Finite Group Databasebeta

← #37574191

Subgroups — #37574191

Order 24448.

270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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#27133227C211yesmaximal, characteristic
2#27132637C211yesmaximal, characteristic, complemented
3#27132455C214yesmaximal, complemented
4#410×C191C211yesmaximal, characteristic, complemented
5C22×D764C411yescharacteristic, complemented
6#20259318C2212yes—
7#20259311C412yescomplemented
8#20259296—21no—
9#20259296—21no—
10#20259290—21no—
11#20259290—21no—
12#20259281—21no—
13#20259281C411yescharacteristic, complemented
14#20259237—21no—
15#20259237C2212yescomplemented
16C2×#41×C191C2211yescharacteristic
17#117×C191—21no—
18#99×C191—21no—
19#99×C191C2212yescomplemented
20C23×D191—21no—
21C2×D764—21no—
22C2×D764—41no—
23C2×D764—41no—
24C2×D764C2×C412yes—
25C2×C22⋊D191—22no—
26C2×C22⋊D191—22no—
27C4⋊Dic191—21no—
28C4⋊Dic191—41no—
29C22⋊Dic191—21no—
30C22⋊Dic191—22no—
31(C2×D191)⋊C4—22no—
32(C2×D191)⋊C4—22no—
33C4×Dic191—41no—
34C4×Dic191C2×C412yes—
35#41×C191—41no—
36#41×C191—41no—
37C2×Q8×C191C2×C411yescharacteristic
38C2×D4×C191D411yescharacteristic
39C2×D4×C191D411yescharacteristic
40C2×D4×C191C2311yescharacteristic
41C22×C4×C191C2×C411yescharacteristic
42C22×C4×C191D411yescharacteristic
43C22×C4×C191D411yescharacteristic
44C4⋊C4×C191—41no—
45C22⋊C4×C191—22no—
46C42×C191—41no—
47C22×D191—22no—
48C22×D191—42no—
49C22×D191—82no—
50D764—42no—
51D764—41no—
52D764—41no—
53C22⋊D191—82no—
54C22⋊D191—82no—
55C2×Dic191—22no—
56C2×Dic191—42no—
57C23×C191C22⋊C411yescharacteristic
58C23×C191C2×D411yescharacteristic
59C23×C191C2×D411yescharacteristic
60Q8×C191—41no—
61D4×C191—41no—
62D4×C191—41no—
63D4×C191—41no—
64C2×C4×C191—21no—
65C2×C4×C191—21no—
66C2×C4×C191—21no—
67C2×C4×C191—21no—
68C2×C4×C191—21no—
69C2×C4×C191—21no—
70C2×C4×C191—42no—
71C2×C4×C191C22⋊C411yescharacteristic
72C2×C4×C191C22⋊C411yescharacteristic
73C2×C4×C191C22⋊C411yescharacteristic
74C2×C4×C191C22×C411yescharacteristic
75C22×C191—21no—
76C22×C191—21no—
77C22×C191—21no—
78C22×C191—41no—
79C22×C191—41no—
80C22×C191—41no—
81C22×C191C2×C22⋊C411yescharacteristic
82C2×D191—42no—
83C2×D191—42no—
84C2×D191—42no—
85C2×D191—84no—
86C4×C191—21no—
87C4×C191—21no—
88C4×C191—21no—
89C4×C191—82no—
90C4×C191#9911yescharacteristic
91C4×C191#9911yescharacteristic
92Dic191—42no—
93Dic191—82no—
94C2×C191—21no—
95C2×C191—41no—
96C2×C191—41no—
97C2×C191—41no—
98C2×C191C2×#9911yescharacteristic
99D191—82no—
100C191#212811yescharacteristic, complemented, Sylow
101#2128—1911nomaximal, Sylow
102#535—1911no—
103#410—1911no—
104#410D19111yescharacteristic, complemented
105#353—1914no—
106C2×#41C2×D19111yescharacteristic
107C22×D4—1911no—
108#127—1912no—
109#124—1912no—
110#121—3821no—
111#121—3821no—
112#120—3821no—
113#120—3821no—
114#117—21no—
115#117—3821no—
116#117—1911no—
117#99—21no—
118#99—3821no—
119#99—1912no—
120#99C2×D19112yescomplemented
121C24—3821no—
122#41—41no—
123#41—41no—
124C2×Q8C4×D19111yescharacteristic
125C2×D4—3822no—
126C2×D4—3822no—
127C2×D4—3821no—
128C2×D4—1912no—
129C2×D4—7641no—
130C2×D4—7641no—
131C2×D4C22⋊D19111yescharacteristic
132C2×D4D76411yescharacteristic
133C2×D4C22×D19111yescharacteristic
134C22×C4C4×D19111yescharacteristic
135C22×C4C22⋊D19111yescharacteristic
136C22×C4D76411yescharacteristic
137C4⋊C4—41no—
138C4⋊C4—3821no—
139C4⋊C4—7641no—
140C22⋊C4—22no—
141C22⋊C4—3821no—
142C22⋊C4—3822no—
143C22⋊C4—3822no—
144C22⋊C4—3822no—
145C42—41no—
146C42—1912no—
147C42—7641no—
148C23—3822no—
149C23—15282no—
150C23—7642no—
151C23(C2×D191)⋊C411yescharacteristic
152C23C2×C22⋊D19111yescharacteristic
153C23C2×D76411yescharacteristic
154Q8—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—15282no—
159D4—15282no—
160D4—7642no—
161D4—7641no—
162D4—7641no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—3822no—
171C2×C4—7642no—
172C2×C4(C2×D191)⋊C411yescharacteristic
173C2×C4(C2×D191)⋊C411yescharacteristic
174C2×C4(C2×D191)⋊C411yescharacteristic
175C2×C4C2×C4×D19111yescharacteristic
176C22—21no—
177C22—21no—
178C22—21no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—15284no—
183C22—7642no—
184C22—7642no—
185C22—7642no—
186C22C2×(C2×D191)⋊C411yescharacteristic
187C4—21no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—15282no—
192C4—7642no—
193C4#2025923611yescharacteristic
194C4#2025923611yescharacteristic
195C2—21no—
196C2—41no—
197C2—41no—
198C2—41no—
199C2—15282no—
200C2C2×#2025923611yescharacteristic
subgroupG/H
centerC2C2×#20259236
commutatorC2×C4×C191C22×C4
FrattiniC2×D4C22×D191
Fitting#410×C191C2
socleC2×C191C2×#99
prime radical#27133227C2
cosocleC2×D4×C191C23
hypercenter#410D191
hypocenterC191#2128
LCSG ▷ C2×C4×C191 ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #27132637C2semidirect
3. #27132455C2semidirect
4. #410×C191C2semidirect
5. C22×D764C4semidirect
7. #20259311C4semidirect
13. #20259281C4semidirect
15. #20259237C22semidirect
19. #99×C191C22semidirect
100. C191#2128semidirect
104. #410D191semidirect
120. #99C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332272
#271326372
#271324552
#410×C1912
#2128191