Finite Group Databasebeta

← #26121796

Subgroups — #26121796

Order 12032.

1350 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689603C211yesmaximal, characteristic
2C22×#13093950C211yesmaximal, characteristic
3C2×#15689122C211yesmaximal, characteristic
4C2×#15688891C211yesmaximal, characteristic, complemented
5C2×#15688882C211yesmaximal, characteristic, complemented
6#20241617C211yesmaximal, characteristic, complemented
7C47×#1736C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10#15689603—22no—
11#15689603—22no—
12#15689603—22no—
13#15689603C414yescomplemented
14C2×C4×Dic94—21no—
15C2×C4×D188—21no—
16C2×(C22⋊D47)⋊C4—22no—
17C2×#13093982—21no—
18C22×C4⋊Dic47C2211yescharacteristic
19C2×C4⋊C4×D47—21no—
20C22×C4×Dic47C2211yescharacteristic
21C2×#13093950—22no—
22C2×#13093950—22no—
23C2×#13093950C414yescomplemented
24#15689122—22no—
25#15689122C414yescomplemented
26C2×#13093947—21no—
27C2×#13093944—21no—
28C2×C47⋊#95—22no—
29#15688891—22no—
30#15688882—22no—
31C22×M16×C47C2211yescharacteristic
32C2×#117×C47C2211yescharacteristic
33C22×C4⋊C4×C47C2211yescharacteristic
34C47×#340—21no—
35C47×#340—21no—
36C2×#10625350—21no—
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350—21no—
42C2×#10625350C2×C412yes—
43C2×#10625350C2×C412yes—
44C2×#10625350C2×C412yes—
45C2×#10625350D412yes—
46C2×#10625350D412yes—
47C2×#10625350Q812yes—
48C22×Dic94D411yescharacteristic
49C22×D188D411yescharacteristic
50C22×C22⋊D47—21no—
51C23×Dic47—21no—
52C23×Dic47D412yes—
53C22×C4×D47—21no—
54C22×C4×D47—22no—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329—21no—
60C2×#10625329C2×C412yescomplemented
61C22×C47⋊C8—21no—
62C4×Dic94—24no—
63C4×Dic94—24no—
64C4×D188—24no—
65C4×D188—24no—
66(C22⋊D47)⋊C4—28no—
67(C22⋊D47)⋊C4—28no—
68#13093982—24no—
69#13093982—24no—
70C2×C4⋊Dic47—21no—
71C2×C4⋊Dic47—21no—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47C2×C412yes—
75C2×C4⋊Dic47D412yes—
76C2×Dic47⋊C4—22no—
77C4⋊C4×D47—24no—
78C4⋊C4×D47—24no—
79C2×(C2×D47)⋊C4—22no—
80C2×C4×Dic47—22no—
81C2×C4×Dic47—21no—
82C2×C4×Dic47—21no—
83C2×C4×Dic47—21no—
84C2×C4×Dic47—21no—
85C2×C4×Dic47—21no—
86C2×C4×Dic47C2×C412yescomplemented
87#13093950—28no—
88#13093947—24no—
89#13093944—24no—
90C47⋊#95—44no—
91C23×C4×C47—21no—
92C23×C4×C47C2311yescharacteristic
93C2×M16×C47—21no—
94C2×M16×C47—21no—
95C2×M16×C47—21no—
96C2×M16×C47—21no—
97C2×M16×C47—21no—
98C2×M16×C47C2×C412yescomplemented
99C22×C8×C47—21no—
100#117×C47—21no—
101#117×C47—21no—
102#117×C47C2×C412yes—
103#117×C47D412yes—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47C2×C412yescomplemented
110C2×C4⋊C4×C47D411yescharacteristic
111C2×C4⋊C4×C47D411yescharacteristic
112C2×C22⋊C4×C47—21no—
113C2×C42×C47—21no—
114C24×C47C2×D411yescharacteristic
115C23×D47—21no—
116C22×C4×C47—21no—
117C22×C4×C47—21no—
118C22×C4×C47—22no—
119C22×C4×C47—42no—
120C22×C4×C47—42no—
