Finite Group Databasebeta

← #37571150

Subgroups — #37571150

Order 24448.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#27133198C211yesmaximal, characteristic
2#27132718C211yesmaximal, characteristic, complemented
3#27132718C211yesmaximal, characteristic, complemented
4#27132405C211yesmaximal, characteristic, complemented
5#27132402C211yesmaximal, characteristic, complemented
6#27132402C211yesmaximal, characteristic, complemented
7#330×C191C211yesmaximal, characteristic, complemented
8#20259317—21no—
9#20259310C2211yescharacteristic
10#20259307—21no—
11#20259302C411yescharacteristic
12#20259297C411yescharacteristic
13#20259287C411yescharacteristic
14#20259284—21no—
15#20259284C411yescharacteristic
16#20259280—21no—
17C42×D191C2211yescharacteristic
18Dic191⋊C8—21no—
19Dic191⋊C8—21no—
20(C2×D191)⋊C8—21no—
21(C2×D191)⋊C8—21no—
22#20259233C2211yescharacteristic
23#20259233C2211yescharacteristic
24#125×C191C2211yescharacteristic
25#97×C191C2211yescharacteristic
26#97×C191C2211yescharacteristic
27C2×Dic382C2×C411yescharacteristic
28C2×D764—21no—
29C2×D764C2×C411yescharacteristic
30C2×C4×D191—21no—
31C2×C4×D191C2×C411yescharacteristic
32C2×C4×D191D411yescharacteristic
33C2×C4×D191D411yescharacteristic
34C2×C191⋊C8—21no—
35C2×C191⋊C8—21no—
36C4⋊Dic191—21no—
37Dic191⋊C4—21no—
38(C2×D191)⋊C4—21no—
39(C2×D191)⋊C4—21no—
40(C2×D191)⋊C4—21no—
41(C2×D191)⋊C4—21no—
42(C2×D191)⋊C4—21no—
43C4×Dic191—21no—
44C4×Dic191C2×C411yescharacteristic
45C4×Dic191D411yescharacteristic
46C4×Dic191D411yescharacteristic
47C2×C8×C191—21no—
48C2×C8×C191—21no—
49C4⋊C4×C191—21no—
50C4⋊C4×C191—21no—
51C4⋊C4×C191C2×C411yescharacteristic
52C4⋊C4×C191C2×C411yescharacteristic
53C42×C191C2311yescharacteristic
54C22×D191—21no—
55C22×D191C22⋊C411yescharacteristic
56Dic382—41no—
57D764—41no—
58D764—42no—
59C2×Dic191—21no—
60C2×Dic191C22⋊C411yescharacteristic
61C2×Dic191C22⋊C411yescharacteristic
62C2×Dic191C22⋊C411yescharacteristic
63C4×D191—41no—
64C4×D191—41no—
65C4×D191—41no—
66C4×D191—42no—
67C191⋊C8—41no—
68C191⋊C8—41no—
69C2×C4×C191—21no—
70C2×C4×C191—21no—
71C2×C4×C191C22×C411yescharacteristic
72C2×C4×C191C2×D411yescharacteristic
73C2×C4×C191C2×D411yescharacteristic
74C8×C191—41no—
75C8×C191—41no—
76C22×C191C2×C22⋊C411yescharacteristic
77C2×D191—21no—
78C2×D191—21no—
79C2×D191—21no—
80C2×D191—41no—
81C2×D191—41no—
82C2×D191—41no—
83C4×C191—21no—
84C4×C191—21no—
85C4×C191—21no—
86C4×C191—41no—
87C4×C191—41no—
88Dic191—21no—
89Dic191—21no—
90Dic191—21no—
91Dic191—41no—
92C2×C191#41311yescharacteristic
93C2×C191#42111yescharacteristic
94C2×C191#42111yescharacteristic
95D191—41no—
96D191—81no—
97C191#153511yescharacteristic, complemented, Sylow
98#1535—1911nomaximal, Sylow
99#529—1911no—
100#432—1911no—
101#432—1911no—
102#330—1911no—
103#330D19111yescharacteristic, complemented
104#329—1911no—
105#329—1911no—
106#126—3821no—
107#125C2×D19111yescharacteristic
108#124—1911no—
109#123—3821no—
110C22⋊Q8—1911no—
111#121—1911no—
112C4×Q8—1911no—
113C4×D4—3821no—
114C4×D4—1911no—
115#117—3821no—
116C2×C42—1911no—
117C4⋊C8—3821no—
118C4⋊C8—3821no—
119C22⋊C8—3821no—
120C22⋊C8—3821no—
121#97—1911no—
122#97—1911no—
123#97C2×D19111yescharacteristic
124#97C2×D19111yescharacteristic
125C2×Q8—1911no—
126C2×D4—3821no—
127C2×D4—1911no—
128C22×C4—3821no—
129C22×C4—1911no—
130C22×C4—1911no—
131C22×C4—1911no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—3821no—
135C2×C8—3821no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—3821no—
139C4⋊C4—3821no—
140C4⋊C4C4×D19111yescharacteristic
141C4⋊C4C4×D19111yescharacteristic
142C22⋊C4—3821no—
143C22⋊C4—3821no—
144C22⋊C4—3821no—
145C22⋊C4—3821no—
146C22⋊C4—3821no—
147C42—3821no—
148C42—1911no—
149C42—1911no—
150C42—1911no—
151C42C22×D19111yescharacteristic
152C23—3821no—
153C23—1911no—
154Q8—7641no—
155D4—7641no—
156D4—7642no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—3821no—
160C2×C4—1911no—
161C2×C4—1911no—
162C2×C4—1911no—
163C2×C4—7641no—
164C2×C4—7641no—
165C2×C4—7641no—
166C2×C4—7642no—
167C2×C4C2×C4×D19111yescharacteristic
168C2×C4D4×D19111yescharacteristic
169C2×C4D4×D19111yescharacteristic
170C8—41no—
171C8—41no—
172C8—7641no—
173C8—7641no—
174C22—3821no—
175C22—3821no—
176C22—3821no—
177C22—7641no—
178C22—7641no—
179C22—7641no—
180C22C22⋊C4×D19111yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—3821no—
187C4—3821no—
188C4—3821no—
189C4—7641no—
190C2—15281no—
191C2—7641no—
192C2#2713264611yescharacteristic
193C2#2713267811yescharacteristic
194C2#2713267811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D191
commutatorC2×C4×C191C22×C4
FrattiniC42C22×D191
Fitting#330×C191C2
socleC22×C191C2×C22⋊C4
prime radical#20259297C4
cosocleC42×C191C23
hypercenter#330D191
hypocenterC191#1535
LCSG ▷ C2×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #27132718C2semidirect
3. #27132718C2semidirect
4. #27132405C2semidirect
5. #27132402C2semidirect
6. #27132402C2semidirect
7. #330×C191C2semidirect
97. C191#1535semidirect
103. #330D191semidirect

Maximal subgroups

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

subgroupindex
#271331982
#271327182
#271324052
#271324022
#330×C1912
#1535191