Finite Group Databasebeta

← C2×#20247596 #26384720

Subgroups — C2×#20247596 #26384720

Order 12032.

3070 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×#13094000C211yesmaximal, characteristic, complemented
2C22×#13093981C211yesmaximal, characteristic, complemented
3#20247596C2116yesmaximal, direct product factor
4C2×#15689065C211yesmaximal, characteristic, complemented
5C2×#15689052C211yesmaximal, characteristic, complemented
6C2×#15689040C211yesmaximal, characteristic
7C2×#15689034C211yesmaximal, characteristic, complemented
8C2×#15689014C211yesmaximal, characteristic, complemented
9C2×#15689012C211yesmaximal, characteristic, complemented
10C2×#15689005C211yesmaximal, characteristic, complemented
11C2×#15689004C211yesmaximal, characteristic, complemented
12C2×#15689001C211yesmaximal, characteristic
13C2×#15689001C211yesmaximal, characteristic
14C2×#15688997C211yesmaximal, characteristic, complemented
15C2×#15688970C211yesmaximal, characteristic, complemented
16C2×C47×#391C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C2×#13094000—28no—
21C2×#13094000C2218yescomplemented
22C2×#13093981—28no—
23C2×#13093981C2218yescomplemented
24C22×C4⋊Dic47C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×C4×Dic47C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41#15689065C2218yescomplemented
42#15689052C2218yescomplemented
43#15689040C2218yes—
44#15689034C2218yescomplemented
45#15689014C2218yescomplemented
46#15689012C2218yescomplemented
47#15689005C2218yescomplemented
48#15689004C2218yescomplemented
49#15689001C2218yes—
50#15689001C2218yes—
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
61C23×Q8×C47C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C42×C47C2211yescharacteristic
64C47×#391C2218yescomplemented
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C24×D47C2311yescharacteristic
70C24×D47C2311yescharacteristic
71C22×D188—24no—
72C22×D188—24no—
73C22×D188—42no—
74C22×D188C2314yes—
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C22×C4×D47—24no—
82C22×C4×D47—24no—
83C22×C4×D47—24no—
84C22×C4×D47—24no—
85C22×C4×D47—24no—
86C22×C4×D47—42no—
87C22×C4×D47C2314yes—
88C22×C4×D47C2314yes—
89#13094000—232no—
90#13093981—232no—
91C2×C4⋊Dic47—24no—
92C2×C4⋊Dic47C2314yes—
93C2×Dic47⋊C4—24no—
94C2×Dic47⋊C4—24no—
95C2×Dic47⋊C4—24no—
96C2×Dic47⋊C4D418yescomplemented
97C2×Dic47⋊C4C2314yes—
98C2×Dic47⋊C4C2314yes—
99C2×Dic47⋊C4C2314yes—
100C2×Dic47⋊C4C2314yes—
101C2×(C2×D47)⋊C4—24no—
102C2×(C2×D47)⋊C4—24no—
103C2×(C2×D47)⋊C4—24no—
104C2×(C2×D47)⋊C4—24no—
105C2×(C2×D47)⋊C4—24no—
106C2×(C2×D47)⋊C4—24no—
107C2×(C2×D47)⋊C4—24no—
108C2×(C2×D47)⋊C4—24no—
109C2×(C2×D47)⋊C4—24no—
110C2×(C2×D47)⋊C4—42no—
111C2×(C2×D47)⋊C4C2314yes—
112C2×(C2×D47)⋊C4C2314yes—
113C2×(C2×D47)⋊C4C2314yes—
114C2×(C2×D47)⋊C4C2314yes—
115C2×(C2×D47)⋊C4C2314yes—
116C2×(C2×D47)⋊C4C2314yes—
117C2×(C2×D47)⋊C4C2314yes—
118C2×(C2×D47)⋊C4C2314yes—
119C2×(C2×D47)⋊C4C2314yes—
120C2×(C2×D47)⋊C4C2314yes—
121C2×C4×Dic47—24no—
122C2×C4×Dic47—42no—
