Finite Group Databasebeta

← C2×#20253690 #27084636

Subgroups — C2×#20253690 #27084636

Order 12032.

1994 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689736C211yesmaximal, characteristic
2C2×#15689599C211yesmaximal, characteristic
3#20253690C2116yesmaximal, direct product factor
4C2×#15689467C211yesmaximal, characteristic
5C2×#15689466C211yesmaximal, characteristic
6C2×#15689427C211yesmaximal, characteristic, complemented
7C2×#15689334C211yesmaximal, characteristic, complemented
8C2×#15689333C211yesmaximal, characteristic, complemented
9C2×#15689280C211yesmaximal, characteristic
10C2×#15689280C211yesmaximal, characteristic
11C2×#15689229C211yesmaximal, characteristic, complemented
12C2×#15689227C211yesmaximal, characteristic, complemented
13C2×#15689217C211yesmaximal, characteristic, complemented
14C2×#15689215C211yesmaximal, characteristic, complemented
15C2×#15689183C211yesmaximal, characteristic
16C2×C47×#479C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C22×Dic188C2211yescharacteristic
19C22×Dic188C2211yescharacteristic
20C22×#10625337C2211yescharacteristic
21C22×#10625337C2211yescharacteristic
22#15689736—24no—
23#15689736C2218yes—
24C2×#13094024C2211yescharacteristic
25C2×#13094019—21no—
26C2×#13094019—21no—
27C2×#13094015—21no—
28C2×#13094015—21no—
29C2×#13094004C2211yescharacteristic
30C2×#13094004C2211yescharacteristic
31#15689599—24no—
32#15689599C2218yes—
33C2×Q8×Dic47C2211yescharacteristic
34C2×C4×Dic94—21no—
35C2×C4×Dic94C2211yescharacteristic
36C2×#13093989—21no—
37C2×#13093989C2211yescharacteristic
38C2×#13093989C2211yescharacteristic
39C2×#13093989C2211yescharacteristic
40C2×#13093982—21no—
41C2×#13093982C2211yescharacteristic
42C2×#13093981—21no—
43C2×#13093981C2211yescharacteristic
44#15689467C2218yes—
45#15689466C2218yes—
46#15689427C2218yescomplemented
47#15689334C2218yescomplemented
48#15689333C2218yescomplemented
49#15689280C2218yes—
50#15689280C2218yes—
51#15689229C2218yescomplemented
52#15689227C2218yescomplemented
53#15689217C2218yescomplemented
54#15689215C2218yescomplemented
55#15689183C2218yes—
56C2×#13093957C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×C4⋊(C47⋊C8)C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093947C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×#125×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C47×#479C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×Dic94C2311yescharacteristic
80C22×Dic94C2311yescharacteristic
81C2×Q8×D47—24no—
82C2×Q8×D47—22no—
83C2×Q8×D47—24no—
84C2×Q8×D47C2314yes—
85C22×C4×D47—21no—
86C22×C4×D47C2311yescharacteristic
87C2×Dic188—24no—
88C2×Dic188—24no—
89C2×Dic188C2314yes—
90C2×Dic188C2314yes—
91C2×#10625337—24no—
92C2×#10625337—24no—
93C2×#10625337C2314yes—
94C2×#10625337C2314yes—
95C22×C47⋊C8C2311yescharacteristic
96C22×C47⋊C8C2311yescharacteristic
97#13094024—22no—
98#13094024C2314yes—
99#13094019—28no—
100#13094019—28no—
101#13094015—28no—
102#13094015—28no—
103#13094004—22no—
104#13094004—22no—
105#13094004C2314yes—
106#13094004C2314yes—
107Q8×Dic47—22no—
108Q8×Dic47C2314yes—
109C4×Dic94—22no—
