Finite Group Databasebeta

← C2×#20249564 #26382871

Subgroups — C2×#20249564 #26382871

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#20249564C2116yesmaximal, direct product factor
2C2×#15689064C211yesmaximal, characteristic, complemented
3C2×#15689061C211yesmaximal, characteristic, complemented
4C2×#15689045C211yesmaximal, characteristic
5C2×#15689045C211yesmaximal, characteristic
6C2×#15689044C211yesmaximal, characteristic, complemented
7C2×#15689043C211yesmaximal, characteristic, complemented
8C2×#15689036C211yesmaximal, characteristic
9C2×#15689036C211yesmaximal, characteristic
10C2×#15689029C211yesmaximal, characteristic, complemented
11C2×#15689027C211yesmaximal, characteristic, complemented
12C2×#15689006C211yesmaximal, characteristic, complemented
13C2×#15688985C211yesmaximal, characteristic
14C2×#15688982C211yesmaximal, characteristic
15C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
16C2×C47×#387C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C23×Dic94C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic
21C22×C4⋊Dic47C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×Dic47⋊C4C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×(C2×D47)⋊C4C2211yescharacteristic
27C22×(C2×D47)⋊C4C2211yescharacteristic
28C22×(C2×D47)⋊C4C2211yescharacteristic
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2211yescharacteristic
32C22×C4×Dic47C2211yescharacteristic
33#15689064C2218yescomplemented
34#15689061C2218yescomplemented
35#15689045C2218yes—
36#15689045C2218yes—
37#15689044C2218yescomplemented
38#15689043C2218yescomplemented
39#15689036C2218yes—
40#15689036C2218yes—
41#15689029C2218yescomplemented
42#15689027C2218yescomplemented
43#15689006C2218yescomplemented
44#15688985C2218yes—
45#15688982C2218yes—
46C4×(C2×D47)⋊C4C2218yes—
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
59C22×C4⋊C4×C47C2211yescharacteristic
60C22×C4⋊C4×C47C2211yescharacteristic
61C22×C42×C47C2211yescharacteristic
62C47×#387C2218yescomplemented
63C2×#95×C47C2211yescharacteristic
64C2×#95×C47C2211yescharacteristic
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C24×D47C2311yescharacteristic
68C22×Dic94—24no—
69C22×Dic94—24no—
70C22×Dic94—42no—
71C22×Dic94—42no—
72C22×Dic94—42no—
73C22×Dic94—42no—
74C22×Dic94C2314yes—
75C22×Dic94C2314yes—
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C22×C4×D47—42no—
84C22×C4×D47—42no—
85C22×C4×D47Q818yescomplemented
86C22×C4×D47C2314yes—
87C2×C4⋊Dic47—24no—
88C2×C4⋊Dic47—42no—
89C2×C4⋊Dic47C2314yes—
90C2×C4⋊Dic47C2314yes—
91C2×Dic47⋊C4—42no—
92C2×Dic47⋊C4—42no—
93C2×Dic47⋊C4—42no—
94C2×Dic47⋊C4—42no—
95C2×Dic47⋊C4C2314yes—
96C2×Dic47⋊C4C2314yes—
97C2×Dic47⋊C4C2314yes—
98C2×Dic47⋊C4C2314yes—
99C2×(C2×D47)⋊C4—24no—
100C2×(C2×D47)⋊C4—24no—
101C2×(C2×D47)⋊C4—42no—
102C2×(C2×D47)⋊C4—42no—
103C2×(C2×D47)⋊C4—42no—
104C2×(C2×D47)⋊C4—42no—
105C2×(C2×D47)⋊C4C2314yes—
106C2×(C2×D47)⋊C4C2314yes—
107C2×(C2×D47)⋊C4C2314yes—
108C2×(C2×D47)⋊C4C2314yes—
109C2×(C2×D47)⋊C4C2314yes—
110C2×(C2×D47)⋊C4C2314yes—
111C2×C4×Dic47—42no—
112C2×C4×Dic47C2314yes—
113C47⋊#95C2314yes—
114C47⋊#95C2314yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
117C47⋊#95C2314yes—
118C47⋊#95C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C23×C4×C47C2311yescharacteristic
