Finite Group Databasebeta

← #26144295

Subgroups — #26144295

Order 12032.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689022C211yesmaximal, characteristic, complemented
2C2×#15689016C211yesmaximal, characteristic
3C2×#15689016C211yesmaximal, characteristic
4C2×#15688983C211yesmaximal, characteristic
5#20241653C211yesmaximal, characteristic, complemented
6#20241645C211yesmaximal, characteristic, complemented
7#20241641C211yesmaximal, characteristic, complemented
8#20241641C211yesmaximal, characteristic, complemented
9#20241633C211yesmaximal, characteristic
10#20241633C211yesmaximal, characteristic
11#20241622C211yesmaximal, characteristic, complemented
12#20241622C211yesmaximal, characteristic, complemented
13#20241617C211yesmaximal, characteristic, complemented
14#20241611C211yesmaximal, characteristic
15C2×C47×#385C211yesmaximal, characteristic
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic
21C22×C4⋊Dic47C2211yescharacteristic
22C22×C22⋊Dic47C2211yescharacteristic
23C22×C22⋊Dic47C2211yescharacteristic
24C22×C22⋊Dic47C2211yescharacteristic
25C22×C22⋊Dic47C2211yescharacteristic
26C22×C4×Dic47C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28#15689022—24no—
29#15689016—24no—
30#15689016—24no—
31#15688983—24no—
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2211yescharacteristic
35C2×C47⋊#95C2211yescharacteristic
36C2×C47⋊#95C2211yescharacteristic
37C2×C47⋊#95C2211yescharacteristic
38C2×C47⋊#95C2211yescharacteristic
39C2×C47⋊#95C2211yescharacteristic
40C2×C47⋊#95C2211yescharacteristic
41C2×C47⋊#95C2211yescharacteristic
42C2×C47⋊#95C2211yescharacteristic
43C2×C47⋊#95C2211yescharacteristic
44C2×C47⋊#95C2211yescharacteristic
45C2×C47⋊#95C2211yescharacteristic
46C2×C47⋊#95C2211yescharacteristic
47C2×C47⋊#95C2211yescharacteristic
48C24×C4×C47C2211yescharacteristic
49C22×C4⋊C4×C47C2211yescharacteristic
50C22×C4⋊C4×C47C2211yescharacteristic
51C22×C22⋊C4×C47C2211yescharacteristic
52C22×C22⋊C4×C47C2211yescharacteristic
53C47×#385C418yescomplemented
54C2×#95×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C23×Dic47C2311yescharacteristic
57C23×Dic47C2311yescharacteristic
58C23×Dic47C2311yescharacteristic
59C23×Dic47C2311yescharacteristic
60C23×Dic47C2311yescharacteristic
61C23×Dic47C2311yescharacteristic
62C23×Dic47C2311yescharacteristic
63C23×Dic47C2311yescharacteristic
64C2×C4⋊Dic47—22no—
65C2×C4⋊Dic47—22no—
66C2×C4⋊Dic47—22no—
67C2×C4⋊Dic47—22no—
68C2×C4⋊Dic47—22no—
69C2×C4⋊Dic47—22no—
70C2×C4⋊Dic47—22no—
71C2×C4⋊Dic47—41no—
72C2×C4⋊Dic47—41no—
73C2×C4⋊Dic47—41no—
74C2×C4⋊Dic47—41no—
75C2×C4⋊Dic47—41no—
76C2×C4⋊Dic47—41no—
77C2×C4⋊Dic47—41no—
78C2×C4⋊Dic47—41no—
79C2×C4⋊Dic47—41no—
80C2×C4⋊Dic47—41no—
81C2×C4⋊Dic47D414yes—
82C2×C22⋊Dic47—22no—
83C2×C22⋊Dic47—22no—
