Finite Group Databasebeta

← #26137572

Subgroups — #26137572

Order 12032.

2686 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D47C211yesmaximal, characteristic
2C2×#15688999C212yesmaximal
3C2×#15688970C211yesmaximal, characteristic, complemented
4C2×#95×D47C211yesmaximal, characteristic, complemented
5#20241625C212yesmaximal, complemented
6#20241619C212yesmaximal, complemented
7#20241612C211yesmaximal, characteristic, complemented
8#20241612C211yesmaximal, characteristic, complemented
9#20241611C211yesmaximal, characteristic, complemented
10(C2×D47)⋊#95C212yesmaximal, complemented
11C47×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D47C2211yescharacteristic
13C23×C4×D47C2212yes—
14C23×C4×D47C2211yescharacteristic
15C2×C4×C22⋊D47—24no—
16C2×C4×C22⋊D47—24no—
17C2×C4×C22⋊D47C418yescomplemented
18C22×Dic47⋊C4C2211yescharacteristic
19C22×C22⋊Dic47C2211yescharacteristic
20C22×C22⋊Dic47C2212yes—
21C22×(C2×D47)⋊C4C2211yescharacteristic
22C22×(C2×D47)⋊C4C2212yes—
23C22×C4×Dic47C2211yescharacteristic
24C22×C4×Dic47C2212yes—
25#15688999C4116yescomplemented
26#15688970—24no—
27C2×C47⋊#95C2211yescharacteristic
28C2×C47⋊#95C2211yescharacteristic
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35#95×D47—24no—
36C24×C4×C47C2211yescharacteristic
37C22×C22⋊C4×C47C2212yes—
38C2×#95×C47C2211yescharacteristic
39C2×#95×C47C2211yescharacteristic
40C2×#95×C47C2212yes—
41C24×D47C2311yescharacteristic
42C22×C22⋊D47—22no—
43C22×C22⋊D47—22no—
44C22×C22⋊D47—24no—
45C22×C22⋊D47C2×C418yes—
46C22×C22⋊D47C2×C414yes—
47C23×Dic47C2312yes—
48C23×Dic47C2312yes—
49C23×Dic47C2311yescharacteristic
50C23×Dic47C2311yescharacteristic
51C23×Dic47C2311yescharacteristic
52C22×C4×D47—24no—
53C22×C4×D47—24no—
54C22×C4×D47—42no—
55C22×C4×D47—42no—
56C22×C4×D47—42no—
57C22×C4×D47—42no—
58C22×C4×D47—42no—
59C22×C4×D47—42no—
60C22×C4×D47C2×C414yes—
61C22×C4×D47C2×C418yescomplemented
62C22×C4×D47D414yes—
63C22×C4×D47D414yes—
64C4×C22⋊D47—232no—
65C2×Dic47⋊C4—22no—
66C2×Dic47⋊C4—22no—
67C2×Dic47⋊C4C2×C414yescomplemented
68C2×C22⋊Dic47—22no—
69C2×C22⋊Dic47—22no—
70C2×C22⋊Dic47—42no—
71C2×C22⋊Dic47—42no—
72C2×C22⋊Dic47C2×C414yescomplemented
73C2×C22⋊Dic47C2×C418yescomplemented
74C2×(C2×D47)⋊C4—24no—
75C2×(C2×D47)⋊C4—22no—
76C2×(C2×D47)⋊C4—22no—
77C2×(C2×D47)⋊C4—24no—
78C2×(C2×D47)⋊C4C2×C414yes—
79C2×(C2×D47)⋊C4C2×C418yescomplemented
80C2×C4×Dic47—22no—
81C2×C4×Dic47—22no—
82C2×C4×Dic47—24no—
83C2×C4×Dic47—42no—
84C2×C4×Dic47—42no—
85C2×C4×Dic47C2×C414yescomplemented
86C47⋊#95—22no—
87C47⋊#95—22no—
88C47⋊#95—24no—
89C47⋊#95—42no—
90C47⋊#95—42no—
91C47⋊#95—42no—
92C47⋊#95C2×C418yescomplemented
93C47⋊#95C2×C418yescomplemented
94C25×C47C2311yescharacteristic
95C23×C4×C47—22no—
