Finite Group Databasebeta

← #26144161

Subgroups — #26144161

Order 12032.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689010C211yesmaximal, characteristic, complemented
2C2×#15688996C211yesmaximal, characteristic
3C2×#15688983C211yesmaximal, characteristic
4#20241652C211yesmaximal, characteristic, complemented
5#20241649C211yesmaximal, characteristic, complemented
6#20241646C211yesmaximal, characteristic, complemented
7#20241642C211yesmaximal, characteristic, complemented
8#20241631C211yesmaximal, characteristic
9#20241631C211yesmaximal, characteristic
10#20241625C211yesmaximal, characteristic
11#20241625C211yesmaximal, characteristic
12#20241622C211yesmaximal, characteristic, complemented
13#20241619C211yesmaximal, characteristic, complemented
14Dic47⋊#95C211yesmaximal, characteristic, complemented
15C47×C22⋊#95C211yesmaximal, characteristic
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2211yescharacteristic
20C22×Dic47⋊C4C2211yescharacteristic
21C22×Dic47⋊C4C2211yescharacteristic
22C22×C22⋊Dic47C2211yescharacteristic
23C22×C22⋊Dic47C2211yescharacteristic
24C22×C22⋊Dic47C2211yescharacteristic
25C22×C22⋊Dic47C2211yescharacteristic
26C22×C4×Dic47C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28#15689010—24no—
29#15688996C418yescomplemented
30#15688983—24no—
31C2×C47⋊#95C2211yescharacteristic
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
47C24×C4×C47C2211yescharacteristic
48C22×C22⋊C4×C47C2211yescharacteristic
49C22×C22⋊C4×C47C2211yescharacteristic
50C2×#95×C47C2211yescharacteristic
51C2×#95×C47C2211yescharacteristic
52C2×#95×C47C2211yescharacteristic
53C2×#95×C47C2211yescharacteristic
54C23×Dic47C2311yescharacteristic
55C23×Dic47C2311yescharacteristic
56C23×Dic47C2311yescharacteristic
57C23×Dic47C2311yescharacteristic
58C23×Dic47C2311yescharacteristic
59C23×Dic47C2311yescharacteristic
60C23×Dic47C2311yescharacteristic
61C23×Dic47C2311yescharacteristic
62C2×C4⋊Dic47—22no—
63C2×C4⋊Dic47—41no—
64C2×C4⋊Dic47—41no—
65C2×C4⋊Dic47—41no—
66C2×C4⋊Dic47—41no—
67C2×C4⋊Dic47D414yes—
68C2×Dic47⋊C4—22no—
69C2×Dic47⋊C4—22no—
70C2×Dic47⋊C4—22no—
71C2×Dic47⋊C4—41no—
72C2×Dic47⋊C4—41no—
73C2×Dic47⋊C4—41no—
74C2×Dic47⋊C4—41no—
75C2×Dic47⋊C4—41no—
76C2×Dic47⋊C4—41no—
77C2×Dic47⋊C4—41no—
78C2×Dic47⋊C4C2×C414yes—
79C2×Dic47⋊C4C2×C414yes—
80C2×C22⋊Dic47—22no—
81C2×C22⋊Dic47—22no—
82C2×C22⋊Dic47—22no—
83C2×C22⋊Dic47—22no—
84C2×C22⋊Dic47—22no—
85C2×C22⋊Dic47—22no—
86C2×C22⋊Dic47—41no—
87C2×C22⋊Dic47—41no—
88C2×C22⋊Dic47—41no—
89C2×C22⋊Dic47—41no—
90C2×C22⋊Dic47C2×C414yes—
91C2×C22⋊Dic47C2×C414yes—
92C2×C4×Dic47—22no—
93C2×C4×Dic47—22no—
94C2×C4×Dic47—41no—
95C2×C4×Dic47—41no—
96C2×C4×Dic47—41no—
97C2×C4×Dic47—41no—
98C47⋊#95—22no—
99C47⋊#95—22no—
100C47⋊#95—22no—
101C47⋊#95—22no—
102C47⋊#95—22no—
103C47⋊#95—22no—
104C47⋊#95—22no—
105C47⋊#95—41no—
106C47⋊#95—41no—
107C47⋊#95—41no—
108C47⋊#95—41no—
109C47⋊#95—41no—
110C47⋊#95—41no—
111C47⋊#95—41no—
112C47⋊#95C2×C414yes—
113C47⋊#95C2×C414yes—
114C25×C47C2311yescharacteristic
115C23×C4×C47—22no—
116C23×C4×C47—22no—
117C23×C4×C47—41no—
118C23×C4×C47—41no—
119C23×C4×C47—41no—
120C23×C4×C47—41no—
121C23×C4×C47C2×C414yes—
