Finite Group Databasebeta

← #37583922

Subgroups — #37583922

Order 24448.

354 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 109 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#27133199C212yesmaximal, complemented
2#27132968C212yesmaximal, complemented
3#27132962C212yesmaximal, complemented
4#27132916C211yesmaximal, characteristic
5#27132911C212yesmaximal, complemented
6#27132887C212yesmaximal, complemented
7#27132881C212yesmaximal, complemented
8#27132686C211yesmaximal, characteristic, complemented
9#470×C191C211yesmaximal, characteristic, complemented
10C2×#15690274C2212yes—
11C2×D1528C2211yescharacteristic
12C2×#15690271C2211yescharacteristic
13#20259317—22no—
14#20259313C2212yes—
15#20259311C2212yes—
16#20259306—22no—
17#20259296C2212yes—
18Q8×Dic191C2212yes—
19#20259284C2212yes—
20(C22⋊D191)⋊C4—22no—
21#20259280—22no—
22C2×C4×Dic191C2211yescharacteristic
23#20259255C2212yes—
24#20259254C2211yescharacteristic
25Dic191⋊C8C2212yes—
26Dic191⋊C8C2212yes—
27#20259246C2212yes—
28#20259244C2212yes—
29#20259242C2212yes—
30C2×Q16×C191C2211yescharacteristic
31C2×M16×C191C2211yescharacteristic
32C22⋊Q8×C191C2212yes—
33#106×C191C2211yescharacteristic
34#103×C191C2212yes—
35C2×D764C2312yes—
36C2×C22⋊D191—22no—
37C22×Dic191D412yes—
38C2×C4×D191—22no—
39#15690274—42no—
40D1528—41no—
41#15690271—41no—
42C2×C191⋊C8C2312yes—
43C4⋊Dic191—22no—
44C4⋊Dic191—22no—
45C4⋊Dic191C2312yes—
46Dic191⋊C4—22no—
47(C2×D191)⋊C4—22no—
48(C2×D191)⋊C4—22no—
49(C2×D191)⋊C4—22no—
50(C2×D191)⋊C4—22no—
51C4×Dic191—22no—
52C4×Dic191D411yescharacteristic
53C4×Dic191D411yescharacteristic
54C4×Dic191C2312yes—
55C2×Q8×C191C2312yes—
56C22×C4×C191C2311yescharacteristic
57Q16×C191—41no—
58M16×C191—41no—
59C2×C8×C191C2311yescharacteristic
60C2×C8×C191C2311yescharacteristic
61C4⋊C4×C191—22no—
62C4⋊C4×C191C2312yes—
63C22⋊C4×C191—22no—
64C22×D191—22no—
65D764—22no—
66D764—22no—
67C22⋊D191—44no—
68C2×Dic191—22no—
69C2×Dic191—42no—
70C2×Dic191C2×D412yes—
71C2×Dic191C2×D412yes—
72C4×D191—44no—
73C191⋊C8—22no—
74C23×C191C2×D411yescharacteristic
75Q8×C191—22no—
76Q8×C191—22no—
77C2×C4×C191—21no—
78C2×C4×C191—21no—
79C2×C4×C191—22no—
80C2×C4×C191—22no—
81C2×C4×C191C2×D411yescharacteristic
82C2×C4×C191C2411yescharacteristic
83C8×C191—21no—
84C8×C191—21no—
85C22×C191—21no—
86C22×C191—22no—
87C22×C191C22×D411yescharacteristic
88C2×D191—42no—
89C2×D191—42no—
90C2×D191—42no—
91C4×C191—21no—
92C4×C191—42no—
93C4×C191—42no—
94C4×C191H(5,𝔽2)11yescharacteristic
95C4×C1912−1+411yescharacteristic
96Dic191—22no—
97Dic191—22no—
98Dic191—42no—
99C2×C191—41no—
100C2×C191#53711yescharacteristic
101C2×C191#57512yes—
102D191—82no—
103C191#325611yescharacteristic, complemented, Sylow
104#3256—1911nomaximal, Sylow
105#529—1912no—
106#479—1912no—
107#478—1912no—
108#470D19111yescharacteristic, complemented
109#469—1911no—
110#468—1912no—
111#464—1912no—
112#463—1912no—
113#423—1911no—
114C2×Q16C2×D19111yescharacteristic
115C2×SD16—1912no—
116C2×D8—1911no—
117C2×M16—1911no—
118C2×M16C2×D19111yescharacteristic
119#126—3822no—
120#125—1912no—
121#124—1912no—
122#123—3822no—
123C22⋊Q8C2×D19112yes—
124#121—1912no—
125C4×Q8—1912no—
126C4×D4—3822no—
127C4×D4—1912no—
128#117—3822no—
129C2×C42—1911no—
130#107—1912no—
131#106—1911no—
132#106C2×D19111yescharacteristic
133C4⋊C8—1912no—
134C4⋊C8—1912no—
135#103—1912no—
136#103C2×D19112yes—
137#102—1912no—
138#102—1912no—
139C2×Q8C22×D19112yes—
140C2×D4—3822no—
141C2×D4—1912no—
142C22×C4—3822no—
143C22×C4—1912no—
144C22×C4C22×D19111yescharacteristic
145Q16—41no—
146SD16—7642no—
147D8—7641no—
148M16—41no—
149M16—7641no—
150C2×C8—1912no—
151C2×C8C22×D19111yescharacteristic
152C2×C8C22×D19111yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—3822no—
155C4⋊C4—3822no—
156C4⋊C4—3822no—
157C4⋊C4—1912no—
158C4⋊C4C22×D19112yes—
159C22⋊C4—22no—
160C22⋊C4—3822no—
161C22⋊C4—3822no—
162C22⋊C4—3822no—
163C22⋊C4—3822no—
164C42—3822no—
165C42—1911no—
166C42—1911no—
167C42—1912no—
168C23—3822no—
169C23D4×D19111yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—3822no—
173D4—3822no—
174D4—7644no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—3822no—
180C2×C4—1912no—
181C2×C4—1912no—
182C2×C4—7644no—
183C2×C4—7642no—
184C2×C4D4×D19111yescharacteristic
185C2×C4C23×D19111yescharacteristic
186C8—21no—
187C8—21no—
188C8—3822no—
189C22—22no—
190C22—21no—
191C22—7642no—
192C22—7642no—
193C22—7642no—
194C22C2×D4×D19111yescharacteristic
195C4—21no—
196C4—42no—
197C4—42no—
198C4—3822no—
199C4—3822no—
200C4—7642no—
201C4#2025936711yescharacteristic
202C4#2025936911yescharacteristic
203C2—41no—
204C2—15282no—
205C2#2713324011yescharacteristic
206C2#2713346212yes—
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#470×C191C2
socleC22×C191C22×D4
prime radical#27132916C2
hypercenter#470D191
hypocenterC191#3256
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #27133199C2semidirect
2. #27132968C2semidirect
3. #27132962C2semidirect
5. #27132911C2semidirect
6. #27132887C2semidirect
7. #27132881C2semidirect
8. #27132686C2semidirect
9. #470×C191C2semidirect
103. C191#3256semidirect
108. #470D191semidirect

Maximal subgroups

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

subgroupindex
#271331992
#271329682
#271329622
#271329162
#271329112
#271328872
#271328812
#271326862
#470×C1912
#3256191