Finite Group Databasebeta

← C2×#20253174 #27083777

Subgroups — C2×#20253174 #27083777

Order 12032.

2162 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689676C211yesmaximal, characteristic, complemented
2C2×#15689591C211yesmaximal, characteristic
3#20253174C2116yesmaximal, direct product factor
4C2×#15689433C211yesmaximal, characteristic, complemented
5C2×#15689429C211yesmaximal, characteristic, complemented
6C2×#15689417C211yesmaximal, characteristic, complemented
7C2×#15689407C211yesmaximal, characteristic, complemented
8C2×#15689426C211yesmaximal, characteristic, complemented
9C2×#15689422C211yesmaximal, characteristic, complemented
10C2×#15689412C211yesmaximal, characteristic, complemented
11C2×#15689402C211yesmaximal, characteristic, complemented
12C2×#15689159C211yesmaximal, characteristic, complemented
13C22×Dic47⋊C8C211yesmaximal, characteristic, complemented
14C2×#15689120C211yesmaximal, characteristic
15C2×#15689117C211yesmaximal, characteristic
16C2×C47×#427C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C23×C47⋊C8C2211yescharacteristic
19#15689676—24no—
20#15689676C2218yescomplemented
21C2×#13094023C2211yescharacteristic
22C2×#13094023C2211yescharacteristic
23C2×#13094015C2211yescharacteristic
24C2×#13094015C2211yescharacteristic
25C2×#13094001—21no—
26C2×#13094001—21no—
27#15689591—24no—
28#15689591C2218yes—
29C2×C4×Dic94—21no—
30C2×C4×Dic94—21no—
31C2×#13093989C2211yescharacteristic
32C2×#13093989C2211yescharacteristic
33C2×#13093986C2211yescharacteristic
34C2×#13093986C2211yescharacteristic
35C2×(C22⋊D47)⋊C4—21no—
36C2×(C22⋊D47)⋊C4—21no—
37C2×#13093983C2211yescharacteristic
38C2×#13093981—21no—
39C22×C4×Dic47C2211yescharacteristic
40C2×C42×D47—21no—
41#15689433C2218yescomplemented
42#15689429C2218yescomplemented
43#15689426C2218yescomplemented
44#15689422C2218yescomplemented
45#15689417C2218yescomplemented
46#15689412C2218yescomplemented
47#15689407C2218yescomplemented
48#15689402C2218yescomplemented
49#15689159C2218yescomplemented
50C2×#13093957C2211yescharacteristic
51C2×#13093957C2211yescharacteristic
52C2×#13093955C2211yescharacteristic
53C2×#13093955C2211yescharacteristic
54C2×Dic47⋊C8C2211yescharacteristic
55C2×Dic47⋊C8C2211yescharacteristic
56C2×Dic47⋊C8C2211yescharacteristic
57C2×Dic47⋊C8C2211yescharacteristic
58C2×Dic47⋊C8C2218yescomplemented
59#15689120C2218yes—
60#15689117C2218yes—
61C2×#13093949C2211yescharacteristic
62C2×#13093949C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093944C2211yescharacteristic
68C2×#13093944C2211yescharacteristic
69C23×C8×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic
71C2×#117×C47C2211yescharacteristic
72C47×#427C2218yescomplemented
73C2×#107×C47C2211yescharacteristic
74C2×#107×C47C2211yescharacteristic
75C2×#106×C47C2211yescharacteristic
