Finite Group Databasebeta

← #26138528

Subgroups — #26138528

Order 12032.

2366 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D47C211yesmaximal, characteristic
2C2×#15689022C211yesmaximal, characteristic, complemented
3C2×#15688980C212yesmaximal
4C2×#15688980C211yesmaximal, characteristic
5C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
6#20241642C212yesmaximal, complemented
7#20241638C212yesmaximal, complemented
8#20241618C211yesmaximal, characteristic, complemented
9#20241617C211yesmaximal, characteristic, complemented
10(C2×D47)⋊#95C212yesmaximal
11C2×C47×#389C211yesmaximal, characteristic, complemented
12C23×C4×D47C2212yes—
13C23×C4×D47C2211yescharacteristic
14C22×C4⋊Dic47C2211yescharacteristic
15C22×C4⋊Dic47C2212yes—
16C22×C4⋊Dic47C2211yescharacteristic
17C22×Dic47⋊C4C2212yes—
18C2×C4⋊C4×D47—24no—
19C2×C4⋊C4×D47—24no—
20C2×C4⋊C4×D47C418yescomplemented
21C22×(C2×D47)⋊C4C2212yes—
22C22×(C2×D47)⋊C4C2211yescharacteristic
23C22×(C2×D47)⋊C4C2211yescharacteristic
24C22×C4×Dic47C2211yescharacteristic
25#15689022—24no—
26#15688980—24no—
27#15688980—28no—
28C4×(C2×D47)⋊C4—24no—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2212yes—
37C22×C4⋊C4×C47C2211yescharacteristic
38C22×C4⋊C4×C47C2212yes—
39C22×C4⋊C4×C47C2211yescharacteristic
40C22×C42×C47C2211yescharacteristic
41C47×#389—24no—
42C2×#95×C47C2212yes—
43C24×D47C2311yescharacteristic
44C23×Dic47C2312yes—
45C23×Dic47C2312yes—
46C23×Dic47C2311yescharacteristic
47C23×Dic47C2311yescharacteristic
48C23×Dic47C2311yescharacteristic
49C22×C4×D47—22no—
50C22×C4×D47—22no—
51C22×C4×D47—22no—
52C22×C4×D47—22no—
53C22×C4×D47—24no—
54C22×C4×D47—24no—
55C22×C4×D47—24no—
56C22×C4×D47—24no—
57C22×C4×D47—42no—
58C22×C4×D47—42no—
59C22×C4×D47C2×C418yes—
60C22×C4×D47C2×C414yes—
61C22×C4×D47D414yes—
62C22×C4×D47Q814yes—
63C2×C4⋊Dic47—22no—
64C2×C4⋊Dic47—22no—
65C2×C4⋊Dic47—22no—
66C2×C4⋊Dic47—24no—
67C2×C4⋊Dic47—22no—
68C2×C4⋊Dic47—22no—
69C2×C4⋊Dic47—24no—
70C2×C4⋊Dic47—42no—
71C2×C4⋊Dic47C2×C414yes—
72C2×Dic47⋊C4—24no—
73C2×Dic47⋊C4—24no—
74C2×Dic47⋊C4C2×C418yes—
75C4⋊C4×D47—232no—
76C2×(C2×D47)⋊C4—22no—
77C2×(C2×D47)⋊C4—22no—
78C2×(C2×D47)⋊C4—22no—
79C2×(C2×D47)⋊C4—22no—
80C2×(C2×D47)⋊C4—24no—
81C2×(C2×D47)⋊C4—24no—
82C2×(C2×D47)⋊C4—24no—
83C2×(C2×D47)⋊C4D414yes—
84C2×(C2×D47)⋊C4Q814yes—
85C2×C4×Dic47—22no—
86C2×C4×Dic47—22no—
87C2×C4×Dic47—22no—
88C47⋊#95—24no—
89C47⋊#95—24no—
90C47⋊#95—22no—
91C47⋊#95—22no—
92C47⋊#95—24no—
93C47⋊#95—24no—
94C47⋊#95—42no—
95C47⋊#95—42no—
96C23×C4×C47C2312yes—
97C23×C4×C47C2311yescharacteristic
98C23×C4×C47C2311yescharacteristic
99C23×C4×C47C2312yes—
100C23×C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47—24no—
102C2×C4⋊C4×C47—22no—
103C2×C4⋊C4×C47—24no—
104C2×C4⋊C4×C47—22no—
105C2×C4⋊C4×C47—22no—
106C2×C4⋊C4×C47—42no—
107C2×C4⋊C4×C47C2×C414yes—
108C2×C4⋊C4×C47D414yes—
109C2×C4⋊C4×C47D414yes—
110C2×C42×C47—22no—
111C2×C42×C47—22no—
112C2×C42×C47—22no—
113#95×C47—24no—