84C2×C22⋊Dic47—22no—
85C2×C22⋊Dic47—22no—
86C2×C22⋊Dic47—22no—
87C2×C22⋊Dic47—22no—
88C2×C22⋊Dic47—22no—
89C2×C22⋊Dic47—22no—
90C2×C22⋊Dic47—41no—
91C2×C22⋊Dic47—41no—
92C2×C22⋊Dic47—41no—
93C2×C22⋊Dic47—41no—
94C2×C4×Dic47—22no—
95C2×C4×Dic47—22no—
96C2×C4×Dic47—22no—
97C2×C4×Dic47—22no—
98C2×C4×Dic47—41no—
99C2×C4×Dic47—41no—
100C47⋊#95—22no—
101C47⋊#95—22no—
102C47⋊#95—22no—
103C47⋊#95—22no—
104C47⋊#95—22no—
105C47⋊#95—22no—
106C47⋊#95—22no—
107C47⋊#95—22no—
108C47⋊#95—22no—
109C47⋊#95—22no—
110C47⋊#95—41no—
111C47⋊#95—41no—
112C47⋊#95—41no—
113C47⋊#95—41no—
114C47⋊#95—41no—
115C47⋊#95—41no—
116C25×C47C2311yescharacteristic
117C23×C4×C47—22no—
118C23×C4×C47—22no—
119C23×C4×C47—41no—
120C23×C4×C47—41no—
121C23×C4×C47—41no—
122C23×C4×C47—41no—
123C23×C4×C47C2×C414yes—
124C23×C4×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C2×C4⋊C4×C47—22no—
131C2×C4⋊C4×C47—22no—
132C2×C4⋊C4×C47—41no—
133C2×C4⋊C4×C47—41no—
134C2×C4⋊C4×C47C2×C414yes—
135C2×C4⋊C4×C47C2×C414yes—
136C2×C22⋊C4×C47—41no—
137C2×C22⋊C4×C47—41no—
138C2×C22⋊C4×C47C2×C414yes—
139C2×C22⋊C4×C47C2×C414yes—
140C2×C22⋊C4×C47D414yes—
141C2×C22⋊C4×C47Q814yes—
142#95×C47C2×C414yes—
143#95×C47C2×C414yes—
144C24×C47—21no—
145C24×C47—21no—
146C24×C47—21no—
147C24×C47—21no—
148C24×C47—21no—
149C24×C47—21no—
150C24×C47—21no—
151C24×C47—21no—
152C24×C47—21no—
153C24×C47—21no—
154C24×C47—21no—
155C24×C47—21no—
156C24×C47C22×C412yes—
157C24×C47C2×D412yes—
158C24×C47C2×Q812yes—
159C24×C47C2411yescharacteristic
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—28no—
191C22×C4×C47—44no—
192C22×C4×C47—44no—
193C22×C4×C47—44no—
194C22×C4×C47—44no—
195C22×C4×C47—44no—
196C22×C4×C47—44no—
197C22×C4×C47C22×C412yes—
198C22×C4×C47C22×C412yes—
199C22×C4×C47C22×C412yes—
200C22×C4×C47C22×C412yes—
201C22×C4×C47C22×C412yes—
202C22×C4×C47C22×C412yes—
203C22×C4×C47C2×D412yes—
204C22×C4×C47C2×D412yes—
205C22×C4×C47C2×D412yes—
206C22×C4×C47C2×Q812yes—
207C22×C4×C47C2×Q812yes—
208C22×C4×C47#4112yes—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—21no—
219C22×Dic47—21no—
220C22×Dic47—21no—
221C22×Dic47—21no—
222C22×Dic47—21no—
223C22×Dic47—21no—
224C22×Dic47—21no—
225C22×Dic47—21no—
226C22×Dic47—21no—
227C22×Dic47—21no—
228C22×Dic47—21no—
229C22×Dic47—21no—
230C22×Dic47—21no—
231C22×Dic47—21no—
232C22×Dic47—21no—
233C22×Dic47—21no—
234C22×Dic47—21no—
235C22×Dic47—21no—
236C22×Dic47—21no—
237C22×Dic47—21no—
238C22×Dic47—21no—
239C22×Dic47—21no—
240C22×Dic47—21no—
241C22×Dic47—21no—
242C22×Dic47—21no—
243C22×Dic47—21no—
244C22×Dic47—21no—
245C22×Dic47—21no—
246C22×Dic47—21no—
247C22×Dic47—21no—
248C22×Dic47—21no—
249C22×Dic47—21no—
250C22×Dic47—21no—
251C22×Dic47—21no—
252C22×Dic47—21no—
253C22×Dic47—21no—
254C22×Dic47—21no—
255C22×Dic47—21no—
256C22×Dic47—21no—
