Finite Group Databasebeta

← #26233267

Subgroups — #26233267

Order 12032.

1100 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689181C211yesmaximal, characteristic, complemented
2#20245771C211yesmaximal, characteristic
3#20244004C211yesmaximal, characteristic, complemented
4#20243998C211yesmaximal, characteristic, complemented
5#20243997C211yesmaximal, characteristic, complemented
6#20243991C211yesmaximal, characteristic, complemented
7#20243566C211yesmaximal, characteristic, complemented
8#20243566C211yesmaximal, characteristic, complemented
9#20243457C211yesmaximal, characteristic, complemented
10#20243370C211yesmaximal, characteristic, complemented
11#20243298C211yesmaximal, characteristic
12#20243164C211yesmaximal, characteristic, complemented
13C8×C22⋊Dic47C211yesmaximal, characteristic, complemented
14#20243156C211yesmaximal, characteristic, complemented
15C22×C22⋊C8×C47C211yesmaximal, characteristic
16C2×#13093983C2211yescharacteristic
17C2×#13093983C2211yescharacteristic
18#15689181—24no—
19C2×Dic47⋊C8C2211yescharacteristic, complemented
20C2×Dic47⋊C8C2211yescharacteristic, complemented
21C2×Dic47⋊C8C2211yescharacteristic, complemented
22C2×Dic47⋊C8C2211yescharacteristic, complemented
23C2×C22⋊(C47⋊C8)C2211yescharacteristic
24C2×C22⋊(C47⋊C8)C2211yescharacteristic
25C2×C22⋊(C47⋊C8)C2211yescharacteristic
26C2×C22⋊(C47⋊C8)C2211yescharacteristic
27C2×C22⋊(C47⋊C8)C2211yescharacteristic
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×#13093934C2211yescharacteristic, complemented
30C2×#13093934C2211yescharacteristic, complemented
31C2×C8×Dic47C2211yescharacteristic, complemented
32C2×C8×Dic47C2211yescharacteristic, complemented
33#15688986C411yescharacteristic
34#15688986C411yescharacteristic
35#15688983C411yescharacteristic
36#15688983C411yescharacteristic
37#15688983C411yescharacteristic
38#15688983C411yescharacteristic
39#15688979C411yescharacteristic
40#15688979C411yescharacteristic
41C4×C22⋊Dic47C2211yescharacteristic
42C4×C22⋊Dic47C2211yescharacteristic
43C4×C22⋊Dic47C2211yescharacteristic
44C4×C22⋊Dic47C2211yescharacteristic
45#15688877C2211yescharacteristic, complemented
46#15688877C2211yescharacteristic, complemented
47#15688877C2211yescharacteristic, complemented
48#15688877C2211yescharacteristic, complemented
49#15688877C2211yescharacteristic, complemented
50#15688877C2211yescharacteristic, complemented
51#15688877C2211yescharacteristic, complemented
52#15688877C2211yescharacteristic, complemented
53C24×C4×C47C2211yescharacteristic
54C23×C8×C47C2211yescharacteristic
55C23×C8×C47C2211yescharacteristic
56C2×C22⋊C8×C47—24no—
57C2×C22⋊C8×C47C2211yescharacteristic
58C2×C22⋊C8×C47C2211yescharacteristic
59C2×C22⋊C8×C47C2211yescharacteristic
60C2×C22⋊C8×C47C2211yescharacteristic
61C22×C47⋊C8C2311yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65#13093983—22no—
66#13093983—22no—
67#13093983—41no—
68#13093983—41no—
69C2×C4⋊Dic47C2×C411yescharacteristic
70C2×C4⋊Dic47C2×C411yescharacteristic
71C2×C4⋊Dic47C2×C411yescharacteristic
72C2×C4⋊Dic47C2×C411yescharacteristic
73C2×C22⋊Dic47C2×C411yescharacteristic
74C2×C22⋊Dic47C2×C411yescharacteristic
75C2×C22⋊Dic47C2×C411yescharacteristic
76C2×C22⋊Dic47C2×C411yescharacteristic
77C2×C22⋊Dic47C2×C411yescharacteristic
78C2×C22⋊Dic47C2×C411yescharacteristic
