Finite Group Databasebeta

← #37582904

Subgroups — #37582904

Order 24448.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#27133216C211yesmaximal, characteristic, complemented
2C2×#20259309C211yesmaximal, characteristic
3#27133021C214yesmaximal, complemented
4#27133016C214yesmaximal, complemented
5#27132673C211yesmaximal, characteristic, complemented
6#27132671C211yesmaximal, characteristic, complemented
7#27132668C211yesmaximal, characteristic
8M16×Dic191C211yesmaximal, characteristic, complemented
9#418×C191C211yesmaximal, characteristic
10C22×Dic382C2211yescharacteristic
11C2×#15690271C2211yescharacteristic
12#20259321C2212yescomplemented
13#20259313C2212yescomplemented
14#20259309—22no—
15#20259309C2212yes—
16#20259309C2212yes—
17#20259299—22no—
18C4×Dic382—22no—
19#20259281C2211yescharacteristic
20C2×C22⋊Dic191—22no—
21C2×C4×Dic191C2211yescharacteristic
22#20259247C2214yescomplemented
23#20259245C2214yescomplemented
24#20259243C2214yes—
25#20259232C2212yescomplemented
26C8×Dic191C2212yescomplemented
27C22×D4×C191C2211yescharacteristic
28C2×M16×C191C2211yescharacteristic
29#117×C191C2211yescharacteristic
30#102×C191C2214yes—
31C2×Dic382—22no—
32C2×Dic382—21no—
33C2×Dic382—22no—
34C2×Dic382—22no—
35C2×Dic382C2312yes—
36C22×Dic191—21no—
37C22×Dic191D412yes—
38#15690271—22no—
39C2×C191⋊C8C2312yes—
40C4⋊Dic191—22no—
41C4⋊Dic191C2312yes—
42Dic191⋊C4—22no—
43Dic191⋊C4—22no—
44C22⋊Dic191—24no—
45C22⋊Dic191—24no—
46C22⋊Dic191—21no—
47C4×Dic191—21no—
48C4×Dic191D412yes—
49C4×Dic191C2311yescharacteristic
50C4×Dic191C2311yescharacteristic
51C24×C191—21no—
52C2×D4×C191—21no—
53C2×D4×C191—22no—
54C2×D4×C191—22no—
55C2×D4×C191C2312yes—
56C22×C4×C191C2311yescharacteristic
57M16×C191—22no—
58C2×C8×C191C2312yes—
59C4⋊C4×C191C2312yes—
60C22⋊C4×C191—21no—
61C42×C191—21no—
62Dic382—22no—
63Dic382—22no—
64Dic382—44no—
65Dic382—42no—
66C2×Dic191—22no—
67C2×Dic191—22no—
68C2×Dic191—42no—
69C2×Dic191—42no—
70C2×Dic191C2×D412yes—
71C2×Dic191C2×D412yes—
72C191⋊C8—22no—
73C23×C191—22no—
74C23×C191—44no—
75C23×C191—42no—
76C23×C191C2×D411yescharacteristic
77D4×C191—22no—
78D4×C191—22no—
79D4×C191—42no—
80C2×C4×C191—22no—
81C2×C4×C191C2×D411yescharacteristic
82C2×C4×C191#4112yes—
83C2×C4×C191#4112yes—
84C2×C4×C191C2411yescharacteristic
85C8×C191—22no—
86C22×C191—22no—
87C22×C191—42no—
88C22×C191—44no—
89C22×C191—84no—
90C22×C191#12412yes—
91C22×C191C22×D411yescharacteristic
92C4×C191—42no—
93C4×C191#12412yes—
94C4×C191C2×#4111yescharacteristic
95C4×C191C2×#4111yescharacteristic
96Dic191—22no—
97Dic191—22no—
98Dic191—42no—
99Dic191—42no—
100C2×C191—22no—
101C2×C191—82no—
102C2×C191C2×#12411yescharacteristic
103C2×C191#57512yes—
104C191#314011yescharacteristic, complemented, Sylow
