Finite Group Databasebeta

← #27087761

Subgroups — #27087761

Order 12032.

2444 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689673C211yesmaximal, characteristic, complemented
2C2×#15689673C211yesmaximal, characteristic, complemented
3#20254385C214yesmaximal, complemented
4#20254377C214yesmaximal, complemented
5#20254323C214yesmaximal, complemented
6#20254315C212yesmaximal, complemented
7#20254308C212yesmaximal, complemented
8#20253840C212yesmaximal, complemented
9#20253782C212yesmaximal, complemented
10#20252854C214yesmaximal, complemented
11#20252642C214yesmaximal, complemented
12C47×#2920C211yesmaximal, characteristic, complemented
13C22×#10625350—21no—
14C22×#10625350C2212yes—
15C2×#13094052C2218yescomplemented
16#15689673—21no—
17#15689673—21no—
18#15689673—21no—
19#15689673—21no—
20#15689673—21no—
21#15689673—21no—
22#15689673—21no—
23#15689673—21no—
24#15689673C2212yes—
25#15689673C2212yes—
26#15689673C2212yes—
27#15689673C2212yes—
28#15689673C2212yescomplemented
29#15689673C2212yescomplemented
30#15689673C2212yescomplemented
31#15689673C2212yescomplemented
32C2×#13094024C2211yescharacteristic, complemented
33C2×#13094024C2211yescharacteristic, complemented
34C2×#13094021C2211yescharacteristic, complemented
35C2×#13094021C2211yescharacteristic, complemented
36C2×#13094012—21no—
37C2×#13094012C2212yescomplemented
38C2×#13093998—21no—
39C2×#13093998—21no—
40C2×#13093998—21no—
41C2×#13093998C2212yes—
42C2×C4×D188—21no—
43C2×C4×D188—21no—
44C2×C4×D188—21no—
45C2×C4×D188C2212yescomplemented
46#15689512C2218yescomplemented
47#15689500C2214yescomplemented
48#15689496C2214yescomplemented
49#15689483C2218yescomplemented
50#15689474C2214yescomplemented
51#15689470C2214yescomplemented
52#15689339C22116yescomplemented
53#15689329C2218yescomplemented
54#15689319C2218yescomplemented
55#15689270C22116yescomplemented
56#15689264C2218yescomplemented
57#15689259C2218yescomplemented
58#15689125C2218yescomplemented
59C22×C42×C47C2211yescharacteristic
60C47×#432C2212yescomplemented
61C47×#432C2212yescomplemented
62C47×#431C2212yescomplemented
63C47×#431C2212yescomplemented
64C47×#423C2212yescomplemented
65C47×#407C2212yes—
66C4×M16×C47C2212yescomplemented
67C2×#10625350—22no—
68C2×#10625350—22no—
69C2×#10625350—22no—
70C2×#10625350—22no—
71C2×#10625350—22no—
72C2×#10625350—22no—
73C2×#10625350—48no—
74C2×#10625350—48no—
75C2×#10625350C2314yes—
76C2×#10625350C2314yes—
77C22×Dic94—21no—
78C22×Dic94C2312yes—
79C22×D188—21no—
80C22×D188—21no—
81C22×D188—21no—
82C22×D188—21no—
83C22×D188C2312yes—
84C22×D188C2312yes—
85C22×C22⋊D47—22no—
86C22×C22⋊D47—22no—
87C22×C4×D47—22no—
88C22×C4×D47—22no—
89#13094052—416no—
90C2×#10625325C23116yes—
91C2×D376C23116yes—
92#13094024—21no—
93#13094024—21no—
94#13094024—21no—
95#13094024—21no—
96#13094024C2312yes—
97#13094024C2312yes—
98#13094024C2312yes—
99#13094024C2312yes—
100#13094021—21no—
101#13094021—21no—
102#13094021—21no—
103#13094021—21no—
104#13094021C2312yes—
105#13094021C2312yes—
106#13094021C2312yes—
107#13094021C2312yes—
108#13094012—22no—
109#13094012—22no—
110#13094012—22no—
