Finite Group Databasebeta

← #37583911

Subgroups — #37583911

Order 24448.

342 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#27133220C211yesmaximal, characteristic
2#27132948C212yesmaximal, complemented
3#27132945C212yesmaximal, complemented
4#27132919C214yesmaximal
5#27132873C212yesmaximal, complemented
6#27132870C212yesmaximal, complemented
7#27132687C211yesmaximal, characteristic
8#533×C191C211yesmaximal, characteristic
9C2×#15690277C2214yes—
10C2×#15690271C2212yes—
11#20259322C2211yescharacteristic
12#20259322C2211yescharacteristic
13#20259314—21no—
14#20259301—21no—
15#20259301C2212yes—
16C4×Dic382—21no—
17C4×Dic382C2212yes—
18#20259281—21no—
19#20259253C2214yes—
20C4⋊(C191⋊C8)C2212yes—
21C4⋊(C191⋊C8)C2212yes—
22#20259246C2214yes—
23#20259245C2214yes—
24C4⋊Q8×C191C2211yescharacteristic
25C4⋊Q8×C191C2211yescharacteristic
26#125×C191—21no—
27C22⋊Q8×C191—21no—
28C22⋊Q8×C191C2212yes—
29C4×Q8×C191—21no—
30C4×Q8×C191C2212yes—
31#117×C191—21no—
32C2×C42×C191C2211yescharacteristic
33C2×Dic382—21no—
34C2×Dic382C2312yes—
35#15690277—44no—
36#15690271—42no—
37C2×C191⋊C8C2314yes—
38C4⋊Dic191—21no—
39C4⋊Dic191—21no—
40C4⋊Dic191—21no—
41C4⋊Dic191C2312yes—
42Dic191⋊C4—22no—
43Dic191⋊C4—22no—
44C22⋊Dic191—22no—
45C4×Dic191—22no—
46C2×Q8×C191—21no—
47C2×Q8×C191C2312yes—
48C22×C4×C191D411yescharacteristic
49C22×C4×C191D411yescharacteristic
50C22×C4×C191C2311yescharacteristic
51C4⋊C4×C191—21no—
52C4⋊C4×C191—21no—
53C4⋊C4×C191—21no—
54C4⋊C4×C191—22no—
55C4⋊C4×C191—22no—
56C4⋊C4×C191C2312yes—
57C22⋊C4×C191—22no—
58C42×C191—22no—
59C42×C191D411yescharacteristic
60C42×C191D411yescharacteristic
61C42×C191C2311yescharacteristic
62C42×C191C2311yescharacteristic
63Dic382—22no—
64Dic382—22no—
65Dic382—42no—
66C2×Dic191—22no—
67C2×Dic191—22no—
68C191⋊C8—24no—
69C23×C191C2×D411yescharacteristic
70Q8×C191—22no—
71Q8×C191—22no—
72Q8×C191—42no—
73C2×C4×C191—22no—
74C2×C4×C191—22no—
75C2×C4×C191—21no—
76C2×C4×C191—21no—
77C2×C4×C191—22no—
78C2×C4×C191—22no—
79C2×C4×C191C2×D411yescharacteristic
80C2×C4×C191C2×D411yescharacteristic
81C2×C4×C191C2×D411yescharacteristic
82C2×C4×C191C2×D411yescharacteristic
83C2×C4×C191C2×D411yescharacteristic
84C2×C4×C191C2411yescharacteristic
85C22×C191—21no—
86C22×C191—21no—
87C22×C191—21no—
88C22×C191C22×D411yescharacteristic
89C4×C191—21no—
90C4×C191—21no—
91C4×C191—21no—
92C4×C191—42no—
93C4×C191—42no—
94C4×C191#13712yes—
95C4×C191#13712yes—
96C4×C191H(5,𝔽2)11yescharacteristic
97C4×C1912−1+411yescharacteristic
98Dic191—42no—
99Dic191—42no—
100C2×C191—41no—
101C2×C191#53711yescharacteristic
102C2×C191C2×#13711yescharacteristic
103C2×C191C2×#13711yescharacteristic
104C191#325511yescharacteristic, complemented, Sylow
105#3255—1911nomaximal, Sylow
106#533—1911no—
107#533D19111yescharacteristic
108#475—1912no—
109#475—1912no—
110#470—1914no—
111#462—1912no—
112#462—1912no—
113#423—1911no—
114C2×Q16—1914no—
115C2×M16—1912no—
116C4⋊Q8—1911no—
117C4⋊Q8—1911no—
118C4⋊Q8C2×D19111yescharacteristic
119C4⋊Q8C2×D19111yescharacteristic
120#125—21no—
121#125—3821no—
122C22⋊Q8—21no—
123C22⋊Q8—3821no—
124C22⋊Q8—1912no—
125C22⋊Q8C2×D19112yes—
126C4×Q8—21no—
127C4×Q8—3821no—
128C4×Q8—1912no—
129C4×Q8C2×D19112yes—
130#117—21no—
131#117—3821no—
132C2×C42C2×D19111yescharacteristic
133#106—1914no—
134C4⋊C8—1912no—
135C4⋊C8—1912no—
136#103—1914no—
137#103—1914no—
138C2×Q8—21no—
139C2×Q8—3821no—
140C2×Q8—1912no—
141C2×Q8C22×D19112yes—
142C22×C4C22⋊D19111yescharacteristic
143C22×C4C22⋊D19111yescharacteristic
144C22×C4C22×D19111yescharacteristic
145Q16—7644no—
146M16—7642no—
147C2×C8—1914no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—3822no—
154C4⋊C4—3822no—
155C4⋊C4—3821no—
156C4⋊C4—3821no—
157C4⋊C4—3821no—
158C4⋊C4—1912no—
159C4⋊C4C22×D19112yes—
160C22⋊C4—22no—
161C22⋊C4—3822no—
162C42—22no—
163C42—3822no—
164C42C22⋊D19111yescharacteristic
165C42C22⋊D19111yescharacteristic
166C42C22×D19111yescharacteristic
167C42C22×D19111yescharacteristic
168C23C2×C22⋊D19111yescharacteristic
169Q8—22no—
170Q8—22no—
171Q8—42no—
172Q8—3822no—
173Q8—3822no—
174Q8—7642no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—3822no—
182C2×C4—3822no—
183C2×C4C2×C22⋊D19111yescharacteristic
184C2×C4C2×C22⋊D19111yescharacteristic
185C2×C4C2×C22⋊D19111yescharacteristic
186C2×C4C2×C22⋊D19111yescharacteristic
187C2×C4C2×C22⋊D19111yescharacteristic
188C2×C4C23×D19111yescharacteristic
189C8—3824no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22C22×C22⋊D19111yescharacteristic
194C4—21no—
195C4—21no—
196C4—21no—
197C4—42no—
198C4—42no—
199C4—7642no—
200C4—7642no—
201C4#2025935212yes—
202C4#2025935312yes—
203C4#2025936811yescharacteristic
204C4#2025936911yescharacteristic
205C2—41no—
206C2#2713324111yescharacteristic
207C2C2×#2025935211yescharacteristic
208C2C2×#2025935311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#533×C191C2
socleC22×C191C22×D4
prime radicalC23×C191C2×D4
hypercenter#533D191
hypocenterC191#3255
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #27132948C2semidirect
3. #27132945C2semidirect
5. #27132873C2semidirect
6. #27132870C2semidirect
104. C191#3255semidirect

Maximal subgroups

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

subgroupindex
#271332202
#271329482
#271329452
#271329192
#271328732
#271328702
#271326872
#533×C1912
#3255191