Finite Group Databasebeta

← #37572910

Subgroups — #37572910

Order 24448.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#20259320C211yesmaximal, characteristic
2#27133140C211yesmaximal, characteristic
3#27132672C211yesmaximal, characteristic
4C2×#20259240C211yesmaximal, characteristic
5#27132424C211yesmaximal, characteristic
6#27132422C211yesmaximal, characteristic
7#419×C191C211yesmaximal, characteristic
8C22×Dic382C2211yescharacteristic
9C2×#15690271C2211yescharacteristic
10#20259320—22no—
11#20259320C414yescomplemented
12C4×Dic382—22no—
13#20259287—22no—
14#20259281C2211yescharacteristic
15#20259278—22no—
16C2×Dic191⋊C4—22no—
17C2×C4×Dic191C2211yescharacteristic
18#20259246—22no—
19#20259240—22no—
20C22×Q8×C191C2211yescharacteristic
21C2×M16×C191C2211yescharacteristic
22#117×C191C2211yescharacteristic
23#103×C191—22no—
24C2×Dic382—21no—
25C2×Dic382—21no—
26C2×Dic382—21no—
27C2×Dic382—21no—
28C2×Dic382C2×C412yes—
29C2×Dic382D412yes—
30C22×Dic191—21no—
31C22×Dic191D412yes—
32#15690271—21no—
33#15690271—21no—
34C2×C191⋊C8—21no—
35C4⋊Dic191D412yes—
36Dic191⋊C4—24no—
37Dic191⋊C4—28no—
38C22⋊Dic191—21no—
39C4×Dic191—24no—
40C4×Dic191—21no—
41C4×Dic191—21no—
42C4×Dic191C2×C412yes—
43C2×Q8×C191—21no—
44C2×Q8×C191—21no—
45C2×Q8×C191—21no—
46C2×Q8×C191—21no—
47C2×Q8×C191—21no—
48C2×Q8×C191C2×C412yes—
49C22×C4×C191—21no—
50C22×C4×C191C2311yescharacteristic
51M16×C191—21no—
52M16×C191—21no—
53C2×C8×C191—21no—
54C4⋊C4×C191D412yes—
55C22⋊C4×C191—21no—
56C42×C191—21no—
57Dic382—22no—
58Dic382—22no—
59Dic382—22no—
60Dic382—22no—
61C2×Dic191—24no—
62C2×Dic191—22no—
63C2×Dic191—22no—
64C2×Dic191—22no—
65C2×Dic191—22no—
66C2×Dic191C22⋊C414yes—
67C191⋊C8—41no—
68C23×C191C2×D411yescharacteristic
69Q8×C191—22no—
70Q8×C191—22no—
71Q8×C191—41no—
72Q8×C191—41no—
73C2×C4×C191—22no—
74C2×C4×C191—22no—
75C2×C4×C191—41no—
76C2×C4×C191—41no—
77C2×C4×C191C22×C411yescharacteristic
78C2×C4×C191C2×D411yescharacteristic
79C2×C4×C191C2×D411yescharacteristic
80C2×C4×C191C2×D411yescharacteristic
81C2×C4×C191#4111yescharacteristic
82C2×C4×C191#4111yescharacteristic
83C8×C191—41no—
84C22×C191—22no—
85C22×C191C2×C22⋊C411yescharacteristic
86C22×C191#12011yescharacteristic
87C22×C191#12311yescharacteristic
88C4×C191—42no—
89C4×C191—42no—
90C4×C191C4×D411yescharacteristic
91C4×C191C4×D411yescharacteristic
92C4×C191#12111yescharacteristic
93C4×C191#12111yescharacteristic
94Dic191—24no—
95Dic191—24no—
96Dic191—42no—
97C2×C191—21no—
98C2×C191—21no—
99C2×C191#38611yescharacteristic
100C2×C191#45612yes—
101C191#188611yescharacteristic, complemented, Sylow
102#1886—1911nomaximal, Sylow
103C2×C4⋊Q8—1911no—
104#519—1911no—
105#419—1911no—
106#419D19111yescharacteristic
107C2×#101—1911no—
108#339—1911no—
109#339—1911no—
110C22×Q8—1911no—
111C22×Q8C2×D19111yescharacteristic
112C2×M16—1911no—
113C2×M16C2×D19111yescharacteristic
114C4⋊Q8—3822no—
115C4⋊Q8—1914no—
116C4×Q8—3822no—
117C4×Q8—3822no—
118#117—3822no—
119#117—1911no—
120#117C2×D19111yescharacteristic
121C2×C4⋊C4—3822no—
122C2×C42—1911no—
123#103—22no—
124#103—3822no—
125#101—3822no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—3821no—
132C2×Q8—3821no—
133C2×Q8—3821no—
134C2×Q8—3821no—
135C2×Q8—1912no—
136C2×Q8—1912no—
137C2×Q8C4×D19112yes—
138C22×C4—21no—
139C22×C4—3821no—
140C22×C4—1912no—
141C22×C4C22×D19111yescharacteristic
142M16—21no—
143M16—21no—
144M16—3821no—
145M16—3821no—
146C2×C8—21no—
147C2×C8—3821no—
148C4⋊C4—3824no—
149C4⋊C4—3828no—
150C4⋊C4—1912no—
151C4⋊C4C22⋊D19112yes—
152C22⋊C4—21no—
153C22⋊C4—3821no—
154C42—21no—
155C42—3824no—
156C42—3821no—
157C42—3821no—
158C42—1912no—
159C23D4×D19111yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164Q8—3822no—
165Q8—3822no—
166Q8—3822no—
167Q8—3822no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—3824no—
173C2×C4—3822no—
174C2×C4—3822no—
175C2×C4—3822no—
176C2×C4—3822no—
177C2×C4—1914no—
178C2×C4C2×C4×D19111yescharacteristic
179C2×C4D4×D19111yescharacteristic
180C2×C4D4×D19111yescharacteristic
181C2×C4C2×C22⋊D19111yescharacteristic
182C2×C4#1569028611yescharacteristic
183C2×C4#1569028711yescharacteristic
184C8—41no—
185C8—7641no—
186C22—22no—
187C22C22⋊C4×D19111yescharacteristic
188C22#2025929011yescharacteristic
189C22#2025930411yescharacteristic
190C4—42no—
191C4—42no—
192C4—3824no—
193C4—3824no—
194C4—7642no—
195C4(C22⋊D191)⋊C411yescharacteristic
196C4C4×C22⋊D19111yescharacteristic
197C4#2025929311yescharacteristic
198C4#2025929511yescharacteristic
199C2—21no—
200C2—21no—
201C2#2713253911yescharacteristic
202C2#2713284412yes—
subgroupG/H
centerC22#20259290
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
Fitting#419×C191C2
socleC22×C191#120
prime radicalC23×C191C2×D4
cosocleC22×C4×C191C23
hypercenter#419D191
hypocenterC191#1886
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
11. #20259320C4semidirect
101. C191#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#202593202
#271331402
#271326722
C2×#202592402
#271324242
#271324222
#419×C1912
#1886191