Finite Group Databasebeta

← C2×#20248059 #26385364

Subgroups — C2×#20248059 #26385364

Order 12032.

2466 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
1C22×#13094017C211yesmaximal, characteristic
2C22×#13094014C211yesmaximal, characteristic, complemented
3#20248059C2116yesmaximal, direct product factor
4C2×#15689059C211yesmaximal, characteristic
5C2×#15689057C211yesmaximal, characteristic, complemented
6C2×#15689056C211yesmaximal, characteristic, complemented
7C2×#15689046C211yesmaximal, characteristic
8C2×#15689021C211yesmaximal, characteristic, complemented
9C2×#15689016C211yesmaximal, characteristic
10C2×#15689011C211yesmaximal, characteristic
11C2×#15689011C211yesmaximal, characteristic
12C2×#15689006C211yesmaximal, characteristic, complemented
13C2×#15688987C211yesmaximal, characteristic, complemented
14C2×C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
15C2×#15688974C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic
17C2×#13094017—28no—
18C2×#13094017C2218yes—
19C2×#13094014—28no—
20C2×#13094014C2218yescomplemented
21C22×C4⋊Dic47C2211yescharacteristic
22C22×C4⋊Dic47C2211yescharacteristic
23C22×C4⋊Dic47C2211yescharacteristic
24C22×C4⋊Dic47C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×C22⋊Dic47C2211yescharacteristic
34C22×C22⋊Dic47C2211yescharacteristic
35C22×C22⋊Dic47C2211yescharacteristic
36C22×C22⋊Dic47C2211yescharacteristic
37C22×C4×Dic47C2211yescharacteristic
38C22×C4×Dic47C2211yescharacteristic
39C22×C4×Dic47C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41#15689059C2218yes—
42#15689057C2218yescomplemented
43#15689056C2218yescomplemented
44#15689046C2218yes—
45#15689021C2218yescomplemented
46#15689016C2218yes—
47#15689011C2218yes—
48#15689011C2218yes—
49#15689006C2218yescomplemented
50#15688987C2218yescomplemented
51C4×C4⋊Dic47C2218yescomplemented
52#15688974C2218yescomplemented
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C22⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C42×C47C2211yescharacteristic
66C47×#388C2218yes—
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C23×Dic47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77#13094017—232no—
78#13094014—232no—
79C2×C4⋊Dic47—24no—
80C2×C4⋊Dic47—24no—
81C2×C4⋊Dic47—24no—
82C2×C4⋊Dic47D418yes—
83C2×C4⋊Dic47C2314yes—
84C2×C4⋊Dic47C2314yes—
85C2×C4⋊Dic47C2314yes—
86C2×C4⋊Dic47C2314yes—
87C2×Dic47⋊C4—24no—
88C2×Dic47⋊C4—24no—
89C2×Dic47⋊C4—24no—
90C2×Dic47⋊C4—24no—
91C2×Dic47⋊C4—24no—
92C2×Dic47⋊C4—24no—
93C2×Dic47⋊C4—24no—
94C2×Dic47⋊C4—24no—
95C2×Dic47⋊C4C2314yes—
96C2×Dic47⋊C4C2314yes—
97C2×Dic47⋊C4C2314yes—
98C2×Dic47⋊C4C2314yes—
99C2×Dic47⋊C4C2314yes—
100C2×Dic47⋊C4C2314yes—
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2314yes—
103C2×C22⋊Dic47—24no—
104C2×C22⋊Dic47—24no—
105C2×C22⋊Dic47—24no—
106C2×C22⋊Dic47—24no—
107C2×C22⋊Dic47C2314yes—
108C2×C22⋊Dic47C2314yes—
109C2×C22⋊Dic47C2314yes—
110C2×C22⋊Dic47C2314yes—
111C2×C4×Dic47—24no—
112C2×C4×Dic47—24no—
113C2×C4×Dic47—24no—
114C2×C4×Dic47—24no—
115C2×C4×Dic47C2314yes—
116C2×C4×Dic47C2314yes—
117C2×C4×Dic47C2314yes—
118C2×C4×Dic47C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C25×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C2×C4⋊C4×C47—24no—
135C2×C4⋊C4×C47C2314yes—
136C2×C22⋊C4×C47—24no—
137C2×C22⋊C4×C47—24no—