122C23×C4×C47C2311yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C2×C22⋊C4×C47—22no—
129C2×C22⋊C4×C47—41no—
130C2×C22⋊C4×C47—41no—
131C2×C22⋊C4×C47—41no—
132C2×C22⋊C4×C47—41no—
133C2×C22⋊C4×C47Q814yes—
134#95×C47—22no—
135#95×C47—22no—
136#95×C47—41no—
137#95×C47—41no—
138C24×C47—21no—
139C24×C47—21no—
140C24×C47—21no—
141C24×C47—21no—
142C24×C47—21no—
143C24×C47—21no—
144C24×C47—21no—
145C24×C47—21no—
146C24×C47—21no—
147C24×C47—21no—
148C24×C47—21no—
149C24×C47—21no—
150C24×C47C22×C412yes—
151C24×C47C2×Q812yes—
152C24×C47#4112yes—
153C24×C47C2411yescharacteristic
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
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—28no—
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—21no—
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×C47C2×D412yes—
200C22×C4×C47C2×Q812yes—
201C22×C4×C47C2×Q812yes—
202C22×C4×C47#4112yes—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—21no—
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×Dic47C22×C412yes—
252C22×Dic47C22×C412yes—
253C22×Dic47C22×C412yes—
254C22×Dic47C22×C412yes—
255C22×Dic47C2×D412yes—
256C22×Dic47C2×D412yes—
257C22×Dic47#4112yes—
258C22×Dic47#4112yes—
259C22⋊C4×C47—44no—
260C22⋊C4×C47—44no—
261C22⋊Dic47—28no—
262C22⋊Dic47—44no—
263C22⋊Dic47—44no—
264C22⋊Dic47—44no—
265C4⋊Dic47—44no—
266C4⋊Dic47—44no—
267Dic47⋊C4—28no—
268Dic47⋊C4—44no—
269Dic47⋊C4—44no—
270Dic47⋊C4—44no—
271C4×Dic47—44no—
272C4×Dic47—44no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47—22no—
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—41no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—41no—
298C23×C47—41no—
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×C47C4×Q814yes—
308C23×C47C23×C411yescharacteristic
309C23×C47C22×D411yescharacteristic
310C23×C47C22×Q811yescharacteristic
311C23×C47C2×#4111yescharacteristic
312C23×C47C2×#4111yescharacteristic
313C23×C47C2×#4111yescharacteristic
314C23×C47C2×#4111yescharacteristic
315C23×C47H(5,𝔽2)11yescharacteristic
316C23×C47H(5,𝔽2)11yescharacteristic
317C23×C47H(5,𝔽2)11yescharacteristic
318C23×C47H(5,𝔽2)11yescharacteristic
319C23×C47H(5,𝔽2)11yescharacteristic
320C23×C47H(5,𝔽2)11yescharacteristic
321C23×C472−1+411yescharacteristic
322C23×C472−1+411yescharacteristic
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
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—416no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47—41no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
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×C47C4×D414yes—
366C2×Dic47—22no—
367C2×Dic47—22no—
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—22no—
371C2×Dic47—22no—
372C2×Dic47—22no—
373C2×Dic47—22no—
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—22no—
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#11714yes—
422#14398—471nomaximal, Sylow
423C22×C47—24no—
424C22×C47—24no—
425C22×C47—24no—
426C22×C47—42no—
427C22×C47—42no—
428C22×C47—42no—
429C22×C47—42no—
430C22×C47—42no—
431C22×C47—42no—
432C22×C47—42no—
433C22×C47—42no—
434C22×C47—42no—
435C22×C47—42no—
436C22×C47—42no—
437C22×C47—42no—
438C22×C47C2×#11711yescharacteristic