123C2×C4×Dic47C2314yes—
124C2×C4×Dic47C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C22×Q8×C47—24no—
134C22×Q8×C47—24no—
135C22×Q8×C47—42no—
136C22×Q8×C47C2314yes—
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2311yescharacteristic
139C23×C4×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C2×C4⋊C4×C47—42no—
145C2×C4⋊C4×C47C2314yes—
146C2×C42×C47—24no—
147C2×C42×C47C2314yes—
148#95×C47C2314yes—
149#95×C47C2314yes—
150#95×C47C2314yes—
151#95×C47C2314yes—
152C24×C47C2411yescharacteristic
153C23×D47—22no—
154C23×D47—22no—
155C23×D47—22no—
156C23×D47—22no—
157C23×D47—22no—
158C23×D47—22no—
159C23×D47—22no—
160C23×D47—22no—
161C23×D47—22no—
162C23×D47—22no—
163C23×D47—22no—
164C23×D47—22no—
165C23×D47#4114yes—
166C23×D47#4114yes—
167C23×D47C2412yes—
168C23×D47C2412yes—
169C2×Q8×C47—28no—
170C2×Q8×C47—28no—
171C2×Q8×C47—44no—
172C2×Q8×C47—416no—
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×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—22no—
189C22×C4×C47—22no—
190C22×C4×C47—22no—
191C22×C4×C47C2×D414yes—
192C22×C4×C47#4114yes—
193C22×C4×C47#4114yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2412yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2412yes—
199C22×C4×C47C2412yes—
200C22×C4×C47C2412yes—
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×Dic47C2×D414yes—
218C22×Dic47C2×D414yes—
219C22×Dic47C2412yes—
220C22×Dic47C2412yes—
221C22×Dic47C2412yes—
222C22×Dic47C2412yes—
223C22×Dic47C2412yes—
224C22×Dic47C2412yes—
225C2×D188—28no—
226C2×D188—28no—
227C2×D188—44no—
228C2×D188—416no—
229C2×C4×D47—232no—
230C2×C4×D47—28no—
231C2×C4×D47—28no—
232C2×C4×D47—28no—
233C2×C4×D47—28no—
234C2×C4×D47—28no—
235C2×C4×D47—44no—
236C2×C4×D47—416no—
237C4⋊C4×C47—44no—
238C42×C47—28no—
239(C2×D47)⋊C4—28no—
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—
245(C2×D47)⋊C4—28no—
246(C2×D47)⋊C4—28no—
247(C2×D47)⋊C4—28no—
248(C2×D47)⋊C4—44no—
249C4⋊Dic47—28no—
250Dic47⋊C4—28no—
251Dic47⋊C4—28no—
252Dic47⋊C4—28no—
253Dic47⋊C4C2×D4116yescomplemented
254C4×Dic47—28no—
255C4×Dic47—44no—
256C23×C47C22×D412yes—
257C23×C47C2×#4112yes—
258C23×C47C2×#4112yes—
259C23×C47C2×#4112yes—
260C23×C47C2×#4112yes—
261C23×C47H(5,𝔽2)12yes—
262C23×C472−1+412yes—
263C23×C47C2511yescharacteristic
264C22×D47—28no—
265C22×D47—28no—
266C22×D47—28no—
267C22×D47—28no—
268C22×D47—28no—
269C22×D47—28no—
270C22×D47—22no—
271C22×D47—22no—
272C22×D47—22no—
273C22×D47—22no—
274C22×D47—22no—
275C22×D47—22no—
276C22×D47—22no—
277C22×D47—22no—
278C22×D47—22no—
279C22×D47—22no—
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—44no—
283C22×D47—44no—
284C22×D47—44no—
285C22×D47—44no—
286C22×D47—44no—
287C22×D47—44no—
288C22×D47—44no—
289C22×D47—44no—
290C22×D47C2×#4114yes—
291C22×D47C2×#4114yes—
292Q8×C47—416no—
293C2×C4×C47—28no—
294C2×C4×C47—28no—
295C2×C4×C47—28no—
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—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—44no—
315C2×C4×C47—44no—
316C2×C4×C47—44no—
317C2×C4×C47—44no—
318C2×C4×C47C22×D414yes—
