Finite Group Databasebeta

← C2×#20248418 #26388095

Subgroups — C2×#20248418 #26388095

Order 12032.

2446 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094014C211yesmaximal, characteristic
2C22×#13094014C211yesmaximal, characteristic
3#20248418C2116yesmaximal, direct product factor
4C2×#15689057C211yesmaximal, characteristic
5C2×#15689056C211yesmaximal, characteristic
6C2×#15689055C211yesmaximal, characteristic
7C2×#15689020C211yesmaximal, characteristic
8C2×#15689020C211yesmaximal, characteristic
9C2×#15689018C211yesmaximal, characteristic
10C2×#15689018C211yesmaximal, characteristic
11C2×#15688992C211yesmaximal, characteristic
12C2×#15688992C211yesmaximal, characteristic
13C2×#15688992C211yesmaximal, characteristic
14C2×#15688974C211yesmaximal, characteristic
15C2×#15688974C211yesmaximal, characteristic
16C2×C47×#398C211yesmaximal, characteristic
17C2×#13094014—28no—
18C2×#13094014—28no—
19C2×#13094014C2218yes—
20C2×#13094014C2218yes—
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×Dic47⋊C4C2211yescharacteristic
34C22×Dic47⋊C4C2211yescharacteristic
35C22×Dic47⋊C4C2211yescharacteristic
36C22×Dic47⋊C4C2211yescharacteristic
37C22×Dic47⋊C4C2211yescharacteristic
38C22×Dic47⋊C4C2211yescharacteristic
39C22×C4×Dic47C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41C22×C4×Dic47C2211yescharacteristic
42C22×C4×Dic47C2211yescharacteristic
43C22×C4×Dic47C2211yescharacteristic
44#15689057C2218yes—
45#15689056C2218yes—
46#15689055C2218yes—
47#15689020C2218yes—
48#15689020C2218yes—
49#15689018C2218yes—
50#15689018C2218yes—
51#15688992C2218yes—
52#15688992C2218yes—
53#15688992C2218yes—
54#15688974C2218yes—
55#15688974C2218yes—
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×C4⋊C4×C47C2211yescharacteristic
65C47×#398C2218yes—
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C23×Dic47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77#13094014—232no—
78#13094014—232no—
79C2×C4⋊Dic47—24no—
80C2×C4⋊Dic47—24no—
81C2×C4⋊Dic47—42no—
82C2×C4⋊Dic47—42no—
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⋊C4—24no—
96C2×Dic47⋊C4—24no—
97C2×Dic47⋊C4—42no—
98C2×Dic47⋊C4—42no—
99C2×Dic47⋊C4D418yes—
100C2×Dic47⋊C4Q818yes—
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2314yes—
103C2×Dic47⋊C4C2314yes—
104C2×Dic47⋊C4C2314yes—
105C2×Dic47⋊C4C2314yes—
106C2×Dic47⋊C4C2314yes—
107C2×Dic47⋊C4C2314yes—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2314yes—
111C2×Dic47⋊C4C2314yes—
112C2×Dic47⋊C4C2314yes—
113C2×Dic47⋊C4C2314yes—
114C2×Dic47⋊C4C2314yes—
115C2×C4×Dic47—24no—
116C2×C4×Dic47—24no—
117C2×C4×Dic47—24no—
118C2×C4×Dic47—24no—
119C2×C4×Dic47Q818yes—
