Finite Group Databasebeta

← C2×#20249557 #26382863

Subgroups — C2×#20249557 #26382863

Order 12032.

2286 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20249557C2116yesmaximal, direct product factor
2C2×#15689064C211yesmaximal, characteristic, complemented
3C2×#15689064C211yesmaximal, characteristic, complemented
4C2×#15689046C211yesmaximal, characteristic
5C2×#15689046C211yesmaximal, characteristic
6C2×#15689044C211yesmaximal, characteristic, complemented
7C2×#15689042C211yesmaximal, characteristic, complemented
8C2×#15689035C211yesmaximal, characteristic
9C2×#15689030C211yesmaximal, characteristic, complemented
10C2×#15689027C211yesmaximal, characteristic, complemented
11C2×#15689008C211yesmaximal, characteristic, complemented
12C2×#15689005C211yesmaximal, characteristic, complemented
13C2×#15688984C211yesmaximal, characteristic
14C2×#15688981C211yesmaximal, characteristic
15C2×C22⋊C4×Dic47C211yesmaximal, characteristic
16C2×C47×#393C211yesmaximal, characteristic
17C23×Dic94C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×Dic47⋊C4C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×C22⋊Dic47C2211yescharacteristic
28C22×C22⋊Dic47C2211yescharacteristic
29C22×C22⋊Dic47C2211yescharacteristic
30C22×C4×Dic47C2211yescharacteristic
31C22×C4×Dic47C2211yescharacteristic
32#15689064C2218yescomplemented
33#15689064C2218yescomplemented
34#15689046C2218yes—
35#15689046C2218yes—
36#15689044C2218yescomplemented
37#15689042C2218yescomplemented
38#15689035C2218yes—
39#15689030C2218yescomplemented
40#15689027C2218yescomplemented
41#15689008C2218yescomplemented
42#15689005C2218yescomplemented
43#15688984C2218yes—
44#15688981C2218yes—
45C22⋊C4×Dic47C2218yes—
46C2×C47⋊#95C2211yescharacteristic
47C2×C47⋊#95C2211yescharacteristic
48C2×C47⋊#95C2211yescharacteristic
49C2×C47⋊#95C2211yescharacteristic
50C2×C47⋊#95C2211yescharacteristic
51C2×C47⋊#95C2211yescharacteristic
52C2×C47⋊#95C2211yescharacteristic
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C23×Q8×C47C2211yescharacteristic
60C22×C22⋊C4×C47C2211yescharacteristic
61C22×C22⋊C4×C47C2211yescharacteristic
62C22×C22⋊C4×C47C2211yescharacteristic
63C47×#393C2218yes—
64C2×#95×C47C2211yescharacteristic
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C22×Dic94—24no—
68C22×Dic94—42no—
69C22×Dic94—42no—
70C22×Dic94C2314yes—
71C23×Dic47—42no—
72C23×Dic47—42no—
73C23×Dic47Q818yescomplemented
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2314yes—
83C2×C4⋊Dic47—24no—
84C2×C4⋊Dic47—42no—
85C2×C4⋊Dic47C2314yes—
86C2×C4⋊Dic47C2314yes—
87C2×Dic47⋊C4—24no—
88C2×Dic47⋊C4—42no—
89C2×Dic47⋊C4—42no—
90C2×Dic47⋊C4—42no—
91C2×Dic47⋊C4—42no—
92C2×Dic47⋊C4—42no—
93C2×Dic47⋊C4C2314yes—
94C2×Dic47⋊C4C2314yes—
95C2×Dic47⋊C4C2314yes—
96C2×Dic47⋊C4C2314yes—
97C2×Dic47⋊C4C2314yes—
98C2×Dic47⋊C4C2314yes—
99C2×C22⋊Dic47—24no—
100C2×C22⋊Dic47—42no—
101C2×C22⋊Dic47—42no—