96C23×C4×C47—22no—
97C23×C4×C47—42no—
98C23×C4×C47—42no—
99C23×C4×C47C2×C414yescomplemented
100C23×C4×C47C2312yes—
101C23×C4×C47C2312yes—
102C23×C4×C47C2311yescharacteristic
103C23×C4×C47C2311yescharacteristic
104C2×C22⋊C4×C47—42no—
105C2×C22⋊C4×C47—42no—
106C2×C22⋊C4×C47C2×C418yescomplemented
107#95×C47—22no—
108#95×C47—22no—
109#95×C47—42no—
110C24×C47—21no—
111C24×C47—21no—
112C24×C47—22no—
113C24×C47—21no—
114C24×C47—22no—
115C24×C47—22no—
116C24×C47—21no—
117C24×C47—21no—
118C24×C47—21no—
119C24×C47C22×C414yes—
120C24×C47C22×C412yes—
121C24×C47C2411yescharacteristic
122C23×D47—22no—
123C23×D47—22no—
124C23×D47—21no—
125C23×D47—21no—
126C23×D47—21no—
127C23×D47—21no—
128C23×D47C22×C412yes—
129C23×D47C22×C414yes—
130C23×D47C2×D412yes—
131C23×D47C2×D412yes—
132C23×D47#4114yes—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—28no—
152C22×C4×C47—44no—
153C22×C4×C47—44no—
154C22×C4×C47—48no—
155C22×C4×C47—48no—
156C22×C4×C47C22×C414yes—
157C22×C4×C47C22×C414yes—
158C22×C4×C47C22×C412yes—
159C22×C4×C47C22×C412yes—
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2×D412yes—
162C2×C22⋊D47—28no—
163C2×C22⋊D47—28no—
164C2×C22⋊D47—216no—
165C2×C22⋊D47—216no—
166C2×C22⋊D47C42116yescomplemented
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—21no—
179C22×Dic47—21no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C22×Dic47—22no—
190C22×Dic47C22×C414yes—
191C22×Dic47C22×C414yes—
192C22×Dic47C22×C412yes—
193C22×Dic47C22×C414yes—
194C22×Dic47C22×C412yes—
195C22×Dic47C22×C412yes—
196C22×Dic47C2×D412yes—
197C22×Dic47C2×D412yes—
198C2×C4×D47—216no—
199C2×C4×D47—44no—
200C2×C4×D47—44no—
201C2×C4×D47—48no—
202C2×C4×D47—48no—
203C2×C4×D47—48no—
204C2×C4×D47—48no—
205C2×C4×D47—48no—
206C2×C4×D47—48no—
207C2×C4×D47—48no—
208C2×C4×D47—48no—
209C2×C4×D47C22⋊C4116yescomplemented
210C22⋊C4×C47—48no—
211C22⋊Dic47—28no—
212C22⋊Dic47—48no—
213(C2×D47)⋊C4—28no—
214(C2×D47)⋊C4—216no—
215Dic47⋊C4—28no—
216C4×Dic47—28no—
217C4×Dic47—48no—
218C23×C47—22no—
219C23×C47—22no—
220C23×C47—24no—
221C23×C47—24no—
222C23×C47—24no—
223C23×C47—24no—
224C23×C47—22no—
225C23×C47—22no—
226C23×C47—24no—
227C23×C47—22no—
228C23×C47—22no—
229C23×C47—24no—
230C23×C47—42no—
231C23×C47—42no—
232C23×C47—41no—
233C23×C47—41no—
234C23×C47—41no—
235C23×C47—41no—
236C23×C47—42no—
237C23×C47—42no—
238C23×C47—42no—
239C23×C47—42no—
240C23×C47C2×C4214yes—
241C23×C47C23×C411yescharacteristic
242C23×C47C23×C412yes—
243C23×C47C22×D411yescharacteristic
244C23×C47C22×D411yescharacteristic
245C23×C47C2×#4112yes—
246C23×C47H(5,𝔽2)12yes—
247C23×C47H(5,𝔽2)12yes—
248C23×C47H(5,𝔽2)11yescharacteristic
249C23×C47H(5,𝔽2)11yescharacteristic
250C23×C472−1+411yescharacteristic
251C23×C472−1+411yescharacteristic
