Finite Group Databasebeta

← #37583261

Subgroups — #37583261

Order 24448.

358 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 129 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#27133059C211yesmaximal, characteristic, complemented
3#27133042C211yesmaximal, characteristic, complemented
4#27133015C211yesmaximal, characteristic, complemented
5#27133013C211yesmaximal, characteristic, complemented
6#27132919C214yesmaximal
7#27132768C214yesmaximal, complemented
8C4×#15690271C211yesmaximal, characteristic
9#533×C191C211yesmaximal, characteristic
10C2×#15690277C2214yes—
11C2×#15690271C2212yes—
12#20259322C2211yescharacteristic
13#20259322C2211yescharacteristic
14#20259314—21no—
15#20259301—21no—
16#20259301C2212yes—
17C4×Dic382—21no—
18C4×Dic382C2212yes—
19#20259281—21no—
20#20259253C2214yes—
21#20259246C2214yes—
22#20259245C2214yes—
23#20259233C2212yes—
24C4×C191⋊C8C2211yescharacteristic
25C4×C191⋊C8C2211yescharacteristic
26C4⋊Q8×C191C2211yescharacteristic
27C4⋊Q8×C191C2211yescharacteristic
28#125×C191—21no—
29C22⋊Q8×C191—21no—
30C22⋊Q8×C191C2212yes—
31C4×Q8×C191—21no—
32C4×Q8×C191C2212yes—
33#117×C191—21no—
34C2×C42×C191C2211yescharacteristic
35C2×Dic382—21no—
36C2×Dic382C2312yes—
37#15690277—28no—
38#15690271—24no—
39C2×C191⋊C8C2312yes—
40C2×C191⋊C8C2312yes—
41C4⋊Dic191—21no—
42C4⋊Dic191—21no—
43C4⋊Dic191—21no—
44C4⋊Dic191C2312yes—
45Dic191⋊C4—22no—
46Dic191⋊C4—22no—
47C22⋊Dic191—22no—
48C4×Dic191—22no—
49C2×Q8×C191—21no—
50C2×Q8×C191C2312yes—
51C22×C4×C191D411yescharacteristic
52C22×C4×C191D411yescharacteristic
53C22×C4×C191C2311yescharacteristic
54C4⋊C4×C191—21no—
55C4⋊C4×C191—21no—
56C4⋊C4×C191—21no—
57C4⋊C4×C191—22no—
58C4⋊C4×C191—22no—
59C4⋊C4×C191C2312yes—
60C22⋊C4×C191—22no—
61C42×C191—22no—
62C42×C191D411yescharacteristic
63C42×C191D411yescharacteristic
64C42×C191C2311yescharacteristic
65C42×C191C2311yescharacteristic
66Dic382—24no—
67Dic382—42no—
68C2×Dic191—22no—
69C2×Dic191—22no—
70C191⋊C8—22no—
71C191⋊C8#4114yes—
72C23×C191C2×D411yescharacteristic
73Q8×C191—24no—
74Q8×C191—42no—
75C2×C4×C191—22no—
76C2×C4×C191—22no—
77C2×C4×C191—22no—
78C2×C4×C191—22no—
79C2×C4×C191—22no—
80C2×C4×C191C2×D411yescharacteristic
81C2×C4×C191C2×D411yescharacteristic
82C2×C4×C191C2×D411yescharacteristic
83C2×C4×C191C2×D411yescharacteristic
84C2×C4×C191C2×D411yescharacteristic
85C2×C4×C191C2411yescharacteristic
86C22×C191—21no—
87C22×C191—21no—
88C22×C191—21no—
89C22×C191C22×D411yescharacteristic
90C4×C191—21no—
91C4×C191—21no—
92C4×C191—21no—
93C4×C191—42no—
94C4×C191—42no—
95C4×C191#13712yes—
96C4×C191#13712yes—
97C4×C191C2×#4112yes—
98Dic191—42no—
99Dic191—42no—
100C2×C191—41no—
101C2×C191#53211yescharacteristic
102C2×C191C2×#13711yescharacteristic
103C2×C191C2×#13711yescharacteristic
104C191#318511yescharacteristic, complemented, Sylow
105#3185—1911nomaximal, Sylow
106#533—1911no—
107#533D19111yescharacteristic
108#498—1911no—
109#494—1911no—
110#487—1911no—
111#487—1911no—
112#470—1914no—
113#441—1914no—
114C4×M16—1911no—
115C2×Q16—1914no—
116C2×M16—1912no—
117C4⋊Q8—1911no—
118C4⋊Q8—1911no—
119C4⋊Q8C2×D19111yescharacteristic
120C4⋊Q8C2×D19111yescharacteristic
121#125—21no—
122#125—3821no—
123C22⋊Q8—21no—
124C22⋊Q8—3821no—
125C22⋊Q8—1912no—
126C22⋊Q8C2×D19112yes—
127C4×Q8—21no—
128C4×Q8—3821no—
129C4×Q8—1912no—
130C4×Q8C2×D19112yes—
131#117—21no—
132#117—3821no—
133C2×C42C2×D19111yescharacteristic
134#106—1914no—
135#103—1914no—
136#103—1914no—
137#97—1912no—
138C4×C8—1911no—
139C4×C8—1911no—
140C2×Q8—21no—
141C2×Q8—3821no—
142C2×Q8—1912no—
143C2×Q8C22×D19112yes—
144C22×C4C22⋊D19111yescharacteristic
145C22×C4C22⋊D19111yescharacteristic
146C22×C4C22×D19111yescharacteristic
147Q16—3828no—
148M16—3824no—
149C2×C8—1912no—
150C2×C8—1912no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—3822no—
157C4⋊C4—3822no—
158C4⋊C4—3821no—
159C4⋊C4—3821no—
160C4⋊C4—3821no—
161C4⋊C4—1912no—
162C4⋊C4C22×D19112yes—
163C22⋊C4—22no—
164C22⋊C4—3822no—
165C42—22no—
166C42—3822no—
167C42C22⋊D19111yescharacteristic
168C42C22⋊D19111yescharacteristic
169C42C22×D19111yescharacteristic
170C42C22×D19111yescharacteristic
171C23C2×C22⋊D19111yescharacteristic
172Q8—24no—
173Q8—42no—
174Q8—3824no—
175Q8—7642no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
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—3822no—
190C8—1914no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22C22×C22⋊D19111yescharacteristic
195C4—21no—
196C4—21no—
197C4—21no—
198C4—42no—
199C4—42no—
200C4—7642no—
201C4—7642no—
202C4#2025935212yes—
203C4#2025935312yes—
204C4#41×D19112yes—
205C2—41no—
206C2#2713320911yescharacteristic
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#3185
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. #27133059C2semidirect
3. #27133042C2semidirect
4. #27133015C2semidirect
5. #27133013C2semidirect
7. #27132768C2semidirect
104. C191#3185semidirect

Maximal subgroups

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

subgroupindex
#271332202
#271330592
#271330422
#271330152
#271330132
#271329192
#271327682
C4×#156902712
#533×C1912
#3185191