Finite Group Databasebeta

← #37575705

Subgroups — #37575705

Order 24448.

408 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 173 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×#20259314C211yesmaximal, characteristic
2#27132560C212yesmaximal
3#27132558C212yesmaximal
4#27132550C212yesmaximal
5#27132548C212yesmaximal
6#27132546C212yesmaximal
7#27132544C212yesmaximal
8#27132529C211yesmaximal, characteristic
9#382×C191C211yesmaximal, characteristic
10#20259314C418yescomplemented
11C2×C4⋊Dic191C2211yescharacteristic
12C2×C4⋊Dic191C2211yescharacteristic
13C2×C4⋊Dic191C2211yescharacteristic
14C2×C4⋊Dic191C2211yescharacteristic
15C2×Dic191⋊C4C2212yes—
16C2×Dic191⋊C4C2212yes—
17C2×Dic191⋊C4C2212yes—
18C2×Dic191⋊C4C2212yes—
19C2×C4×Dic191C2212yes—
20C2×C4×Dic191C2212yes—
21C191⋊#95C2212yes—
22C191⋊#95C2212yes—
23C191⋊#95C2212yes—
24C191⋊#95C2212yes—
25C191⋊#95C2212yes—
26C191⋊#95C2212yes—
27C2×C4⋊C4×C191C2211yescharacteristic
28C2×C4⋊C4×C191C2211yescharacteristic
29C2×C42×C191C2211yescharacteristic
30#95×C191C2212yes—
31#95×C191C2212yes—
32C22×Dic191C2312yes—
33C22×Dic191C2312yes—
34C22×Dic191C2312yes—
35C22×Dic191C2312yes—
36C4⋊Dic191—41no—
37C4⋊Dic191—41no—
38C4⋊Dic191C2×C414yes—
39C4⋊Dic191C2×C414yes—
40Dic191⋊C4—42no—
41Dic191⋊C4—42no—
42Dic191⋊C4C2×C418yes—
43Dic191⋊C4C2×C418yes—
44C4×Dic191—42no—
45C4×Dic191—42no—
46C22×C4×C191C2312yes—
47C22×C4×C191C2312yes—
48C22×C4×C191C2311yescharacteristic
49C22×C4×C191C2311yescharacteristic
50C22×C4×C191C2311yescharacteristic
51C4⋊C4×C191—41no—
52C4⋊C4×C191—41no—
53C42×C191C2×C414yes—
54C2×Dic191—22no—
55C2×Dic191—22no—
56C2×Dic191—22no—
57C2×Dic191—22no—
58C2×Dic191—22no—
59C2×Dic191—22no—
60C2×Dic191—22no—
61C2×Dic191—22no—
62C2×Dic191—22no—
63C2×Dic191—22no—
64C2×Dic191C22×C414yes—
65C2×Dic191C22×C414yes—
66C23×C191C2411yescharacteristic
67C2×C4×C191—21no—
68C2×C4×C191—21no—
69C2×C4×C191—21no—
70C2×C4×C191—21no—
71C2×C4×C191—21no—
72C2×C4×C191—21no—
73C2×C4×C191—22no—
74C2×C4×C191—22no—
75C2×C4×C191—22no—
76C2×C4×C191—22no—
77C2×C4×C191—22no—
78C2×C4×C191—22no—
79C2×C4×C191C22×C412yes—
80C2×C4×C191C22×C412yes—
81C2×C4×C191C22×C412yes—
82C22×C191C23×C411yescharacteristic
83C22×C191H(5,𝔽2)11yescharacteristic
84C22×C191H(5,𝔽2)11yescharacteristic
85C22×C1912−1+411yescharacteristic
86C22×C1912−1+411yescharacteristic
87C22×C1912−1+411yescharacteristic
88C22×C1912−1+411yescharacteristic
89C4×C191—22no—
90C4×C191—22no—
91C4×C191—22no—
92C4×C191—42no—
93C4×C191—42no—
94Dic191—24no—
95Dic191—24no—
96Dic191—42no—
97Dic191—42no—
98C2×C191#51911yescharacteristic
99C2×C191#52011yescharacteristic
100C2×C191#52011yescharacteristic
101C2×C191#56211yescharacteristic
