Finite Group Databasebeta

← #27087023

Subgroups — #27087023

Order 12032.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic, complemented
2C22×#13093998C211yesmaximal, characteristic, complemented
3#20254204C214yesmaximal, complemented
4#20254195C212yesmaximal, complemented
5#20254188C212yesmaximal, complemented
6#20254155C214yesmaximal, complemented
7#20254146C212yesmaximal, complemented
8#20254139C212yesmaximal, complemented
9#20253329C212yesmaximal, complemented
10#20253313C212yesmaximal, complemented
11#20253007C214yesmaximal, complemented
12#20252642C212yesmaximal, complemented
13#20252618C212yesmaximal, complemented
14C2×C47×#407C211yesmaximal, characteristic, complemented
15C22×#10625350C2211yescharacteristic, complemented
16C23×D188C2211yescharacteristic, complemented
17C23×C22⋊D47—21no—
18C2×#13094052C2214yescomplemented
19#15689634—21no—
20#15689634—21no—
21#15689634—21no—
22#15689634—21no—
23#15689634C2212yes—
24#15689634C2212yescomplemented
25#15689634C2212yescomplemented
26#15689634C2212yescomplemented
27C2×#13094007—21no—
28C2×#13094003C2211yescharacteristic, complemented
29C2×#13094003C2211yescharacteristic, complemented
30C2×#13093998—21no—
31C2×#13093998—21no—
32C2×#13093998—21no—
33C2×#13093998—21no—
34C2×#13093998—21no—
35C2×#13093998—21no—
36C2×#13093998C2212yes—
37C2×#13093998C2212yes—
38C2×#13093998C2212yes—
39C2×#13093998C2212yescomplemented
40C2×#13093998C2212yescomplemented
41C2×#13093998C2212yescomplemented
42C2×#13093998C2211yescharacteristic, complemented
43C2×#13093998C2211yescharacteristic, complemented
44C2×#13093993—21no—
45C2×C4×C22⋊D47—21no—
46C2×C4×C22⋊D47—21no—
47C2×#13093983C2211yescharacteristic, complemented
48C22×C4⋊Dic47C2211yescharacteristic, complemented
49C22×(C2×D47)⋊C4—21no—
50#15689459C2214yescomplemented
51#15689454C2214yescomplemented
52#15689448C2218yescomplemented
53#15689442C2214yescomplemented
54#15689442C2214yescomplemented
55#15689437C2214yescomplemented
56#15689437C2214yescomplemented
57#15689376C2218yescomplemented
58#15689369C2218yescomplemented
59#15689359C2218yescomplemented
60#15689352C2218yescomplemented
61#15689276C2214yescomplemented
62#15689276C2214yescomplemented
63#15689270C2218yescomplemented
64#15689264C2214yescomplemented
65#15689259C2214yescomplemented
66#15689259C2214yescomplemented
67#15689259C2214yescomplemented
68#15689165C2214yescomplemented
69#15689129C2214yescomplemented
70#15689125C2214yescomplemented
71C24×C4×C47C2211yescharacteristic
72C22×M16×C47C2212yescomplemented
73C47×#407C2212yescomplemented
74C47×#407C2212yescomplemented
75C47×#407C2212yescomplemented
76C47×#407C2212yescomplemented
77C2×C22⋊C8×C47C2212yescomplemented
78C2×C22⋊C8×C47C2212yescomplemented
79C24×D47—21no—
80C2×#10625350—21no—
81C2×#10625350—21no—
82C2×#10625350—44no—
83C2×#10625350C2312yes—
84C2×#10625350C2312yescomplemented
85C22×Dic94C2311yescharacteristic, complemented
86C22×D188—21no—
87C22×D188—21no—
88C22×D188—21no—
89C22×D188—44no—
90C22×D188C2312yes—
91C22×D188C2312yes—
92C22×D188C2312yes—
93C22×D188C2311yescharacteristic, complemented
94C22×C22⋊D47—21no—
