Finite Group Databasebeta

← #26121586

Subgroups — #26121586

Order 12032.

1374 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D47C211yesmaximal, characteristic
2C2×#15689086C211yesmaximal, characteristic
3C2×#15689086C211yesmaximal, characteristic
4C2×#15688895C211yesmaximal, characteristic, complemented
5C2×#15688894C211yesmaximal, characteristic, complemented
6C2×#15688893C211yesmaximal, characteristic, complemented
7C2×C47×#344C211yesmaximal, characteristic, complemented
8C23×C4×D47C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C2×#13093983C2211yescharacteristic
12C2×#13093982—21no—
13C2×#13093981—21no—
14C2×#13093980C412yes—
15#117×D47—22no—
16#117×D47—22no—
17#117×D47—22no—
18#117×D47—22no—
19C2×C4⋊C4×D47—21no—
20C2×C22⋊C4×D47C412yes—
21C2×C42×D47—21no—
22#15689086—21no—
23#15689086—21no—
24#15689086—22no—
25#15689086—21no—
26#15689086—21no—
27#15689086C414yescomplemented
28C2×(C2×D47)⋊C8—22no—
29C2×(C2×D47)⋊C8C414yescomplemented
30#15688895—22no—
31#15688894—22no—
32#15688893—22no—
33C22×M16×C47C2211yescharacteristic
34C22×M16×C47C2211yescharacteristic
35C2×#117×C47C2211yescharacteristic
36C47×#344—22no—
37C24×D47C2×C411yescharacteristic
38C23×Dic47C2×C411yescharacteristic
39C22×C4×D47—21no—
40C22×C4×D47—21no—
41C22×C4×D47—21no—
42C22×C4×D47—21no—
43C22×C4×D47—21no—
44C22×C4×D47—21no—
45C22×C4×D47—21no—
46C22×C4×D47—21no—
47C22×C4×D47—22no—
48C22×C4×D47C2×C412yes—
49C22×C4×D47C2×C412yes—
50C22×C4×D47D412yes—
51C22×C4×D47D411yescharacteristic
52C22×C4×D47D411yescharacteristic
53C22×C4×D47D411yescharacteristic
54C22×C4×D47D411yescharacteristic
55C22×C4×D47Q812yes—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329—21no—
60C2×#10625329—21no—
61C2×#10625329—21no—
62C2×#10625329—21no—
63C2×#10625329—21no—
64C2×#10625329—21no—
65C2×#10625329—21no—
66C2×#10625329—21no—
67C2×#10625329C2×C412yescomplemented
68C22×C47⋊C8—21no—
69C22×C47⋊C8C2×C412yescomplemented
70#13093983—21no—
71#13093983—21no—
72#13093983D412yes—
73#13093983D412yes—
74#13093982—24no—
75#13093982—24no—
76#13093981—24no—
77#13093981—24no—
78#13093980—24no—
79#13093980—24no—
80C2×C4⋊Dic47—21no—
81C2×Dic47⋊C4—22no—
82C4⋊C4×D47—24no—
83C4⋊C4×D47—24no—
84C2×C22⋊Dic47C2×C412yes—
85C2×(C2×D47)⋊C4—22no—
86C22⋊C4×D47—24no—
87C22⋊C4×D47—24no—
88C2×C4×Dic47—21no—
89C2×C4×Dic47—22no—
90C42×D47—24no—
91C42×D47—24no—
92(C2×D47)⋊C8—24no—
93(C2×D47)⋊C8—24no—
94(C2×D47)⋊C8—24no—
95(C2×D47)⋊C8—24no—
96C23×C4×C47C2311yescharacteristic
97C2×M16×C47—21no—
98C2×M16×C47—21no—
99C2×M16×C47—21no—
100C2×M16×C47—21no—
101C2×M16×C47—21no—
102C2×M16×C47—21no—
103C2×M16×C47—21no—
104C2×M16×C47—21no—
105C2×M16×C47—21no—
106C2×M16×C47—21no—
107C2×M16×C47—21no—
108C2×M16×C47C2×C412yescomplemented
109C22×C8×C47—21no—
110C22×C8×C47C2×C412yescomplemented
111#117×C47—21no—
112#117×C47—21no—
113#117×C47D412yes—
114#117×C47D412yes—
