Finite Group Databasebeta

← C2×#20246323 #26375612

Subgroups — C2×#20246323 #26375612

Order 12032.

3374 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
2#20246323C2116yesmaximal, direct product factor
3C2×#15689016C211yesmaximal, characteristic, complemented
4C2×#15689010C211yesmaximal, characteristic, complemented
5C2×#15689004C211yesmaximal, characteristic, complemented
6C2×#15688999C211yesmaximal, characteristic
7C2×#15688999C211yesmaximal, characteristic
8C2×#15688990C211yesmaximal, characteristic, complemented
9C2×#15688984C211yesmaximal, characteristic, complemented
10C2×#15688980C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
13C2×#15688970C211yesmaximal, characteristic, complemented
14C2×#15688969C211yesmaximal, characteristic, complemented
15C2×#95×D47C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D47C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C2×(C22⋊D47)⋊C4C4116yescomplemented
23C2×(C22⋊D47)⋊C4C2218yes—
24C22×C4⋊Dic47C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×C22⋊Dic47C2211yescharacteristic
27C22×C22⋊Dic47C2211yescharacteristic
28C22×(C2×D47)⋊C4C2211yescharacteristic
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×C4×Dic47C2211yescharacteristic
32C22×C4×Dic47C2211yescharacteristic
33C22×C4×Dic47C2211yescharacteristic
34C22×C4×Dic47C2211yescharacteristic
35#15689016C2218yescomplemented
36#15689010C2218yescomplemented
37#15689004C2218yescomplemented
38#15688999C2218yes—
39#15688999C2218yes—
40#15688990C2218yescomplemented
41#15688984C2218yescomplemented
42#15688980C2218yescomplemented
43C22⋊C4×Dic47C2218yescomplemented
44C4×(C2×D47)⋊C4C2218yescomplemented
45#15688970C2218yescomplemented
46#15688969C2218yescomplemented
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
59#95×D47C2218yescomplemented
60C22×C4⋊C4×C47C2211yescharacteristic
61C22×C22⋊C4×C47C2211yescharacteristic
62C22×C22⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C42×C47C2211yescharacteristic
65C47×#388C2218yescomplemented
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C24×D47C2311yescharacteristic
69C22×C22⋊D47—24no—
70C22×C22⋊D47—24no—
71C22×C22⋊D47C2×C418yes—
72C22×C22⋊D47C2314yes—
73C23×Dic47—42no—
74C23×Dic47—42no—
75C23×Dic47C2×C418yescomplemented
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2314yes—
84C22×C4×D47—24no—
85C22×C4×D47—24no—
86C22×C4×D47—24no—
87C22×C4×D47—24no—
88C22×C4×D47—42no—
89C22×C4×D47—42no—
90C22×C4×D47—42no—
91C22×C4×D47—42no—
92C22×C4×D47C2×C418yes—
93C22×C4×D47C2314yes—
94C22×C4×D47C2314yes—
95C22×C4×D47C2314yes—
96(C22⋊D47)⋊C4C2×C4164yescomplemented
97C2×C4⋊Dic47—42no—
98C2×C4⋊Dic47C2314yes—
99C2×Dic47⋊C4C2×C418yescomplemented
100C2×Dic47⋊C4C2314yes—
101C2×C22⋊Dic47—24no—
102C2×C22⋊Dic47—42no—
103C2×C22⋊Dic47C2314yes—
104C2×C22⋊Dic47C2314yes—
105C2×(C2×D47)⋊C4—24no—
106C2×(C2×D47)⋊C4—24no—
107C2×(C2×D47)⋊C4C2×C418yes—
108C2×(C2×D47)⋊C4C2314yes—
109C2×(C2×D47)⋊C4C2314yes—
110C2×(C2×D47)⋊C4C2314yes—
111C2×C4×Dic47—24no—
112C2×C4×Dic47—42no—
113C2×C4×Dic47—42no—
114C2×C4×Dic47C2×C418yescomplemented
