Finite Group Databasebeta

← C2×#20241646 #26137966

Subgroups — C2×#20241646 #26137966

Order 12032.

2942 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic47⋊C4C211yesmaximal, characteristic
2C22×C47⋊#95C211yesmaximal, characteristic
3C22×C47⋊#95C211yesmaximal, characteristic
4C22×C47⋊#95C211yesmaximal, characteristic
5C22×C47⋊#95C211yesmaximal, characteristic
6C22×C47⋊#95C211yesmaximal, characteristic
7#20241646C218yesmaximal, direct product factor
8C22×#95×C47C211yesmaximal, characteristic
9C24×Dic47C2211yescharacteristic
10C24×Dic47C2211yescharacteristic
11C24×Dic47C2211yescharacteristic
12C24×Dic47C2211yescharacteristic
13C22×Dic47⋊C4—24no—
14C22×Dic47⋊C4—24no—
15C22×Dic47⋊C4—24no—
16C22×Dic47⋊C4C2214yes—
17C2×C47⋊#95—24no—
18C2×C47⋊#95—24no—
19C2×C47⋊#95—24no—
20C2×C47⋊#95—24no—
21C2×C47⋊#95C418yescomplemented
22C2×C47⋊#95C2214yes—
23C2×C47⋊#95C2214yes—
24C2×C47⋊#95C2214yes—
25C2×C47⋊#95C2214yes—
26C2×C47⋊#95C2214yes—
27C24×C4×C47C2211yescharacteristic
28C24×C4×C47C2211yescharacteristic
29C24×C4×C47C2211yescharacteristic
30C2×#95×C47—24no—
31C2×#95×C47C2214yes—
32C23×Dic47—22no—
33C23×Dic47—22no—
34C23×Dic47—22no—
35C23×Dic47—22no—
36C23×Dic47—22no—
37C23×Dic47—22no—
38C23×Dic47—22no—
39C23×Dic47—22no—
40C23×Dic47—22no—
41C23×Dic47—22no—
42C23×Dic47—22no—
43C23×Dic47—22no—
44C23×Dic47—22no—
45C23×Dic47—22no—
46C23×Dic47—22no—
47C23×Dic47—22no—
48C23×Dic47—22no—
49C23×Dic47—22no—
50C23×Dic47—22no—
51C23×Dic47—22no—
52C23×Dic47—22no—
53C23×Dic47—22no—
54C23×Dic47C2×C414yes—
55C23×Dic47C2×C414yes—
56C23×Dic47D414yes—
57C23×Dic47D414yes—
58C23×Dic47D414yes—
59C23×Dic47Q814yes—
60C23×Dic47C2312yes—
61C23×Dic47C2312yes—
62C23×Dic47C2312yes—
63C23×Dic47C2312yes—
64C2×Dic47⋊C4—232no—
65C2×Dic47⋊C4—28no—
66C2×Dic47⋊C4—28no—
67C2×Dic47⋊C4—28no—
68C47⋊#95—28no—
69C47⋊#95—28no—
70C47⋊#95—28no—
71C47⋊#95—28no—
72C47⋊#95C2×C4116yescomplemented
73C25×C47C2311yescharacteristic
74C23×C4×C47—22no—
75C23×C4×C47—22no—
76C23×C4×C47—22no—
77C23×C4×C47—22no—
78C23×C4×C47—22no—
79C23×C4×C47—22no—
80C23×C4×C47—22no—
81C23×C4×C47—22no—
82C23×C4×C47—22no—
83C23×C4×C47—22no—
84C23×C4×C47—22no—
85C23×C4×C47—22no—
86C23×C4×C47—22no—
87C23×C4×C47—22no—
88C23×C4×C47—22no—
89C23×C4×C47—22no—
90C23×C4×C47—22no—
91C23×C4×C47—22no—
92C23×C4×C47C2×C414yes—
93C23×C4×C47D414yes—
94C23×C4×C47Q814yes—
95C23×C4×C47C2312yes—
96C23×C4×C47C2312yes—
97C23×C4×C47C2312yes—
98#95×C47—28no—
99C24×C47C22×C412yes—
100C24×C47C2×D412yes—
101C24×C47C2×D412yes—
102C24×C47C2×D412yes—
103C24×C47C2×D412yes—
104C24×C47C2×Q812yes—
105C24×C47C2×Q812yes—
106C24×C47#4112yes—
107C24×C47#4112yes—
108C24×C47#4112yes—
109C24×C47#4112yes—
110C24×C47#4112yes—
111C24×C47#4112yes—
112C24×C47#4112yes—
113C24×C47#4112yes—
114C24×C47C2411yescharacteristic
115C22×C4×C47—28no—
116C22×C4×C47—28no—
