Finite Group Databasebeta

← C2×#20247483 #26384791

Subgroups — C2×#20247483 #26384791

Order 12032.

3006 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094006C211yesmaximal, characteristic
2C22×#13093983C211yesmaximal, characteristic, complemented
3#20247483C2116yesmaximal, direct product factor
4C2×#15689065C211yesmaximal, characteristic, complemented
5C2×#15689051C211yesmaximal, characteristic, complemented
6C2×#15689045C211yesmaximal, characteristic, complemented
7C2×#15689039C211yesmaximal, characteristic
8C2×#15689022C211yesmaximal, characteristic, complemented
9C2×#15689020C211yesmaximal, characteristic, complemented
10C2×#15689017C211yesmaximal, characteristic, complemented
11C2×#15689013C211yesmaximal, characteristic, complemented
12C2×#15689009C211yesmaximal, characteristic, complemented
13C2×#15689002C211yesmaximal, characteristic
14C2×#15688997C211yesmaximal, characteristic, complemented
15C2×#15688970C211yesmaximal, characteristic, complemented
16C2×C47×#385C211yesmaximal, characteristic, complemented
17C23×C22⋊D47C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C2×#13094006—28no—
20C2×#13094006C2218yes—
21C2×#13093983—28no—
22C2×#13093983C2218yescomplemented
23C22×C4⋊Dic47C2211yescharacteristic
24C22×C4⋊Dic47C2211yescharacteristic
25C22×C4⋊Dic47C2211yescharacteristic
26C22×C4⋊Dic47C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×C22⋊Dic47C2211yescharacteristic
31C22×C22⋊Dic47C2211yescharacteristic
32C22×C22⋊Dic47C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×C4×Dic47C2211yescharacteristic
39C22×C4×Dic47C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41#15689065C2218yescomplemented
42#15689051C2218yescomplemented
43#15689045C2218yescomplemented
44#15689039C2218yes—
45#15689022C2218yescomplemented
46#15689020C2218yescomplemented
47#15689017C2218yescomplemented
48#15689013C2218yescomplemented
49#15689009C2218yescomplemented
50#15689002C2218yes—
51#15688997C2218yescomplemented
52#15688970C2218yescomplemented
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C24×C4×C47C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C47×#385C2218yescomplemented
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C24×D47C2311yescharacteristic
70C22×C22⋊D47—24no—
71C22×C22⋊D47—24no—
72C22×C22⋊D47—42no—
73C22×C22⋊D47C2314yes—
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C22×C4×D47—24no—
82C22×C4×D47—24no—
83C22×C4×D47—42no—
84C22×C4×D47C2314yes—
85#13094006—232no—
86#13093983—232no—
87C2×C4⋊Dic47—24no—
88C2×C4⋊Dic47—24no—
89C2×C4⋊Dic47—24no—
90C2×C4⋊Dic47—42no—
91C2×C4⋊Dic47C2314yes—
92C2×C4⋊Dic47C2314yes—
93C2×C4⋊Dic47C2314yes—
94C2×C4⋊Dic47C2314yes—
95C2×Dic47⋊C4—24no—
96C2×Dic47⋊C4—24no—
97C2×Dic47⋊C4—42no—
98C2×Dic47⋊C4C2314yes—
99C2×Dic47⋊C4C2314yes—
100C2×Dic47⋊C4C2314yes—
101C2×C22⋊Dic47—24no—
102C2×C22⋊Dic47—42no—
103C2×C22⋊Dic47D418yes—
104C2×C22⋊Dic47C2314yes—
105C2×C22⋊Dic47C2314yes—
106C2×C22⋊Dic47C2314yes—
107C2×(C2×D47)⋊C4—24no—
108C2×(C2×D47)⋊C4—24no—
109C2×(C2×D47)⋊C4—24no—
110C2×(C2×D47)⋊C4—24no—
111C2×(C2×D47)⋊C4—24no—
112C2×(C2×D47)⋊C4C2314yes—
113C2×(C2×D47)⋊C4C2314yes—
114C2×(C2×D47)⋊C4C2314yes—
115C2×(C2×D47)⋊C4C2314yes—
