Finite Group Databasebeta

← #26379113

Subgroups — #26379113

Order 12032.

2510 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689670C211yesmaximal, characteristic
2#20246541C214yesmaximal, complemented
3#20246431C212yesmaximal, complemented
4#20246428C212yesmaximal, complemented
5#20246335C211yesmaximal, characteristic, complemented
6#20246319C212yesmaximal, complemented
7#20246318C212yesmaximal, complemented
8D4×C4⋊Dic47C211yesmaximal, characteristic, complemented
9#20246288C211yesmaximal, characteristic, complemented
10#20246195C214yesmaximal, complemented
11#20246132C212yesmaximal, complemented
12#20246112C212yesmaximal, complemented
13#20245977C212yesmaximal, complemented
14#20245976C212yesmaximal, complemented
15#20245793C211yesmaximal, characteristic, complemented
16#20245784C211yesmaximal, characteristic, complemented
17C47×#2354C211yesmaximal, characteristic, complemented
18C22×#10625350C2212yes—
19#15689670C4116yescomplemented
20C2×#13094023C2211yescharacteristic
21C2×#13094020C2211yescharacteristic
22C2×#13094010C2212yes—
23C2×#13093999C2211yescharacteristic
24C2×#13093997C2212yes—
25C2×#13093995C2211yescharacteristic
26C2×C4×D188C2211yescharacteristic
27C2×D4×Dic47C2212yes—
28C2×#13093986C2212yes—
29C2×C4×C22⋊D47C2212yes—
30C2×#13093982C2212yes—
31C2×#13093982C2212yes—
32C22×C4⋊Dic47C2212yes—
33C2×C4⋊C4×D47C2212yes—
34C2×C42×D47C2211yescharacteristic
35#15689029C2214yes—
36#15689027C2214yes—
37#15689025C2214yes—
38#15689025C2212yes—
39#15689023C2214yes—
40#15689022C2212yes—
41#15689019C2212yes—
42#15689017C2214yes—
43#15689015C2214yes—
44#15689015C2214yes—
45#15689010C2214yes—
46#15689007C2214yes—
47#15689001C2214yes—
48#15689000C2214yes—
49#15689000C2214yes—
50#15689000C2214yes—
51#15688999C2214yes—
52#15688999C2214yes—
53#15688998C2214yes—
54#15688994C2214yes—
55#15688993C2211yescharacteristic
56#15688990C2212yes—
57#15688988C2211yescharacteristic
58#15688988C2211yescharacteristic
59#15688988C2212yes—
60#15688985C2212yes—
61#15688983C2212yes—
62#15688980C2212yes—
63#15688980C2212yes—
64#15688980C2211yescharacteristic
65#15688980C2211yescharacteristic
66#15688980C2212yes—
67#15688980C2212yes—
68C4⋊C4×Dic47C2212yes—
69C4⋊C4×Dic47C2212yes—
70C4×C4⋊Dic47C2211yescharacteristic
71C4×C4⋊Dic47C2212yes—
72C22⋊C4×Dic47C2214yes—
73C4×(C2×D47)⋊C4C2212yes—
74C4×(C2×D47)⋊C4C2214yes—
75#15688969C2212yes—
76C2×C4×D4×C47C2211yescharacteristic
77C2×#117×C47C2212yes—
78C47×#390C2212yes—
79C47×#388C2214yes—
80C47×#384C2211yescharacteristic
81C47×#380C2212yes—
82C4×C4⋊C4×C47C2211yescharacteristic
83C4×C4⋊C4×C47C2212yes—
84C2×#10625350—44no—
85C2×#10625350—44no—
86C2×#10625350C2×C4116yescomplemented
87C22×Dic94C2312yes—
88C22×D188C2311yescharacteristic
89C22×D188C2312yes—
90C22×C22⋊D47C2312yes—
91C22×C22⋊D47C2312yes—
92C22×C22⋊D47C2312yes—
93C23×Dic47C2314yes—
94C22×C4×D47C2311yescharacteristic
95C22×C4×D47C2311yescharacteristic
96C22×C4×D47C2312yes—
97C22×C4×D47C2314yes—
98C22×C4×D47C2311yescharacteristic
