Finite Group Databasebeta

← #37573649

Subgroups — #37573649

Order 24448.

430 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 75 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×#20259303C212yesmaximal, complemented
2C2×#20259237C212yesmaximal, complemented
3#27132524C211yesmaximal, characteristic, complemented
4#27132430C211yesmaximal, characteristic, complemented
5#534×C191C211yesmaximal, characteristic
6C23×Dic191C2211yescharacteristic
7#20259303—24no—
8#20259303—24no—
9C2×Dic191⋊C4—22no—
10C2×C22⋊Dic191—22no—
11C2×C22⋊Dic191C2211yescharacteristic
12C2×C22⋊Dic191C2212yes—
13#20259237—24no—
14C191⋊#95—22no—
15C22×D4×C191C2212yes—
16#123×C191—22no—
17#121×C191—22no—
18#120×C191—22no—
19C2×C22⋊C4×C191C2211yescharacteristic
20C22×Dic191—21no—
21C22×Dic191—22no—
22C22×Dic191—22no—
23C22×Dic191—22no—
24C22×Dic191—21no—
25C22×Dic191—21no—
26C22×Dic191D412yescomplemented
27Dic191⋊C4—28no—
28C22⋊Dic191—28no—
29C22⋊Dic191—22no—
30C22⋊Dic191—22no—
31C22⋊Dic191D414yescomplemented
32C24×C191D412yes—
33C24×C191C2311yescharacteristic
34C2×D4×C191—22no—
35C2×D4×C191—22no—
36C2×D4×C191—22no—
37C2×D4×C191—22no—
38C2×D4×C191—22no—
39C2×D4×C191—22no—
40C2×D4×C191—22no—
41C22×C4×C191D412yes—
42C22×C4×C191D412yes—
43C4⋊C4×C191—22no—
44C22⋊C4×C191—24no—
45C22⋊C4×C191—22no—
46C2×Dic191—24no—
47C2×Dic191—24no—
48C2×Dic191—22no—
49C2×Dic191—44no—
50C2×Dic191—41no—
51C2×Dic191—42no—
52C2×Dic191—41no—
53C2×Dic191—42no—
54C2×Dic191—41no—
55C23×C191—22no—
56C23×C191—22no—
57C23×C191—22no—
58C23×C191—42no—
59C23×C191—44no—
60C23×C191C2×D411yescharacteristic
61C23×C191C2×D412yes—
62C23×C191C2×D412yes—
63C23×C191C2×D411yescharacteristic
64C23×C191#4111yescharacteristic
65D4×C191—42no—
66D4×C191—42no—
67D4×C191—42no—
68D4×C191—42no—
69D4×C191—82no—
70C2×C4×C191—22no—
71C2×C4×C191—22no—
72C2×C4×C191—22no—
73C2×C4×C191—22no—
74C2×C4×C191—42no—
75C22×C191—22no—
76C22×C191—24no—
77C22×C191—41no—
78C22×C191—42no—
79C22×C191—41no—
80C22×C191—44no—
81C22×C191—42no—
82C22×C191—44no—
83C22×C191—82no—
84C22×C191#12012yes—
85C22×C191#12011yescharacteristic
86C22×C191#12111yescharacteristic
87C22×C191#12112yes—
88C22×C191#12711yescharacteristic
89C4×C191—42no—
90C4×C191—42no—
91Dic191—44no—
92Dic191—42no—
93Dic191—81no—
94C2×C191—22no—
95C2×C191—21no—
96C2×C191—22no—
97C2×C191—21no—
98C2×C191—82no—
99C2×C191#39211yescharacteristic
100C2×C191#45812yes—
101C191#202211yescharacteristic, complemented, Sylow
102#2022—1911nomaximal, Sylow
103#534D19111yescharacteristic
104C2×#123—1912no—
105C2×#99—1912no—
106#381—1911no—
107#342—1911no—
108C22×D4C2×D19112yes—
109C23×C4—1911no—
110#123—22no—
111#123—3824no—
112#123—3824no—
113#121—22no—
114#120—22no—
115C2×C4⋊C4—3822no—
116C2×C22⋊C4—3822no—
117C2×C22⋊C4—1911no—
118C2×C22⋊C4—1912no—
119C2×C22⋊C4C2×D19111yescharacteristic
120#99—3824no—
121#95—3822no—
122C24C22⋊D19112yes—
123C24C22×D19111yescharacteristic
124C2×D4—22no—
125C2×D4—22no—
126C2×D4—22no—
127C2×D4—22no—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—22no—
131C22×C4—3822no—
132C22×C4—3821no—
133C22×C4—3822no—
134C22×C4—3822no—
135C22×C4—3821no—
136C22×C4—3821no—
137C22×C4—1912no—
138C22×C4C22⋊D19112yes—
139C22×C4C22⋊D19112yes—
140C4⋊C4—22no—
141C4⋊C4—3828no—
142C22⋊C4—24no—
143C22⋊C4—22no—
144C22⋊C4—3828no—
145C22⋊C4—3822no—
146C22⋊C4—3822no—
147C22⋊C4—1914no—
148C23—22no—
149C23—22no—
150C23—22no—
151C23—42no—
152C23—44no—
153C23D4×D19111yescharacteristic
154C23D4×D19112yes—
155C23C2×C22⋊D19112yes—
156C23C2×C22⋊D19111yescharacteristic
157C23#1569028611yescharacteristic
158D4—42no—
159D4—42no—
160D4—42no—
161D4—42no—
162D4—82no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—3824no—
169C2×C4—3824no—
170C2×C4—3822no—
171C2×C4—7642no—
172C2×C4—7641no—
173C2×C4—7644no—
174C2×C4—7641no—
175C2×C4—7642no—
176C2×C4—7641no—
177C22—22no—
178C22—24no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—44no—
183C22—42no—
184C22—44no—
185C22—82no—
186C22#2025929012yes—
187C22#2025929111yescharacteristic
188C22#2025929311yescharacteristic
189C22#2025929412yes—
190C22#2025931811yescharacteristic
191C4—42no—
192C4—42no—
193C4—15281no—
194C4—7644no—
195C4—7642no—
196C2—21no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—82no—
201C2#2713257111yescharacteristic
202C2#2713285312yes—
subgroupG/H
centerC22#20259291
commutator, cosocleC24×C191C23
FrattiniC24C22×D191
Fitting, prime radical#534×C191C2
socleC22×C191#120
hypercenter#534D191
hypocenterC191#2022
LCSG ▷ C24×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C24 ◁ #534

Complements

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

NH ≅ G/Ntype
1. C2×#20259303C2semidirect
2. C2×#20259237C2semidirect
3. #27132524C2semidirect
4. #27132430C2semidirect
26. C22×Dic191D4semidirect
31. C22⋊Dic191D4semidirect
101. C191#2022semidirect

Maximal subgroups

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

subgroupindex
C2×#202593032
C2×#202592372
#271325242
#271324302
#534×C1912
#2022191