114C24×C47C2411yescharacteristic
115C23×D47—21no—
116C23×D47—21no—
117C23×D47—21no—
118C23×D47—21no—
119C23×D47—21no—
120C23×D47—21no—
121C23×D47—21no—
122C23×D47—21no—
123C23×D47C22×C412yes—
124C23×D47C2×D412yes—
125C23×D47C2×D412yes—
126C23×D47C2×Q812yes—
127C23×D47C2×Q812yes—
128C23×D47#4112yes—
129C23×D47#4112yes—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47C22×C414yes—
154C22×C4×C47C22×C412yes—
155C22×C4×C47C2×D412yes—
156C22×C4×C47C2×D414yes—
157C22×C4×C47C2×D414yes—
158C22×C4×C47C2×D412yes—
159C22×C4×C47C2×D412yes—
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2×Q812yes—
162C22×C4×C47C2×Q812yes—
163C22×C4×C47#4112yes—
164C22×C4×C47#4112yes—
165C22×Dic47—21no—
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—22no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—21no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—21no—
179C22×Dic47—21no—
180C22×Dic47—22no—
181C22×Dic47—21no—
182C22×Dic47—22no—
183C22×Dic47—22no—
184C22×Dic47—21no—
185C22×Dic47—21no—
186C22×Dic47—21no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47C22×C414yes—
195C22×Dic47C22×C412yes—
196C22×Dic47C2×D412yes—
197C22×Dic47C2×D412yes—
198C22×Dic47C2×Q812yes—
199C22×Dic47C2×Q812yes—
200C2×C4×D47—28no—
201C2×C4×D47—28no—
202C2×C4×D47—28no—
203C2×C4×D47—28no—
204C2×C4×D47—28no—
205C2×C4×D47—28no—
206C2×C4×D47—216no—
207C2×C4×D47—216no—
208C2×C4×D47—48no—
209C2×C4×D47—48no—
210C2×C4×D47—48no—
211C2×C4×D47—48no—
212C2×C4×D47—48no—
213C2×C4×D47C4⋊C4116yescomplemented
214C4⋊C4×C47—48no—
215C4⋊C4×C47—44no—
216C4⋊C4×C47C22⋊C4116yescomplemented
217C42×C47—44no—
218(C2×D47)⋊C4—28no—
219(C2×D47)⋊C4—28no—
220(C2×D47)⋊C4—48no—
221C4⋊Dic47—28no—
222C4⋊Dic47—48no—
223C4⋊Dic47—44no—
224Dic47⋊C4—216no—
225C4×Dic47—44no—
226C23×C47C23×C411yescharacteristic
227C23×C47C22×D411yescharacteristic
228C23×C47C22×D411yescharacteristic
229C23×C47C22×D411yescharacteristic
230C23×C47C22×D411yescharacteristic
231C23×C47C22×Q811yescharacteristic
232C23×C47C22×Q811yescharacteristic
233C23×C47C2×#4111yescharacteristic
234C23×C47C2×#4111yescharacteristic
235C23×C47C2×#4111yescharacteristic
236C23×C47C2×#4111yescharacteristic
237C23×C47H(5,𝔽2)11yescharacteristic
238C23×C47H(5,𝔽2)11yescharacteristic
239C23×C472−1+411yescharacteristic
240C23×C472−1+411yescharacteristic
241C22×D47—22no—
242C22×D47—22no—
243C22×D47—22no—
244C22×D47—22no—
245C22×D47—22no—
246C22×D47—22no—
247C22×D47—22no—
248C22×D47—22no—
249C22×D47—22no—
250C22×D47—22no—
251C22×D47—22no—
252C22×D47—22no—
253C22×D47—22no—
254C22×D47—22no—
255C22×D47—22no—
256C22×D47—22no—
257C22×D47—22no—
258C22×D47—22no—
259C22×D47—22no—
260C22×D47—22no—
261C22×D47—22no—
262C22×D47—22no—
263C22×D47—22no—
264C22×D47—22no—
265C22×D47—22no—
266C22×D47—22no—
267C22×D47—22no—
268C22×D47—22no—
269C22×D47C2×C4⋊C414yes—
270C22×D47C4×D414yes—
271C22×D47C4×Q814yes—
272C22×D47#12114yes—
273C22×D47C22⋊Q814yes—
274C22×D47#12514yes—
275C22×D47C4⋊Q814yes—