102C2×C191#56311yescharacteristic
103C2×C191#56311yescharacteristic
104C2×C191#56411yescharacteristic
105C191#238211yescharacteristic, complemented, Sylow
106#2382—1911nomaximal, Sylow
107C2×#125—1911no—
108#389—1912no—
109#389—1912no—
110#387—1912no—
111#387—1912no—
112#387—1912no—
113#387—1912no—
114#382—1911no—
115#382D19111yescharacteristic
116#125—1918no—
117C2×C4⋊C4—1911no—
118C2×C4⋊C4—1911no—
119C2×C4⋊C4—1912no—
120C2×C4⋊C4—1912no—
121C2×C4⋊C4—1911no—
122C2×C4⋊C4—1911no—
123C2×C4⋊C4—1912no—
124C2×C4⋊C4—1912no—
125C2×C4⋊C4C2×D19111yescharacteristic
126C2×C4⋊C4C2×D19111yescharacteristic
127C2×C42—1912no—
128C2×C42—1912no—
129C2×C42C2×D19111yescharacteristic
130#95—1912no—
131#95—1912no—
132#95—1912no—
133#95—1912no—
134#95—1912no—
135#95—1912no—
136#95C2×D19112yes—
137#95C2×D19112yes—
138C22×C4—1912no—
139C22×C4—1912no—
140C22×C4—1912no—
141C22×C4—1912no—
142C22×C4C22×D19112yes—
143C22×C4C22×D19112yes—
144C22×C4C22×D19111yescharacteristic
145C22×C4C22×D19111yescharacteristic
146C22×C4C22×D19111yescharacteristic
147C4⋊C4—41no—
148C4⋊C4—41no—
149C4⋊C4—1918no—
150C4⋊C4—1918no—
151C4⋊C4—1914no—
152C4⋊C4—1914no—
153C4⋊C4—7642no—
154C4⋊C4—7642no—
155C4⋊C4—7641no—
156C4⋊C4—7641no—
157C42—7642no—
158C42—7642no—
159C42C4×D19114yes—
160C23C23×D19111yescharacteristic
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—3822no—
174C2×C4—3822no—
175C2×C4—3822no—
176C2×C4—3822no—
177C2×C4—3822no—
178C2×C4—3822no—
179C2×C4—3822no—
180C2×C4—3822no—
181C2×C4—3822no—
182C2×C4—3822no—
183C2×C4—1914no—
184C2×C4—1914no—
185C2×C4C2×C4×D19112yes—
186C2×C4C2×C4×D19112yes—
187C2×C4C2×C4×D19112yes—
188C22C22×C4×D19111yescharacteristic
189C22#2025936711yescharacteristic
190C22#2025936811yescharacteristic
191C22#2025936911yescharacteristic
192C22#2025936911yescharacteristic
193C22#2025936911yescharacteristic
194C22#2025937011yescharacteristic
195C4—22no—
196C4—22no—
197C4—22no—
198C4—42no—
199C4—42no—
200C4—3824no—
201C4—3824no—
202C4—7642no—
203C4—7642no—
204C2#2713314011yescharacteristic
205C2#2713314311yescharacteristic
206C2#2713314411yescharacteristic
207C2#2713340711yescharacteristic
208C2#2713341311yescharacteristic
209C2#2713341711yescharacteristic
210C2C191⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutatorC22×C191C23×C4
Fitting#382×C191C2
socle, prime radical, cosocleC23×C191C24
hypercenter#382D191
hypocenterC191#2382
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
10. #20259314C4semidirect
105. C191#2382semidirect

Maximal subgroups

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

subgroupindex
C2×#202593142
#271325602
#271325582
#271325502
#271325482
#271325462
#271325442
#271325292
#382×C1912
#2382191