99#13094023C2×C418yescomplemented
100#13094020C2×C418yes—
101#13094010C2×C4116yescomplemented
102#13093999C2×C418yescomplemented
103#13093997C2×C4116yescomplemented
104#13093995C2×C418yescomplemented
105C4×D188C2×C418yescomplemented
106D4×Dic47—44no—
107#13093986—44no—
108C4×C22⋊D47C2×C4116yescomplemented
109#13093982—44no—
110#13093982—44no—
111C2×C4⋊Dic47—44no—
112C2×C4⋊Dic47C2311yescharacteristic
113C2×C4⋊Dic47C2311yescharacteristic
114C2×C4⋊Dic47C2312yes—
115C2×C4⋊Dic47C2312yes—
116C2×C4⋊Dic47C2312yes—
117C2×C4⋊Dic47C2314yes—
118C2×C4⋊Dic47C2311yescharacteristic
119C2×Dic47⋊C4C2314yes—
120C2×Dic47⋊C4C2312yes—
121C4⋊C4×D47—44no—
122C2×C22⋊Dic47C2314yes—
123C2×C22⋊Dic47C2312yes—
124C2×(C2×D47)⋊C4C2312yes—
125C2×(C2×D47)⋊C4C2312yes—
126C2×(C2×D47)⋊C4C2314yes—
127C2×(C2×D47)⋊C4C2314yes—
128C2×(C2×D47)⋊C4C2314yes—
129C2×(C2×D47)⋊C4C2314yes—
130C2×(C2×D47)⋊C4C2312yes—
131C2×(C2×D47)⋊C4C2312yes—
132C2×C4×Dic47C2312yes—
133C2×C4×Dic47C2314yes—
134C2×C4×Dic47C2314yes—
135C2×C4×Dic47C2311yescharacteristic
136C2×C4×Dic47C2311yescharacteristic
137C2×C4×Dic47C2311yescharacteristic
138C42×D47C2×C418yescomplemented
139C47⋊#95C2312yes—
140C47⋊#95C2312yes—
141C47⋊#95C2312yes—
142C47⋊#95C2312yes—
143C47⋊#95C2312yes—
144C47⋊#95C2312yes—
145C47⋊#95C2314yes—
146C47⋊#95C2314yes—
147C47⋊#95C2314yes—
148C47⋊#95C2312yes—
149C47⋊#95C2314yes—
150C47⋊#95C2314yes—
151C22×D4×C47C2311yescharacteristic
152C23×C4×C47C2312yes—
153C4×D4×C47C2×C418yescomplemented
154#117×C47—44no—
155C2×C4⋊C4×C47C2312yes—
156C2×C4⋊C4×C47C2311yescharacteristic
157C2×C4⋊C4×C47C2311yescharacteristic
158C2×C4⋊C4×C47C2312yes—
159C2×C4⋊C4×C47C2312yes—
160C2×C4⋊C4×C47C2311yescharacteristic
161C2×C22⋊C4×C47C2314yes—
162C2×C22⋊C4×C47C2314yes—
163C2×C22⋊C4×C47C2312yes—
164C2×C42×C47C2312yes—
165C2×C42×C47C2314yes—
166C2×C42×C47C2311yescharacteristic
167#95×C47C2312yes—
168#95×C47C2314yes—
169C24×C47C2412yes—
170C23×D47C2411yescharacteristic
171C23×D47C2412yes—
172C2×D4×C47—22no—
173C2×D4×C47—22no—
174C2×D4×C47C22×C414yes—
175C22×C4×C47—24no—
176C22×C4×C47—24no—
177C22×C4×C47C22×C418yes—
178C22×C4×C47C2412yes—
179C22×C4×C47C2414yes—
180C22×C4×C47C2412yes—
181C22×C4×C47C2412yes—
182C22×C4×C47C2411yescharacteristic
183C22×C4×C47C2411yescharacteristic
184C22×C4×C47C2411yescharacteristic
185C2×C22⋊D47—42no—
186C2×C22⋊D47—42no—
187C2×C22⋊D47—42no—
188C2×C22⋊D47—42no—
189C2×C22⋊D47—42no—
190C2×C22⋊D47—42no—
191C2×C22⋊D47C22×C418yes—
192C2×C22⋊D47C22×C418yes—
193C2×C22⋊D47C22×C418yes—
194C22×Dic47—44no—
195C22×Dic47—44no—
196C22×Dic47—44no—
197C22×Dic47C2412yes—
198C22×Dic47C2412yes—
199C22×Dic47C2414yes—
200C22×Dic47C2411yescharacteristic
201C22×Dic47C2411yescharacteristic
202C22×Dic47C2411yescharacteristic
203C22×Dic47C2412yes—
204#10625350—432no—
205C2×D188—22no—
206C2×D188—22no—
207C2×D188—42no—
208C2×D188—42no—
209C2×D188C22×C414yes—
210C2×D188C22×C418yes—
211C2×C4×D47—24no—
212C2×C4×D47—22no—
213C2×C4×D47—24no—
214C2×C4×D47—22no—
215C2×C4×D47—22no—
216C2×C4×D47—22no—