117C22×C4×C47—28no—
118C22×C4×C47—28no—
119C22×C4×C47—28no—
120C22×C4×C47—28no—
121C22×C4×C47—28no—
122C22×C4×C47—28no—
123C22×C4×C47—28no—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—44no—
143C22×C4×C47—44no—
144C22×C4×C47—44no—
145C22×C4×C47—44no—
146C22×C4×C47—44no—
147C22×C4×C47—44no—
148C22×C4×C47—44no—
149C22×C4×C47—44no—
150C22×C4×C47—44no—
151C22×C4×C47—44no—
152C22×C4×C47—44no—
153C22×C4×C47—44no—
154C22×C4×C47C22×C414yes—
155C22×C4×C47C2×D414yes—
156C22×C4×C47C2×Q814yes—
157C22×Dic47—28no—
158C22×Dic47—28no—
159C22×Dic47—28no—
160C22×Dic47—28no—
161C22×Dic47—28no—
162C22×Dic47—28no—
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—28no—
168C22×Dic47—28no—
169C22×Dic47—28no—
170C22×Dic47—28no—
171C22×Dic47—28no—
172C22×Dic47—28no—
173C22×Dic47—28no—
174C22×Dic47—28no—
175C22×Dic47—28no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47—44no—
195C22×Dic47—44no—
196C22×Dic47—44no—
197C22×Dic47—44no—
198C22×Dic47—44no—
199C22×Dic47—44no—
200C22×Dic47—44no—
201C22×Dic47—44no—
202C22×Dic47—44no—
203C22×Dic47—44no—
204C22×Dic47—44no—
205C22×Dic47—44no—
206C22×Dic47C4⋊C4116yes—
207C22×Dic47C22×C414yes—
208C22×Dic47C22×C414yes—
209C22×Dic47C2×D414yes—
210C22×Dic47C2×D414yes—
211C22×Dic47C2×D414yes—
212C22×Dic47C2×Q814yes—
213Dic47⋊C4—232no—
214C23×C47C2×C4⋊C414yes—
215C23×C47#11714yes—
216C23×C47#11714yes—
217C23×C47C4×D414yes—
218C23×C47C4×D414yes—
219C23×C47C4×D414yes—
220C23×C47C4×Q814yes—
221C23×C47#12014yes—
222C23×C47#12114yes—
223C23×C47#12114yes—
224C23×C47#12114yes—
225C23×C47C22⋊Q814yes—
226C23×C47C22⋊Q814yes—
227C23×C47C22⋊Q814yes—
228C23×C47C22⋊Q814yes—
229C23×C47C22⋊Q814yes—
230C23×C47#12314yes—
231C23×C47#12314yes—
232C23×C47#12314yes—
233C23×C47#12314yes—
234C23×C47#12314yes—
235C23×C47#12414yes—
236C23×C47#12414yes—
237C23×C47#12414yes—
238C23×C47#12414yes—
239C23×C47#12514yes—
240C23×C47#12514yes—
241C23×C47#12514yes—
242C23×C47#12514yes—
243C23×C47#12514yes—
244C23×C47#12614yes—
245C23×C47#12614yes—
246C23×C47#12614yes—
247C23×C47#12614yes—
248C23×C47C4⋊Q814yes—
249C23×C47C23×C411yescharacteristic
250C23×C47C22×D411yescharacteristic
251C23×C47C22×D411yescharacteristic
252C23×C47C22×D411yescharacteristic
253C23×C47C22×D411yescharacteristic
254C23×C47C22×Q811yescharacteristic
255C23×C47C22×Q811yescharacteristic
256C23×C47C2×#4111yescharacteristic
257C23×C47C2×#4111yescharacteristic
258C23×C47C2×#4111yescharacteristic
259C23×C47C2×#4111yescharacteristic
260C23×C47C2×#4111yescharacteristic
261C23×C47C2×#4111yescharacteristic
262C23×C47C2×#4111yescharacteristic
263C23×C47C2×#4111yescharacteristic
264C2×C4×C47—24no—
265C2×C4×C47—24no—
266C2×C4×C47—24no—
267C2×C4×C47—24no—
268C2×C4×C47—24no—
269C2×C4×C47—24no—
270C2×C4×C47—24no—
271C2×C4×C47—24no—
272C2×C4×C47—24no—
273C2×C4×C47—42no—
274C2×C4×C47—42no—