120C2×C4×Dic47C2314yes—
121C2×C4×Dic47C2314yes—
122C2×C4×Dic47C2314yes—
123C2×C4×Dic47C2314yes—
124C2×C4×Dic47C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C2×C4⋊C4×C47—24no—
138C2×C4⋊C4×C47—24no—
139C2×C4⋊C4×C47—42no—
140C2×C4⋊C4×C47—42no—
141C2×C4⋊C4×C47C2314yes—
142C2×C4⋊C4×C47C2314yes—
143C2×C4⋊C4×C47C2314yes—
144C2×C4⋊C4×C47C2314yes—
145#95×C47C2314yes—
146#95×C47C2314yes—
147#95×C47C2314yes—
148C24×C47C2411yescharacteristic
149C22×C4×C47—22no—
150C22×C4×C47—22no—
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×C47C2×D414yes—
168C22×C4×C47C2×Q814yes—
169C22×C4×C47C2×Q814yes—
170C22×C4×C47C2412yes—
171C22×C4×C47C2412yes—
172C22×C4×C47C2412yes—
173C22×C4×C47C2412yes—
174C22×C4×C47C2412yes—
175C22×C4×C47C2412yes—
176C22×C4×C47C2412yes—
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×Dic47C2×D414yes—
194C22×Dic47C2×D414yes—
195C22×Dic47C2×Q814yes—
196C22×Dic47C2×Q814yes—
197C22×Dic47C2×Q814yes—
198C22×Dic47C2×Q814yes—
199C22×Dic47#4114yes—
200C22×Dic47#4114yes—
201C22×Dic47C2412yes—
202C22×Dic47C2412yes—
203C22×Dic47C2412yes—
204C22×Dic47C2412yes—
205C22×Dic47C2412yes—
206C22×Dic47C2412yes—
207C22×Dic47C2412yes—
208C22×Dic47C2412yes—
209C4⋊C4×C47—28no—
210C4⋊C4×C47—28no—
211C4⋊C4×C47—44no—
212C4⋊C4×C47—44no—
213C4⋊Dic47—28no—
214C4⋊Dic47—28no—
215C4⋊Dic47—44no—
216C4⋊Dic47—44no—
217Dic47⋊C4—28no—
218Dic47⋊C4—28no—
219Dic47⋊C4—28no—
220Dic47⋊C4—28no—
221Dic47⋊C4—28no—
222Dic47⋊C4—28no—
223Dic47⋊C4—28no—
224Dic47⋊C4—28no—
225Dic47⋊C4—28no—
226Dic47⋊C4—28no—
227Dic47⋊C4—44no—
228Dic47⋊C4—44no—
229Dic47⋊C4C2×D4116yes—
230Dic47⋊C4C2×Q8116yes—
231C4×Dic47—28no—
232C4×Dic47—28no—
233C4×Dic47—28no—
234C4×Dic47—28no—
235C4×Dic47C2×Q8116yes—
236C23×C47C22×D412yes—
237C23×C47C22×Q812yes—
238C23×C47C22×Q812yes—
239C23×C47C2×#4112yes—
240C23×C47C2×#4112yes—
241C23×C47H(5,𝔽2)12yes—
242C23×C472−1+412yes—
243C23×C47C2511yescharacteristic
244C2×C4×C47—28no—
245C2×C4×C47—28no—
246C2×C4×C47—28no—
247C2×C4×C47—22no—
248C2×C4×C47—22no—
249C2×C4×C47—22no—
250C2×C4×C47—22no—
251C2×C4×C47—22no—
252C2×C4×C47—22no—
253C2×C4×C47—22no—
254C2×C4×C47—22no—
255C2×C4×C47—22no—
256C2×C4×C47—22no—
257C2×C4×C47—22no—
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—44no—
266C2×C4×C47—44no—
267C2×C4×C47—44no—
268C2×C4×C47—44no—
269C2×C4×C47C22×D414yes—
270C2×C4×C47C22×Q814yes—
271C2×C4×C47C22×Q814yes—
272C2×Dic47—28no—
273C2×Dic47—28no—
274C2×Dic47—22no—
275C2×Dic47—22no—
276C2×Dic47—22no—
277C2×Dic47—22no—
278C2×Dic47—22no—
279C2×Dic47—22no—
280C2×Dic47—22no—
281C2×Dic47—22no—
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—44no—
291C2×Dic47—44no—
292C2×Dic47—44no—
293C2×Dic47—44no—