76C2×#106×C47C2211yescharacteristic
77C2×#10625350—22no—
78C2×#10625350—24no—
79C2×#10625350Q818yescomplemented
80C2×#10625350C2314yes—
81C22×Dic94—21no—
82C22×Dic94—21no—
83C22×Dic94C2311yescharacteristic
84C22×D188C2311yescharacteristic
85C22×C22⋊D47—21no—
86C23×Dic47D411yescharacteristic
87C23×Dic47D411yescharacteristic
88C22×C4×D47—21no—
89C22×C4×D47—21no—
90C22×C4×D47—21no—
91C22×C47⋊C8—24no—
92C22×C47⋊C8C2311yescharacteristic
93C22×C47⋊C8C2311yescharacteristic
94C22×C47⋊C8C2314yes—
95#13094023—22no—
96#13094023—22no—
97#13094023C2314yes—
98#13094023C2314yes—
99#13094015—22no—
100#13094015—22no—
101#13094015C2314yes—
102#13094015C2314yes—
103#13094001—28no—
104#13094001—28no—
105C4×Dic94—28no—
106C4×Dic94—28no—
107#13093989—22no—
108#13093989—22no—
109#13093989C2314yes—
110#13093989C2314yes—
111#13093986—22no—
112#13093986—22no—
113#13093986C2314yes—
114#13093986C2314yes—
115(C22⋊D47)⋊C4—28no—
116(C22⋊D47)⋊C4—28no—
117#13093983—22no—
118#13093983C2314yes—
119#13093981—28no—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47C2311yescharacteristic
123C2×C4⋊Dic47C2311yescharacteristic
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×C22⋊Dic47—21no—
131C2×(C2×D47)⋊C4—21no—
132C2×(C2×D47)⋊C4—21no—
133C2×C4×Dic47—21no—
134C2×C4×Dic47—21no—
135C2×C4×Dic47—21no—
136C2×C4×Dic47D411yescharacteristic
137C2×C4×Dic47D411yescharacteristic
138C2×C4×Dic47D414yes—
139C2×C4×Dic47C2311yescharacteristic
140C2×C4×Dic47C2311yescharacteristic
141C2×C4×Dic47C2314yes—
142C42×D47—28no—
143#13093957C2314yes—
144#13093957C2314yes—
145#13093955C2314yes—
146#13093955C2314yes—
147Dic47⋊C8C2314yes—
148Dic47⋊C8C2314yes—
149Dic47⋊C8C2314yes—
150Dic47⋊C8C2314yes—
151#13093949C2314yes—
152#13093949C2314yes—
153#13093947C2314yes—
154#13093947C2314yes—
155#13093946C2314yes—
156#13093946C2314yes—
157#13093944C2314yes—
158#13093944C2314yes—
159C23×C4×C47C2311yescharacteristic
160C22×C8×C47—24no—
161C22×C8×C47C2311yescharacteristic
162C22×C8×C47C2311yescharacteristic
163C22×C8×C47C2314yes—
164#117×C47—22no—
165#117×C47—22no—
166#117×C47C2314yes—
167#117×C47C2314yes—
168C2×C4⋊C4×C47C2311yescharacteristic
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C22⋊C4×C47—21no—
173C2×C22⋊C4×C47—21no—
174C2×C42×C47—21no—
175C2×C42×C47—21no—
176#107×C47C2314yes—
177#107×C47C2314yes—
178#106×C47C2314yes—
179#106×C47C2314yes—
180C24×C47C2×D411yescharacteristic
181C23×D47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47C2×D412yes—
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×Q814yes—
189C22×C4×C47#4114yes—
190C22×C4×C47C2411yescharacteristic
191C22×C4×C47C2412yes—
192C2×C22⋊D47—28no—
193C2×C22⋊D47—24no—
194C22×Dic47—21no—
195C22×Dic47—24no—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—42no—
199C22×Dic47C2×D411yescharacteristic
200C22×Dic47C2×D411yescharacteristic
