Finite Group Databasebeta

← C2×#20246858 #26383977

Subgroups — C2×#20246858 #26383977

Order 12032.

3222 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094006C211yesmaximal, characteristic
2C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
3#20246858C2116yesmaximal, direct product factor
4C2×#15689065C211yesmaximal, characteristic, complemented
5C2×#15689057C211yesmaximal, characteristic, complemented
6C2×#15689051C211yesmaximal, characteristic, complemented
7C2×#15689009C211yesmaximal, characteristic, complemented
8C2×#15689006C211yesmaximal, characteristic, complemented
9C2×#15688999C211yesmaximal, characteristic
10C2×#15688998C211yesmaximal, characteristic, complemented
11C2×#15688997C211yesmaximal, characteristic, complemented
12C2×#15688985C211yesmaximal, characteristic, complemented
13C2×#15688984C211yesmaximal, characteristic, complemented
14C2×#15688980C211yesmaximal, characteristic, complemented
15C2×#95×D47C211yesmaximal, characteristic, complemented
16C2×C47×#397C211yesmaximal, characteristic, complemented
17C23×C22⋊D47C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C2×#13094006—28no—
23C2×#13094006C2218yes—
24C2×(C22⋊D47)⋊C4—28no—
25C2×(C22⋊D47)⋊C4C2218yes—
26C22×C4⋊Dic47C2211yescharacteristic
27C22×C4⋊Dic47C2211yescharacteristic
28C22×C4⋊Dic47C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×C22⋊Dic47C2211yescharacteristic
33C22×C22⋊Dic47C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×C4×Dic47C2211yescharacteristic
38#15689065C2218yescomplemented
39#15689057C2218yescomplemented
40#15689051C2218yescomplemented
41#15689009C2218yescomplemented
42#15689006C2218yescomplemented
43#15688999C2218yes—
44#15688998C2218yescomplemented
45#15688997C2218yescomplemented
46#15688985C2218yescomplemented
47#15688984C2218yescomplemented
48#15688980C2218yescomplemented
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
59C2×C47⋊#95C2211yescharacteristic
60#95×D47C2218yescomplemented
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C22⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C47×#397C2218yescomplemented
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C24×D47C2311yescharacteristic
70C22×C22⋊D47—24no—
71C22×C22⋊D47—24no—
72C22×C22⋊D47D418yes—
73C22×C22⋊D47C2314yes—
74C23×Dic47—24no—
75C23×Dic47—24no—
76C23×Dic47—42no—
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2314yes—
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C22×C4×D47—24no—
86C22×C4×D47—24no—
87C22×C4×D47—24no—
88C22×C4×D47—24no—
89C22×C4×D47—24no—
90C22×C4×D47—24no—
91C22×C4×D47—24no—
92C22×C4×D47—42no—
93C22×C4×D47—42no—
94C22×C4×D47C2314yes—
95C22×C4×D47C2314yes—
96C22×C4×D47C2314yes—
97#13094006—232no—
98(C22⋊D47)⋊C4—232no—
99C2×C4⋊Dic47—24no—
100C2×C4⋊Dic47—24no—
101C2×C4⋊Dic47—42no—
102C2×C4⋊Dic47C2314yes—
103C2×C4⋊Dic47C2314yes—
104C2×C4⋊Dic47C2314yes—
105C2×Dic47⋊C4—24no—
106C2×Dic47⋊C4—24no—
107C2×Dic47⋊C4—42no—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2314yes—
111C2×C22⋊Dic47—24no—
112C2×C22⋊Dic47—42no—