138C2×C22⋊C4×C47—24no—
139C2×C22⋊C4×C47C2314yes—
140C2×C22⋊C4×C47C2314yes—
141C2×C22⋊C4×C47C2314yes—
142C2×C42×C47—24no—
143C2×C42×C47C2314yes—
144#95×C47C2314yes—
145#95×C47C2314yes—
146C24×C47—22no—
147C24×C47—22no—
148C24×C47—22no—
149C24×C47—22no—
150C24×C47—22no—
151C24×C47—22no—
152C24×C47—22no—
153C24×C47C2412yes—
154C24×C47C2411yescharacteristic
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×D414yes—
171C22×C4×C47#4114yes—
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×Dic47C2×D414yes—
200C22×Dic47C2×D414yes—
201C22×Dic47#4114yes—
202C22×Dic47#4114yes—
203C22×Dic47C2412yes—
204C22×Dic47C2412yes—
205C22×Dic47C2412yes—
206C22×Dic47C2412yes—
207C22×Dic47C2412yes—
208C22×Dic47C2412yes—
209C22×Dic47C2412yes—
210C22×Dic47C2412yes—
211C4⋊C4×C47—28no—
212C22⋊C4×C47—28no—
213C22⋊C4×C47—28no—
214C22⋊C4×C47—28no—
215C42×C47—28no—
216C22⋊Dic47—28no—
217C22⋊Dic47—28no—
218C22⋊Dic47—28no—
219C22⋊Dic47—28no—
220C4⋊Dic47—28no—
221C4⋊Dic47—28no—
222C4⋊Dic47—28no—
223C4⋊Dic47C2×D4116yes—
224Dic47⋊C4—28no—
225Dic47⋊C4—28no—
226Dic47⋊C4—28no—
227Dic47⋊C4—28no—
228Dic47⋊C4—28no—
229Dic47⋊C4—28no—
230Dic47⋊C4—28no—
231Dic47⋊C4—28no—
232C4×Dic47—28no—
233C4×Dic47—28no—
234C4×Dic47—28no—
235C4×Dic47—28no—
236C23×C47—22no—
237C23×C47—22no—
238C23×C47—22no—
239C23×C47—22no—
240C23×C47—22no—
241C23×C47—22no—
242C23×C47—22no—
243C23×C47—44no—
244C23×C47—44no—
245C23×C47—44no—
246C23×C47—44no—
247C23×C47—44no—
248C23×C47—44no—
249C23×C47—44no—
250C23×C47C22×D412yes—
251C23×C47C2×#4112yes—
252C23×C47C2×#4112yes—
253C23×C47C2×#4112yes—
254C23×C47C2×#4112yes—
255C23×C472−1+412yes—
256C23×C472−1+412yes—
257C23×C47C2511yescharacteristic
258C2×C4×C47—28no—
259C2×C4×C47—28no—
260C2×C4×C47—28no—
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×C47C22×D414yes—
280C2×C4×C47C2×#4114yes—
281C2×C4×C47C2×#4114yes—
282C2×Dic47—28no—
283C2×Dic47—28no—
284C2×Dic47—28no—
285C2×Dic47—28no—
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—44no—
307C2×Dic47—44no—
308C2×Dic47—44no—
309C2×Dic47—44no—
310C2×Dic47C22×D414yes—
311C2×Dic47C22×D414yes—
312C2×Dic47C2×#4114yes—
313C2×Dic47C2×#4114yes—
314C2×#2519—471nomaximal, Sylow
315C22×C47—42no—
316C22×C47—42no—
317C22×C47—42no—
318C22×C47—42no—
319C22×C47—42no—
320C22×C47—42no—
321C22×C47—42no—
322C22×C47—88no—
323C22×C47#52914yes—
324C22×C47#53214yes—
325C22×C47#54114yes—
326C22×C47#54714yes—
327C22×C47#54814yes—
328C22×C47#55214yes—
329C22×C47#55214yes—
330C22×C47C23×D411yescharacteristic
331C22×C47C22×#4111yescharacteristic
332C22×C47C22×#4111yescharacteristic
333C22×C47C22×#4111yescharacteristic
334C22×C47C22×#4111yescharacteristic
335C22×C47C2×2−1+411yescharacteristic
336C22×C47C2×2−1+411yescharacteristic
337C4×C47—24no—
338C4×C47—24no—
339C4×C47—24no—
340C4×C47—42no—
341C4×C47—42no—
342C4×C47—42no—
343Dic47—24no—
344Dic47—24no—
345Dic47—24no—
346Dic47—24no—
347Dic47—42no—
348Dic47—42no—
349Dic47—42no—
350Dic47—42no—
351C22×#126—471no—
352C22×#125—471no—
353#2519—4716no—
354C2×#399—471no—
355C2×#398—471no—
356C2×#398—471no—
357C2×#396—471no—
358C2×#389—471no—
359C2×#388—471no—
360C2×#388—471no—
361C2×#388—471no—
362C2×#388D4711yescharacteristic
363C2×#387—471no—
364C2×#382—471no—
365C2×C4×C4⋊C4—471no—
366C2×C4×C4⋊C4—471no—
367C2×C47—82no—