294C2×Dic47#125116yescomplemented
295C2×Dic47C4⋊Q8116yes—
296C2×Dic47C22×D414yes—
297C2×Dic47C22×D414yes—
298C2×Dic47C22×Q814yes—
299C2×Dic47C22×Q814yes—
300C2×Dic47C22×Q814yes—
301C2×Dic47C22×Q814yes—
302C2×Dic47C2×#4114yes—
303C2×Dic47C2×#4114yes—
304C2×#2552—471nomaximal, Sylow
305C22×C47C2×#12514yes—
306C22×C47C2×C4⋊Q814yes—
307C22×C47#54414yes—
308C22×C47#54714yes—
309C22×C47#55014yes—
310C22×C47#55414yes—
311C22×C47#55714yes—
312C22×C47C23×D411yescharacteristic
313C22×C47C23×Q811yescharacteristic
314C22×C47C23×Q811yescharacteristic
315C22×C47C22×#4111yescharacteristic
316C22×C47C22×#4111yescharacteristic
317C22×C47C2×H(5,𝔽2)11yescharacteristic
318C22×C47C2×2−1+411yescharacteristic
319C4×C47—24no—
320C4×C47—24no—
321C4×C47—24no—
322C4×C47—42no—
323C4×C47—42no—
324C4×C47—42no—
325C4×C47—42no—
326Dic47—24no—
327Dic47—24no—
328Dic47—42no—
329Dic47—42no—
330Dic47—42no—
331Dic47—42no—
332Dic47C2×#12518yescomplemented
333Dic47C2×C4⋊Q818yes—
334C22×#125—471no—
335C22×#125—471no—
336#2552—4716no—
337C2×#398—471no—
338C2×#398—471no—
339C2×#398—471no—
340C2×#398D4711yescharacteristic
341C2×#389—471no—
342C2×#389—471no—
343C2×#389—471no—
344C2×#389—471no—
345C2×#384—471no—
346C2×#384—471no—
347C2×#384—471no—
348C2×C4×C4⋊C4—471no—
349C2×C4×C4⋊C4—471no—
350C2×C47#255218yescomplemented
351C2×C47C22×#12511yescharacteristic
352C2×C47C22×C4⋊Q811yescharacteristic
353C2×C47C2×#54411yescharacteristic
354C2×C47C2×#54711yescharacteristic
355C2×C47C2×#55011yescharacteristic
356C2×C47C2×#55411yescharacteristic
357C2×C47C2×#55711yescharacteristic
358C2×#125—478no—
359C2×#125—478no—
360C2×#125—948no—
361C2×#125—948no—
362C22×C4⋊C4—471no—
363C22×C4⋊C4—471no—
364C22×C4⋊C4—471no—
365C22×C4⋊C4—471no—
366C22×C4⋊C4—471no—
367C22×C4⋊C4—471no—
368C22×C4⋊C4—471no—
369C22×C4⋊C4—471no—
370C22×C4⋊C4—471no—
371C22×C4⋊C4—471no—
372C22×C4⋊C4—471no—
373C22×C4⋊C4—471no—
374C22×C4⋊C4—471no—
375C22×C4⋊C4—471no—
376C22×C4⋊C4—471no—
377C22×C4⋊C4—471no—
378C22×C4⋊C4—471no—
379C22×C4⋊C4—471no—
380C22×C4⋊C4C2×D4711yescharacteristic
381C22×C4⋊C4C2×D4711yescharacteristic
382C22×C4⋊C4C2×D4711yescharacteristic
383C22×C4⋊C4C2×D4711yescharacteristic
384C22×C42—471no—
385C22×C42—471no—
386C22×C42—471no—
387C22×C42—471no—
388C22×C42—471no—
389#398—478no—
390#398—478no—
391#398—478no—
392#398C2×D4718yes—
393#389—478no—
394#389—478no—
395#389—478no—
396#389—478no—
397#384—478no—
398#384—478no—
399#384—478no—
400C4×C4⋊C4—478no—
401C4×C4⋊C4—478no—
402C2×#95—471no—
403C2×#95—471no—
404C2×#95—471no—
405C2×#95—471no—
406C2×#95—471no—
407C2×#95C2×D4711yescharacteristic
408C2×#95C2×D4711yescharacteristic
409C2×#95C2×D4711yescharacteristic
