Finite Group Databasebeta

← #26137751

Subgroups — #26137751

Order 12032.

2154 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊Dic47C213yesmaximal
2C2×#15688968C211yesmaximal, characteristic, complemented
3#20241614C213yesmaximal, complemented
4#20241612C213yesmaximal, complemented
5#20241611C213yesmaximal
6#95×Dic47C211yesmaximal, characteristic, complemented
7C22×#95×C47C211yesmaximal, characteristic
8C22×C22⋊Dic47C2213yes—
9C22×C22⋊Dic47C2211yescharacteristic
10C22×C4×Dic47C2213yes—
11C22×C4×Dic47C2213yes—
12C4×C22⋊Dic47C4124yescomplemented
13#15688968—24no—
14C2×C47⋊#95C2213yes—
15C2×C47⋊#95C2213yes—
16C2×C47⋊#95C2216yes—
17C2×C47⋊#95C2213yes—
18C2×C47⋊#95C2213yes—
19C24×C4×C47C2213yes—
20C2×#95×C47—24no—
21C2×#95×C47C2213yes—
22C2×#95×C47C2211yescharacteristic
23C23×Dic47C2313yes—
24C23×Dic47C2313yes—
25C23×Dic47C2311yescharacteristic
26C23×Dic47C2311yescharacteristic
27C2×C22⋊Dic47—26no—
28C2×C22⋊Dic47—26no—
29C2×C22⋊Dic47C2×C4112yes—
30C2×C22⋊Dic47C2×C4112yes—
31C2×C4×Dic47—26no—
32C2×C4×Dic47—26no—
33C2×C4×Dic47—46no—
34C2×C4×Dic47C2×C4112yescomplemented
35C2×C4×Dic47C2×C4112yescomplemented
36C47⋊#95—26no—
37C47⋊#95—26no—
38C47⋊#95—46no—
39C47⋊#95C2×C4112yescomplemented
40C47⋊#95C2×C4112yescomplemented
41C25×C47C2311yescharacteristic
42C23×C4×C47—212no—
43C23×C4×C47—26no—
44C23×C4×C47—26no—
45C23×C4×C47—46no—
46C23×C4×C47C2×C4112yes—
47C23×C4×C47C2313yes—
48C23×C4×C47C2313yes—
49#95×C47—26no—
50#95×C47D414yes—
51C24×C47—21no—
52C24×C47—23no—
53C24×C47—23no—
54C24×C47—21no—
55C24×C47C22×C416yes—
56C24×C47#4116yes—
57C24×C47#4112yes—
58C24×C47C2411yescharacteristic
59C22×C4×C47—26no—
60C22×C4×C47—26no—
61C22×C4×C47—224no—
62C22×C4×C47—23no—
63C22×C4×C47—26no—
64C22×C4×C47—23no—
65C22×C4×C47—26no—
66C22×C4×C47—224no—
67C22×C4×C47—412no—
68C22×C4×C47—424no—
69C22×C4×C47—424no—
70C22×C4×C47C22×C416yes—
71C22×C4×C47C22×C416yes—
72C22×C4×C47C2×D416yes—
73C22×C4×C47#4116yes—
74C22×Dic47—21no—
75C22×Dic47—23no—
76C22×Dic47—23no—
77C22×Dic47—21no—
78C22×Dic47—23no—
79C22×Dic47—26no—
80C22×Dic47—23no—
81C22×Dic47—23no—
82C22×Dic47—23no—
83C22×Dic47—23no—
84C22×Dic47—23no—
85C22×Dic47—23no—
86C22×Dic47—26no—
87C22×Dic47—23no—
88C22×Dic47C22×C416yes—
89C22×Dic47C22×C416yes—
90C22×Dic47C22×C416yes—
91C22×Dic47C22×C416yes—
92C22⋊Dic47—224no—
93C22⋊Dic47C42116yes—
94C4×Dic47—224no—
95C4×Dic47—412no—
96C23×C47—26no—
97C23×C47—26no—
98C23×C47—26no—
99C23×C47—26no—
100C23×C47—26no—
101C23×C47—22no—
102C23×C47—212no—
103C23×C47—26no—
104C23×C47—26no—
105C23×C47C2×C4214yes—
106C23×C47#117112yes—
107C23×C47#117112yes—
108C23×C47C23×C413yes—
109C23×C47C22×D411yescharacteristic
110C23×C47C2×#4113yes—
111C23×C47C2×#4113yes—
112C23×C47C2×#4111yescharacteristic
