Finite Group Databasebeta

← C2×#20248802 #26386554

Subgroups — C2×#20248802 #26386554

Order 12032.

2270 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20248802C2116yesmaximal, direct product factor
2C2×#15689063C211yesmaximal, characteristic, complemented
3C2×#15689056C211yesmaximal, characteristic, complemented
4C2×#15689046C211yesmaximal, characteristic
5C2×#15689022C211yesmaximal, characteristic, complemented
6C2×#15689022C211yesmaximal, characteristic, complemented
7C2×#15689018C211yesmaximal, characteristic, complemented
8C2×#15689017C211yesmaximal, characteristic
9C2×#15689011C211yesmaximal, characteristic
10C2×#15689008C211yesmaximal, characteristic, complemented
11C2×#15689004C211yesmaximal, characteristic, complemented
12C2×#15688998C211yesmaximal, characteristic
13C2×#15688998C211yesmaximal, characteristic
14C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic47C211yesmaximal, characteristic
16C2×C47×#396C211yesmaximal, characteristic
17C24×Dic47C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic
21C22×C4⋊Dic47C2211yescharacteristic
22C22×C4⋊Dic47C2211yescharacteristic
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
32C22×C4×Dic47C2211yescharacteristic
33C22×C4×Dic47C2211yescharacteristic
34#15689063C2218yescomplemented
35#15689056C2218yescomplemented
36#15689046C2218yes—
37#15689022C2218yescomplemented
38#15689022C2218yescomplemented
39#15689018C2218yescomplemented
40#15689017C2218yes—
41#15689011C2218yes—
42#15689008C2218yescomplemented
43#15689004C2218yescomplemented
44#15688998C2218yes—
45#15688998C2218yes—
46C4⋊C4×Dic47C2218yescomplemented
47C22⋊C4×Dic47C2218yes—
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×C4⋊C4×C47C2211yescharacteristic
62C22×C22⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C47×#396C2218yes—
66C2×#95×C47C2211yescharacteristic
67C23×Dic47—24no—
68C23×Dic47—42no—
69C23×Dic47—42no—
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2314yes—
79C2×C4⋊Dic47—24no—
80C2×C4⋊Dic47—24no—
81C2×C4⋊Dic47—42no—
82C2×C4⋊Dic47—42no—
83C2×C4⋊Dic47—42no—
84C2×C4⋊Dic47C2314yes—
85C2×C4⋊Dic47C2314yes—
86C2×C4⋊Dic47C2314yes—
87C2×C4⋊Dic47C2314yes—
88C2×C4⋊Dic47C2314yes—
89C2×Dic47⋊C4—24no—
90C2×Dic47⋊C4—24no—
91C2×Dic47⋊C4—42no—
92C2×Dic47⋊C4—42no—
93C2×Dic47⋊C4C2314yes—
94C2×Dic47⋊C4C2314yes—
95C2×Dic47⋊C4C2314yes—
96C2×Dic47⋊C4C2314yes—
97C2×C22⋊Dic47—42no—
98C2×C22⋊Dic47—42no—
99C2×C22⋊Dic47Q818yes—
100C2×C22⋊Dic47C2314yes—
101C2×C22⋊Dic47C2314yes—
102C2×C22⋊Dic47C2314yes—
103C2×C4×Dic47—24no—
104C2×C4×Dic47—42no—
105C2×C4×Dic47—42no—
106C2×C4×Dic47—42no—
107C2×C4×Dic47C2314yes—
108C2×C4×Dic47C2314yes—
109C2×C4×Dic47C2314yes—
110C2×C4×Dic47C2314yes—
111C47⋊#95C2314yes—
112C47⋊#95C2314yes—
113C47⋊#95C2314yes—