111#13094012—22no—
112#13094012—22no—
113#13094012—22no—
114#13094012C2314yes—
115#13094012C2314yes—
116#13093998—22no—
117#13093998—22no—
118#13093998—22no—
119#13093998—22no—
120#13093998—22no—
121#13093998—22no—
122#13093998—22no—
123#13093998—22no—
124#13093998—22no—
125#13093998—22no—
126#13093998—22no—
127#13093998—22no—
128#13093998—22no—
129#13093998—22no—
130#13093998C2314yes—
131#13093998C2314yes—
132C4×D188—22no—
133C4×D188—22no—
134C4×D188—22no—
135C4×D188—22no—
136C4×D188—22no—
137C4×D188—22no—
138C4×D188—22no—
139C4×D188—22no—
140C4×D188—22no—
141C4×D188—22no—
142C4×D188—22no—
143C4×D188—22no—
144C4×D188—22no—
145C4×D188—22no—
146C4×D188C2314yes—
147C4×D188C2314yes—
148C2×C4⋊Dic47—21no—
149C2×C4⋊Dic47—21no—
150C2×C4⋊Dic47—21no—
151C2×C4⋊Dic47C2312yes—
152C2×(C2×D47)⋊C4—22no—
153C2×(C2×D47)⋊C4—22no—
154C2×(C2×D47)⋊C4—22no—
155C2×(C2×D47)⋊C4—22no—
156#13093949C23116yes—
157#13093946C23116yes—
158C23×C4×C47D411yescharacteristic
159C23×C4×C47D411yescharacteristic
160C23×C4×C47C2311yescharacteristic
161C2×M16×C47C2314yes—
162C2×C42×C47D411yescharacteristic
163C2×C42×C47D411yescharacteristic
164C2×C42×C47D411yescharacteristic
165C2×C42×C47D411yescharacteristic
166C2×C42×C47D411yescharacteristic
167C2×C42×C47D411yescharacteristic
168C2×C42×C47C2311yescharacteristic
169C2×C42×C47C2311yescharacteristic
170C2×C42×C47C2311yescharacteristic
171C2×C42×C47C2311yescharacteristic
172C2×C42×C47C2311yescharacteristic
173C2×C42×C47C2311yescharacteristic
174C4⋊C8×C47C2314yes—
175C4⋊C8×C47C2314yes—
176C22⋊C8×C47C2314yes—
177C22⋊C8×C47C2314yes—
178#97×C47C2314yes—
179C4×C8×C47C2314yes—
180C24×C47C2×D411yescharacteristic
181C23×D47—22no—
182C23×D47—22no—
183C22×C4×C47—24no—
184C22×C4×C47—24no—
185C22×C4×C47—42no—
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2411yescharacteristic
202C22×C4×C47C2411yescharacteristic
203C22×C4×C47C2411yescharacteristic
204C2×C22⋊D47—24no—
205C2×C22⋊D47—24no—
206C2×C22⋊D47—24no—
207C2×C22⋊D47—24no—
208C2×C22⋊D47—48no—
209C2×C22⋊D47—48no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212#10625350—216no—
213#10625350—48no—
214#10625350—48no—
215#10625350—48no—
216#10625350—48no—
217#10625350—48no—
218#10625350—48no—
219#10625350—48no—
220C2×D188—28no—
221C2×D188—22no—
222C2×D188—22no—
223C2×D188—22no—
224C2×D188—22no—
225C2×D188—22no—
226C2×D188—22no—
227C2×D188—22no—
228C2×D188—22no—
229C2×D188—22no—
230C2×D188—22no—
231C2×D188—44no—
232C2×D188—44no—
233C2×D188—44no—
234C2×D188—44no—
235C2×D188—44no—
236C2×D188C2414yes—
237C2×D188C2414yes—
238C2×C4×D47—24no—
239C2×C4×D47—24no—
240C2×C4×D47—24no—
241C2×C4×D47—24no—
242C2×C4×D47—48no—
243C2×C4×D47—48no—
244C2×Dic94—22no—
245C2×Dic94—22no—
246C2×Dic94—22no—
247C2×Dic94—44no—
248C2×Dic94—44no—
249C2×Dic94C2414yes—
250M16×C47—28no—
251C2×C8×C47C2418yes—
252C42×C47C2×D411yescharacteristic
253C42×C47C2×D411yescharacteristic
254C42×C47C2×D411yescharacteristic
255C42×C47C2×D411yescharacteristic
256C42×C47C2×D411yescharacteristic
257C42×C47C2×D411yescharacteristic
258C42×C47C2×D411yescharacteristic
259C42×C47C2×D411yescharacteristic
