Finite Group Databasebeta

← #26137359

Subgroups — #26137359

Order 12032.

2598 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×(C2×D47)⋊C4C213yesmaximal
2C2×#15688970C213yesmaximal
3C2×#95×D47C211yesmaximal, characteristic
4C4×C47⋊#95C213yesmaximal, complemented
5#95×Dic47C213yesmaximal, complemented
6#95×Dic47C211yesmaximal, characteristic, complemented
7C4×#95×C47C211yesmaximal, characteristic, complemented
8C23×C4×D47C2213yes—
9C22×(C2×D47)⋊C4C2213yes—
10C22×(C2×D47)⋊C4C2211yescharacteristic
11C22×C4×Dic47C2213yes—
12C22×C4×Dic47C2216yes—
13C4×(C2×D47)⋊C4C4124yescomplemented
14#15688970C4124yescomplemented
15C2×C47⋊#95C2213yes—
16C2×C47⋊#95C2213yes—
17C2×C47⋊#95C2213yes—
18C2×C47⋊#95C2213yes—
19#95×D47C418yescomplemented
20C22×C42×C47C2213yes—
21C2×#95×C47C2211yescharacteristic
22C2×#95×C47C2213yes—
23C24×D47C2311yescharacteristic
24C23×Dic47C2313yes—
25C23×Dic47C2311yescharacteristic
26C23×Dic47C2313yes—
27C22×C4×D47—46no—
28C22×C4×D47—46no—
29C22×C4×D47C2×C4112yes—
30C22×C4×D47C2×C4112yes—
31C22×C4×D47C2×C4112yes—
32C2×(C2×D47)⋊C4C2×C4124yes—
33C2×(C2×D47)⋊C4C2×C4112yes—
34C2×(C2×D47)⋊C4C2×C4112yes—
35C2×C4×Dic47—46no—
36C2×C4×Dic47—46no—
37C2×C4×Dic47—46no—
38C2×C4×Dic47C2×C4124yescomplemented
39C2×C4×Dic47C2×C4112yescomplemented
40C47⋊#95C2×C4112yes—
41C47⋊#95C2×C4112yescomplemented
42C47⋊#95C2×C4112yescomplemented
43C47⋊#95C2×C4112yescomplemented
44C23×C4×C47C2311yescharacteristic
45C23×C4×C47C2313yes—
46C23×C4×C47C2313yes—
47C2×C42×C47—46no—
48C2×C42×C47C2×C4112yescomplemented
49#95×C47C2×C414yes—
50#95×C47C2×C4112yescomplemented
51C24×C47C2411yescharacteristic
52C23×D47—23no—
53C23×D47—23no—
54C23×D47—21no—
55C23×D47—21no—
56C23×D47C22×C416yes—
57C23×D47C22×C416yes—
58C23×D47C22×C412yes—
59C22×C4×C47—23no—
60C22×C4×C47—26no—
61C22×C4×C47—26no—
62C22×C4×C47—23no—
63C22×C4×C47—26no—
64C22×C4×C47—23no—
65C22×C4×C47—21no—
66C22×C4×C47C22×C416yes—
67C22×C4×C47C22×C416yes—
68C22×C4×C47C22×C416yes—
69C22×C4×C47C22×C416yes—
70C22×C4×C47C22×C416yes—
71C22×C4×C47C22×C4112yes—
72C22×Dic47—23no—
73C22×Dic47—26no—
74C22×Dic47—23no—
75C22×Dic47—26no—
76C22×Dic47—26no—
77C22×Dic47—21no—
78C22×Dic47—23no—
79C22×Dic47C22×C416yes—
80C22×Dic47C22×C416yes—
81C22×Dic47C22×C4112yes—
82C22×Dic47C22×C416yes—
83C22×Dic47C22×C416yes—
84C22×Dic47C22×C416yes—
85C2×C4×D47—424no—
86C2×C4×D47—412no—
87C2×C4×D47—412no—
88C2×C4×D47—424no—
89C2×C4×D47C42148yescomplemented
90C42×C47—412no—
91(C2×D47)⋊C4C42148yescomplemented
92(C2×D47)⋊C4C42116yescomplemented
93C4×Dic47—424no—
94C4×Dic47—412no—
95C23×C47C23×C411yescharacteristic
96C23×C47C23×C413yes—
97C23×C47C23×C413yes—
98C23×C47H(5,𝔽2)13yes—
99C23×C47H(5,𝔽2)13yes—
100C23×C472−1+411yescharacteristic
101C23×C472−1+411yescharacteristic
102C22×D47—26no—
103C22×D47—212no—
104C22×D47—26no—
105C22×D47—26no—
106C22×D47—22no—
107C22×D47—26no—