95C22×C22⋊D47—21no—
96C22×C22⋊D47—21no—
97C22×C22⋊D47—22no—
98C22×C22⋊D47—22no—
99C22×C22⋊D47—22no—
100C22×C22⋊D47—22no—
101C22×C22⋊D47—22no—
102C22×C22⋊D47—22no—
103C22×C22⋊D47—48no—
104C23×Dic47—21no—
105C22×C4×D47—21no—
106#13094052—48no—
107C2×#10625325C2318yescomplemented
108C2×D376C2318yescomplemented
109#13094007—22no—
110#13094007—22no—
111#13094007—22no—
112#13094007—22no—
113#13094003—21no—
114#13094003—21no—
115#13094003—21no—
116#13094003—21no—
117#13094003C2312yes—
118#13094003C2312yes—
119#13094003C2312yescomplemented
120#13094003C2312yescomplemented
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#13093998—22no—
131#13093998—22no—
132#13093998—22no—
133#13093998—21no—
134#13093998—21no—
135#13093998—21no—
136#13093998—21no—
137#13093998C2312yes—
138#13093998C2312yes—
139#13093998C2314yes—
140#13093998C2314yes—
141#13093998C2314yes—
142#13093998C2314yes—
143#13093998C2312yescomplemented
144#13093998C2312yescomplemented
145#13093993—22no—
146#13093993—22no—
147#13093993—22no—
148#13093993—22no—
149C4×C22⋊D47—22no—
150C4×C22⋊D47—22no—
151C4×C22⋊D47—22no—
152C4×C22⋊D47—22no—
153C4×C22⋊D47—22no—
154C4×C22⋊D47—22no—
155C4×C22⋊D47—22no—
156C4×C22⋊D47—22no—
157#13093983—21no—
158#13093983—21no—
159#13093983C2312yes—
160#13093983C2312yescomplemented
161C2×C4⋊Dic47—21no—
162C2×C4⋊Dic47—21no—
163C2×C4⋊Dic47—21no—
164C2×C4⋊Dic47C2312yes—
165C2×C4⋊Dic47C2312yes—
166C2×C4⋊Dic47C2312yes—
167C2×C4⋊Dic47C2311yescharacteristic, complemented
168C2×C4⋊Dic47C2311yescharacteristic, complemented
169C2×Dic47⋊C4—21no—
170C2×Dic47⋊C4—21no—
171C2×C22⋊Dic47—21no—
172C2×C22⋊Dic47—21no—
173C2×C22⋊Dic47—21no—
174C2×(C2×D47)⋊C4—22no—
175C2×(C2×D47)⋊C4—22no—
176C2×(C2×D47)⋊C4—22no—
177C2×(C2×D47)⋊C4—22no—
178C2×(C2×D47)⋊C4—22no—
179C2×(C2×D47)⋊C4—22no—
180C2×(C2×D47)⋊C4—21no—
181C2×(C2×D47)⋊C4—21no—
182C2×C4×Dic47—21no—
183#13093958C2318yescomplemented
184#13093956C2318yescomplemented
185#13093949C2318yescomplemented
186#13093946C2318yescomplemented
187#13093946C2318yescomplemented
188#13093946C2318yescomplemented
189C25×C47D411yescharacteristic
190C23×C4×C47—44no—
191C23×C4×C47D411yescharacteristic
192C23×C4×C47D411yescharacteristic
193C23×C4×C47D411yescharacteristic
194C23×C4×C47D411yescharacteristic
195C23×C4×C47D411yescharacteristic
196C23×C4×C47D411yescharacteristic
197C23×C4×C47D411yescharacteristic
198C23×C4×C47C2311yescharacteristic
199C23×C4×C47C2311yescharacteristic
200C23×C4×C47C2311yescharacteristic
201C23×C4×C47C2311yescharacteristic
202C23×C4×C47C2311yescharacteristic
203C23×C4×C47C2311yescharacteristic
204C23×C4×C47C2311yescharacteristic
205C2×M16×C47—44no—
206C2×M16×C47C2314yes—
207C2×M16×C47C2314yescomplemented
208C22×C8×C47C2314yescomplemented
209C22⋊C8×C47C2314yes—
210C22⋊C8×C47C2314yes—
211C22⋊C8×C47C2314yescomplemented
212C22⋊C8×C47C2314yescomplemented
213C24×C47—24no—
214C24×C47—42no—
215C24×C47—42no—
216C24×C47C2×D411yescharacteristic
217C24×C47C2×D411yescharacteristic
218C24×C47C2×D411yescharacteristic
219C24×C47C2×D411yescharacteristic
220C24×C47C2×D411yescharacteristic
221C24×C47C2×D411yescharacteristic