439C22×C47C2×C4×D411yescharacteristic
440C22×C47C2×C4×Q811yescharacteristic
441C22×C47#51811yescharacteristic
442C22×C47#51811yescharacteristic
443C22×C47#52011yescharacteristic
444C22×C47#52011yescharacteristic
445C22×C47#53411yescharacteristic
446C22×C47#53511yescharacteristic
447C22×C47#53811yescharacteristic
448C22×C47#53811yescharacteristic
449C22×C47#53811yescharacteristic
450C22×C47#53811yescharacteristic
451C22×C47#53811yescharacteristic
452C22×C47#53911yescharacteristic
453C22×C47#53911yescharacteristic
454C22×C47#53911yescharacteristic
455C22×C47#54311yescharacteristic
456C22×C47#54411yescharacteristic
457C22×C47#54611yescharacteristic
458C22×C47#54711yescharacteristic
459C22×C47D4×Q811yescharacteristic
460C22×C47#55011yescharacteristic
461C22×C47#55211yescharacteristic
462C22×C47#55311yescharacteristic
463C22×C47#55311yescharacteristic
464C22×C47#55411yescharacteristic
465C22×C47#55411yescharacteristic
466C22×C47#55411yescharacteristic
467C22×C47#55511yescharacteristic
468C22×C47#55611yescharacteristic
469C22×C47#56011yescharacteristic
470C22×C47#56211yescharacteristic
471C22×C47#56211yescharacteristic
472C22×C47#56311yescharacteristic
473C4×C47—24no—
474C4×C47—42no—
475C4×C47—42no—
476C4×C47—42no—
477C4×C47—81no—
478C4×C47—81no—
479Dic47—24no—
480Dic47—42no—
481Dic47—42no—
482Dic47—42no—
483Dic47—42no—
484Dic47—42no—
485Dic47—81no—
486Dic47—81no—
487C2×#387—471no—
488C2×#385—471no—
489C2×#380—471no—
490#1444—471no—
491#1443—471no—
492#1442—471no—
493#1441—471no—
494#1439—471no—
495#1439—471no—
496#1437—471no—
497#1437—471no—
498#1436—471no—
499#1436—471no—
500C4⋊#95—471no—
501C22⋊#95D4711yescharacteristic
502C2×C47—44no—
503C2×C47#231811yescharacteristic
504C2×C47#232111yescharacteristic
505C2×C47#232911yescharacteristic
506C2×C47#234511yescharacteristic
507C2×C47#235411yescharacteristic
508C2×C47#236011yescharacteristic
509C2×C47#237611yescharacteristic
510C2×C47#270811yescharacteristic
511C2×C47#271411yescharacteristic
512C2×C47#272011yescharacteristic
513C2×C47#273211yescharacteristic
514C2×C47#278111yescharacteristic
515C2×C47#278411yescharacteristic
516C2×C47#278711yescharacteristic
517C2×C47#278811yescharacteristic
518C24×C4C2×D4711yescharacteristic
519C22×C4⋊C4—471no—
520C22×C4⋊C4—471no—
521C22×C4⋊C4—471no—
522C22×C4⋊C4—471no—
523C22×C4⋊C4—471no—
524C22×C4⋊C4—471no—
525C22×C22⋊C4—471no—
526C22×C22⋊C4—471no—
527C22×C22⋊C4—471no—
528C22×C22⋊C4—471no—
529C22×C22⋊C4C2×D4711yescharacteristic
530C22×C22⋊C4C2×D4711yescharacteristic
531C22×C42—471no—
532C22×C42—471no—
533#387—944no—
534#385—478no—
535#380—944no—
536C2×#95—471no—
537C2×#95—471no—
538C2×#95—471no—
539C2×#95—471no—
540C2×#95—471no—
541C2×#95—471no—
542C2×#95—471no—
543C2×#95—471no—
544C2×#95—471no—
545C2×#95—471no—
546C2×#95—471no—
547C2×#95—471no—
548C2×#95—471no—
549C2×#95—471no—
550C2×#95—471no—
551C2×#95—471no—
552C2×#95C2×D4711yescharacteristic
553C2×#95C2×D4711yescharacteristic
554C2×#95C2×D4711yescharacteristic
555C2×#95C2×D4711yescharacteristic
556C47#1439811yescharacteristic, complemented, Sylow
557C25C22×D4711yescharacteristic
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—41no—