115C2×C4⋊C4×C47—21no—
116C2×C22⋊C4×C47C2×C412yes—
117C2×C42×C47—21no—
118C24×C47C22×C411yescharacteristic
119C23×D47—21no—
120C23×D47—21no—
121C23×D47—21no—
122C23×D47—21no—
123C23×D47—44no—
124C23×D47C4212yes—
125C23×D47C22⋊C411yescharacteristic
126C23×D47C22⋊C411yescharacteristic
127C23×D47C4⋊C412yes—
128C22×C4×C47—22no—
129C22×C4×C47C22×C411yescharacteristic
130C22×C4×C47C22×C411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2×Q811yescharacteristic
139C22×C4×C47#4111yescharacteristic
140C22×C4×C47#4111yescharacteristic
141C22×C4×C47#4111yescharacteristic
142C22×C4×C47#4111yescharacteristic
143C22×Dic47—21no—
144C22×Dic47—21no—
145C22×Dic47—21no—
146C22×Dic47—21no—
147C22×Dic47—22no—
148C22×Dic47C4212yes—
149C22×Dic47C22⋊C411yescharacteristic
150C22×Dic47C22⋊C411yescharacteristic
151C22×Dic47C4⋊C412yes—
152C2×C4×D47—22no—
153C2×C4×D47—22no—
154C2×C4×D47—22no—
155C2×C4×D47—22no—
156C2×C4×D47—22no—
157C2×C4×D47—22no—
158C2×C4×D47—22no—
159C2×C4×D47—22no—
160C2×C4×D47—21no—
161C2×C4×D47—21no—
162C2×C4×D47—21no—
163C2×C4×D47—21no—
164C2×C4×D47—21no—
165C2×C4×D47—21no—
166C2×C4×D47—21no—
167C2×C4×D47—21no—
168C2×C4×D47—22no—
169C2×C4×D47—22no—
170C2×C4×D47—22no—
171C2×C4×D47—22no—
172C2×C4×D47—22no—
173C2×C4×D47—22no—
174C2×C4×D47—22no—
175C2×C4×D47—22no—
176C2×C4×D47—21no—
177C2×C4×D47—21no—
178C2×C4×D47—21no—
179C2×C4×D47—21no—
180C2×C4×D47—21no—
181C2×C4×D47—21no—
182C2×C4×D47—21no—
183C2×C4×D47—21no—
184C2×C4×D47—28no—
185C2×C4×D47—48no—
186C2×C4×D47C22⋊C412yes—
187C2×C4×D47C22⋊C412yes—
188C2×C4×D47C22⋊C412yes—
189C2×C4×D47C22⋊C412yes—
190C2×C4×D47C4⋊C412yes—
191C2×C4×D47C4⋊C412yes—
192C2×C4×D47C4⋊C412yes—
193C2×C4×D47C4⋊C412yes—
194M16×C47—22no—
195M16×C47—22no—
196M16×C47—41no—
197M16×C47—41no—
198M16×C47—41no—
199M16×C47—41no—
200M16×C47—41no—
201M16×C47—41no—
202C2×C8×C47—22no—
203C2×C8×C47—22no—
204C2×C8×C47—22no—
205C2×C8×C47—22no—
206C2×C8×C47—41no—
207C2×C8×C47—41no—
208C4⋊C4×C47—22no—
209C4⋊C4×C47—22no—
210C22⋊C4×C47—22no—
211C22⋊C4×C47C22⋊C414yes—
212C42×C47—22no—
213C42×C47—22no—
214C22⋊Dic47—22no—
215C22⋊Dic47C22⋊C414yes—
216(C2×D47)⋊C4—28no—
217C4⋊Dic47—22no—
218C4⋊Dic47—22no—
219Dic47⋊C4—28no—
220C4×Dic47—28no—
221C4×Dic47—22no—
222C4×Dic47—22no—
223#10625329—22no—
224#10625329—22no—
225#10625329—41no—
226#10625329—41no—
227#10625329—41no—
228#10625329—41no—
229#10625329—41no—
230#10625329—41no—
231C2×C47⋊C8—22no—
232C2×C47⋊C8—22no—
233C2×C47⋊C8—22no—
234C2×C47⋊C8—22no—
235C2×C47⋊C8—41no—
236C2×C47⋊C8—41no—
237C23×C47—42no—
238C23×C47C2×C4211yescharacteristic
239C23×C47C2×C22⋊C411yescharacteristic
240C23×C47C2×C22⋊C411yescharacteristic
241C23×C47C2×C22⋊C411yescharacteristic
242C23×C47C2×C4⋊C411yescharacteristic
243C23×C47#11711yescharacteristic
244C23×C47#11711yescharacteristic
245C22×D47—21no—
246C22×D47—21no—
247C22×D47—24no—
248C22×D47—22no—