260C42×C47C2×D411yescharacteristic
261C42×C47C2×D411yescharacteristic
262C42×C47C2×D411yescharacteristic
263C42×C47C2×D411yescharacteristic
264C42×C47C2411yescharacteristic
265C42×C47C2411yescharacteristic
266C42×C47C2411yescharacteristic
267C42×C47C2411yescharacteristic
268(C2×D47)⋊C4—24no—
269(C2×D47)⋊C4—24no—
270(C2×D47)⋊C4—24no—
271(C2×D47)⋊C4—24no—
272(C2×D47)⋊C4—24no—
273(C2×D47)⋊C4—24no—
274(C2×D47)⋊C4—24no—
275(C2×D47)⋊C4—24no—
276C4⋊Dic47—22no—
277C4⋊Dic47—22no—
278C4⋊Dic47—22no—
279C4⋊Dic47—22no—
280C4⋊Dic47—22no—
281C4⋊Dic47—22no—
282C4⋊Dic47—22no—
283C4⋊Dic47C2414yes—
284D376—416no—
285#10625325—416no—
286C23×C47—22no—
287C23×C47—22no—
288C23×C47—41no—
289C23×C47C22×D411yescharacteristic
290C23×C47C22×D411yescharacteristic
291C23×C47C22×D411yescharacteristic
292C22×D47—24no—
293C22×D47—24no—
294C22×D47—44no—
295C22×D47—44no—
296C22×D47—44no—
297C22×D47—44no—
298C22×D47—44no—
299C22×D47—44no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47AGL(1,ℤ/8)14yescomplemented
317C2×C4×C47C22×D411yescharacteristic
318C2×C4×C47C22×D411yescharacteristic
319C2×C4×C47C22×D411yescharacteristic
320C2×C4×C47C22×D411yescharacteristic
321C2×C4×C47C22×D411yescharacteristic
322C2×C4×C47C22×D411yescharacteristic
323C2×C4×C47C22×D411yescharacteristic
324C2×C4×C47C22×D411yescharacteristic
325C2×C4×C47C22×D411yescharacteristic
326C2×C4×C47C22×D411yescharacteristic
327C2×C4×C47C22×D411yescharacteristic
328C2×C4×C47H(5,𝔽2)14yes—
329C2×C4×C47C2511yescharacteristic
330C22⋊D47—48no—
331C22⋊D47—48no—
332C22⋊D47—48no—
333C22⋊D47—48no—
334C2×Dic47—24no—
335C2×Dic47—24no—
336C2×Dic47—44no—
337C2×Dic47—44no—
338D188—28no—
339D188—28no—
340D188—44no—
341D188—44no—
342D188—44no—
343D188—44no—
344D188—44no—
345D188—44no—
346D188—44no—
347D188—44no—
348D188—44no—
349D188—44no—
350C4×D47—48no—
351C4×D47—48no—
352C4×D47—48no—
353C4×D47—48no—
354Dic94—28no—
355Dic94—44no—
356Dic94—44no—
357Dic94—44no—
358C8×C47—28no—
359#60803—471nomaximal, Sylow
360C22×C47—21no—
361C22×C47—21no—
362C22×C47—21no—
363C22×C47—21no—
364C22×C47—21no—
365C22×C47—21no—
366C22×C47—21no—
367C22×C47—44no—
368C22×C47#53512yes—
369C22×C47C2×AGL(1,ℤ/8)12yes—
370C22×C47C23×D411yescharacteristic
371C2×D47—44no—
372C2×D47—44no—
373C2×D47—44no—
374C2×D47—44no—
375C2×D47—44no—
376C2×D47—44no—
377C2×D47—88no—
378C2×D47—88no—
379C4×C47—21no—
380C4×C47—21no—
381C4×C47—21no—
382C4×C47—21no—
383C4×C47—21no—
384C4×C47—21no—
385C4×C47—21no—
386C4×C47#53512yes—
387C4×C47C2×AGL(1,ℤ/8)12yes—
388C4×C47C2×AGL(1,ℤ/8)12yes—
389C4×C47#57512yes—
390C4×C47C2×H(5,𝔽2)12yes—
391Dic47—44no—
392Dic47—44no—
393C2×#532—471no—
394C2×#532—471no—
395#3214—474no—
396#3213—474no—
397#3207—474no—
398#3206—472no—
399#3205—472no—
400#3151—472no—
401#3141—472no—
402#3036—474no—
403#3006—474no—
404#2920D4711yescharacteristic, complemented
405C2×C47—22no—
406C2×C47—22no—
407C2×C47—41no—
408C2×C47C2×#53511yescharacteristic
409C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
410C2×C47C2×#57511yescharacteristic
411D47—84no—
412D47—84no—
413C22×#41—472no—
414C22×#41—941no—
415C2×AGL(1,ℤ/8)—478no—
416#532—472no—