561C23×C4—41no—
562C23×C4—41no—
563C23×C4—41no—
564C23×C4—471no—
565C23×C4—471no—
566C23×C4—471no—
567C23×C4—471no—
568C23×C4—471no—
569C23×C4—471no—
570C23×C4—471no—
571C23×C4—471no—
572C23×C4C4×D4714yes—
573C23×C4C22×D4711yescharacteristic
574C23×C4C22×D4711yescharacteristic
575C23×C4C22×D4711yescharacteristic
576C23×C4C22×D4711yescharacteristic
577C23×C4C22×D4711yescharacteristic
578C23×C4C22×D4711yescharacteristic
579C2×C4⋊C4—474no—
580C2×C4⋊C4—474no—
581C2×C4⋊C4—474no—
582C2×C4⋊C4—942no—
583C2×C4⋊C4—942no—
584C2×C4⋊C4—942no—
585C2×C4⋊C4—942no—
586C2×C4⋊C4—1881no—
587C2×C4⋊C4—1881no—
588C2×C4⋊C4—1881no—
589C2×C4⋊C4—1881no—
590C2×C4⋊C4—1881no—
591C2×C4⋊C4—1881no—
592C2×C4⋊C4—1881no—
593C2×C4⋊C4—1881no—
594C2×C4⋊C4—1881no—
595C2×C4⋊C4—1881no—
596C2×C4⋊C4—1881no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—41no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—474no—
603C2×C22⋊C4—474no—
604C2×C22⋊C4—942no—
605C2×C22⋊C4—942no—
606C2×C22⋊C4—942no—
607C2×C22⋊C4—942no—
608C2×C22⋊C4—942no—
609C2×C22⋊C4—942no—
610C2×C22⋊C4—1881no—
611C2×C22⋊C4—1881no—
612C2×C22⋊C4—1881no—
613C2×C22⋊C4—1881no—
614C2×C22⋊C4Dic9414yes—
615C2×C42—942no—
616C2×C42—942no—
617C2×C42—1881no—
618C2×C42—1881no—
619C2×C42—1881no—
620C2×C42—1881no—
621#95—22no—
622#95—22no—
623#95—41no—
624#95—41no—
625#95—474no—
626#95—474no—
627#95—942no—
628#95—942no—
629#95—942no—
630#95—942no—
631#95—942no—
632#95—942no—
633#95—942no—
634#95—1881no—
635#95—1881no—
636#95—1881no—
637#95—1881no—
638#95—1881no—
639#95—1881no—
640#95—1881no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C2×Dic9412yes—
654C24C2×C4×D4712yes—
655C24#1062535012yes—
656C24C23×D4711yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
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—28no—
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—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—472no—
701C22×C4—472no—
702C22×C4—472no—
703C22×C4—472no—
704C22×C4—472no—
705C22×C4—472no—
706C22×C4—472no—
707C22×C4—472no—
708C22×C4—941no—
709C22×C4—941no—
710C22×C4—941no—
711C22×C4—941no—
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×C4C2×Dic9412yes—
757C22×C4C2×Dic9412yes—
758C22×C4C2×C4×D4712yes—
759C22×C4C2×C4×D4712yes—
760C22×C4D4×D4712yes—
761C22×C4#1062535212yes—
762C4⋊C4—948no—
763C4⋊C4—1884no—
764C4⋊C4—1884no—
765C4⋊C4—1884no—
766C4⋊C4—1884no—
767C4⋊C4—1884no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—948no—
771C22⋊C4—1884no—
772C22⋊C4—1884no—
773C22⋊C4—1884no—
774C42—1884no—
775C42—1884no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C4×Dic9414yes—
811C23C22×C4×D4711yescharacteristic
812C23C2×D4×D4711yescharacteristic
813C23C22×Dic9411yescharacteristic
814C23#41×D4711yescharacteristic
815C23#41×D4711yescharacteristic
816C23C2×#1062535211yescharacteristic
817C23C2×#1062535011yescharacteristic
818C23#1309406911yescharacteristic
819C23#1309406911yescharacteristic
820C23#1309406911yescharacteristic
821C23#1309406911yescharacteristic
822C23#1309406911yescharacteristic
823C23#1309407011yescharacteristic
824C23#1309407111yescharacteristic
825C23#1309407211yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—416no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—474no—