116C2×(C2×D47)⋊C4C2314yes—
117C2×C4×Dic47—24no—
118C2×C4×Dic47—24no—
119C2×C4×Dic47—42no—
120C2×C4×Dic47C2314yes—
121C2×C4×Dic47C2314yes—
122C2×C4×Dic47C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C25×C47C2311yescharacteristic
132C23×C4×C47—24no—
133C23×C4×C47—24no—
134C23×C4×C47—24no—
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2314yes—
139C23×C4×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C23×C4×C47C2311yescharacteristic
142C2×C4⋊C4×C47—24no—
143C2×C4⋊C4×C47—24no—
144C2×C4⋊C4×C47C2314yes—
145C2×C4⋊C4×C47C2314yes—
146C2×C22⋊C4×C47—24no—
147C2×C22⋊C4×C47—24no—
148C2×C22⋊C4×C47C2314yes—
149C2×C22⋊C4×C47C2314yes—
150#95×C47C2314yes—
151#95×C47C2314yes—
152C24×C47—22no—
153C24×C47—22no—
154C24×C47—22no—
155C24×C47—22no—
156C24×C47—22no—
157C24×C47—22no—
158C24×C47C2×D414yes—
159C24×C47C2412yes—
160C24×C47C2411yescharacteristic
161C23×D47—22no—
162C23×D47—22no—
163C23×D47—22no—
164C23×D47—22no—
165C23×D47—22no—
166C23×D47—22no—
167C23×D47#4114yes—
168C23×D47C2412yes—
169C22×C4×C47—232no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47—28no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—28no—
178C22×C4×C47—28no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47#4114yes—
189C22×C4×C47#4114yes—
190C22×C4×C47#4114yes—
191C22×C4×C47C2412yes—
192C22×C4×C47C2412yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2412yes—
197C2×C22⋊D47—28no—
198C2×C22⋊D47—28no—
199C2×C22⋊D47—44no—
200C2×C22⋊D47—416no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—22no—
213C22×Dic47—22no—
214C22×Dic47—22no—
215C22×Dic47—22no—
216C22×Dic47—22no—
217C22×Dic47—22no—
218C22×Dic47—22no—
219C22×Dic47—22no—
220C22×Dic47C2×D414yes—
221C22×Dic47C2×D414yes—
222C22×Dic47C2412yes—
223C22×Dic47C2412yes—
224C22×Dic47C2412yes—
225C22×Dic47C2412yes—
226C22×Dic47C2412yes—
227C22×Dic47C2412yes—
228C22×Dic47C2412yes—
229C2×C4×D47—28no—
230C2×C4×D47—28no—
231C2×C4×D47—44no—
232C2×C4×D47—416no—
233C4⋊C4×C47—28no—
234C4⋊C4×C47—28no—
235C22⋊C4×C47—28no—
236C22⋊C4×C47—28no—
237C22⋊Dic47—28no—
238C22⋊Dic47—44no—
239C22⋊Dic47C2×D4116yes—
240(C2×D47)⋊C4—28no—
241(C2×D47)⋊C4—28no—
242(C2×D47)⋊C4—28no—
243(C2×D47)⋊C4—28no—
244(C2×D47)⋊C4—28no—
245C4⋊Dic47—28no—
246C4⋊Dic47—28no—
247C4⋊Dic47—28no—
248C4⋊Dic47—44no—
249Dic47⋊C4—28no—
250Dic47⋊C4—28no—
251Dic47⋊C4—44no—
252C4×Dic47—28no—
253C4×Dic47—28no—
254C4×Dic47—44no—
255C23×C47—28no—
256C23×C47—28no—
257C23×C47—28no—
258C23×C47—22no—
259C23×C47—22no—
260C23×C47—22no—
261C23×C47—22no—
262C23×C47—22no—
263C23×C47—22no—
264C23×C47—44no—
265C23×C47—44no—
266C23×C47—44no—
267C23×C47—44no—
268C23×C47C22×D414yes—
269C23×C47C22×D412yes—
270C23×C47C2×#4112yes—
271C23×C47C2×#4112yes—
272C23×C47C2×#4112yes—
273C23×C47C2×#4112yes—
274C23×C47H(5,𝔽2)12yes—
275C23×C472−1+412yes—
276C23×C47C2511yescharacteristic
277C22×D47—28no—
278C22×D47—28no—
279C22×D47—28no—
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—22no—
284C22×D47—22no—
285C22×D47—22no—
286C22×D47—44no—
287C22×D47—44no—
288C22×D47—44no—
289C22×D47—44no—
290C22×D47C2×#4114yes—
291C2×C4×C47—232no—
292C2×C4×C47—28no—
293C2×C4×C47—28no—
294C2×C4×C47—28no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—44no—