276C2×C4×C47—24no—
277C2×C4×C47—24no—
278C2×C4×C47—24no—
279C2×C4×C47—24no—
280C2×C4×C47—24no—
281C2×C4×C47—24no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47—42no—
303C2×C4×C47C2×C22⋊C418yes—
304C2×C4×C47C2×C22⋊C414yes—
305C2×C4×C47C2×C4⋊C414yes—
306C2×C4×C47#11714yes—
307C2×C4×C47#12114yes—
308C2×C4×C47#12114yes—
309C2×C4×C47C22⋊Q814yes—
310C2×C4×C47C22⋊Q814yes—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—24no—
318C2×Dic47—24no—
319C2×Dic47—24no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—41no—
327C2×Dic47—41no—
328C2×Dic47—41no—
329C2×Dic47—41no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47—42no—
333C2×Dic47—42no—
334C2×Dic47—41no—
335C2×Dic47—41no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—42no—
339C2×Dic47—42no—
340C2×Dic47—42no—
341C2×Dic47—42no—
342C2×Dic47—42no—
343C2×Dic47—42no—
344C2×Dic47—42no—
345C2×Dic47C2×C4⋊C414yes—
346C4×D47—232no—
347C4×D47—432no—
348#13907—471nomaximal, Sylow
349C22×C47C22×C22⋊C411yescharacteristic
350C22×C47C22×C4⋊C411yescharacteristic
351C22×C47C2×#11711yescharacteristic
352C22×C47C2×C4×D411yescharacteristic
353C22×C47C2×C4×Q811yescharacteristic
354C22×C47#51811yescharacteristic
355C22×C47#51911yescharacteristic
356C22×C47C2×#12111yescharacteristic
357C22×C47C2×#12111yescharacteristic
358C22×C47C2×#12111yescharacteristic
359C22×C47C2×C22⋊Q811yescharacteristic
360C22×C47C2×C22⋊Q811yescharacteristic
361C22×C47C2×C22⋊Q811yescharacteristic
362C22×C47C2×#12511yescharacteristic
363C22×C47C2×C4⋊Q811yescharacteristic
364C22×C47#53711yescharacteristic
365C22×C47#53711yescharacteristic
366C22×C47#54411yescharacteristic
367C22×C47#54411yescharacteristic
368C22×C47D4211yescharacteristic
369C22×C47D4211yescharacteristic
370C22×C47#54611yescharacteristic
371C22×C47#54611yescharacteristic
372C22×C47#54711yescharacteristic
373C22×C47#54711yescharacteristic
374C22×C47#54811yescharacteristic
375C22×C47#54811yescharacteristic
376C22×C47D4×Q811yescharacteristic
377C22×C47D4×Q811yescharacteristic
378C22×C47#55211yescharacteristic
379C22×C47#55211yescharacteristic
380C22×C47#55311yescharacteristic
381C22×C47#55311yescharacteristic
382C22×C47#55411yescharacteristic
383C22×C47#55411yescharacteristic
384C2×D47—24no—
385C2×D47—24no—
386C2×D47—24no—
387C2×D47—24no—
388C2×D47—24no—
389C2×D47—24no—
390C2×D47—24no—
391C2×D47—24no—
392C2×D47—24no—
393C2×D47—24no—
394C2×D47—24no—
395C2×D47—24no—
396C2×D47—24no—
397C2×D47—24no—
398C2×D47#38918yescomplemented
399C4×C47—28no—
400C4×C47—42no—
401C4×C47—42no—
402C4×C47—82no—
403C4×C47#38018yescomplemented
404Dic47—24no—
405Dic47—44no—
406Dic47—42no—
407Dic47—42no—
408Dic47—82no—
409C23×C4⋊C4—471no—
410C2×#389—471no—
411C2×#389D4711yescharacteristic, complemented
412C2×#380—472no—
413C2×#380—471no—
414C2×C4×C22⋊C4—471no—
415#1441—472no—
416#1441—472no—
417C4⋊#95—471no—
418C4⋊#95—471no—
419C22⋊#95—472no—
420C2×C47C2×#38011yescharacteristic
421C2×C47C2×#38911yescharacteristic