201C22×Dic47C2×D411yescharacteristic
202C22×Dic47C2×D414yes—
203C22×Dic47C2×D414yes—
204C22×Dic47C2×D411yescharacteristic
205#10625350—216no—
206#10625350—28no—
207#10625350C2×Q8116yescomplemented
208C2×D188—21no—
209C2×D188—22no—
210C2×D188C2×Q814yes—
211C2×D188C2412yes—
212C2×C4×D47—28no—
213C2×C4×D47—24no—
214C2×C4×D47—24no—
215C2×C4×D47—24no—
216C2×C4×D47—44no—
217C2×C4×D47—44no—
218C2×Dic94—21no—
219C2×Dic94—22no—
220C2×Dic94—24no—
221C2×Dic94—24no—
222C2×Dic94—44no—
223C2×Dic94—44no—
224C2×Dic94C2×Q814yes—
225C2×Dic94C2412yes—
226C2×C8×C47—22no—
227C2×C8×C47—22no—
228C2×C8×C47—28no—
229C2×C8×C47C2412yes—
230C2×C8×C47C2412yes—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47C2412yes—
236C4⋊C4×C47C2412yes—
237C4⋊C4×C47C2412yes—
238C4⋊C4×C47C2412yes—
239C22⋊C4×C47—24no—
240C22⋊C4×C47—24no—
241C42×C47—24no—
242C42×C47—24no—
243C22⋊Dic47—24no—
244(C2×D47)⋊C4—24no—
245(C2×D47)⋊C4—24no—
246C4⋊Dic47—21no—
247C4⋊Dic47—21no—
248C4⋊Dic47—24no—
249C4⋊Dic47—24no—
250C4⋊Dic47C2412yes—
251C4⋊Dic47C2412yes—
252Dic47⋊C4—24no—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258C4×Dic47—24no—
259C4×Dic47—24no—
260C4×Dic47—24no—
261C4×Dic47C2×D414yes—
262C4×Dic47C2×D414yes—
263C4×Dic47C2×D412yes—
264C4×Dic47C2×D412yes—
265C4×Dic47C2412yes—
266C4×Dic47C2412yes—
267C2×C47⋊C8—22no—
268C2×C47⋊C8—22no—
269C2×C47⋊C8—28no—
270C2×C47⋊C8C2412yes—
271C2×C47⋊C8C2412yes—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47C22⋊Q814yes—
275C23×C47C22×D412yes—
276C23×C47C22×D411yescharacteristic
277C22×D47—24no—
278C22×D47—22no—
279C22×D47—42no—
280C22×D47—42no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—42no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—42no—
289C2×C4×C47C22⋊Q814yes—
290C2×C4×C47C22⋊Q818yes—
291C2×C4×C47C22×D412yes—
292C2×C4×C47C22×D411yescharacteristic
293C2×C4×C47C22×Q812yes—
294C2×C4×C47C22×Q814yes—
295C2×C4×C47C2×#4112yes—
296C2×C4×C47C2×#4114yes—
297C2×C4×C47C2511yescharacteristic
298C22⋊D47—216no—
299C2×Dic47—24no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—28no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—44no—
308C2×Dic47—42no—
309C2×Dic47—42no—
310C2×Dic47#13514yes—
311C2×Dic47C22×D412yes—
312C2×Dic47C22×D412yes—
313C2×Dic47C22×D412yes—
314C2×Dic47C22×D412yes—
315D188—24no—
316D188—22no—
317D188C22×Q814yes—
318C4×D47—216no—
319C4×D47—48no—
320C4×D47—48no—
321Dic94—24no—
322Dic94—22no—
323Dic94—48no—
324Dic94—48no—
325Dic94C22×Q814yes—
326C8×C47—22no—
327C8×C47—22no—
328C47⋊C8—22no—
329C47⋊C8—22no—
330C2×#3076—471nomaximal, Sylow
331C22×C47—28no—
332C22×C47—22no—
333C22×C47—22no—
334C22×C47C2×C22⋊Q814yes—
335C22×C47C2×C22⋊Q812yes—
336C22×C47C2×#13512yes—
337C22×C47#57512yes—
338C22×C47C23×D411yescharacteristic
339C2×D47—24no—
340C2×D47—48no—
341C2×D47—42no—
342C2×D47—42no—
343C4×C47—42no—
344C4×C47—42no—