114C47⋊#95C2314yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
117C47⋊#95C2314yes—
118C47⋊#95C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C25×C47C2311yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C2×C4⋊C4×C47—24no—
130C2×C4⋊C4×C47—24no—
131C2×C4⋊C4×C47—24no—
132C2×C4⋊C4×C47C2314yes—
133C2×C4⋊C4×C47C2314yes—
134C2×C4⋊C4×C47C2314yes—
135C2×C22⋊C4×C47—24no—
136C2×C22⋊C4×C47—24no—
137C2×C22⋊C4×C47—24no—
138C2×C22⋊C4×C47C2314yes—
139C2×C22⋊C4×C47C2314yes—
140C2×C22⋊C4×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
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#4114yes—
167C22×C4×C47#4114yes—
168C22×C4×C47#4114yes—
169C22×C4×C47C2412yes—
170C22×C4×C47C2412yes—
171C22×C4×C47C2412yes—
172C22×C4×C47C2412yes—
173C22×C4×C47C2412yes—
174C22×C4×C47C2412yes—
175C22×Dic47—22no—
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—22no—
195C22×Dic47—22no—
196C22×Dic47—28no—
197C22×Dic47—44no—
198C22×Dic47—44no—
199C22×Dic47—416no—
200C22×Dic47C2×Q814yes—
201C22×Dic47C2×Q814yes—
202C22×Dic47#4114yes—
203C22×Dic47C2412yes—
204C22×Dic47C2412yes—
205C22×Dic47C2412yes—
206C22×Dic47C2412yes—
207C22×Dic47C2412yes—
208C22×Dic47C2412yes—
209C22×Dic47C2412yes—
210C22×Dic47C2412yes—
211C4⋊C4×C47—28no—
212C4⋊C4×C47—28no—
213C4⋊C4×C47—28no—
214C22⋊C4×C47—28no—
215C22⋊C4×C47—28no—
216C22⋊C4×C47—28no—
217C22⋊Dic47—44no—
218C22⋊Dic47—44no—
219C22⋊Dic47C2×Q8116yes—
220C4⋊Dic47—28no—
221C4⋊Dic47—28no—
222C4⋊Dic47—44no—
223C4⋊Dic47—44no—
224C4⋊Dic47—44no—
225Dic47⋊C4—28no—
226Dic47⋊C4—28no—
227Dic47⋊C4—44no—
228Dic47⋊C4—44no—
229C4×Dic47—28no—
230C4×Dic47—44no—
231C4×Dic47—44no—
232C4×Dic47—44no—
233C23×C47—28no—
234C23×C47—28no—
235C23×C47—28no—
236C23×C47—22no—
237C23×C47—22no—
238C23×C47—22no—
239C23×C47—22no—
240C23×C47—22no—
241C23×C47—22no—
242C23×C47—44no—
243C23×C47—44no—
244C23×C47—44no—
245C23×C47—44no—
246C23×C47C22×Q814yes—
247C23×C47C22×Q812yes—
248C23×C47C2×#4112yes—
249C23×C47C2×#4112yes—
250C23×C47C2×#4112yes—
251C23×C47C2×#4112yes—
252C23×C47H(5,𝔽2)12yes—
253C23×C47H(5,𝔽2)12yes—
254C23×C47C2511yescharacteristic
255C2×C4×C47—28no—
256C2×C4×C47—28no—
257C2×C4×C47—28no—
258C2×C4×C47—22no—
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—44no—
274C2×C4×C47—44no—
275C2×C4×C47—44no—
276C2×C4×C47C2×#4114yes—
277C2×C4×C47C2×#4114yes—
278C2×C4×C47C2×#4114yes—
279C2×Dic47—28no—
280C2×Dic47—28no—
281C2×Dic47—28no—
282C2×Dic47—22no—
283C2×Dic47—22no—
284C2×Dic47—22no—
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—416no—
304C2×Dic47—44no—
305C2×Dic47—44no—
306C2×Dic47—44no—
307C2×Dic47—44no—
308C2×Dic47—44no—
309C2×Dic47C22×Q814yes—
310C2×Dic47C22×Q814yes—
311C2×Dic47C2×#4114yes—
312C2×#2587—471nomaximal, Sylow
313C22×C47—24no—