249C22×D47—22no—
250C22×D47—21no—
251C22×D47—22no—
252C22×D47—22no—
253C22×D47—21no—
254C22×D47—24no—
255C22×D47—24no—
256C22×D47—42no—
257C22×D47—42no—
258C22×D47—42no—
259C22×D47—44no—
260C22×D47—44no—
261C22×D47—44no—
262C22×D47—44no—
263C22×D47#9512yes—
264C22×D47#9512yes—
265C2×C4×C47—24no—
266C2×C4×C47—44no—
267C2×C4×C47C2×C22⋊C411yescharacteristic
268C2×C4×C47C2×C22⋊C411yescharacteristic
269C2×C4×C47C2×C4⋊C411yescharacteristic
270C2×C4×C47C2×C4⋊C411yescharacteristic
271C2×C4×C47C4×D411yescharacteristic
272C2×C4×C47C4×D411yescharacteristic
273C2×C4×C47C4×D411yescharacteristic
274C2×C4×C47C4×D411yescharacteristic
275C2×C4×C47C4×D411yescharacteristic
276C2×C4×C47C4×D411yescharacteristic
277C2×C4×C47C4×D411yescharacteristic
278C2×C4×C47C4×D411yescharacteristic
279C2×C4×C47#12011yescharacteristic
280C2×C4×C47#12011yescharacteristic
281C2×C4×C47#12011yescharacteristic
282C2×C4×C47#12011yescharacteristic
283C2×C4×C47#12111yescharacteristic
284C2×C4×C47#12111yescharacteristic
285C2×C4×C47#12111yescharacteristic
286C2×C4×C47#12111yescharacteristic
287C2×C4×C47C22⋊Q811yescharacteristic
288C2×C4×C47C22⋊Q811yescharacteristic
289C2×C4×C47C22⋊Q811yescharacteristic
290C2×C4×C47C22⋊Q811yescharacteristic
291C2×C4×C47#12311yescharacteristic
292C2×C4×C47#12311yescharacteristic
293C2×C4×C47#12311yescharacteristic
294C2×C4×C47#12311yescharacteristic
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—21no—
298C2×Dic47—21no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—21no—
302C2×Dic47—21no—
303C2×Dic47—24no—
304C2×Dic47—44no—
305C2×Dic47#9512yes—
306C2×Dic47#9512yes—
307C4×D47—22no—
308C4×D47—22no—
309C4×D47—22no—
310C4×D47—22no—
311C4×D47—22no—
312C4×D47—22no—
313C4×D47—22no—
314C4×D47—22no—
315C4×D47—22no—
316C4×D47—22no—
317C4×D47—22no—
318C4×D47—22no—
319C4×D47—22no—
320C4×D47—22no—
321C4×D47—22no—
322C4×D47—22no—
323C4×D47—416no—
324C8×C47—42no—
325C8×C47—42no—
326C47⋊C8—42no—
327C47⋊C8—42no—
328#10738—471nomaximal, Sylow
329C22×C47—22no—
330C22×C47—22no—
331C22×C47—22no—
332C22×C47—41no—
333C22×C47—41no—
334C22×C47—41no—
335C22×C47—41no—
336C22×C47C2×#9511yescharacteristic
337C22×C47C4×C22⋊C411yescharacteristic
338C22×C47C4×C22⋊C411yescharacteristic
339C22×C47#37911yescharacteristic
340C22×C47#38011yescharacteristic
341C22×C47#38011yescharacteristic
342C22×C47#38111yescharacteristic
343C2×D47—24no—
344C2×D47—24no—
345C2×D47—22no—
346C2×D47—22no—
347C2×D47—22no—
348C2×D47—22no—
349C2×D47—22no—
350C2×D47—44no—
351C2×D47—44no—
352C2×D47—44no—
353C2×D47—44no—
354C2×D47—42no—
355C2×D47—42no—
356C2×D47#34414yescomplemented
357C4×C47—44no—
358C4×C47#38511yescharacteristic
359C4×C47#38511yescharacteristic
360C4×C47#38511yescharacteristic
361C4×C47#38511yescharacteristic
362C4×C47#38611yescharacteristic
363C4×C47#38611yescharacteristic
364C4×C47#38611yescharacteristic