422C2×C47#231611yescharacteristic
423C2×C47D4×C22⋊C411yescharacteristic
424C2×C47Q8×C22⋊C411yescharacteristic
425C2×C47#234411yescharacteristic
426C2×C47#234511yescharacteristic
427C2×C47#241611yescharacteristic
428C2×C47#241611yescharacteristic
429C2×C47#241711yescharacteristic
430C2×C47#241711yescharacteristic
431C2×C47#244011yescharacteristic
432C2×C47#244011yescharacteristic
433C2×C47#244211yescharacteristic
434C2×C47#244211yescharacteristic
435D47—28no—
436C24×C4—471no—
437C24×C4—472no—
438C22×C4⋊C4—472no—
439C22×C4⋊C4—471no—
440C22×C4⋊C4—478no—
441C22×C4⋊C4—471no—
442C22×C4⋊C4—472no—
443C22×C4⋊C4—944no—
444C22×C4⋊C4—944no—
445C22×C4⋊C4C2×D4711yescharacteristic
446C22×C4⋊C4C2×D4712yes—
447C22×C4⋊C4C2×D4711yescharacteristic
448C22×C22⋊C4—471no—
449C22×C22⋊C4—471no—
450C22×C22⋊C4—472no—
451C22×C42—471no—
452C22×C42C2×D4711yescharacteristic
453#389—24no—
454#389—944no—
455#380—948no—
456#380—944no—
457C4×C22⋊C4—944no—
458C2×#95—472no—
459C2×#95—472no—
460C2×#95—472no—
461C2×#95—471no—
462C2×#95—471no—
463C2×#95—472no—
464C2×#95—472no—
465C2×#95—472no—
466C2×#95C2×D4712yes—
467C47#1390711yescharacteristic, complemented, Sylow
468C25—471no—
469C23×C4—471no—
470C23×C4—474no—
471C23×C4—474no—
472C23×C4—474no—
473C23×C4—471no—
474C23×C4—471no—
475C23×C4—472no—
476C23×C4—478no—
477C23×C4—472no—
478C23×C4—944no—
479C23×C4—944no—
480C23×C4—942no—
481C23×C4—942no—
482C23×C4—942no—
483C23×C4—942no—
484C23×C4—944no—
485C23×C4—944no—
486C23×C4—1882no—
487C23×C4—1882no—
488C23×C4C22×D4712yes—
489C23×C4C22×D4711yescharacteristic
490C23×C4C22×D4711yescharacteristic
491C23×C4C22×D4712yes—
492C23×C4C22×D4711yescharacteristic
493C2×C4⋊C4—24no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—42no—
499C2×C4⋊C4—478no—
500C2×C4⋊C4—474no—
501C2×C4⋊C4—944no—
502C2×C4⋊C4—942no—
503C2×C4⋊C4—944no—
504C2×C4⋊C4—942no—
505C2×C4⋊C4—9432no—
506C2×C4⋊C4—944no—
507C2×C4⋊C4—944no—
508C2×C4⋊C4—942no—
509C2×C4⋊C4—942no—
510C2×C4⋊C4—942no—
511C2×C4⋊C4—1882no—
512C2×C4⋊C4C4×D4714yes—
513C2×C4⋊C4D18814yes—
514C2×C4⋊C4C22⋊D4714yes—
515C2×C22⋊C4—474no—
516C2×C22⋊C4—474no—
517C2×C22⋊C4—942no—
518C2×C22⋊C4—942no—
519C2×C22⋊C4—942no—
520C2×C22⋊C4—942no—
521C2×C22⋊C4—944no—
522C2×C22⋊C4—944no—
523C2×C22⋊C4—944no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—942no—
528C2×C42—942no—
529C2×C42—942no—
530#95—24no—
531#95—942no—
532#95—942no—
533#95—944no—
534#95—944no—
535#95—944no—
536#95—944no—
537#95—1882no—
538#95—1882no—
539C24—472no—
540C24—472no—
541C24—472no—
542C24—472no—
543C24—472no—
544C24—472no—
545C24—472no—
546C24—941no—
547C24—941no—
548C24—941no—
549C24—941no—
550C24—941no—
551C24—941no—
552C24—941no—
553C24—941no—
554C24C23×D4711yescharacteristic
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—472no—
579C22×C4—472no—
580C22×C4—472no—
581C22×C4—4716no—
582C22×C4—474no—
583C22×C4—472no—
584C22×C4—472no—
585C22×C4—9416no—
586C22×C4—941no—
