Finite Group Databasebeta

← #37571508

Subgroups — #37571508

Order 24448.

280 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 53 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#27133225C211yesmaximal, characteristic
2#27132977C212yesmaximal, complemented
3#27132588C211yesmaximal, characteristic, complemented
4#27132398C212yesmaximal, complemented
5#323×C191C211yesmaximal, characteristic, complemented
6C22×C22⋊D191—21no—
7#20259306—22no—
8#20259296—21no—
9#20259296C2212yes—
10#20259292—22no—
11C2×C4⋊Dic191C2211yescharacteristic, complemented
12C2×C22⋊Dic191—21no—
13#20259256—22no—
14#20259244—22no—
15C191⋊#95—21no—
16C191⋊#95C2211yescharacteristic, complemented
17C2×C22⋊C4×C191C2211yescharacteristic
18C22⋊C8×C191C2212yescomplemented
19C23×D191—21no—
20C2×D764—21no—
21C2×D764D412yes—
22C2×C22⋊D191—22no—
23C2×C22⋊D191—22no—
24C2×C22⋊D191—42no—
25C2×C22⋊D191—42no—
26C22×Dic191—21no—
27C22×Dic191—21no—
28C22×Dic191—21no—
29C4⋊Dic191—21no—
30C4⋊Dic191—22no—
31C4⋊Dic191D412yes—
32C22⋊Dic191—42no—
33(C2×D191)⋊C4—22no—
34(C2×D191)⋊C4—22no—
35C24×C191D411yescharacteristic
36C22×C4×C191D411yescharacteristic
37C22×C4×C191C2311yescharacteristic
38C2×C8×C191—22no—
39C22⋊C4×C191—22no—
40C22×D191—22no—
41C22×D191—42no—
42C22×D191—81no—
43C22×D191—81no—
44D764—42no—
45D764—81no—
46C22⋊D191—44no—
47C22⋊D191—42no—
48C22⋊D191—42no—
49C2×Dic191—22no—
50C2×Dic191—42no—
51C2×Dic191—41no—
52C2×Dic191—41no—
53C2×Dic191—41no—
54C2×Dic191—41no—
55C2×Dic191—41no—
56C2×Dic191—41no—
57C23×C191—21no—
58C23×C191—21no—
59C23×C191—41no—
60C23×C191—41no—
61C23×C191D812yes—
62C23×C191C2×D411yescharacteristic
63C2×C4×C191—21no—
64C2×C4×C191—41no—
65C2×C4×C191—41no—
66C2×C4×C191C2×D412yes—
67C8×C191—42no—
68C22×C191—21no—
69C22×C191—21no—
70C22×C191—22no—
71C22×C191—42no—
72C22×C191—41no—
73C22×C191—41no—
74C22×C191—81no—
75C22×C191#12011yescharacteristic
76C22×C191C2×D811yescharacteristic
77C22×C191AGL(1,ℤ/8)11yescharacteristic
78C2×D191—42no—
79C2×D191—42no—
80C2×D191—42no—
81C2×D191—84no—
82C4×C191—22no—
83C4×C191—41no—
84Dic191—42no—
85Dic191—81no—
86Dic191—81no—
87C2×C191—21no—
88C2×C191—21no—
89C2×C191—42no—
90C2×C191#44711yescharacteristic
91C2×C191#45511yescharacteristic
92C2×C191#45811yescharacteristic
93D191—82no—
94C191#160711yescharacteristic, complemented, Sylow
95#1607—1911nomaximal, Sylow
96#534—1911no—
97#480—1912no—
98#397—1911no—
99#327—1912no—
100#323D19111yescharacteristic, complemented
101C22×D4—3821no—
102#123—3822no—
103#121—3821no—
104#121—1912no—
105#120—3822no—
106C2×C4⋊C4—1911no—
107C2×C22⋊C4—3821no—
108C2×C22⋊C4C2×D19111yescharacteristic
109#107—3822no—
110#102—3822no—
111C22⋊C8C2×D19112yescomplemented
112#95—3821no—
113#95—1911no—
114C24—3821no—
115C24D76411yescharacteristic
116C2×D4—3821no—
117C2×D4—3822no—
118C2×D4—3822no—
119C2×D4—1912no—
120C2×D4—7642no—
121C2×D4—7642no—
122C22×C4—3821no—
123C22×C4—3821no—
124C22×C4—3821no—
125C22×C4D76411yescharacteristic
126C22×C4C22×D19111yescharacteristic
127C2×C8—22no—
128C4⋊C4—3821no—
129C4⋊C4—3822no—
130C4⋊C4—1912no—
131C22⋊C4—22no—
132C22⋊C4—3822no—
133C22⋊C4—3822no—
134C22⋊C4—7642no—
135C23—21no—
136C23—21no—
137C23—41no—
138C23—41no—
139C23—3822no—
140C23—15281no—
141C23—15281no—
142C23—7642no—
143C23D152812yes—
144C23C2×D76411yescharacteristic
145D4—15281no—
146D4—7642no—
147D4—7644no—
148D4—7642no—
149D4—7642no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—3822no—
154C2×C4—7641no—
155C2×C4—7641no—
156C2×C4—7641no—
157C2×C4—7641no—
158C2×C4—7641no—
159C2×C4—7641no—
160C2×C4—7642no—
161C2×C4D4×D19112yes—
162C8—42no—
163C22—21no—
164C22—21no—
165C22—22no—
166C22—42no—
167C22—41no—
168C22—41no—
169C22—81no—
170C22—15284no—
171C22—7642no—
172C22—7642no—
173C22—7642no—
174C22#2025929211yescharacteristic
175C22C2×D152811yescharacteristic
176C22#2025935011yescharacteristic
177C4—22no—
178C4—41no—
179C4—15281no—
180C4—15281no—
181C4—7642no—
182C2—21no—
183C2—21no—
184C2—42no—
185C2—15282no—
186C2#2713279911yescharacteristic
187C2#2713284311yescharacteristic
188C2#2713285411yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#323×C191C2
socleC22×C191#120
prime radical#27133225C2
hypercenter#323D191
hypocenterC191#1607
LCSG ▷ C22×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #27132977C2semidirect
3. #27132588C2semidirect
4. #27132398C2semidirect
5. #323×C191C2semidirect
11. C2×C4⋊Dic191C22semidirect
16. C191⋊#95C22semidirect
18. C22⋊C8×C191C22semidirect
94. C191#1607semidirect
100. #323D191semidirect
111. C22⋊C8C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332252
#271329772
#271325882
#271323982
#323×C1912
#1607191