257C22×Dic47—21no—
258C22×Dic47—21no—
259C22×Dic47—21no—
260C22×Dic47—21no—
261C22×Dic47C2×D412yes—
262C22×Dic47C2×D412yes—
263C22×Dic47#4112yes—
264C22×Dic47#4112yes—
265C4⋊C4×C47—28no—
266C4⋊C4×C47—44no—
267C22⋊C4×C47—44no—
268C22⋊C4×C47C4⋊C4116yescomplemented
269C22⋊Dic47—44no—
270C22⋊Dic47—44no—
271C22⋊Dic47—44no—
272C22⋊Dic47—44no—
273C4⋊Dic47—44no—
274C4⋊Dic47—44no—
275C4⋊Dic47—44no—
276C4⋊Dic47—44no—
277C4⋊Dic47—44no—
278C4⋊Dic47—44no—
279C4×Dic47—44no—
280C4×Dic47—44no—
281C23×C47—22no—
282C23×C47—22no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—22no—
287C23×C47—22no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47—41no—
308C23×C47—41no—
309C23×C47—41no—
310C23×C47—41no—
311C23×C47—41no—
312C23×C47—41no—
313C23×C47—41no—
314C23×C47—41no—
315C23×C47C2×C4⋊C414yes—
316C23×C47C23×C411yescharacteristic
317C23×C47C22×D411yescharacteristic
318C23×C47C22×D411yescharacteristic
319C23×C47C22×Q811yescharacteristic
320C23×C47C2×#4111yescharacteristic
321C23×C47C2×#4111yescharacteristic
322C23×C47C2×#4111yescharacteristic
323C23×C47H(5,𝔽2)11yescharacteristic
324C23×C47H(5,𝔽2)11yescharacteristic
325C23×C47H(5,𝔽2)11yescharacteristic
326C23×C47H(5,𝔽2)11yescharacteristic
327C23×C47H(5,𝔽2)11yescharacteristic
328C23×C472−1+411yescharacteristic
329C23×C472−1+411yescharacteristic
330C23×C472−1+411yescharacteristic
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—416no—
359C2×C4×C47—41no—
360C2×C4×C47—41no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47C2×C4⋊C414yes—
372C2×C4×C47C2×C4⋊C414yes—
373C2×C4×C47C4×D414yes—
374C2×Dic47—22no—
375C2×Dic47—22no—
376C2×Dic47—22no—
377C2×Dic47—22no—
378C2×Dic47—22no—
379C2×Dic47—22no—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—22no—
383C2×Dic47—22no—
384C2×Dic47—22no—
385C2×Dic47—22no—
386C2×Dic47—41no—
387C2×Dic47—41no—
388C2×Dic47—41no—
389C2×Dic47—41no—
390C2×Dic47—41no—
391C2×Dic47—41no—
392C2×Dic47—41no—
393C2×Dic47—41no—
394C2×Dic47—41no—
395C2×Dic47—41no—
396C2×Dic47—41no—
397C2×Dic47—41no—
398C2×Dic47—41no—
399C2×Dic47—41no—
400C2×Dic47—41no—
401C2×Dic47—41no—
402C2×Dic47—41no—
403C2×Dic47—41no—
404C2×Dic47—41no—
405C2×Dic47—41no—
406C2×Dic47—41no—
407C2×Dic47—41no—
408C2×Dic47—41no—
409C2×Dic47—41no—
410C2×Dic47—41no—
411C2×Dic47—41no—
412C2×Dic47—41no—
413C2×Dic47—41no—
414C2×Dic47—41no—
415C2×Dic47—41no—
416C2×Dic47—41no—
417C2×Dic47—41no—
418C2×Dic47—41no—
419C2×Dic47—41no—
420C2×Dic47—41no—
421C2×Dic47—41no—
422C2×Dic47—41no—
423C2×Dic47—41no—
424C2×Dic47—41no—
425C2×Dic47—41no—
426C2×Dic47—41no—
427C2×Dic47—41no—
428C2×Dic47—41no—
429C2×Dic47—41no—
430#14408—471nomaximal, Sylow
431C22×C47—24no—
432C22×C47—24no—
433C22×C47—24no—
434C22×C47—42no—
435C22×C47—42no—
436C22×C47—42no—
437C22×C47—42no—
438C22×C47—42no—
439C22×C47—42no—