311C2×C4×C47—44no—
312C2×C4×C47—44no—
313C2×C4×C47C2×#4114yes—
314C2×C4×C47C2×#4114yes—
315C2×C4×C47C2×#4114yes—
316C22⋊D47—416no—
317C2×Dic47—28no—
318C2×Dic47—28no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—44no—
339C2×Dic47—44no—
340C2×Dic47—44no—
341C2×Dic47—44no—
342C2×Dic47—44no—
343C2×Dic47C22×D414yes—
344C2×Dic47C22×D414yes—
345C4×D47—416no—
346C2×#2470—471nomaximal, Sylow
347C22×C47—24no—
348C22×C47—24no—
349C22×C47—24no—
350C22×C47—42no—
351C22×C47—42no—
352C22×C47—42no—
353C22×C47—42no—
354C22×C47—416no—
355C22×C47#52514yes—
356C22×C47#52914yes—
357C22×C47#54214yes—
358C22×C47#54614yes—
359C22×C47#54714yes—
360C22×C47#55214yes—
361C22×C47#55314yes—
362C22×C47C23×D411yescharacteristic
363C22×C47C22×#4111yescharacteristic
364C22×C47C22×#4111yescharacteristic
365C22×C47C22×#4111yescharacteristic
366C22×C47C22×#4111yescharacteristic
367C22×C47C2×H(5,𝔽2)11yescharacteristic
368C22×C47C2×2−1+411yescharacteristic
369C2×D47—24no—
370C2×D47—24no—
371C2×D47—24no—
372C2×D47—42no—
373C2×D47—42no—
374C2×D47—42no—
375C2×D47—42no—
376C2×D47—416no—
377C4×C47—24no—
378C4×C47—24no—
379C4×C47—24no—
380C4×C47—42no—
381C4×C47—42no—
382C4×C47—42no—
383Dic47—24no—
384Dic47—24no—
385Dic47—42no—
386Dic47—42no—
387Dic47—42no—
388Dic47—42no—
389Dic47—42no—
390C22×#123—471no—
391C22×#117—471no—
392#2470—4716no—
393C2×#400—471no—
394C2×#397—471no—
395C2×#396—471no—
396C2×#394—471no—
397C2×#389—471no—
398C2×#389—471no—
399C2×#388—471no—
400C2×#388—471no—
401C2×#387—471no—
402C2×#386—471no—
403C2×#385—471no—
404C2×#385D4711yescharacteristic, complemented
405C2×C4×C22⋊C4—471no—
406C2×C47—44no—
407C2×C47#247018yescomplemented
408C2×C47C2×#52511yescharacteristic
409C2×C47C2×#52911yescharacteristic
410C2×C47C2×#54211yescharacteristic
411C2×C47C2×#54611yescharacteristic
412C2×C47C2×#54711yescharacteristic
413C2×C47C2×#55211yescharacteristic
414C2×C47C2×#55311yescharacteristic
415D47—44no—
416C23×D4—471no—
417C24×C4—471no—
418C24×C4C2×D4711yescharacteristic
419C2×#123—478no—
420C2×#123—948no—
421C2×#117—478no—
422C2×#117—948no—
423C22×C4⋊C4—471no—
424C22×C4⋊C4—471no—
425C22×C4⋊C4—471no—
426C22×C4⋊C4—471no—
427C22×C4⋊C4—471no—
428C22×C4⋊C4—471no—
429C22×C4⋊C4—471no—
430C22×C4⋊C4C2×D4711yescharacteristic
431C22×C4⋊C4C2×D4711yescharacteristic
432C22×C22⋊C4—471no—
433C22×C22⋊C4—471no—
434C22×C22⋊C4—471no—
435C22×C22⋊C4—471no—
436C22×C22⋊C4—471no—
437C22×C22⋊C4—471no—
438C22×C22⋊C4—471no—
439C22×C22⋊C4—471no—
440C22×C22⋊C4C2×D4711yescharacteristic
441C22×C22⋊C4C2×D4711yescharacteristic
442C22×C42—471no—
443C22×C42—471no—
444C22×C42—471no—
445#400—478no—
446#397—478no—
447#396—478no—
448#394—478no—
449#389—478no—
450#389—478no—
451#388—478no—
452#388—478no—
453#387—478no—
454#386—478no—
455#385—478no—
456#385C2×D4718yescomplemented
457C4×C22⋊C4—478no—
458C2×#95—471no—
459C2×#95—471no—
460C2×#95—471no—
461C2×#95—471no—
462C2×#95—471no—
463C2×#95—471no—
464C2×#95—471no—
465C2×#95—471no—
466C2×#95C2×D4711yescharacteristic
467C2×#95C2×D4711yescharacteristic
468C47C2×#247011yescharacteristic, complemented, Sylow
469C25—471no—
470C25C22×D4711yescharacteristic
471C22×D4—474no—
472C22×D4—944no—
473C22×D4—944no—