417#532—472no—
418#532—472no—
419#532—472no—
420#532—472no—
421#532—472no—
422#532—472no—
423#532—472no—
424#532—941no—
425#532—941no—
426#532—941no—
427#532—941no—
428#532—941no—
429#532—941no—
430#532—941no—
431#532—941no—
432C2×C4⋊Q8—471no—
433C2×C4⋊Q8—471no—
434C2×#127—471no—
435C2×#127—471no—
436C2×#124—472no—
437C2×#124—941no—
438C2×#121—472no—
439C2×#121—941no—
440C2×#121—941no—
441C2×#121—941no—
442C2×C4×D4—472no—
443C2×C4×D4—941no—
444C2×C4×D4—941no—
445C2×C4×D4—941no—
446C22×C42C2×D4711yescharacteristic
447#496—478no—
448#493—474no—
449#492—474no—
450#489—478no—
451#487—474no—
452#486—474no—
453#463—4716no—
454#461—478no—
455#459—478no—
456#449—4716no—
457#448—478no—
458#447—478no—
459#432C2×D4712yescomplemented
460#432C2×D4712yescomplemented
461#431C2×D4712yescomplemented
462#431C2×D4712yescomplemented
463#423C2×D4712yescomplemented
464#417—478no—
465#407C2×D4712yes—
466C4×M16C2×D4712yescomplemented
467C47#6080311yescharacteristic, complemented, Sylow
468C2×#41—474no—
469C2×#41—474no—
470C2×#41—942no—
471C2×#41—942no—
472C2×#41—942no—
473C2×#41—942no—
474C2×#41—942no—
475C2×#41—942no—
476C2×#41—1888no—
477C2×#41—1888no—
478C22×Q8—472no—
479C22×Q8—941no—
480C22×D4—472no—
481C22×D4—472no—
482C22×D4—942no—
483C22×D4—942no—
484C22×D4—941no—
485C22×D4—941no—
486C22×D4—941no—
487C22×D4—941no—
488C23×C4—942no—
489C23×C4—942no—
490C23×C4D18811yescharacteristic
491C23×C4D18811yescharacteristic
492C23×C4C22×D4711yescharacteristic
493AGL(1,ℤ/8)—18816no—
494C2×SD16—4716no—
495C2×D8—4716no—
496C2×M16C22×D4714yes—
497C4⋊Q8—472no—
498C4⋊Q8—472no—
499C4⋊Q8—472no—
500C4⋊Q8—472no—
501C4⋊Q8—941no—
502C4⋊Q8—941no—
503C4⋊Q8—941no—
504C4⋊Q8—941no—
505#127—472no—
506#127—472no—
507#127—472no—
508#127—472no—
509#127—941no—
510#127—941no—
511#127—941no—
512#127—941no—
513#124—474no—
514#124—474no—
515#124—942no—
516#124—942no—
517#124—942no—
518#124—942no—
519#124—942no—
520#124—942no—
521#121—474no—
522#121—474no—
523#121—942no—
524#121—942no—
525#121—942no—
526#121—942no—
527#121—942no—
528#121—942no—
529#121—942no—
530#121—942no—
531#121—942no—
532#121—942no—
533#121—942no—
534#121—942no—
535#121—942no—
536#121—942no—
537C4×D4—474no—
538C4×D4—474no—
539C4×D4—942no—
540C4×D4—942no—
541C4×D4—942no—
542C4×D4—942no—
543C4×D4—942no—
544C4×D4—942no—
545C4×D4—942no—
546C4×D4—942no—
547C4×D4—942no—
548C4×D4—942no—
549C4×D4—942no—
550C4×D4—942no—
551C4×D4—942no—
552C4×D4—942no—
553C2×C4⋊C4—472no—
554C2×C4⋊C4—941no—
555C2×C4⋊C4—941no—
556C2×C4⋊C4—941no—
557C2×C22⋊C4—942no—
558C2×C22⋊C4—942no—
559C2×C22⋊C4—942no—
560C2×C22⋊C4—942no—
561C2×C42D18811yescharacteristic
562C2×C42D18811yescharacteristic
563C2×C42D18811yescharacteristic
564C2×C42D18811yescharacteristic
565C2×C42D18811yescharacteristic
566C2×C42D18811yescharacteristic
567C2×C42C22×D4711yescharacteristic
568C2×C42C22×D4711yescharacteristic
569C2×C42C22×D4711yescharacteristic
570C2×C42C22×D4711yescharacteristic
571C2×C42C22×D4711yescharacteristic
572C2×C42C22×D4711yescharacteristic
573C4⋊C8C22×D4714yes—
574C4⋊C8C22×D4714yes—
575#103—4716no—
576#102—4716no—
577C22⋊C8C22×D4714yes—
