Finite Group Databasebeta

← #26430907

Subgroups — #26430907

Order 12032.

1356 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251781C211yesmaximal, characteristic
2#20251767C211yesmaximal, characteristic, complemented
3#20251260C211yesmaximal, characteristic
4#20251205C211yesmaximal, characteristic, complemented
5#20251192C211yesmaximal, characteristic
6#20251185C211yesmaximal, characteristic, complemented
7#20251166C211yesmaximal, characteristic, complemented
8#20251146C211yesmaximal, characteristic, complemented
9#20251133C211yesmaximal, characteristic
10#20251129C211yesmaximal, characteristic
11#20250886C211yesmaximal, characteristic
12#20250885C211yesmaximal, characteristic
13#20250881C211yesmaximal, characteristic, complemented
14#20250794C211yesmaximal, characteristic, complemented
15#20250749C211yesmaximal, characteristic
16#20250742C211yesmaximal, characteristic, complemented
17#20250680C211yesmaximal, characteristic
18#20249478C211yesmaximal, characteristic, complemented
19#20249413C211yesmaximal, characteristic
20#20249081C211yesmaximal, characteristic
21#20249034C211yesmaximal, characteristic, complemented
22#20248960C211yesmaximal, characteristic
23#20248895C211yesmaximal, characteristic
24#20248820C211yesmaximal, characteristic, complemented
25#20248582C211yesmaximal, characteristic, complemented
26#20248260C211yesmaximal, characteristic, complemented
27#20248256C211yesmaximal, characteristic
28#20246188C211yesmaximal, characteristic, complemented
29#20245994C211yesmaximal, characteristic
30#20245863C211yesmaximal, characteristic, complemented
31C47×#2799C211yesmaximal, characteristic, complemented
32C2×#13094015C2211yescharacteristic
33C2×Q8×Dic47C2211yescharacteristic
34C2×#13093982C2211yescharacteristic
35C47⋊#401C2211yescharacteristic
36C47⋊#401C2211yescharacteristic
37#15689065C2211yescharacteristic
38#15689065C2211yescharacteristic
39#15689065C2211yescharacteristic
40#15689065C2211yescharacteristic
41#15689064C2211yescharacteristic
42#15689064C2211yescharacteristic
43#15689063C2211yescharacteristic
44#15689063C2211yescharacteristic
45#15689063C2211yescharacteristic
46#15689062C2211yescharacteristic
47#15689062C2211yescharacteristic
48#15689061C2211yescharacteristic
49#15689061C2211yescharacteristic
50#15689061C2211yescharacteristic
51#15689060C2211yescharacteristic
52#15689057C2211yescharacteristic
53#15689057C2211yescharacteristic
54#15689057C2211yescharacteristic
55#15689057C2211yescharacteristic
56#15689057C2211yescharacteristic
57#15689056C2211yescharacteristic
58#15689056C2211yescharacteristic
59#15689055C2211yescharacteristic
60#15689054C2211yescharacteristic
61#15689053C2211yescharacteristic
62#15689052C2211yescharacteristic
63#15689052C2211yescharacteristic
64#15689050C2211yescharacteristic
65#15689050C2211yescharacteristic
66#15689049C2211yescharacteristic
67#15689049C2211yescharacteristic
68#15689047C2211yescharacteristic
69#15689045C2211yescharacteristic
70#15689044C2211yescharacteristic
71#15689044C2211yescharacteristic
72#15689043C2211yescharacteristic
73#15689042C2211yescharacteristic
74#15689036C2211yescharacteristic
75#15689034C2211yescharacteristic
76#15689034C2211yescharacteristic
77#15689030C2211yescharacteristic
78#15689030C2211yescharacteristic
79#15689030C2211yescharacteristic
80#15689030C2211yescharacteristic
81#15689029C2211yescharacteristic
82#15689027C2211yescharacteristic
83#15689027C2211yescharacteristic
84#15689022C2211yescharacteristic
85#15689022C2211yescharacteristic
86#15689022C2211yescharacteristic
87#15689021C2211yescharacteristic
88#15689021C2211yescharacteristic
89#15689020C2211yescharacteristic
90#15689019C2211yescharacteristic
91#15689019C2211yescharacteristic
92#15689018C2211yescharacteristic
93#15689018C2211yescharacteristic
94#15689015C2211yescharacteristic
