharacteristic
593C22×C4C2×C22⋊D4711yescharacteristic
594C22×C4C2×C22⋊D4711yescharacteristic
595C22×C4C2×C22⋊D4711yescharacteristic
596C22×C4C23×D4711yescharacteristic
597Q16—948no—
598SD16—948no—
599C2×C8—472no—
600C2×C8—472no—
601C2×C8—941no—
602C2×C8—941no—
603C2×C8—941no—
604C2×C8—941no—
605C2×C8—941no—
606C2×C8—941no—
607C2×C8—941no—
608C2×C8—941no—
609C2×C8—941no—
610C2×C8—941no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—24no—
615C4⋊C4—22no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—472no—
619C4⋊C4—944no—
620C4⋊C4—941no—
621C4⋊C4—941no—
622C4⋊C4—941no—
623C4⋊C4—941no—
624C4⋊C4—941no—
625C4⋊C4—3761no—
626C4⋊C4—1882no—
627C4⋊C4C2×C22⋊D4712yes—
628C4⋊C4C2×C22⋊D4712yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—944no—
634C22⋊C4—3761no—
635C42—24no—
636C42—24no—
637C42—21no—
638C42—21no—
639C42—3761no—
640C42—1882no—
641C42C2×C22⋊D4712yes—
642C42C2×C22⋊D4712yes—
643C23—22no—
644C23—21no—
645C23—22no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23C4×C22⋊D4712yes—
657C23C22×C22⋊D4711yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—942no—
662Q8—942no—
663Q8—1881no—
664Q8—1881no—
665Q8C4×C22⋊D4714yes—
666D4—216no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4C4×C22⋊D4714yes—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4—84no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—1881no—
703C2×C4—1881no—
704C2×C4—1881no—
705C2×C4—1881no—
706C2×C4—1881no—
707C2×C4—1881no—
708C2×C4—1881no—
709C2×C4—1881no—
710C2×C4—1881no—
711C2×C4—1881no—
712C2×C4C4×C22⋊D4712yes—
713C2×C4#1309399312yes—
714C2×C4#1309399312yes—
715C2×C4C22×C4×D4711yescharacteristic
716C2×C4C22×C22⋊D4711yescharacteristic
717C2×C4C22×C22⋊D4711yescharacteristic
718C2×C4C2×#1062535011yescharacteristic
719C2×C4C2×#1062535011yescharacteristic
720C2×C4C2×#1062535011yescharacteristic
721C8—942no—
722C8—942no—
723C8—1881no—
724C8—1881no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—24no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—41no—
734C22—42no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—42no—
739C22C2×C4×C22⋊D4711yescharacteristic
740C22C2×#1309399311yescharacteristic
741C22#1568963411yescharacteristic
742C22#1568993111yescharacteristic
743C22#1568993411yescharacteristic
744C22#1568993411yescharacteristic
745C22#1568993811yescharacteristic
746C4—22no—
747C4—22no—
748C4—24no—
749C4—22no—
750C4—41no—
751C4—41no—
752C4—42no—
753C4—42no—
754C4—3761no—
755C4—3761no—
756C4—1882no—
757C4—1882no—
758C4C2×C4×C22⋊D4711yescharacteristic
759C4C2×C4×C22⋊D4711yescharacteristic
760C4#1568963411yescharacteristic
761C4#1568963411yescharacteristic
762C2—42no—
763C2—44no—
764C2C4×#1309399311yescharacteristic
765C2#2025222711yescharacteristic
766C2#2025226911yescharacteristic
767C2#2025266511yescharacteristic
768C2#2025270311yescharacteristic
769C2#2025360211yescharacteristic
770C2#2025366511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#520C2
socleC23×C47C22×D4
prime radicalC22×#41×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#520D47
hypocenterC47#21461
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. C2×#15689228C2semidirect
3. C2×C4×#10625335C2semidirect
4. #20246070C2semidirect
5. #20243729C2semidirect
6. #20243722C2semidirect
7. #20243695C2semidirect
8. #20243656C2semidirect
9. #20243649C2semidirect
10. #20243581C2semidirect
12. #20243213C2semidirect
13. C4×#13093948C2semidirect
14. #20243154C2semidirect
20. #15689285C4semidirect
67. C2×#10625337C2×C4semidirect
70. C2×#10625335C2×C4semidirect
76. #13094003C2×C4semidirect
93. #13093948C2×C4semidirect
98. #13093945C2×C4semidirect
100. C22⋊(C47⋊C8)C2×C4semidirect
449. C47#21461semidirect

Maximal subgroups

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

subgroupindex
C2×#156892852
C2×#156892282
C2×C4×#106253352
#202460702
#202437292
#202437222
#202436952
#202436562
#202436492
#202435812
#202433282
#202432132
C4×#130939482
#202431542
C2×C47×#5202
#2146147