Finite Group Databasebeta

← #26138603

Subgroups — #26138603

Order 12032.

1730 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×#15689016C211yesmaximal, characteristic
2C2×#15688988C211yesmaximal, characteristic, complemented
3C2×#15688981C211yesmaximal, characteristic
4C2×C22⋊C4×Dic47C211yesmaximal, characteristic
5#20241652C211yesmaximal, characteristic, complemented
6#20241651C211yesmaximal, characteristic, complemented
7#20241631C211yesmaximal, characteristic
8#20241631C211yesmaximal, characteristic
9#20241621C211yesmaximal, characteristic, complemented
10#20241619C211yesmaximal, characteristic, complemented
11Dic47⋊#95C211yesmaximal, characteristic, complemented
12#20241614C211yesmaximal, characteristic, complemented
13#20241610C211yesmaximal, characteristic
14C4×C47⋊#95C211yesmaximal, characteristic, complemented
15C2×C47×#388C211yesmaximal, characteristic
16C24×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×C4×Dic47C2211yescharacteristic
26C22×C4×Dic47C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28#15689016—24no—
29#15688988—24no—
30#15688981—24no—
31C22⋊C4×Dic47C418yescomplemented
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
48C22×C4⋊C4×C47C2211yescharacteristic
49C22×C22⋊C4×C47C2211yescharacteristic
50C22×C22⋊C4×C47C2211yescharacteristic
51C22×C22⋊C4×C47C2211yescharacteristic
52C22×C42×C47C2211yescharacteristic
53C47×#388—24no—
54C2×#95×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C23×Dic47—22no—
57C23×Dic47—22no—
58C23×Dic47—22no—
59C23×Dic47—22no—
60C23×Dic47—41no—
61C23×Dic47—41no—
62C23×Dic47C2×C414yes—
63C23×Dic47C2311yescharacteristic
64C23×Dic47C2311yescharacteristic
65C23×Dic47C2311yescharacteristic
66C23×Dic47C2311yescharacteristic
67C23×Dic47C2311yescharacteristic
68C23×Dic47C2311yescharacteristic
69C23×Dic47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C2×C4⋊Dic47—22no—
72C2×C4⋊Dic47—22no—
73C2×C4⋊Dic47—41no—
74C2×Dic47⋊C4—22no—
75C2×Dic47⋊C4—22no—
76C2×Dic47⋊C4—22no—
77C2×Dic47⋊C4—22no—
78C2×Dic47⋊C4—22no—
79C2×Dic47⋊C4—22no—
80C2×Dic47⋊C4—41no—
81C2×Dic47⋊C4—41no—
82C2×Dic47⋊C4—41no—
83C2×Dic47⋊C4—41no—
84C2×Dic47⋊C4—41no—
85C2×Dic47⋊C4—41no—
86C2×C22⋊Dic47—22no—
87C2×C22⋊Dic47—22no—
88C2×C22⋊Dic47—22no—
89C2×C22⋊Dic47—22no—
90C2×C22⋊Dic47—22no—
91C2×C22⋊Dic47—22no—
92C2×C22⋊Dic47—41no—
93C2×C22⋊Dic47—41no—
94C2×C22⋊Dic47C2×C414yes—
95C2×C4×Dic47—22no—
96C2×C4×Dic47—22no—
97C2×C4×Dic47—22no—
98C2×C4×Dic47—22no—
99C2×C4×Dic47—41no—
100C2×C4×Dic47—41no—
101C2×C4×Dic47—41no—
102C2×C4×Dic47C2×C414yes—
103C2×C4×Dic47C2×C414yes—
104C47⋊#95—22no—
105C47⋊#95—22no—
106C47⋊#95—22no—
107C47⋊#95—22no—
108C47⋊#95—22no—
109C47⋊#95—22no—
110C47⋊#95—22no—
111C47⋊#95—22no—
112C47⋊#95—22no—
113C47⋊#95—22no—
114C47⋊#95—22no—
115C47⋊#95—22no—
116C47⋊#95—22no—
117C47⋊#95C2×C414yes—
118C47⋊#95C2×C414yes—
119C47⋊#95D414yes—
120C25×C47C2311yescharacteristic
121C23×C4×C47C2311yescharacteristic
122C23×C4×C47C2311yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C23×C4×C47C2311yescharacteristic
127C2×C4⋊C4×C47—22no—
128C2×C4⋊C4×C47—22no—
129C2×C4⋊C4×C47—41no—
130C2×C22⋊C4×C47—22no—
131C2×C22⋊C4×C47—22no—
132C2×C22⋊C4×C47—22no—
133C2×C22⋊C4×C47—22no—
134C2×C22⋊C4×C47—41no—
135C2×C22⋊C4×C47—41no—
136C2×C22⋊C4×C47C2×C414yes—
137C2×C22⋊C4×C47D414yes—
138C2×C22⋊C4×C47Q814yes—
139C2×C42×C47—22no—
140C2×C42×C47—22no—
141C2×C42×C47—41no—
142#95×C47—22no—
143#95×C47—22no—
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—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47C22×C412yes—
195C22×C4×C47C22×C412yes—
196C22×C4×C47C2×D412yes—
197C22×C4×C47C2×D412yes—
198C22×C4×C47C2×D412yes—