345C4×C47—42no—
346C4×C47—42no—
347C4×C47C2×C22⋊Q812yes—
348C4×C47C2×C22⋊Q814yes—
349C4×C47C23×Q811yescharacteristic
350C4×C47C22×#4111yescharacteristic
351Dic47—24no—
352Dic47—22no—
353Dic47—22no—
354Dic47—22no—
355Dic47—42no—
356Dic47—42no—
357Dic47C2×#13514yes—
358C2×#533—471no—
359C2×C4×#41—471no—
360#3076—4716no—
361C2×#479—471no—
362C2×#479—471no—
363C2×#477—471no—
364C2×#475—471no—
365C2×#478—471no—
366C2×#478—471no—
367C2×#476—471no—
368C2×#474—471no—
369C2×#427—471no—
370C2×#427D4711yescharacteristic, complemented
371C22×C4⋊C8—471no—
372C2×#416—471no—
373C2×#416—471no—
374C2×C47—24no—
375C2×C47#307614yescomplemented
376C2×C47C22×C22⋊Q811yescharacteristic
377C2×C47C22×#13511yescharacteristic
378C2×C47C2×#57511yescharacteristic
379D47—44no—
380C22×#41—471no—
381C23×C8—471no—
382C23×C8C2×D4711yescharacteristic
383#533—478no—
384#533—944no—
385C2×C4⋊Q8—471no—
386C2×C4⋊Q8—471no—
387C2×#125—471no—
388C2×#125—471no—
389C2×C22⋊Q8—941no—
390C2×C22⋊Q8—941no—
391C4×#41—478no—
392C4×#41—944no—
393C2×C4×Q8—471no—
394C2×C4×Q8—471no—
395C2×C4×Q8—941no—
396C2×C4×Q8—941no—
397C2×C4×D4—471no—
398C2×C4×D4—471no—
399C2×C4×D4—941no—
400C2×C4×D4—941no—
401C2×#117—471no—
402C2×#117—941no—
403C2×#117C2×D4711yescharacteristic
404C2×#117C2×D4711yescharacteristic
405C22×C42—471no—
406C22×C42—941no—
407#479—478no—
408#479—478no—
409#478—478no—
410#478—478no—
411#477—478no—
412#476—478no—
413#475—478no—
414#474—478no—
415#427—478no—
416#427C2×D4718yescomplemented
417C2×#107—471no—
418C2×#107—471no—
419C2×#107C2×D4711yescharacteristic
420C2×#107C2×D4711yescharacteristic
421C2×#106—471no—
422C2×#106—471no—
423C2×#106C2×D4711yescharacteristic
424C2×#106C2×D4711yescharacteristic
425C2×C4⋊C8—471no—
426C2×C4⋊C8—471no—
427C2×C4⋊C8—471no—
428C2×C4⋊C8—471no—
429C2×C4⋊C8—478no—
430#416—478no—
431#416—478no—
432C2×#103—471no—
433C2×#103—471no—
434C2×#103—471no—
435C2×#103—471no—
436C2×#102—471no—
437C2×#102—471no—
438C2×#102—471no—
439C2×#102—471no—
440C47C2×#307611yescharacteristic, complemented, Sylow
441C2×#41—478no—
442C2×#41—474no—
443C2×#41—944no—
444C2×#41—942no—
445C22×Q8—471no—
446C22×Q8—941no—
447C22×Q8—941no—
448C22×D4—471no—
449C22×D4—941no—
450C23×C4—471no—
451C23×C4—471no—
452C23×C4—941no—
453C23×C4—941no—
454C23×C4—941no—
455C23×C4C22×D4711yescharacteristic
456C22×C8—24no—
457C22×C8—471no—
458C22×C8—471no—
459C22×C8—474no—
460C22×C8—944no—
461C22×C8C22×D4711yescharacteristic
462C22×C8C22×D4711yescharacteristic
463C22×C8C22×D4714yes—
464C4⋊Q8—474no—
465C4⋊Q8—474no—
466C4⋊Q8—942no—
467C4⋊Q8—942no—
468#125—474no—
469#125—474no—
470#125—942no—
471#125—942no—
472C22⋊Q8—948no—
473C22⋊Q8—948no—
474C4×Q8—474no—
475C4×Q8—474no—
476C4×Q8—948no—
477C4×Q8—948no—
478C4×Q8—942no—
479C4×Q8—942no—
480C4×D4—474no—
481C4×D4—474no—
482C4×D4—942no—
483C4×D4—942no—
484C4×D4—948no—