121C22×C4×C47—41no—
122C22×C4×C47—41no—
123C22×C4×C47C22×C411yescharacteristic
124C22×C4×C47C22×C411yescharacteristic
125C22×C4×C47C22×C411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×Q811yescharacteristic
133C22×C4×C47#4111yescharacteristic
134C22×C4×C47#4111yescharacteristic
135C22×C4×C47#4111yescharacteristic
136C22×C4×C47#4111yescharacteristic
137C2×C22⋊D47—22no—
138C2×C22⋊D47—22no—
139C2×C22⋊D47—22no—
140C2×C22⋊D47—22no—
141C2×C22⋊D47—22no—
142C2×C22⋊D47—22no—
143C22×Dic47—21no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—22no—
148C22×Dic47—22no—
149C22×Dic47—41no—
150C22×Dic47—41no—
151C22×Dic47—41no—
152C22×Dic47—41no—
153C22×Dic47—42no—
154C22×Dic47—42no—
155C22×Dic47C22⋊C414yes—
156#10625350—22no—
157#10625350—22no—
158#10625350—22no—
159#10625350—22no—
160#10625350—22no—
161#10625350—22no—
162#10625350—22no—
163#10625350—22no—
164#10625350—22no—
165#10625350—22no—
166#10625350—22no—
167#10625350—22no—
168#10625350C4214yes—
169#10625350C22⋊C414yes—
170#10625350C4⋊C414yes—
171#10625350C4⋊C414yes—
172C2×D188—21no—
173C2×D188—21no—
174C2×D188—21no—
175C2×D188C22⋊C412yes—
176C2×D188C22⋊C412yes—
177C2×D188C4⋊C412yes—
178C2×C4×D47—22no—
179C2×C4×D47—22no—
180C2×C4×D47—22no—
181C2×C4×D47—22no—
182C2×C4×D47—22no—
183C2×C4×D47—22no—
184C2×C4×D47—28no—
185C2×C4×D47—82no—
186C2×C4×D47—82no—
187C2×Dic94—21no—
188C2×Dic94—21no—
189C2×Dic94—21no—
190C2×Dic94C22⋊C412yes—
191C2×Dic94C22⋊C412yes—
192C2×Dic94C4⋊C412yes—
193M16×C47—22no—
194M16×C47—22no—
195M16×C47—41no—
196M16×C47—41no—
197C2×C8×C47—22no—
198C2×C8×C47—41no—
199C2×C8×C47—41no—
200C4⋊C4×C47—21no—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—22no—
203C4⋊C4×C47—22no—
204C4⋊C4×C47—41no—
205C4⋊C4×C47—41no—
206C4⋊C4×C47C22⋊C412yes—
207C4⋊C4×C47C22⋊C412yes—
208C22⋊C4×C47—22no—
209C22⋊C4×C47—22no—
210C42×C47—22no—
211C42×C47—22no—
212(C2×D47)⋊C4—28no—
213C4⋊Dic47—22no—
214C4⋊Dic47—22no—
215C4⋊Dic47—22no—
216C4⋊Dic47—22no—
217Dic47⋊C4—28no—
218C4×Dic47—28no—
219C4×Dic47—22no—
220C4×Dic47—22no—
221C4×Dic47—41no—
222C4×Dic47—41no—
223#10625329—22no—
224#10625329—22no—
225#10625329—41no—
226#10625329—41no—
227C2×C47⋊C8—22no—
228C2×C47⋊C8—41no—
229C2×C47⋊C8—41no—
230C23×C47—21no—
231C23×C47—21no—
232C23×C47—21no—
233C23×C47—21no—
234C23×C47C2×C22⋊C411yescharacteristic
235C23×C47C4×D411yescharacteristic
236C23×C47C4×D411yescharacteristic
237C23×C47#12011yescharacteristic
238C23×C47#12011yescharacteristic
239C23×C47#12111yescharacteristic
240C23×C47C22⋊Q811yescharacteristic
241C22×D47—22no—
242C22×D47—22no—
243C22×D47—22no—
244C22×D47—41no—
245C22×D47—41no—
246C22×D47—41no—
247C22×D47—41no—
248C2×C4×C47—22no—
249C2×C4×C47—22no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—41no—
253C2×C4×C47—41no—
254C2×C4×C47—44no—
255C2×C4×C47—42no—
256C2×C4×C47—82no—
257C2×C4×C47—81no—
258C2×C4×C47—81no—
259C2×C4×C47C2×C4211yescharacteristic