365C4×C47#38611yescharacteristic
366Dic47—22no—
367Dic47—22no—
368Dic47—44no—
369C22×#117—471no—
370C2×#407—471no—
371C2×#407—471no—
372C2×#344—471no—
373C2×#344—471no—
374C2×#344—471no—
375C2×#344D4711yescharacteristic, complemented
376C2×C47—21no—
377C2×C47—21no—
378C2×C47—21no—
379C2×C47—21no—
380C2×C47—21no—
381C2×C47—21no—
382C2×C47C22⋊#9511yescharacteristic
383C2×C47C2×#34412yes—
384D47—24no—
385D47—42no—
386C24×C4—471no—
387C22×M16—471no—
388C22×M16—471no—
389C22×M16C2×D4711yescharacteristic
390C22×M16C2×D4711yescharacteristic
391C2×#117—471no—
392C2×#117—472no—
393C2×#117—941no—
394C2×#117—941no—
395C2×#117—942no—
396C2×#117—942no—
397C2×#117—942no—
398C2×#117—942no—
399C2×#117C2×D4711yescharacteristic
400C22×C4⋊C4—941no—
401C22×C22⋊C4—472no—
402C22×C42—941no—
403#407—474no—
404#407—941no—
405#407—942no—
406#407—941no—
407#407—941no—
408#407—941no—
409C2×C22⋊C8—474no—
410C2×C22⋊C8—942no—
411#344—22no—
412#344—942no—
413#344—942no—
414#344—942no—
415C47#1073811yescharacteristic, complemented, Sylow
416C25—471no—
417C23×C4—471no—
418C23×C4—472no—
419C23×C4—472no—
420C23×C4—471no—
421C23×C4—471no—
422C23×C4—471no—
423C23×C4—472no—
424C23×C4—471no—
425C23×C4—472no—
426C23×C4—942no—
427C23×C4—941no—
428C23×C4—941no—
429C23×C4—941no—
430C23×C4—941no—
431C23×C4—941no—
432C23×C4—941no—
433C23×C4—941no—
434C23×C4—941no—
435C23×C4C22×D4711yescharacteristic
436C2×M16—21no—
437C2×M16—21no—
438C2×M16—21no—
439C2×M16—21no—
440C2×M16—21no—
441C2×M16—21no—
442C2×M16—21no—
443C2×M16—21no—
444C2×M16—21no—
445C2×M16—21no—
446C2×M16—21no—
447C2×M16—472no—
448C2×M16—941no—
449C2×M16—941no—
450C2×M16—941no—
451C2×M16—941no—
452C2×M16—941no—
453C2×M16—941no—
454C2×M16—941no—
455C2×M16—941no—
456C2×M16—941no—
457C2×M16—941no—
458C2×M16—941no—
459C2×M16C4×D4712yescomplemented
460C22×C8—21no—
461C22×C8—472no—
462C22×C8—941no—
463C22×C8C4×D4712yescomplemented
464#117—21no—
465#117—21no—
466#117—472no—
467#117—472no—
468#117—944no—
469#117—944no—
470#117—944no—
471#117—944no—
472#117—944no—
473#117—941no—
474#117—941no—
475#117—944no—
476#117D18812yes—
477#117C22⋊D4712yes—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—944no—
480C2×C4⋊C4—944no—
481C2×C4⋊C4—942no—
482C2×C4⋊C4—941no—
483C2×C22⋊C4—472no—
484C2×C22⋊C4—944no—
485C2×C22⋊C4—942no—
486C2×C22⋊C4—944no—
487C2×C22⋊C4C4×D4712yes—
488C2×C42—21no—
489C2×C42—944no—
490C2×C42—944no—
491C2×C42—942no—
492C2×C42—941no—
493C22⋊C8—944no—
494C22⋊C8—944no—
495C22⋊C8—944no—
496C22⋊C8—944no—
497C24—471no—
498C24—472no—
499C24—472no—
500C24—471no—
501C24—941no—
502C24—941no—
503C24—941no—
504C24—941no—
505C24—1884no—
506C24C2×C4×D4711yescharacteristic
507C22×C4—22no—
508C22×C4—472no—
509C22×C4—471no—
510C22×C4—471no—
511C22×C4—472no—
512C22×C4—472no—
513C22×C4—472no—
514C22×C4—472no—
515C22×C4—472no—
516C22×C4—472no—
517C22×C4—472no—
518C22×C4—472no—