113C2×C22⋊Dic47C2314yes—
114C2×C22⋊Dic47C2314yes—
115C2×(C2×D47)⋊C4—24no—
116C2×(C2×D47)⋊C4—24no—
117C2×(C2×D47)⋊C4—24no—
118C2×(C2×D47)⋊C4C2314yes—
119C2×(C2×D47)⋊C4C2314yes—
120C2×(C2×D47)⋊C4C2314yes—
121C2×C4×Dic47—24no—
122C2×C4×Dic47C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C25×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2311yescharacteristic
139C23×C4×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C2×C4⋊C4×C47—24no—
142C2×C4⋊C4×C47C2314yes—
143C2×C22⋊C4×C47—24no—
144C2×C22⋊C4×C47—24no—
145C2×C22⋊C4×C47—24no—
146C2×C22⋊C4×C47C2314yes—
147C2×C22⋊C4×C47C2314yes—
148C2×C22⋊C4×C47C2314yes—
149#95×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×D47C2×D414yes—
166C23×D47#4114yes—
167C23×D47#4114yes—
168C23×D47C2412yes—
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×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47#4114yes—
187C22×C4×C47C2412yes—
188C22×C4×C47C2412yes—
189C22×C4×C47C2412yes—
190C22×C4×C47C2412yes—
191C22×C4×C47C2412yes—
192C22×C4×C47C2412yes—
193C2×C22⋊D47—232no—
194C2×C22⋊D47—28no—
195C2×C22⋊D47—28no—
196C2×C22⋊D47C2×D4116yes—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—28no—
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—28no—
218C22×Dic47—44no—
219C22×Dic47—416no—
220C22×Dic47C2×D414yes—
221C22×Dic47#4114yes—
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—28no—
232C2×C4×D47—28no—
233C2×C4×D47—28no—
234C2×C4×D47—28no—
235C2×C4×D47—28no—
236C2×C4×D47—44no—
237C2×C4×D47—44no—
238C2×C4×D47—416no—
239C2×C4×D47—416no—
240C2×C4×D47—416no—
241C4⋊C4×C47—28no—
242C22⋊C4×C47—28no—
243C22⋊C4×C47—28no—
244C22⋊C4×C47—28no—
245C22⋊Dic47—28no—
246C22⋊Dic47—44no—
247(C2×D47)⋊C4—28no—
248(C2×D47)⋊C4—28no—
249(C2×D47)⋊C4—28no—
250C4⋊Dic47—28no—
251C4⋊Dic47—28no—
252C4⋊Dic47—44no—
253Dic47⋊C4—28no—
254Dic47⋊C4—28no—
255Dic47⋊C4—44no—
256C4×Dic47—28no—
257C23×C47—28no—
258C23×C47—28no—
259C23×C47—28no—
260C23×C47—22no—
261C23×C47—22no—
262C23×C47—22no—
263C23×C47—22no—
264C23×C47—22no—
265C23×C47—22no—
266C23×C47—44no—
267C23×C47—44no—
268C23×C47—44no—
269C23×C47—44no—
270C23×C47C22×D414yes—
271C23×C47C22×D412yes—
272C23×C47C2×#4112yes—
273C23×C47C2×#4112yes—
274C23×C47C2×#4112yes—
275C23×C47C2×#4112yes—
276C23×C47H(5,𝔽2)12yes—
277C23×C472−1+412yes—
278C23×C47C2511yescharacteristic
279C22×D47—28no—
280C22×D47—28no—
281C22×D47—28no—
282C22×D47—28no—
283C22×D47—28no—
284C22×D47—28no—
285C22×D47—22no—
286C22×D47—22no—
287C22×D47—22no—
288C22×D47—22no—
289C22×D47#123116yes—
290C22×D47C22×D414yes—
291C22×D47C2×#4114yes—
292C22×D47C2×#4114yes—
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—22no—
310C2×C4×C47—22no—
311C2×C4×C47—44no—
312C2×C4×C47—44no—
313C2×C4×C47—44no—
314C2×C4×C47—44no—
315C2×C4×C47—44no—
316C2×C4×C47C2×#4114yes—
317C22⋊D47—232no—
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—22no—
338C2×Dic47—22no—
339C2×Dic47—416no—
340C2×Dic47—44no—
341C2×Dic47—44no—
342C2×Dic47—44no—
343C2×Dic47—44no—
344C2×Dic47—44no—
345C2×Dic47C22×D414yes—
346C2×Dic47C2×#4114yes—