217C2×C4×D47—41no—
218C2×C4×D47—41no—
219C2×C4×D47—44no—
220C2×C4×D47—44no—
221C2×C4×D47—44no—
222C2×C4×D47C22×C414yes—
223C2×C4×D47C22×C414yes—
224C2×C4×D47C22×C418yes—
225C2×C4×D47C22×C414yes—
226C2×Dic94—42no—
227C2×Dic94—42no—
228C2×Dic94C22×C418yes—
229C4⋊C4×C47—22no—
230C4⋊C4×C47—24no—
231C4⋊C4×C47—22no—
232C4⋊C4×C47—24no—
233C4⋊C4×C47—42no—
234C4⋊C4×C47C22×C414yes—
235C22⋊C4×C47—44no—
236C22⋊C4×C47—44no—
237C22⋊C4×C47C22×C418yes—
238C42×C47—24no—
239C42×C47—44no—
240C42×C47C22×C414yes—
241C22⋊Dic47—44no—
242C22⋊Dic47C22×C418yes—
243(C2×D47)⋊C4—44no—
244(C2×D47)⋊C4—42no—
245(C2×D47)⋊C4—42no—
246(C2×D47)⋊C4—44no—
247(C2×D47)⋊C4—44no—
248(C2×D47)⋊C4—44no—
249(C2×D47)⋊C4C22×C418yes—
250(C2×D47)⋊C4C22×C418yes—
251C4⋊Dic47—22no—
252C4⋊Dic47—22no—
253C4⋊Dic47—24no—
254C4⋊Dic47—24no—
255C4⋊Dic47—44no—
256C4⋊Dic47—42no—
257C4⋊Dic47C22×C414yes—
258Dic47⋊C4—44no—
259Dic47⋊C4C22×C418yes—
260C4×Dic47—24no—
261C4×Dic47—44no—
262C4×Dic47—44no—
263C4×Dic47C22×C414yes—
264C4×Dic47C22×C414yes—
265C4×Dic47C22×C414yes—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47C23×C414yes—
273C23×C47C2511yescharacteristic
274C22×D47—21no—
275C22×D47—22no—
276C22×D47—22no—
277C22×D47—22no—
278C22×D47—21no—
279C22×D47—21no—
280C22×D47—21no—
281C22×D47—22no—
282C22×D47—21no—
283C22×D47—21no—
284C22×D47—22no—
285C22×D47—22no—
286C22×D47C23×C414yes—
287C22×D47C23×C412yes—
288D4×C47—28no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—216no—
294C2×C4×C47—22no—
295C2×C4×C47—24no—
296C2×C4×C47—24no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—24no—
303C2×C4×C47C23×C412yes—
304C2×C4×C47C23×C414yes—
305C2×C4×C47C23×C412yes—
306C2×C4×C47C23×C412yes—
307C2×C4×C47H(5,𝔽2)12yes—
308C2×C4×C47H(5,𝔽2)12yes—
309C2×C4×C47H(5,𝔽2)12yes—
310C2×C4×C472−1+412yes—
311C22⋊D47—48no—
312C22⋊D47—48no—
313C22⋊D47—48no—
314C2×Dic47—21no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—21no—
318C2×Dic47—21no—
319C2×Dic47—21no—
320C2×Dic47—21no—
321C2×Dic47—21no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—24no—
325C2×Dic47—24no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—24no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—88no—
332C2×Dic47C23×C412yes—
333C2×Dic47C23×C412yes—
334C2×Dic47C23×C412yes—
335C2×Dic47C23×C414yes—
336D188—28no—
337D188—48no—
338C4×D47—216no—
339C4×D47—28no—
340C4×D47—28no—
341C4×D47—44no—
342C4×D47—88no—
343Dic94—48no—
344#34367—471nomaximal, Sylow
345C22×C47—24no—
346C22×C47—24no—
347C22×C47—24no—
348C22×C47—42no—
349C22×C47—42no—
350C22×C47—42no—
351C22×C47—42no—
352C22×C47C24×C411yescharacteristic
353C22×C47C2×H(5,𝔽2)11yescharacteristic
354C22×C47C2×H(5,𝔽2)11yescharacteristic
355C22×C47C2×H(5,𝔽2)11yescharacteristic
356C22×C47C2×2−1+411yescharacteristic
357C22×C47#58511yescharacteristic
358C22×C47#58511yescharacteristic
359C2×D47—22no—
360C2×D47—24no—
361C2×D47—22no—
362C2×D47—24no—
363C2×D47—22no—
364C2×D47—24no—
365C2×D47—42no—
366C2×D47—41no—
367C2×D47—41no—
368C2×D47—42no—
369C2×D47—42no—
370C2×D47—41no—