587C22×C4—941no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—948no—
591C22×C4—948no—
592C22×C4—948no—
593C22×C4—948no—
594C22×C4—948no—
595C22×C4—948no—
596C22×C4—942no—
597C22×C4—941no—
598C22×C4—941no—
599C22×C4—942no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—942no—
603C22×C4—941no—
604C22×C4—941no—
605C22×C4—942no—
606C22×C4—941no—
607C22×C4—941no—
608C22×C4—941no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—941no—
612C22×C4—941no—
613C22×C4—941no—
614C22×C4—9416no—
615C22×C4—942no—
616C22×C4—942no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—942no—
620C22×C4—942no—
621C22×C4—942no—
622C22×C4—1888no—
623C22×C4—1888no—
624C22×C4—1888no—
625C22×C4—1888no—
626C22×C4—1888no—
627C22×C4C2×C4×D4714yes—
628C22×C4C2×C4×D4712yes—
629C22×C4C2×D18814yes—
630C22×C4C2×D18812yes—
631C22×C4D4×D4712yes—
632C22×C4D4×D4712yes—
633C22×C4#1062535212yes—
634C22×C4Q8×D4712yes—
635C22×C4Q8×D4712yes—
636C22×C4#1062535412yes—
637C22×C4C2×C22⋊D4714yes—
638C22×C4C2×C22⋊D4712yes—
639C4⋊C4—48no—
640C4⋊C4—44no—
641C4⋊C4—9416no—
642C4⋊C4—948no—
643C4⋊C4—1888no—
644C4⋊C4—1884no—
645C4⋊C4(C2×D47)⋊C4116yescomplemented
646C22⋊C4—948no—
647C22⋊C4—948no—
648C22⋊C4—1888no—
649C42—44no—
650C42—1884no—
651C23—474no—
652C23—474no—
653C23—474no—
654C23—474no—
655C23—474no—
656C23—474no—
657C23—474no—
658C23—942no—
659C23—942no—
660C23—942no—
661C23—942no—
662C23—942no—
663C23—942no—
664C23—942no—
665C23—942no—
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—942no—
679C23—942no—
680C23—942no—
681C23—942no—
682C23—942no—
683C23—942no—
684C23—942no—
685C23—942no—
686C23C22×C4×D4711yescharacteristic
687C23C2×D4×D4711yescharacteristic
688C23C2×D4×D4711yescharacteristic
689C23C22×C22⋊D4711yescharacteristic
690C23C22×D18811yescharacteristic
691C23C2×Q8×D4711yescharacteristic
692C23C2×Q8×D4711yescharacteristic
693C23#41×D4711yescharacteristic
694C23#41×D4711yescharacteristic
695C23C2×#1062535211yescharacteristic
696C23C2×#1062535411yescharacteristic
697C23#1309406911yescharacteristic
698C23#1309407011yescharacteristic
699C23#1309407111yescharacteristic
700C23#1309407211yescharacteristic
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—474no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—9432no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—942no—
739C2×C4—944no—
740C2×C4—942no—
741C2×C4—944no—
742C2×C4—944no—
743C2×C4—942no—
744C2×C4—942no—
745C2×C4—18832no—
746C2×C4—1882no—
747C2×C4—1882no—
748C2×C4—1882no—
749C2×C4—1882no—
750C2×C4—1882no—
751C2×C4—1882no—
752C2×C4—1882no—
753C2×C4—1882no—
754C2×C4—1882no—
755C2×C4—1882no—
756C2×C4—1881no—
757C2×C4—1882no—
758C2×C4—1881no—
759C2×C4—1881no—
760C2×C4—1881no—
761C2×C4—1881no—
762C2×C4—1881no—
763C2×C4—1881no—
764C2×C4—1881no—
765C2×C4C2×(C2×D47)⋊C418yes—
766C2×C4C2×(C2×D47)⋊C414yes—
767C2×C4C4⋊C4×D4714yes—
768C2×C4#1309398214yes—
769C2×C4#1309399514yes—
770C2×C4#1309399914yes—
771C2×C4#1309400014yes—
772C2×C4#1309400414yes—