110C4×Dic94—28no—
111C4×Dic94C2314yes—
112#13093989—28no—
113#13093989—22no—
114#13093989—22no—
115#13093989—22no—
116#13093989C2314yes—
117#13093989C2314yes—
118#13093989C2314yes—
119#13093982—22no—
120#13093982—28no—
121#13093982C2314yes—
122#13093981—28no—
123#13093981D414yes—
124#13093981C2314yes—
125C2×C4⋊Dic47—21no—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47—21no—
129C2×C4⋊Dic47—21no—
130C2×C4⋊Dic47C2311yescharacteristic
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4D411yescharacteristic
136C2×Dic47⋊C4D411yescharacteristic
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4D411yescharacteristic
141C2×(C2×D47)⋊C4D411yescharacteristic
142C2×C4×Dic47—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47—21no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093957C2314yes—
150#13093955C2314yes—
151C4⋊(C47⋊C8)C2314yes—
152#13093949C2314yes—
153#13093949C2314yes—
154#13093947C2314yes—
155#13093947C2314yes—
156#13093947C2314yes—
157#13093947C2314yes—
158(C2×D47)⋊C8C2314yes—
159(C2×D47)⋊C8C2314yes—
160#13093934C2314yes—
161C8×Dic47C2314yes—
162C22×Q8×C47C2311yescharacteristic
163C22×C8×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165#125×C47—22no—
166#125×C47C2314yes—
167C4×Q8×C47—22no—
168C4×Q8×C47C2314yes—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C42×C47—21no—
176C2×C42×C47C2311yescharacteristic
177#107×C47C2314yes—
178#106×C47C2314yes—
179C4⋊C8×C47C2314yes—
180#103×C47C2314yes—
181#103×C47C2314yes—
182C23×D47C2×D411yescharacteristic
183C2×Q8×C47—21no—
184C2×Q8×C47—22no—
185C2×Q8×C47#4114yes—
186C2×Q8×C47C2412yes—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2411yescharacteristic
194C22×Dic47—21no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47C2×D411yescharacteristic
199C22×Dic47C2×D411yescharacteristic
200C22×Dic47C2×D411yescharacteristic
201Q8×D47—216no—
202Q8×D47—28no—
203Q8×D47—28no—
204C2×C4×D47—28no—
205C2×C4×D47—24no—
206C2×C4×D47—22no—
207C2×C4×D47—22no—
208C2×C4×D47C2×D412yes—
209C2×C4×D47C2412yes—
210C2×Dic94—28no—
211C2×Dic94—21no—
212C2×Dic94—22no—
213C2×Dic94—24no—
214C2×Dic94—22no—
215C2×Dic94—22no—
216C2×Dic94—22no—
217C2×Dic94—22no—
218C2×Dic94—21no—
219C2×Dic94—21no—
220C2×Dic94#4114yes—
221C2×Dic94C2412yes—
222C2×Dic94C2412yes—
223C2×Dic94C2412yes—
224C2×C8×C47—22no—
225C2×C8×C47—22no—
226C2×C8×C47C2412yes—
227C2×C8×C47C2412yes—
228C4⋊C4×C47—24no—
229C4⋊C4×C47—24no—
230C4⋊C4×C47—24no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47C2412yes—
235C4⋊C4×C47C2412yes—
236C4⋊C4×C47C2412yes—
237C42×C47—24no—
238C42×C47C2×D412yes—
239C42×C47C2412yes—
240#10625337—28no—
241#10625337—28no—
242(C2×D47)⋊C4—24no—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245(C2×D47)⋊C4C2×D414yes—
246(C2×D47)⋊C4C2×D414yes—
247C4⋊Dic47—24no—
248C4⋊Dic47—24no—
249C4⋊Dic47—21no—
250C4⋊Dic47—24no—
251C4⋊Dic47—24no—
252C4⋊Dic47—24no—
253C4⋊Dic47C2412yes—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4C2×D414yes—
259Dic47⋊C4C2×D414yes—
260C4×Dic47—24no—
261C4×Dic47—24no—
262C4×Dic47—24no—
263C4×Dic47—24no—
264C4×Dic47—24no—
265C4×Dic47—24no—
266C4×Dic47C2×D412yes—