222C24×C47C2×D411yescharacteristic
223C23×D47—21no—
224C23×D47—22no—
225C23×D47—22no—
226C23×D47—22no—
227C23×D47—44no—
228C23×D47—44no—
229C23×D47—44no—
230C22×C4×C47—24no—
231C22×C4×C47—24no—
232C22×C4×C47—24no—
233C22×C4×C47—42no—
234C22×C4×C47—42no—
235C22×C4×C47—42no—
236C22×C4×C47—42no—
237C22×C4×C47—42no—
238C22×C4×C47—42no—
239C22×C4×C47—42no—
240C22×C4×C47—42no—
241C22×C4×C47—42no—
242C22×C4×C47—42no—
243C22×C4×C47—42no—
244C22×C4×C47C2×D411yescharacteristic
245C22×C4×C47C2×D411yescharacteristic
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47C2×D411yescharacteristic
248C22×C4×C47C2×D411yescharacteristic
249C22×C4×C47C2×D411yescharacteristic
250C22×C4×C47C2×D411yescharacteristic
251C22×C4×C47C2×D411yescharacteristic
252C22×C4×C47C2×D411yescharacteristic
253C22×C4×C47C2×D411yescharacteristic
254C22×C4×C47C2×D411yescharacteristic
255C22×C4×C47C2×D411yescharacteristic
256C22×C4×C47C2×D411yescharacteristic
257C22×C4×C47C2×D411yescharacteristic
258C22×C4×C47C2×D411yescharacteristic
259C22×C4×C47C2×D411yescharacteristic
260C22×C4×C47C2×D411yescharacteristic
261C22×C4×C47C2×D411yescharacteristic
262C22×C4×C47C2×D411yescharacteristic
263C22×C4×C47C2×D411yescharacteristic
264C22×C4×C47C2×D411yescharacteristic
265C22×C4×C47C2411yescharacteristic
266C22×C4×C47C2411yescharacteristic
267C22×C4×C47C2411yescharacteristic
268C22×C4×C47C2411yescharacteristic
269C22×C4×C47C2411yescharacteristic
270C22×C4×C47C2411yescharacteristic
271C22×C4×C47C2411yescharacteristic
272C2×C22⋊D47—22no—
273C2×C22⋊D47—22no—
274C2×C22⋊D47—22no—
275C2×C22⋊D47—22no—
276C2×C22⋊D47—22no—
277C2×C22⋊D47—22no—
278C2×C22⋊D47—24no—
279C2×C22⋊D47—24no—
280C2×C22⋊D47—24no—
281C2×C22⋊D47—24no—
282C2×C22⋊D47—44no—
283C2×C22⋊D47—48no—
284C2×C22⋊D47—48no—
285C2×C22⋊D47—48no—
286C2×C22⋊D47—48no—
287C2×C22⋊D47—48no—
288C2×C22⋊D47—44no—
289C2×C22⋊D47—44no—
290C2×C22⋊D47—48no—
291C22×Dic47—21no—
292C22×Dic47—21no—
293C22×Dic47—22no—
294C22×Dic47—22no—
295C22×Dic47—22no—
296C22×Dic47—21no—
297C22×Dic47—44no—
298#10625350—28no—
299#10625350—44no—
300#10625350—44no—
301#10625350—44no—
302C2×D188—28no—
303C2×D188—22no—
304C2×D188—22no—
305C2×D188—22no—
306C2×D188—21no—
307C2×D188—44no—
308C2×D188—44no—
309C2×D188—42no—
310C2×D188—44no—
311C2×D188—44no—
312C2×D188—44no—
313C2×D188C2414yes—
314C2×D188C2412yes—
315C2×C4×D47—22no—
316C2×C4×D47—22no—
317C2×C4×D47—44no—
318C2×Dic94—21no—
319C2×Dic94—42no—
320C2×Dic94C2412yes—
321M16×C47—28no—
322M16×C47—44no—
323C2×C8×C47—44no—
324C2×C8×C47C2418yes—
325C22⋊Dic47—22no—
326C22⋊Dic47—22no—
327C22⋊Dic47—22no—
328C22⋊Dic47—22no—
329C22⋊Dic47—22no—
330C22⋊Dic47—22no—
331(C2×D47)⋊C4—24no—
332(C2×D47)⋊C4—24no—
333(C2×D47)⋊C4—24no—
334(C2×D47)⋊C4—24no—
335(C2×D47)⋊C4—22no—
336(C2×D47)⋊C4—22no—
337(C2×D47)⋊C4—22no—
338(C2×D47)⋊C4—22no—
339C4⋊Dic47—22no—
340C4⋊Dic47—22no—
341C4⋊Dic47—22no—
342C4⋊Dic47—21no—
343C4⋊Dic47—21no—
344C4⋊Dic47C2412yes—
345C4⋊Dic47C2412yes—
346C4⋊Dic47C2414yes—
347Dic47⋊C4—22no—
348Dic47⋊C4—22no—
349Dic47⋊C4—22no—
350Dic47⋊C4—22no—
351C4×Dic47—22no—
352C4×Dic47—22no—
353D376—48no—
354#10625325—48no—
355C23×C47—22no—