102C2×C22⋊Dic47C2314yes—
103C2×C22⋊Dic47C2314yes—
104C2×C22⋊Dic47C2314yes—
105C2×C4×Dic47—42no—
106C2×C4×Dic47—42no—
107C2×C4×Dic47C2314yes—
108C2×C4×Dic47C2314yes—
109C47⋊#95C2314yes—
110C47⋊#95C2314yes—
111C47⋊#95C2314yes—
112C47⋊#95C2314yes—
113C47⋊#95C2314yes—
114C47⋊#95C2314yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
117C47⋊#95C2314yes—
118C47⋊#95C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C25×C47C2311yescharacteristic
123C22×Q8×C47—24no—
124C22×Q8×C47—42no—
125C22×Q8×C47—42no—
126C22×Q8×C47C2314yes—
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C2×C22⋊C4×C47—24no—
134C2×C22⋊C4×C47—42no—
135C2×C22⋊C4×C47—42no—
136C2×C22⋊C4×C47C2314yes—
137C2×C22⋊C4×C47C2314yes—
138C2×C22⋊C4×C47C2314yes—
139#95×C47C2314yes—
140#95×C47C2314yes—
141#95×C47C2314yes—
142C24×C47—22no—
143C24×C47—22no—
144C24×C47—22no—
145C24×C47—22no—
146C24×C47—22no—
147C24×C47—22no—
148C24×C47C2×Q814yes—
149C24×C47C2412yes—
150C24×C47C2411yescharacteristic
151C2×Q8×C47—28no—
152C2×Q8×C47—44no—
153C2×Q8×C47—44no—
154C2×Q8×C47—416no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—22no—
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47#4114yes—
173C22×C4×C47C2412yes—
174C22×C4×C47C2412yes—
175C22×C4×C47C2412yes—
176C22×C4×C47C2412yes—
177C22×C4×C47C2412yes—
178C22×C4×C47C2412yes—
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—22no—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—416no—
201C22×Dic47—44no—
202C22×Dic47—44no—
203C22×Dic47C2×Q814yes—
204C22×Dic47C2×Q814yes—
205C22×Dic47C2×Q8116yescomplemented
206C22×Dic47#4114yes—
207C22×Dic47C2412yes—
208C22×Dic47C2412yes—
209C22×Dic47C2412yes—
210C22×Dic47C2412yes—
211C22×Dic47C2412yes—
212C22×Dic47C2412yes—
213C22×Dic47C2412yes—
214C22×Dic47C2412yes—
215C2×Dic94—28no—
216C2×Dic94—44no—
217C2×Dic94—44no—
218C2×Dic94—416no—
219C22⋊C4×C47—28no—
220C22⋊C4×C47—44no—
221C22⋊C4×C47—44no—
222C22⋊Dic47—28no—
223C22⋊Dic47—44no—
224C22⋊Dic47—44no—
225C4⋊Dic47—28no—
226C4⋊Dic47—44no—
227Dic47⋊C4—28no—
228Dic47⋊C4—44no—
229Dic47⋊C4—44no—
230Dic47⋊C4—44no—
231Dic47⋊C4—44no—
232Dic47⋊C4—44no—
233C4×Dic47—44no—
234C4×Dic47—44no—
235C23×C47—28no—
236C23×C47—28no—
237C23×C47—28no—
238C23×C47—22no—
239C23×C47—22no—
240C23×C47—22no—
241C23×C47—22no—
242C23×C47—22no—
243C23×C47—22no—
244C23×C47—44no—
245C23×C47—44no—
246C23×C47—44no—
247C23×C47—44no—
248C23×C47C22×Q814yes—
249C23×C47C22×Q812yes—
250C23×C47C2×#4112yes—
251C23×C47C2×#4112yes—
252C23×C47H(5,𝔽2)12yes—
253C23×C47H(5,𝔽2)12yes—
254C23×C47H(5,𝔽2)12yes—
255C23×C472−1+412yes—
256C23×C47C2511yescharacteristic
257Q8×C47—416no—
258C2×C4×C47—28no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—44no—
277C2×C4×C47—44no—
278C2×C4×C47—44no—
279C2×C4×C47—44no—
280C2×C4×C47—44no—
281C2×C4×C47C2×#4114yes—
282C2×Dic47—28no—
283C2×Dic47—28no—
284C2×Dic47—28no—
285C2×Dic47—22no—
286C2×Dic47—22no—
287C2×Dic47—22no—
288C2×Dic47—22no—
