Finite Group Databasebeta

← #37582643

Subgroups — #37582643

Order 24448.

424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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#27133213C211yesmaximal, characteristic
2C2×C4×Dic382C211yesmaximal, characteristic, complemented
3#27132977C212yesmaximal, complemented
4#27132959C212yesmaximal, complemented
5#27132864C212yesmaximal, complemented
6#27132804C212yesmaximal, complemented
7#27132765C214yesmaximal, complemented
8#432×C191C211yesmaximal, characteristic, complemented
9C2×#15690287—21no—
10C22×Dic382C2211yescharacteristic
11C2×#15690276C2214yes—
12#20259322C2211yescharacteristic
13#20259319C2211yescharacteristic
14#20259310—21no—
15#20259296—21no—
16#20259296C2212yes—
17C4×Dic382—21no—
18C4×Dic382—21no—
19C4×Dic382C2212yes—
20C4×Dic382C2212yes—
21C4×D764—21no—
22C4×D764C2212yes—
23C2×C4⋊Dic191C2211yescharacteristic
24C2×Dic191⋊C4—21no—
25C2×C4×Dic191—21no—
26#20259256C2214yes—
27#20259247C2214yes—
28#20259244C2214yes—
29C2×C42×C191C2211yescharacteristic
30C4⋊C8×C191C2212yes—
31C22⋊C8×C191C2212yes—
32#97×C191C2212yes—
33#15690287—44no—
34C2×Dic382—24no—
35C2×Dic382—21no—
36C2×Dic382—21no—
37C2×Dic382C2312yes—
38C2×D764—21no—
39C2×D764—21no—
40C2×D764C2312yes—
41C2×C22⋊D191—22no—
42C22×Dic191—21no—
43C22×Dic191—21no—
44C2×C4×D191—22no—
45#15690276—28no—
46C4⋊Dic191—21no—
47C4⋊Dic191—21no—
48C4⋊Dic191C2312yes—
49C4⋊Dic191C2312yes—
50Dic191⋊C4—22no—
51Dic191⋊C4—22no—
52(C2×D191)⋊C4—22no—
53(C2×D191)⋊C4—22no—
54C4×Dic191—22no—
55C4×Dic191—22no—
56C22×C4×C191D411yescharacteristic
57C22×C4×C191D411yescharacteristic
58C22×C4×C191C2311yescharacteristic
59C2×C8×C191C2314yes—
60C42×C191D411yescharacteristic
61C42×C191D411yescharacteristic
62C42×C191C2311yescharacteristic
63C42×C191C2311yescharacteristic
64C22×D191—22no—
65Dic382—24no—
66Dic382—22no—
67Dic382—42no—
68Dic382#4114yescomplemented
69D764—24no—
70D764—42no—
71D764—42no—
72C22⋊D191—44no—
73C2×Dic191—24no—
74C2×Dic191—22no—
75C2×Dic191—22no—
76C2×Dic191—22no—
77C2×Dic191—42no—
78C4×D191—44no—
79C23×C191C2×D411yescharacteristic
80C2×C4×C191—22no—
81C2×C4×C191—22no—
82C2×C4×C191—22no—
83C2×C4×C191C2×D411yescharacteristic
84C2×C4×C191C2×D411yescharacteristic
85C2×C4×C191C2×D411yescharacteristic
86C2×C4×C191C2×D411yescharacteristic
87C2×C4×C191C2×D411yescharacteristic
88C2×C4×C191C2411yescharacteristic
89C8×C191—24no—
90C22×C191—21no—
91C22×C191—21no—
92C22×C191AGL(1,ℤ/8)12yes—
93C22×C191C22×D411yescharacteristic
94C2×D191—42no—
95C2×D191—42no—
96C2×D191—42no—
97C4×C191—21no—
98C4×C191—21no—
99C4×C191—21no—
100C4×C191—21no—
101C4×C191#13712yes—
102C4×C191C2×#4112yes—
103Dic191—24no—
104Dic191—42no—
105Dic191—42no—
106C2×C191—22no—
107C2×C191#52511yescharacteristic
108C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
109C2×C191C2×#13711yescharacteristic
110D191—82no—
111C191#311211yescharacteristic, complemented, Sylow
