Finite Group Databasebeta

← #37583326

Subgroups — #37583326

Order 24448.

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

normal subgroups only

This group has 462 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
1C2×#20259301C211yesmaximal, characteristic, complemented
2#27132998C212yesmaximal, complemented
3#27132974C212yesmaximal, complemented
4#27132907C214yesmaximal, complemented
5#27132814C212yesmaximal, complemented
6#27132801C212yesmaximal, complemented
7#27132627C211yesmaximal, characteristic, complemented
8C2×#121×C191C211yesmaximal, characteristic
9C22×Dic382C2211yescharacteristic, complemented
10C2×#15690275C2214yescomplemented
11C2×#15690271C2212yescomplemented
12#20259301—21no—
13#20259301—21no—
14#20259301C2212yes—
15#20259301C2212yescomplemented
16C2×C4⋊Dic191C2211yescharacteristic, complemented
17C2×Dic191⋊C4—21no—
18C2×C22⋊Dic191—21no—
19#20259255C2214yescomplemented
20#20259245C2214yescomplemented
21#20259243C2214yescomplemented
22C22⋊(C191⋊C8)C2212yes—
23C22⋊(C191⋊C8)C2212yescomplemented
24C22×D4×C191—21no—
25C22×D4×C191C2211yescharacteristic
26C23×C4×C191C2211yescharacteristic
27#121×C191—21no—
28#121×C191—21no—
29#121×C191C2212yes—
30#121×C191C2212yes—
31C2×C4⋊C4×C191C2211yescharacteristic
32C2×C22⋊C4×C191—21no—
33C2×Dic382—21no—
34C2×Dic382—42no—
35C2×Dic382C2312yes—
36C22×Dic191—21no—
37C22×Dic191—21no—
38#15690275—44no—
39#15690271—42no—
40C2×C191⋊C8C2314yes—
41C4⋊Dic191—21no—
42C4⋊Dic191C2312yes—
43Dic191⋊C4—22no—
44Dic191⋊C4—22no—
45C22⋊Dic191—22no—
46C22⋊Dic191—22no—
47C24×C191—21no—
48C24×C191D411yescharacteristic
49C2×D4×C191—22no—
50C2×D4×C191—22no—
51C2×D4×C191—21no—
52C2×D4×C191—42no—
53C2×D4×C191—44no—
54C2×D4×C191C2312yes—
55C22×C4×C191—21no—
56C22×C4×C191—42no—
57C22×C4×C191D411yescharacteristic
58C22×C4×C191D411yescharacteristic
59C22×C4×C191D411yescharacteristic
60C22×C4×C191C2311yescharacteristic
61C22×C4×C191C2311yescharacteristic
62C22×C4×C191C2311yescharacteristic
63C4⋊C4×C191—21no—
64C4⋊C4×C191C2312yes—
65C22⋊C4×C191—22no—
66C22⋊C4×C191—22no—
67Dic382—24no—
68Dic382—42no—
69C2×Dic191—22no—
70C2×Dic191—22no—
71C2×Dic191—42no—
72C2×Dic191—42no—
73C191⋊C8—24no—
74C23×C191—22no—
75C23×C191—22no—
76C23×C191—22no—
77C23×C191—41no—
78C23×C191—42no—
79C23×C191—42no—
80C23×C191—42no—
81C23×C191C2×D411yescharacteristic
82C23×C191C2×D411yescharacteristic
83C23×C191C2×D411yescharacteristic
84D4×C191—24no—
85D4×C191—42no—
86D4×C191—44no—
87D4×C191—44no—
88C2×C4×C191—22no—
89C2×C4×C191—22no—
90C2×C4×C191—22no—
91C2×C4×C191—22no—
92C2×C4×C191—41no—
93C2×C4×C191—41no—
94C2×C4×C191—41no—
95C2×C4×C191—42no—
96C2×C4×C191C2×D411yescharacteristic
97C2×C4×C191C2×D411yescharacteristic
