Finite Group Databasebeta

← #26109740

Subgroups — #26109740

Order 12032.

514 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688849C212yesmaximal
2#20241236C214yesmaximal
3C47×#2274C211yesmaximal, characteristic
4C2×C22⋊(C47⋊C8)C2214yes—
5#15688849—22no—
6#15688849—22no—
7C2×#117×C47C411yescharacteristic
8C2×#117×C47C411yescharacteristic
9C22×C4⋊C4×C47C2211yescharacteristic
10C4×C4⋊C4×C47—22no—
11C4×C4⋊C4×C47—22no—
12C4×C22⋊C4×C47C412yes—
13C4×C22⋊C4×C47C2212yes—
14C22×C47⋊C8—24no—
15C22⋊(C47⋊C8)—24no—
16C22⋊(C47⋊C8)—24no—
17C23×C4×C47C2×C411yescharacteristic
18C23×C4×C47C2×C411yescharacteristic
19C23×C4×C47C2311yescharacteristic
20#117×C47—22no—
21#117×C47—24no—
22#117×C47C814yescomplemented
23C2×C4⋊C4×C47—21no—
24C2×C4⋊C4×C47—21no—
25C2×C4⋊C4×C47—24no—
26C2×C4⋊C4×C47D412yes—
27C2×C4⋊C4×C47D412yes—
28C2×C22⋊C4×C47C2×C412yes—
29C2×C22⋊C4×C47C2×C412yes—
30C2×C42×C47—21no—
31C2×C42×C47—21no—
32C2×C42×C47—22no—
33C2×C42×C47—22no—
34#95×C47—22no—
35#95×C47—22no—
36C24×C47C22×C411yescharacteristic
37C22×C4×C47—22no—
38C22×C4×C47—22no—
39C22×C4×C47—22no—
40C22×C4×C47—22no—
41C22×C4×C47—22no—
42C22×C4×C47—81no—
43C22×C4×C47—81no—
44C22×C4×C47C22⋊C411yescharacteristic
45C22×C4×C47C22⋊C411yescharacteristic
46C22×C4×C47C22⋊C412yes—
47C22×C4×C47C2×C812yes—
48C22×C4×C47M1612yes—
49C22×C4×C47C2×D412yes—
50C22×C4×C47#4114yes—
51C4⋊C4×C47—24no—
52C4⋊C4×C47—24no—
53C4⋊C4×C47—24no—
54C4⋊C4×C47—24no—
55C22⋊C4×C47—22no—
56C22⋊C4×C47—22no—
57C22⋊C4×C47C2×C814yes—
58C22⋊C4×C47M1614yes—
59C42×C47—24no—
60C42×C47—24no—
61C42×C47—82no—
62C42×C47—82no—
63C2×C47⋊C8—44no—
64C2×C47⋊C8—84no—
65C23×C47—41no—
66C23×C47—41no—
67C23×C47C2×C22⋊C411yescharacteristic
68C23×C47#11712yes—
69C23×C47C22×C811yescharacteristic
70C23×C47C2×M1611yescharacteristic
71C23×C47C2×M1612yes—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—24no—
77C2×C4×C47—24no—
78C2×C4×C47—22no—
79C2×C4×C47—24no—
80C2×C4×C47—24no—
81C2×C4×C47—44no—
82C2×C4×C47—42no—
83C2×C4×C47—42no—
84C2×C4×C47—42no—
85C2×C4×C47—42no—
86C2×C4×C47—42no—
87C2×C4×C47—42no—
88C2×C4×C47—82no—
89C2×C4×C47C22⋊C812yes—
90C2×C4×C47C22⋊C812yes—
91C2×C4×C47#12314yes—
92C47⋊C8—84no—
93#8735—471nomaximal, Sylow
94C22×C47—21no—
95C22×C47—22no—
96C22×C47—21no—
97C22×C47—22no—
98C22×C47—41no—
99C22×C47—41no—
100C22×C47—42no—
101C22×C47#38111yescharacteristic
102C22×C47C2×C22⋊C811yescharacteristic
103C22×C47#40711yescharacteristic
104C22×C47#43112yes—
105C22×C47#43212yes—
106C4×C47—22no—
107C4×C47—22no—
108C4×C47—24no—
109C4×C47—44no—
110C4×C47—44no—
111C4×C47—42no—
112#2274D4711yescharacteristic
113C2×#324—472no—
114#1282—474no—
115C2×C47—21no—
116C2×C47—21no—
117C2×C47—22no—
118C2×C47—22no—
119C2×C47#181711yescharacteristic
120C2×C47#182811yescharacteristic
121C2×C47#183011yescharacteristic