519C22×C4—472no—
520C22×C4—948no—
521C22×C4—941no—
522C22×C4—941no—
523C22×C4—941no—
524C22×C4—941no—
525C22×C4—942no—
526C22×C4—942no—
527C22×C4—942no—
528C22×C4—942no—
529C22×C4—942no—
530C22×C4—942no—
531C22×C4—942no—
532C22×C4—942no—
533C22×C4—941no—
534C22×C4—941no—
535C22×C4—941no—
536C22×C4—941no—
537C22×C4—941no—
538C22×C4—941no—
539C22×C4—941no—
540C22×C4—941no—
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—941no—
550C22×C4—941no—
551C22×C4—941no—
552C22×C4—941no—
553C22×C4—941no—
554C22×C4—941no—
555C22×C4—941no—
556C22×C4—941no—
557C22×C4—942no—
558C22×C4—1888no—
559C22×C4C2×C4×D4711yescharacteristic
560C22×C4C2×C4×D4711yescharacteristic
561C22×C4C2×D18811yescharacteristic
562C22×C4#1062535011yescharacteristic
563C22×C4#1062535011yescharacteristic
564C22×C4D4×D4711yescharacteristic
565C22×C4D4×D4711yescharacteristic
566C22×C4D4×D4711yescharacteristic
567C22×C4D4×D4711yescharacteristic
568C22×C4D4×D4711yescharacteristic
569C22×C4#1062535211yescharacteristic
570C22×C4Q8×D4711yescharacteristic
571C22×C4#1062535411yescharacteristic
572C22×C4C2×C22⋊D4711yescharacteristic
573M16—22no—
574M16—22no—
575M16—41no—
576M16—41no—
577M16—41no—
578M16—41no—
579M16—41no—
580M16—41no—
581M16—942no—
582M16—942no—
583M16—1881no—
584M16—1881no—
585M16—1881no—
586M16—1881no—
587M16—1881no—
588M16—1881no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—942no—
596C2×C8—942no—
597C2×C8—942no—
598C2×C8—942no—
599C2×C8—1881no—
600C2×C8—1881no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—948no—
604C4⋊C4—942no—
605C4⋊C4—942no—
606C22⋊C4—22no—
607C22⋊C4—474no—
608C22⋊C4—948no—
609C22⋊C4—942no—
610C22⋊C4(C2×D47)⋊C414yes—
611C42—22no—
612C42—22no—
613C42—948no—
614C42—942no—
615C42—942no—
616C23—42no—
617C23—472no—
618C23—472no—
619C23—944no—
620C23—944no—
621C23—944no—
622C23—941no—
623C23—941no—
624C23—942no—
625C23—942no—
626C23—941no—
627C23—942no—
628C23—942no—
629C23—941no—
630C23—1882no—
631C23—1882no—
632C23—1882no—
633C23—1884no—
634C23—1884no—
635C23—1884no—
636C23—1884no—
637C23C42×D4711yescharacteristic
638C23C22⋊C4×D4711yescharacteristic
639C23C22⋊C4×D4711yescharacteristic
640C23C2×(C2×D47)⋊C411yescharacteristic
641C23C4⋊C4×D4711yescharacteristic
642C23#1309398111yescharacteristic
643C23#1309398211yescharacteristic
644C2×C4—24no—
645C2×C4—44no—
646C2×C4—472no—
647C2×C4—472no—
648C2×C4—942no—
649C2×C4—942no—
650C2×C4—941no—
651C2×C4—941no—
652C2×C4—942no—
653C2×C4—942no—
654C2×C4—941no—
655C2×C4—941no—
656C2×C4—942no—
657C2×C4—942no—
658C2×C4—942no—
659C2×C4—942no—
660C2×C4—942no—
661C2×C4—942no—
662C2×C4—942no—
663C2×C4—942no—
664C2×C4—942no—
665C2×C4—942no—
666C2×C4—942no—
667C2×C4—942no—
668C2×C4—942no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—944no—
673C2×C4—18816no—
674C2×C4—1884no—
675C2×C4C22⋊C4×D4711yescharacteristic
676C2×C4C22⋊C4×D4711yescharacteristic