440C22×C47—42no—
441C22×C47—42no—
442C22×C47—42no—
443C22×C47—42no—
444C22×C47—42no—
445C22×C47—42no—
446C22×C47C22×C4⋊C411yescharacteristic
447C22×C47C2×C4×D411yescharacteristic
448C22×C47C4×#4111yescharacteristic
449C22×C47#51811yescharacteristic
450C22×C47#51811yescharacteristic
451C22×C47#51911yescharacteristic
452C22×C47#52011yescharacteristic
453C22×C47#53411yescharacteristic
454C22×C47#53511yescharacteristic
455C22×C47#53711yescharacteristic
456C22×C47#53711yescharacteristic
457C22×C47#53811yescharacteristic
458C22×C47#53811yescharacteristic
459C22×C47#53811yescharacteristic
460C22×C47#53911yescharacteristic
461C22×C47#54011yescharacteristic
462C22×C47#54211yescharacteristic
463C22×C47#54411yescharacteristic
464C22×C47#54411yescharacteristic
465C22×C47D4211yescharacteristic
466C22×C47#54611yescharacteristic
467C22×C47#54611yescharacteristic
468C22×C47#54711yescharacteristic
469C22×C47#54711yescharacteristic
470C22×C47#54811yescharacteristic
471C22×C47D4×Q811yescharacteristic
472C22×C47#55211yescharacteristic
473C22×C47#55411yescharacteristic
474C22×C47#55411yescharacteristic
475C22×C47#55411yescharacteristic
476C22×C47#55611yescharacteristic
477C22×C47#56211yescharacteristic
478C22×C47#56211yescharacteristic
479C22×C47#56311yescharacteristic
480C22×C47#56311yescharacteristic
481C4×C47—24no—
482C4×C47—24no—
483C4×C47—24no—
484C4×C47—42no—
485C4×C47—42no—
486C4×C47—42no—
487Dic47—42no—
488Dic47—42no—
489Dic47—42no—
490Dic47—42no—
491Dic47—81no—
492Dic47—81no—
493Dic47—81no—
494Dic47—81no—
495C2×#389—471no—
496C2×#388—471no—
497C2×#388—471no—
498C2×#385D4711yescharacteristic
499C2×#380—471no—
500#1444—471no—
501#1442—471no—
502#1441—471no—
503#1441—471no—
504#1439—471no—
505#1439—471no—
506#1436—471no—
507#1436—471no—
508C4⋊#95—471no—
509C22⋊#95—471no—
510C2×C47—44no—
511C2×C47#231611yescharacteristic
512C2×C47#232111yescharacteristic
513C2×C47#233511yescharacteristic
514C2×C47D4×C4⋊C411yescharacteristic
515C2×C47#234911yescharacteristic
516C2×C47#236211yescharacteristic
517C2×C47#237811yescharacteristic
518C2×C47#267111yescharacteristic
519C2×C47#267611yescharacteristic
520C2×C47#269511yescharacteristic
521C2×C47#271511yescharacteristic
522C2×C47#272011yescharacteristic
523C2×C47#272911yescharacteristic
524C2×C47#276811yescharacteristic
525C2×C47#278811yescharacteristic
526C24×C4C2×D4711yescharacteristic
527C22×C4⋊C4—471no—
528C22×C4⋊C4—471no—
529C22×C4⋊C4—471no—
530C22×C4⋊C4—471no—
531C22×C4⋊C4—471no—
532C22×C4⋊C4—471no—
533C22×C4⋊C4C2×D4711yescharacteristic
534C22×C4⋊C4C2×D4711yescharacteristic
535C22×C22⋊C4—471no—
536C22×C22⋊C4—471no—
537C22×C22⋊C4—471no—
538C22×C22⋊C4—471no—
539C22×C22⋊C4C2×D4711yescharacteristic
540C22×C22⋊C4C2×D4711yescharacteristic
541C22×C42—471no—
542C22×C42—471no—