347C4×D47—416no—
348C4×D47—416no—
349C4×D47—416no—
350C2×#2419—471nomaximal, Sylow
351C22×C47—24no—
352C22×C47—24no—
353C22×C47—24no—
354C22×C47—42no—
355C22×C47—416no—
356C22×C47—42no—
357C22×C47—42no—
358C22×C47—42no—
359C22×C47C2×#12314yes—
360C22×C47#52914yes—
361C22×C47#53914yes—
362C22×C47#54614yes—
363C22×C47#54714yes—
364C22×C47#55114yes—
365C22×C47#55214yes—
366C22×C47C23×D411yescharacteristic
367C22×C47C22×#4111yescharacteristic
368C22×C47C22×#4111yescharacteristic
369C22×C47C22×#4111yescharacteristic
370C22×C47C22×#4111yescharacteristic
371C22×C47C2×H(5,𝔽2)11yescharacteristic
372C22×C47C2×2−1+411yescharacteristic
373C2×D47—24no—
374C2×D47—232no—
375C2×D47—24no—
376C2×D47—24no—
377C2×D47—24no—
378C2×D47—24no—
379C2×D47—24no—
380C2×D47C2×#12318yes—
381C4×C47—24no—
382C4×C47—42no—
383C4×C47—42no—
384C4×C47—42no—
385C4×C47—42no—
386C4×C47—42no—
387Dic47—24no—
388Dic47—24no—
389Dic47—42no—
390Dic47—42no—
391Dic47—42no—
392Dic47—42no—
393Dic47—42no—
394C22×#123—471no—
395C22×C4×D4—471no—
396#2419—4716no—
397C2×#400—471no—
398C2×#398—471no—
399C2×#397—471no—
400C2×#397D4711yescharacteristic, complemented
401C2×#387—471no—
402C2×#387—471no—
403C2×#386—471no—
404C2×#385—471no—
405C2×#385—471no—
406C2×#381—471no—
407C2×#381—471no—
408C2×#380—471no—
409C22×#95—471no—
410C2×C47—44no—
411C2×C47#241918yescomplemented
412C2×C47C22×#12311yescharacteristic
413C2×C47C2×#52911yescharacteristic
414C2×C47C2×#53911yescharacteristic
415C2×C47C2×#54611yescharacteristic
416C2×C47C2×#54711yescharacteristic
417C2×C47C2×#55111yescharacteristic
418C2×C47C2×#55211yescharacteristic
419D47—28no—
420C23×D4—471no—
421C24×C4—471no—
422C24×C4—471no—
423C24×C4—471no—
424C24×C4—471no—
425C2×#123—478no—
426C2×#123—948no—
427C2×C4×D4—478no—
428C2×C4×D4—948no—
429C22×C4⋊C4—471no—
430C22×C4⋊C4—471no—
431C22×C4⋊C4—471no—
432C22×C4⋊C4—471no—
433C22×C4⋊C4—471no—
434C22×C4⋊C4—471no—
435C22×C4⋊C4C2×D4711yescharacteristic
436C22×C22⋊C4—471no—
437C22×C22⋊C4—471no—
438C22×C22⋊C4—471no—
439C22×C22⋊C4—471no—
440C22×C22⋊C4—471no—
441C22×C22⋊C4C2×D4711yescharacteristic
442C22×C22⋊C4C2×D4711yescharacteristic
443C22×C22⋊C4C2×D4711yescharacteristic
444C22×C42—471no—
445#400—478no—
446#398—478no—
447#397—478no—
448#397C2×D4718yescomplemented
449#387—478no—
450#387—478no—
451#386—478no—
452#385—478no—
453#385—478no—
454#381—478no—
455#381—478no—
456#380—478no—
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—471no—
467C2×#95—471no—
468C2×#95—478no—
469C2×#95C2×D4711yescharacteristic
470C2×#95C2×D4711yescharacteristic
471C2×#95C2×D4711yescharacteristic
472C47C2×#241911yescharacteristic, complemented, Sylow
473C25—471no—
474C25C22×D4711yescharacteristic
475C22×D4—478no—
476C22×D4—474no—
477C22×D4—944no—
478C22×D4—944no—
479C23×C4—471no—
480C23×C4—471no—
481C23×C4—471no—
482C23×C4—471no—
483C23×C4—471no—
484C23×C4—471no—
485C23×C4—471no—
486C23×C4—474no—
487C23×C4—474no—
488C23×C4—474no—
489C23×C4—474no—
490C23×C4—944no—
491C23×C4—944no—
492C23×C4—944no—
493C23×C4—944no—
494C23×C4—944no—