578C22⋊C8C22×D4714yes—
579#97C22×D4714yes—
580C4×C8C22×D4714yes—
581C24—942no—
582C24—942no—
583C24C2×D18811yescharacteristic
584#41—9416no—
585#41—1888no—
586#41—1888no—
587#41—1888no—
588#41—1888no—
589#41—1888no—
590#41—1888no—
591#41—1888no—
592C2×Q8—474no—
593C2×Q8—942no—
594C2×Q8—942no—
595C2×Q8—942no—
596C2×Q8—1884no—
597C2×Q8—1884no—
598C2×D4—474no—
599C2×D4—474no—
600C2×D4—944no—
601C2×D4—944no—
602C2×D4—944no—
603C2×D4—944no—
604C2×D4—942no—
605C2×D4—942no—
606C2×D4—942no—
607C2×D4—942no—
608C2×D4—942no—
609C2×D4—942no—
610C2×D4—942no—
611C2×D4—942no—
612C2×D4—942no—
613C2×D4—942no—
614C2×D4—948no—
615C2×D4—1884no—
616C2×D4—1884no—
617C2×D4—1884no—
618C2×D4—1884no—
619C2×D4—1888no—
620C2×D4—1888no—
621C2×D4—1884no—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—42no—
625C22×C4—942no—
626C22×C4—942no—
627C22×C4—944no—
628C22×C4—944no—
629C22×C4—944no—
630C22×C4—944no—
631C22×C4—1888no—
632C22×C4—1888no—
633C22×C4C2×D18811yescharacteristic
634C22×C4C2×D18811yescharacteristic
635C22×C4C2×D18811yescharacteristic
636C22×C4C2×D18811yescharacteristic
637C22×C4C2×D18811yescharacteristic
638C22×C4C2×D18811yescharacteristic
639C22×C4C2×D18811yescharacteristic
640C22×C4C2×D18811yescharacteristic
641C22×C4C2×D18811yescharacteristic
642C22×C4C2×D18811yescharacteristic
643C22×C4C2×D18811yescharacteristic
644C22×C4C2×D18811yescharacteristic
645C22×C4C2×D18811yescharacteristic
646C22×C4C2×D18811yescharacteristic
647C22×C4C2×D18811yescharacteristic
648C22×C4C23×D4711yescharacteristic
649C22×C4C23×D4711yescharacteristic
650C22×C4C23×D4711yescharacteristic
651SD16—18816no—
652D8—18816no—
653M16—28no—
654C2×C8C23×D4718yes—
655C4⋊C4—474no—
656C4⋊C4—942no—
657C4⋊C4—942no—
658C4⋊C4—942no—
659C4⋊C4—942no—
660C4⋊C4—942no—
661C4⋊C4—942no—
662C4⋊C4—942no—
663C22⋊C4—944no—
664C22⋊C4—944no—
665C22⋊C4—944no—
666C22⋊C4—944no—
667C22⋊C4—944no—
668C22⋊C4—944no—
669C22⋊C4—944no—
670C22⋊C4—944no—
671C42C2×D18811yescharacteristic
672C42C2×D18811yescharacteristic
673C42C2×D18811yescharacteristic
674C42C2×D18811yescharacteristic
675C42C2×D18811yescharacteristic
676C42C2×D18811yescharacteristic
677C42C2×D18811yescharacteristic
678C42C2×D18811yescharacteristic
679C42C2×D18811yescharacteristic
680C42C2×D18811yescharacteristic
681C42C2×D18811yescharacteristic
682C42C2×D18811yescharacteristic
683C42C23×D4711yescharacteristic
684C42C23×D4711yescharacteristic
685C42C23×D4711yescharacteristic
686C42C23×D4711yescharacteristic
687C23—22no—
688C23—22no—
689C23—41no—
690C23—944no—
691C23—944no—
692C23—1884no—
693C23—1884no—
694C23—1884no—
695C23—1884no—
696C23—1884no—
697C23—1884no—
698C23C22×D18811yescharacteristic
699C23C22×D18811yescharacteristic
700C23C22×D18811yescharacteristic
701Q8—948no—
702Q8—1884no—
703Q8—1884no—
704Q8—1884no—
705D4—948no—
706D4—948no—
707D4—1884no—
708D4—1884no—
709D4—1884no—
710D4—1884no—
711D4—1888no—
712D4—1888no—
713D4—1888no—
714D4—1888no—
715D4—1884no—
716D4—1884no—
717D4—1884no—
718D4—1884no—
719D4—1884no—
720D4—1884no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—944no—
738C2×C4—944no—
739C2×C4—1888no—