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—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C25×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C2×C4⋊C4×C47—42no—
139C2×C4⋊C4×C47C2314yes—
140C2×C22⋊C4×C47—24no—
141C2×C22⋊C4×C47—42no—
142C2×C22⋊C4×C47C2×C418yescomplemented
143C2×C22⋊C4×C47C2314yes—
144C2×C22⋊C4×C47C2314yes—
145C2×C22⋊C4×C47C2314yes—
146C2×C42×C47—24no—
147C2×C42×C47C2314yes—
148#95×C47C2314yes—
149#95×C47C2314yes—
150C24×C47—22no—
151C24×C47—22no—
152C24×C47—22no—
153C24×C47—22no—
154C24×C47—22no—
155C24×C47—22no—
156C24×C47C22×C414yes—
157C24×C47C2412yes—
158C24×C47C2411yescharacteristic
159C23×D47—22no—
160C23×D47—22no—
161C23×D47—22no—
162C23×D47—22no—
163C23×D47C22×C414yes—
164C23×D47#4114yes—
165C23×D47#4114yes—
166C23×D47C2412yes—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47C22×C414yes—
183C22×C4×C47C22×C414yes—
184C22×C4×C47#4114yes—
185C22×C4×C47C2412yes—
186C22×C4×C47C2412yes—
187C22×C4×C47C2412yes—
188C22×C4×C47C2412yes—
189C22×C4×C47C2412yes—
190C22×C4×C47C2412yes—
191C2×C22⋊D47—232no—
192C2×C22⋊D47—28no—
193C2×C22⋊D47—28no—
194C2×C22⋊D47C22×C4116yes—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
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—416no—
213C22×Dic47—44no—
214C22×Dic47—44no—
215C22×Dic47C22×C414yes—
216C22×Dic47C22×C414yes—
217C22×Dic47C22×C414yes—
218C22×Dic47C22×C4116yescomplemented
219C22×Dic47#4114yes—
220C22×Dic47C2412yes—
221C22×Dic47C2412yes—
222C22×Dic47C2412yes—
223C22×Dic47C2412yes—
224C22×Dic47C2412yes—
225C22×Dic47C2412yes—
226C22×Dic47C2412yes—
227C2×C4×D47—28no—
228C2×C4×D47—28no—
229C2×C4×D47—28no—
230C2×C4×D47—28no—
231C2×C4×D47—416no—
232C2×C4×D47—44no—
233C2×C4×D47—44no—
234C2×C4×D47—44no—
235C2×C4×D47—44no—
236C2×C4×D47—416no—
237C2×C4×D47—416no—
238C2×C4×D47C22×C4116yes—
239C4⋊C4×C47—44no—
240C22⋊C4×C47—28no—
241C22⋊C4×C47—44no—
242C22⋊C4×C47C22×C4116yescomplemented
243C42×C47—28no—
244C22⋊Dic47—28no—
245C22⋊Dic47—44no—
246(C2×D47)⋊C4—28no—
247(C2×D47)⋊C4—28no—
248(C2×D47)⋊C4C22×C4116yes—
249C4⋊Dic47—44no—
250Dic47⋊C4C22×C4116yescomplemented
251C4×Dic47—28no—
252C4×Dic47—44no—
253C4×Dic47—44no—
254C4×Dic47C22×C4116yescomplemented
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×C47C23×C414yes—
269C23×C47C23×C412yes—
270C23×C47C2×#4112yes—
271C23×C47C2×#4112yes—
272C23×C47C2×#4112yes—
273C23×C47C2×#4112yes—
274C23×C47H(5,𝔽2)12yes—
275C23×C47H(5,𝔽2)12yes—
276C23×C47C2511yescharacteristic
277C22×D47—28no—
278C22×D47—28no—
279C22×D47—28no—
280C22×D47—28no—
281C22×D47—28no—
282C22×D47—28no—
283C22×D47—22no—
284C22×D47—22no—
285C22×D47—22no—
286C22×D47—22no—
287C22×D47#117116yes—
288C22×D47C23×C414yes—
289C22×D47C2×#4114yes—
290C22×D47C2×#4114yes—
291C2×C4×C47—28no—
292C2×C4×C47—28no—
293C2×C4×C47—28no—
294C2×C4×C47—22no—
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—44no—
310C2×C4×C47—44no—
311C2×C4×C47—44no—
312C2×C4×C47C23×C414yes—
313C2×C4×C47C23×C414yes—
314C2×C4×C47C2×#4114yes—
315C22⋊D47—232no—
316C2×Dic47—28no—
317C2×Dic47—28no—
318C2×Dic47—28no—
319C2×Dic47—28no—
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—416no—
338C2×Dic47—44no—
339C2×Dic47—44no—
340C2×Dic47—44no—
341C2×Dic47C23×C414yes—
342C2×Dic47C23×C414yes—