122C2×#117Dic4711yescharacteristic
123C2×#117Dic4711yescharacteristic
124C22×C4⋊C4C2×D4711yescharacteristic
125C2×C22⋊C8—474no—
126C4×C4⋊C4—22no—
127C4×C4⋊C4—22no—
128C4×C22⋊C4Dic4712yes—
129C4×C22⋊C4C2×D4712yes—
130#324—942no—
131#324—942no—
132C47#873511yescharacteristic, complemented, Sylow
133C23×C4C2×Dic4711yescharacteristic
134C23×C4C2×Dic4711yescharacteristic
135C23×C4C22×D4711yescharacteristic
136C22×C8—944no—
137#117—22no—
138#117—24no—
139#117C47⋊C814yescomplemented
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—24no—
143C2×C4⋊C4C22⋊D4712yes—
144C2×C4⋊C4C22⋊D4712yes—
145C2×C22⋊C4C2×Dic4712yes—
146C2×C22⋊C4C2×Dic4712yes—
147C2×C42—21no—
148C2×C42—21no—
149C2×C42—22no—
150C2×C42—22no—
151C22⋊C8—944no—
152C22⋊C8—944no—
153#95—22no—
154#95—22no—
155C24C22×Dic4711yescharacteristic
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—81no—
162C22×C4—81no—
163C22×C4C2×C47⋊C812yes—
164C22×C4#1062532912yes—
165C22×C4C22⋊Dic4711yescharacteristic
166C22×C4C22⋊Dic4711yescharacteristic
167C22×C4C22⋊Dic4712yes—
168C22×C4#1062535014yes—
169C22×C4C2×C22⋊D4712yes—
170C2×C8—3764no—
171C2×C8—1884no—
172C4⋊C4—24no—
173C4⋊C4—24no—
174C4⋊C4—24no—
175C4⋊C4—24no—
176C22⋊C4—22no—
177C22⋊C4—22no—
178C22⋊C4C2×C47⋊C814yes—
179C22⋊C4#1062532914yes—
180C42—24no—
181C42—24no—
182C42—82no—
183C42—82no—
184C23—41no—
185C23—41no—
186C23C2×C22⋊Dic4711yescharacteristic
187C23#1309398312yes—
188C23C22×C47⋊C811yescharacteristic
189C23C2×#1062532911yescharacteristic
190C23C2×#1062532912yes—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—22no—
198C2×C4—24no—
199C2×C4—24no—
200C2×C4—42no—
201C2×C4—44no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—82no—
208C2×C4C22⋊(C47⋊C8)12yes—
209C2×C4C22⋊(C47⋊C8)12yes—
210C2×C4#1309400714yes—
211C8—3764no—
212C22—21no—
213C22—22no—
214C22—21no—
215C22—22no—
216C22—41no—
217C22—41no—
218C22—42no—
219C22#1568898611yescharacteristic
220C22C2×C22⋊(C47⋊C8)11yescharacteristic
221C22#1568908711yescharacteristic
222C22#1568917612yes—
223C22#1568918012yes—
224C4—22no—
225C4—22no—
226C4—24no—
227C4—44no—
228C4—44no—
229C4—42no—
230C2—21no—
231C2—21no—
232C2—22no—
233C2—22no—
234C2#2024345611yescharacteristic
235C2#2024349611yescharacteristic
236C2#2024350211yescharacteristic
subgroupG/H
centerC22#15688986
commutatorC23×C47C22×C8
FrattiniC23×C4C22×D47
FittingC47×#2274C2
socleC22×C47#381
prime radicalC24×C47C22×C4
cosocleC23×C4×C47C23
hypercenter#2274D47
hypocenterC47#8735
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2274

Complements

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

NH ≅ G/Ntype
22. #117×C47C8semidirect
132. C47#8735semidirect
139. #117C47⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×#156888492
#202412362
C47×#22742
#873547