95#15689015C2211yescharacteristic
96#15689015C2211yescharacteristic
97#15689015C2211yescharacteristic
98#15689015C2211yescharacteristic
99#15689015C2211yescharacteristic
100#15689014C2211yescharacteristic
101#15689014C2211yescharacteristic
102#15689014C2211yescharacteristic
103#15689013C2211yescharacteristic
104#15689013C2211yescharacteristic
105#15689013C2211yescharacteristic
106#15689013C2211yescharacteristic
107#15689012C2211yescharacteristic
108#15689012C2211yescharacteristic
109#15689012C2211yescharacteristic
110#15689010C2211yescharacteristic
111#15689010C2211yescharacteristic
112#15689010C2211yescharacteristic
113#15689010C2211yescharacteristic
114#15689010C2211yescharacteristic
115#15689010C2211yescharacteristic
116#15689010C2211yescharacteristic
117#15689010C2211yescharacteristic
118#15689009C2211yescharacteristic
119#15689009C2211yescharacteristic
120#15689009C2211yescharacteristic
121#15689009C2211yescharacteristic
122#15689009C2211yescharacteristic
123#15689009C2211yescharacteristic
124#15689009C2211yescharacteristic
125#15689008C2211yescharacteristic
126#15689008C2211yescharacteristic
127#15689008C2211yescharacteristic
128#15689008C2211yescharacteristic
129#15689008C2211yescharacteristic
130#15689008C2211yescharacteristic
131#15689008C2211yescharacteristic
132#15689007C2211yescharacteristic
133#15689007C2211yescharacteristic
134#15689006C2211yescharacteristic
135#15689006C2211yescharacteristic
136#15689006C2211yescharacteristic
137#15689006C2211yescharacteristic
138#15689006C2211yescharacteristic
139#15689006C2211yescharacteristic
140#15689006C2211yescharacteristic
141#15689006C2211yescharacteristic
142#15689006C2211yescharacteristic
143#15689005C2211yescharacteristic
144#15689005C2211yescharacteristic
145#15689005C2211yescharacteristic
146#15689005C2211yescharacteristic
147#15689004C2211yescharacteristic
148#15688997C2211yescharacteristic
149#15688997C2211yescharacteristic
150#15688994C2211yescharacteristic
151#15688994C2211yescharacteristic
152#15688992C2211yescharacteristic
153#15688992C2211yescharacteristic
154#15688990C2211yescharacteristic
155#15688990C2211yescharacteristic
156#15688990C2211yescharacteristic
157#15688990C2211yescharacteristic
158#15688990C2211yescharacteristic
159#15688989C2211yescharacteristic
160#15688987C2211yescharacteristic
161#15688982C2211yescharacteristic
162#15688982C2211yescharacteristic
163C4⋊C4×Dic47C2211yescharacteristic
164C4⋊C4×Dic47C2211yescharacteristic
165C4×Dic47⋊C4C2211yescharacteristic
166C4×C4⋊Dic47C2211yescharacteristic
167#15688974C2211yescharacteristic
168#15688974C2211yescharacteristic
169#15688968C2211yescharacteristic
170#15688968C2211yescharacteristic
171C42×Dic47C2211yescharacteristic
172C47×#400C2211yescharacteristic
173C47×#400C2211yescharacteristic
174C47×#400C2211yescharacteristic
175C47×#398C2211yescharacteristic
176C47×#398C2211yescharacteristic
177C47×#395C2211yescharacteristic
178C47×#391C2211yescharacteristic
179C47×#391C2211yescharacteristic
180C47×#391C2211yescharacteristic
181C47×#391C2211yescharacteristic
182C47×#391C2211yescharacteristic
183C47×#387C2211yescharacteristic
184C47×#387C2211yescharacteristic
185C47×#387C2211yescharacteristic
186C47×#387C2211yescharacteristic
187C22×Dic94C2311yescharacteristic
188C22×C4×D47C2311yescharacteristic
189#13094015—24no—
190Q8×Dic47—24no—
191#13093982—24no—
192C2×C4⋊Dic47C2311yescharacteristic
193C2×C4⋊Dic47C2311yescharacteristic
194C2×C4⋊Dic47C2311yescharacteristic
195C2×C4⋊Dic47C2311yescharacteristic
196C2×C4⋊Dic47C2311yescharacteristic
197C2×C4⋊Dic47C2311yescharacteristic
198C2×C4⋊Dic47C2311yescharacteristic
199C2×C4⋊Dic47C2311yescharacteristic
200C2×C4⋊Dic47C2311yescharacteristic
201C2×C4⋊Dic47C2311yescharacteristic
202C2×C4⋊Dic47C2311yescharacteristic
203C2×C4⋊Dic47C2311yescharacteristic