343C2×Dic47C23×C414yes—
344C2×Dic47C2×#4114yes—
345C4×D47—416no—
346C4×D47—416no—
347C4×D47—416no—
348C2×#2353—471nomaximal, Sylow
349C22×C47—24no—
350C22×C47—24no—
351C22×C47—24no—
352C22×C47—416no—
353C22×C47—42no—
354C22×C47—42no—
355C22×C47—42no—
356C22×C47—42no—
357C22×C47C2×#11714yes—
358C22×C47C4×#4114yes—
359C22×C47#51814yes—
360C22×C47#55114yes—
361C22×C47#55114yes—
362C22×C47#55314yes—
363C22×C47#55314yes—
364C22×C47C24×C411yescharacteristic
365C22×C47C22×#4111yescharacteristic
366C22×C47C22×#4111yescharacteristic
367C22×C47C22×#4111yescharacteristic
368C22×C47C22×#4111yescharacteristic
369C22×C47C2×H(5,𝔽2)11yescharacteristic
370C22×C47C2×H(5,𝔽2)11yescharacteristic
371C2×D47—232no—
372C2×D47—24no—
373C2×D47—24no—
374C2×D47—24no—
375C2×D47—24no—
376C2×D47—24no—
377C2×D47—24no—
378C2×D47C2×#11718yes—
379C4×C47—24no—
380C4×C47—24no—
381C4×C47—24no—
382C4×C47—42no—
383C4×C47—42no—
384C4×C47—42no—
385Dic47—24no—
386Dic47—24no—
387Dic47—24no—
388Dic47—24no—
389Dic47—42no—
390Dic47—42no—
391Dic47—42no—
392C22×C4×D4—471no—
393#2353—4716no—
394C2×#388—471no—
395C2×#388D4711yescharacteristic, complemented
396C2×#387—471no—
397C2×#387—471no—
398C2×#386—471no—
399C2×#386—471no—
400C2×#383—471no—
401C2×#381—471no—
402C2×#380—471no—
403C2×C4×C22⋊C4—471no—
404C2×C4×C22⋊C4—471no—
405C2×C4×C22⋊C4—471no—
406C2×#376—471no—
407C22×#95—471no—
408C2×C47—44no—
409C2×C47#235318yescomplemented
410C2×C47C22×#11711yescharacteristic
411C2×C47C2×C4×#4111yescharacteristic
412C2×C47C2×#51811yescharacteristic
413C2×C47C2×#55111yescharacteristic
414C2×C47C2×#55111yescharacteristic
415C2×C47C2×#55311yescharacteristic
416C2×C47C2×#55311yescharacteristic
417D47—28no—
418C23×D4—471no—
419C24×C4—471no—
420C24×C4—471no—
421C24×C4—471no—
422C24×C4—471no—
423C2×C4×D4—4716no—
424C2×C4×D4—478no—
425C22×C4⋊C4—471no—
426C22×C4⋊C4—471no—
427C22×C4⋊C4C2×D4711yescharacteristic
428C22×C22⋊C4—471no—
429C22×C22⋊C4—471no—
430C22×C22⋊C4—471no—
431C22×C22⋊C4—471no—
432C22×C22⋊C4—471no—
433C22×C22⋊C4C2×D4711yescharacteristic
434C22×C22⋊C4C2×D4711yescharacteristic
435C22×C22⋊C4C2×D4711yescharacteristic
436C22×C42—471no—
437C22×C42—471no—
438C22×C42—471no—
439C22×C42—471no—
440C22×C42C2×D4711yescharacteristic
441#388—478no—
442#388C2×D4718yescomplemented
443#387—478no—
444#387—478no—
445#386—478no—
446#386—478no—
447#383—478no—
448#381—478no—
449#380—478no—
450C4×C22⋊C4—478no—
451C4×C22⋊C4—478no—
452C4×C22⋊C4—478no—
453#376—478no—
454C2×#95—471no—
455C2×#95—471no—
456C2×#95—471no—
457C2×#95—471no—
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×#95—478no—
467C2×#95C2×D4711yescharacteristic
468C2×#95C2×D4711yescharacteristic
469C47C2×#235311yescharacteristic, complemented, Sylow
470C25—471no—
471C25C22×D4711yescharacteristic
472C22×D4—478no—
473C22×D4—474no—
474C22×D4—944no—
475C22×D4—944no—
476C23×C4—471no—
477C23×C4—471no—
478C23×C4—471no—
479C23×C4—471no—
480C23×C4—478no—
481C23×C4—474no—
482C23×C4—478no—
483C23×C4—474no—
484C23×C4—471no—
485C23×C4—471no—
486C23×C4—471no—
487C23×C4—474no—
488C23×C4—474no—
489C23×C4—944no—
490C23×C4—944no—
491C23×C4—944no—
492C23×C4—944no—