543#389—944no—
544#388—944no—
545#388—944no—
546#385Dic4718yescomplemented
547#380—944no—
548C2×#95—471no—
549C2×#95—471no—
550C2×#95—471no—
551C2×#95—471no—
552C2×#95—471no—
553C2×#95—471no—
554C2×#95—471no—
555C2×#95—471no—
556C2×#95—471no—
557C2×#95—471no—
558C2×#95—471no—
559C2×#95—471no—
560C2×#95—471no—
561C2×#95—471no—
562C2×#95—471no—
563C2×#95—471no—
564C2×#95C2×D4711yescharacteristic
565C2×#95C2×D4711yescharacteristic
566C47#1440811yescharacteristic, complemented, Sylow
567C25C22×D4711yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—41no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4—471no—
575C23×C4—471no—
576C23×C4—471no—
577C23×C4—471no—
578C23×C4—471no—
579C23×C4—471no—
580C23×C4—471no—
581C23×C4—471no—
582C23×C4C2×Dic4714yes—
583C23×C4C22×D4711yescharacteristic
584C23×C4C22×D4711yescharacteristic
585C23×C4C22×D4711yescharacteristic
586C23×C4C22×D4711yescharacteristic
587C23×C4C22×D4711yescharacteristic
588C23×C4C22×D4711yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—474no—
594C2×C4⋊C4—942no—
595C2×C4⋊C4—942no—
596C2×C4⋊C4—942no—
597C2×C4⋊C4—942no—
598C2×C4⋊C4—942no—
599C2×C4⋊C4—942no—
600C2×C4⋊C4—942no—
601C2×C4⋊C4—1881no—
602C2×C4⋊C4—1881no—
603C2×C4⋊C4—1881no—
604C2×C4⋊C4—1881no—
605C2×C4⋊C4—1881no—
606C2×C4⋊C4—1881no—
607C2×C4⋊C4—1881no—
608C2×C4⋊C4—1881no—
609C2×C4⋊C4—1881no—
610C2×C4⋊C4—1881no—
611C2×C4⋊C4C2×Dic4714yes—
612C2×C4⋊C4C2×Dic4714yes—
613C2×C22⋊C4—41no—
614C2×C22⋊C4—41no—
615C2×C22⋊C4—942no—
616C2×C22⋊C4—942no—
617C2×C22⋊C4—942no—
618C2×C22⋊C4—942no—
619C2×C22⋊C4—942no—
620C2×C22⋊C4—942no—
621C2×C22⋊C4—942no—
622C2×C22⋊C4—942no—
623C2×C22⋊C4—1881no—
624C2×C22⋊C4—1881no—
625C2×C22⋊C4—1881no—
626C2×C22⋊C4—1881no—
627C2×C22⋊C4Dic9414yes—
628C2×C22⋊C4D18814yes—
629C2×C22⋊C4C2×Dic4714yes—
630C2×C22⋊C4C2×Dic4714yes—
631C2×C42—942no—
632C2×C42—942no—
633C2×C42—942no—
634C2×C42—942no—
635C2×C42—1881no—
636C2×C42—1881no—
637#95—942no—
638#95—942no—
639#95—942no—
640#95—942no—
641#95—942no—
642#95—942no—
643#95—942no—
644#95—942no—
645#95—942no—
646#95—942no—
647#95—1881no—
648#95—1881no—
649#95—1881no—
650#95—1881no—
651#95—1881no—
652#95—1881no—
653#95C2×Dic4714yes—
654#95C2×Dic4714yes—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C2×Dic9412yes—
668C24C2×D18812yes—
669C24C22×Dic4712yes—
670C24C23×D4711yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—28no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—472no—
709C22×C4—472no—
710C22×C4—472no—
711C22×C4—472no—
712C22×C4—941no—
713C22×C4—941no—
714C22×C4—941no—
715C22×C4—941no—
716C22×C4—941no—
717C22×C4—941no—
718C22×C4—941no—
719C22×C4—941no—
720C22×C4—941no—
721C22×C4—941no—
722C22×C4—941no—
723C22×C4—941no—
724C22×C4—941no—
725C22×C4—941no—
726C22×C4—941no—
727C22×C4—941no—
728C22×C4—941no—