260C2×C4×C47C2×C22⋊C411yescharacteristic
261C2×C4×C47C2×C22⋊C411yescharacteristic
262C2×C4×C47C2×C22⋊C411yescharacteristic
263C2×C4×C47C2×C22⋊C411yescharacteristic
264C2×C4×C47C2×C4⋊C411yescharacteristic
265C2×C4×C47C2×C4⋊C411yescharacteristic
266C2×C4×C47C2×C4⋊C411yescharacteristic
267C2×C4×C47#11711yescharacteristic
268C2×C4×C47#11711yescharacteristic
269C2×C4×C47C4×D411yescharacteristic
270C2×C4×C47C4×D411yescharacteristic
271C2×C4×C47C4×D411yescharacteristic
272C2×C4×C47C4×D411yescharacteristic
273C2×C4×C47C4×D411yescharacteristic
274C2×C4×C47C4×D411yescharacteristic
275C2×C4×C47#12011yescharacteristic
276C2×C4×C47#12011yescharacteristic
277C2×C4×C47#12111yescharacteristic
278C2×C4×C47#12111yescharacteristic
279C2×C4×C47#12111yescharacteristic
280C2×C4×C47C22⋊Q811yescharacteristic
281C2×C4×C47C22⋊Q811yescharacteristic
282C2×C4×C47C22⋊Q811yescharacteristic
283C2×C4×C47#12311yescharacteristic
284C2×C4×C47#12311yescharacteristic
285C2×C4×C47#12311yescharacteristic
286C2×C4×C47#12311yescharacteristic
287C22⋊D47—24no—
288C22⋊D47—24no—
289C22⋊D47—24no—
290C22⋊D47—24no—
291C2×Dic47—22no—
292C2×Dic47—22no—
293C2×Dic47—22no—
294C2×Dic47—24no—
295C2×Dic47—24no—
296C2×Dic47—42no—
297C2×Dic47—42no—
298C2×Dic47—42no—
299C2×Dic47—42no—
300C2×Dic47—42no—
301C2×Dic47—42no—
302C2×Dic47—42no—
303C2×Dic47—42no—
304C2×Dic47—44no—
305C2×Dic47—82no—
306D188—22no—
307D188—22no—
308D188—22no—
309D188#9514yescomplemented
310C4×D47—24no—
311C4×D47—24no—
312C4×D47—24no—
313C4×D47—24no—
314C4×D47—88no—
315Dic94—22no—
316Dic94—22no—
317Dic94—22no—
318Dic94#9514yescomplemented
319C8×C47—42no—
320C47⋊C8—42no—
321#10781—471nomaximal, Sylow
322C22×C47—21no—
323C22×C47—21no—
324C22×C47—21no—
325C22×C47—21no—
326C22×C47—21no—
327C22×C47—21no—
328C22×C47—21no—
329C22×C47—21no—
330C22×C47—21no—
331C22×C47—21no—
332C22×C47—21no—
333C22×C47—21no—
334C22×C47C4×C22⋊C411yescharacteristic
335C22×C47#37911yescharacteristic
336C22×C47#38011yescharacteristic
337C22×C47#38511yescharacteristic
338C22×C47#38511yescharacteristic
339C22×C47#38611yescharacteristic
340C22×C47#38611yescharacteristic
341C22×C47#45311yescharacteristic
342C22×C47#45411yescharacteristic
343C22×C47#45511yescharacteristic
344C22×C47#45611yescharacteristic
345C2×D47—24no—
346C2×D47—42no—
347C2×D47—42no—
348C2×D47—42no—
349C2×D47—42no—
350C2×D47—42no—
351C2×D47—42no—
352C4×C47—42no—
353C4×C47—42no—
354C4×C47—82no—
355C4×C47C2×#9511yescharacteristic
356C4×C47C4×C22⋊C411yescharacteristic
357C4×C47#38011yescharacteristic
358C4×C47#38111yescharacteristic
359C4×C47#38511yescharacteristic
360C4×C47#38511yescharacteristic
361C4×C47#38611yescharacteristic
362C4×C47#38611yescharacteristic
363Dic47—24no—
364Dic47—44no—
365Dic47—44no—
366C2×#520—471no—
367C22×#104—471no—
368C2×#417—471no—
369C2×#343—471no—
370#1736D4711yescharacteristic, complemented
371C2×#339—471no—