495C23×C4—944no—
496C23×C4—944no—
497C23×C4—944no—
498C23×C4—944no—
499C23×C4—1882no—
500C23×C4—1882no—
501C23×C4—1882no—
502C23×C4C22×D4711yescharacteristic
503C23×C4C22×D4711yescharacteristic
504C23×C4C22×D4711yescharacteristic
505C23×C4C22×D4711yescharacteristic
506C23×C4C22×D4711yescharacteristic
507C23×C4C22×D4711yescharacteristic
508#123—9432no—
509C4×D4—9432no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—474no—
512C2×C4⋊C4—474no—
513C2×C4⋊C4—474no—
514C2×C4⋊C4—474no—
515C2×C4⋊C4—474no—
516C2×C4⋊C4—474no—
517C2×C4⋊C4—944no—
518C2×C4⋊C4—944no—
519C2×C4⋊C4—944no—
520C2×C4⋊C4—944no—
521C2×C4⋊C4—1882no—
522C2×C4⋊C4—1882no—
523C2×C4⋊C4C22×D4714yes—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—474no—
528C2×C22⋊C4—474no—
529C2×C22⋊C4—474no—
530C2×C22⋊C4—474no—
531C2×C22⋊C4—474no—
532C2×C22⋊C4—944no—
533C2×C22⋊C4—944no—
534C2×C22⋊C4—944no—
535C2×C22⋊C4—944no—
536C2×C22⋊C4—1882no—
537C2×C22⋊C4C22×D4714yes—
538C2×C22⋊C4C22×D4714yes—
539C2×C22⋊C4C22×D4714yes—
540C2×C42—474no—
541C2×C42—944no—
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#95—474no—
551#95—474no—
552#95—474no—
553#95C22×D4714yes—
554#95C22×D4714yes—
555#95C22×D4714yes—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—474no—
563C24—474no—
564C24—474no—
565C24—472no—
566C24—942no—
567C24—942no—
568C24—942no—
569C24—942no—
570C24D4×D4714yes—
571C24C23×D4712yes—
572C24C23×D4711yescharacteristic
573C2×D4—4716no—
574C2×D4—9432no—
575C2×D4—948no—
576C2×D4—948no—
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—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—474no—
595C22×C4—474no—
596C22×C4—472no—
597C22×C4—472no—
598C22×C4—472no—
599C22×C4—472no—
600C22×C4—472no—
601C22×C4—472no—
602C22×C4—472no—
603C22×C4—948no—
604C22×C4—948no—
605C22×C4—948no—
606C22×C4—948no—
607C22×C4—948no—
608C22×C4—948no—
609C22×C4—948no—
610C22×C4—942no—
611C22×C4—942no—
612C22×C4—942no—
613C22×C4—942no—
614C22×C4—942no—
615C22×C4—942no—
616C22×C4—942no—
617C22×C4—948no—
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—942no—
627C22×C4—942no—
628C22×C4—942no—
629C22×C4—942no—
630C22×C4—948no—
631C22×C4—1884no—
632C22×C4—1884no—
633C22×C4—18816no—
634C22×C4—18816no—
635C22×C4—18816no—
636C22×C4—1884no—
637C22×C4—18816no—
638C22×C4#1062535214yes—
639C22×C4C23×D4712yes—
640C22×C4C23×D4712yes—
641C22×C4C23×D4712yes—
642C22×C4C23×D4712yes—
643C22×C4C23×D4712yes—
644C22×C4C23×D4712yes—
645C4⋊C4—28no—
646C4⋊C4—948no—
647C4⋊C4—948no—
648C4⋊C4—948no—
649C4⋊C4—948no—
650C4⋊C4—1884no—
651C4⋊C4—1884no—
652C22⋊C4—28no—
653C22⋊C4—28no—
654C22⋊C4—28no—
655C22⋊C4—948no—
656C22⋊C4—948no—
657C22⋊C4—948no—
658C22⋊C4—948no—
659C22⋊C4—1884no—
660C42—948no—
661C23—28no—
662C23—28no—
663C23—28no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—4716no—
675C23—474no—
676C23—474no—
677C23—474no—
678C23—948no—
679C23—948no—
680C23—948no—
681C23—948no—
682C23—948no—
683C23—942no—
684C23—942no—
685C23—942no—
686C23—942no—
687C23—948no—
688C23C2×D4×D4714yes—
689C23C2×D4×D4712yes—
690C23#41×D4712yes—