252C22×D47—24no—
253C22×D47—22no—
254C22×D47—22no—
255C22×D47—24no—
256C22×D47—24no—
257C22×D47—22no—
258C22×D47—22no—
259C22×D47—24no—
260C22×D47—24no—
261C22×D47—24no—
262C22×D47—22no—
263C22×D47—22no—
264C22×D47—22no—
265C22×D47—22no—
266C22×D47—24no—
267C22×D47—24no—
268C22×D47—24no—
269C22×D47—24no—
270C22×D47C2×C4214yes—
271C22×D47C2×C22⋊C414yes—
272C22×D47#11714yes—
273C22×D47C4×D418yes—
274C22×D47C4×D418yes—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—24no—
278C2×C4×C47—24no—
279C2×C4×C47—22no—
280C2×C4×C47—24no—
281C2×C4×C47—24no—
282C2×C4×C47—24no—
283C2×C4×C47—24no—
284C2×C4×C47—24no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—24no—
288C2×C4×C47—416no—
289C2×C4×C47—42no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47C2×C22⋊C414yes—
300C22⋊D47—232no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—24no—
304C2×Dic47—24no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—24no—
308C2×Dic47—24no—
309C2×Dic47—22no—
310C2×Dic47—24no—
311C2×Dic47—24no—
312C2×Dic47—24no—
313C2×Dic47—24no—
314C2×Dic47—24no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—24no—
318C2×Dic47—42no—
319C2×Dic47—42no—
320C2×Dic47—42no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323C2×Dic47—41no—
324C2×Dic47—41no—
325C2×Dic47—42no—
326C2×Dic47—42no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330C2×Dic47C2×C4214yes—
331C2×Dic47C2×C22⋊C414yes—
332C4×D47—416no—
333C4×D47—432no—
334#13784—471nomaximal, Sylow
335C22×C47—24no—
336C22×C47—24no—
337C22×C47—24no—
338C22×C47—42no—
339C22×C47—42no—
340C22×C47—42no—
341C22×C47—42no—
342C22×C47—44no—
343C22×C47—44no—
344C22×C47—44no—
345C22×C47—44no—
346C22×C47C22×C4211yescharacteristic
347C22×C47C22×C22⋊C411yescharacteristic
348C22×C47C2×#11711yescharacteristic
349C22×C47C2×C4×D412yes—
350C22×C47C2×C4×D412yes—
351C22×C47#51812yes—
352C22×C47#51811yescharacteristic
353C22×C47#51811yescharacteristic
354C22×C47#51812yes—
355C22×C47#52012yes—
356C22×C47#52011yescharacteristic
357C22×C47#52011yescharacteristic
358C22×C47#52012yes—
359C22×C47#53412yes—
360C22×C47#53412yes—
361C22×C47#53511yescharacteristic
362C22×C47#53611yescharacteristic
363C22×C47#53711yescharacteristic
364C22×C47#53711yescharacteristic
365C22×C47#53812yes—
366C22×C47#53812yes—
367C22×C47#53912yes—
368C22×C47#53912yes—
369C2×D47—24no—
370C2×D47—24no—
371C2×D47—24no—
372C2×D47—24no—
373C2×D47—28no—
374C2×D47—28no—
375C2×D47—28no—
376C2×D47—28no—
377C2×D47—24no—
378C2×D47—24no—
379C2×D47C4×C22⋊C418yes—
380C4×C47—24no—
381C4×C47—42no—
382C4×C47—44no—
383C4×C47—44no—
384Dic47—24no—
385Dic47—24no—
386Dic47—42no—
387Dic47—44no—
388Dic47—44no—
389C22×C4×D4—471no—
390C2×#386—472no—
391C2×C4×C22⋊C4—471no—
392C22×#95—471no—