356C23×C47—22no—
357C23×C47—22no—
358C23×C47—22no—
359C23×C47—22no—
360C23×C47—22no—
361C23×C47—22no—
362C23×C47—22no—
363C23×C47—22no—
364C23×C47—22no—
365C23×C47—22no—
366C23×C47—22no—
367C23×C47—41no—
368C23×C47—41no—
369C23×C47—41no—
370C23×C47—41no—
371C23×C47—41no—
372C23×C47—41no—
373C23×C47—41no—
374C23×C47—41no—
375C23×C47—416no—
376C23×C47AGL(1,ℤ/8)14yescomplemented
377C23×C47C22×D411yescharacteristic
378C23×C47C22×D411yescharacteristic
379C23×C47C22×D411yescharacteristic
380C23×C47C22×D411yescharacteristic
381C23×C47C22×D411yescharacteristic
382C23×C47C22×D411yescharacteristic
383C23×C47C22×D411yescharacteristic
384C22×D47—22no—
385C22×D47—24no—
386C22×D47—42no—
387C22×D47—44no—
388C22×D47—44no—
389C22×D47—44no—
390C22×D47—44no—
391C22×D47—42no—
392C22×D47—44no—
393C22×D47—44no—
394C22×D47—44no—
395C22×D47—44no—
396C22×D47—42no—
397C22×D47—44no—
398C22×D47—816no—
399C2×C4×C47—22no—
400C2×C4×C47—22no—
401C2×C4×C47—22no—
402C2×C4×C47—22no—
403C2×C4×C47—22no—
404C2×C4×C47—22no—
405C2×C4×C47—22no—
406C2×C4×C47—22no—
407C2×C4×C47—22no—
408C2×C4×C47—22no—
409C2×C4×C47—22no—
410C2×C4×C47—22no—
411C2×C4×C47—22no—
412C2×C4×C47—22no—
413C2×C4×C47—22no—
414C2×C4×C47—41no—
415C2×C4×C47—41no—
416C2×C4×C47—41no—
417C2×C4×C47—41no—
418C2×C4×C47—41no—
419C2×C4×C47—41no—
420C2×C4×C47—41no—
421C2×C4×C47—41no—
422C2×C4×C47—41no—
423C2×C4×C47—41no—
424C2×C4×C47—41no—
425C2×C4×C47—41no—
426C2×C4×C47C22×D411yescharacteristic
427C2×C4×C47C22×D411yescharacteristic
428C2×C4×C47C22×D411yescharacteristic
429C2×C4×C47C22×D411yescharacteristic
430C2×C4×C47C22×D411yescharacteristic
431C2×C4×C47C22×D411yescharacteristic
432C2×C4×C47C22×D411yescharacteristic
433C2×C4×C47H(5,𝔽2)14yes—
434C2×C4×C47C2511yescharacteristic
435C22⋊D47—44no—
436C22⋊D47—44no—
437C22⋊D47—48no—
438C22⋊D47—48no—
439C22⋊D47—44no—
440C22⋊D47—44no—
441C22⋊D47—44no—
442C22⋊D47—48no—
443C22⋊D47—48no—
444C22⋊D47—44no—
445C2×Dic47—22no—
446C2×Dic47—22no—
447C2×Dic47—22no—
448C2×Dic47—24no—
449C2×Dic47—42no—
450C2×Dic47—44no—
451C2×Dic47—44no—
452C2×Dic47—42no—
453C2×Dic47—44no—
454C2×Dic47—42no—
455D188—28no—
456D188—24no—
457D188—44no—
458D188—44no—
459D188—42no—
460D188—44no—
461C4×D47—44no—
462C4×D47—44no—
463Dic94—24no—
464Dic94—42no—
465C8×C47—28no—
466#60750—471nomaximal, Sylow
467C22×C47—28no—
468C22×C47—21no—
469C22×C47—21no—
470C22×C47—21no—
471C22×C47—21no—
472C22×C47—21no—
473C22×C47—21no—
474C22×C47—21no—
475C22×C47—21no—
476C22×C47—21no—
477C22×C47—21no—
478C22×C47—21no—
479C22×C47—21no—
480C22×C47—21no—
481C22×C47—21no—
482C22×C47—21no—
483C22×C47—21no—
484C22×C47—44no—
485C22×C47—44no—
486C22×C47—44no—
487C22×C47—44no—
488C22×C47—44no—
489C22×C47—44no—
490C22×C47#53412yes—
491C22×C47C2×AGL(1,ℤ/8)12yes—
492C22×C47C2×AGL(1,ℤ/8)12yes—
493C22×C47C2×AGL(1,ℤ/8)12yes—
494C22×C47#57512yes—
495C22×C47C23×D411yescharacteristic
496C2×D47—42no—
497C2×D47—44no—
498C2×D47—44no—
499C2×D47—42no—
500C2×D47—42no—
501C2×D47—44no—
502C2×D47—84no—
503C2×D47—88no—
504C2×D47—88no—
505C2×D47—88no—
506C4×C47—21no—
507C4×C47—21no—
508C4×C47—21no—
509C4×C47—21no—
510C4×C47—21no—
511C4×C47—21no—