204C2×C4⋊Dic47C2311yescharacteristic
205C2×C4⋊Dic47C2311yescharacteristic
206C2×C4⋊Dic47C2311yescharacteristic
207C2×Dic47⋊C4C2311yescharacteristic
208C2×Dic47⋊C4C2311yescharacteristic
209C2×Dic47⋊C4C2311yescharacteristic
210C2×Dic47⋊C4C2311yescharacteristic
211C2×Dic47⋊C4C2311yescharacteristic
212C2×Dic47⋊C4C2311yescharacteristic
213C2×Dic47⋊C4C2311yescharacteristic
214C2×Dic47⋊C4C2311yescharacteristic
215C2×Dic47⋊C4C2311yescharacteristic
216C2×Dic47⋊C4C2311yescharacteristic
217C2×Dic47⋊C4C2311yescharacteristic
218C2×Dic47⋊C4C2311yescharacteristic
219C2×Dic47⋊C4C2311yescharacteristic
220C2×Dic47⋊C4C2311yescharacteristic
221C2×Dic47⋊C4C2311yescharacteristic
222C2×Dic47⋊C4C2311yescharacteristic
223C2×Dic47⋊C4C2311yescharacteristic
224C2×Dic47⋊C4C2311yescharacteristic
225C2×Dic47⋊C4C2311yescharacteristic
226C2×Dic47⋊C4C2311yescharacteristic
227C2×(C2×D47)⋊C4C2311yescharacteristic
228C2×(C2×D47)⋊C4C2311yescharacteristic
229C2×(C2×D47)⋊C4C2311yescharacteristic
230C2×(C2×D47)⋊C4C2311yescharacteristic
231C2×(C2×D47)⋊C4C2311yescharacteristic
232C2×(C2×D47)⋊C4C2311yescharacteristic
233C2×(C2×D47)⋊C4C2311yescharacteristic
234C2×(C2×D47)⋊C4C2311yescharacteristic
235C2×(C2×D47)⋊C4C2311yescharacteristic
236C2×(C2×D47)⋊C4C2311yescharacteristic
237C2×(C2×D47)⋊C4C2311yescharacteristic
238C2×(C2×D47)⋊C4C2311yescharacteristic
239C2×(C2×D47)⋊C4C2311yescharacteristic
240C2×(C2×D47)⋊C4C2311yescharacteristic
241C2×C4×Dic47C2311yescharacteristic
242C2×C4×Dic47C2311yescharacteristic
243C2×C4×Dic47C2311yescharacteristic
244C2×C4×Dic47C2311yescharacteristic
245C2×C4×Dic47C2311yescharacteristic
246C2×C4×Dic47C2311yescharacteristic
247C2×C4×Dic47C2311yescharacteristic
248C2×C4×Dic47C2311yescharacteristic
249C2×C4×Dic47C2311yescharacteristic
250C2×C4×Dic47C2311yescharacteristic
251C2×C4×Dic47C2311yescharacteristic
252C2×C4×Dic47C2311yescharacteristic
253C2×C4×Dic47C2311yescharacteristic
254C2×C4×Dic47C2311yescharacteristic
255C2×C4×Dic47C2311yescharacteristic
256C47⋊#95C2311yescharacteristic
257C47⋊#95C2311yescharacteristic
258C47⋊#95C2311yescharacteristic
259C47⋊#95C2311yescharacteristic
260C47⋊#95C2311yescharacteristic
261C47⋊#95C2311yescharacteristic
262C47⋊#95C2311yescharacteristic
263C47⋊#95C2311yescharacteristic
264C47⋊#95C2311yescharacteristic
265C47⋊#95C2311yescharacteristic
266C47⋊#95C2311yescharacteristic
267C47⋊#95C2311yescharacteristic
268C47⋊#95C2311yescharacteristic
269C47⋊#95C2311yescharacteristic
270C47⋊#95C2311yescharacteristic
271C47⋊#95C2311yescharacteristic
272C47⋊#95C2311yescharacteristic
273C47⋊#95C2311yescharacteristic
274C47⋊#95C2311yescharacteristic
275C47⋊#95C2311yescharacteristic
276C47⋊#95C2311yescharacteristic
277C47⋊#95C2311yescharacteristic
278C47⋊#95C2311yescharacteristic
279C47⋊#95C2311yescharacteristic
280C47⋊#95C2311yescharacteristic
281C47⋊#95C2311yescharacteristic
282C47⋊#95C2311yescharacteristic
283C47⋊#95C2311yescharacteristic
284C47⋊#95C2311yescharacteristic
285C47⋊#95C2311yescharacteristic
286C47⋊#95C2311yescharacteristic
287C47⋊#95C2311yescharacteristic
288C47⋊#95C2311yescharacteristic
289C47⋊#95C2311yescharacteristic
290C47⋊#95C2311yescharacteristic
291C47⋊#95C2311yescharacteristic
292C47⋊#95C2311yescharacteristic
293C47⋊#95C2311yescharacteristic
294C47⋊#95C2311yescharacteristic
295C47⋊#95C2311yescharacteristic
296C47⋊#95C2311yescharacteristic
297C47⋊#95C2311yescharacteristic
298C47⋊#95C2311yescharacteristic
299C47⋊#95C2311yescharacteristic
300C47⋊#95C2311yescharacteristic
301C47⋊#95C2311yescharacteristic
302C47⋊#95C2311yescharacteristic
303C47⋊#95C2311yescharacteristic
304C47⋊#95C2311yescharacteristic
305C47⋊#95C2311yescharacteristic
306C47⋊#95C2311yescharacteristic
307C47⋊#95C2311yescharacteristic
308C47⋊#95C2311yescharacteristic
309C47⋊#95C2311yescharacteristic
310C22×Q8×C47C2311yescharacteristic