289C2×Dic47—22no—
290C2×Dic47—22no—
291C2×Dic47—22no—
292C2×Dic47—22no—
293C2×Dic47—22no—
294C2×Dic47—22no—
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—416no—
307C2×Dic47—44no—
308C2×Dic47—44no—
309C2×Dic47—44no—
310C2×Dic47—44no—
311C2×Dic47—44no—
312C2×Dic47C22×Q814yes—
313C2×Dic47C22×Q814yes—
314C2×Dic47C2×#4114yes—
315Dic94—416no—
316C2×#2665—471nomaximal, Sylow
317C22×C47—24no—
318C22×C47—24no—
319C22×C47—24no—
320C22×C47—416no—
321C22×C47—42no—
322C22×C47—42no—
323C22×C47—42no—
324C22×C47—42no—
325C22×C47#53314yes—
326C22×C47#53814yes—
327C22×C47#53814yes—
328C22×C47#54214yes—
329C22×C47#54214yes—
330C22×C47#54314yes—
331C22×C47#54414yes—
332C22×C47C23×Q811yescharacteristic
333C22×C47C22×#4111yescharacteristic
334C22×C47C22×#4111yescharacteristic
335C22×C47C2×H(5,𝔽2)11yescharacteristic
336C22×C47C2×H(5,𝔽2)11yescharacteristic
337C22×C47C2×H(5,𝔽2)11yescharacteristic
338C22×C47C2×2−1+411yescharacteristic
339C4×C47—24no—
340C4×C47—42no—
341C4×C47—42no—
342C4×C47—42no—
343C4×C47—42no—
344C4×C47—42no—
345Dic47—24no—
346Dic47—24no—
347Dic47—24no—
348Dic47—42no—
349Dic47—42no—
350Dic47—42no—
351Dic47—42no—
352Dic47—42no—
353#2665—4716no—
354C2×#400—471no—
355C2×#400—471no—
356C2×#396—471no—
357C2×#396—471no—
358C2×#395—471no—
359C2×#395—471no—
360C2×#393—471no—
361C2×#393D4711yescharacteristic
362C2×#391—471no—
363C2×#391—471no—
364C2×#387—471no—
365C2×#387—471no—
366C2×#381—471no—
367C2×#380—471no—
368C2×C4×C22⋊C4—471no—
369C2×C47—44no—
370C2×C47#266518yescomplemented
371C2×C47C2×#53311yescharacteristic
372C2×C47C2×#53811yescharacteristic
373C2×C47C2×#53811yescharacteristic
374C2×C47C2×#54211yescharacteristic
375C2×C47C2×#54211yescharacteristic
376C2×C47C2×#54311yescharacteristic
377C2×C47C2×#54411yescharacteristic
378C23×Q8—471no—
379C23×Q8C2×D4711yescharacteristic
380C24×C4—471no—
381C22×C4⋊C4—471no—
382C22×C4⋊C4—471no—
383C22×C4⋊C4—471no—
384C22×C4⋊C4—471no—
385C22×C4⋊C4—471no—
386C22×C4⋊C4—471no—
387C22×C4⋊C4—471no—
388C22×C4⋊C4—471no—
389C22×C22⋊C4—471no—
390C22×C22⋊C4—471no—
391C22×C22⋊C4—471no—
392C22×C22⋊C4C2×D4711yescharacteristic
393C22×C22⋊C4C2×D4711yescharacteristic
394C22×C22⋊C4C2×D4711yescharacteristic
395C22×C42—471no—
396C22×C42—471no—
397#400—478no—
398#400—478no—
399#396—478no—
400#396—478no—
401#395—478no—
402#395—478no—
403#393—478no—
404#393C2×D4718yes—
405#391—478no—
406#391—478no—
407#387—478no—
408#387—478no—
409#381—478no—
410#380—478no—
411C4×C22⋊C4—478no—
412C2×#95—471no—
413C2×#95—471no—
414C2×#95—471no—
415C2×#95—471no—
416C2×#95—471no—
417C2×#95—471no—
418C2×#95—471no—
419C2×#95—471no—
420C2×#95—471no—
421C2×#95—471no—
422C2×#95—471no—
423C2×#95—471no—
424C2×#95—471no—
425C2×#95C2×D4711yescharacteristic
426C2×#95C2×D4711yescharacteristic
427C2×#95C2×D4711yescharacteristic
428C47C2×#266511yescharacteristic, complemented, Sylow
429C25C22×D4711yescharacteristic
430C22×Q8—24no—