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C2×C4⋊C4×C47—24no—
133C2×C4⋊C4×C47—42no—
134C2×C4⋊C4×C47C2314yes—
135C2×C4⋊C4×C47C2314yes—
136C2×C42×C47—42no—
137C2×C42×C47C2314yes—
138#95×C47C2314yes—
139#95×C47C2314yes—
140#95×C47C2314yes—
141#95×C47C2314yes—
142C24×C47C2411yescharacteristic
143C23×D47—22no—
144C23×D47—22no—
145C23×D47—22no—
146C23×D47—22no—
147C23×D47—22no—
148C23×D47—22no—
149C23×D47C2×Q814yes—
150C23×D47C2412yes—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
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×C47C2×Q814yes—
171C22×C4×C47#4114yes—
172C22×C4×C47C2412yes—
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×Dic47C2×Q814yes—
199C22×Dic47#4114yes—
200C22×Dic47C2412yes—
201C22×Dic47C2412yes—
202C22×Dic47C2412yes—
203C22×Dic47C2412yes—
204C22×Dic47C2412yes—
205C22×Dic47C2412yes—
206C22×Dic47C2412yes—
207C2×C4×D47—416no—
208C2×C4×D47—44no—
209C2×C4×D47—44no—
210C2×C4×D47C2×Q8116yescomplemented
211C2×Dic94—28no—
212C2×Dic94—28no—
213C2×Dic94—44no—
214C2×Dic94—44no—
215C2×Dic94—44no—
216C2×Dic94—44no—
217C2×Dic94—416no—
218C2×Dic94—416no—
219C4⋊C4×C47—28no—
220C4⋊C4×C47—44no—
221C42×C47—44no—
222(C2×D47)⋊C4—28no—
223(C2×D47)⋊C4—28no—
224(C2×D47)⋊C4—44no—
225(C2×D47)⋊C4—44no—
226(C2×D47)⋊C4—44no—
227(C2×D47)⋊C4—44no—
228C4⋊Dic47—28no—
229C4⋊Dic47—44no—
230Dic47⋊C4—44no—
231Dic47⋊C4—44no—
232Dic47⋊C4—44no—
233Dic47⋊C4—44no—
234C4×Dic47—44no—
235C23×C47C22×Q812yes—
236C23×C47C2×#4112yes—
237C23×C47C2×#4112yes—
238C23×C47H(5,𝔽2)12yes—
239C23×C47H(5,𝔽2)12yes—
240C23×C47H(5,𝔽2)12yes—
241C23×C472−1+412yes—
242C23×C47C2511yescharacteristic
243C22×D47—28no—
244C22×D47—28no—
245C22×D47—28no—
246C22×D47—22no—
247C22×D47—22no—
248C22×D47—22no—
249C22×D47—22no—
250C22×D47—22no—
251C22×D47—22no—
252C22×D47—44no—
253C22×D47—44no—
254C22×D47—44no—
255C22×D47—44no—
256C22×D47C22×Q814yes—
257C2×C4×C47—28no—
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—22no—
277C2×C4×C47—22no—
278C2×C4×C47—44no—
279C2×C4×C47—44no—
280C2×C4×C47—44no—
281C2×C4×C47—44no—
282C2×C4×C47—44no—
283C2×C4×C47C22×Q814yes—
284C2×C4×C47C2×#4114yes—
285C2×Dic47—28no—
286C2×Dic47—28no—
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—44no—
307C2×Dic47—44no—
308C2×Dic47—44no—
309C2×Dic47—44no—
310C2×Dic47—44no—
311C2×Dic47C22×Q814yes—
312C2×Dic47C2×#4114yes—
313C4×D47—416no—
314Dic94—416no—
315Dic94—416no—
316C2×#2665—471nomaximal, Sylow
317C22×C47#53314yes—
318C22×C47#53814yes—
319C22×C47#53814yes—
320C22×C47#54214yes—
321C22×C47#54214yes—
322C22×C47#54314yes—
323C22×C47#54414yes—
324C22×C47C23×Q811yescharacteristic
325C22×C47C22×#4111yescharacteristic
326C22×C47C22×#4111yescharacteristic
327C22×C47C2×H(5,𝔽2)11yescharacteristic
328C22×C47C2×H(5,𝔽2)11yescharacteristic
329C22×C47C2×H(5,𝔽2)11yescharacteristic
330C22×C47C2×2−1+411yescharacteristic
331C2×D47—24no—
332C2×D47—24no—
333C2×D47—24no—
334C2×D47—416no—
335C2×D47—42no—
336C2×D47—42no—
337C2×D47—42no—
338C2×D47—42no—
339C4×C47—24no—
340C4×C47—24no—
341C4×C47—42no—
342C4×C47—42no—
343C4×C47—42no—
344C4×C47—42no—
345C4×C47—42no—
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×#393—471no—
362C2×#391—471no—
363C2×#391—471no—
364C2×#387—471no—
365C2×#387D4711yescharacteristic, complemented