113C23×C47H(5,𝔽2)13yes—
114C23×C472−1+411yescharacteristic
115C2×C4×C47—26no—
116C2×C4×C47—26no—
117C2×C4×C47—212no—
118C2×C4×C47—212no—
119C2×C4×C47—26no—
120C2×C4×C47—26no—
121C2×C4×C47—26no—
122C2×C4×C47—448no—
123C2×C4×C47—46no—
124C2×C4×C47—46no—
125C2×C4×C47C4×D4112yes—
126C2×Dic47—26no—
127C2×Dic47—26no—
128C2×Dic47—26no—
129C2×Dic47—26no—
130C2×Dic47—26no—
131C2×Dic47—26no—
132C2×Dic47—26no—
133C2×Dic47—26no—
134C2×Dic47—26no—
135C2×Dic47—26no—
136C2×Dic47—43no—
137C2×Dic47—43no—
138C2×Dic47—46no—
139C2×Dic47—43no—
140C2×Dic47—43no—
141C2×Dic47—46no—
142C2×Dic47C2×C4214yes—
143C2×Dic47C2×C4214yes—
144#13809—471nomaximal, Sylow
145C22×C47—212no—
146C22×C47—212no—
147C22×C47—212no—
148C22×C47—212no—
149C22×C47—24no—
150C22×C47—24no—
151C22×C47#37618yescomplemented
152C22×C47C22×C4211yescharacteristic
153C22×C47C2×#11713yes—
154C22×C47C2×#11713yes—
155C22×C47C2×C4×D413yes—
156C22×C47C4×#4113yes—
157C22×C47#51813yes—
158C22×C47#52013yes—
159C22×C47#54613yes—
160C22×C47#54811yescharacteristic
161C22×C47#55116yes—
162C22×C47#55213yes—
163C22×C47#55313yes—
164C4×C47—212no—
165C4×C47—46no—
166Dic47—24no—
167Dic47—24no—
168Dic47—46no—
169Dic47—46no—
170C2×C4×C22⋊C4—473no—
171C2×#376—471no—
172C22×#95D4711yescharacteristic
173#1434—473no—
174#1434—473no—
175C22⋊#95—473no—
176C4×#95—471no—
177C2×C47—28no—
178C2×C47C2×#37611yescharacteristic
179C2×C47C42×D411yescharacteristic
180C2×C47#227511yescharacteristic
181C2×C47#234213yes—
182C2×C47#234313yes—
183C2×C47#235213yes—
184C2×C47#235313yes—
185C24×C4C2×D4713yes—
186C22×C22⋊C4—471no—
187C22×C22⋊C4—473no—
188C22×C42—473no—
189C22×C42—473no—
190C4×C22⋊C4—4724no—
191#376—944no—
192C2×#95—24no—
193C2×#95—473no—
194C2×#95—473no—
195C2×#95—473no—
196C2×#95—473no—
197C2×#95—476no—
198C2×#95C2×D4713yes—
199C2×#95C2×D4711yescharacteristic
200C47#1380911yescharacteristic, complemented, Sylow
201C25C22×D4711yescharacteristic
202C23×C4—212no—
203C23×C4—26no—
204C23×C4—26no—
205C23×C4—46no—
206C23×C4—471no—
207C23×C4—471no—
208C23×C4—473no—
209C23×C4—473no—
210C23×C4C4×D47112yes—
211C23×C4C22×D4713yes—
212C23×C4C22×D4713yes—
213C2×C22⋊C4—4712no—
214C2×C22⋊C4—4712no—
215C2×C22⋊C4—946no—
216C2×C22⋊C4—946no—
217C2×C42—4712no—
218C2×C42—4712no—
219C2×C42—946no—
220C2×C42—946no—
221C2×C42—1886no—
222#95—26no—
223#95—4712no—
224#95—4712no—
225#95—946no—
226#95—946no—
227#95—1886no—
228#95C22⋊D4714yes—
229C24—21no—
230C24—23no—
231C24—23no—
232C24—21no—
233C24C2×C4×D4716yes—
234C24#1062535216yes—
235C24#1062535412yes—
236C24C23×D4711yescharacteristic
237C22×C4—26no—
238C22×C4—26no—
239C22×C4—224no—
240C22×C4—23no—
241C22×C4—26no—
242C22×C4—23no—
243C22×C4—26no—
244C22×C4—224no—
245C22×C4—412no—
246C22×C4—424no—
247C22×C4—424no—