410C47C2×#255211yescharacteristic, complemented, Sylow
411C23×C4—471no—
412C23×C4—471no—
413C23×C4—471no—
414C23×C4—471no—
415C23×C4—471no—
416C23×C4—471no—
417C23×C4—471no—
418C23×C4—471no—
419C23×C4C22×D4711yescharacteristic
420C23×C4C22×D4711yescharacteristic
421C23×C4C22×D4711yescharacteristic
422C23×C4C22×D4711yescharacteristic
423C23×C4C22×D4711yescharacteristic
424C23×C4C22×D4711yescharacteristic
425C23×C4C22×D4711yescharacteristic
426#125—9432no—
427#125—9432no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4—42no—
432C2×C4⋊C4—478no—
433C2×C4⋊C4—478no—
434C2×C4⋊C4—474no—
435C2×C4⋊C4—474no—
436C2×C4⋊C4—474no—
437C2×C4⋊C4—474no—
438C2×C4⋊C4—474no—
439C2×C4⋊C4—474no—
440C2×C4⋊C4—474no—
441C2×C4⋊C4—474no—
442C2×C4⋊C4—474no—
443C2×C4⋊C4—474no—
444C2×C4⋊C4—474no—
445C2×C4⋊C4—474no—
446C2×C4⋊C4—474no—
447C2×C4⋊C4—474no—
448C2×C4⋊C4—474no—
449C2×C4⋊C4—474no—
450C2×C4⋊C4—474no—
451C2×C4⋊C4—474no—
452C2×C4⋊C4—944no—
453C2×C4⋊C4—944no—
454C2×C4⋊C4—944no—
455C2×C4⋊C4—944no—
456C2×C4⋊C4—944no—
457C2×C4⋊C4—944no—
458C2×C4⋊C4—944no—
459C2×C4⋊C4—944no—
460C2×C4⋊C4—944no—
461C2×C4⋊C4—944no—
462C2×C4⋊C4—944no—
463C2×C4⋊C4—944no—
464C2×C4⋊C4—1882no—
465C2×C4⋊C4—1882no—
466C2×C4⋊C4—1882no—
467C2×C4⋊C4—1882no—
468C2×C4⋊C4C22×D4714yes—
469C2×C4⋊C4C22×D4714yes—
470C2×C4⋊C4C22×D4714yes—
471C2×C4⋊C4C22×D4714yes—
472C2×C42—478no—
473C2×C42—474no—
474C2×C42—474no—
475C2×C42—474no—
476C2×C42—474no—
477C2×C42—474no—
478C2×C42—944no—
479C2×C42—944no—
480C2×C42—944no—
481C2×C42—944no—
482#95—474no—
483#95—474no—
484#95—474no—
485#95—474no—
486#95—474no—
487#95C22×D4714yes—
488#95C22×D4714yes—
489#95C22×D4714yes—
490C24C23×D4711yescharacteristic
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—474no—
510C22×C4—474no—
511C22×C4—474no—
512C22×C4—474no—
513C22×C4—474no—
514C22×C4—474no—
515C22×C4—472no—
516C22×C4—472no—
517C22×C4—474no—
518C22×C4—474no—
519C22×C4—472no—
520C22×C4—472no—
521C22×C4—472no—
522C22×C4—472no—
523C22×C4—472no—
524C22×C4—472no—
525C22×C4—942no—
526C22×C4—942no—
527C22×C4—942no—
528C22×C4—942no—
529C22×C4—942no—
530C22×C4—942no—
531C22×C4—942no—
532C22×C4—942no—
533C22×C4—942no—
534C22×C4—942no—
535C22×C4—942no—
536C22×C4—942no—
537C22×C4—942no—
538C22×C4—942no—
539C22×C4—942no—
540C22×C4—942no—
541C22×C4D4×D4714yes—
542C22×C4Q8×D4714yes—
543C22×C4Q8×D4714yes—
544C22×C4C23×D4712yes—
545C22×C4C23×D4712yes—
546C22×C4C23×D4712yes—
547C22×C4C23×D4712yes—
548C22×C4C23×D4712yes—
549C22×C4C23×D4712yes—
550C22×C4C23×D4712yes—
551C4⋊C4—28no—
552C4⋊C4—28no—
553C4⋊C4—44no—
554C4⋊C4—44no—
555C4⋊C4—4716no—
556C4⋊C4—4716no—
557C4⋊C4—948no—
558C4⋊C4—948no—
559C4⋊C4—948no—
560C4⋊C4—948no—