431C22×Q8—42no—
432C22×Q8—42no—
433C22×Q8—474no—
434C22×Q8—944no—
435C22×Q8—1882no—
436C22×Q8—1882no—
437C22×Q8C22×D4714yes—
438C23×C4—471no—
439C23×C4—471no—
440C23×C4—471no—
441C23×C4—478no—
442C23×C4—474no—
443C23×C4—471no—
444C23×C4—471no—
445C23×C4—471no—
446C23×C4—471no—
447C23×C4—471no—
448C23×C4—1882no—
449C23×C4—1882no—
450C23×C4C22×D4711yescharacteristic
451C23×C4C22×D4711yescharacteristic
452C23×C4C22×D4711yescharacteristic
453C23×C4C22×D4711yescharacteristic
454C23×C4C22×D4711yescharacteristic
455C23×C4C22×D4711yescharacteristic
456C2×C4⋊C4—474no—
457C2×C4⋊C4—474no—
458C2×C4⋊C4—474no—
459C2×C4⋊C4—474no—
460C2×C4⋊C4—474no—
461C2×C4⋊C4—474no—
462C2×C4⋊C4—474no—
463C2×C4⋊C4—474no—
464C2×C4⋊C4—944no—
465C2×C4⋊C4—944no—
466C2×C4⋊C4—1882no—
467C2×C4⋊C4—1882no—
468C2×C4⋊C4—1882no—
469C2×C4⋊C4—1882no—
470C2×C4⋊C4—1882no—
471C2×C4⋊C4—1882no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—42no—
475C2×C22⋊C4—474no—
476C2×C22⋊C4—474no—
477C2×C22⋊C4—474no—
478C2×C22⋊C4—944no—
479C2×C22⋊C4—1882no—
480C2×C22⋊C4—1882no—
481C2×C22⋊C4C22×D4714yes—
482C2×C22⋊C4C22×D4714yes—
483C2×C22⋊C4C22×D4714yes—
484C2×C42—474no—
485C2×C42—474no—
486C2×C42—1882no—
487C2×C42—1882no—
488#95—474no—
489#95—474no—
490#95—474no—
491#95—474no—
492#95—474no—
493#95—474no—
494#95—474no—
495#95—474no—
496#95—474no—
497#95—474no—
498#95—474no—
499#95—474no—
500#95—474no—
501#95C22×D4714yes—
502#95C22×D4714yes—
503#95C22×D4714yes—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24Q8×D4714yes—
511C24C23×D4712yes—
512C24C23×D4711yescharacteristic
513C2×Q8—28no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8—416no—
517C2×Q8—948no—
518C2×Q8—1884no—
519C2×Q8—1884no—
520C2×Q8—18816no—
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—22no—
537C22×C4—22no—
538C22×C4—474no—
539C22×C4—474no—
540C22×C4—474no—
541C22×C4—472no—
542C22×C4—472no—
543C22×C4—472no—
544C22×C4—4716no—
545C22×C4—472no—
546C22×C4—472no—
547C22×C4—472no—
548C22×C4—472no—
549C22×C4—472no—
550C22×C4—942no—
551C22×C4—942no—
552C22×C4—942no—
553C22×C4—942no—
554C22×C4—942no—
555C22×C4—942no—
556C22×C4—942no—
557C22×C4—942no—
558C22×C4—942no—
559C22×C4—942no—
560C22×C4—942no—
561C22×C4—942no—
562C22×C4—942no—
563C22×C4—942no—
564C22×C4—942no—
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—18816no—
572C22×C4—1884no—
573C22×C4—1884no—
574C22×C4#1062535214yes—
575C22×C4C23×D4712yes—
576C22×C4C23×D4712yes—
577C22×C4C23×D4712yes—
578C22×C4C23×D4712yes—
579C22×C4C23×D4712yes—
580C22×C4C23×D4712yes—
581C4⋊C4—948no—
582C4⋊C4—948no—
583C4⋊C4—1884no—
584C4⋊C4—1884no—
585C4⋊C4—1884no—
586C4⋊C4—1884no—
587C4⋊C4—1884no—
588C4⋊C4—1884no—
589C22⋊C4—28no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—948no—
593C22⋊C4—1884no—
594C22⋊C4—1884no—
595C42—1884no—
596C42—1884no—
597C23—28no—
598C23—28no—