372C4⋊#95—471no—
373C2×C47—21no—
374C2×C47—21no—
375C2×C47—21no—
376C2×C47—21no—
377C2×C47C22⋊#9511yescharacteristic
378C2×C47#179211yescharacteristic
379C2×C47#179311yescharacteristic
380C2×C47#185911yescharacteristic
381C2×C47#186011yescharacteristic
382C2×C47#188211yescharacteristic
383C2×C47#188311yescharacteristic
384D47—44no—
385C22×#41—471no—
386C22×M16—471no—
387C22×M16C2×D4711yescharacteristic
388#520—474no—
389#520—942no—
390#520—942no—
391#520—942no—
392C2×C4×Q8—941no—
393C2×C4×D4—941no—
394C2×C4×D4—942no—
395C2×#117—941no—
396C2×#117C2×D4711yescharacteristic
397C22×C4⋊C4—471no—
398C22×C4⋊C4—941no—
399C22×C4⋊C4C2×D4711yescharacteristic
400C22×C42—471no—
401C2×#104—474no—
402C2×#104—942no—
403C2×#104—942no—
404#417—474no—
405#417—942no—
406C2×#103—941no—
407C2×#102—941no—
408C2×#95—942no—
409#343—942no—
410#340—21no—
411#340—21no—
412#339—942no—
413C47#1078111yescharacteristic, complemented, Sylow
414C2×#41—472no—
415C2×#41—472no—
416C2×#41—472no—
417C2×#41—472no—
418C2×#41—472no—
419C2×#41—472no—
420C2×#41—941no—
421C2×#41—941no—
422C2×#41—941no—
423C2×#41—941no—
424C2×#41—941no—
425C2×#41—941no—
426C22×Q8—471no—
427C22×D4—471no—
428C22×D4—941no—
429C23×C4—21no—
430C23×C4—472no—
431C23×C4—942no—
432C23×C4—941no—
433C23×C4—941no—
434C23×C4C22×D4711yescharacteristic
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—21no—
438C2×M16—21no—
439C2×M16—21no—
440C2×M16—472no—
441C2×M16—941no—
442C2×M16—941no—
443C2×M16—941no—
444C2×M16—941no—
445C2×M16—941no—
446C2×M16C4×D4712yescomplemented
447C22×C8—21no—
448C22×C8—941no—
449C4×Q8—944no—
450C4×Q8—944no—
451C4×D4—944no—
452C4×D4—944no—
453C4×D4—948no—
454C4×D4—948no—
455#117—21no—
456#117—21no—
457#117—944no—
458#117—944no—
459#117C4×D4712yes—
460#117D18812yes—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—472no—
467C2×C4⋊C4—472no—
468C2×C4⋊C4—944no—
469C2×C4⋊C4—942no—
470C2×C4⋊C4—941no—
471C2×C4⋊C4—941no—
472C2×C4⋊C4—941no—
473C2×C4⋊C4—941no—
474C2×C4⋊C4—944no—
475C2×C4⋊C4C4×D4712yescomplemented
476C2×C4⋊C4C22⋊D4711yescharacteristic
477C2×C4⋊C4C22⋊D4711yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—942no—
480C2×C42—21no—
481C2×C42—472no—
482C2×C42—942no—
483C2×C42—941no—
484C2×C42—941no—
485C2×C42—941no—
486C2×C42—941no—
487C2×C42—941no—
488#104—948no—
489#103—944no—
490#102—944no—
491#95—1884no—
492C24—941no—
493C24D4×D4711yescharacteristic
494#41—474no—
495#41—474no—
496#41—474no—
497#41—474no—
498#41—942no—
499#41—942no—
500#41—942no—
501#41—942no—
502#41—942no—
503#41—942no—
504#41—942no—
505#41—942no—
506#41—942no—
507#41—942no—
508#41—942no—
509#41—942no—
510C2×Q8—472no—
511C2×Q8—472no—
512C2×Q8—472no—
513C2×Q8—941no—
514C2×Q8—941no—
515C2×Q8—941no—
516C2×D4—472no—
517C2×D4—472no—
518C2×D4—472no—
519C2×D4—942no—
520C2×D4—942no—
521C2×D4—942no—
522C2×D4—942no—
523C2×D4—942no—
524C2×D4—942no—
525C2×D4—941no—