677C2×C4C4⋊C4×D4711yescharacteristic
678C2×C4C4⋊C4×D4711yescharacteristic
679C2×C4(C22⋊D47)⋊C411yescharacteristic
680C2×C4(C22⋊D47)⋊C411yescharacteristic
681C2×C4C4×C22⋊D4711yescharacteristic
682C2×C4C4×C22⋊D4711yescharacteristic
683C2×C4#1309398611yescharacteristic
684C2×C4#1309398611yescharacteristic
685C2×C4C4×D18811yescharacteristic
686C2×C4C4×D18811yescharacteristic
687C2×C4#1309399211yescharacteristic
688C2×C4#1309399211yescharacteristic
689C2×C4#1309399411yescharacteristic
690C2×C4#1309399411yescharacteristic
691C2×C4#1309399511yescharacteristic
692C2×C4#1309399711yescharacteristic
693C2×C4#1309399711yescharacteristic
694C2×C4#1309399911yescharacteristic
695C2×C4#1309400011yescharacteristic
696C2×C4#1309400211yescharacteristic
697C2×C4#1309400211yescharacteristic
698C2×C4#1309400411yescharacteristic
699C2×C4#1309400611yescharacteristic
700C2×C4#1309400611yescharacteristic
701C2×C4#1309400911yescharacteristic
702C2×C4#1309400911yescharacteristic
703C8—42no—
704C8—42no—
705C8—1882no—
706C8—1882no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—474no—
715C22—944no—
716C22—944no—
717C22—942no—
718C22—942no—
719C22—942no—
720C22—942no—
721C22—942no—
722C22—1884no—
723C22—1884no—
724C22—1884no—
725C22—1884no—
726C22—1882no—
727C22—1882no—
728C22#95×D4711yescharacteristic
729C22#1568897011yescharacteristic
730C22C4×(C2×D47)⋊C411yescharacteristic
731C22#1568897811yescharacteristic
732C22#1568898011yescharacteristic
733C22#1568898211yescharacteristic
734C22#1568898511yescharacteristic
735C4—44no—
736C4—942no—
737C4—942no—
738C4—1884no—
739C4#1568899411yescharacteristic
740C4#1568899411yescharacteristic
741C4#1568899711yescharacteristic
742C4#1568899711yescharacteristic
743C4#1568899911yescharacteristic
744C4#1568899911yescharacteristic
745C4#1568900111yescharacteristic
746C4#1568900111yescharacteristic
747C2—21no—
748C2—21no—
749C2—21no—
750C2—21no—
751C2—21no—
752C2—21no—
753C2—944no—
754C2—1882no—
755C2(C2×D47)⋊#9511yescharacteristic
756C2#344×D4712yes—
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC23×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×#344C2
socleC22×C47C2×#95
prime radicalC24×D47C2×C4
cosocleC23×C4×C47C23
hypercenterC2×#344D47
hypocenterC47#10738
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. C2×#15688895C2semidirect
5. C2×#15688894C2semidirect
6. C2×#15688893C2semidirect
7. C2×C47×#344C2semidirect
27. #15689086C4semidirect
29. C2×(C2×D47)⋊C8C4semidirect
67. C2×#10625329C2×C4semidirect
69. C22×C47⋊C8C2×C4semidirect
108. C2×M16×C47C2×C4semidirect
110. C22×C8×C47C2×C4semidirect
356. C2×D47#344semidirect
375. C2×#344D47semidirect
415. C47#10738semidirect
459. C2×M16C4×D47semidirect
463. C22×C8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D472
C2×#156890862
C2×#156888952
C2×#156888942
C2×#156888932
C2×C47×#3442
#1073847