267C4×Dic47C2412yes—
268C2×C47⋊C8—22no—
269C2×C47⋊C8—22no—
270C2×C47⋊C8C2412yes—
271C2×C47⋊C8C2412yes—
272Dic188—28no—
273Dic188—28no—
274C23×C47C22×D411yescharacteristic
275C22×D47—22no—
276C22×D47—22no—
277C22×D47—22no—
278C22×D47C22×D412yes—
279Q8×C47—24no—
280Q8×C47—22no—
281Q8×C47C2×#4114yes—
282C2×C4×C47—24no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—42no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47C22×D412yes—
293C2×C4×C47C22×D412yes—
294C2×C4×C47C22×D411yescharacteristic
295C2×C4×C47C2×#4112yes—
296C2×C4×C47C2×#4112yes—
297C2×C4×C47C2511yescharacteristic
298C2×Dic47—22no—
299C2×Dic47—24no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—42no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309C2×Dic47C22×D412yes—
310C2×Dic47C22×D412yes—
311C2×Dic47C22×D412yes—
312C4×D47—216no—
313C4×D47—24no—
314C4×D47—22no—
315C4×D47—22no—
316Dic94—216no—
317Dic94—24no—
318Dic94—22no—
319Dic94—22no—
320Dic94—22no—
321Dic94—22no—
322Dic94—22no—
323Dic94—42no—
324Dic94—42no—
325Dic94C2×#4114yes—
326C8×C47—22no—
327C8×C47—22no—
328C47⋊C8—22no—
329C47⋊C8—22no—
330C2×#3127—471nomaximal, Sylow
331C22×C47#52512yes—
332C22×C47#57812yes—
333C22×C47#57812yes—
334C22×C47C23×D411yescharacteristic
335C2×D47—22no—
336C2×D47—22no—
337C2×D47—22no—
338C2×D47—44no—
339C4×C47—24no—
340C4×C47—22no—
341C4×C47—22no—
342C4×C47—42no—
343C4×C47—42no—
344C4×C47—42no—
345C4×C47#52512yes—
346C4×C47C22×#4111yescharacteristic
347C4×C47C22×#4111yescharacteristic
348Dic47—22no—
349Dic47—24no—
350Dic47—22no—
351Dic47—22no—
352Dic47—42no—
353Dic47—42no—
354Dic47—42no—
355C2×#541—471no—
356C2×#519—471no—
357#3127—4716no—
358C2×#485—471no—
359C2×#485—471no—
360C2×#479—471no—
361C2×#479D4711yescharacteristic, complemented
362C2×#462—471no—
363C2×#462—471no—
364C2×#451—471no—
365C2×#451—471no—
366C2×#441—471no—
367C2×#441—471no—
368C2×C4×Q16—471no—
369C2×C4×Q16—471no—
370C2×#433—471no—
371C2×C47#312714yescomplemented
372C2×C47C2×#52511yescharacteristic
373C2×C47C2×#57811yescharacteristic
374C2×C47C2×#57811yescharacteristic
375D47—42no—
376C23×Q8—471no—
377C22×Q16—471no—
378C22×Q16—471no—
379C22×Q16—471no—
380C22×Q16—471no—
381#541—478no—
382#541—944no—
383C2×C4⋊Q8—471no—
384C2×#126—941no—
385C2×#126—941no—
386C2×#125—941no—
387C2×#125—941no—
388C2×#125C2×D4711yescharacteristic
389C2×C22⋊Q8—471no—
390C2×C22⋊Q8—471no—
391#519—478no—
392#519—944no—
393C2×C4×Q8—471no—
394C2×C4×Q8—471no—
395C2×C4×Q8—471no—
396C2×C4×Q8—471no—
397C2×C4×Q8—471no—
398C2×C4×Q8—941no—
399C2×C4×Q8—941no—
400C2×C4×Q8C2×D4711yescharacteristic
401C2×#117—471no—
402C2×#117—471no—
403C2×#117—941no—
404C2×#117—941no—
405#485—478no—
406#485—478no—
407#479—478no—
408#479C2×D4718yescomplemented
409#462—478no—
410#462—478no—
411#451—478no—
412#451—478no—
413#441—478no—
414#441—478no—
415C4×Q16—478no—
416C4×Q16—478no—
417#433—478no—
418C2×#107—471no—
419C2×#107C2×D4711yescharacteristic
420C2×#106—471no—
421C2×#106C2×D4711yescharacteristic
422C2×C4⋊C8—471no—
423C2×C4⋊C8C2×D4711yescharacteristic
424C2×#103—471no—
425C2×#103—471no—
426C2×#103—471no—
427C2×#103—471no—
428C2×#103—471no—