275C2×C4×C47—42no—
276C2×C4×C47—42no—
277C2×C4×C47—42no—
278C2×C4×C47—42no—
279C2×C4×C47—42no—
280C2×C4×C47—42no—
281C2×C4×C47—42no—
282C2×C4×C47—42no—
283C2×C4×C47—42no—
284C2×C4×C47—42no—
285C2×C4×C47—416no—
286C2×C4×C47—416no—
287C2×C4×C47—416no—
288C2×Dic47—24no—
289C2×Dic47—24no—
290C2×Dic47—24no—
291C2×Dic47—24no—
292C2×Dic47—24no—
293C2×Dic47—24no—
294C2×Dic47—232no—
295C2×Dic47—24no—
296C2×Dic47—24no—
297C2×Dic47—24no—
298C2×Dic47—24no—
299C2×Dic47—24no—
300C2×Dic47—24no—
301C2×Dic47—24no—
302C2×Dic47—24no—
303C2×Dic47—24no—
304C2×Dic47—42no—
305C2×Dic47—42no—
306C2×Dic47—42no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—416no—
317C2×Dic47—416no—
318C2×Dic47—416no—
319C2×Dic47C2×C4⋊C418yes—
320C2×#1442—471nomaximal, Sylow
321C22×C47#38218yes—
322C22×C47#38518yes—
323C22×C47#38718yes—
324C22×C47#38718yes—
325C22×C47#38818yes—
326C22×C47#38818yes—
327C22×C47#38918yes—
328C22×C47#39318yes—
329C22×C47#39418yes—
330C22×C47#39718yes—
331C22×C47#39818yes—
332C22×C47#39818yes—
333C22×C47#40018yes—
334C22×C47#40018yes—
335C22×C47#40018yes—
336C22×C47C22×C4⋊C411yescharacteristic
337C22×C47C2×#11711yescharacteristic
338C22×C47C2×#11711yescharacteristic
339C22×C47C2×C4×D411yescharacteristic
340C22×C47C2×C4×D411yescharacteristic
341C22×C47C2×C4×D411yescharacteristic
342C22×C47C2×C4×Q811yescharacteristic
343C22×C47C2×#12011yescharacteristic
344C22×C47C2×#12111yescharacteristic
345C22×C47C2×#12111yescharacteristic
346C22×C47C2×#12111yescharacteristic
347C22×C47C2×C22⋊Q811yescharacteristic
348C22×C47C2×C22⋊Q811yescharacteristic
349C22×C47C2×C22⋊Q811yescharacteristic
350C22×C47C2×C22⋊Q811yescharacteristic
351C22×C47C2×C22⋊Q811yescharacteristic
352C22×C47C2×#12311yescharacteristic
353C22×C47C2×#12311yescharacteristic
354C22×C47C2×#12311yescharacteristic
355C22×C47C2×#12311yescharacteristic
356C22×C47C2×#12311yescharacteristic
357C22×C47C2×#12411yescharacteristic
358C22×C47C2×#12411yescharacteristic
359C22×C47C2×#12411yescharacteristic
360C22×C47C2×#12411yescharacteristic
361C22×C47C2×#12511yescharacteristic
362C22×C47C2×#12511yescharacteristic
363C22×C47C2×#12511yescharacteristic
364C22×C47C2×#12511yescharacteristic
365C22×C47C2×#12511yescharacteristic
366C22×C47C2×#12611yescharacteristic
367C22×C47C2×#12611yescharacteristic
368C22×C47C2×#12611yescharacteristic
369C22×C47C2×#12611yescharacteristic
370C22×C47C2×C4⋊Q811yescharacteristic
371C4×C47—44no—
372C4×C47—44no—
373C4×C47—44no—
374Dic47—28no—
375Dic47—44no—
376Dic47—44no—
377Dic47—44no—
378C23×C4⋊C4—471no—
379C22×#95—471no—
380C22×#95—471no—
381C22×#95—471no—
382C22×#95—471no—
383C22×#95—471no—
384C22×#95D4711yescharacteristic
385#1442—478no—
386C2×C47#1442116yescomplemented
387C2×C47C2×#38211yescharacteristic
388C2×C47C2×#38511yescharacteristic
389C2×C47C2×#38711yescharacteristic