599C23—28no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—44no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23C2×Q8×D4714yes—
611C23C2×Q8×D4712yes—
612C23#41×D4712yes—
613C23C2×#1062535212yes—
614C23#1309406912yes—
615C23#1309406912yes—
616C23#1309407012yes—
617C23#1309407112yes—
618C23C24×D4711yescharacteristic
619Q8—416no—
620Q8—18816no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—28no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—474no—
645C2×C4—474no—
646C2×C4—474no—
647C2×C4—948no—
648C2×C4—948no—
649C2×C4—942no—
650C2×C4—942no—
651C2×C4—942no—
652C2×C4—942no—
653C2×C4—942no—
654C2×C4—942no—
655C2×C4—948no—
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—18816no—
672C2×C4—1884no—
673C2×C4—1884no—
674C2×C4—1884no—
675C2×C4—1884no—
676C2×C4—1884no—
677C2×C4C2×#1062535214yes—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—42no—
682C22—416no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22#1568967514yes—
687C22#1568970714yes—
688C22#1568970814yes—
689C22#1568973714yes—
690C22#1568974214yes—
691C22#1568974814yes—
692C22#1568975214yes—
693C22C22×Q8×D4711yescharacteristic
694C22C2×#41×D4711yescharacteristic
695C22C22×#1062535211yescharacteristic
696C22C2×#1309406911yescharacteristic
697C22C2×#1309406911yescharacteristic
698C22C2×#1309407011yescharacteristic
699C22C2×#1309407111yescharacteristic
700C4—24no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—944no—
707C4—944no—
708C4—944no—
709C4—1882no—
710C4—1882no—
711C4—1882no—
712C4—1882no—
713C4—1882no—
714C2—44no—
715C2#2024955718yesdirect product factor
716C2C2×#1568967511yescharacteristic
717C2C2×#1568970711yescharacteristic
718C2C2×#1568970811yescharacteristic
719C2C2×#1568973711yescharacteristic
720C2C2×#1568974211yescharacteristic
721C2C2×#1568974811yescharacteristic
722C2C2×#1568975211yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#393C2
socleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#393D47
hypocenterC47C2×#2665
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. #20249557C2direct (N × H)
2. C2×#15689064C2semidirect
3. C2×#15689064C2semidirect
6. C2×#15689044C2semidirect
7. C2×#15689042C2semidirect
9. C2×#15689030C2semidirect
10. C2×#15689027C2semidirect
11. C2×#15689008C2semidirect
12. C2×#15689005C2semidirect
32. #15689064C22semidirect
33. #15689064C22semidirect
36. #15689044C22semidirect
37. #15689042C22semidirect
39. #15689030C22semidirect
40. #15689027C22semidirect
41. #15689008C22semidirect
42. #15689005C22semidirect
73. C23×Dic47Q8semidirect
205. C22×Dic47C2×Q8semidirect
370. C2×C47#2665semidirect
428. C47C2×#2665semidirect
715. C2#20249557direct (N × H)

Maximal subgroups

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

subgroupindex
#202495572
C2×#156890642
C2×#156890462
C2×#156890442
C2×#156890422
C2×#156890352
C2×#156890302
C2×#156890272
C2×#156890082
C2×#156890052
C2×#156889842
C2×#156889812
C2×C22⋊C4×Dic472
C2×C47×#3932
C2×#266547