311C22×Q8×C47C2311yescharacteristic
312C2×C4⋊C4×C47C2311yescharacteristic
313C2×C4⋊C4×C47C2311yescharacteristic
314C2×C4⋊C4×C47C2311yescharacteristic
315C2×C4⋊C4×C47C2311yescharacteristic
316C2×C4⋊C4×C47C2311yescharacteristic
317C2×C4⋊C4×C47C2311yescharacteristic
318C2×C4⋊C4×C47C2311yescharacteristic
319C2×C4⋊C4×C47C2311yescharacteristic
320C2×C4⋊C4×C47C2311yescharacteristic
321C2×C4⋊C4×C47C2311yescharacteristic
322C2×C42×C47C2311yescharacteristic
323C2×C42×C47C2311yescharacteristic
324C2×C42×C47C2311yescharacteristic
325#95×C47C2311yescharacteristic
326#95×C47C2311yescharacteristic
327#95×C47C2311yescharacteristic
328#95×C47C2311yescharacteristic
329#95×C47C2311yescharacteristic
330#95×C47C2311yescharacteristic
331#95×C47C2311yescharacteristic
332#95×C47C2311yescharacteristic
333#95×C47C2311yescharacteristic
334#95×C47C2311yescharacteristic
335#95×C47C2311yescharacteristic
336#95×C47C2311yescharacteristic
337#95×C47C2311yescharacteristic
338#95×C47C2311yescharacteristic
339#95×C47C2311yescharacteristic
340#95×C47C2311yescharacteristic
341#95×C47C2311yescharacteristic
342#95×C47C2311yescharacteristic
343#95×C47C2311yescharacteristic
344#95×C47C2311yescharacteristic
345C23×D47C2411yescharacteristic
346C2×Q8×C47—22no—
347C2×Q8×C47—22no—
348C2×Q8×C47—22no—
349C2×Q8×C47—41no—
350C2×Q8×C47—41no—
351C2×Q8×C47—41no—
352C22×C4×C47C2411yescharacteristic
353C22×C4×C47C2411yescharacteristic
354C22×C4×C47C2411yescharacteristic
355C22×C4×C47C2411yescharacteristic
356C22×C4×C47C2411yescharacteristic
357C22×C4×C47C2411yescharacteristic
358C22×C4×C47C2411yescharacteristic
359C22×C4×C47C2411yescharacteristic
360C22×C4×C47C2411yescharacteristic
361C22×C4×C47C2411yescharacteristic
362C22×C4×C47C2411yescharacteristic
363C22×C4×C47C2411yescharacteristic
364C22×C4×C47C2411yescharacteristic
365C22×C4×C47C2411yescharacteristic
366C22×C4×C47C2411yescharacteristic
367C22×Dic47C2411yescharacteristic
368C22×Dic47C2411yescharacteristic
369C22×Dic47C2411yescharacteristic
370C22×Dic47C2411yescharacteristic
371C22×Dic47C2411yescharacteristic
372C22×Dic47C2411yescharacteristic
373C22×Dic47C2411yescharacteristic
374C22×Dic47C2411yescharacteristic
375C22×Dic47C2411yescharacteristic
376C22×Dic47C2411yescharacteristic
377C22×Dic47C2411yescharacteristic
378C22×Dic47C2411yescharacteristic
379C22×Dic47C2411yescharacteristic
380C22×Dic47C2411yescharacteristic
381C22×Dic47C2411yescharacteristic
382C2×C4×D47—22no—
383C2×C4×D47—41no—
384C2×C4×D47—41no—
385C2×Dic94—41no—
386C2×Dic94—41no—
387C2×Dic94—41no—
388C4⋊C4×C47—22no—
389C4⋊C4×C47—22no—
390C4⋊C4×C47—22no—
391C4⋊C4×C47—22no—
392C4⋊C4×C47—41no—
393C4⋊C4×C47—41no—
394C4⋊C4×C47—41no—
395C4⋊C4×C47—41no—
396C4⋊C4×C47—41no—
397C4⋊C4×C47—41no—
398C42×C47—41no—
399C42×C47—41no—
400C42×C47—41no—
401(C2×D47)⋊C4—22no—
402(C2×D47)⋊C4—22no—
403(C2×D47)⋊C4—22no—
404(C2×D47)⋊C4—22no—
405(C2×D47)⋊C4—41no—
406(C2×D47)⋊C4—41no—
407(C2×D47)⋊C4—41no—
408(C2×D47)⋊C4—41no—
409(C2×D47)⋊C4—41no—
410(C2×D47)⋊C4—41no—
411(C2×D47)⋊C4—41no—
412(C2×D47)⋊C4—41no—
413(C2×D47)⋊C4—41no—
414(C2×D47)⋊C4—41no—
415C4⋊Dic47—22no—
416C4⋊Dic47—22no—
417C4⋊Dic47—22no—
418C4⋊Dic47—22no—
419C4⋊Dic47—22no—
420C4⋊Dic47—22no—
421C4⋊Dic47—22no—
422C4⋊Dic47—22no—
423C4⋊Dic47—41no—
424C4⋊Dic47—41no—
425C4⋊Dic47—41no—
426C4⋊Dic47—41no—
427C4⋊Dic47—41no—
428C4⋊Dic47—41no—
429C4⋊Dic47—41no—
430Dic47⋊C4—22no—
431Dic47⋊C4—22no—
432Dic47⋊C4—22no—
433Dic47⋊C4—41no—
434Dic47⋊C4—41no—
435Dic47⋊C4—41no—
436Dic47⋊C4—41no—
437Dic47⋊C4—41no—
438Dic47⋊C4—41no—
439Dic47⋊C4—41no—
440Dic47⋊C4—41no—
441Dic47⋊C4—41no—
442Dic47⋊C4—41no—
443Dic47⋊C4—41no—
444Dic47⋊C4—41no—
445Dic47⋊C4—41no—
446Dic47⋊C4—41no—
447Dic47⋊C4—41no—
448Dic47⋊C4—41no—
449Dic47⋊C4—41no—
450C4×Dic47—22no—
451C4×Dic47—22no—
452C4×Dic47—22no—
453C4×Dic47—22no—
454C4×Dic47—22no—
455C4×Dic47—41no—
456C4×Dic47—41no—