773C22—478no—
774C22—944no—
775C22—944no—
776C22—944no—
777C22—944no—
778C22—944no—
779C22—944no—
780C22—944no—
781C22—944no—
782C22—944no—
783C22—944no—
784C22—944no—
785C22—944no—
786C22—944no—
787C22—944no—
788C22C22×(C2×D47)⋊C411yescharacteristic
789C22C2×C4⋊C4×D4711yescharacteristic
790C22C2×#1309398211yescharacteristic
791C22C4×D4×D4711yescharacteristic
792C22C4×Q8×D4711yescharacteristic
793C22#1568959511yescharacteristic
794C22#1568959911yescharacteristic
795C22#121×D4711yescharacteristic
796C22C2×#1309399511yescharacteristic
797C22C2×#1309399911yescharacteristic
798C22C22⋊Q8×D4711yescharacteristic
799C22C2×#1309400011yescharacteristic
800C22C2×#1309400411yescharacteristic
801C22#125×D4711yescharacteristic
802C22C4⋊Q8×D4711yescharacteristic
803C22#1568970211yescharacteristic
804C22#1568970311yescharacteristic
805C22#1568975011yescharacteristic
806C22#1568975311yescharacteristic
807C22D4×C22⋊D4711yescharacteristic
808C22D4×D18811yescharacteristic
809C22#1568976111yescharacteristic
810C22#1568976811yescharacteristic
811C22#1568977311yescharacteristic
812C22#1568977611yescharacteristic
813C22#1568978011yescharacteristic
814C22#1568978511yescharacteristic
815C22Q8×C22⋊D4711yescharacteristic
816C22Q8×D18811yescharacteristic
817C22#1568980711yescharacteristic
818C22#1568981111yescharacteristic
819C22#1568982011yescharacteristic
820C22#1568982611yescharacteristic
821C22#1568983111yescharacteristic
822C22#1568983411yescharacteristic
823C4—28no—
824C4—42no—
825C4—42no—
826C4—82no—
827C4—944no—
828C4—3762no—
829C4—1882no—
830C4—1882no—
831C4—1884no—
832C4#1568898018yescomplemented
833C2—948no—
834C2C2×#1568898011yescharacteristic
835C2#389×D4711yescharacteristic
836C2#2024600311yescharacteristic
837C2D4×(C2×D47)⋊C411yescharacteristic
838C2Q8×(C2×D47)⋊C411yescharacteristic
839C2#2024625611yescharacteristic
840C2#2024626411yescharacteristic
841C2#2024682411yescharacteristic
842C2#2024682611yescharacteristic
843C2#2024683511yescharacteristic
844C2#2024683711yescharacteristic
845C2#2024708611yescharacteristic
846C2#2024708811yescharacteristic
847C2#2024710811yescharacteristic
848C2#2024711011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#389C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenterC2×#389D47
hypocenterC47#13907
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#15689022C2semidirect
6. #20241642C2semidirect
7. #20241638C2semidirect
8. #20241618C2semidirect
9. #20241617C2semidirect
11. C2×C47×#389C2semidirect
20. C2×C4⋊C4×D47C4semidirect
213. C2×C4×D47C4⋊C4semidirect
216. C4⋊C4×C47C22⋊C4semidirect
398. C2×D47#389semidirect
403. C4×C47#380semidirect
411. C2×#389D47semidirect
467. C47#13907semidirect
645. C4⋊C4(C2×D47)⋊C4semidirect
832. C4#15688980semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D472
C2×#156890222
C2×#156889802
C2×C4×(C2×D47)⋊C42
#202416422
#202416382
#202416182
#202416172
(C2×D47)⋊#952
C2×C47×#3892
#1390747