485C4×D4—948no—
486#117—22no—
487#117—22no—
488#117—474no—
489#117—948no—
490#117—942no—
491#117C22×D4714yes—
492#117C22×D4714yes—
493C2×C4⋊C4—471no—
494C2×C4⋊C4—471no—
495C2×C4⋊C4—941no—
496C2×C4⋊C4—941no—
497C2×C4⋊C4—941no—
498C2×C4⋊C4—941no—
499C2×C4⋊C4—941no—
500C2×C4⋊C4—941no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4C22×D4711yescharacteristic
504C2×C4⋊C4C22×D4711yescharacteristic
505C2×C4⋊C4C22×D4711yescharacteristic
506C2×C4⋊C4C22×D4711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—941no—
510C2×C22⋊C4—941no—
511C2×C22⋊C4—941no—
512C2×C42—21no—
513C2×C42—21no—
514C2×C42—474no—
515C2×C42—471no—
516C2×C42—471no—
517C2×C42—471no—
518C2×C42—471no—
519C2×C42—474no—
520C2×C42—948no—
521C2×C42—941no—
522C2×C42—941no—
523C2×C42—941no—
524#107—474no—
525#107—474no—
526#107C22×D4714yes—
527#107C22×D4714yes—
528#106—474no—
529#106—474no—
530#106C22×D4714yes—
531#106C22×D4714yes—
532C4⋊C8—474no—
533C4⋊C8—474no—
534C4⋊C8—474no—
535C4⋊C8—474no—
536#103—474no—
537#103—474no—
538#103—474no—
539#103—474no—
540#102—474no—
541#102—474no—
542#102—474no—
543#102—474no—
544C24—941no—
545C24D4×D4711yescharacteristic
546#41—4716no—
547#41—9416no—
548#41—948no—
549C2×Q8—474no—
550C2×Q8—472no—
551C2×Q8—944no—
552C2×Q8—944no—
553C2×Q8—941no—
554C2×Q8—942no—
555C2×Q8—1884no—
556C2×Q8—1884no—
557C2×D4—474no—
558C2×D4—472no—
559C2×D4—948no—
560C2×D4—944no—
561C2×D4—941no—
562C2×D4—942no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—471no—
568C22×C4—471no—
569C22×C4—471no—
570C22×C4—471no—
571C22×C4—474no—
572C22×C4—474no—
573C22×C4—944no—
574C22×C4—944no—
575C22×C4—944no—
576C22×C4—941no—
577C22×C4—948no—
578C22×C4—944no—
579C22×C4—941no—
580C22×C4—941no—
581C22×C4—1884no—
582C22×C4—1884no—
583C22×C4—1882no—
584C22×C4#1062535014yes—
585C22×C4D4×D4712yes—
586C22×C4D4×D4711yescharacteristic
587C22×C4Q8×D4714yes—
588C22×C4C23×D4711yescharacteristic
589C22×C4C23×D4712yes—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—472no—
594C2×C8—472no—
595C2×C8—942no—
596C2×C8—942no—
597C2×C8—948no—
598C2×C8C23×D4712yes—
599C2×C8C23×D4712yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—472no—
605C4⋊C4—472no—
606C4⋊C4—944no—
607C4⋊C4—944no—
608C4⋊C4—944no—
609C4⋊C4—944no—
610C4⋊C4—944no—
611C4⋊C4—944no—
612C4⋊C4—944no—
613C4⋊C4—944no—
614C4⋊C4—941no—
615C4⋊C4—941no—
616C4⋊C4C23×D4712yes—
617C4⋊C4C23×D4712yes—
618C4⋊C4C23×D4712yes—
619C4⋊C4C23×D4712yes—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—944no—
623C22⋊C4—944no—
624C22⋊C4—944no—
625C42—24no—
626C42—24no—
627C42—474no—
628C42—474no—
629C42—472no—
630C42—472no—
631C42—472no—
632C42—472no—
633C42—944no—
634C42—944no—
635C42—944no—
636C23—22no—
637C23—22no—
638C23—944no—
639C23—942no—
640C23—1882no—
641C23—1882no—
642C23#1309400214yes—
643C23C2×D4×D4712yes—
644C23C2×D4×D4711yescharacteristic