457C4×Dic47—41no—
458C4×Dic47—41no—
459C4×Dic47—41no—
460C4×Dic47—41no—
461C4×Dic47—41no—
462C4×Dic47—41no—
463C4×Dic47—41no—
464C4×Dic47#4114yes—
465C23×C47C2511yescharacteristic
466C22×D47—21no—
467C22×D47—21no—
468C22×D47—21no—
469C22×D47—21no—
470C22×D47—21no—
471C22×D47—21no—
472C22×D47—21no—
473Q8×C47—44no—
474Q8×C47—82no—
475C2×C4×C47—21no—
476C2×C4×C47—21no—
477C2×C4×C47—21no—
478C2×C4×C47—21no—
479C2×C4×C47—21no—
480C2×C4×C47—21no—
481C2×C4×C47—21no—
482C2×C4×C47—21no—
483C2×C4×C47—21no—
484C2×C4×C47—21no—
485C2×C4×C47—21no—
486C2×C4×C47—21no—
487C2×C4×C47—21no—
488C2×C4×C47—21no—
489C2×C4×C47—21no—
490C2×C4×C47—21no—
491C2×C4×C47—21no—
492C2×C4×C47—21no—
493C2×C4×C47—21no—
494C2×C4×C47—21no—
495C2×C4×C47—21no—
496C2×C4×C47—21no—
497C2×C4×C47—21no—
498C2×C4×C47—21no—
499C2×C4×C47—21no—
500C2×C4×C47—21no—
501C2×C4×C47—21no—
502C2×C4×C47—21no—
503C2×C4×C47—21no—
504C2×C4×C47—21no—
505C2×C4×C47—21no—
506C2×C4×C47—21no—
507C2×C4×C47—21no—
508C2×C4×C47—21no—
509C2×C4×C47—21no—
510C2×C4×C47—21no—
511C2×C4×C47—21no—
512C2×C4×C47—21no—
513C2×C4×C47—21no—
514C2×C4×C47—21no—
515C2×C4×C47—21no—
516C2×C4×C47—21no—
517C2×C4×C47C2×#4112yes—
518C2×C4×C472−1+412yes—
519C2×C4×C472−1+412yes—
520C2×Dic47—21no—
521C2×Dic47—21no—
522C2×Dic47—21no—
523C2×Dic47—21no—
524C2×Dic47—21no—
525C2×Dic47—21no—
526C2×Dic47—21no—
527C2×Dic47—21no—
528C2×Dic47—21no—
529C2×Dic47—21no—
530C2×Dic47—21no—
531C2×Dic47—21no—
532C2×Dic47—21no—
533C2×Dic47—21no—
534C2×Dic47—21no—
535C2×Dic47—21no—
536C2×Dic47—21no—
537C2×Dic47—21no—
538C2×Dic47—21no—
539C2×Dic47—21no—
540C2×Dic47—21no—
541C2×Dic47—21no—
542C2×Dic47—21no—
543C2×Dic47—21no—
544C2×Dic47—21no—
545C2×Dic47—21no—
546C2×Dic47—21no—
547C2×Dic47—21no—
548C2×Dic47—21no—
549C2×Dic47—21no—
550C2×Dic47—21no—
551C2×Dic47—21no—
552C2×Dic47—21no—
553C2×Dic47—21no—
554C2×Dic47—21no—
555C2×Dic47—21no—
556C2×Dic47—21no—
557C2×Dic47—21no—
558C2×Dic47—21no—
559C2×Dic47—21no—
560C2×Dic47—21no—
561C2×Dic47—21no—
562C2×Dic47—21no—
563C2×Dic47C2×#4112yes—
564C2×Dic47C2×#4112yes—
565C4×D47—44no—
566Dic94—82no—
567#37001—471nomaximal, Sylow
568C22×C47C22×#4111yescharacteristic
569C22×C47C2×2−1+411yescharacteristic
570C22×C47C2×2−1+411yescharacteristic
571C22×C47#58511yescharacteristic
572C22×C47#58511yescharacteristic
573C22×C47#58511yescharacteristic
574C22×C47#58511yescharacteristic
575C2×D47—41no—
576C2×D47—41no—
577C2×D47—41no—
578C2×D47—41no—
579C2×D47—41no—
580C2×D47—41no—
581C2×D47—41no—
582C4×C47—22no—
583C4×C47—22no—
584C4×C47—22no—
585C4×C47—41no—
586C4×C47—41no—
587C4×C47—41no—
588C4×C47—41no—
589C4×C47—41no—
590C4×C47—41no—
591C4×C47—41no—
592C4×C47—41no—
593C4×C47—41no—
594C4×C47—41no—
595C4×C47—41no—
596C4×C47—41no—
597Dic47—22no—
598Dic47—22no—
599Dic47—41no—
600Dic47—41no—
601Dic47—41no—
602Dic47—41no—
603Dic47—41no—
604Dic47—41no—
605Dic47—41no—
606Dic47—41no—
607Dic47—41no—
608Dic47—41no—
609Dic47—41no—
610Dic47—41no—
611Dic47—41no—
612#2866—471no—
613#2863—471no—
614#2799D4711yescharacteristic, complemented
615#2798—471no—
616#2794—471no—
617#2793—471no—
618#2792—471no—
619#2791—471no—
620#2789—471no—
621#2788—471no—
622#2788—471no—
623#2770—471no—
624#2770—471no—
625#2769—471no—
626#2762—471no—
627#2759—471no—
628#2758—471no—
629#2754—471no—
630#2655—471no—
631#2650—471no—
632#2611—471no—
633#2605—471no—
634#2599—471no—
635#2594—471no—
636#2588—471no—
637#2565—471no—
638#2533—471no—
639#2532—471no—
640#2336—471no—
641#2314—471no—
642#2295—471no—
643C2×C47#345511yescharacteristic
644C2×C47#349511yescharacteristic
645C2×C47#350711yescharacteristic
646C2×C47#355511yescharacteristic
647C2×C47#356411yescharacteristic
648C2×C47#356511yescharacteristic
649C2×C47#356611yescharacteristic
650D47—81no—
651C2×#125—471no—
652C2×C4×Q8—471no—
653C2×#117—471no—
654#401—471no—
655#401—471no—
656#400—471no—