493C23×C4—1882no—
494C23×C4—1882no—
495C23×C4—1882no—
496C23×C4—1882no—
497C23×C4—1882no—
498C23×C4—1882no—
499C23×C4C22×D4711yescharacteristic
500C23×C4C22×D4711yescharacteristic
501C23×C4C22×D4711yescharacteristic
502C23×C4C22×D4711yescharacteristic
503C23×C4C22×D4711yescharacteristic
504C23×C4C22×D4711yescharacteristic
505C4×D4—4764no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—478no—
508C2×C4⋊C4—474no—
509C2×C4⋊C4—474no—
510C2×C4⋊C4—1882no—
511C2×C4⋊C4C22×D4714yes—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—478no—
515C2×C22⋊C4—474no—
516C2×C22⋊C4—474no—
517C2×C22⋊C4—474no—
518C2×C22⋊C4—474no—
519C2×C22⋊C4—474no—
520C2×C22⋊C4—944no—
521C2×C22⋊C4—944no—
522C2×C22⋊C4—944no—
523C2×C22⋊C4—1882no—
524C2×C22⋊C4C4×D4718yescomplemented
525C2×C22⋊C4C22×D4714yes—
526C2×C22⋊C4C22×D4714yes—
527C2×C22⋊C4C22×D4714yes—
528C2×C42—24no—
529C2×C42—478no—
530C2×C42—474no—
531C2×C42—474no—
532C2×C42—474no—
533C2×C42—474no—
534C2×C42—944no—
535C2×C42—1882no—
536C2×C42—1882no—
537C2×C42C22×D4714yes—
538#95—474no—
539#95—474no—
540#95—474no—
541#95—474no—
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—474no—
560C24—474no—
561C24—472no—
562C24—942no—
563C24—942no—
564C24—942no—
565C24—942no—
566C24C2×C4×D4714yes—
567C24C23×D4712yes—
568C24C23×D4711yescharacteristic
569C2×D4—4716no—
570C2×D4—9432no—
571C2×D4—948no—
572C2×D4—948no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—474no—
589C22×C4—474no—
590C22×C4—474no—
591C22×C4—474no—
592C22×C4—472no—
593C22×C4—472no—
594C22×C4—472no—
595C22×C4—472no—
596C22×C4—4716no—
597C22×C4—4716no—
598C22×C4—472no—
599C22×C4—472no—
600C22×C4—472no—
601C22×C4—948no—
602C22×C4—948no—
603C22×C4—948no—
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—948no—
622C22×C4—18816no—
623C22×C4—1884no—
624C22×C4—1884no—
625C22×C4—1884no—
626C22×C4—1884no—
627C22×C4—18816no—
628C22×C4—18816no—
629C22×C4—18816no—
630C22×C4—1884no—
631C22×C4—1884no—
632C22×C4C2×C4×D4714yes—
633C22×C4C2×C4×D4714yes—
634C22×C4#1062535214yes—
635C22×C4C23×D4712yes—
636C22×C4C23×D4712yes—
637C22×C4C23×D4712yes—
638C22×C4C23×D4712yes—
639C22×C4C23×D4712yes—
640C22×C4C23×D4712yes—
641C4⋊C4—44no—
642C4⋊C4—4716no—
643C4⋊C4—1884no—
644C22⋊C4—28no—
645C22⋊C4—44no—
646C22⋊C4—4716no—
647C22⋊C4—948no—
648C22⋊C4—948no—
649C22⋊C4—948no—
650C22⋊C4—1884no—
651C22⋊C4C2×C4×D47116yescomplemented
652C42—28no—
653C42—4716no—
654C42—948no—
655C42—1884no—
656C42—1884no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—4716no—
671C23—474no—
672C23—474no—
673C23—474no—
674C23—948no—
675C23—948no—
676C23—948no—
677C23—948no—
678C23—948no—
679C23—948no—
680C23—942no—
681C23—942no—
682C23—942no—
683C23—942no—
684C23C22×C4×D4714yes—
685C23C22×C4×D4712yes—
686C23#41×D4712yes—
687C23#41×D4712yes—
688C23#41×D4712yes—
689C23C2×#1062535212yes—
690C23#1309406912yes—
691C23#1309407012yes—
692C23C24×D4711yescharacteristic
693D4—9432no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
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—22no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—474no—
716C2×C4—474no—
717C2×C4—474no—
718C2×C4—474no—
719C2×C4—948no—