645Q8—474no—
646Q8—944no—
647Q8—942no—
648Q8—1888no—
649Q8—1888no—
650D4—474no—
651D4—9416no—
652D4—944no—
653D4—942no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—474no—
663C2×C4—472no—
664C2×C4—472no—
665C2×C4—472no—
666C2×C4—472no—
667C2×C4—948no—
668C2×C4—944no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—942no—
673C2×C4—9416no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—1888no—
677C2×C4—1888no—
678C2×C4—1884no—
679C2×C4—1882no—
680C2×C4—1882no—
681C2×C4#1309400214yes—
682C2×C4#1309400218yes—
683C2×C4C2×D4×D4712yes—
684C2×C4C2×D4×D4711yescharacteristic
685C2×C4C2×Q8×D4712yes—
686C2×C4C2×Q8×D4714yes—
687C2×C4C2×#1062535012yes—
688C2×C4C2×#1062535014yes—
689C2×C4C24×D4711yescharacteristic
690C8—22no—
691C8—22no—
692C8—942no—
693C8—942no—
694C22—22no—
695C22—22no—
696C22—28no—
697C22—944no—
698C22—1882no—
699C22—1882no—
700C22—1888no—
701C22C2×#1309400214yes—
702C22C2×#1309400212yes—
703C22#135×D4712yes—
704C22#1568992012yes—
705C22C22×D4×D4711yescharacteristic
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—474no—
711C4—942no—
712C4—942no—
713C4—942no—
714C4—944no—
715C4—1882no—
716C4—1882no—
717C4C2×#1309400214yes—
718C4C2×#1309400212yes—
719C4C22×Q8×D4711yescharacteristic
720C4C22×#1062535011yescharacteristic
721C2—24no—
722C2—1884no—
723C2#2025317414yesdirect product factor
724C2C22×#1309400211yescharacteristic
725C2C2×#135×D4711yescharacteristic
726C2C2×#1568992011yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#427C2
socleC23×C47C22×D4
prime radicalC22×#10625350C22
hypercenterC2×#427D47
hypocenterC47C2×#3076
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
1. C2×#15689676C2semidirect
3. #20253174C2direct (N × H)
4. C2×#15689433C2semidirect
5. C2×#15689429C2semidirect
6. C2×#15689417C2semidirect
7. C2×#15689407C2semidirect
8. C2×#15689426C2semidirect
9. C2×#15689422C2semidirect
10. C2×#15689412C2semidirect
11. C2×#15689402C2semidirect
12. C2×#15689159C2semidirect
13. C22×Dic47⋊C8C2semidirect
16. C2×C47×#427C2semidirect
20. #15689676C22semidirect
41. #15689433C22semidirect
42. #15689429C22semidirect
43. #15689426C22semidirect
44. #15689422C22semidirect
45. #15689417C22semidirect
46. #15689412C22semidirect
47. #15689407C22semidirect
48. #15689402C22semidirect
49. #15689159C22semidirect
58. C2×Dic47⋊C8C22semidirect
72. C47×#427C22semidirect
79. C2×#10625350Q8semidirect
207. #10625350C2×Q8semidirect
370. C2×#427D47semidirect
375. C2×C47#3076semidirect
416. #427C2×D47semidirect
440. C47C2×#3076semidirect
723. C2#20253174direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896762
C2×#156895912
#202531742
C2×#156894332
C2×#156894292
C2×#156894172
C2×#156894072
C2×#156894262
C2×#156894222
C2×#156894122
C2×#156894022
C2×#156891592
C22×Dic47⋊C82
C2×#156891202
C2×#156891172
C2×C47×#4272
C2×#307647