393#1437—472no—
394#1436—472no—
395#1434—471no—
396#1434—471no—
397C22⋊#95—472no—
398C22⋊#95—471no—
399C22⋊#95D4711yescharacteristic, complemented
400C2×C47—44no—
401C2×C47C2×C4×C22⋊C411yescharacteristic
402C2×C47#227511yescharacteristic
403C2×C47#227511yescharacteristic
404C2×C47#230811yescharacteristic
405C2×C47#231111yescharacteristic
406C2×C47#231811yescharacteristic
407C2×C47#231811yescharacteristic
408C2×C47#232112yes—
409C2×C47#232212yes—
410C2×C47#232512yes—
411C2×C47#232512yes—
412D47—28no—
413C23×D4—471no—
414C24×C4—471no—
415C24×C4—472no—
416C24×C4C2×D4711yescharacteristic
417C2×C4×D4—478no—
418C2×C4×D4—944no—
419C2×C4×D4—944no—
420C22×C4⋊C4—471no—
421C22×C22⋊C4—471no—
422C22×C22⋊C4—471no—
423C22×C22⋊C4—472no—
424C22×C22⋊C4—472no—
425C22×C22⋊C4C2×D4712yes—
426C22×C42—471no—
427C22×C42—472no—
428#386—4716no—
429C4×C22⋊C4—944no—
430C2×#95—472no—
431C2×#95—472no—
432C2×#95—471no—
433C2×#95—471no—
434C2×#95—472no—
435C2×#95—472no—
436C2×#95—472no—
437C2×#95—472no—
438C2×#95—944no—
439C2×#95C2×D4711yescharacteristic
440C2×#95C2×D4711yescharacteristic
441C2×#95C2×D4712yes—
442C47#1378411yescharacteristic, complemented, Sylow
443C25—471no—
444C25C22×D4711yescharacteristic
445C22×D4—474no—
446C22×D4—478no—
447C22×D4—942no—
448C22×D4—942no—
449C22×D4—944no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—42no—
453C23×C4—42no—
454C23×C4—471no—
455C23×C4—471no—
456C23×C4—474no—
457C23×C4—474no—
458C23×C4—474no—
459C23×C4—472no—
460C23×C4—471no—
461C23×C4—472no—
462C23×C4—478no—
463C23×C4—944no—
464C23×C4—944no—
465C23×C4—1882no—
466C23×C4—1882no—
467C23×C4—1882no—
468C23×C4—1882no—
469C23×C4—1882no—
470C23×C4—1882no—
471C23×C4C4×D4714yescomplemented
472C23×C4C22×D4712yes—
473C23×C4C22×D4711yescharacteristic
474C23×C4C22×D4712yes—
475C23×C4C22×D4711yescharacteristic
476C4×D4—9432no—
477C2×C4⋊C4—474no—
478C2×C4⋊C4—942no—
479C2×C4⋊C4—942no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—42no—
482C2×C22⋊C4—474no—
483C2×C22⋊C4—474no—
484C2×C22⋊C4—478no—
485C2×C22⋊C4—478no—
486C2×C22⋊C4—942no—
487C2×C22⋊C4—942no—
488C2×C22⋊C4—944no—
489C2×C22⋊C4—944no—
490C2×C22⋊C4—942no—
491C2×C22⋊C4—942no—
492C2×C22⋊C4—1882no—
493C2×C22⋊C4—1882no—
494C2×C22⋊C4C4×D4718yescomplemented
495C2×C42—474no—
496C2×C42—942no—
497C2×C42—942no—
498C2×C42—944no—
499C2×C42—1882no—
500C2×C42—1882no—
501#95—22no—
502#95—22no—
503#95—42no—
504#95—478no—
505#95—478no—
506#95—944no—
507#95—942no—
508#95—942no—
509#95—1882no—
510#95—1882no—
511#95—1882no—
512C24—21no—
513C24—21no—
514C24—22no—
515C24—21no—
516C24—22no—
517C24—22no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—472no—
522C24—474no—
523C24—472no—
524C24—472no—
525C24—474no—
526C24—942no—
527C24—942no—
528C24—941no—