79C2×C22⋊Dic47C2×C411yescharacteristic
80C2×C22⋊Dic47C2×C411yescharacteristic
81C2×C22⋊Dic47C2×C411yescharacteristic
82C2×C22⋊Dic47C2×C411yescharacteristic
83C2×C22⋊Dic47C2×C411yescharacteristic
84C2×C22⋊Dic47C2×C411yescharacteristic
85C2×C4×Dic47C2311yescharacteristic
86C2×C4×Dic47C2311yescharacteristic
87C2×C4×Dic47C2311yescharacteristic
88C2×C4×Dic47C2311yescharacteristic
89Dic47⋊C8—22no—
90Dic47⋊C8—22no—
91Dic47⋊C8—41no—
92Dic47⋊C8—41no—
93C22⋊(C47⋊C8)—22no—
94C22⋊(C47⋊C8)—22no—
95C22⋊(C47⋊C8)—22no—
96C22⋊(C47⋊C8)—22no—
97C22⋊(C47⋊C8)—41no—
98C22⋊(C47⋊C8)—41no—
99#13093934—22no—
100#13093934—41no—
101C8×Dic47—22no—
102C8×Dic47—41no—
103C47⋊#95C2×C411yescharacteristic
104C47⋊#95C2×C411yescharacteristic
105C47⋊#95C2×C411yescharacteristic
106C47⋊#95C2×C411yescharacteristic
107C47⋊#95C2×C411yescharacteristic
108C47⋊#95C2×C411yescharacteristic
109C47⋊#95C2×C411yescharacteristic
110C47⋊#95C2×C411yescharacteristic
111C25×C47C2×C411yescharacteristic
112C23×C4×C47—22no—
113C23×C4×C47—22no—
114C23×C4×C47—22no—
115C23×C4×C47—22no—
116C23×C4×C47—41no—
117C23×C4×C47—41no—
118C23×C4×C47C2×C411yescharacteristic
119C23×C4×C47C2×C411yescharacteristic
120C23×C4×C47C2×C411yescharacteristic
121C23×C4×C47C2311yescharacteristic
122C23×C4×C47C2311yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C22×C8×C47—22no—
125C22×C8×C47—22no—
126C22×C8×C47—22no—
127C22×C8×C47—22no—
128C22×C8×C47—41no—
129C22×C8×C47—41no—
130C22×C8×C47C2311yescharacteristic
131C22×C8×C47C2311yescharacteristic
132C22×C8×C47C2311yescharacteristic
133C22×C8×C47C2311yescharacteristic
134C22⋊C8×C47—22no—
135C22⋊C8×C47—22no—
136C22⋊C8×C47—22no—
137C22⋊C8×C47D414yes—
138C24×C47—22no—
139C24×C47—22no—
140C24×C47—22no—
141C24×C47—22no—
142C24×C47—22no—
143C24×C47—41no—
144C24×C47—41no—
145C24×C47C22×C411yescharacteristic
146C24×C47C22×C411yescharacteristic
147C24×C47C22×C411yescharacteristic
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—22no—
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
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—41no—
169C22×C4×C47—41no—
170C22×C4×C47—41no—
171C22×C4×C47—44no—
172C22×C4×C47—44no—
173C22×C4×C47—44no—
174C22×C4×C47—44no—
175C22×C4×C47C22×C411yescharacteristic
176C22×C4×C47C22×C411yescharacteristic
177C22×C4×C47C22×C411yescharacteristic
178C22×C4×C47C2×D412yes—
179C22×C4×C47#4112yes—
180C22×C4×C47#4112yes—
181C22×C4×C47#4112yes—
182C22×C4×C47C2411yescharacteristic
183C22×Dic47C22×C411yescharacteristic
184C22×Dic47C22×C411yescharacteristic
185C22×Dic47C22×C411yescharacteristic
186C22×Dic47C22×C411yescharacteristic
187C22×Dic47C22×C411yescharacteristic
188C22×Dic47C22×C411yescharacteristic
189C22×Dic47C22×C411yescharacteristic
190C22×Dic47C22×C411yescharacteristic
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—44no—
202C2×C8×C47—44no—
203C2×C8×C47C2×D412yes—
204C2×C8×C47C2×D412yes—
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—41no—
214C22⋊Dic47—41no—
215C22⋊Dic47—41no—
216C22⋊Dic47—41no—
217C4⋊Dic47—22no—
218C4⋊Dic47—22no—
219C4⋊Dic47—41no—
220C4⋊Dic47—41no—
221C4×Dic47—21no—
222C4×Dic47—21no—
223C4×Dic47—21no—
224C4×Dic47—21no—
225C4×Dic47—21no—
226C4×Dic47—21no—
227C4×Dic47—21no—
228C4×Dic47—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C2×C47⋊C8—21no—
238C2×C47⋊C8—21no—
239C2×C47⋊C8—21no—