474C22×D4—1882no—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—24no—
478C23×C4—471no—
479C23×C4—471no—
480C23×C4—471no—
481C23×C4—471no—
482C23×C4—471no—
483C23×C4—471no—
484C23×C4—471no—
485C23×C4—474no—
486C23×C4—944no—
487C23×C4—944no—
488C23×C4—1882no—
489C23×C4C22×D4714yes—
490C23×C4C22×D4711yescharacteristic
491C23×C4C22×D4711yescharacteristic
492C23×C4C22×D4711yescharacteristic
493C23×C4C22×D4711yescharacteristic
494C23×C4C22×D4711yescharacteristic
495C23×C4C22×D4711yescharacteristic
496#123—9432no—
497#117—9432no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—474no—
501C2×C4⋊C4—474no—
502C2×C4⋊C4—474no—
503C2×C4⋊C4—474no—
504C2×C4⋊C4—474no—
505C2×C4⋊C4—474no—
506C2×C4⋊C4—474no—
507C2×C4⋊C4—944no—
508C2×C4⋊C4—944no—
509C2×C4⋊C4—944no—
510C2×C4⋊C4—944no—
511C2×C4⋊C4—944no—
512C2×C4⋊C4—1882no—
513C2×C4⋊C4—1882no—
514C2×C4⋊C4C22×D4714yes—
515C2×C4⋊C4C22×D4714yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—478no—
519C2×C22⋊C4—474no—
520C2×C22⋊C4—474no—
521C2×C22⋊C4—474no—
522C2×C22⋊C4—474no—
523C2×C22⋊C4—474no—
524C2×C22⋊C4—474no—
525C2×C22⋊C4—474no—
526C2×C22⋊C4—474no—
527C2×C22⋊C4—944no—
528C2×C22⋊C4—944no—
529C2×C22⋊C4—944no—
530C2×C22⋊C4—944no—
531C2×C22⋊C4—944no—
532C2×C22⋊C4—944no—
533C2×C22⋊C4—1882no—
534C2×C22⋊C4C22×D4714yes—
535C2×C22⋊C4C22×D4714yes—
536C2×C42—474no—
537C2×C42—474no—
538C2×C42—474no—
539C2×C42—944no—
540C2×C42—944no—
541C2×C42—1882no—
542#95—474no—
543#95—474no—
544#95—474no—
545#95—474no—
546#95—474no—
547#95—474no—
548#95—474no—
549#95—474no—
550#95C22×D4714yes—
551#95C22×D4714yes—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—474no—
559C24—472no—
560C24—942no—
561C24—942no—
562C24—942no—
563C24—942no—
564C24—942no—
565C24—942no—
566C24D4×D4714yes—
567C24C23×D4712yes—
568C24C23×D4711yescharacteristic
569C2×D4—948no—
570C2×D4—948no—
571C2×D4—1884no—
572C2×D4—18816no—
573C22×C4—232no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—28no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—474no—
593C22×C4—474no—
594C22×C4—472no—
595C22×C4—472no—
596C22×C4—472no—
597C22×C4—472no—
598C22×C4—472no—
599C22×C4—472no—
600C22×C4—472no—
601C22×C4—948no—
602C22×C4—948no—
603C22×C4—942no—
604C22×C4—942no—
605C22×C4—942no—
606C22×C4—942no—
607C22×C4—942no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—942no—
612C22×C4—942no—
613C22×C4—942no—
614C22×C4—942no—
615C22×C4—942no—
616C22×C4—942no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—942no—
620C22×C4—942no—
621C22×C4—942no—
622C22×C4—1884no—
623C22×C4—18816no—
624C22×C4#1062535014yes—
625C22×C4#1062535214yes—
626C22×C4#1062535214yes—
627C22×C4C23×D4712yes—
628C22×C4C23×D4712yes—
629C22×C4C23×D4712yes—
630C22×C4C23×D4712yes—
631C22×C4C23×D4712yes—
632C22×C4C23×D4712yes—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—948no—
636C4⋊C4—948no—
637C4⋊C4—948no—
638C4⋊C4—948no—
639C4⋊C4—948no—
640C4⋊C4—1884no—
641C4⋊C4—1884no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—4716no—
645C22⋊C4—948no—
646C22⋊C4—948no—
647C22⋊C4—948no—
648C22⋊C4—948no—
649C22⋊C4—948no—
650C22⋊C4—948no—
651C22⋊C4—1884no—
652C42—948no—
653C42—948no—
654C42—1884no—
655C23—28no—
656C23—28no—