248C22×C4—476no—
249C22×C4—476no—
250C22×C4—476no—
251C22×C4—476no—
252C22×C4—941no—
253C22×C4—943no—
254C22×C4—943no—
255C22×C4—941no—
256C22×C4—943no—
257C22×C4—943no—
258C22×C4—943no—
259C22×C4—946no—
260C22×C4—943no—
261C22×C4—943no—
262C22×C4—943no—
263C22×C4—943no—
264C22×C4—946no—
265C22×C4—943no—
266C22×C4C2×C4×D4716yes—
267C22×C4C2×C4×D4716yes—
268C22×C4#1062535016yes—
269C22×C4C2×C22⋊D4716yes—
270C22⋊C4—4716no—
271C22⋊C4—9424no—
272C42—9424no—
273C42—18812no—
274C23—26no—
275C23—22no—
276C23—212no—
277C23—26no—
278C23—26no—
279C23—26no—
280C23—26no—
281C23—26no—
282C23—26no—
283C23C42×D4714yes—
284C23#13093980112yes—
285C23#13093982112yes—
286C23C22×C4×D4713yes—
287C23C22×C22⋊D4711yescharacteristic
288C23C2×#1062535213yes—
289C23C2×#1062535013yes—
290C23C2×#1062535411yescharacteristic
291C23#1309406913yes—
292C23#1309407211yescharacteristic
293C2×C4—212no—
294C2×C4—212no—
295C2×C4—26no—
296C2×C4—26no—
297C2×C4—26no—
298C2×C4—26no—
299C2×C4—26no—
300C2×C4—448no—
301C2×C4—46no—
302C2×C4—46no—
303C2×C4—474no—
304C2×C4—474no—
305C2×C4—946no—
306C2×C4—946no—
307C2×C4—946no—
308C2×C4—946no—
309C2×C4—946no—
310C2×C4—946no—
311C2×C4—946no—
312C2×C4—946no—
313C2×C4—946no—
314C2×C4—946no—
315C2×C4—1883no—
316C2×C4—1883no—
317C2×C4—1886no—
318C2×C4—1883no—
319C2×C4—1883no—
320C2×C4—1886no—
321C2×C4C4×C22⋊D47112yes—
322C22—212no—
323C22—212no—
324C22—212no—
325C22—212no—
326C22—24no—
327C22—24no—
328C22#1568896818yescomplemented
329C22C2×C42×D4711yescharacteristic
330C22C2×#1309398013yes—
331C22C2×#1309398213yes—
332C22C2×C4×C22⋊D4713yes—
333C22C4×#1062535013yes—
334C22#1568959613yes—
335C22#1568960413yes—
336C22#1568976713yes—
337C22#1568978411yescharacteristic
338C22#1568979916yes—
339C22#1568980813yes—
340C22#1568982113yes—
341C4—212no—
342C4—46no—
343C4—944no—
344C4—944no—
345C4—1886no—
346C4—1886no—
347C2—28no—
348C2C2×#1568896811yescharacteristic
349C2C42×C22⋊D4711yescharacteristic
350C2#2024574611yescharacteristic
351C2#2024623313yes—
352C2#2024624413yes—
353C2#2024631313yes—
354C2#2024632413yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC22×#95×C47C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC22×#95D47
hypocenterC47#13809
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
2. C2×#15688968C2semidirect
3. #20241614C2semidirect
4. #20241612C2semidirect
6. #95×Dic47C2semidirect
12. C4×C22⋊Dic47C4semidirect
34. C2×C4×Dic47C2×C4semidirect
35. C2×C4×Dic47C2×C4semidirect
39. C47⋊#95C2×C4semidirect
40. C47⋊#95C2×C4semidirect
151. C22×C47#376semidirect
200. C47#13809semidirect
328. C22#15688968semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊Dic472
C2×#156889682
#202416142
#202416122
#202416112
#95×Dic472
C22×#95×C472
#1380947