240C2×C47⋊C8—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—28no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—44no—
259C23×C47—44no—
260C23×C47—44no—
261C23×C47—44no—
262C23×C47—44no—
263C23×C47—44no—
264C23×C47#11712yes—
265C23×C47C4×D412yes—
266C23×C47#13112yes—
267C23×C47#13112yes—
268C23×C47#13112yes—
269C23×C47C23×C411yescharacteristic
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—44no—
286C2×C4×C47—44no—
287C2×C4×C47—44no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47#11712yes—
293C2×C4×C47C4×D412yes—
294C2×C4×C47C22×D411yescharacteristic
295C2×C4×C47C2×#4111yescharacteristic
296C2×C4×C47C2×#4111yescharacteristic
297C2×C4×C47C2×#4111yescharacteristic
298C2×C4×C47H(5,𝔽2)11yescharacteristic
299C2×C4×C47H(5,𝔽2)11yescharacteristic
300C2×Dic47—21no—
301C2×Dic47—21no—
302C2×Dic47—21no—
303C2×Dic47—21no—
304C2×Dic47—21no—
305C2×Dic47—21no—
306C2×Dic47—21no—
307C2×Dic47—21no—
308C2×Dic47—21no—
309C2×Dic47—21no—
310C2×Dic47—21no—
311C2×Dic47—21no—
312C2×Dic47—21no—
313C2×Dic47—21no—
314C2×Dic47—21no—
315C2×Dic47—21no—
316C2×Dic47—21no—
317C2×Dic47—21no—
318C2×Dic47—21no—
319C2×Dic47—21no—
320C2×Dic47—21no—
321C2×Dic47—21no—
322C2×Dic47—21no—
323C2×Dic47—21no—
324C8×C47—22no—
325C8×C47—22no—
326C8×C47—41no—
327C8×C47—41no—
328C47⋊C8—41no—
329C47⋊C8—41no—
330C47⋊C8—41no—
331C47⋊C8—41no—
332#22558—471nomaximal, Sylow
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—22no—
338C22×C47—22no—
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—416no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47—41no—
350C22×C47—41no—
351C22×C47—41no—
352C22×C47—41no—
353C22×C47—41no—
354C22×C47#43314yescomplemented
355C22×C47C2×#11711yescharacteristic
356C22×C47C2×C4×D411yescharacteristic
357C22×C47#51811yescharacteristic
358C22×C47C2×#13111yescharacteristic
359C22×C47C2×#13111yescharacteristic
360C22×C47C2×#13111yescharacteristic
361C22×C47#56811yescharacteristic
362C4×C47—22no—
363C4×C47—22no—
364C4×C47—41no—
365C4×C47#54611yescharacteristic
366C4×C47#54611yescharacteristic
367C4×C47#55111yescharacteristic
368C4×C47#55111yescharacteristic
369Dic47—41no—
370Dic47—41no—
371Dic47—41no—
372Dic47—41no—
373Dic47—41no—
374Dic47—41no—
375Dic47—41no—
376Dic47—41no—
377C2×#433—471no—
378C22×C22⋊C8D4711yescharacteristic
379#2280—471no—
380#1924—471no—
381#1924—471no—
382#1923—471no—
383#1923—471no—
384#1850—471no—
385#1850—471no—
386#1818—471no—
387#1798—471no—
388#1779—471no—
389#1752—471no—
390C8×C22⋊C4—471no—
391#1750—471no—
392C2×C47—24no—
393C2×C47—42no—
394C2×C47—42no—
395C2×C47#234211yescharacteristic
396C2×C47C2×#43311yescharacteristic
397C2×C47#292411yescharacteristic
398C2×C47#292911yescharacteristic
399C2×C47#293311yescharacteristic
400C2×C47#297611yescharacteristic
401C2×C47#297711yescharacteristic
402C24×C4C2×D4711yescharacteristic
403C23×C8C2×D4711yescharacteristic
404C23×C8C2×D4711yescharacteristic
405C2×#117—471no—
406C2×#117—471no—
407#433—944no—
408C2×C4⋊C8—471no—
409C2×C4⋊C8—471no—
410C2×C4⋊C8—471no—
411C2×C4⋊C8—471no—
412C2×C22⋊C8—24no—
413C2×C22⋊C8—471no—
414C2×C22⋊C8—471no—
415C2×C22⋊C8—471no—
416C2×C22⋊C8—471no—
417C2×C22⋊C8—471no—
418C2×C22⋊C8—471no—
419C2×C22⋊C8C2×D4711yescharacteristic
420C2×C22⋊C8C2×D4711yescharacteristic
421C2×C22⋊C8C2×D4711yescharacteristic
422C2×C22⋊C8C2×D4711yescharacteristic