368C2×C47#251918yescomplemented
369C2×C47C2×#52911yescharacteristic
370C2×C47C2×#53211yescharacteristic
371C2×C47C2×#54111yescharacteristic
372C2×C47C2×#54711yescharacteristic
373C2×C47C2×#54811yescharacteristic
374C2×C47C2×#55211yescharacteristic
375C2×C47C2×#55211yescharacteristic
376C2×#126—478no—
377C2×#126—948no—
378C2×#125—478no—
379C2×#125—948no—
380C22×C4⋊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×C4⋊C4—471no—
390C22×C4⋊C4—471no—
391C22×C4⋊C4—471no—
392C22×C4⋊C4C2×D4711yescharacteristic
393C22×C22⋊C4—471no—
394C22×C22⋊C4—471no—
395C22×C22⋊C4—471no—
396C22×C22⋊C4—471no—
397C22×C22⋊C4C2×D4711yescharacteristic
398C22×C22⋊C4C2×D4711yescharacteristic
399C22×C22⋊C4C2×D4711yescharacteristic
400C22×C42—471no—
401C22×C42—471no—
402C22×C42—471no—
403C22×C42—471no—
404C22×C42C2×D4711yescharacteristic
405#399—478no—
406#398—478no—
407#398—478no—
408#396—478no—
409#389—478no—
410#388—478no—
411#388—478no—
412#388—478no—
413#388C2×D4718yes—
414#387—478no—
415#382—478no—
416C4×C4⋊C4—478no—
417C4×C4⋊C4—478no—
418C2×#95—471no—
419C2×#95—471no—
420C2×#95—471no—
421C2×#95—471no—
422C2×#95—471no—
423C2×#95—471no—
424C2×#95—471no—
425C2×#95—471no—
426C2×#95C2×D4711yescharacteristic
427C2×#95C2×D4711yescharacteristic
428C47C2×#251911yescharacteristic, complemented, Sylow
429C25C22×D4711yescharacteristic
430C23×C4—471no—
431C23×C4—471no—
432C23×C4—471no—
433C23×C4—471no—
434C23×C4—471no—
435C23×C4—471no—
436C23×C4—471no—
437C23×C4—471no—
438C23×C4C22×D4711yescharacteristic
439C23×C4C22×D4711yescharacteristic
440C23×C4C22×D4711yescharacteristic
441C23×C4C22×D4711yescharacteristic
442C23×C4C22×D4711yescharacteristic
443C23×C4C22×D4711yescharacteristic
444#126—9432no—
445#125—9432no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—478no—
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—474no—
457C2×C4⋊C4—474no—
458C2×C4⋊C4—474no—
459C2×C4⋊C4—474no—
460C2×C4⋊C4—944no—
461C2×C4⋊C4—944no—
462C2×C4⋊C4—944no—
463C2×C4⋊C4—944no—
464C2×C4⋊C4—944no—
465C2×C4⋊C4—944no—
466C2×C4⋊C4—944no—
467C2×C4⋊C4—944no—
468C2×C4⋊C4—944no—
469C2×C4⋊C4—944no—
470C2×C4⋊C4—944no—
471C2×C4⋊C4C22×D4714yes—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—474no—
476C2×C22⋊C4—474no—
477C2×C22⋊C4—474no—
478C2×C22⋊C4—474no—
479C2×C22⋊C4—944no—
480C2×C22⋊C4—944no—
481C2×C22⋊C4—944no—
482C2×C22⋊C4—944no—
483C2×C22⋊C4C22×D4714yes—
484C2×C22⋊C4C22×D4714yes—
485C2×C22⋊C4C22×D4714yes—
486C2×C42—24no—
487C2×C42—474no—
488C2×C42—474no—
489C2×C42—474no—
490C2×C42—474no—
491C2×C42—944no—
492C2×C42—944no—
493C2×C42—944no—
494C2×C42—944no—
495C2×C42C22×D4714yes—
496#95—474no—
497#95—474no—
498#95—474no—
499#95—474no—
500#95—474no—
501#95—474no—
502#95—474no—
503#95—474no—
504#95C22×D4714yes—
505#95C22×D4714yes—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24C23×D4712yes—
514C24C23×D4711yescharacteristic
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—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—474no—
531C22×C4—474no—
532C22×C4—474no—
533C22×C4—474no—
534C22×C4—472no—
535C22×C4—472no—
536C22×C4—472no—
537C22×C4—472no—
538C22×C4—472no—
539C22×C4—472no—
540C22×C4—472no—
541C22×C4—472no—
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—942no—
558C22×C4—942no—
559C22×C4—942no—
560C22×C4—942no—
561C22×C4—942no—
562C22×C4#1062535014yes—