105#3140—1911nomaximal, Sylow
106#533—1911no—
107C2×#124—1911no—
108#489—1914no—
109#488—1914no—
110#419—1911no—
111#419—1911no—
112#418—1911no—
113#418D19111yescharacteristic
114C4×M16—1911no—
115C22×Q8—1911no—
116C22×D4C2×D19111yescharacteristic
117C2×M16—1911no—
118C2×M16C2×D19111yescharacteristic
119C4⋊Q8—1912no—
120#125—1912no—
121#124—3822no—
122#124—1912no—
123#124—1912no—
124C22⋊Q8—3822no—
125C4×Q8—3822no—
126#117—1911no—
127#117C2×D19111yescharacteristic
128C2×C22⋊C4—3822no—
129C2×C42—1911no—
130#103—1914no—
131#103—1914no—
132#102—1914no—
133#102C2×D19114yes—
134#97—1912no—
135C4×C8—1912no—
136C24—21no—
137C2×Q8—3822no—
138C2×Q8—3821no—
139C2×Q8—3822no—
140C2×Q8—3822no—
141C2×Q8—1912no—
142C2×D4—21no—
143C2×D4—22no—
144C2×D4—22no—
145C2×D4C22×D19112yes—
146C22×C4—3821no—
147C22×C4—1912no—
148C22×C4C22×D19111yescharacteristic
149M16—22no—
150M16—3822no—
151C2×C8—1912no—
152C2×C8C22×D19112yes—
153C4⋊C4—3822no—
154C4⋊C4—3822no—
155C4⋊C4—3822no—
156C4⋊C4—1912no—
157C4⋊C4C22×D19112yes—
158C22⋊C4—21no—
159C22⋊C4—3821no—
160C22⋊C4—3824no—
161C22⋊C4—3824no—
162C42—21no—
163C42—3821no—
164C42—1912no—
165C42—1911no—
166C42—1911no—
167C23—22no—
168C23—44no—
169C23—42no—
170C23D4×D19111yescharacteristic
171Q8—3822no—
172Q8—3822no—
173Q8—7644no—
174Q8—7642no—
175D4—22no—
176D4—22no—
177D4—42no—
178C2×C4—22no—
179C2×C4—3822no—
180C2×C4—3822no—
181C2×C4—1912no—
182C2×C4—1912no—
183C2×C4—7642no—
184C2×C4—7642no—
185C2×C4D4×D19111yescharacteristic
186C2×C4#1569028612yes—
187C2×C4#1569028712yes—
188C2×C4C23×D19111yescharacteristic
189C8—22no—
190C8—3822no—
191C22—22no—
192C22—44no—
193C22—42no—
194C22—84no—
195C22#2025930812yes—
196C22C2×D4×D19111yescharacteristic
197C4—42no—
198C4—3822no—
199C4—3822no—
200C4—7642no—
201C4—7642no—
202C4#2025930812yes—
203C4C2×#1569028611yescharacteristic
204C4C2×#1569028711yescharacteristic
205C2—22no—
206C2—82no—
207C2C2×#2025930811yescharacteristic
208C2#2713345912yes—
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#418×C191C2
socleC22×C191C22×D4
prime radicalC22×D4×C191C22
hypercenter#418D191
hypocenterC191#3140
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #27133216C2semidirect
3. #27133021C2semidirect
4. #27133016C2semidirect
5. #27132673C2semidirect
6. #27132671C2semidirect
8. M16×Dic191C2semidirect
12. #20259321C22semidirect
13. #20259313C22semidirect
22. #20259247C22semidirect
23. #20259245C22semidirect
25. #20259232C22semidirect
26. C8×Dic191C22semidirect
104. C191#3140semidirect

Maximal subgroups

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

subgroupindex
#271332162
C2×#202593092
#271330212
#271330162
#271326732
#271326712
#271326682
M16×Dic1912
#418×C1912
#3140191