390C2×C47C2×#38711yescharacteristic
391C2×C47C2×#38811yescharacteristic
392C2×C47C2×#38811yescharacteristic
393C2×C47C2×#38911yescharacteristic
394C2×C47C2×#39311yescharacteristic
395C2×C47C2×#39411yescharacteristic
396C2×C47C2×#39711yescharacteristic
397C2×C47C2×#39811yescharacteristic
398C2×C47C2×#39811yescharacteristic
399C2×C47C2×#40011yescharacteristic
400C2×C47C2×#40011yescharacteristic
401C2×C47C2×#40011yescharacteristic
402C24×C4—471no—
403C24×C4—471no—
404C24×C4—471no—
405C24×C4—471no—
406C24×C4C2×D4711yescharacteristic
407C24×C4C2×D4711yescharacteristic
408C24×C4C2×D4711yescharacteristic
409C22×C4⋊C4—474no—
410C22×C4⋊C4—944no—
411C22×C4⋊C4—944no—
412C22×C4⋊C4—944no—
413C2×#95—24no—
414C2×#95—478no—
415C2×#95—474no—
416C2×#95—474no—
417C2×#95—474no—
418C2×#95—474no—
419C2×#95—474no—
420C2×#95—944no—
421C2×#95—944no—
422C2×#95—944no—
423C2×#95—944no—
424C2×#95C2×D4714yes—
425C47C2×#144211yescharacteristic, complemented, Sylow
426C25C22×D4711yescharacteristic
427C23×C4—22no—
428C23×C4—22no—
429C23×C4—22no—
430C23×C4—22no—
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—22no—
440C23×C4—22no—
441C23×C4—22no—
442C23×C4—22no—
443C23×C4—22no—
444C23×C4—22no—
445C23×C4—474no—
446C23×C4—474no—
447C23×C4—474no—
448C23×C4—472no—
449C23×C4—474no—
450C23×C4—474no—
451C23×C4—474no—
452C23×C4—472no—
453C23×C4—472no—
454C23×C4—472no—
455C23×C4—942no—
456C23×C4—942no—
457C23×C4—942no—
458C23×C4—942no—
459C23×C4—942no—
460C23×C4—942no—
461C23×C4—942no—
462C23×C4—942no—
463C23×C4—942no—
464C23×C4—942no—
465C23×C4—942no—
466C23×C4—942no—
467C23×C4—942no—
468C23×C4—942no—
469C23×C4—942no—
470C23×C4—942no—
471C23×C4—942no—
472C23×C4—942no—
473C23×C4—942no—
474C23×C4—942no—
475C23×C4—942no—
476C23×C4—942no—
477C23×C4Dic9414yes—
478C23×C4C4×D4714yes—
479C23×C4C22⋊D4714yes—
480C23×C4C22×D4712yes—
481C23×C4C22×D4712yes—
482C23×C4C22×D4712yes—
483C2×C4⋊C4—948no—
484C2×C4⋊C4—948no—
485C2×C4⋊C4—9432no—
486C2×C4⋊C4—948no—
487#95—28no—
488#95—4716no—
489#95—948no—
490#95—948no—
491#95—948no—
492#95—948no—
493C24C2×Dic9412yes—
494C24C2×C4×D4712yes—
495C24#1062535012yes—
496C24#1062535012yes—
497C24#1062535012yes—
498C24#1062535012yes—
499C24D4×D4712yes—
500C24D4×D4712yes—
501C24D4×D4712yes—
502C24#1062535212yes—
503C24#1062535212yes—
504C24#1062535212yes—
505C24Q8×D4712yes—
506C24#1062535412yes—
507C24C2×C22⋊D4712yes—
508C24C23×D4711yescharacteristic
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—4716no—
549C22×C4—474no—
550C22×C4—474no—
551C22×C4—474no—
552C22×C4—474no—
553C22×C4—474no—
554C22×C4—474no—
555C22×C4—948no—
556C22×C4—948no—
557C22×C4—948no—
558C22×C4—948no—
559C22×C4—948no—
560C22×C4—948no—
561C22×C4—942no—
562C22×C4—942no—
563C22×C4—942no—
564C22×C4—942no—
565C22×C4—948no—
566C22×C4—948no—
567C22×C4—948no—
568C22×C4—948no—