657C23—28no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—474no—
669C23—948no—
670C23—948no—
671C23—948no—
672C23—942no—
673C23—942no—
674C23—942no—
675C23—942no—
676C23—942no—
677C23—942no—
678C23—1884no—
679C23—1884no—
680C23—1884no—
681C23—1884no—
682C23C2×D4×D4714yes—
683C23C2×D4×D4712yes—
684C23#41×D4712yes—
685C23C2×#1062535212yes—
686C23C2×#1062535212yes—
687C23C2×#1062535012yes—
688C23#1309407012yes—
689C23#1309407212yes—
690C23C24×D4711yescharacteristic
691D4—18816no—
692C2×C4—232no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—474no—
715C2×C4—474no—
716C2×C4—948no—
717C2×C4—948no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—18816no—
738C2×C4—1884no—
739C2×C4—1884no—
740C2×C4—1884no—
741C2×C4—1884no—
742C2×C4—1884no—
743C2×C4C2×#1062535214yes—
744C2×C4C2×#1062535214yes—
745C2×C4C2×#1062535014yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—416no—
754C22—944no—
755C22—944no—
756C22—944no—
757C22—1882no—
758C22—1882no—
759C22—1882no—
760C22—1882no—
761C22—18816no—
762C22#1568962914yes—
763C22#1568965514yes—
764C22#1568974614yes—
765C22#1568976514yes—
766C22#1568977414yes—
767C22#1568980714yes—
768C22#1568981914yes—
769C22C22×D4×D4711yescharacteristic
770C22C2×#41×D4711yescharacteristic
771C22C22×#1062535211yescharacteristic
772C22C22×#1062535211yescharacteristic
773C22C22×#1062535011yescharacteristic
774C22C2×#1309407011yescharacteristic
775C22C2×#1309407211yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—944no—
783C4—944no—
784C4—1882no—
785C4—1882no—
786C4—1882no—
787C4—1882no—
788C4—1882no—
789C2—44no—
790C2—1884no—
791C2#2024748318yesdirect product factor
792C2C2×#1568962911yescharacteristic
793C2C2×#1568965511yescharacteristic
794C2C2×#1568974611yescharacteristic
795C2C2×#1568976511yescharacteristic
796C2C2×#1568977411yescharacteristic
797C2C2×#1568980711yescharacteristic
798C2C2×#1568981911yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#385C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC2×#385D47
hypocenterC47C2×#2470
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#13093983C2semidirect
3. #20247483C2direct (N × H)
4. C2×#15689065C2semidirect
5. C2×#15689051C2semidirect
6. C2×#15689045C2semidirect
8. C2×#15689022C2semidirect
9. C2×#15689020C2semidirect
10. C2×#15689017C2semidirect
11. C2×#15689013C2semidirect
12. C2×#15689009C2semidirect
14. C2×#15688997C2semidirect
15. C2×#15688970C2semidirect
16. C2×C47×#385C2semidirect
22. C2×#13093983C22semidirect
41. #15689065C22semidirect
42. #15689051C22semidirect
43. #15689045C22semidirect
45. #15689022C22semidirect
46. #15689020C22semidirect
47. #15689017C22semidirect
48. #15689013C22semidirect
49. #15689009C22semidirect
51. #15688997C22semidirect
52. #15688970C22semidirect
66. C47×#385C22semidirect
404. C2×#385D47semidirect
407. C2×C47#2470semidirect
456. #385C2×D47semidirect
468. C47C2×#2470semidirect
791. C2#20247483direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940062
C22×#130939832
#202474832
C2×#156890652
C2×#156890512
C2×#156890452
C2×#156890392
C2×#156890222
C2×#156890202
C2×#156890172
C2×#156890132
C2×#156890092
C2×#156890022
C2×#156889972
C2×#156889702
C2×C47×#3852
C2×#247047