657#400—471no—
658#400—471no—
659#400—471no—
660#400—471no—
661#400—471no—
662#400—471no—
663#400—471no—
664#400—471no—
665#400—471no—
666#400—471no—
667#400—471no—
668#400—471no—
669#400—471no—
670#400C2×D4711yescharacteristic
671#400C2×D4711yescharacteristic
672#400C2×D4711yescharacteristic
673#399—471no—
674#398—471no—
675#398—471no—
676#398—471no—
677#398—471no—
678#398—471no—
679#398—471no—
680#398—471no—
681#398—471no—
682#398—471no—
683#398—471no—
684#398C2×D4711yescharacteristic
685#398C2×D4711yescharacteristic
686#397—471no—
687#397—471no—
688#397—471no—
689#397—471no—
690#397—471no—
691#397—471no—
692#396—471no—
693#396—471no—
694#395—471no—
695#395—471no—
696#395—471no—
697#395—471no—
698#395C2×D4711yescharacteristic
699#393—471no—
700#393—471no—
701#393—471no—
702#391—471no—
703#391—471no—
704#391—471no—
705#391—471no—
706#391—471no—
707#391—471no—
708#391—471no—
709#391C2×D4711yescharacteristic
710#391C2×D4711yescharacteristic
711#391C2×D4711yescharacteristic
712#391C2×D4711yescharacteristic
713#391C2×D4711yescharacteristic
714#389—471no—
715#389—471no—
716#389—471no—
717#389—471no—
718#389—471no—
719#389—471no—
720#389—471no—
721#389—471no—
722#389—471no—
723#389—471no—
724#388—471no—
725#388—471no—
726#388—471no—
727#388—471no—
728#388—471no—
729#388—471no—
730#388—471no—
731#388—471no—
732#388—471no—
733#388—471no—
734#388—471no—
735#388—471no—
736#388—471no—
737#388—471no—
738#388—471no—
739#388—471no—
740#387—471no—
741#387—471no—
742#387—471no—
743#387—471no—
744#387—471no—
745#387—471no—
746#387—471no—
747#387—471no—
748#387—471no—
749#387—471no—
750#387—471no—
751#387—471no—
752#387—471no—
753#387—471no—
754#387—471no—
755#387—471no—
756#387—471no—
757#387—471no—
758#387—471no—
759#387—471no—
760#387—471no—
761#387—471no—
762#387—471no—
763#387—471no—
764#387—471no—
765#387—471no—
766#387—471no—
767#387—471no—
768#387—471no—
769#387—471no—
770#387—471no—
771#387—471no—
772#387—471no—
773#387—471no—
774#387—471no—
775#387—471no—
776#387—471no—
777#387—471no—
778#387C2×D4711yescharacteristic
779#387C2×D4711yescharacteristic
780#387C2×D4711yescharacteristic
781#387C2×D4711yescharacteristic
782#385—471no—
783#385—471no—
784#385—471no—
785#385—471no—
786#384—471no—
787#384—471no—
788#383—471no—
789#383—471no—
790#383—471no—
791#383—471no—
792#383—471no—
793#382—471no—
794#382—471no—
795#380—471no—
796#380—471no—
797C4×C4⋊C4—471no—
798C4×C4⋊C4—471no—
799C4×C4⋊C4—471no—
800C4×C4⋊C4—471no—
801C4×C4⋊C4—471no—
802C4×C4⋊C4—471no—
803#376—471no—
804#376—471no—
805C43—471no—
806C47#3700111yescharacteristic, complemented, Sylow
807C22×Q8—471no—
808C22×Q8C22×D4711yescharacteristic
809C22×Q8C22×D4711yescharacteristic
810C23×C4—471no—
811#125—944no—
812C4×Q8—944no—
813#117—944no—
814C2×C4⋊C4—471no—
815C2×C4⋊C4—471no—
816C2×C4⋊C4—471no—
817C2×C4⋊C4—471no—
818C2×C4⋊C4—471no—
819C2×C4⋊C4—471no—
820C2×C4⋊C4—471no—
821C2×C4⋊C4—471no—
822C2×C4⋊C4—471no—
823C2×C4⋊C4—471no—
824C2×C4⋊C4—471no—
825C2×C4⋊C4—471no—
826C2×C4⋊C4—471no—
827C2×C4⋊C4—471no—
828C2×C4⋊C4—471no—
829C2×C4⋊C4—471no—
830C2×C4⋊C4—471no—
831C2×C4⋊C4—471no—
832C2×C4⋊C4—471no—
833C2×C4⋊C4—471no—
834C2×C4⋊C4—471no—
835C2×C4⋊C4—471no—
836C2×C4⋊C4—471no—
837C2×C4⋊C4—471no—
838C2×C4⋊C4—471no—
839C2×C4⋊C4—471no—
840C2×C4⋊C4—471no—
841C2×C4⋊C4—471no—
842C2×C4⋊C4—471no—
843C2×C4⋊C4—471no—
844C2×C4⋊C4—471no—
845C2×C4⋊C4—471no—
846C2×C4⋊C4—471no—
847C2×C4⋊C4—471no—
848C2×C4⋊C4—471no—
849C2×C4⋊C4C22×D4711yescharacteristic
850C2×C4⋊C4C22×D4711yescharacteristic
851C2×C4⋊C4C22×D4711yescharacteristic
852C2×C4⋊C4C22×D4711yescharacteristic
853C2×C4⋊C4C22×D4711yescharacteristic
854C2×C4⋊C4C22×D4711yescharacteristic
855C2×C4⋊C4C22×D4711yescharacteristic
856C2×C4⋊C4C22×D4711yescharacteristic
857C2×C4⋊C4C22×D4711yescharacteristic
858C2×C4⋊C4C22×D4711yescharacteristic
859C2×C22⋊C4—471no—
