Finite Group Databasebeta

← #37573566

Subgroups — #37573566

Order 24448.

370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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×#20259353C212yesmaximal, complemented
2#27133244C211yesmaximal, characteristic
3C2×#20259250C212yesmaximal, complemented
4#27132432C211yesmaximal, characteristic, complemented
5#391×C191C211yesmaximal, characteristic, complemented
6C2×#15690287C2212yes—
7#20259353—24no—
8#20259353—24no—
9C2×#15690277—22no—
10C2×#15690274—22no—
11C2×#15690271C2212yes—
12#20259302—22no—
13#20259297—22no—
14#20259296—22no—
15#20259250—24no—
16C22×Q8×C191C2211yescharacteristic
17C2×C4⋊C4×C191C2211yescharacteristic
18C2×C42×C191C2211yescharacteristic
19#95×C191—22no—
20#15690287—22no—
21#15690287—22no—
22#15690287—22no—
23#15690287—22no—
24C2×Dic382D412yes—
25C2×D764—22no—
26C2×D764D412yes—
27C2×C22⋊D191—22no—
28C2×C4×D191—22no—
29#15690277—28no—
30#15690274—28no—
31#15690271—22no—
32#15690271D414yescomplemented
33C2×C191⋊C8—22no—
34C4⋊Dic191—22no—
35(C2×D191)⋊C4—24no—
36C2×Q8×C191—21no—
37C2×Q8×C191—22no—
38C2×Q8×C191—22no—
39C2×Q8×C191D412yescomplemented
40C22×C4×C191—21no—
41C22×C4×C191—21no—
42C22×C4×C191D412yes—
43C22×C4×C191C2311yescharacteristic
44C4⋊C4×C191—22no—
45C42×C191—22no—
46C22×D191—22no—
47Dic382—22no—
48Dic382—22no—
49D764—22no—
50D764—22no—
51D764—82no—
52C22⋊D191—42no—
53C22⋊D191—42no—
54C2×Dic191—22no—
55C4×D191—42no—
56C4×D191—42no—
57C191⋊C8—24no—
58C23×C191C2×D411yescharacteristic
59Q8×C191—24no—
60Q8×C191—42no—
61C2×C4×C191—22no—
62C2×C4×C191—22no—
63C2×C4×C191—22no—
64C2×C4×C191—41no—
65C2×C4×C191—41no—
66C2×C4×C191—41no—
67C2×C4×C191—41no—
68C2×C4×C191—42no—
69C2×C4×C191C2×D412yes—
70C2×C4×C191C2×D412yes—
71C2×C4×C191C2×D411yescharacteristic
72C2×C4×C191#4111yescharacteristic
73C22×C191—21no—
74C22×C191—21no—
75C22×C191#12011yescharacteristic
76C22×C191#12111yescharacteristic
77C22×C191#12711yescharacteristic
78C2×D191—42no—
79C2×D191—42no—
80C2×D191—42no—
81C4×C191—42no—
82C4×C191—42no—
83C4×C191—42no—
84C4×C191#12012yes—
85C4×C191#12112yes—
86Dic191—42no—
87C2×C191—21no—
88C2×C191—21no—
89C2×C191#39211yescharacteristic
90C2×C191#45511yescharacteristic
91C2×C191#45611yescharacteristic
92D191—82no—
93C191#200711yescharacteristic, complemented, Sylow
94#2007—1911nomaximal, Sylow
95C2×#137—1912no—
96#537—1911no—
97C2×#104—1912no—
98#391D19111yescharacteristic, complemented
99#343—1911no—
100C2×#41—1912no—
101C22×Q8C2×D19111yescharacteristic
102#137—3824no—
103#137—3824no—
104C2×Q16—3822no—
105C2×SD16—3822no—
106C2×M16—1912no—
107C22⋊Q8—3822no—
108#121—3822no—
109#121—3822no—
110C2×C4⋊C4C2×D19111yescharacteristic
111C2×C42C2×D19111yescharacteristic
112#104—3824no—
113#95—22no—
114#41—3822no—
115#41—3822no—
116#41—3822no—
117#41—3822no—
118C2×Q8—21no—
119C2×Q8—22no—
120C2×Q8—22no—
121C2×Q8—1912no—
122C2×Q8D76412yescomplemented
123C2×D4—3822no—
124C2×D4—3822no—
125C2×D4—1912no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—3822no—
129C22×C4C22⋊D19112yes—
130C22×C4C22×D19111yescharacteristic
131Q16—3828no—
132SD16—3828no—
133M16—3822no—
134M16—1914no—
135C2×C8—3822no—
136C4⋊C4—22no—
137C4⋊C4—3822no—
138C22⋊C4—3824no—
139C42—22no—
140C23—3822no—
141C23C2×C22⋊D19111yescharacteristic
142Q8—24no—
143Q8—42no—
144Q8—3822no—
145Q8—3822no—
146D4—3822no—
147D4—3822no—
148D4—15282no—
149D4—7642no—
150D4—7642no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—3822no—
160C2×C4—7642no—
161C2×C4—7642no—
162C2×C4D4×D19112yes—
163C2×C4D4×D19112yes—
164C2×C4C2×D76411yescharacteristic
165C2×C4#1569028711yescharacteristic
166C8—3824no—
167C22—21no—
168C22—21no—
169C22—7642no—
170C22—7642no—
171C22—7642no—
172C22#2025929011yescharacteristic
173C22#2025929611yescharacteristic
174C22#2025931811yescharacteristic
175C4—42no—
176C4—42no—
177C4—42no—
178C4—7642no—
179C4#2025929212yes—
180C4#2025929512yes—
181C2—21no—
182C2—21no—
183C2—15282no—
184C2#2713257211yescharacteristic
185C2#2713284011yescharacteristic
186C2#2713284511yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#391×C191C2
socleC22×C191#120
prime radical#27133244C2
hypercenter#391D191
hypocenterC191#2007
LCSG ▷ C22×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#20259353C2semidirect
3. C2×#20259250C2semidirect
4. #27132432C2semidirect
5. #391×C191C2semidirect
32. #15690271D4semidirect
39. C2×Q8×C191D4semidirect
93. C191#2007semidirect
98. #391D191semidirect
122. C2×Q8D764semidirect

Maximal subgroups

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

subgroupindex
C2×#202593532
#271332442
C2×#202592502
#271324322
#391×C1912
#2007191