423C2×#97—471no—
424C2×#97—471no—
425C2×C4×C8—471no—
426C2×C4×C8—471no—
427#381—471no—
428#381—471no—
429#380—471no—
430#380—471no—
431#380—471no—
432#380—471no—
433#379—471no—
434#379—471no—
435C4×C22⋊C4—471no—
436C4×C22⋊C4—471no—
437C4×C22⋊C4—471no—
438C4×C22⋊C4—471no—
439#336—471no—
440#336—471no—
441#336—471no—
442#336—471no—
443#336—471no—
444#336—471no—
445#336—471no—
446#336—471no—
447C47#2255811yescharacteristic, complemented, Sylow
448C25C4×D4711yescharacteristic
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—41no—
454C23×C4—41no—
455C23×C4C4×D4711yescharacteristic
456C23×C4C4×D4711yescharacteristic
457C23×C4C4×D4711yescharacteristic
458C23×C4C22×D4711yescharacteristic
459C23×C4C22×D4711yescharacteristic
460C23×C4C22×D4711yescharacteristic
461C22×C8—22no—
462C22×C8—22no—
463C22×C8—22no—
464C22×C8—22no—
465C22×C8—41no—
466C22×C8—41no—
467C22×C8—471no—
468C22×C8—471no—
469C22×C8—471no—
470C22×C8—471no—
471C22×C8C22×D4711yescharacteristic
472C22×C8C22×D4711yescharacteristic
473C22×C8C22×D4711yescharacteristic
474C22×C8C22×D4711yescharacteristic
475#117—942no—
476#117—942no—
477#117—1881no—
478#117—1881no—
479C2×C4⋊C4—471no—
480C2×C4⋊C4—471no—
481C2×C4⋊C4—471no—
482C2×C4⋊C4—471no—
483C2×C22⋊C4—471no—
484C2×C22⋊C4—471no—
485C2×C22⋊C4—471no—
486C2×C22⋊C4—471no—
487C2×C22⋊C4—471no—
488C2×C22⋊C4—471no—
489C2×C22⋊C4—471no—
490C2×C22⋊C4—471no—
491C2×C22⋊C4—471no—
492C2×C22⋊C4—471no—
493C2×C22⋊C4—471no—
494C2×C22⋊C4—471no—
495C2×C42—471no—
496C2×C42—471no—
497C2×C42—471no—
498C2×C42—471no—
499C4⋊C8—942no—
500C4⋊C8—942no—
501C4⋊C8—1881no—
502C4⋊C8—1881no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506C22⋊C8—942no—
507C22⋊C8—942no—
508C22⋊C8—942no—
509C22⋊C8—942no—
510C22⋊C8—1881no—
511C22⋊C8—1881no—
512C22⋊C8C22⋊D4714yes—
513#97—942no—
514#97—1881no—
515C4×C8—942no—
516C4×C8—1881no—
517#95—471no—
518#95—471no—
519#95—471no—
520#95—471no—
521#95—471no—
522#95—471no—
523#95—471no—
524#95—471no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—41no—
531C24—41no—
532C24C2×C4×D4711yescharacteristic
533C24C2×C4×D4711yescharacteristic
534C24C2×C4×D4711yescharacteristic
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—471no—
563C22×C4—471no—
564C22×C4—471no—
565C22×C4—471no—
566C22×C4—471no—
567C22×C4—471no—
568C22×C4—471no—
569C22×C4—471no—
570C22×C4C2×C4×D4711yescharacteristic
571C22×C4C2×C4×D4711yescharacteristic
572C22×C4C2×C4×D4711yescharacteristic
573C22×C4#1062535012yes—
574C22×C4#1062535212yes—
575C22×C4#1062535212yes—
576C22×C4C2×C22⋊D4712yes—
577C22×C4C23×D4711yescharacteristic
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—44no—
589C2×C8—44no—
590C2×C8—941no—
591C2×C8—941no—
592C2×C8—941no—
593C2×C8—941no—
594C2×C8—941no—
595C2×C8—941no—
596C2×C8—941no—
597C2×C8—941no—
598C2×C8—941no—
599C2×C8—941no—
600C2×C8—941no—
601C2×C8—941no—
602C2×C8C2×C22⋊D4712yes—
603C2×C8C2×C22⋊D4712yes—
604C4⋊C4—942no—
605C4⋊C4—942no—
606C4⋊C4—1881no—
607C4⋊C4—1881no—
608C22⋊C4—942no—
609C22⋊C4—942no—
610C22⋊C4—942no—
611C22⋊C4—942no—
612C22⋊C4—942no—
613C22⋊C4—942no—
614C22⋊C4—942no—
615C22⋊C4—942no—
616C22⋊C4—1881no—
617C22⋊C4—1881no—
618C22⋊C4—1881no—
619C22⋊C4—1881no—
620C42—941no—
621C42—941no—
622C42—941no—
623C42—941no—
624C42—941no—
625C42—941no—
626C42—941no—