366C2×#381—471no—
367C2×#380—471no—
368C2×C4×C22⋊C4—471no—
369C2×C47#266518yescomplemented
370C2×C47C2×#53311yescharacteristic
371C2×C47C2×#53811yescharacteristic
372C2×C47C2×#53811yescharacteristic
373C2×C47C2×#54211yescharacteristic
374C2×C47C2×#54211yescharacteristic
375C2×C47C2×#54311yescharacteristic
376C2×C47C2×#54411yescharacteristic
377D47—44no—
378C23×Q8—471no—
379C23×Q8—471no—
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⋊C4C2×D4711yescharacteristic
388C22×C4⋊C4C2×D4711yescharacteristic
389C22×C22⋊C4—471no—
390C22×C22⋊C4—471no—
391C22×C22⋊C4—471no—
392C22×C22⋊C4—471no—
393C22×C22⋊C4—471no—
394C22×C22⋊C4—471no—
395C22×C42—471no—
396C22×C42C2×D4711yescharacteristic
397#400—478no—
398#400—478no—
399#396—478no—
400#396—478no—
401#395—478no—
402#395—478no—
403#393—478no—
404#393—478no—
405#391—478no—
406#391—478no—
407#387—478no—
408#387C2×D4718yescomplemented
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×#95C2×D4711yescharacteristic
425C2×#95C2×D4711yescharacteristic
426C2×#95C2×D4711yescharacteristic
427C2×#95C2×D4711yescharacteristic
428C47C2×#266511yescharacteristic, complemented, Sylow
429C25—471no—
430C22×Q8—474no—
431C22×Q8—474no—
432C22×Q8—944no—
433C22×Q8—944no—
434C22×Q8—1882no—
435C22×Q8—1882no—
436C22×Q8—1882no—
437C22×Q8—1882no—
438C23×C4—471no—
439C23×C4—471no—
440C23×C4—478no—
441C23×C4—474no—
442C23×C4—471no—
443C23×C4—471no—
444C23×C4—471no—
445C23×C4—471no—
446C23×C4—471no—
447C23×C4—1882no—
448C23×C4—1882no—
449C23×C4C22×D4711yescharacteristic
450C23×C4C22×D4711yescharacteristic
451C23×C4C22×D4711yescharacteristic
452C23×C4C22×D4711yescharacteristic
453C23×C4C22×D4711yescharacteristic
454C23×C4C22×D4711yescharacteristic
455C23×C4C22×D4711yescharacteristic
456C2×C4⋊C4—24no—
457C2×C4⋊C4—42no—
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—1882no—
466C2×C4⋊C4—1882no—
467C2×C4⋊C4—1882no—
468C2×C4⋊C4—1882no—
469C2×C4⋊C4—1882no—
470C2×C4⋊C4C22×D4714yes—
471C2×C4⋊C4C22×D4714yes—
472C2×C22⋊C4—474no—
473C2×C22⋊C4—474no—
474C2×C22⋊C4—474no—
475C2×C22⋊C4—474no—
476C2×C22⋊C4—474no—
477C2×C22⋊C4—474no—
478C2×C22⋊C4—944no—
479C2×C22⋊C4—944no—
480C2×C22⋊C4—1882no—
481C2×C22⋊C4—1882no—
482C2×C22⋊C4—1882no—
483C2×C22⋊C4—1882no—
484C2×C42—42no—
485C2×C42—474no—
486C2×C42—1882no—
487C2×C42C22×D4714yes—
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#95C22×D4714yes—
501#95C22×D4714yes—
502#95C22×D4714yes—
503#95C22×D4714yes—
504C24—474no—
505C24—472no—
506C24—942no—
507C24—942no—
508C24—942no—
509C24—942no—
510C24—942no—
511C24—942no—
512C24C23×D4711yescharacteristic
513C2×Q8—948no—
514C2×Q8—948no—
515C2×Q8—1884no—
516C2×Q8—1884no—
517C2×Q8—1884no—
518C2×Q8—1884no—
519C2×Q8—18816no—
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—22no—
539C22×C4—22no—
540C22×C4—474no—
541C22×C4—474no—
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—18816no—
570C22×C4—1884no—
571C22×C4—1884no—
572C22×C4#1062535014yes—
573C22×C4Q8×D4714yes—
574C22×C4C23×D4712yes—
575C22×C4C23×D4712yes—
576C22×C4C23×D4712yes—
577C22×C4C23×D4712yes—
578C22×C4C23×D4712yes—
579C22×C4C23×D4712yes—
580C22×C4C23×D4712yes—
581C4⋊C4—28no—
582C4⋊C4—44no—
583C4⋊C4—948no—
584C4⋊C4—1884no—
585C4⋊C4—1884no—
586C4⋊C4—1884no—
587C4⋊C4—1884no—
588C4⋊C4—1884no—
