Finite Group Databasebeta

← #37571007

Subgroups — #37571007

Order 24448.

238 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 73 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#27133197C211yesmaximal, characteristic
2#27132509C211yesmaximal, characteristic, complemented
3#27132401C212yesmaximal, complemented
4#27132398C212yesmaximal
5#431×C191C211yesmaximal, characteristic, complemented
6#20259316—21no—
7#20259314C411yescharacteristic, complemented
8#20259310C411yescharacteristic, complemented
9#20259305—21no—
10#20259301C2211yescharacteristic
11#20259296C2211yescharacteristic
12C4×Dic382C411yescharacteristic, complemented
13C4×D764C411yescharacteristic, complemented
14C4×C22⋊D191—21no—
15#20259279—21no—
16C2×C4×Dic191—21no—
17C191⋊#95—21no—
18C191⋊#95C2212yes—
19C2×C42×C191C2211yescharacteristic
20C4⋊C8×C191—21no—
21C22⋊C8×C191C2212yes—
22C4×C8×C191—21no—
23C2×Dic382C2×C411yescharacteristic
24C2×D764C2×C411yescharacteristic
25C2×C22⋊D191—21no—
26C22×Dic191—22no—
27C2×C4×D191—21no—
28C4⋊Dic191C2×C411yescharacteristic
29C4⋊Dic191C2×C411yescharacteristic
30Dic191⋊C4—21no—
31Dic191⋊C4—21no—
32Dic191⋊C4—21no—
33Dic191⋊C4—21no—
34C22⋊Dic191—21no—
35(C2×D191)⋊C4—21no—
36(C2×D191)⋊C4—21no—
37(C2×D191)⋊C4—21no—
38(C2×D191)⋊C4—21no—
39C4×Dic191—24no—
40C4×Dic191—21no—
41C22×C4×C191D411yescharacteristic
42C22×C4×C191D411yescharacteristic
43C22×C4×C191C2311yescharacteristic
44C2×C8×C191—22no—
45C42×C191C2×C411yescharacteristic
46C42×C191C2×C411yescharacteristic
47C42×C191D411yescharacteristic
48C42×C191D411yescharacteristic
49C22×D191—21no—
50Dic382—41no—
51D764—41no—
52C22⋊D191—42no—
53C2×Dic191—24no—
54C2×Dic191—21no—
55C2×Dic191—21no—
56C2×Dic191—21no—
57C2×Dic191—42no—
58C2×Dic191—42no—
59C4×D191—42no—
60C23×C191C2×D411yescharacteristic
61C2×C4×C191—22no—
62C2×C4×C191—22no—
63C2×C4×C191—41no—
64C2×C4×C191C22⋊C411yescharacteristic
65C2×C4×C191C22⋊C411yescharacteristic
66C2×C4×C191C22⋊C411yescharacteristic
67C2×C4×C191C22⋊C411yescharacteristic
68C2×C4×C191C22×C411yescharacteristic
69C2×C4×C191C2×D411yescharacteristic
70C8×C191—42no—
71C22×C191—21no—
72C22×C191—21no—
73C22×C191C2×C22⋊C411yescharacteristic
74C22×C191#13512yes—
75C2×D191—41no—
76C2×D191—41no—
77C2×D191—41no—
78C4×C191—21no—
79C4×C191—21no—
80C4×C191—21no—
81C4×C191—21no—
82C4×C191—21no—
83C4×C191#10412yes—
84Dic191—44no—
85Dic191—41no—
86Dic191—41no—
87Dic191—41no—
88C2×C191—22no—
89C2×C191#41011yescharacteristic
90C2×C191#41611yescharacteristic
91C2×C191C2×#10411yescharacteristic
92D191—81no—
93C191#150011yescharacteristic, complemented, Sylow
94#1500—1911nomaximal, Sylow
95#529—1911no—
96#431D19111yescharacteristic, complemented
97#376—1911no—
98#328—1912no—
99#327—1912no—
100#126—3821no—
101#125—1911no—
102#124—1911no—
103#123—3821no—
104C22⋊Q8—1911no—
105#121—1911no—
106C4×Q8—1911no—
107C4×D4—3821no—
108C4×D4—1911no—
109#117—3821no—
110C2×C42—3821no—
111C2×C42C2×D19111yescharacteristic
112C4⋊C8—21no—
113C22⋊C8C2×D19112yes—
114C4×C8—21no—
115#95—3821no—
116#95—1912no—
117C2×Q8—1911no—
118C2×D4—3821no—
119C2×D4—1911no—
120C22×C4—3822no—
121C22×C4—3821no—
122C22×C4D76411yescharacteristic
123C22×C4D76411yescharacteristic
124C22×C4C22×D19111yescharacteristic
125C2×C8—22no—
126C4⋊C4—3821no—
127C4⋊C4—3821no—
128C4⋊C4—3821no—
129C4⋊C4—3821no—
130C4⋊C4—1911no—
131C4⋊C4—1911no—
132C22⋊C4—3821no—
133C22⋊C4—3821no—
134C22⋊C4—3821no—
135C22⋊C4—3821no—
136C22⋊C4—3821no—
137C42—3824no—
138C42—3821no—
139C42C4×D19111yescharacteristic
140C42C4×D19111yescharacteristic
141C42C22⋊D19111yescharacteristic
142C42C22⋊D19111yescharacteristic
143C23—3821no—
144C23C2×D76411yescharacteristic
145Q8—7641no—
146D4—7641no—
147D4—7642no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—3824no—
152C2×C4—3821no—
153C2×C4—3821no—
154C2×C4—3821no—
155C2×C4—7642no—
156C2×C4—7642no—
157C2×C4—7642no—
158C2×C4(C2×D191)⋊C411yescharacteristic
159C2×C4(C2×D191)⋊C411yescharacteristic
160C2×C4(C2×D191)⋊C411yescharacteristic
161C2×C4(C2×D191)⋊C411yescharacteristic
162C2×C4C2×C4×D19111yescharacteristic
163C2×C4C2×C22⋊D19111yescharacteristic
164C8—42no—
165C22—21no—
166C22—21no—
167C22—7641no—
168C22—7641no—
169C22—7641no—
170C22C2×(C2×D191)⋊C411yescharacteristic
171C22#2025934412yes—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—7644no—
178C4—7641no—
179C4—7641no—
180C4—7641no—
181C4#2025924812yes—
182C2—22no—
183C2—15281no—
184C2#2713263611yescharacteristic
185C2#2713266011yescharacteristic
186C2C2×#2025924811yescharacteristic
subgroupG/H
centerC2×C4(C2×D191)⋊C4
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
Fitting#431×C191C2
socleC22×C191C2×C22⋊C4
prime radical#20259296C22
cosocleC22×C4×C191C23
hypercenter#431D191
hypocenterC191#1500
LCSG ▷ C2×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #27132509C2semidirect
3. #27132401C2semidirect
5. #431×C191C2semidirect
7. #20259314C4semidirect
8. #20259310C4semidirect
12. C4×Dic382C4semidirect
13. C4×D764C4semidirect
93. C191#1500semidirect
96. #431D191semidirect

Maximal subgroups

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

subgroupindex
#271331972
#271325092
#271324012
#271323982
#431×C1912
#1500191