199C22×C4×C47C2×Q812yes—
200C22×C4×C47C2×Q812yes—
201C22×C4×C47#4112yes—
202C22×Dic47—21no—
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—28no—
233C22×Dic47—28no—
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—44no—
249C22×Dic47—44no—
250C22×Dic47—44no—
251C22×Dic47—44no—
252C22×Dic47—44no—
253C22×Dic47C22×C412yes—
254C22×Dic47C22×C412yes—
255C22×Dic47C22×C412yes—
256C22×Dic47C22×C412yes—
257C22×Dic47C2×D412yes—
258C22×Dic47C2×D412yes—
259C22×Dic47#4112yes—
260C22×Dic47#4112yes—
261C22×Dic47#4112yes—
262C22×Dic47#4112yes—
263C22×Dic47#4112yes—
264C22×Dic47#4112yes—
265C4⋊C4×C47—44no—
266C22⋊C4×C47—44no—
267C22⋊C4×C47—44no—
268C22⋊C4×C47C4⋊C4116yescomplemented
269C42×C47—44no—
270C22⋊Dic47—28no—
271C22⋊Dic47—44no—
272C22⋊Dic47—44no—
273C4⋊Dic47—44no—
274Dic47⋊C4—44no—
275Dic47⋊C4—44no—
276Dic47⋊C4—44no—
277Dic47⋊C4—44no—
278C4×Dic47—28no—
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×C47C2×#4111yescharacteristic
324C23×C47C2×#4111yescharacteristic
325C23×C47C2×#4111yescharacteristic
326C23×C47C2×#4111yescharacteristic
327C23×C47H(5,𝔽2)11yescharacteristic
328C23×C47H(5,𝔽2)11yescharacteristic
329C23×C47H(5,𝔽2)11yescharacteristic
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—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×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×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—22no—
388C2×Dic47—22no—
389C2×Dic47—22no—
390C2×Dic47—22no—
391C2×Dic47—22no—
392C2×Dic47—22no—
393C2×Dic47—22no—
394C2×Dic47—22no—
395C2×Dic47—22no—
396C2×Dic47—22no—
397C2×Dic47—22no—
398C2×Dic47—22no—
399C2×Dic47—22no—
400C2×Dic47—416no—
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#11714yes—
428C2×Dic47#11714yes—
429C2×Dic47C4×D414yes—
430#13915—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×#11711yescharacteristic
448C22×C47C2×#11711yescharacteristic
449C22×C47C2×C4×D411yescharacteristic
450C22×C47C4×#4111yescharacteristic
451C22×C47#51811yescharacteristic
452C22×C47#52011yescharacteristic
453C22×C47#52911yescharacteristic
454C22×C47#52911yescharacteristic
455C22×C47#53211yescharacteristic
456C22×C47#53211yescharacteristic
457C22×C47#53211yescharacteristic
458C22×C47#53211yescharacteristic
459C22×C47#53311yescharacteristic
460C22×C47#53311yescharacteristic
461C22×C47#53811yescharacteristic
462C22×C47#53811yescharacteristic
463C22×C47#53911yescharacteristic
464C22×C47#53911yescharacteristic
465C22×C47D4211yescharacteristic
466C22×C47#54611yescharacteristic
467C22×C47#54611yescharacteristic
468C22×C47#54611yescharacteristic
469C22×C47#54611yescharacteristic
470C22×C47#54711yescharacteristic
471C22×C47D4×Q811yescharacteristic
472C22×C47#55111yescharacteristic
473C22×C47#55111yescharacteristic
474C22×C47#55211yescharacteristic
475C22×C47#55211yescharacteristic
476C22×C47#55411yescharacteristic
477C22×C47#55411yescharacteristic
478C22×C47#55411yescharacteristic
479C22×C47#55511yescharacteristic
480C22×C47#55511yescharacteristic
481C4×C47—24no—
482C4×C47—24no—
483C4×C47—42no—
484C4×C47—42no—
485C4×C47—81no—
486C4×C47—81no—
487Dic47—24no—
488Dic47—24no—
489Dic47—24no—
490Dic47—42no—
491Dic47—42no—
492Dic47—42no—
493Dic47—81no—
494Dic47—81no—
495C2×#388—471no—
496C2×#388D4711yescharacteristic
497C2×#382—471no—
498C2×#380—471no—
499C2×C4×C22⋊C4—471no—
500#1444—471no—
501#1444—471no—
502#1439—471no—
503#1439—471no—
504#1436—471no—
505#1436—471no—
506C4⋊#95—471no—
507#1434—471no—
508C22⋊#95—471no—
509C4×#95—471no—
510C2×C47—44no—
511C2×C47#228511yescharacteristic
512C2×C47#229311yescharacteristic
513C2×C47#231811yescharacteristic
514C2×C47#234211yescharacteristic
515C2×C47#234611yescharacteristic