314C22×C47—24no—
315C22×C47—24no—
316C22×C47—416no—
317C22×C47—42no—
318C22×C47—42no—
319C22×C47—42no—
320C22×C47—42no—
321C22×C47#52914yes—
322C22×C47#53314yes—
323C22×C47#53814yes—
324C22×C47#55314yes—
325C22×C47#55314yes—
326C22×C47#55414yes—
327C22×C47#55414yes—
328C22×C47C23×Q811yescharacteristic
329C22×C47C22×#4111yescharacteristic
330C22×C47C22×#4111yescharacteristic
331C22×C47C22×#4111yescharacteristic
332C22×C47C22×#4111yescharacteristic
333C22×C47C2×H(5,𝔽2)11yescharacteristic
334C22×C47C2×H(5,𝔽2)11yescharacteristic
335C4×C47—24no—
336C4×C47—24no—
337C4×C47—24no—
338C4×C47—42no—
339C4×C47—42no—
340C4×C47—42no—
341Dic47—24no—
342Dic47—24no—
343Dic47—24no—
344Dic47—42no—
345Dic47—42no—
346Dic47—42no—
347Dic47—42no—
348Dic47—42no—
349#2587—4716no—
350C2×#400—471no—
351C2×#398—471no—
352C2×#396—471no—
353C2×#396D4711yescharacteristic
354C2×#389—471no—
355C2×#389—471no—
356C2×#389—471no—
357C2×#388—471no—
358C2×#388—471no—
359C2×#387—471no—
360C2×#387—471no—
361C2×#385—471no—
362C2×#385—471no—
363C2×C4×C4⋊C4—471no—
364C2×C4×C22⋊C4—471no—
365C2×C47—44no—
366C2×C47#258718yescomplemented
367C2×C47C2×#52911yescharacteristic
368C2×C47C2×#53311yescharacteristic
369C2×C47C2×#53811yescharacteristic
370C2×C47C2×#55311yescharacteristic
371C2×C47C2×#55311yescharacteristic
372C2×C47C2×#55411yescharacteristic
373C2×C47C2×#55411yescharacteristic
374C24×C4—471no—
375C22×C4⋊C4—471no—
376C22×C4⋊C4—471no—
377C22×C4⋊C4—471no—
378C22×C4⋊C4—471no—
379C22×C4⋊C4—471no—
380C22×C4⋊C4—471no—
381C22×C4⋊C4—471no—
382C22×C4⋊C4—471no—
383C22×C4⋊C4—471no—
384C22×C4⋊C4C2×D4711yescharacteristic
385C22×C4⋊C4C2×D4711yescharacteristic
386C22×C4⋊C4C2×D4711yescharacteristic
387C22×C22⋊C4—471no—
388C22×C22⋊C4—471no—
389C22×C22⋊C4—471no—
390C22×C22⋊C4C2×D4711yescharacteristic
391C22×C22⋊C4C2×D4711yescharacteristic
392C22×C22⋊C4C2×D4711yescharacteristic
393C22×C42—471no—
394C22×C42—471no—
395C22×C42—471no—
396C22×C42—471no—
397#400—478no—
398#398—478no—
399#396—478no—
400#396C2×D4718yes—
401#389—478no—
402#389—478no—
403#389—478no—
404#388—478no—
405#388—478no—
406#387—478no—
407#387—478no—
408#385—478no—
409#385—478no—
410C4×C4⋊C4—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×#95C2×D4711yescharacteristic
424C47C2×#258711yescharacteristic, complemented, Sylow
425C25C22×D4711yescharacteristic
426C23×C4—471no—
427C23×C4—471no—
428C23×C4—471no—
429C23×C4—471no—
430C23×C4—471no—
431C23×C4—471no—
432C23×C4—471no—
433C23×C4—471no—
434C23×C4—474no—
435C23×C4—944no—
436C23×C4—1882no—
437C23×C4—1882no—
438C23×C4C22×D4711yescharacteristic
439C23×C4C22×D4711yescharacteristic
440C23×C4C22×D4711yescharacteristic
441C23×C4C22×D4711yescharacteristic
442C23×C4C22×D4711yescharacteristic