720C2×C4—948no—
721C2×C4—948no—
722C2×C4—948no—
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—942no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—18816no—
741C2×C4—18816no—
742C2×C4—18816no—
743C2×C4—18816no—
744C2×C4—1884no—
745C2×C4—1884no—
746C2×C4—1884no—
747C2×C4C22×C4×D4714yes—
748C2×C4C22×C4×D4714yes—
749C2×C4C2×#1062535214yes—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—416no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—478no—
759C22—9432no—
760C22—944no—
761C22—944no—
762C22—944no—
763C22—944no—
764C22—944no—
765C22—944no—
766C22#117×D4714yes—
767C22C4×#1062535214yes—
768C22#1568959514yes—
769C22#1568979614yes—
770C22#1568980314yes—
771C22#1568982014yes—
772C22#1568982414yes—
773C22C23×C4×D4711yescharacteristic
774C22C2×#41×D4711yescharacteristic
775C22C2×#41×D4711yescharacteristic
776C22C2×#41×D4711yescharacteristic
777C22C22×#1062535211yescharacteristic
778C22C2×#1309406911yescharacteristic
779C22C2×#1309407011yescharacteristic
780C4—24no—
781C4—24no—
782C4—24no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—944no—
787C4—944no—
788C4—944no—
789C4—944no—
790C4—1882no—
791C4—1882no—
792C4—1882no—
793C2—44no—
794C2—948no—
795C2#2024632318yesdirect product factor
796C2C2×#117×D4711yescharacteristic
797C2C2×C4×#1062535211yescharacteristic
798C2C2×#1568959511yescharacteristic
799C2C2×#1568979611yescharacteristic
800C2C2×#1568980311yescharacteristic
801C2C2×#1568982011yescharacteristic
802C2C2×#1568982411yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C2×#2353
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #20246323C2direct (N × H)
3. C2×#15689016C2semidirect
4. C2×#15689010C2semidirect
5. C2×#15689004C2semidirect
8. C2×#15688990C2semidirect
9. C2×#15688984C2semidirect
10. C2×#15688980C2semidirect
11. C2×C22⋊C4×Dic47C2semidirect
12. C2×C4×(C2×D47)⋊C4C2semidirect
13. C2×#15688970C2semidirect
14. C2×#15688969C2semidirect
15. C2×#95×D47C2semidirect
16. C2×C47×#388C2semidirect
22. C2×(C22⋊D47)⋊C4C4semidirect
35. #15689016C22semidirect
36. #15689010C22semidirect
37. #15689004C22semidirect
40. #15688990C22semidirect
41. #15688984C22semidirect
42. #15688980C22semidirect
43. C22⋊C4×Dic47C22semidirect
44. C4×(C2×D47)⋊C4C22semidirect
45. #15688970C22semidirect
46. #15688969C22semidirect
59. #95×D47C22semidirect
65. C47×#388C22semidirect
75. C23×Dic47C2×C4semidirect
96. (C22⋊D47)⋊C4C2×C4semidirect
99. C2×Dic47⋊C4C2×C4semidirect
114. C2×C4×Dic47C2×C4semidirect
142. C2×C22⋊C4×C47C2×C4semidirect
218. C22×Dic47C22×C4semidirect
242. C22⋊C4×C47C22×C4semidirect
250. Dic47⋊C4C22×C4semidirect
254. C4×Dic47C22×C4semidirect
395. C2×#388D47semidirect
409. C2×C47#2353semidirect
442. #388C2×D47semidirect
469. C47C2×#2353semidirect
524. C2×C22⋊C4C4×D47semidirect
651. C22⋊C4C2×C4×D47semidirect
795. C2#20246323direct (N × H)

Maximal subgroups

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

subgroupindex
C22×(C22⋊D47)⋊C42
#202463232
C2×#156890162
C2×#156890102
C2×#156890042
C2×#156889992
C2×#156889902
C2×#156889842
C2×#156889802
C2×C22⋊C4×Dic472
C2×C4×(C2×D47)⋊C42
C2×#156889702
C2×#156889692
C2×#95×D472
C2×C47×#3882
C2×#235347