429C2×#103—471no—
430C2×#103C2×D4711yescharacteristic
431C2×#103C2×D4711yescharacteristic
432C2×C22⋊C8—471no—
433C2×C22⋊C8—471no—
434C2×#97—471no—
435C2×C4×C8—471no—
436C47C2×#312711yescharacteristic, complemented, Sylow
437C22×Q8—474no—
438C22×Q8—471no—
439C22×Q8—471no—
440C22×Q8—471no—
441C22×Q8—941no—
442C22×Q8—942no—
443C22×Q8—944no—
444C22×Q8—944no—
445C22×Q8C22×D4711yescharacteristic
446C23×C4—471no—
447C23×C4—941no—
448C2×Q16—474no—
449C2×Q16—474no—
450C2×Q16—474no—
451C2×Q16—474no—
452C2×Q16—944no—
453C2×Q16—944no—
454C2×Q16—944no—
455C2×Q16—944no—
456C22×C8—471no—
457C22×C8—471no—
458C22×C8C22×D4711yescharacteristic
459C22×C8C22×D4711yescharacteristic
460C4⋊Q8—474no—
461C4⋊Q8—942no—
462#126—948no—
463#126—948no—
464#125—22no—
465#125—948no—
466#125—948no—
467#125C22×D4714yes—
468C22⋊Q8—474no—
469C22⋊Q8—474no—
470C22⋊Q8—942no—
471C22⋊Q8—942no—
472C4×Q8—22no—
473C4×Q8—474no—
474C4×Q8—474no—
475C4×Q8—474no—
476C4×Q8—474no—
477C4×Q8—474no—
478C4×Q8—948no—
479C4×Q8—942no—
480C4×Q8—942no—
481C4×Q8—942no—
482C4×Q8—942no—
483C4×Q8—948no—
484C4×Q8—942no—
485C4×Q8C22×D4714yes—
486#117—474no—
487#117—474no—
488#117—474no—
489#117—948no—
490#117—948no—
491#117—942no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—471no—
496C2×C4⋊C4—471no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—941no—
499C2×C4⋊C4—941no—
500C2×C4⋊C4—941no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4—941no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4C22×D4711yescharacteristic
508C2×C4⋊C4C22×D4711yescharacteristic
509C2×C4⋊C4C22×D4711yescharacteristic
510C2×C22⋊C4—471no—
511C2×C22⋊C4—471no—
512C2×C22⋊C4—941no—
513C2×C22⋊C4—941no—
514C2×C22⋊C4—941no—
515C2×C42—21no—
516C2×C42—471no—
517C2×C42—941no—
518C2×C42—941no—
519C2×C42—941no—
520C2×C42—941no—
521C2×C42—941no—
522C2×C42—941no—
523C2×C42C22×D4711yescharacteristic
524#107—474no—
525#107C22×D4714yes—
526#106—474no—
527#106C22×D4714yes—
528C4⋊C8—474no—
529C4⋊C8C22×D4714yes—
530#103—474no—
531#103—474no—
532#103—474no—
533#103—474no—
534#103—474no—
535#103—474no—
536#103C22×D4714yes—
537#103C22×D4714yes—
538C22⋊C8—474no—
539C22⋊C8—474no—
540#97—474no—
541C4×C8—474no—
542C24—471no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—474no—
546C2×Q8—472no—
547C2×Q8—472no—
548C2×Q8—472no—
549C2×Q8—944no—
550C2×Q8—948no—
551C2×Q8—948no—
552C2×Q8—9416no—
553C2×Q8—948no—
554C2×Q8—941no—
555C2×Q8—941no—
556C2×Q8—941no—
557C2×Q8—942no—
558C2×Q8—942no—
559C2×Q8—942no—
560C2×Q8—942no—
561C2×Q8—942no—
562C2×Q8#1062535414yes—
563C2×Q8C23×D4712yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—471no—
569C22×C4—471no—
570C22×C4—471no—
571C22×C4—472no—
572C22×C4—472no—
573C22×C4—944no—
574C22×C4—948no—
575C22×C4—941no—
576C22×C4—942no—
577C22×C4—942no—
578C22×C4—941no—
579C22×C4—941no—
580C22×C4—941no—
581C22×C4D4×D4711yescharacteristic
582C22×C4D4×D4711yescharacteristic
583C22×C4C23×D4711yescharacteristic
584Q16—948no—
585Q16—948no—
586Q16—948no—
587Q16—948no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—472no—
591C2×C8—472no—
592C2×C8—942no—
593C2×C8—942no—
594C2×C8C23×D4712yes—