108C22×D47—26no—
109C22×D47—26no—
110C22×D47—26no—
111C22×D47C2×C4214yes—
112C22×D47C2×C42112yes—
113C22×D47C2×C42112yes—
114C2×C4×C47—26no—
115C2×C4×C47—212no—
116C2×C4×C47—26no—
117C2×C4×C47—26no—
118C2×C4×C47—26no—
119C2×C4×C47—212no—
120C2×C4×C47—212no—
121C2×C4×C47—212no—
122C2×C4×C47—26no—
123C2×C4×C47—26no—
124C2×C4×C47C2×C4214yes—
125C2×C4×C47C2×C42112yes—
126C2×C4×C47C2×C42112yes—
127C2×Dic47—212no—
128C2×Dic47—212no—
129C2×Dic47—26no—
130C2×Dic47—26no—
131C2×Dic47—212no—
132C2×Dic47—26no—
133C2×Dic47—26no—
134C2×Dic47—26no—
135C2×Dic47—26no—
136C2×Dic47—212no—
137C2×Dic47C2×C42112yes—
138C2×Dic47C2×C4214yes—
139C2×Dic47C2×C42112yes—
140C4×D47—448no—
141#13749—471nomaximal, Sylow
142C22×C47C22×C4213yes—
143C22×C47C22×C4211yescharacteristic
144C22×C47C22×C4213yes—
145C22×C47#51813yes—
146C22×C47#51816yes—
147C22×C47#51813yes—
148C22×C47#51813yes—
149C22×C47#51911yescharacteristic
150C22×C47#52013yes—
151C22×C47#52013yes—
152C22×C47#52013yes—
153C22×C47#52013yes—
154C2×D47—212no—
155C2×D47—212no—
156C2×D47—24no—
157C2×D47—212no—
158C2×D47—212no—
159C2×D47—24no—
160C2×D47C4318yes—
161C4×C47—212no—
162C4×C47—24no—
163C4×C47—212no—
164Dic47—212no—
165Dic47—212no—
166Dic47—24no—
167C2×C4×C22⋊C4—473no—
168C2×C4×C22⋊C4—473no—
169C22×#95—471no—
170C4×#95—473no—
171C4×#95—473no—
172C4×#95—471no—
173C4×#95D4711yescharacteristic, complemented
174C2×C47C2×C4311yescharacteristic
175C2×C47#227313yes—
176C2×C47#227413yes—
177C2×C47#227511yescharacteristic
178C2×C47#227513yes—
179C2×C47#227513yes—
180C2×C47#227511yescharacteristic
181D47—28no—
182C24×C4—473no—
183C22×C22⋊C4—471no—
184C22×C22⋊C4—473no—
185C22×C42—473no—
186C22×C42—476no—
187C22×C42C2×D4713yes—
188C4×C22⋊C4—4724no—
189C4×C22⋊C4—4724no—
190C2×#95—473no—
191C2×#95—473no—
192C2×#95—473no—
193C2×#95—473no—
194C2×#95—478no—
195C2×#95C2×D4711yescharacteristic
196C2×#95C2×D4713yes—
197C47#1374911yescharacteristic, complemented, Sylow
198C25—471no—
199C23×C4—473no—
200C23×C4—471no—
201C23×C4—473no—
202C23×C4—4712no—
203C23×C4—4712no—
204C23×C4—4712no—
205C23×C4—1886no—
206C23×C4—1886no—
207C23×C4C22×D4711yescharacteristic
208C23×C4C22×D4713yes—
209C23×C4C22×D4713yes—
210C2×C22⋊C4—4712no—
211C2×C22⋊C4—4712no—
212C2×C22⋊C4—4724no—
213C2×C42—46no—
214C2×C42—4712no—
215C2×C42—4724no—
216C2×C42—1886no—
217C2×C42—1886no—
218C2×C42—1886no—
219C2×C42C4×D47112yescomplemented
220#95—4712no—
221#95—4712no—
222#95—4712no—
223#95—4712no—
224#95C4×D4714yes—
225#95C4×D47112yescomplemented
226C24—476no—
227C24—476no—
228C24—472no—
229C24—943no—
230C24—943no—
231C24—941no—
232C24—941no—
233C24C23×D4711yescharacteristic
234C22×C4—23no—
235C22×C4—26no—
236C22×C4—26no—
237C22×C4—23no—
238C22×C4—26no—
239C22×C4—23no—
240C22×C4—21no—
241C22×C4—476no—
242C22×C4—476no—
243C22×C4—4712no—
244C22×C4—476no—
245C22×C4—476no—
246C22×C4—476no—
247C22×C4—4748no—