371C2×D47—42no—
372C2×D47—41no—
373C4×C47—24no—
374C4×C47—22no—
375C4×C47—44no—
376C4×C47—42no—
377C4×C47—42no—
378C4×C47#51814yes—
379C4×C47#52014yes—
380Dic47—22no—
381Dic47—24no—
382Dic47—22no—
383Dic47—22no—
384Dic47—42no—
385Dic47—44no—
386Dic47—42no—
387C2×#532—471no—
388#2377—474no—
389#2363—472no—
390#2363—472no—
391#2354—471no—
392#2354D4711yescharacteristic, complemented
393#2352—472no—
394#2352—472no—
395D4×C4⋊C4—471no—
396D4×C4⋊C4—471no—
397#2337—474no—
398#2331—472no—
399#2328—472no—
400#2311—472no—
401#2311—472no—
402#2285—471no—
403#2283—471no—
404C2×C47—44no—
405C2×C47C2×#51811yescharacteristic
406C2×C47C2×#52011yescharacteristic
407C2×C47#342811yescharacteristic
408C2×C47#354611yescharacteristic
409C2×C47#354611yescharacteristic
410C2×C47#354711yescharacteristic
411C2×C47#354711yescharacteristic
412D47—42no—
413D47—44no—
414C22×#41—472no—
415#532—4716no—
416C2×C4⋊Q8—471no—
417C2×#127—471no—
418C2×#124—472no—
419C2×#121—471no—
420C2×#121—471no—
421C2×#121—472no—
422C2×C4×D4—472no—
423C2×C4×D4—472no—
424C2×C4×D4—472no—
425C2×C4×D4—471no—
426C2×C4×D4C2×D4711yescharacteristic
427C2×#117—472no—
428C2×#117—472no—
429C2×#117C2×D4712yes—
430C22×C4⋊C4—472no—
431C22×C4⋊C4—472no—
432C22×C42—471no—
433#391—474no—
434#391—474no—
435#390—474no—
436#390—474no—
437#390—472no—
438#390C2×D4712yes—
439#389—472no—
440#389—472no—
441#388—474no—
442#388—474no—
443#388—474no—
444#388C2×D4714yes—
445#387—474no—
446#387—474no—
447#386—474no—
448#386—474no—
449#386—474no—
450#386—474no—
451#386—474no—
452#386—474no—
453#385—474no—
454#385—474no—
455#384—471no—
456#384C2×D4711yescharacteristic
457#383—472no—
458#382—472no—
459#382—471no—
460#382—471no—
461#381—472no—
462#380—472no—
463#380—471no—
464#380—471no—
465#380—472no—
466#380—472no—
467#380—472no—
468#380—472no—
469#380C2×D4712yes—
470C4×C4⋊C4—472no—
471C4×C4⋊C4—472no—
472C4×C4⋊C4—472no—
473C4×C4⋊C4—471no—
474C4×C4⋊C4C2×D4712yes—
475C4×C4⋊C4C2×D4711yescharacteristic
476C4×C22⋊C4—474no—
477C4×C22⋊C4—474no—
478C4×C22⋊C4—472no—
479#376—472no—
480C47#3436711yescharacteristic, complemented, Sylow
481C2×#41—4716no—
482C2×#41—1884no—
483C2×#41—1884no—
484C22×Q8—472no—
485C22×D4—472no—
486C22×D4—472no—
487C22×D4—472no—
488C22×D4—471no—
489C22×D4—472no—
490C22×D4C22×D4711yescharacteristic
491C23×C4—472no—
492C23×C4—471no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—474no—
496C23×C4—474no—
497C23×C4C22×D4712yes—
498C4⋊Q8—478no—
499#127—478no—
500#124—4716no—
501#121—478no—
502#121—478no—
503#121—4716no—
504C4×D4—4716no—
505C4×D4—478no—
506C4×D4—1884no—
507C4×D4—1884no—
508C4×D4C4×D4718yescomplemented
509#117—44no—
510#117—1884no—
511#117—1884no—
512C2×C4⋊C4—472no—
513C2×C4⋊C4—471no—
514C2×C4⋊C4—471no—
515C2×C4⋊C4—471no—
516C2×C4⋊C4—472no—
517C2×C4⋊C4—472no—
518C2×C4⋊C4—474no—
519C2×C4⋊C4—474no—
520C2×C4⋊C4—472no—
521C2×C4⋊C4—1884no—
522C2×C4⋊C4—1884no—
523C2×C4⋊C4C22×D4712yes—
524C2×C4⋊C4C22×D4711yescharacteristic
525C2×C4⋊C4C22×D4712yes—
526C2×C4⋊C4C22×D4711yescharacteristic