589C22⋊C4—948no—
590C22⋊C4—948no—
591C22⋊C4—1884no—
592C22⋊C4—1884no—
593C22⋊C4—1884no—
594C22⋊C4—1884no—
595C42—44no—
596C42—1884no—
597C23—474no—
598C23—948no—
599C23—948no—
600C23—948no—
601C23—942no—
602C23—942no—
603C23—942no—
604C23—942no—
605C23—942no—
606C23—942no—
607C23—1884no—
608C23—1884no—
609C23—1884no—
610C23—1884no—
611C23C2×Q8×D4712yes—
612C23#41×D4712yes—
613C23C2×#1062535012yes—
614C23#1309406912yes—
615C23#1309407012yes—
616C23#1309407012yes—
617C23#1309407112yes—
618C23C24×D4711yescharacteristic
619Q8—18816no—
620Q8—18816no—
621C2×C4—28no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—28no—
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—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—474no—
648C2×C4—474no—
649C2×C4—948no—
650C2×C4—942no—
651C2×C4—942no—
652C2×C4—942no—
653C2×C4—942no—
654C2×C4—948no—
655C2×C4—942no—
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—18816no—
671C2×C4—1884no—
672C2×C4—1884no—
673C2×C4—1884no—
674C2×C4—1884no—
675C2×C4—1884no—
676C2×C4C2×Q8×D4714yes—
677C2×C4C2×#1062535014yes—
678C22—944no—
679C22—944no—
680C22—944no—
681C22—1882no—
682C22—1882no—
683C22—18816no—
684C22—1882no—
685C22—1882no—
686C22#1568967714yes—
687C22#1568970614yes—
688C22#1568971214yes—
689C22#1568974114yes—
690C22#1568974414yes—
691C22#1568974814yes—
692C22#1568975314yes—
693C22C22×Q8×D4711yescharacteristic
694C22C2×#41×D4711yescharacteristic
695C22C22×#1062535011yescharacteristic
696C22C2×#1309406911yescharacteristic
697C22C2×#1309407011yescharacteristic
698C22C2×#1309407011yescharacteristic
699C22C2×#1309407111yescharacteristic
700C4—24no—
701C4—24no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—944no—
708C4—944no—
709C4—1882no—
710C4—1882no—
711C4—1882no—
712C4—1882no—
713C4—1882no—
714C2—1884no—
715C2#2024956418yesdirect product factor
716C2C2×#1568967711yescharacteristic
717C2C2×#1568970611yescharacteristic
718C2C2×#1568971211yescharacteristic
719C2C2×#1568974111yescharacteristic
720C2C2×#1568974411yescharacteristic
721C2C2×#1568974811yescharacteristic
722C2C2×#1568975311yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#387C2
socleC24×C47C24
prime radicalC24×D47C23
hypercenterC2×#387D47
hypocenterC47C2×#2665
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. #20249564C2direct (N × H)
2. C2×#15689064C2semidirect
3. C2×#15689061C2semidirect
6. C2×#15689044C2semidirect
7. C2×#15689043C2semidirect
10. C2×#15689029C2semidirect
11. C2×#15689027C2semidirect
12. C2×#15689006C2semidirect
16. C2×C47×#387C2semidirect
33. #15689064C22semidirect
34. #15689061C22semidirect
37. #15689044C22semidirect
38. #15689043C22semidirect
41. #15689029C22semidirect
42. #15689027C22semidirect
43. #15689006C22semidirect
62. C47×#387C22semidirect
85. C22×C4×D47Q8semidirect
210. C2×C4×D47C2×Q8semidirect
365. C2×#387D47semidirect
369. C2×C47#2665semidirect
408. #387C2×D47semidirect
428. C47C2×#2665semidirect
715. C2#20249564direct (N × H)

Maximal subgroups

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

subgroupindex
#202495642
C2×#156890642
C2×#156890612
C2×#156890452
C2×#156890442
C2×#156890432
C2×#156890362
C2×#156890292
C2×#156890272
C2×#156890062
C2×#156889852
C2×#156889822
C2×C4×(C2×D47)⋊C42
C2×C47×#3872
C2×#266547