Finite Group Databasebeta

← #37574182

Subgroups — #37574182

Order 24448.

258 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 55 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#27133211C211yesmaximal, characteristic
2#27132635C212yesmaximal, complemented
3#27132457C212yesmaximal, complemented
4#27132456C211yesmaximal, characteristic, complemented
5#353×C191C211yesmaximal, characteristic, complemented
6C2×#15690286C411yescharacteristic, complemented
7C2×#15690286C2211yescharacteristic
8#20259322C411yescharacteristic, complemented
9#20259309C411yescharacteristic, complemented
10#20259309C2211yescharacteristic
11#20259293—22no—
12D4×Dic191—22no—
13#20259278—22no—
14C42×D191C411yescharacteristic, complemented
15#20259237C2212yes—
16#20259236—22no—
17#127×C191C2211yescharacteristic
18#99×C191C2212yes—
19#15690286—41no—
20#15690286—41no—
21#15690286—41no—
22#15690286—41no—
23C2×Dic382C2×C411yescharacteristic
24C2×Dic382C2×C411yescharacteristic
25C2×C22⋊D191—21no—
26C2×C22⋊D191D412yes—
27C22×Dic191—21no—
28C22×Dic191D412yes—
29C2×C4×D191—21no—
30C2×C4×D191C2×C411yescharacteristic
31C4⋊Dic191—22no—
32Dic191⋊C4—42no—
33C22⋊Dic191—22no—
34C22⋊Dic191—22no—
35C22⋊Dic191—22no—
36C4×Dic191—21no—
37C4×Dic191—42no—
38C4×Dic191C2×C411yescharacteristic
39C2×D4×C191—22no—
40C2×D4×C191C2×C411yescharacteristic
41C2×D4×C191C2311yescharacteristic
42C22⋊C4×C191—22no—
43C42×C191C2×C411yescharacteristic
44C22×D191C22⋊C411yescharacteristic
45Dic382—41no—
46Dic382—41no—
47C22⋊D191—42no—
48C22⋊D191—42no—
49C2×Dic191—22no—
50C2×Dic191—22no—
51C2×Dic191—21no—
52C2×Dic191—21no—
53C2×Dic191—41no—
54C2×Dic191—41no—
55C2×Dic191—42no—
56C2×Dic191C22⋊C412yes—
57C2×Dic191C22⋊C411yescharacteristic
58C4×D191—21no—
59C4×D191—21no—
60C4×D191—42no—
61C23×C191—21no—
62C23×C191C2×D412yes—
63D4×C191—41no—
64D4×C191—41no—
65D4×C191—44no—
66C2×C4×C191—21no—
67C2×C4×C191—42no—
68C2×C4×C191C22×C411yescharacteristic
69C22×C191—22no—
70C22×C191—42no—
71C22×C191—42no—
72C22×C191—41no—
73C22×C191C2×C22⋊C411yescharacteristic
74C2×D191—21no—
75C2×D191—41no—
76C4×C191—22no—
77C4×C191—21no—
78C4×C191—82no—
79Dic191—22no—
80Dic191—41no—
81Dic191—41no—
82Dic191—82no—
83Dic191#9911yescharacteristic
84Dic191#9911yescharacteristic
85C2×C191—21no—
86C2×C191—42no—
87C2×C191—81no—
88C2×C191C2×#9911yescharacteristic
89D191—41no—
90C191#212611yescharacteristic, complemented, Sylow
91#2126—1911nomaximal, Sylow
92#532—1911no—
93#410—1912no—
94#354—1912no—
95#353—1911no—
96#353D19111yescharacteristic, complemented
97C2×#41—1911no—
98C2×#41—1911no—
99C4⋊Q8—1911no—
100#127C2×D19111yescharacteristic
101#124—1911no—
102#124—1911no—
103#121—3822no—
104C4×D4—3822no—
105#117—3822no—
106C2×C42—1911no—
107#99—3822no—
108#99—1912no—
109#99C2×D19112yes—
110#41—7641no—
111#41—7641no—
112#41—7641no—
113#41—7641no—
114C2×Q8—1911no—
115C2×Q8—1911no—
116C2×D4—22no—
117C2×D4—3821no—
118C2×D4—1912no—
119C2×D4C4×D19111yescharacteristic
120C2×D4C22×D19111yescharacteristic
121C22×C4—3821no—
122C22×C4—3821no—
123C22×C4—1912no—
124C22×C4—1911no—
125C4⋊C4—3822no—
126C4⋊C4—7642no—
127C22⋊C4—22no—
128C22⋊C4—3822no—
129C22⋊C4—3822no—
130C22⋊C4—3822no—
131C42—3821no—
132C42—1911no—
133C42—7642no—
134C42C4×D19111yescharacteristic
135C23—21no—
136C23—1911no—
137C23D4×D19112yes—
138Q8—7641no—
139Q8—7641no—
140D4—41no—
141D4—41no—
142D4—44no—
143D4—7642no—
144D4—7642no—
145C2×C4—21no—
146C2×C4—42no—
147C2×C4—3821no—
148C2×C4—3821no—
149C2×C4—3822no—
150C2×C4—3822no—
151C2×C4—3821no—
152C2×C4—3821no—
153C2×C4—1912no—
154C2×C4—1911no—
155C2×C4—7642no—
156C2×C4—7641no—
157C2×C4—7641no—
158C2×C4—7642no—
159C2×C4C2×C4×D19111yescharacteristic
160C22—22no—
161C22—42no—
162C22—42no—
163C22—41no—
164C22—3821no—
165C22—7641no—
166C22C22⋊C4×D19111yescharacteristic
167C4—22no—
168C4—21no—
169C4—82no—
170C4—3822no—
171C4—1911no—
172C4—1911no—
173C4—15282no—
174C4—7641no—
175C4—7641no—
176C2—21no—
177C2—42no—
178C2—81no—
179C2—7641no—
180C2#99×D19111yescharacteristic
subgroupG/H
centerC2#99×D191
commutatorC2×C4×C191C22×C4
FrattiniC2×D4C22×D191
Fitting#353×C191C2
socleC2×C191C2×#99
prime radical#27133211C2
cosocleC2×D4×C191C23
hypercenter#353D191
hypocenterC191#2126
LCSG ▷ C2×C4×C191 ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #27132635C2semidirect
3. #27132457C2semidirect
4. #27132456C2semidirect
5. #353×C191C2semidirect
6. C2×#15690286C4semidirect
8. #20259322C4semidirect
9. #20259309C4semidirect
14. C42×D191C4semidirect
90. C191#2126semidirect
96. #353D191semidirect

Maximal subgroups

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

subgroupindex
#271332112
#271326352
#271324572
#271324562
#353×C1912
#2126191