527C2×C4⋊C4C22×D4712yes—
528C2×C4⋊C4C22×D4711yescharacteristic
529C2×C22⋊C4—472no—
530C2×C22⋊C4—472no—
531C2×C22⋊C4—472no—
532C2×C22⋊C4—474no—
533C2×C22⋊C4—474no—
534C2×C22⋊C4—474no—
535C2×C22⋊C4—474no—
536C2×C22⋊C4—472no—
537C2×C22⋊C4—472no—
538C2×C22⋊C4—474no—
539C2×C22⋊C4C22×D4714yes—
540C2×C22⋊C4C22×D4714yes—
541C2×C22⋊C4C22×D4712yes—
542C2×C42—471no—
543C2×C42—471no—
544C2×C42—471no—
545C2×C42—478no—
546C2×C42—472no—
547C2×C42—474no—
548C2×C42—474no—
549C2×C42C22×D4712yes—
550C2×C42C22×D4714yes—
551C2×C42C22×D4711yescharacteristic
552#95—472no—
553#95—472no—
554#95—472no—
555#95—472no—
556#95—472no—
557#95—472no—
558#95—474no—
559#95—474no—
560#95—474no—
561#95—474no—
562#95—474no—
563#95—472no—
564#95C22×D4714yes—
565#95C22×D4712yes—
566C24—472no—
567C24—471no—
568C24C23×D4712yes—
569#41—18832no—
570C2×Q8—478no—
571C2×Q8—1882no—
572C2×Q8—1882no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—478no—
576C2×D4—478no—
577C2×D4—478no—
578C2×D4—474no—
579C2×D4—478no—
580C2×D4—942no—
581C2×D4—942no—
582C2×D4—1882no—
583C2×D4—1882no—
584C2×D4—1882no—
585C2×D4—1882no—
586C2×D4—1882no—
587C2×D4—1882no—
588C2×D4—1882no—
589C2×D4—1882no—
590C2×D4C2×C4×D4714yes—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—471no—
594C22×C4—471no—
595C22×C4—471no—
596C22×C4—472no—
597C22×C4—474no—
598C22×C4—474no—
599C22×C4—478no—
600C22×C4—474no—
601C22×C4—472no—
602C22×C4—472no—
603C22×C4—474no—
604C22×C4—944no—
605C22×C4—942no—
606C22×C4—942no—
607C22×C4—944no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4—1884no—
611C22×C4—1884no—
612C22×C4—1884no—
613C22×C4—1881no—
614C22×C4—1881no—
615C22×C4—1884no—
616C22×C4—1884no—
617C22×C4—1884no—
618C22×C4C2×C4×D4718yes—
619C22×C4C23×D4712yes—
620C22×C4C23×D4712yes—
621C22×C4C23×D4714yes—
622C22×C4C23×D4711yescharacteristic
623C22×C4C23×D4712yes—
624C22×C4C23×D4711yescharacteristic
625C22×C4C23×D4711yescharacteristic
626C4⋊C4—24no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—24no—
630C4⋊C4—42no—
631C4⋊C4—478no—
632C4⋊C4—474no—
633C4⋊C4—942no—
634C4⋊C4—942no—
635C4⋊C4—944no—
636C4⋊C4—944no—
637C4⋊C4—1884no—
638C4⋊C4—1882no—
639C4⋊C4—1884no—
640C4⋊C4C2×C4×D4714yes—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—478no—
644C22⋊C4—478no—
645C22⋊C4—478no—
646C22⋊C4—1882no—
647C22⋊C4—1884no—
648C22⋊C4—1882no—
649C22⋊C4—1884no—
650C22⋊C4—1884no—
651C22⋊C4—1884no—
652C22⋊C4—1884no—
653C22⋊C4C2×C4×D4718yes—
654C42—24no—
655C42—44no—
656C42—474no—
657C42—474no—
658C42—474no—
659C42—944no—
660C42—1884no—
661C42—1884no—
662C42C2×C4×D4714yes—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—474no—
670C23—472no—
671C23—942no—
672C23—941no—
673C23—941no—
674C23—942no—
675C23—942no—
676C23—941no—
677C23—941no—
678C23—942no—
679C23—941no—
680C23—942no—
681C23—941no—
682C23—942no—
683C23C22×C4×D4714yes—
684C23C24×D4711yescharacteristic
685Q8—1888no—
686D4—28no—
687D4—948no—
688D4—1888no—
689D4—1888no—
690D4—1888no—