860C2×C22⋊C4—471no—
861C2×C22⋊C4—471no—
862C2×C22⋊C4—471no—
863C2×C22⋊C4—471no—
864C2×C22⋊C4—471no—
865C2×C22⋊C4—471no—
866C2×C22⋊C4—471no—
867C2×C22⋊C4—471no—
868C2×C22⋊C4—471no—
869C2×C22⋊C4—471no—
870C2×C22⋊C4—471no—
871C2×C22⋊C4—471no—
872C2×C22⋊C4—471no—
873C2×C42—471no—
874C2×C42—471no—
875C2×C42—471no—
876C2×C42—471no—
877C2×C42—471no—
878C2×C42—471no—
879C2×C42—471no—
880C2×C42—471no—
881C2×C42—471no—
882C2×C42—471no—
883C2×C42—471no—
884C2×C42—471no—
885C2×C42—471no—
886C2×C42—471no—
887C2×C42—471no—
888C2×C42C22×D4711yescharacteristic
889C2×C42C22×D4711yescharacteristic
890C2×C42C22×D4711yescharacteristic
891#95—471no—
892#95—471no—
893#95—471no—
894#95—471no—
895#95—471no—
896#95—471no—
897#95—471no—
898#95—471no—
899#95—471no—
900#95—471no—
901#95—471no—
902#95—471no—
903#95—471no—
904#95—471no—
905#95—471no—
906#95—471no—
907#95—471no—
908#95—471no—
909#95—471no—
910#95—471no—
911#95—471no—
912#95—471no—
913#95—471no—
914#95—471no—
915#95—471no—
916#95—471no—
917#95—471no—
918#95—471no—
919#95—471no—
920#95—471no—
921#95—471no—
922#95—471no—
923#95—471no—
924#95—471no—
925#95—471no—
926#95—471no—
927#95—471no—
928#95—471no—
929#95—471no—
930#95—471no—
931#95—471no—
932#95—471no—
933#95—471no—
934#95—471no—
935#95—471no—
936#95—471no—
937#95—471no—
938#95—471no—
939#95—471no—
940#95—471no—
941#95—471no—
942#95—471no—
943#95—471no—
944#95—471no—
945#95C22×D4711yescharacteristic
946#95C22×D4711yescharacteristic
947#95C22×D4711yescharacteristic
948#95C22×D4711yescharacteristic
949#95C22×D4711yescharacteristic
950#95C22×D4711yescharacteristic
951#95C22×D4711yescharacteristic
952#95C22×D4711yescharacteristic
953#95C22×D4711yescharacteristic
954#95C22×D4711yescharacteristic
955#95C22×D4711yescharacteristic
956#95C22×D4711yescharacteristic
957#95C22×D4711yescharacteristic
958#95C22×D4711yescharacteristic
959#95C22×D4711yescharacteristic
960#95C22×D4711yescharacteristic
961#95C22×D4711yescharacteristic
962#95C22×D4711yescharacteristic
963#95C22×D4711yescharacteristic
964#95C22×D4711yescharacteristic
965C24—471no—
966C2×Q8—22no—
967C2×Q8—22no—
968C2×Q8—22no—
969C2×Q8—41no—
970C2×Q8—41no—
971C2×Q8—41no—
972C2×Q8—1881no—
973C2×Q8—1881no—
974C2×Q8—1881no—
975C22×C4—471no—
976C22×C4—471no—
977C22×C4—471no—
978C22×C4—471no—
979C22×C4—471no—
980C22×C4—471no—
981C22×C4—471no—
982C22×C4—471no—
983C22×C4—471no—
984C22×C4—471no—
985C22×C4—471no—
986C22×C4—471no—
987C22×C4—471no—
988C22×C4—471no—
989C22×C4—471no—
990C22×C4—942no—
991C22×C4—1881no—
992C22×C4—1881no—
993C22×C4C23×D4711yescharacteristic
994C22×C4C23×D4711yescharacteristic
995C22×C4C23×D4711yescharacteristic
996C22×C4C23×D4711yescharacteristic
997C22×C4C23×D4711yescharacteristic
998C22×C4C23×D4711yescharacteristic
999C22×C4C23×D4711yescharacteristic
1000C22×C4C23×D4711yescharacteristic
1001C22×C4C23×D4711yescharacteristic
1002C22×C4C23×D4711yescharacteristic
1003C22×C4C23×D4711yescharacteristic
1004C22×C4C23×D4711yescharacteristic
1005C22×C4C23×D4711yescharacteristic
1006C22×C4C23×D4711yescharacteristic
1007C22×C4C23×D4711yescharacteristic
1008C4⋊C4—22no—
1009C4⋊C4—22no—
1010C4⋊C4—22no—
1011C4⋊C4—22no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—942no—
1019C4⋊C4—942no—
1020C4⋊C4—942no—
1021C4⋊C4—942no—
1022C4⋊C4—942no—
1023C4⋊C4—942no—
1024C4⋊C4—942no—
1025C4⋊C4—942no—
1026C4⋊C4—942no—
1027C4⋊C4—942no—
1028C4⋊C4—942no—
1029C4⋊C4—1881no—
1030C4⋊C4—1881no—
1031C4⋊C4—1881no—
1032C4⋊C4—1881no—
1033C4⋊C4—1881no—
1034C4⋊C4—1881no—
1035C4⋊C4—1881no—
1036C4⋊C4—1881no—
1037C4⋊C4—1881no—
1038C4⋊C4—1881no—
1039C4⋊C4—1881no—
1040C4⋊C4—1881no—
1041C4⋊C4—1881no—
1042C4⋊C4—1881no—
1043C4⋊C4—1881no—
1044C4⋊C4—1881no—
1045C4⋊C4—1881no—
1046C4⋊C4—1881no—
1047C4⋊C4—1881no—
1048C4⋊C4—1881no—
1049C4⋊C4—1881no—
1050C4⋊C4—1881no—
1051C4⋊C4—1881no—
1052C4⋊C4—1881no—
1053C22⋊C4—942no—