516C2×C47D4×C4⋊C411yescharacteristic
517C2×C47#234911yescharacteristic
518C2×C47#255311yescharacteristic
519C2×C47#255311yescharacteristic
520C2×C47#255511yescharacteristic
521C2×C47#255511yescharacteristic
522C2×C47#255611yescharacteristic
523C2×C47#255611yescharacteristic
524C2×C47#257411yescharacteristic
525C2×C47#257411yescharacteristic
526C24×C4—471no—
527C22×C4⋊C4—471no—
528C22×C4⋊C4—471no—
529C22×C4⋊C4—471no—
530C22×C4⋊C4—471no—
531C22×C4⋊C4—471no—
532C22×C4⋊C4C2×D4711yescharacteristic
533C22×C22⋊C4—471no—
534C22×C22⋊C4—471no—
535C22×C22⋊C4—471no—
536C22×C22⋊C4C2×D4711yescharacteristic
537C22×C22⋊C4C2×D4711yescharacteristic
538C22×C22⋊C4C2×D4711yescharacteristic
539C22×C42—471no—
540C22×C42—471no—
541C22×C42—471no—
542C22×C42C2×D4711yescharacteristic
543#388—24no—
544#388—944no—
545#382—944no—
546#380—944no—
547C4×C22⋊C4—478no—
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#1391511yescharacteristic, complemented, Sylow
567C25C22×D4711yescharacteristic
568C23×C4—471no—
569C23×C4—471no—
570C23×C4—471no—
571C23×C4—471no—
572C23×C4—471no—
573C23×C4—471no—
574C23×C4—474no—
575C23×C4—471no—
576C23×C4—471no—
577C23×C4—942no—
578C23×C4—942no—
579C23×C4—942no—
580C23×C4—942no—
581C23×C4—1881no—
582C23×C4—1881no—
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—942no—
593C2×C4⋊C4—942no—
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—1881no—
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×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—41no—
612C2×C22⋊C4—41no—
613C2×C22⋊C4—474no—
614C2×C22⋊C4—942no—
615C2×C22⋊C4—942no—
616C2×C22⋊C4—942no—
617C2×C22⋊C4—942no—
618C2×C22⋊C4—942no—
619C2×C22⋊C4—942no—
620C2×C22⋊C4—1881no—
621C2×C22⋊C4—1881no—
622C2×C22⋊C4Dic9414yes—
623C2×C22⋊C4C4×D4714yes—
624C2×C22⋊C4C22⋊D4714yes—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42—41no—
628C2×C42—474no—
629C2×C42—474no—
630C2×C42—942no—
631C2×C42—942no—
632C2×C42—942no—
633C2×C42—942no—
634C2×C42—1881no—
635C2×C42—1881no—
636C2×C42—1881no—
637#95—22no—
638#95—22no—
639#95—474no—
640#95—474no—
641#95—474no—
642#95—942no—
643#95—942no—
644#95—942no—
645#95—942no—
646#95—942no—
647#95—942no—
648#95—942no—
649#95—942no—
650#95—942no—
651#95—942no—
652#95—942no—
653#95—942no—
654#95—942no—
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×C4×D4712yes—
669C24C2×C22⋊D4712yes—
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—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—472no—
706C22×C4—472no—
707C22×C4—472no—
708C22×C4—472no—
709C22×C4—472no—
710C22×C4—472no—
711C22×C4—472no—
712C22×C4—472no—
713C22×C4—472no—
714C22×C4—472no—
715C22×C4—472no—
716C22×C4—472no—
717C22×C4—948no—
718C22×C4—948no—
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—1884no—
764C22×C4—1884no—
765C22×C4—1884no—
766C22×C4—1884no—
767C22×C4—1884no—
768C22×C4C2×Dic9412yes—
769C22×C4C2×Dic9412yes—
770C22×C4C2×C4×D4712yes—
771C22×C4C2×C4×D4712yes—
772C22×C4D4×D4712yes—
773C22×C4#1062535212yes—
774C22×C4C2×C22⋊D4712yes—
775C22×C4C2×C22⋊D4712yes—
776C4⋊C4—44no—
777C4⋊C4—1884no—
778C4⋊C4—1884no—
779C4⋊C4—1884no—
780C4⋊C4—1884no—
781C4⋊C4—1884no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4—948no—
785C22⋊C4—1884no—
786C22⋊C4—1884no—
787C22⋊C4Dic47⋊C4116yescomplemented
788C42—44no—
789C42—948no—
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×Dic47⋊C414yes—
827C23C22×C4×D4711yescharacteristic
828C23C2×D4×D4711yescharacteristic
829C23C22×C22⋊D4711yescharacteristic
830C23C22×Dic9411yescharacteristic
831C23#41×D4711yescharacteristic
832C23#41×D4711yescharacteristic
833C23#41×D4711yescharacteristic
834C23#41×D4711yescharacteristic