563C22×C4D4×D4714yes—
564C22×C4#1062535214yes—
565C22×C4C23×D4712yes—
566C22×C4C23×D4712yes—
567C22×C4C23×D4712yes—
568C22×C4C23×D4712yes—
569C22×C4C23×D4712yes—
570C22×C4C23×D4712yes—
571C4⋊C4—28no—
572C4⋊C4—4716no—
573C4⋊C4—948no—
574C4⋊C4—948no—
575C4⋊C4—948no—
576C4⋊C4—948no—
577C4⋊C4—948no—
578C4⋊C4—948no—
579C4⋊C4—948no—
580C4⋊C4—948no—
581C4⋊C4—948no—
582C4⋊C4—948no—
583C4⋊C4—948no—
584C22⋊C4—28no—
585C22⋊C4—28no—
586C22⋊C4—28no—
587C22⋊C4—948no—
588C22⋊C4—948no—
589C22⋊C4—948no—
590C22⋊C4—948no—
591C42—28no—
592C42—948no—
593C42—948no—
594C42—948no—
595C42—948no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23C2×D4×D4712yes—
611C23#41×D4712yes—
612C23#41×D4712yes—
613C23C2×#1062535212yes—
614C23C2×#1062535012yes—
615C23#1309407112yes—
616C23#1309407112yes—
617C23C24×D4711yescharacteristic
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—28no—
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—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—474no—
640C2×C4—474no—
641C2×C4—474no—
642C2×C4—474no—
643C2×C4—948no—
644C2×C4—948no—
645C2×C4—948no—
646C2×C4—948no—
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—942no—
662C2×C4—942no—
663C2×C4—942no—
664C2×C4—942no—
665C2×C4—942no—
666C2×C4—942no—
667C2×C4—1884no—
668C2×C4—1884no—
669C2×C4—1884no—
670C2×C4—1884no—
671C2×C4C2×D4×D4714yes—
672C2×C4C2×#1062535214yes—
673C2×C4C2×#1062535014yes—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—88no—
682C22#1568965114yes—
683C22#1568966814yes—
684C22#1568973014yes—
685C22#1568977814yes—
686C22#1568978114yes—
687C22#1568981014yes—
688C22#1568981314yes—
689C22C22×D4×D4711yescharacteristic
690C22C2×#41×D4711yescharacteristic
691C22C2×#41×D4711yescharacteristic
692C22C22×#1062535211yescharacteristic
693C22C22×#1062535011yescharacteristic
694C22C2×#1309407111yescharacteristic
695C22C2×#1309407111yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—944no—
703C4—944no—
704C4—944no—
705C4—944no—
706C4—1882no—
707C4—1882no—
708C4—1882no—
709C4—1882no—
710C2—82no—
711C2#2024805918yesdirect product factor
712C2C2×#1568965111yescharacteristic
713C2C2×#1568966811yescharacteristic
714C2C2×#1568973011yescharacteristic
715C2C2×#1568977811yescharacteristic
716C2C2×#1568978111yescharacteristic
717C2C2×#1568981011yescharacteristic
718C2C2×#1568981311yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#388D47
hypocenterC47C2×#2519
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#13094014C2semidirect
3. #20248059C2direct (N × H)
5. C2×#15689057C2semidirect
6. C2×#15689056C2semidirect
8. C2×#15689021C2semidirect
12. C2×#15689006C2semidirect
13. C2×#15688987C2semidirect
14. C2×C4×C4⋊Dic47C2semidirect
15. C2×#15688974C2semidirect
20. C2×#13094014C22semidirect
42. #15689057C22semidirect
43. #15689056C22semidirect
45. #15689021C22semidirect
49. #15689006C22semidirect
50. #15688987C22semidirect
51. C4×C4⋊Dic47C22semidirect
52. #15688974C22semidirect
368. C2×C47#2519semidirect
428. C47C2×#2519semidirect
711. C2#20248059direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940172
C22×#130940142
#202480592
C2×#156890592
C2×#156890572
C2×#156890562
C2×#156890462
C2×#156890212
C2×#156890162
C2×#156890112
C2×#156890062
C2×#156889872
C2×C4×C4⋊Dic472
C2×#156889742
C2×C47×#3882
C2×#251947