Finite Group Databasebeta

← #37570931

Subgroups — #37570931

Order 24448.

234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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
2C4×#15690271C211yesmaximal, characteristic, complemented
3#27132393C212yesmaximal, complemented
4#27132390C212yesmaximal, complemented
5C2×C4⋊C8×C191C211yesmaximal, characteristic, complemented
6C2×#15690271—21no—
7#20259316—21no—
8#20259314C411yescharacteristic
9#20259310C411yescharacteristic
10#20259305—21no—
11#20259301C411yescharacteristic
12#20259296C411yescharacteristic
13C4×Dic382C2211yescharacteristic
14C4×D764C2211yescharacteristic
15C4×C22⋊D191—21no—
16#20259279—21no—
17#20259233—21no—
18C4×C191⋊C8C2212yes—
19C22×C8×C191—21no—
20C2×C42×C191C2211yescharacteristic
21C4⋊C8×C191—21no—
22C4⋊C8×C191C2212yes—
23C2×Dic382C2×C411yescharacteristic
24C2×D764C2×C411yescharacteristic
25C2×C22⋊D191—21no—
26C2×C4×D191—21no—
27#15690271—24no—
28C2×C191⋊C8—22no—
29C4⋊Dic191C2×C411yescharacteristic
30C4⋊Dic191C2×C411yescharacteristic
31Dic191⋊C4—21no—
32Dic191⋊C4—21no—
33Dic191⋊C4—21no—
34Dic191⋊C4—21no—
35C22⋊Dic191—21no—
36(C2×D191)⋊C4—21no—
37(C2×D191)⋊C4—21no—
38(C2×D191)⋊C4—21no—
39(C2×D191)⋊C4—21no—
40C4×Dic191—21no—
41C22×C4×C191C2×C411yescharacteristic
42C22×C4×C191D411yescharacteristic
43C22×C4×C191D411yescharacteristic
44C2×C8×C191—22no—
45C2×C8×C191—42no—
46C42×C191C2×C411yescharacteristic
47C42×C191D411yescharacteristic
48C42×C191D411yescharacteristic
49C42×C191C2311yescharacteristic
50C22×D191—21no—
51Dic382—22no—
52D764—22no—
53C22⋊D191—42no—
54C2×Dic191—21no—
55C2×Dic191—21no—
56C2×Dic191—21no—
57C4×D191—41no—
58C4×D191—41no—
59C191⋊C8—24no—
60C23×C191C22⋊C411yescharacteristic
61C2×C4×C191—22no—
62C2×C4×C191—22no—
63C2×C4×C191—21no—
64C2×C4×C191—21no—
65C2×C4×C191C22⋊C411yescharacteristic
66C2×C4×C191C22⋊C411yescharacteristic
67C2×C4×C191C22⋊C411yescharacteristic
68C2×C4×C191C22×C411yescharacteristic
69C2×C4×C191C2×D411yescharacteristic
70C2×C4×C191C2×D411yescharacteristic
71C8×C191—42no—
72C22×C191—21no—
73C22×C191—21no—
74C22×C191#10412yes—
75C22×C191C2×C22⋊C411yescharacteristic
76C2×D191—41no—
77C2×D191—41no—
78C2×D191—41no—
79C4×C191—21no—
80C4×C191—21no—
81C4×C191—21no—
82C4×C191—21no—
83C4×C191#13112yes—
84C4×C191AGL(1,ℤ/8)11yescharacteristic
85C4×C191#13711yescharacteristic
86Dic191—41no—
87Dic191—41no—
88Dic191—41no—
89C2×C191—22no—
90C2×C191#40811yescharacteristic
91C2×C191#41711yescharacteristic
92C2×C191C2×#10411yescharacteristic
93D191—81no—
94C191#148311yescharacteristic, complemented, Sylow
95#1483—1911nomaximal, Sylow
96#529—1911no—
97C2×C4⋊C8D19111yescharacteristic, complemented
98C4×M16—1911no—
99Q8⋊C8—1912no—
100D4⋊C8—1912no—
101C2×M16—3821no—
102C22×C8—21no—
103#126—3821no—
104#125—1911no—
105#124—1911no—
106#123—3821no—
107C22⋊Q8—1911no—
108#121—1911no—
109C4×Q8—1911no—
110C4×D4—3821no—
111C4×D4—1911no—
112#117—3821no—
113C2×C42C2×D19111yescharacteristic
114C4⋊C8—21no—
115C4⋊C8C2×D19112yes—
116#97—3821no—
117C4×C8—1912no—
118C2×Q8—1911no—
119C2×D4—3821no—
120C2×D4—1911no—
121C22×C4—3821no—
122C22×C4C4×D19111yescharacteristic
123C22×C4C22⋊D19111yescharacteristic
124C22×C4D76411yescharacteristic
125M16—3824no—
126C2×C8—22no—
127C2×C8—42no—
128C2×C8—3822no—
129C4⋊C4—3821no—
130C4⋊C4—3821no—
131C4⋊C4—3821no—
132C4⋊C4—3821no—
133C4⋊C4—1911no—
134C4⋊C4—1911no—
135C22⋊C4—3821no—
136C22⋊C4—3821no—
137C22⋊C4—3821no—
138C22⋊C4—3821no—
139C22⋊C4—3821no—
140C42—3821no—
141C42C4×D19111yescharacteristic
142C42C22⋊D19111yescharacteristic
143C42D76411yescharacteristic
144C42C22×D19111yescharacteristic
145C23—3821no—
146C23(C2×D191)⋊C411yescharacteristic
147Q8—3822no—
148D4—3822no—
149D4—7642no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—3821no—
155C2×C4—3821no—
156C2×C4—3821no—
157C2×C4—7641no—
158C2×C4—7641no—
159C2×C4(C2×D191)⋊C411yescharacteristic
160C2×C4(C2×D191)⋊C411yescharacteristic
161C2×C4(C2×D191)⋊C411yescharacteristic
162C2×C4C2×C4×D19111yescharacteristic
163C2×C4C2×C22⋊D19111yescharacteristic
164C2×C4C2×D76411yescharacteristic
165C8—42no—
166C8—3824no—
167C22—21no—
168C22—21no—
169C22—7641no—
170C22—7641no—
171C22—7641no—
172C22#2025924812yes—
173C22C2×(C2×D191)⋊C411yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—7641no—
179C4—7641no—
180C4—7641no—
181C4#2025932812yes—
182C4#2025934811yescharacteristic
183C4#2025935311yescharacteristic
184C2—22no—
185C2—15281no—
186C2#2713262911yescharacteristic
187C2#2713266211yescharacteristic
188C2C2×#2025924811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D191
commutatorC2×C4×C191C22×C4
FrattiniC42C22×D191
FittingC2×C4⋊C8×C191C2
socleC22×C191C2×C22⋊C4
prime radical#20259296C4
cosocleC42×C191C23
hypercenterC2×C4⋊C8D191
hypocenterC191#1483
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×#15690271C2semidirect
3. #27132393C2semidirect
4. #27132390C2semidirect
5. C2×C4⋊C8×C191C2semidirect
94. C191#1483semidirect
97. C2×C4⋊C8D191semidirect

Maximal subgroups

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

subgroupindex
#271331972
C4×#156902712
#271323932
#271323902
C2×C4⋊C8×C1912
#1483191