740C2×C4—1888no—
741C2×C4—1884no—
742C2×C4—1884no—
743C2×C4—1888no—
744C2×C4—1888no—
745C2×C4#1309405214yescomplemented
746C2×C4C22×D18811yescharacteristic
747C2×C4C22×D18811yescharacteristic
748C2×C4C22×D18811yescharacteristic
749C2×C4C22×D18811yescharacteristic
750C2×C4C22×D18811yescharacteristic
751C2×C4C22×D18811yescharacteristic
752C2×C4C22×D18811yescharacteristic
753C2×C4C22×D18811yescharacteristic
754C2×C4C22×D18811yescharacteristic
755C2×C4C22×D18811yescharacteristic
756C2×C4C22×D18811yescharacteristic
757C2×C4#1309407014yes—
758C2×C4C24×D4711yescharacteristic
759C8—28no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—44no—
768C22—3768no—
769C22—3768no—
770C22—1884no—
771C22—1884no—
772C22—1884no—
773C22—1884no—
774C22—1884no—
775C22—1884no—
776C22#1568969212yes—
777C22C2×#1309405212yes—
778C22C23×D18811yescharacteristic
779C4—21no—
780C4—21no—
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—21no—
786C4—1884no—
787C4—1884no—
788C4#1568969212yes—
789C4C2×#1309405212yes—
790C4C2×#1309405212yes—
791C4#1568992312yes—
792C4C2×#1309407012yes—
793C2—22no—
794C2—22no—
795C2—41no—
796C2—3764no—
797C2—3764no—
798C2C2×#1568969211yescharacteristic
799C2C22×#1309405211yescharacteristic
800C2C2×#1568992311yescharacteristic
subgroupG/H
centerC22C23×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#2920C2
socleC22×C47C23×D4
hypercenter#2920D47
hypocenterC47#60803
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
1. C2×#15689673C2semidirect
2. C2×#15689673C2semidirect
3. #20254385C2semidirect
4. #20254377C2semidirect
5. #20254323C2semidirect
6. #20254315C2semidirect
7. #20254308C2semidirect
8. #20253840C2semidirect
9. #20253782C2semidirect
10. #20252854C2semidirect
11. #20252642C2semidirect
12. C47×#2920C2semidirect
15. C2×#13094052C22semidirect
28. #15689673C22semidirect
29. #15689673C22semidirect
30. #15689673C22semidirect
31. #15689673C22semidirect
32. C2×#13094024C22semidirect
33. C2×#13094024C22semidirect
34. C2×#13094021C22semidirect
35. C2×#13094021C22semidirect
37. C2×#13094012C22semidirect
45. C2×C4×D188C22semidirect
46. #15689512C22semidirect
47. #15689500C22semidirect
48. #15689496C22semidirect
49. #15689483C22semidirect
50. #15689474C22semidirect
51. #15689470C22semidirect
52. #15689339C22semidirect
53. #15689329C22semidirect
54. #15689319C22semidirect
55. #15689270C22semidirect
56. #15689264C22semidirect
57. #15689259C22semidirect
58. #15689125C22semidirect
60. C47×#432C22semidirect
61. C47×#432C22semidirect
62. C47×#431C22semidirect
63. C47×#431C22semidirect
64. C47×#423C22semidirect
66. C4×M16×C47C22semidirect
316. C2×C4×C47AGL(1,ℤ/8)semidirect
404. #2920D47semidirect
459. #432C2×D47semidirect
460. #432C2×D47semidirect
461. #431C2×D47semidirect
462. #431C2×D47semidirect
463. #423C2×D47semidirect
466. C4×M16C2×D47semidirect
467. C47#60803semidirect
745. C2×C4#13094052semidirect

Maximal subgroups

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

subgroupindex
C2×#156896732
#202543852
#202543772
#202543232
#202543152
#202543082
#202538402
#202537822
#202528542
#202526422
C47×#29202
#6080347