627C42—941no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—28no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23#1309398012yes—
652C23C4×C22⋊D4712yes—
653C23#1309403012yes—
654C23#1309403012yes—
655C23#1309403212yes—
656C23C22×C4×D4711yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—941no—
680C2×C4—941no—
681C2×C4—941no—
682C2×C4—941no—
683C2×C4—941no—
684C2×C4—941no—
685C2×C4—941no—
686C2×C4—941no—
687C2×C4—941no—
688C2×C4—941no—
689C2×C4—941no—
690C2×C4—941no—
691C2×C4—941no—
692C2×C4—941no—
693C2×C4—941no—
694C2×C4—941no—
695C2×C4—941no—
696C2×C4—941no—
697C2×C4—941no—
698C2×C4—941no—
699C2×C4—941no—
700C2×C4—941no—
701C2×C4—941no—
702C2×C4—941no—
703C2×C4#1309398012yes—
704C2×C4C4×C22⋊D4712yes—
705C2×C4C22×C22⋊D4711yescharacteristic
706C2×C4C2×#1062535211yescharacteristic
707C2×C4C2×#1062535211yescharacteristic
708C2×C4C2×#1062535011yescharacteristic
709C2×C4#1309406911yescharacteristic
710C2×C4#1309406911yescharacteristic
711C8—22no—
712C8—22no—
713C8—41no—
714C8—41no—
715C8—1881no—
716C8—1881no—
717C8—1881no—
718C8—1881no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—416no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22#1568918114yescomplemented
741C22C2×#1309398011yescharacteristic
742C22C2×C4×C22⋊D4711yescharacteristic
743C22#1568959611yescharacteristic
744C22C2×#1309403011yescharacteristic
745C22C2×#1309403011yescharacteristic
746C22C2×#1309403211yescharacteristic
747C22#1568988911yescharacteristic
748C4—22no—
749C4—22no—
750C4—41no—
751C4—1881no—
752C4—1881no—
753C4—1881no—
754C4—1881no—
755C4—1881no—
756C4—1881no—
757C4—1881no—
758C4—1881no—
759C4#1568976711yescharacteristic
760C4#1568976711yescharacteristic
761C4#1568979911yescharacteristic
762C4#1568979911yescharacteristic
763C2—24no—
764C2—42no—
765C2—42no—
766C2#2024623311yescharacteristic
767C2C2×#1568918111yescharacteristic
768C2#2025204211yescharacteristic
769C2#2025208211yescharacteristic
770C2#2025211311yescharacteristic
771C2#2025243311yescharacteristic
772C2#2025244211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC22×C22⋊C8×C47C2
prime radicalC25×C47C2×C4
cosocleC22×C4×C47C24
hypercenterC22×C22⋊C8D47
hypocenterC47#22558
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#15689181C2semidirect
3. #20244004C2semidirect
4. #20243998C2semidirect
5. #20243997C2semidirect
6. #20243991C2semidirect
7. #20243566C2semidirect
8. #20243566C2semidirect
9. #20243457C2semidirect
10. #20243370C2semidirect
12. #20243164C2semidirect
13. C8×C22⋊Dic47C2semidirect
14. #20243156C2semidirect
19. C2×Dic47⋊C8C22semidirect
20. C2×Dic47⋊C8C22semidirect
21. C2×Dic47⋊C8C22semidirect
22. C2×Dic47⋊C8C22semidirect
29. C2×#13093934C22semidirect
30. C2×#13093934C22semidirect
31. C2×C8×Dic47C22semidirect
32. C2×C8×Dic47C22semidirect
45. #15688877C22semidirect
46. #15688877C22semidirect
47. #15688877C22semidirect
48. #15688877C22semidirect
49. #15688877C22semidirect
50. #15688877C22semidirect
51. #15688877C22semidirect
52. #15688877C22semidirect
354. C22×C47#433semidirect
447. C47#22558semidirect
740. C22#15689181semidirect

Maximal subgroups

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

subgroupindex
C2×#156891812
#202457712
#202440042
#202439982
#202439972
#202439912
#202435662
#202434572
#202433702
#202432982
#202431642
C8×C22⋊Dic472
#202431562
C22×C22⋊C8×C472
#2255847