248C22×C4—943no—
249C22×C4—946no—
250C22×C4—946no—
251C22×C4—943no—
252C22×C4—946no—
253C22×C4—941no—
254C22×C4—943no—
255C22×C4—18824no—
256C22×C4—18824no—
257C22×C4—18812no—
258C22×C4—18812no—
259C22×C4C2×C4×D4716yes—
260C22×C4C2×C4×D4716yes—
261C22×C4C2×C4×D4716yes—
262C22×C4C2×C4×D4716yes—
263C22×C4C2×C4×D47112yes—
264C22×C4C2×C4×D4716yes—
265C22⋊C4—4748no—
266C22⋊C4—4716no—
267C42—412no—
268C42—18824no—
269C42—18812no—
270C23—474no—
271C23—4712no—
272C23—4712no—
273C23—946no—
274C23—9412no—
275C23—946no—
276C23—946no—
277C23—942no—
278C23—946no—
279C23—946no—
280C23—946no—
281C23—946no—
282C23C22×C4×D4711yescharacteristic
283C23C22×C4×D4713yes—
284C23C22×C4×D4713yes—
285C23#1309406913yes—
286C23#1309407013yes—
287C23#1309407111yescharacteristic
288C23#1309407211yescharacteristic
289C2×C4—212no—
290C2×C4—212no—
291C2×C4—212no—
292C2×C4—26no—
293C2×C4—26no—
294C2×C4—26no—
295C2×C4—26no—
296C2×C4—212no—
297C2×C4—26no—
298C2×C4—26no—
299C2×C4—4712no—
300C2×C4—474no—
301C2×C4—4712no—
302C2×C4—9412no—
303C2×C4—9412no—
304C2×C4—9412no—
305C2×C4—946no—
306C2×C4—946no—
307C2×C4—946no—
308C2×C4—946no—
309C2×C4—946no—
310C2×C4—946no—
311C2×C4—9412no—
312C2×C4—18848no—
313C2×C4C42×D4714yes—
314C2×C4C42×D47112yes—
315C2×C4C42×D47112yes—
316C22—478no—
317C22—9412no—
318C22—9412no—
319C22—944no—
320C22—9412no—
321C22—9412no—
322C22—944no—
323C22C2×C42×D4713yes—
324C22C2×C42×D4711yescharacteristic
325C22C2×C42×D4713yes—
326C22#1568959513yes—
327C22#1568959516yes—
328C22#1568959613yes—
329C22#1568959713yes—
330C22#1568959911yescharacteristic
331C22#1568960213yes—
332C22#1568960313yes—
333C22#1568960413yes—
334C22#1568960513yes—
335C4—212no—
336C4—24no—
337C4—212no—
338C4—9412no—
339C4—9412no—
340C4—944no—
341C2—948no—
342C2C43×D4711yescharacteristic
343C2#2024574013yes—
344C2#2024574213yes—
345C2#2024574611yescharacteristic
346C2#2024574713yes—
347C2#2024574813yes—
348C2#2024575011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC2×C47C2×C43
FittingC4×#95×C47C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenterC4×#95D47
hypocenterC47#13749
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
4. C4×C47⋊#95C2semidirect
5. #95×Dic47C2semidirect
6. #95×Dic47C2semidirect
7. C4×#95×C47C2semidirect
13. C4×(C2×D47)⋊C4C4semidirect
14. #15688970C4semidirect
19. #95×D47C4semidirect
38. C2×C4×Dic47C2×C4semidirect
39. C2×C4×Dic47C2×C4semidirect
41. C47⋊#95C2×C4semidirect
42. C47⋊#95C2×C4semidirect
43. C47⋊#95C2×C4semidirect
48. C2×C42×C47C2×C4semidirect
50. #95×C47C2×C4semidirect
89. C2×C4×D47C42semidirect
91. (C2×D47)⋊C4C42semidirect
92. (C2×D47)⋊C4C42semidirect
173. C4×#95D47semidirect
197. C47#13749semidirect
219. C2×C42C4×D47semidirect
225. #95C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4×(C2×D47)⋊C42
C2×#156889702
C2×#95×D472
C4×C47⋊#952
#95×Dic472
C4×#95×C472
#1374947