569C22×C4—948no—
570C22×C4—948no—
571C22×C4—948no—
572C22×C4—948no—
573C22×C4—948no—
574C22×C4—942no—
575C22×C4—942no—
576C22×C4—942no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—942no—
581C22×C4—942no—
582C22×C4—942no—
583C22×C4—942no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—942no—
590C22×C4—942no—
591C22×C4—942no—
592C22×C4—1884no—
593C22×C4—1884no—
594C22×C4—1884no—
595C22×C4—1884no—
596C22×C4—1884no—
597C22×C4—1884no—
598C22×C4—1884no—
599C22×C4—1884no—
600C22×C4—1884no—
601C22×C4—1884no—
602C22×C4—1884no—
603C22×C4—1884no—
604C22×C4C2×Dic9414yes—
605C22×C4C2×C4×D4714yes—
606C22×C4C2×C22⋊D4714yes—
607C4⋊C4—9432no—
608C23C4⋊C4×D4714yes—
609C23#1309398014yes—
610C23#1309398114yes—
611C23(C22⋊D47)⋊C414yes—
612C23C4×C22⋊D4714yes—
613C23#1309398614yes—
614C23C4×Dic9414yes—
615C23#1309399214yes—
616C23#1309399614yes—
617C23#1309399714yes—
618C23#1309399714yes—
619C23#1309400014yes—
620C23#1309400114yes—
621C23#1309400114yes—
622C23#1309400214yes—
623C23#1309400314yes—
624C23#1309400614yes—
625C23#1309400614yes—
626C23#1309400714yes—
627C23#1309400914yes—
628C23#1309400914yes—
629C23#1309401014yes—
630C23#1309401014yes—
631C23#1309401014yes—
632C23#1309401114yes—
633C23#1309401414yes—
634C23#1309401414yes—
635C23#1309401414yes—
636C23#1309401514yes—
637C23#1309401614yes—
638C23#1309401714yes—
639C23#1309401814yes—
640C23#1309401914yes—
641C23#1309401914yes—
642C23#1309402314yes—
643C23C22×C4×D4711yescharacteristic
644C23C2×D4×D4711yescharacteristic
645C23C2×D4×D4711yescharacteristic
646C23C2×D4×D4711yescharacteristic
647C23C22×C22⋊D4711yescharacteristic
648C23C2×Q8×D4711yescharacteristic
649C23C22×Dic9411yescharacteristic
650C23C2×#1062535211yescharacteristic
651C23C2×#1062535211yescharacteristic
652C23C2×#1062535211yescharacteristic
653C23C2×#1062535011yescharacteristic
654C23C2×#1062535011yescharacteristic
655C23C2×#1062535011yescharacteristic
656C23C2×#1062535011yescharacteristic
657C23C2×#1062535411yescharacteristic
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—416no—
668C2×C4—416no—
669C2×C4—416no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—478no—
683C2×C4—9432no—
684C2×C4—944no—
685C2×C4—944no—
686C2×C4—944no—
687C2×C4—944no—
688C2×C4—944no—
689C2×C4—944no—
690C2×C4—944no—
691C2×C4—944no—
692C2×C4—944no—
693C2×C4—944no—
694C2×C4—944no—
695C2×C4—944no—
696C2×C4—944no—
697C2×C4—944no—
698C2×C4—944no—
699C2×C4—18816no—
700C2×C4—18816no—
701C2×C4—18816no—
702C2×C4—1882no—
703C2×C4—1882no—
704C2×C4—1882no—
705C2×C4—1882no—
706C2×C4—1882no—
707C2×C4—1882no—
708C2×C4—1882no—
709C2×C4—1882no—
710C2×C4—1882no—
711C2×C4—1882no—
712C2×C4—1882no—
713C2×C4—1882no—
714C22#1568898718yes—
715C22#1568899418yes—
716C22#1568900618yes—
717C22#1568900718yes—
718C22#1568901218yes—
719C22#1568901718yes—