512C4×C47#53412yes—
513C4×C47C2×H(5,𝔽2)12yes—
514Dic47—42no—
515Dic47—44no—
516Dic47—42no—
517Dic47—42no—
518C2×#525—471no—
519C22×#121—471no—
520#3194—474no—
521#3193—472no—
522#3192—472no—
523#3188—474no—
524#3187—472no—
525#3186—472no—
526#3094—472no—
527#3092—472no—
528#3055—474no—
529#3006—472no—
530#3003—472no—
531C2×#407D4711yescharacteristic, complemented
532C2×C47—22no—
533C2×C47—22no—
534C2×C47—22no—
535C2×C47—22no—
536C2×C47—22no—
537C2×C47—41no—
538C2×C47—41no—
539C2×C47C2×#53411yescharacteristic
540C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
541C2×C47C2×#57511yescharacteristic
542D47—82no—
543D47—84no—
544C22×#41—471no—
545C23×D4—471no—
546C23×D4—941no—
547C24×C4C2×D4711yescharacteristic
548C2×AGL(1,ℤ/8)—474no—
549C22×M16C2×D4712yescomplemented
550#525—472no—
551#525—472no—
552#525—472no—
553#525—472no—
554#525—941no—
555#525—941no—
556#525—941no—
557#525—941no—
558C2×#123—941no—
559C2×C22⋊Q8—471no—
560C2×C22⋊Q8—471no—
561C2×#121—472no—
562C2×#121—472no—
563C2×#121—472no—
564C2×#121—472no—
565C2×#121—472no—
566C2×#121—472no—
567C2×#121—471no—
568C2×#121—471no—
569C2×#121—941no—
570C2×#121—941no—
571C2×#121—941no—
572C2×#121—941no—
573C2×#121—941no—
574C2×#121—941no—
575C2×#120—941no—
576C2×C4×D4—941no—
577C2×C4×D4—941no—
578C2×#117—471no—
579C22×C4⋊C4—471no—
580C22×C22⋊C4—941no—
581#484—474no—
582#483—474no—
583#482—478no—
584#481—474no—
585#481—474no—
586#480—474no—
587#480—474no—
588#469—478no—
589#468—478no—
590#466—478no—
591#465—478no—
592#450—474no—
593#450—474no—
594#449—478no—
595#448—474no—
596#447—474no—
597#447—474no—
598#447—474no—
599#428—474no—
600#418—474no—
601#417—474no—
602#407C2×D4712yescomplemented
603#407C2×D4712yescomplemented
604#407C2×D4712yescomplemented
605#407C2×D4712yescomplemented
606C2×C22⋊C8C2×D4712yescomplemented
607C2×C22⋊C8C2×D4712yescomplemented
608C47#6075011yescharacteristic, complemented, Sylow
609C25—941no—
610C25D18811yescharacteristic
611C2×#41—472no—
612C2×#41—472no—
613C2×#41—941no—
614C2×#41—941no—
615C2×#41—1884no—
616C22×Q8—471no—
617C22×D4—472no—
618C22×D4—472no—
619C22×D4—472no—
620C22×D4—471no—
621C22×D4—941no—
622C22×D4—941no—
623C22×D4—941no—
624C22×D4—942no—
625C22×D4—942no—
626C22×D4—942no—
627C22×D4—942no—
628C22×D4—942no—
629C22×D4—942no—
630C22×D4—941no—
631C22×D4—941no—
632C22×D4—941no—
633C22×D4—1884no—
634C22×D4—1888no—
635C23×C4—44no—
636C23×C4—941no—
637C23×C4—941no—
638C23×C4D18811yescharacteristic
639C23×C4D18811yescharacteristic
640C23×C4D18811yescharacteristic
641C23×C4D18811yescharacteristic
642C23×C4D18811yescharacteristic
643C23×C4D18811yescharacteristic
644C23×C4D18811yescharacteristic
645C23×C4C22×D4711yescharacteristic
646C23×C4C22×D4711yescharacteristic
647C23×C4C22×D4711yescharacteristic
648C23×C4C22×D4711yescharacteristic
649C23×C4C22×D4711yescharacteristic
650C23×C4C22×D4711yescharacteristic
651C23×C4C22×D4711yescharacteristic
652AGL(1,ℤ/8)—1888no—
653C2×SD16—478no—
654C2×D8—478no—
655C2×M16—44no—
656C2×M16C22×D4714yes—
657C2×M16C22×D4714yescomplemented
658C22×C8C22×D4714yescomplemented
659#123—942no—
660#123—942no—
661#123—942no—