526C2×D4—941no—
527C2×D4—941no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—474no—
536C22×C4—948no—
537C22×C4—941no—
538C22×C4—942no—
539C22×C4—942no—
540C22×C4—942no—
541C22×C4—942no—
542C22×C4—942no—
543C22×C4—942no—
544C22×C4—942no—
545C22×C4—942no—
546C22×C4—942no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—3762no—
550C22×C4—3762no—
551C22×C4—1882no—
552C22×C4—1882no—
553C22×C4—1881no—
554C22×C4—1881no—
555C22×C4—1881no—
556C22×C4—1881no—
557C22×C4C2×C4×D4711yescharacteristic
558C22×C4C2×C4×D4711yescharacteristic
559C22×C4C2×C4×D4711yescharacteristic
560C22×C4C2×D18811yescharacteristic
561C22×C4#1062535011yescharacteristic
562C22×C4#1062535011yescharacteristic
563C22×C4D4×D4711yescharacteristic
564C22×C4D4×D4711yescharacteristic
565C22×C4D4×D4711yescharacteristic
566C22×C4D4×D4711yescharacteristic
567C22×C4#1062535211yescharacteristic
568C22×C4Q8×D4711yescharacteristic
569C22×C4#1062535411yescharacteristic
570C22×C4C2×C22⋊D4711yescharacteristic
571M16—22no—
572M16—22no—
573M16—41no—
574M16—41no—
575M16—942no—
576M16—942no—
577M16—1881no—
578M16—1881no—
579C2×C8—22no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—942no—
583C2×C8—1881no—
584C2×C8—1881no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—41no—
590C4⋊C4—41no—
591C4⋊C4—948no—
592C4⋊C4—942no—
593C4⋊C4—942no—
594C4⋊C4—942no—
595C4⋊C4—942no—
596C4⋊C4(C2×D47)⋊C412yes—
597C4⋊C4(C2×D47)⋊C412yes—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—948no—
601C42—22no—
602C42—22no—
603C42—948no—
604C42—942no—
605C42—942no—
606C42—1881no—
607C42—1881no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—942no—
613C23—942no—
614C23—942no—
615C23—1881no—
616C23—1881no—
617C23—1881no—
618C23—1881no—
619C23C22⋊C4×D4711yescharacteristic
620C23(C22⋊D47)⋊C411yescharacteristic
621C23#1309398611yescharacteristic
622C23#1309399211yescharacteristic
623C23#1309399411yescharacteristic
624C23#1309399711yescharacteristic
625C23#1309400211yescharacteristic
626Q8—474no—
627Q8—942no—
628Q8—942no—
629Q8—942no—
630D4—474no—
631D4—944no—
632D4—944no—
633D4—944no—
634D4—944no—
635D4—942no—
636D4—942no—
637D4—942no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—44no—
645C2×C4—42no—
646C2×C4—82no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—942no—
650C2×C4—942no—
651C2×C4—942no—
652C2×C4—944no—
653C2×C4—944no—
654C2×C4—944no—
655C2×C4—944no—
656C2×C4—944no—
657C2×C4—944no—
658C2×C4—3768no—
659C2×C4—3762no—
660C2×C4—1882no—
661C2×C4—1882no—
662C2×C4—1882no—
663C2×C4—1882no—
664C2×C4—1882no—
665C2×C4—1882no—
666C2×C4—1882no—
667C2×C4—1882no—
668C2×C4—1884no—
669C2×C4C42×D4711yescharacteristic
670C2×C4C22⋊C4×D4711yescharacteristic
671C2×C4C22⋊C4×D4711yescharacteristic
672C2×C4C22⋊C4×D4711yescharacteristic
673C2×C4C2×(C2×D47)⋊C411yescharacteristic
674C2×C4C4⋊C4×D4711yescharacteristic
675C2×C4C4⋊C4×D4711yescharacteristic