319C2×C4×C47C2×#4114yes—
320C2×C4×C47C2×#4114yes—
321C2×Dic47—28no—
322C2×Dic47—28no—
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—22no—
339C2×Dic47—44no—
340C2×Dic47—44no—
341C2×Dic47—44no—
342C2×Dic47—44no—
343C2×Dic47C22×D414yes—
344C2×Dic47C22×D414yes—
345D188—416no—
346C4×D47—232no—
347C4×D47—416no—
348C2×#2477—471nomaximal, Sylow
349C22×C47#52514yes—
350C22×C47#52914yes—
351C22×C47#54214yes—
352C22×C47#54614yes—
353C22×C47#54814yes—
354C22×C47#55114yes—
355C22×C47#55214yes—
356C22×C47C23×D411yescharacteristic
357C22×C47C22×#4111yescharacteristic
358C22×C47C22×#4111yescharacteristic
359C22×C47C22×#4111yescharacteristic
360C22×C47C22×#4111yescharacteristic
361C22×C47C2×H(5,𝔽2)11yescharacteristic
362C22×C47C2×2−1+411yescharacteristic
363C2×D47—24no—
364C2×D47—24no—
365C2×D47—24no—
366C2×D47—24no—
367C2×D47—24no—
368C2×D47—24no—
369C2×D47—42no—
370C2×D47—42no—
371C2×D47—42no—
372C2×D47—42no—
373C2×D47—42no—
374C2×D47—42no—
375C2×D47—42no—
376C2×D47—42no—
377C2×D47—416no—
378C2×D47—416no—
379C4×C47—24no—
380C4×C47—24no—
381C4×C47—24no—
382C4×C47—42no—
383C4×C47—42no—
384C4×C47—42no—
385C4×C47—42no—
386Dic47—24no—
387Dic47—24no—
388Dic47—42no—
389Dic47—42no—
390Dic47—42no—
391Dic47—42no—
392C22×C22⋊Q8—471no—
393C22×#117—471no—
394#2477—4716no—
395C2×#400—471no—
396C2×#397—471no—
397C2×#394—471no—
398C2×#393—471no—
399C2×#391D4711yescharacteristic, complemented
400C2×#388—471no—
401C2×#388—471no—
402C2×#387—471no—
403C2×#387—471no—
404C2×#386—471no—
405C2×#386—471no—
406C2×#385—471no—
407C2×C4×C22⋊C4—471no—
408C2×C47#247718yescomplemented
409C2×C47C2×#52511yescharacteristic
410C2×C47C2×#52911yescharacteristic
411C2×C47C2×#54211yescharacteristic
412C2×C47C2×#54611yescharacteristic
413C2×C47C2×#54811yescharacteristic
414C2×C47C2×#55111yescharacteristic
415C2×C47C2×#55211yescharacteristic
416D47—44no—
417D47—44no—
418C23×Q8C2×D4711yescharacteristic
419C23×D4—471no—
420C24×C4—471no—
421C24×C4—471no—
422C2×C22⋊Q8—478no—
423C2×C22⋊Q8—948no—
424C2×#117—478no—
425C2×#117—948no—
426C22×C4⋊C4—471no—
427C22×C4⋊C4—471no—
428C22×C4⋊C4—471no—
429C22×C4⋊C4—471no—
430C22×C4⋊C4—471no—
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⋊C4—471no—
441C22×C22⋊C4—471no—
442C22×C42—471no—
443C22×C42—471no—
444C22×C42C2×D4711yescharacteristic
445#400—478no—
446#397—478no—
447#394—478no—
448#393—478no—
449#391C2×D4718yescomplemented
450#388—478no—
451#388—478no—
452#387—478no—
453#387—478no—
454#386—478no—
455#386—478no—
456#385—478no—
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
468C2×#95C2×D4711yescharacteristic
469C2×#95C2×D4711yescharacteristic
470C47C2×#247711yescharacteristic, complemented, Sylow
471C25—471no—
472C25—471no—
473C22×Q8—24no—
474C22×Q8—24no—
475C22×Q8—42no—
476C22×Q8C22×D4714yes—
477C22×D4—474no—
478C22×D4—944no—
479C22×D4—944no—
480C22×D4—1882no—
481C23×C4—471no—
482C23×C4—471no—
483C23×C4—471no—
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—944no—
494C23×C4—1882no—
495C23×C4C22×D4711yescharacteristic