662#123—942no—
663C22⋊Q8—472no—
664C22⋊Q8—472no—
665C22⋊Q8—472no—
666C22⋊Q8—472no—
667C22⋊Q8—941no—
668C22⋊Q8—941no—
669C22⋊Q8—941no—
670C22⋊Q8—941no—
671#121—474no—
672#121—474no—
673#121—474no—
674#121—474no—
675#121—472no—
676#121—472no—
677#121—472no—
678#121—472no—
679#121—942no—
680#121—942no—
681#121—942no—
682#121—942no—
683#121—942no—
684#121—942no—
685#121—942no—
686#121—942no—
687#121—942no—
688#121—942no—
689#121—942no—
690#121—942no—
691#121—941no—
692#121—941no—
693#121—941no—
694#121—941no—
695#120—942no—
696#120—942no—
697#120—942no—
698#120—942no—
699C4×D4—942no—
700C4×D4—942no—
701C4×D4—942no—
702C4×D4—942no—
703C4×D4—942no—
704C4×D4—942no—
705C4×D4—942no—
706C4×D4—942no—
707#117—472no—
708#117—472no—
709#117—941no—
710#117—941no—
711C2×C4⋊C4—472no—
712C2×C4⋊C4—472no—
713C2×C4⋊C4—472no—
714C2×C4⋊C4—471no—
715C2×C4⋊C4—471no—
716C2×C4⋊C4—941no—
717C2×C4⋊C4—941no—
718C2×C4⋊C4—941no—
719C2×C4⋊C4—941no—
720C2×C4⋊C4—941no—
721C2×C22⋊C4—941no—
722C2×C22⋊C4—941no—
723C2×C22⋊C4—941no—
724C2×C22⋊C4—942no—
725C2×C22⋊C4—942no—
726C2×C22⋊C4—942no—
727C2×C22⋊C4—942no—
728C2×C22⋊C4—942no—
729C2×C22⋊C4—942no—
730C2×C22⋊C4—941no—
731C2×C22⋊C4—941no—
732C2×C42—941no—
733#107—478no—
734#106—478no—
735#103—478no—
736#102—478no—
737#102—478no—
738#102—478no—
739C22⋊C8C22×D4714yes—
740C22⋊C8C22×D4714yes—
741C22⋊C8C22×D4714yescomplemented
742C22⋊C8C22×D4714yescomplemented
743C24—24no—
744C24—42no—
745C24—42no—
746C24—941no—
747C24—942no—
748C24—942no—
749C24—942no—
750C24—1884no—
751C24—1884no—
752C24—1884no—
753C24C2×D18811yescharacteristic
754C24C2×D18811yescharacteristic
755C24C2×D18811yescharacteristic
756C24C2×D18811yescharacteristic
757C24C2×D18811yescharacteristic
758C24C2×D18811yescharacteristic
759C24C2×D18811yescharacteristic
760#41—948no—
761#41—1884no—
762#41—1884no—
763#41—1884no—
764C2×Q8—472no—
765C2×Q8—941no—
766C2×Q8—1882no—
767C2×D4—472no—
768C2×D4—474no—
769C2×D4—942no—
770C2×D4—942no—
771C2×D4—942no—
772C2×D4—942no—
773C2×D4—942no—
774C2×D4—942no—
775C2×D4—944no—
776C2×D4—944no—
777C2×D4—944no—
778C2×D4—944no—
779C2×D4—942no—
780C2×D4—942no—
781C2×D4—942no—
782C2×D4—941no—
783C2×D4—948no—
784C2×D4—1884no—
785C2×D4—1884no—
786C2×D4—1882no—
787C2×D4—1884no—
788C2×D4—1884no—
789C2×D4—1884no—
790C2×D4—1884no—
791C2×D4—1888no—
792C2×D4—1888no—
793C2×D4—1888no—
794C2×D4—1888no—
795C2×D4—1888no—
796C2×D4—1884no—
797C2×D4—1884no—
798C2×D4—1888no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—941no—
814C22×C4—941no—
815C22×C4—942no—
816C22×C4—942no—
817C22×C4—942no—
818C22×C4—941no—
819C22×C4—942no—
820C22×C4—942no—
821C22×C4—1884no—
822C22×C4—1884no—
823C22×C4C2×D18811yescharacteristic
824C22×C4C2×D18811yescharacteristic
825C22×C4C2×D18811yescharacteristic
826C22×C4C2×D18811yescharacteristic
827C22×C4C2×D18811yescharacteristic
828C22×C4C2×D18811yescharacteristic
829C22×C4C2×D18811yescharacteristic
830C22×C4C2×D18811yescharacteristic
831C22×C4C2×D18811yescharacteristic
832C22×C4C2×D18811yescharacteristic
833C22×C4C2×D18811yescharacteristic
834C22×C4C2×D18811yescharacteristic
835C22×C4C2×D18811yescharacteristic