835C23#41×D4711yescharacteristic
836C23#41×D4711yescharacteristic
837C23C2×#1062535211yescharacteristic
838C23#1309406911yescharacteristic
839C23#1309406911yescharacteristic
840C23#1309407011yescharacteristic
841C23#1309407111yescharacteristic
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—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
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—474no—
883C2×C4—474no—
884C2×C4—474no—
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—942no—
895C2×C4—942no—
896C2×C4—942no—
897C2×C4—942no—
898C2×C4—942no—
899C2×C4—942no—
900C2×C4—942no—
901C2×C4—942no—
902C2×C4—942no—
903C2×C4—942no—
904C2×C4—942no—
905C2×C4—942no—
906C2×C4—942no—
907C2×C4—942no—
908C2×C4—942no—
909C2×C4—942no—
910C2×C4—942no—
911C2×C4—942no—
912C2×C4—18816no—
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×C4—1881no—
939C2×C4C2×Dic47⋊C414yes—
940C2×C4C2×Dic47⋊C414yes—
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×Dic47⋊C411yescharacteristic
957C22#117×D4711yescharacteristic
958C22#117×D4711yescharacteristic
959C22C4×D4×D4711yescharacteristic
960C22C4×#1062535211yescharacteristic
961C22#1568959511yescharacteristic
962C22#1568960211yescharacteristic
963C22#1568965011yescharacteristic
964C22#1568965611yescharacteristic
965C22#1568966811yescharacteristic
966C22#1568966911yescharacteristic
967C22#1568966911yescharacteristic
968C22#1568967211yescharacteristic
969C22#1568967611yescharacteristic
970C22#1568967611yescharacteristic
971C22#1568970511yescharacteristic
972C22#1568970711yescharacteristic
973C22#1568971411yescharacteristic
974C22#1568971611yescharacteristic
975C22D4×C22⋊D4711yescharacteristic
976C22#1568976111yescharacteristic
977C22#1568976211yescharacteristic
978C22#1568976611yescharacteristic
979C22#1568976711yescharacteristic
980C22#1568977211yescharacteristic
981C22D4×Dic9411yescharacteristic
982C22#1568979811yescharacteristic
983C22#1568980111yescharacteristic
984C22#1568980911yescharacteristic
985C22#1568981011yescharacteristic
986C22#1568983011yescharacteristic
987C22#1568983211yescharacteristic
988C22#1568983211yescharacteristic
989C22#1568983511yescharacteristic
990C22#1568983711yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—81no—
996C4—81no—
997C4—944no—
998C4—944no—
999C4—944no—
1000C4—3761no—
1001C4—3761no—
1002C4—1882no—
1003C4—1882no—
1004C4—1882no—
1005C2—44no—
1006C2#2024579111yescharacteristic
1007C2#2024584811yescharacteristic
1008C2#2024601811yescharacteristic
1009C2#2024623611yescharacteristic
1010C2#2024627011yescharacteristic
1011C2D4×Dic47⋊C411yescharacteristic
1012C2#2024629311yescharacteristic
1013C2#2024842911yescharacteristic
1014C2#2024843111yescharacteristic
1015C2#2024845911yescharacteristic
1016C2#2024846111yescharacteristic
1017C2#2024847111yescharacteristic
1018C2#2024847911yescharacteristic
1019C2#2024866111yescharacteristic
1020C2#2024866911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#388C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#388D47
hypocenterC47#13915
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#15688988C2semidirect
5. #20241652C2semidirect
6. #20241651C2semidirect
9. #20241621C2semidirect
10. #20241619C2semidirect
11. Dic47⋊#95C2semidirect
12. #20241614C2semidirect
14. C4×C47⋊#95C2semidirect
31. C22⋊C4×Dic47C4semidirect
268. C22⋊C4×C47C4⋊C4semidirect
566. C47#13915semidirect
787. C22⋊C4Dic47⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#156890162
C2×#156889882
C2×#156889812
C2×C22⋊C4×Dic472
#202416522
#202416512
#202416312
#202416212
#202416192
Dic47⋊#952
#202416142
#202416102
C4×C47⋊#952
C2×C47×#3882
#1391547