561C4⋊C4—948no—
562C4⋊C4—948no—
563C4⋊C4—948no—
564C4⋊C4—948no—
565C4⋊C4—948no—
566C4⋊C4—948no—
567C4⋊C4—948no—
568C4⋊C4—948no—
569C4⋊C4—1884no—
570C4⋊C4—1884no—
571C4⋊C4—1884no—
572C4⋊C4—1884no—
573C42—4716no—
574C42—948no—
575C42—948no—
576C42—948no—
577C42—948no—
578C23C2×D4×D4712yes—
579C23C2×Q8×D4712yes—
580C23C2×Q8×D4712yes—
581C23#41×D4712yes—
582C23#41×D4712yes—
583C23#1309406912yes—
584C23#1309407112yes—
585C23C24×D4711yescharacteristic
586C2×C4—28no—
587C2×C4—28no—
588C2×C4—28no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—44no—
608C2×C4—44no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—4716no—
612C2×C4—4716no—
613C2×C4—474no—
614C2×C4—474no—
615C2×C4—474no—
616C2×C4—474no—
617C2×C4—474no—
618C2×C4—474no—
619C2×C4—474no—
620C2×C4—474no—
621C2×C4—948no—
622C2×C4—948no—
623C2×C4—942no—
624C2×C4—942no—
625C2×C4—942no—
626C2×C4—942no—
627C2×C4—942no—
628C2×C4—942no—
629C2×C4—942no—
630C2×C4—942no—
631C2×C4—942no—
632C2×C4—942no—
633C2×C4—942no—
634C2×C4—942no—
635C2×C4—942no—
636C2×C4—942no—
637C2×C4—942no—
638C2×C4—942no—
639C2×C4—1884no—
640C2×C4—1884no—
641C2×C4—1884no—
642C2×C4—1884no—
643C2×C4C2×D4×D4714yes—
644C2×C4C2×Q8×D4714yes—
645C2×C4C2×Q8×D4714yes—
646C22#125×D4714yes—
647C22C4⋊Q8×D4714yes—
648C22#1568975214yes—
649C22#1568977114yes—
650C22#1568979114yes—
651C22#1568982714yes—
652C22#1568985014yes—
653C22C22×D4×D4711yescharacteristic
654C22C22×Q8×D4711yescharacteristic
655C22C22×Q8×D4711yescharacteristic
656C22C2×#41×D4711yescharacteristic
657C22C2×#41×D4711yescharacteristic
658C22C2×#1309406911yescharacteristic
659C22C2×#1309407111yescharacteristic
660C4—24no—
661C4—24no—
662C4—24no—
663C4—42no—
664C4—42no—
665C4—42no—
666C4—42no—
667C4—478no—
668C4—478no—
669C4—944no—
670C4—944no—
671C4—1882no—
672C4—1882no—
673C4—1882no—
674C4—1882no—
675C2#2024841818yesdirect product factor
676C2C2×#125×D4711yescharacteristic
677C2C2×C4⋊Q8×D4711yescharacteristic
678C2C2×#1568975211yescharacteristic
679C2C2×#1568977111yescharacteristic
680C2C2×#1568979111yescharacteristic
681C2C2×#1568982711yescharacteristic
682C2C2×#1568985011yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#398C2
socle, prime radicalC24×C47C24
hypercenterC2×#398D47
hypocenterC47C2×#2552
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. #20248418C2direct (N × H)
294. C2×Dic47#125semidirect
332. Dic47C2×#125semidirect
350. C2×C47#2552semidirect
410. C47C2×#2552semidirect
675. C2#20248418direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940142
#202484182
C2×#156890572
C2×#156890562
C2×#156890552
C2×#156890202
C2×#156890182
C2×#156889922
C2×#156889742
C2×C47×#3982
C2×#255247