529C24—941no—
530C24—941no—
531C24—941no—
532C24C2×C4×D4714yes—
533C24C2×C4×D4712yes—
534C24C23×D4711yescharacteristic
535C2×D4—4716no—
536C2×D4—948no—
537C2×D4—948no—
538C2×D4—9416no—
539C2×D4—9416no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—28no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—474no—
564C22×C4—472no—
565C22×C4—472no—
566C22×C4—472no—
567C22×C4—472no—
568C22×C4—4716no—
569C22×C4—474no—
570C22×C4—474no—
571C22×C4—472no—
572C22×C4—9416no—
573C22×C4—941no—
574C22×C4—941no—
575C22×C4—942no—
576C22×C4—942no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—941no—
581C22×C4—941no—
582C22×C4—942no—
583C22×C4—942no—
584C22×C4—941no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—942no—
590C22×C4—941no—
591C22×C4—942no—
592C22×C4—942no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4—942no—
596C22×C4—1884no—
597C22×C4—1884no—
598C22×C4—1888no—
599C22×C4—1888no—
600C22×C4—1888no—
601C22×C4—1888no—
602C22×C4—1888no—
603C22×C4—1888no—
604C22×C4—1888no—
605C22×C4—1888no—
606C22×C4C2×C4×D4714yes—
607C22×C4C2×C4×D4714yes—
608C22×C4C2×C4×D4712yes—
609C22×C4C2×C4×D4712yes—
610C22×C4D4×D4712yes—
611C22×C4D4×D4712yes—
612C4⋊C4—948no—
613C22⋊C4—48no—
614C22⋊C4—9416no—
615C22⋊C4—948no—
616C22⋊C4—948no—
617C22⋊C4—1888no—
618C42—948no—
619C42—1888no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—22no—
627C23—22no—
628C23—24no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—42no—
633C23—42no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—474no—
643C23—474no—
644C23—474no—
645C23—478no—
646C23—478no—
647C23—944no—
648C23—942no—
649C23—942no—
650C23—944no—
651C23—944no—
652C23—942no—
653C23—942no—
654C23—944no—
655C23—944no—
656C23—944no—
657C23—942no—
658C23—942no—
659C23—942no—
660C23—942no—
661C23—944no—
662C23—944no—
663C23—944no—
664C23—944no—
665C23C42×D4714yes—
666C23C22×C4×D4711yescharacteristic
667C23C22×C4×D4712yes—
668C23C2×D4×D4711yescharacteristic
669C23C2×D4×D4711yescharacteristic
670C23#41×D4712yes—
671C23#1309406912yes—
672C23#1309406912yes—
673C23#1309406911yescharacteristic
674C23#1309407011yescharacteristic
675C23#1309407111yescharacteristic
676C23#1309407211yescharacteristic
677D4—9432no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—416no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—474no—
703C2×C4—474no—
704C2×C4—942no—
705C2×C4—942no—
706C2×C4—944no—
707C2×C4—944no—
708C2×C4—942no—
709C2×C4—942no—
710C2×C4—944no—
711C2×C4—944no—
712C2×C4—942no—
713C2×C4—944no—
714C2×C4—944no—
715C2×C4—944no—
716C2×C4—944no—
717C2×C4—944no—
718C2×C4—942no—
719C2×C4—944no—
720C2×C4—942no—
721C2×C4—18816no—
722C2×C4—18832no—
723C2×C4—1882no—
724C2×C4—1882no—
725C2×C4—1881no—
726C2×C4—1882no—