836C22×C4C2×D18811yescharacteristic
837C22×C4C2×D18811yescharacteristic
838C22×C4C2×D18811yescharacteristic
839C22×C4C2×D18811yescharacteristic
840C22×C4C2×D18811yescharacteristic
841C22×C4C2×D18811yescharacteristic
842C22×C4C2×D18811yescharacteristic
843C22×C4C2×D18811yescharacteristic
844C22×C4C23×D4711yescharacteristic
845C22×C4C23×D4711yescharacteristic
846C22×C4C23×D4711yescharacteristic
847C22×C4C23×D4711yescharacteristic
848C22×C4C23×D4711yescharacteristic
849C22×C4C23×D4711yescharacteristic
850C22×C4C23×D4711yescharacteristic
851SD16—1888no—
852D8—1888no—
853M16—28no—
854M16—44no—
855C2×C8—44no—
856C2×C8C23×D4718yes—
857C4⋊C4—472no—
858C4⋊C4—472no—
859C4⋊C4—474no—
860C4⋊C4—942no—
861C4⋊C4—942no—
862C4⋊C4—942no—
863C4⋊C4—942no—
864C4⋊C4—942no—
865C4⋊C4—942no—
866C4⋊C4—942no—
867C4⋊C4—941no—
868C4⋊C4—941no—
869C22⋊C4—942no—
870C22⋊C4—942no—
871C22⋊C4—942no—
872C22⋊C4—942no—
873C22⋊C4—942no—
874C22⋊C4—942no—
875C22⋊C4—944no—
876C22⋊C4—944no—
877C22⋊C4—944no—
878C22⋊C4—944no—
879C22⋊C4—942no—
880C22⋊C4—942no—
881C22⋊C4—942no—
882C22⋊C4—942no—
883C42—942no—
884C42—942no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—416no—
906C23—942no—
907C23—944no—
908C23—37616no—
909C23—1882no—
910C23—1884no—
911C23—1884no—
912C23—1884no—
913C23—1884no—
914C23—1882no—
915C23—1884no—
916C23—1884no—
917C23—1884no—
918C23—1882no—
919C23—1884no—
920C23—1884no—
921C23#1309405214yescomplemented
922C23C22×D18811yescharacteristic
923C23C22×D18811yescharacteristic
924C23C22×D18811yescharacteristic
925C23C22×D18811yescharacteristic
926C23C22×D18811yescharacteristic
927C23C22×D18811yescharacteristic
928C23C22×D18811yescharacteristic
929Q8—944no—
930Q8—1882no—
931D4—944no—
932D4—948no—
933D4—1884no—
934D4—1884no—
935D4—1882no—
936D4—1884no—
937D4—1888no—
938D4—1888no—
939D4—1884no—
940D4—1884no—
941D4—1884no—
942D4—1888no—
943D4—1888no—
944D4—1884no—
945D4—1884no—
946D4—1884no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—942no—
975C2×C4—942no—
976C2×C4—944no—
977C2×C4—942no—
978C2×C4—1884no—
979C2×C4—1884no—
980C2×C4—1884no—
981C2×C4—1882no—
982C2×C4—1882no—
983C2×C4—1884no—
984C2×C4—1882no—
985C2×C4—1884no—
986C2×C4C22×D18811yescharacteristic
987C2×C4C22×D18811yescharacteristic
988C2×C4C22×D18811yescharacteristic
989C2×C4C22×D18811yescharacteristic
990C2×C4C22×D18811yescharacteristic
991C2×C4C22×D18811yescharacteristic
992C2×C4C22×D18811yescharacteristic
993C2×C4#1309406914yes—
994C2×C4C24×D4711yescharacteristic
995C8—28no—
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—3768no—
1020C22—3768no—
1021C22—3768no—
1022C22—3764no—
1023C22—1884no—
1024C22—1882no—
1025C22—1882no—
1026C22—1884no—
1027C22—1882no—
1028C22—1884no—
1029C22#1568968512yes—
1030C22C2×#1309405212yes—
1031C22C2×#1309405212yes—
1032C22C2×#1309405212yes—
1033C22#1568992312yes—
1034C22C23×D18811yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—1884no—
1042C4—1882no—
1043C4—1882no—
1044C4—1882no—
1045C4#1568968512yes—
1046C4C2×#1309406912yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—3764no—
1055C2—3762no—
1056C2C2×#1568968511yescharacteristic