1054C22⋊C4—942no—
1055C22⋊C4—942no—
1056C22⋊C4—942no—
1057C22⋊C4—1881no—
1058C22⋊C4—1881no—
1059C22⋊C4—1881no—
1060C22⋊C4—1881no—
1061C22⋊C4—1881no—
1062C22⋊C4—1881no—
1063C22⋊C4—1881no—
1064C22⋊C4—1881no—
1065C22⋊C4—1881no—
1066C22⋊C4—1881no—
1067C42—41no—
1068C42—41no—
1069C42—41no—
1070C42—474no—
1071C42—942no—
1072C42—942no—
1073C42—942no—
1074C42—942no—
1075C42—942no—
1076C42—1881no—
1077C42—1881no—
1078C42—1881no—
1079C42—1881no—
1080C42—1881no—
1081C42—1881no—
1082C42—1881no—
1083C42—1881no—
1084C42—1881no—
1085C23—941no—
1086C23—941no—
1087C23—941no—
1088C23—941no—
1089C23—941no—
1090C23—941no—
1091C23—941no—
1092C23C24×D4711yescharacteristic
1093Q8—44no—
1094Q8—82no—
1095Q8—3762no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—472no—
1139C2×C4—472no—
1140C2×C4—941no—
1141C2×C4—941no—
1142C2×C4—941no—
1143C2×C4—941no—
1144C2×C4—941no—
1145C2×C4—941no—
1146C2×C4—941no—
1147C2×C4—941no—
1148C2×C4—941no—
1149C2×C4—941no—
1150C2×C4—941no—
1151C2×C4—941no—
1152C2×C4—941no—
1153C2×C4—941no—
1154C2×C4—941no—
1155C2×C4—941no—
1156C2×C4—941no—
1157C2×C4—941no—
1158C2×C4—941no—
1159C2×C4—941no—
1160C2×C4—941no—
1161C2×C4—941no—
1162C2×C4—941no—
1163C2×C4—941no—
1164C2×C4—941no—
1165C2×C4—941no—
1166C2×C4—941no—
1167C2×C4—941no—
1168C2×C4—941no—
1169C2×C4—941no—
1170C2×C4—941no—
1171C2×C4—941no—
1172C2×C4—941no—
1173C2×C4—941no—
1174C2×C4—941no—
1175C2×C4—941no—
1176C2×C4—941no—
1177C2×C4—941no—
1178C2×C4—941no—
1179C2×C4—941no—
1180C2×C4—941no—
1181C2×C4—941no—
1182C2×C4—941no—
1183C2×C4—1884no—
1184C2×C4#41×D4712yes—
1185C2×C4#1309407112yes—
1186C2×C4#1309407212yes—
1187C22—1881no—
1188C22—1881no—
1189C22—1881no—
1190C22—1881no—
1191C22—1881no—
1192C22—1881no—
1193C22—1881no—
1194C22C2×#41×D4711yescharacteristic
1195C22C2×#1309407111yescharacteristic
1196C22C2×#1309407211yescharacteristic
1197C22#1568995811yescharacteristic
1198C22#1568995811yescharacteristic
1199C22#1568996011yescharacteristic
1200C22#1568996011yescharacteristic
1201C4—22no—
1202C4—22no—
1203C4—22no—
1204C4—41no—
1205C4—41no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—41no—
1211C4—41no—
1212C4—41no—
1213C4—41no—
1214C4—41no—
1215C4—41no—
1216C4—942no—
1217C4—942no—
1218C4—1881no—
1219C4—1881no—
1220C4—1881no—
1221C4—1881no—
1222C4—1881no—
1223C4—1881no—
1224C4—1881no—
1225C4—1881no—
1226C4—1881no—
1227C4—1881no—
1228C4—1881no—
1229C4—1881no—
1230C4—1881no—
1231C2—3761no—
1232C2#2025677511yescharacteristic
1233C2#2025712711yescharacteristic
1234C2#2025725411yescharacteristic
1235C2#2025787211yescharacteristic
1236C2#2025800211yescharacteristic
1237C2#2025803911yescharacteristic
1238C2#2025806911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2799C2
prime radicalC23×D47C24
hypercenter#2799D47
hypocenterC47#37001
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2799

Complements

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

NH ≅ G/Ntype
2. #20251767C2semidirect
4. #20251205C2semidirect
6. #20251185C2semidirect
7. #20251166C2semidirect
8. #20251146C2semidirect
13. #20250881C2semidirect
14. #20250794C2semidirect
16. #20250742C2semidirect
18. #20249478C2semidirect
21. #20249034C2semidirect
24. #20248820C2semidirect
25. #20248582C2semidirect
26. #20248260C2semidirect
28. #20246188C2semidirect
30. #20245863C2semidirect
31. C47×#2799C2semidirect
614. #2799D47semidirect
806. C47#37001semidirect

Maximal subgroups

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

subgroupindex
#202517812
#202517672
#202512602
#202512052
#202511922
#202511852
#202511662
#202511462
#202511332
#202511292
#202508862
#202508852
#202508812
#202507942
#202507492
#202507422
#202506802
#202494782
#202494132
#202490812
#202490342
#202489602
#202488952
#202488202
#202485822
#202482602
#202482562
#202461882
#202459942
#202458632
C47×#27992
#3700147