443C23×C4C22×D4711yescharacteristic
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—474no—
448C2×C4⋊C4—474no—
449C2×C4⋊C4—474no—
450C2×C4⋊C4—474no—
451C2×C4⋊C4—474no—
452C2×C4⋊C4—474no—
453C2×C4⋊C4—474no—
454C2×C4⋊C4—474no—
455C2×C4⋊C4—474no—
456C2×C4⋊C4—944no—
457C2×C4⋊C4—944no—
458C2×C4⋊C4—944no—
459C2×C4⋊C4—944no—
460C2×C4⋊C4—1882no—
461C2×C4⋊C4—1882no—
462C2×C4⋊C4—1882no—
463C2×C4⋊C4—1882no—
464C2×C4⋊C4—1882no—
465C2×C4⋊C4C22×D4714yes—
466C2×C4⋊C4C22×D4714yes—
467C2×C4⋊C4C22×D4714yes—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—478no—
472C2×C22⋊C4—474no—
473C2×C22⋊C4—474no—
474C2×C22⋊C4—474no—
475C2×C22⋊C4—1882no—
476C2×C22⋊C4—1882no—
477C2×C22⋊C4C22×D4714yes—
478C2×C22⋊C4C22×D4714yes—
479C2×C22⋊C4C22×D4714yes—
480C2×C42—474no—
481C2×C42—474no—
482C2×C42—474no—
483C2×C42—474no—
484C2×C42—944no—
485C2×C42—1882no—
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#95C22×D4714yes—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24Q8×D4714yes—
507C24C23×D4712yes—
508C24C23×D4711yescharacteristic
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—474no—
525C22×C4—474no—
526C22×C4—474no—
527C22×C4—472no—
528C22×C4—472no—
529C22×C4—472no—
530C22×C4—472no—
531C22×C4—472no—
532C22×C4—472no—
533C22×C4—472no—
534C22×C4—472no—
535C22×C4—948no—
536C22×C4—942no—
537C22×C4—942no—
538C22×C4—942no—
539C22×C4—942no—
540C22×C4—942no—
541C22×C4—942no—
542C22×C4—942no—
543C22×C4—942no—
544C22×C4—942no—
545C22×C4—942no—
546C22×C4—942no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—942no—
550C22×C4—942no—
551C22×C4—942no—
552C22×C4—942no—
553C22×C4—942no—
554C22×C4—942no—
555C22×C4—942no—
556C22×C4—942no—
557C22×C4—1884no—
558C22×C4—1884no—
559C22×C4—18816no—
560C22×C4#1062535214yes—
561C22×C4#1062535214yes—
562C22×C4#1062535214yes—
563C22×C4C23×D4712yes—
564C22×C4C23×D4712yes—
565C22×C4C23×D4712yes—
566C22×C4C23×D4712yes—
567C22×C4C23×D4712yes—
568C22×C4C23×D4712yes—
569C4⋊C4—28no—
570C4⋊C4—28no—
571C4⋊C4—28no—
572C4⋊C4—948no—
573C4⋊C4—948no—
574C4⋊C4—948no—
575C4⋊C4—948no—
576C4⋊C4—1884no—
577C4⋊C4—1884no—
578C4⋊C4—1884no—
579C4⋊C4—1884no—
580C4⋊C4—1884no—
581C22⋊C4—28no—
582C22⋊C4—28no—
583C22⋊C4—28no—
584C22⋊C4—4716no—
585C22⋊C4—1884no—
586C22⋊C4—1884no—
587C42—948no—
588C42—1884no—
589C42—1884no—
590C42—1884no—
591C23—28no—
592C23—28no—
593C23—28no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—44no—
601C23—44no—
602C23—44no—
603C23—44no—
604C23C2×Q8×D4714yes—
605C23C2×Q8×D4712yes—
606C23#41×D4712yes—
607C23C2×#1062535212yes—
608C23C2×#1062535212yes—
609C23C2×#1062535212yes—
610C23#1309407012yes—
611C23#1309407012yes—
612C23C24×D4711yescharacteristic
613C2×C4—28no—
614C2×C4—28no—
615C2×C4—28no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—44no—