1057C2C22×#1309405211yescharacteristic
1058C2C2×#1568992311yescharacteristic
subgroupG/H
centerC22C23×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#407C2
socleC22×C47C23×D4
hypercenterC2×#407D47
hypocenterC47#60750
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#15689634C2semidirect
2. C22×#13093998C2semidirect
3. #20254204C2semidirect
4. #20254195C2semidirect
5. #20254188C2semidirect
6. #20254155C2semidirect
7. #20254146C2semidirect
8. #20254139C2semidirect
9. #20253329C2semidirect
10. #20253313C2semidirect
11. #20253007C2semidirect
12. #20252642C2semidirect
13. #20252618C2semidirect
14. C2×C47×#407C2semidirect
15. C22×#10625350C22semidirect
16. C23×D188C22semidirect
18. C2×#13094052C22semidirect
24. #15689634C22semidirect
25. #15689634C22semidirect
26. #15689634C22semidirect
28. C2×#13094003C22semidirect
29. C2×#13094003C22semidirect
39. C2×#13093998C22semidirect
40. C2×#13093998C22semidirect
41. C2×#13093998C22semidirect
42. C2×#13093998C22semidirect
43. C2×#13093998C22semidirect
47. C2×#13093983C22semidirect
48. C22×C4⋊Dic47C22semidirect
50. #15689459C22semidirect
51. #15689454C22semidirect
52. #15689448C22semidirect
53. #15689442C22semidirect
54. #15689442C22semidirect
55. #15689437C22semidirect
56. #15689437C22semidirect
57. #15689376C22semidirect
58. #15689369C22semidirect
59. #15689359C22semidirect
60. #15689352C22semidirect
61. #15689276C22semidirect
62. #15689276C22semidirect
63. #15689270C22semidirect
64. #15689264C22semidirect
65. #15689259C22semidirect
66. #15689259C22semidirect
67. #15689259C22semidirect
68. #15689165C22semidirect
69. #15689129C22semidirect
70. #15689125C22semidirect
72. C22×M16×C47C22semidirect
73. C47×#407C22semidirect
74. C47×#407C22semidirect
75. C47×#407C22semidirect
76. C47×#407C22semidirect
77. C2×C22⋊C8×C47C22semidirect
78. C2×C22⋊C8×C47C22semidirect
84. C2×#10625350C23semidirect
85. C22×Dic94C23semidirect
93. C22×D188C23semidirect
107. C2×#10625325C23semidirect
108. C2×D376C23semidirect
119. #13094003C23semidirect
120. #13094003C23semidirect
143. #13093998C23semidirect
144. #13093998C23semidirect
160. #13093983C23semidirect
167. C2×C4⋊Dic47C23semidirect
168. C2×C4⋊Dic47C23semidirect
183. #13093958C23semidirect
184. #13093956C23semidirect
185. #13093949C23semidirect
186. #13093946C23semidirect
187. #13093946C23semidirect
188. #13093946C23semidirect
207. C2×M16×C47C23semidirect
208. C22×C8×C47C23semidirect
211. C22⋊C8×C47C23semidirect
212. C22⋊C8×C47C23semidirect
376. C23×C47AGL(1,ℤ/8)semidirect
531. C2×#407D47semidirect
549. C22×M16C2×D47semidirect
602. #407C2×D47semidirect
603. #407C2×D47semidirect
604. #407C2×D47semidirect
605. #407C2×D47semidirect
606. C2×C22⋊C8C2×D47semidirect
607. C2×C22⋊C8C2×D47semidirect
608. C47#60750semidirect
657. C2×M16C22×D47semidirect
658. C22×C8C22×D47semidirect
741. C22⋊C8C22×D47semidirect
742. C22⋊C8C22×D47semidirect
921. C23#13094052semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
C22×#130939982
#202542042
#202541952
#202541882
#202541552
#202541462
#202541392
#202533292
#202533132
#202530072
#202526422
#202526182
C2×C47×#4072
#6075047