729C22×C4—941no—
730C22×C4—941no—
731C22×C4—941no—
732C22×C4—941no—
733C22×C4—941no—
734C22×C4—941no—
735C22×C4—941no—
736C22×C4—941no—
737C22×C4—941no—
738C22×C4—941no—
739C22×C4—941no—
740C22×C4—941no—
741C22×C4—941no—
742C22×C4—941no—
743C22×C4—941no—
744C22×C4—941no—
745C22×C4—941no—
746C22×C4—941no—
747C22×C4—941no—
748C22×C4—941no—
749C22×C4—941no—
750C22×C4—941no—
751C22×C4—941no—
752C22×C4—941no—
753C22×C4—941no—
754C22×C4—941no—
755C22×C4—941no—
756C22×C4—941no—
757C22×C4—941no—
758C22×C4—941no—
759C22×C4—941no—
760C22×C4—941no—
761C22×C4—941no—
762C22×C4—941no—
763C22×C4—941no—
764C22×C4C2×Dic9412yes—
765C22×C4C2×Dic9412yes—
766C22×C4C2×D18812yes—
767C22×C4C2×D18812yes—
768C22×C4D4×D4712yes—
769C22×C4#1062535212yes—
770C22×C4C22×Dic4712yes—
771C22×C4C22×Dic4712yes—
772C22×C4C22×Dic4712yes—
773C22×C4C22×Dic4712yes—
774C22×C4C22×Dic4712yes—
775C22×C4C22×Dic4712yes—
776C4⋊C4—28no—
777C4⋊C4—44no—
778C4⋊C4—1884no—
779C4⋊C4—1884no—
780C4⋊C4—1884no—
781C4⋊C4—1884no—
782C4⋊C4—1884no—
783C4⋊C4—1884no—
784C22⋊C4—44no—
785C22⋊C4—1884no—
786C22⋊C4—1884no—
787C22⋊C4—1884no—
788C22⋊C4—1884no—
789C22⋊C4C4⋊Dic47116yescomplemented
790C42—1884no—
791C42—1884no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊Dic4714yes—
827C23C23×Dic4711yescharacteristic
828C23C2×D4×D4711yescharacteristic
829C23C22×D18811yescharacteristic
830C23C22×Dic9411yescharacteristic
831C23#41×D4711yescharacteristic
832C23#41×D4711yescharacteristic
833C23C2×#1062535211yescharacteristic
834C23#1309406911yescharacteristic
835C23#1309406911yescharacteristic
836C23#1309406911yescharacteristic
837C23#1309406911yescharacteristic
838C23#1309407011yescharacteristic
839C23#1309407111yescharacteristic
840C23#1309407211yescharacteristic
841C23#1309407211yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—416no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—942no—
883C2×C4—942no—
884C2×C4—942no—
885C2×C4—942no—
886C2×C4—942no—
887C2×C4—942no—
888C2×C4—942no—
889C2×C4—942no—
890C2×C4—942no—
891C2×C4—942no—
892C2×C4—942no—
893C2×C4—942no—
894C2×C4—1881no—
895C2×C4—1881no—
896C2×C4—1881no—
897C2×C4—1881no—
898C2×C4—1881no—
899C2×C4—1881no—
900C2×C4—1881no—
901C2×C4—1881no—
902C2×C4—1881no—
903C2×C4—1881no—
904C2×C4—1881no—
905C2×C4—1881no—
906C2×C4—1881no—
907C2×C4—1881no—
908C2×C4—1881no—
909C2×C4—1881no—
910C2×C4—1881no—
911C2×C4—1881no—
912C2×C4—1881no—
913C2×C4—1881no—
914C2×C4—1881no—
915C2×C4—1881no—
916C2×C4—1881no—
917C2×C4—1881no—
918C2×C4—1881no—
919C2×C4—1881no—
920C2×C4—1881no—
921C2×C4—1881no—
922C2×C4—1881no—
923C2×C4—1881no—
924C2×C4—1881no—
925C2×C4—1881no—
926C2×C4—1881no—
927C2×C4—1881no—
928C2×C4—1881no—
929C2×C4—1881no—
930C2×C4—1881no—
931C2×C4—1881no—
932C2×C4—1881no—
933C2×C4—1881no—
934C2×C4—1881no—
935C2×C4—1881no—
