Finite Group Databasebeta

← #37574184

Subgroups — #37574184

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#27133212C211yesmaximal, characteristic
2#27132635C212yesmaximal, complemented
3#27132458C211yesmaximal, characteristic, complemented
4#27132455C212yesmaximal, complemented
5#354×C191C211yesmaximal, characteristic, complemented
6C2×#15690288C411yescharacteristic, complemented
7C2×#15690286C2211yescharacteristic
8#20259320C411yescharacteristic, complemented
9#20259318C2211yescharacteristic
10#20259310C411yescharacteristic, complemented
11#20259295—22no—
12(C22⋊D191)⋊C4—22no—
13#20259278—22no—
14C42×D191C411yescharacteristic, complemented
15#20259237C2212yes—
16#20259236—22no—
17#124×C191C2211yescharacteristic
18#99×C191C2212yes—
19#15690288—41no—
20#15690288—41no—
21#15690286—41no—
22#15690286—41no—
23C2×Dic382C2×C411yescharacteristic
24C2×D764—21no—
25C2×D764C2×C411yescharacteristic
26C2×C22⋊D191—22no—
27C2×C22⋊D191D412yes—
28C22×Dic191D412yes—
29C2×C4×D191—21no—
30C2×C4×D191—21no—
31C2×C4×D191C2×C411yescharacteristic
32Dic191⋊C4—22no—
33Dic191⋊C4—42no—
34C22⋊Dic191—22no—
35(C2×D191)⋊C4—22no—
36C4×Dic191—21no—
37C4×Dic191—42no—
38C4×Dic191C2×C411yescharacteristic
39C2×Q8×C191C2×C411yescharacteristic
40C2×D4×C191C2311yescharacteristic
41C22⋊C4×C191—22no—
42C22⋊C4×C191—22no—
43C42×C191C2×C411yescharacteristic
44C22×D191—21no—
45C22×D191C22⋊C411yescharacteristic
46Dic382—41no—
47D764—41no—
48D764—42no—
49C22⋊D191—42no—
50C22⋊D191—44no—
51C2×Dic191—21no—
52C2×Dic191—22no—
53C2×Dic191—22no—
54C2×Dic191—42no—
55C2×Dic191C22⋊C412yes—
56C2×Dic191C22⋊C411yescharacteristic
57C4×D191—21no—
58C4×D191—21no—
59C4×D191—42no—
60C4×D191—41no—
61C4×D191—41no—
62C23×C191C2×D412yes—
63Q8×C191—41no—
64D4×C191—41no—
65C2×C4×C191—21no—
66C2×C4×C191—21no—
67C2×C4×C191—42no—
68C2×C4×C191C22×C411yescharacteristic
69C22×C191—22no—
70C22×C191—42no—
71C22×C191C2×C22⋊C411yescharacteristic
72C2×D191—21no—
73C2×D191—41no—
74C2×D191—42no—
75C2×D191—41no—
76C4×C191—21no—
77C4×C191—41no—
78C4×C191—41no—
79C4×C191—82no—
80Dic191—22no—
81Dic191—22no—
82Dic191—82no—
83Dic191#9911yescharacteristic
84Dic191#9911yescharacteristic
85C2×C191—21no—
86C2×C191—42no—
87C2×C191C2×#9911yescharacteristic
88D191—41no—
89D191—81no—
90C191#212611yescharacteristic, complemented, Sylow
91#2126—1911nomaximal, Sylow
92#532—1911no—
93#410—1912no—
94#354—1911no—
95#354D19111yescharacteristic, complemented
96#353—1912no—
97C2×#41—1911no—
98C2×#41—1911no—
99C4⋊Q8—1911no—
100#127—1911no—
101#124—1911no—
102#124C2×D19111yescharacteristic
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×Q8C4×D19111yescharacteristic
116C2×D4—3821no—
117C2×D4—3822no—
118C2×D4—1912no—
119C2×D4—1911no—
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—22no—
129C22⋊C4—3822no—
130C22⋊C4—3822no—
131C42—3821no—
132C42—1911no—
133C42—7642no—
134C42C4×D19111yescharacteristic
135C23—3821no—
136C23—1911no—
137C23D4×D19112yes—
138Q8—41no—
139Q8—7641no—
140D4—41no—
141D4—7641no—
142D4—7642no—
143D4—7642no—
144D4—7644no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—3821no—
149C2×C4—3821no—
150C2×C4—3821no—
151C2×C4—3822no—
152C2×C4—3822no—
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—3821no—
163C22—7642no—
164C22—7641no—
165C22—7641no—
166C22C22⋊C4×D19111yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—82no—
171C4—3822no—
172C4—3822no—
173C4—1911no—
174C4—1911no—
175C4—15282no—
176C2—21no—
177C2—42no—
178C2—15281no—
179C2—7641no—
180C2#99×D19111yescharacteristic
subgroupG/H
centerC2#99×D191
commutatorC2×C4×C191C22×C4
FrattiniC2×D4C22×D191
Fitting#354×C191C2
socleC2×C191C2×#99
prime radical#27133212C2
cosocleC2×D4×C191C23
hypercenter#354D191
hypocenterC191#2126
LCSG ▷ C2×C4×C191 ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #27132635C2semidirect
3. #27132458C2semidirect
4. #27132455C2semidirect
5. #354×C191C2semidirect
6. C2×#15690288C4semidirect
8. #20259320C4semidirect
10. #20259310C4semidirect
14. C42×D191C4semidirect
90. C191#2126semidirect
95. #354D191semidirect

Maximal subgroups

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

subgroupindex
#271332122
#271326352
#271324582
#271324552
#354×C1912
#2126191