496C23×C4C22×D4711yescharacteristic
497C23×C4C22×D4711yescharacteristic
498C23×C4C22×D4711yescharacteristic
499C23×C4C22×D4711yescharacteristic
500C23×C4C22×D4711yescharacteristic
501C23×C4C22×D4711yescharacteristic
502C22⋊Q8—9432no—
503#117—9432no—
504C2×C4⋊C4—42no—
505C2×C4⋊C4—478no—
506C2×C4⋊C4—474no—
507C2×C4⋊C4—474no—
508C2×C4⋊C4—474no—
509C2×C4⋊C4—474no—
510C2×C4⋊C4—474no—
511C2×C4⋊C4—944no—
512C2×C4⋊C4—944no—
513C2×C4⋊C4—944no—
514C2×C4⋊C4—944no—
515C2×C4⋊C4C22×D4714yes—
516C2×C22⋊C4—474no—
517C2×C22⋊C4—474no—
518C2×C22⋊C4—474no—
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—944no—
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—944no—
534C2×C22⋊C4—944no—
535C2×C22⋊C4—1882no—
536C2×C42—24no—
537C2×C42—474no—
538C2×C42—474no—
539C2×C42—944no—
540C2×C42—1882no—
541C2×C42C22×D4714yes—
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—
552#95C22×D4714yes—
553#95C22×D4714yes—
554C24—474no—
555C24—474no—
556C24—472no—
557C24—472no—
558C24—942no—
559C24—942no—
560C24—942no—
561C24—942no—
562C24—942no—
563C24—942no—
564C24—942no—
565C24—942no—
566C24—942no—
567C24—942no—
568C24—942no—
569C24—942no—
570C24C23×D4711yescharacteristic
571C2×Q8—28no—
572C2×Q8—28no—
573C2×Q8—44no—
574C2×Q8—416no—
575C2×D4—948no—
576C2×D4—948no—
577C2×D4—1884no—
578C2×D4—18816no—
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—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—474no—
598C22×C4—474no—
599C22×C4—472no—
600C22×C4—472no—
601C22×C4—472no—
602C22×C4—472no—
603C22×C4—472no—
604C22×C4—472no—
605C22×C4—948no—
606C22×C4—948no—
607C22×C4—948no—
608C22×C4—9432no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—942no—
612C22×C4—942no—
613C22×C4—948no—
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—942no—
623C22×C4—942no—
624C22×C4—942no—
625C22×C4—942no—
626C22×C4—948no—
627C22×C4—1884no—
628C22×C4—18816no—
629C22×C4#1062535014yes—
630C22×C4D4×D4714yes—
631C22×C4#1062535414yes—
632C22×C4C23×D4712yes—
633C22×C4C23×D4712yes—
634C22×C4C23×D4712yes—
635C22×C4C23×D4712yes—
636C22×C4C23×D4712yes—
637C22×C4C23×D4712yes—
638C22×C4C23×D4712yes—
639C4⋊C4—44no—
640C4⋊C4—4716no—
641C4⋊C4—948no—
642C4⋊C4—948no—
643C4⋊C4—948no—
644C4⋊C4—948no—
645C22⋊C4—948no—
646C22⋊C4—948no—
647C22⋊C4—948no—
648C22⋊C4—948no—
649C22⋊C4—948no—
650C22⋊C4—948no—
651C22⋊C4—948no—
652C22⋊C4—948no—
653C22⋊C4—948no—
654C22⋊C4—1884no—
655C42—28no—
656C42—948no—
657C42—1884no—
658C23—474no—
659C23—474no—
660C23—948no—
661C23—948no—
662C23—948no—
663C23—948no—
664C23—948no—
665C23—948no—
666C23—942no—
667C23—942no—
668C23—942no—
669C23—942no—
670C23—942no—
671C23—942no—
672C23—942no—
673C23—942no—
674C23—942no—
675C23—942no—
676C23—942no—
677C23—942no—
678C23—1884no—
679C23—1884no—
680C23—1884no—
681C23—1884no—
682C23—1884no—
683C23—1884no—
684C23—1884no—
685C23—1884no—
686C23C2×D4×D4712yes—
687C23#41×D4712yes—
688C23#41×D4712yes—
689C23C2×#1062535012yes—
690C23C2×#1062535412yes—
691C23#1309406912yes—
692C23#1309407212yes—
693C23C24×D4711yescharacteristic