632C2×C4—44no—
633C2×C4—44no—
634C2×C4—474no—
635C2×C4—474no—
636C2×C4—474no—
637C2×C4—948no—
638C2×C4—948no—
639C2×C4—942no—
640C2×C4—942no—
641C2×C4—942no—
642C2×C4—942no—
643C2×C4—942no—
644C2×C4—942no—
645C2×C4—948no—
646C2×C4—942no—
647C2×C4—942no—
648C2×C4—942no—
649C2×C4—942no—
650C2×C4—942no—
651C2×C4—942no—
652C2×C4—942no—
653C2×C4—942no—
654C2×C4—942no—
655C2×C4—942no—
656C2×C4—942no—
657C2×C4—942no—
658C2×C4—942no—
659C2×C4—942no—
660C2×C4—942no—
661C2×C4—18816no—
662C2×C4—1884no—
663C2×C4—1884no—
664C2×C4—1884no—
665C2×C4—1884no—
666C2×C4—1884no—
667C2×C4C2×#1062535214yes—
668C2×C4C2×#1062535214yes—
669C2×C4C2×#1062535214yes—
670C22—24no—
671C22—24no—
672C22—24no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—416no—
678C22#1568965414yes—
679C22#1568967514yes—
680C22#1568971214yes—
681C22#1568982514yes—
682C22#1568982514yes—
683C22#1568983114yes—
684C22#1568983114yes—
685C22C22×Q8×D4711yescharacteristic
686C22C2×#41×D4711yescharacteristic
687C22C22×#1062535211yescharacteristic
688C22C22×#1062535211yescharacteristic
689C22C22×#1062535211yescharacteristic
690C22C2×#1309407011yescharacteristic
691C22C2×#1309407011yescharacteristic
692C4—24no—
693C4—24no—
694C4—24no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—944no—
699C4—944no—
700C4—944no—
701C4—1882no—
702C4—1882no—
703C4—1882no—
704C4—1882no—
705C4—1882no—
706C2—44no—
707C2#2024880218yesdirect product factor
708C2C2×#1568965411yescharacteristic
709C2C2×#1568967511yescharacteristic
710C2C2×#1568971211yescharacteristic
711C2C2×#1568982511yescharacteristic
712C2C2×#1568982511yescharacteristic
713C2C2×#1568983111yescharacteristic
714C2C2×#1568983111yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#396C2
socleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#396D47
hypocenterC47C2×#2587
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. #20248802C2direct (N × H)
2. C2×#15689063C2semidirect
3. C2×#15689056C2semidirect
5. C2×#15689022C2semidirect
6. C2×#15689022C2semidirect
7. C2×#15689018C2semidirect
10. C2×#15689008C2semidirect
11. C2×#15689004C2semidirect
14. C2×C4⋊C4×Dic47C2semidirect
34. #15689063C22semidirect
35. #15689056C22semidirect
37. #15689022C22semidirect
38. #15689022C22semidirect
39. #15689018C22semidirect
42. #15689008C22semidirect
43. #15689004C22semidirect
46. C4⋊C4×Dic47C22semidirect
366. C2×C47#2587semidirect
424. C47C2×#2587semidirect
707. C2#20248802direct (N × H)

Maximal subgroups

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

subgroupindex
#202488022
C2×#156890632
C2×#156890562
C2×#156890462
C2×#156890222
C2×#156890182
C2×#156890172
C2×#156890112
C2×#156890082
C2×#156890042
C2×#156889982
C2×C4⋊C4×Dic472
C2×C22⋊C4×Dic472
C2×C47×#3962
C2×#258747