112#3112—1911nomaximal, Sylow
113#532—1911no—
114C2×C4×Q8—1911no—
115#480—1912no—
116#477—1912no—
117#460—1912no—
118#448—1912no—
119#440—1914no—
120#432D19111yescharacteristic, complemented
121C2×#41—3821no—
122C22×Q8—1911no—
123C2×SD16—1914no—
124C4⋊Q8—1911no—
125#127—1911no—
126#124—3821no—
127#121—3821no—
128#121—1912no—
129C4×Q8—3821no—
130C4×Q8—3821no—
131C4×Q8—1912no—
132C4×Q8—1912no—
133C4×D4—3821no—
134C4×D4—1912no—
135C2×C4⋊C4—3821no—
136C2×C4⋊C4—1911no—
137C2×C42—3821no—
138C2×C42C2×D19111yescharacteristic
139#107—1914no—
140C4⋊C8C2×D19112yes—
141#103—1914no—
142#102—1914no—
143C22⋊C8C2×D19112yes—
144#97C2×D19112yes—
145#41—7644no—
146C2×Q8—3824no—
147C2×Q8—3821no—
148C2×Q8—3821no—
149C2×Q8—1912no—
150C2×D4—3822no—
151C2×D4—3821no—
152C2×D4—3821no—
153C2×D4—1912no—
154C22×C4—3821no—
155C22×C4—3821no—
156C22×C4—3822no—
157C22×C4D76411yescharacteristic
158C22×C4D76411yescharacteristic
159C22×C4C22×D19111yescharacteristic
160SD16—3828no—
161C2×C8C22×D19114yes—
162C4⋊C4—3822no—
163C4⋊C4—3822no—
164C4⋊C4—3821no—
165C4⋊C4—3821no—
166C4⋊C4—1912no—
167C4⋊C4—1912no—
168C22⋊C4—3822no—
169C22⋊C4—3822no—
170C42—3822no—
171C42—3822no—
172C42D76411yescharacteristic
173C42D76411yescharacteristic
174C42C22×D19111yescharacteristic
175C42C22×D19111yescharacteristic
176C23—3822no—
177C23C2×D76411yescharacteristic
178Q8—3824no—
179Q8—3822no—
180Q8—1914no—
181Q8—7642no—
182D4—3824no—
183D4—7642no—
184D4—7644no—
185D4—7642no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—3824no—
190C2×C4—3822no—
191C2×C4—3822no—
192C2×C4—3822no—
193C2×C4—7644no—
194C2×C4—7642no—
195C2×C4C2×D76411yescharacteristic
196C2×C4C2×D76411yescharacteristic
197C2×C4C2×D76411yescharacteristic
198C2×C4C2×D76411yescharacteristic
199C2×C4C2×D76411yescharacteristic
200C2×C4C23×D19111yescharacteristic
201C8—24no—
202C22—21no—
203C22—21no—
204C22—7642no—
205C22—7642no—
206C22—7642no—
207C22#2025935012yes—
208C22C22×D76411yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—3824no—
214C4—7642no—
215C4—7642no—
216C4#2025935512yes—
217C4#41×D19112yes—
218C2—22no—
219C2—15282no—
220C2#2713317511yescharacteristic
221C2C2×#2025935011yescharacteristic
222C2C2×#2025935511yescharacteristic
subgroupG/H
centerC22C22×D764
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#432×C191C2
socleC22×C191C22×D4
prime radical#27133213C2
hypercenter#432D191
hypocenterC191#3112
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic382C2semidirect
3. #27132977C2semidirect
4. #27132959C2semidirect
5. #27132864C2semidirect
6. #27132804C2semidirect
7. #27132765C2semidirect
8. #432×C191C2semidirect
68. Dic382#41semidirect
111. C191#3112semidirect
120. #432D191semidirect

Maximal subgroups

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

subgroupindex
#271332132
C2×C4×Dic3822
#271329772
#271329592
#271328642
#271328042
#271327652
#432×C1912
#3112191