720C22#1568902018yes—
721C22#1568903518yes—
722C22#1568903818yes—
723C22#1568905218yes—
724C22#1568905618yes—
725C22#1568905718yes—
726C22#1568906118yes—
727C22#1568906418yes—
728C22#1568906518yes—
729C22C2×C4⋊C4×D4711yescharacteristic
730C22C2×#1309398011yescharacteristic
731C22C2×#1309398111yescharacteristic
732C22C2×(C22⋊D47)⋊C411yescharacteristic
733C22C2×C4×C22⋊D4711yescharacteristic
734C22C2×#1309398611yescharacteristic
735C22C2×C4×Dic9411yescharacteristic
736C22C2×#1309399211yescharacteristic
737C22C2×#1309399611yescharacteristic
738C22C2×#1309399711yescharacteristic
739C22C2×#1309399711yescharacteristic
740C22C2×#1309400011yescharacteristic
741C22C2×#1309400111yescharacteristic
742C22C2×#1309400111yescharacteristic
743C22C2×#1309400211yescharacteristic
744C22C2×#1309400311yescharacteristic
745C22C2×#1309400611yescharacteristic
746C22C2×#1309400611yescharacteristic
747C22C2×#1309400711yescharacteristic
748C22C2×#1309400911yescharacteristic
749C22C2×#1309400911yescharacteristic
750C22C2×#1309401011yescharacteristic
751C22C2×#1309401011yescharacteristic
752C22C2×#1309401011yescharacteristic
753C22C2×#1309401111yescharacteristic
754C22C2×#1309401411yescharacteristic
755C22C2×#1309401411yescharacteristic
756C22C2×#1309401411yescharacteristic
757C22C2×#1309401511yescharacteristic
758C22C2×#1309401611yescharacteristic
759C22C2×#1309401711yescharacteristic
760C22C2×#1309401811yescharacteristic
761C22C2×#1309401911yescharacteristic
762C22C2×#1309401911yescharacteristic
763C22C2×#1309402311yescharacteristic
764C4—44no—
765C4—44no—
766C4—44no—
767C4—948no—
768C4—1884no—
769C4—1884no—
770C4—1884no—
771C2#20241646116yesdirect product factor
772C2C2×#1568898711yescharacteristic
773C2C2×#1568899411yescharacteristic
774C2C2×#1568900611yescharacteristic
775C2C2×#1568900711yescharacteristic
776C2C2×#1568901211yescharacteristic
777C2C2×#1568901711yescharacteristic
778C2C2×#1568902011yescharacteristic
779C2C2×#1568903511yescharacteristic
780C2C2×#1568903811yescharacteristic
781C2C2×#1568905211yescharacteristic
782C2C2×#1568905611yescharacteristic
783C2C2×#1568905711yescharacteristic
784C2C2×#1568906111yescharacteristic
785C2C2×#1568906411yescharacteristic
786C2C2×#1568906511yescharacteristic
subgroupG/H
centerC25C22×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC22×#95×C47C2
socle, prime radicalC25×C47C23
cosocleC24×C47C24
hypercenterC22×#95D47
hypocenterC47C2×#1442
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C25 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
7. #20241646C2direct (N × H)
21. C2×C47⋊#95C4semidirect
72. C47⋊#95C2×C4semidirect
386. C2×C47#1442semidirect
425. C47C2×#1442semidirect
771. C2#20241646direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Dic47⋊C42
C22×C47⋊#952
#202416462
C22×#95×C472
C2×#144247