595C2×C8C23×D4712yes—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—474no—
603C4⋊C4—474no—
604C4⋊C4—472no—
605C4⋊C4—944no—
606C4⋊C4—944no—
607C4⋊C4—944no—
608C4⋊C4—944no—
609C4⋊C4—944no—
610C4⋊C4—944no—
611C4⋊C4—944no—
612C4⋊C4—941no—
613C4⋊C4—944no—
614C4⋊C4—944no—
615C4⋊C4C23×D4712yes—
616C4⋊C4C23×D4712yes—
617C4⋊C4C23×D4712yes—
618C22⋊C4—474no—
619C22⋊C4—474no—
620C22⋊C4—944no—
621C22⋊C4—944no—
622C22⋊C4—944no—
623C42—24no—
624C42—472no—
625C42—472no—
626C42—944no—
627C42—944no—
628C42—944no—
629C42—944no—
630C42—944no—
631C42—944no—
632C42D4×D4712yes—
633C42C23×D4712yes—
634C23—472no—
635C23—942no—
636C23—942no—
637C23—942no—
638C23C2×D4×D4711yescharacteristic
639Q8—24no—
640Q8—22no—
641Q8—474no—
642Q8—9416no—
643Q8—944no—
644Q8—942no—
645Q8—942no—
646Q8—942no—
647Q8—942no—
648Q8—942no—
649Q8—1882no—
650Q8—1882no—
651Q8C2×#1062535414yes—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—472no—
663C2×C4—472no—
664C2×C4—472no—
665C2×C4—9416no—
666C2×C4—942no—
667C2×C4—944no—
668C2×C4—942no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—944no—
672C2×C4—942no—
673C2×C4—942no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—942no—
677C2×C4—1882no—
678C2×C4—1882no—
679C2×C4—1882no—
680C2×C4C2×D4×D4712yes—
681C2×C4C2×D4×D4712yes—
682C2×C4C2×D4×D4711yescharacteristic
683C2×C4#41×D4712yes—
684C2×C4C2×#1062535412yes—
685C2×C4C24×D4711yescharacteristic
686C8—22no—
687C8—22no—
688C8—942no—
689C8—942no—
690C22—942no—
691C22—942no—
692C22—942no—
693C22—1884no—
694C22#1568963612yes—
695C22#1568993712yes—
696C22#1568993912yes—
697C22C22×D4×D4711yescharacteristic
698C4—22no—
699C4—22no—
700C4—24no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—942no—
705C4—942no—
706C4—942no—
707C4—944no—
708C4—1882no—
709C4—1882no—
710C4—1882no—
711C4#1568963612yes—
712C4C2×#41×D4711yescharacteristic
713C4C22×#1062535411yescharacteristic
714C2—1882no—
715C2#2025369014yesdirect product factor
716C2C2×#1568963611yescharacteristic
717C2C2×#1568993711yescharacteristic
718C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#479C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
hypercenterC2×#479D47
hypocenterC47C2×#3127
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
3. #20253690C2direct (N × H)
6. C2×#15689427C2semidirect
7. C2×#15689334C2semidirect
8. C2×#15689333C2semidirect
11. C2×#15689229C2semidirect
12. C2×#15689227C2semidirect
13. C2×#15689217C2semidirect
14. C2×#15689215C2semidirect
16. C2×C47×#479C2semidirect
46. #15689427C22semidirect
47. #15689334C22semidirect
48. #15689333C22semidirect
51. #15689229C22semidirect
52. #15689227C22semidirect
53. #15689217C22semidirect
54. #15689215C22semidirect
71. C47×#479C22semidirect
361. C2×#479D47semidirect
371. C2×C47#3127semidirect
408. #479C2×D47semidirect
436. C47C2×#3127semidirect
715. C2#20253690direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897362
C2×#156895992
#202536902
C2×#156894672
C2×#156894662
C2×#156894272
C2×#156893342
C2×#156893332
C2×#156892802
C2×#156892292
C2×#156892272
C2×#156892172
C2×#156892152
C2×#156891832
C2×C47×#4792
C2×#312747