694Q8—416no—
695D4—18816no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—28no—
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—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—474no—
722C2×C4—474no—
723C2×C4—9432no—
724C2×C4—948no—
725C2×C4—948no—
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—942no—
741C2×C4—942no—
742C2×C4—18816no—
743C2×C4—1884no—
744C2×C4—1884no—
745C2×C4—1884no—
746C2×C4—1884no—
747C2×C4C2×D4×D4714yes—
748C2×C4C2×#1062535014yes—
749C2×C4C2×#1062535414yes—
750C22—944no—
751C22—944no—
752C22—944no—
753C22—944no—
754C22—944no—
755C22—944no—
756C22—1882no—
757C22—1882no—
758C22—18816no—
759C22—18816no—
760C22—1882no—
761C22—1882no—
762C22—1882no—
763C22—1882no—
764C22—1882no—
765C22—1882no—
766C22#1568963614yes—
767C22#1568966014yes—
768C22#1568974714yes—
769C22#1568976314yes—
770C22#1568978314yes—
771C22#1568980314yes—
772C22#1568981414yes—
773C22C22×D4×D4711yescharacteristic
774C22C2×#41×D4711yescharacteristic
775C22C2×#41×D4711yescharacteristic
776C22C22×#1062535011yescharacteristic
777C22C22×#1062535411yescharacteristic
778C22C2×#1309406911yescharacteristic
779C22C2×#1309407211yescharacteristic
780C4—24no—
781C4—24no—
782C4—24no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—944no—
788C4—944no—
789C4—1882no—
790C4—1882no—
791C4—1882no—
792C4—1882no—
793C2—1884no—
794C2—1884no—
795C2#2024759618yesdirect product factor
796C2C2×#1568963611yescharacteristic
797C2C2×#1568966011yescharacteristic
798C2C2×#1568974711yescharacteristic
799C2C2×#1568976311yescharacteristic
800C2C2×#1568978311yescharacteristic
801C2C2×#1568980311yescharacteristic
802C2C2×#1568981411yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#391C2
socleC24×C47C24
prime radicalC23×D188C22
hypercenterC2×#391D47
hypocenterC47C2×#2477
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
1. C22×#13094000C2semidirect
2. C22×#13093981C2semidirect
3. #20247596C2direct (N × H)
4. C2×#15689065C2semidirect
5. C2×#15689052C2semidirect
7. C2×#15689034C2semidirect
8. C2×#15689014C2semidirect
9. C2×#15689012C2semidirect
10. C2×#15689005C2semidirect
11. C2×#15689004C2semidirect
14. C2×#15688997C2semidirect
15. C2×#15688970C2semidirect
16. C2×C47×#391C2semidirect
21. C2×#13094000C22semidirect
23. C2×#13093981C22semidirect
41. #15689065C22semidirect
42. #15689052C22semidirect
44. #15689034C22semidirect
45. #15689014C22semidirect
46. #15689012C22semidirect
47. #15689005C22semidirect
48. #15689004C22semidirect
51. #15688997C22semidirect
52. #15688970C22semidirect
64. C47×#391C22semidirect
96. C2×Dic47⋊C4D4semidirect
253. Dic47⋊C4C2×D4semidirect
399. C2×#391D47semidirect
408. C2×C47#2477semidirect
449. #391C2×D47semidirect
470. C47C2×#2477semidirect
795. C2#20247596direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940002
C22×#130939812
#202475962
C2×#156890652
C2×#156890522
C2×#156890402
C2×#156890342
C2×#156890142
C2×#156890122
C2×#156890052
C2×#156890042
C2×#156890012
C2×#156889972
C2×#156889702
C2×C47×#3912
C2×#247747