936C2×C4—1881no—
937C2×C4—1881no—
938C2×C4C2×C4⋊Dic4714yes—
939C2×C4C2×C4⋊Dic4714yes—
940C2×C4D4×Dic4714yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊Dic4711yescharacteristic
957C22C2×D4×Dic4711yescharacteristic
958C22#41×Dic4711yescharacteristic
959C22#1568959811yescharacteristic
960C22#1568959811yescharacteristic
961C22#1568960111yescharacteristic
962C22#1568960611yescharacteristic
963C22#1568968311yescharacteristic
964C22#1568968811yescharacteristic
965C22#1568970411yescharacteristic
966C22#1568970411yescharacteristic
967C22#1568970811yescharacteristic
968C22#1568970811yescharacteristic
969C22#1568970911yescharacteristic
970C22#1568971611yescharacteristic
971C22#1568972511yescharacteristic
972C22#1568974111yescharacteristic
973C22#1568975411yescharacteristic
974C22#1568975411yescharacteristic
975C22D4×D18811yescharacteristic
976C22#1568976811yescharacteristic
977C22#1568976811yescharacteristic
978C22#1568977511yescharacteristic
979C22#1568977711yescharacteristic
980C22#1568978311yescharacteristic
981C22D4×Dic9411yescharacteristic
982C22#1568980711yescharacteristic
983C22#1568983011yescharacteristic
984C22#1568983211yescharacteristic
985C22#1568983211yescharacteristic
986C22#1568984411yescharacteristic
987C22#1568986911yescharacteristic
988C22#1568986911yescharacteristic
989C22#1568987411yescharacteristic
990C22#1568987411yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—3761no—
998C4—3761no—
999C4—3761no—
1000C4—3761no—
1001C4—1882no—
1002C4—1882no—
1003C4—1882no—
1004C4—1882no—
1005C2—44no—
1006C2#2024600611yescharacteristic
1007C2#2024604911yescharacteristic
1008C2#2024618211yescharacteristic
1009C2D4×C4⋊Dic4711yescharacteristic
1010C2#2024629811yescharacteristic
1011C2#2024641911yescharacteristic
1012C2#2024655411yescharacteristic
1013C2#2024962711yescharacteristic
1014C2#2024969211yescharacteristic
1015C2#2024992111yescharacteristic
1016C2#2025019711yescharacteristic
1017C2#2025026911yescharacteristic
1018C2#2025037411yescharacteristic
1019C2#2025086511yescharacteristic
1020C2#2025113811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#385C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#385D47
hypocenterC47#14408
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#15689022C2semidirect
5. #20241653C2semidirect
6. #20241645C2semidirect
7. #20241641C2semidirect
8. #20241641C2semidirect
11. #20241622C2semidirect
12. #20241622C2semidirect
13. #20241617C2semidirect
53. C47×#385C4semidirect
268. C22⋊C4×C47C4⋊C4semidirect
546. #385Dic47semidirect
566. C47#14408semidirect
789. C22⋊C4C4⋊Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156890222
C2×#156890162
C2×#156889832
#202416532
#202416452
#202416412
#202416332
#202416222
#202416172
#202416112
C2×C47×#3852
#1440847