691D4—1888no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—216no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—472no—
707C2×C4—472no—
708C2×C4—472no—
709C2×C4—474no—
710C2×C4—942no—
711C2×C4—941no—
712C2×C4—941no—
713C2×C4—942no—
714C2×C4—941no—
715C2×C4—941no—
716C2×C4—941no—
717C2×C4—941no—
718C2×C4—9416no—
719C2×C4—948no—
720C2×C4—948no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—944no—
725C2×C4—944no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—944no—
729C2×C4—942no—
730C2×C4—3768no—
731C2×C4—3768no—
732C2×C4—1884no—
733C2×C4C22×C4×D4712yes—
734C2×C4C22×C4×D4714yes—
735C2×C4C22×C4×D4712yes—
736C2×C4C22×C4×D4712yes—
737C2×C4#1309406912yes—
738C2×C4#1309407012yes—
739C2×C4#1309407012yes—
740C2×C4#1309407112yes—
741C22—24no—
742C22—24no—
743C22—24no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—942no—
749C22—944no—
750C22—942no—
751C22—944no—
752C22—942no—
753C22—944no—
754C22—1882no—
755C22—1881no—
756C22—1881no—
757C22—1882no—
758C22—1882no—
759C22—1881no—
760C22—1882no—
761C22—1881no—
762C22C23×C4×D4711yescharacteristic
763C22C2×#1309406911yescharacteristic
764C22C2×#1309407011yescharacteristic
765C22C2×#1309407011yescharacteristic
766C22C2×#1309407111yescharacteristic
767C22#1568995811yescharacteristic
768C22#1568996011yescharacteristic
769C4—24no—
770C4—22no—
771C4—44no—
772C4—42no—
773C4—42no—
774C4—942no—
775C4—944no—
776C4—942no—
777C4—942no—
778C4—1882no—
779C4—1882no—
780C4—1884no—
781C4#1568959514yes—
782C4#1568960314yes—
783C2—44no—
784C2—1882no—
785C2—1884no—
786C2C2×#1568959511yescharacteristic
787C2C2×#1568960311yescharacteristic
788C2#2025658811yescharacteristic
789C2#2025774811yescharacteristic
790C2#2025776311yescharacteristic
791C2#2025776511yescharacteristic
792C2#2025778011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2354C2
socle, cosocleC23×C47C25
prime radicalC2×#15689670C2
hypercenter#2354D47
hypocenterC47#34367
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #20246541C2semidirect
3. #20246431C2semidirect
4. #20246428C2semidirect
5. #20246335C2semidirect
6. #20246319C2semidirect
7. #20246318C2semidirect
8. D4×C4⋊Dic47C2semidirect
9. #20246288C2semidirect
10. #20246195C2semidirect
11. #20246132C2semidirect
12. #20246112C2semidirect
13. #20245977C2semidirect
14. #20245976C2semidirect
15. #20245793C2semidirect
16. #20245784C2semidirect
17. C47×#2354C2semidirect
19. #15689670C4semidirect
86. C2×#10625350C2×C4semidirect
99. #13094023C2×C4semidirect
101. #13094010C2×C4semidirect
102. #13093999C2×C4semidirect
103. #13093997C2×C4semidirect
104. #13093995C2×C4semidirect
105. C4×D188C2×C4semidirect
108. C4×C22⋊D47C2×C4semidirect
138. C42×D47C2×C4semidirect
153. C4×D4×C47C2×C4semidirect
392. #2354D47semidirect
480. C47#34367semidirect
508. C4×D4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896702
#202465412
#202464312
#202464282
#202463352
#202463192
#202463182
D4×C4⋊Dic472
#202462882
#202461952
#202461322
#202461122
#202459772
#202459762
#202457932
#202457842
C47×#23542
#3436747