676C2×C4C4⋊C4×D4711yescharacteristic
677C2×C4#1309398111yescharacteristic
678C2×C4#1309398211yescharacteristic
679C2×C4(C22⋊D47)⋊C411yescharacteristic
680C2×C4C4×C22⋊D4711yescharacteristic
681C2×C4C4×C22⋊D4711yescharacteristic
682C2×C4#1309398611yescharacteristic
683C2×C4C4×D18811yescharacteristic
684C2×C4C4×D18811yescharacteristic
685C2×C4#1309399211yescharacteristic
686C2×C4#1309399411yescharacteristic
687C2×C4#1309399511yescharacteristic
688C2×C4#1309399711yescharacteristic
689C2×C4#1309399911yescharacteristic
690C2×C4#1309400011yescharacteristic
691C2×C4#1309400211yescharacteristic
692C2×C4#1309400411yescharacteristic
693C2×C4#1309400611yescharacteristic
694C2×C4#1309400611yescharacteristic
695C2×C4#1309400911yescharacteristic
696C2×C4#1309400911yescharacteristic
697C8—42no—
698C8—1882no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—944no—
712C22—1882no—
713C22—1882no—
714C22—1882no—
715C22—1882no—
716C22—1882no—
717C22—1882no—
718C22#1568897011yescharacteristic
719C22#1568897811yescharacteristic
720C22#1568898211yescharacteristic
721C22#1568899411yescharacteristic
722C22#1568899711yescharacteristic
723C22#1568899911yescharacteristic
724C22#1568900111yescharacteristic
725C22#1568928911yescharacteristic
726C22#1568929411yescharacteristic
727C22#1568929911yescharacteristic
728C22#1568930411yescharacteristic
729C4—42no—
730C4—42no—
731C4—82no—
732C4—944no—
733C4—1884no—
734C4—1884no—
735C4#95×D4711yescharacteristic
736C4C4×(C2×D47)⋊C411yescharacteristic
737C4#1568898011yescharacteristic
738C4#1568898511yescharacteristic
739C4#1568899411yescharacteristic
740C4#1568899711yescharacteristic
741C4#1568899911yescharacteristic
742C4#1568900111yescharacteristic
743C2—21no—
744C2—21no—
745C2—21no—
746C2—21no—
747C2—1884no—
748C2(C2×D47)⋊#9511yescharacteristic
749C2#2024334011yescharacteristic
750C2#2024334511yescharacteristic
751C2#2024361111yescharacteristic
752C2#2024361811yescharacteristic
753C2#2024375411yescharacteristic
754C2#2024376111yescharacteristic
subgroupG/H
centerC23#13093992
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC47×#1736C2
socleC23×C47#120
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenter#1736D47
hypocenterC47#10781
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. C2×#15688891C2semidirect
5. C2×#15688882C2semidirect
6. #20241617C2semidirect
7. C47×#1736C2semidirect
13. #15689603C4semidirect
23. C2×#13093950C4semidirect
25. #15689122C4semidirect
60. C2×#10625329C2×C4semidirect
86. C2×C4×Dic47C2×C4semidirect
98. C2×M16×C47C2×C4semidirect
109. C2×C4⋊C4×C47C2×C4semidirect
309. D188#95semidirect
318. Dic94#95semidirect
370. #1736D47semidirect
413. C47#10781semidirect
446. C2×M16C4×D47semidirect
475. C2×C4⋊C4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896032
C22×#130939502
C2×#156891222
C2×#156888912
C2×#156888822
#202416172
C47×#17362
#1078147