691C23#41×D4712yes—
692C23#41×D4712yes—
693C23C2×#1062535212yes—
694C23#1309407012yes—
695C23#1309407112yes—
696C23C24×D4711yescharacteristic
697D4—9432no—
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—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—474no—
722C2×C4—474no—
723C2×C4—948no—
724C2×C4—948no—
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—942no—
741C2×C4—942no—
742C2×C4—942no—
743C2×C4—942no—
744C2×C4—18816no—
745C2×C4—18816no—
746C2×C4—18816no—
747C2×C4—18816no—
748C2×C4—1884no—
749C2×C4—1884no—
750C2×C4—1884no—
751C2×C4—1884no—
752C2×C4—1884no—
753C2×C4C2×#1062535214yes—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—416no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—478no—
763C22—944no—
764C22—9432no—
765C22—944no—
766C22—944no—
767C22—944no—
768C22—944no—
769C22—944no—
770C22#123×D4714yes—
771C22#1568965214yes—
772C22#1568971414yes—
773C22#1568976514yes—
774C22#1568977314yes—
775C22#1568979614yes—
776C22#1568980914yes—
777C22C22×D4×D4711yescharacteristic
778C22C2×#41×D4711yescharacteristic
779C22C2×#41×D4711yescharacteristic
780C22C2×#41×D4711yescharacteristic
781C22C22×#1062535211yescharacteristic
782C22C2×#1309407011yescharacteristic
783C22C2×#1309407111yescharacteristic
784C4—24no—
785C4—42no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—944no—
791C4—944no—
792C4—1882no—
793C4—1882no—
794C4—1882no—
795C4—1882no—
796C4—1882no—
797C2—44no—
798C2—948no—
799C2#2024685818yesdirect product factor
800C2C2×#123×D4711yescharacteristic
801C2C2×#1568965211yescharacteristic
802C2C2×#1568971411yescharacteristic
803C2C2×#1568976511yescharacteristic
804C2C2×#1568977311yescharacteristic
805C2C2×#1568979611yescharacteristic
806C2C2×#1568980911yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#397C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC2×#397D47
hypocenterC47C2×#2419
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
3. #20246858C2direct (N × H)
4. C2×#15689065C2semidirect
5. C2×#15689057C2semidirect
6. C2×#15689051C2semidirect
7. C2×#15689009C2semidirect
8. C2×#15689006C2semidirect
10. C2×#15688998C2semidirect
11. C2×#15688997C2semidirect
12. C2×#15688985C2semidirect
13. C2×#15688984C2semidirect
14. C2×#15688980C2semidirect
15. C2×#95×D47C2semidirect
16. C2×C47×#397C2semidirect
38. #15689065C22semidirect
39. #15689057C22semidirect
40. #15689051C22semidirect
41. #15689009C22semidirect
42. #15689006C22semidirect
44. #15688998C22semidirect
45. #15688997C22semidirect
46. #15688985C22semidirect
47. #15688984C22semidirect
48. #15688980C22semidirect
60. #95×D47C22semidirect
65. C47×#397C22semidirect
400. C2×#397D47semidirect
411. C2×C47#2419semidirect
448. #397C2×D47semidirect
472. C47C2×#2419semidirect
799. C2#20246858direct (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×(C22⋊D47)⋊C42
#202468582
C2×#156890652
C2×#156890572
C2×#156890512
C2×#156890092
C2×#156890062
C2×#156889992
C2×#156889982
C2×#156889972
C2×#156889852
C2×#156889842
C2×#156889802
C2×#95×D472
C2×C47×#3972
C2×#241947