727C2×C4—1881no—
728C2×C4—1881no—
729C2×C4—1882no—
730C2×C4—1881no—
731C2×C4—1882no—
732C2×C4—1882no—
733C2×C4—1882no—
734C2×C4—1882no—
735C2×C4C22⋊C4×D4714yes—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—42no—
740C22—42no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—42no—
746C22—42no—
747C22—478no—
748C22—944no—
749C22—944no—
750C22—948no—
751C22—948no—
752C22—948no—
753C22—948no—
754C22—944no—
755C22—944no—
756C22—944no—
757C22—944no—
758C22C2×C42×D4711yescharacteristic
759C22C2×C22⋊C4×D4711yescharacteristic
760C22#117×D4711yescharacteristic
761C22C4×D4×D4712yes—
762C22C4×D4×D4712yes—
763C22#1568959512yes—
764C22#1568959611yescharacteristic
765C22#1568959611yescharacteristic
766C22#1568959612yes—
767C22#1568960212yes—
768C22#1568960311yescharacteristic
769C22#1568960411yescharacteristic
770C22#1568960412yes—
771C22#1568968312yes—
772C22#1568968312yes—
773C22#1568968911yescharacteristic
774C22#1568969611yescharacteristic
775C22#1568970211yescharacteristic
776C22#1568970311yescharacteristic
777C22#1568970512yes—
778C22#1568970912yes—
779C22#1568971612yes—
780C22#1568971912yes—
781C4—24no—
782C4—44no—
783C4—44no—
784C4—42no—
785C4—944no—
786C4—944no—
787C4—1884no—
788C4—1884no—
789C4—1882no—
790C2—44no—
791C2—948no—
792C2C4×C22⋊C4×D4711yescharacteristic
793C2#2024574611yescharacteristic
794C2#2024574711yescharacteristic
795C2#2024596411yescharacteristic
796C2#2024597711yescharacteristic
797C2#2024601711yescharacteristic
798C2#2024602311yescharacteristic
799C2#2024604412yes—
800C2#2024605512yes—
801C2#2024608512yes—
802C2#2024609012yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC47×C22⋊#95C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC22⋊#95D47
hypocenterC47#13784
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#15688970C2semidirect
4. C2×#95×D47C2semidirect
5. #20241625C2semidirect
6. #20241619C2semidirect
7. #20241612C2semidirect
8. #20241612C2semidirect
9. #20241611C2semidirect
10. (C2×D47)⋊#95C2semidirect
11. C47×C22⋊#95C2semidirect
17. C2×C4×C22⋊D47C4semidirect
25. #15688999C4semidirect
61. C22×C4×D47C2×C4semidirect
67. C2×Dic47⋊C4C2×C4semidirect
72. C2×C22⋊Dic47C2×C4semidirect
73. C2×C22⋊Dic47C2×C4semidirect
79. C2×(C2×D47)⋊C4C2×C4semidirect
85. C2×C4×Dic47C2×C4semidirect
92. C47⋊#95C2×C4semidirect
93. C47⋊#95C2×C4semidirect
99. C23×C4×C47C2×C4semidirect
106. C2×C22⋊C4×C47C2×C4semidirect
166. C2×C22⋊D47C42semidirect
209. C2×C4×D47C22⋊C4semidirect
399. C22⋊#95D47semidirect
442. C47#13784semidirect
471. C23×C4C4×D47semidirect
494. C2×C22⋊C4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D472
C2×#156889992
C2×#156889702
C2×#95×D472
#202416252
#202416192
#202416122
#202416112
(C2×D47)⋊#952
C47×C22⋊#952
#1378447