869C2×C4—942no—
870C2×C4—942no—
871C2×C4—942no—
872C2×C4—942no—
873C2×C4—942no—
874C2×C4—942no—
875C2×C4—942no—
876C2×C4—942no—
877C2×C4—942no—
878C2×C4—942no—
879C2×C4—942no—
880C2×C4—942no—
881C2×C4—942no—
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—1881no—
891C2×C4—1881no—
892C2×C4—1881no—
893C2×C4—1881no—
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(C22⋊D47)⋊C414yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22#117×D4711yescharacteristic
941C22C2×(C22⋊D47)⋊C411yescharacteristic
942C22C2×C4×Dic9411yescharacteristic
943C22#1568959611yescharacteristic
944C22#1568959611yescharacteristic
945C22#1568960311yescharacteristic
946C22#1568960411yescharacteristic
947C22#1568968311yescharacteristic
948C22#1568968811yescharacteristic
949C22#1568970811yescharacteristic
950C22#1568970811yescharacteristic
951C22#1568970911yescharacteristic
952C22#1568970911yescharacteristic
953C22#1568971111yescharacteristic
954C22#1568971611yescharacteristic
955C22#1568971611yescharacteristic
956C22#1568972011yescharacteristic
957C22#1568974911yescharacteristic
958C22#1568975411yescharacteristic
959C22#1568976911yescharacteristic
960C22#1568977511yescharacteristic
961C22D4×Dic9411yescharacteristic
962C22#1568979111yescharacteristic
963C22#1568981311yescharacteristic
964C22#1568982211yescharacteristic
965C22#1568982211yescharacteristic
966C22#1568983011yescharacteristic
967C22#1568983211yescharacteristic
968C22#1568983211yescharacteristic
969C22#1568983711yescharacteristic
970C22#1568984411yescharacteristic
971C22#1568986111yescharacteristic
972C22#1568986811yescharacteristic
973C22#1568986911yescharacteristic
974C22#1568987411yescharacteristic
975C4—24no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—81no—
980C4—81no—
981C4—944no—
982C4—3761no—
983C4—3761no—
984C4—1882no—
985C4—1882no—
986C4—1882no—
987C4—1882no—
988C4—1882no—
989C2—44no—
990C2#2024601711yescharacteristic
991C2#2024604311yescharacteristic
992C2#2024612111yescharacteristic
993C2#2024626611yescharacteristic
994C2#2024633211yescharacteristic
995C2#2024639111yescharacteristic
996C2#2024653211yescharacteristic
997C2#2025010911yescharacteristic
998C2#2025018711yescharacteristic
999C2#2025026911yescharacteristic
1000C2#2025040811yescharacteristic
1001C2#2025105411yescharacteristic
1002C2#2025108611yescharacteristic
1003C2#2025112311yescharacteristic
1004C2#2025113811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×C22⋊#95C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC22⋊#95D47
hypocenterC47#14398
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#15689010C2semidirect
4. #20241652C2semidirect
5. #20241649C2semidirect
6. #20241646C2semidirect
7. #20241642C2semidirect
12. #20241622C2semidirect
13. #20241619C2semidirect
14. Dic47⋊#95C2semidirect
29. #15688996C4semidirect
556. C47#14398semidirect

Maximal subgroups

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

subgroupindex
C2×#156890102
C2×#156889962
C2×#156889832
#202416522
#202416492
#202416462
#202416422
#202416312
#202416252
#202416222
#202416192
Dic47⋊#952
C47×C22⋊#952
#1439847