98C2×C4×C191C2×D411yescharacteristic
99C2×C4×C191C2411yescharacteristic
100C22×C191—21no—
101C22×C191—21no—
102C22×C191—21no—
103C22×C191—21no—
104C22×C191—21no—
105C22×C191—21no—
106C22×C191—21no—
107C22×C191—44no—
108C22×C191—42no—
109C22×C191—42no—
110C22×C191—42no—
111C22×C191—84no—
112C22×C191AGL(1,ℤ/8)12yes—
113C22×C191#13712yes—
114C22×C191C22×D411yescharacteristic
115C4×C191—21no—
116C4×C191—21no—
117C4×C191—21no—
118C4×C191—42no—
119C4×C191H(5,𝔽2)12yes—
120Dic191—42no—
121Dic191—42no—
122C2×C191—22no—
123C2×C191—22no—
124C2×C191—41no—
125C2×C191—82no—
126C2×C191#53411yescharacteristic
127C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
128C2×C191C2×#13711yescharacteristic
129C191#319311yescharacteristic, complemented, Sylow
130#3193—1911nomaximal, Sylow
131C2×C22⋊Q8—1911no—
132C2×#121D19111yescharacteristic
133#484—1912no—
134#480—1912no—
135#468—1914no—
136#450—1912no—
137#448—1912no—
138#407—1911no—
139C22×Q8—1911no—
140C22×D4—21no—
141C22×D4C2×D19111yescharacteristic
142C23×C4C2×D19111yescharacteristic
143C2×SD16—1914no—
144C2×M16—1912no—
145C22⋊Q8—3821no—
146C22⋊Q8—3821no—
147C22⋊Q8—1912no—
148C22⋊Q8—1912no—
149#121—21no—
150#121—21no—
151#121C2×D19112yes—
152#121C2×D19112yes—
153C2×C4⋊C4—3821no—
154C2×C4⋊C4—1911no—
155C2×C4⋊C4C2×D19111yescharacteristic
156C2×C22⋊C4—21no—
157C2×C22⋊C4—3821no—
158#107—1914no—
159#103—1914no—
160#102—1914no—
161C22⋊C8—1912no—
162C22⋊C8—1912no—
163C24—21no—
164C24C22⋊D19111yescharacteristic
165C2×Q8—3821no—
166C2×Q8—1912no—
167C2×Q8—7642no—
168C2×D4—22no—
169C2×D4—22no—
170C2×D4—21no—
171C2×D4—42no—
172C2×D4—44no—
173C2×D4C22×D19112yes—
174C22×C4—21no—
175C22×C4—42no—
176C22×C4—3821no—
177C22×C4—3821no—
178C22×C4C22⋊D19111yescharacteristic
179C22×C4C22⋊D19111yescharacteristic
180C22×C4C22⋊D19111yescharacteristic
181C22×C4C22×D19111yescharacteristic
182C22×C4C22×D19111yescharacteristic
183C22×C4C22×D19111yescharacteristic
184SD16—7644no—
185M16—7642no—
186C2×C8—1914no—
187C4⋊C4—21no—
188C4⋊C4—3822no—
189C4⋊C4—3822no—
190C4⋊C4—3821no—
191C4⋊C4—1912no—
192C4⋊C4C22×D19112yes—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—3822no—
196C22⋊C4—3822no—
197C23—22no—
198C23—22no—
199C23—22no—
200C23—41no—
201C23—42no—
202C23—42no—
203C23—42no—
204C23C2×C22⋊D19111yescharacteristic
205C23C2×C22⋊D19111yescharacteristic
206C23C2×C22⋊D19111yescharacteristic
207Q8—3824no—
208Q8—7642no—
209D4—24no—
210D4—42no—
211D4—44no—
212D4—44no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—3822no—
222C2×C4—3822no—
223C2×C4—7642no—
224C2×C4—7642no—
225C2×C4C2×C22⋊D19111yescharacteristic
226C2×C4C2×C22⋊D19111yescharacteristic
227C2×C4C2×C22⋊D19111yescharacteristic
228C2×C4C23×D19111yescharacteristic
229C8—3824no—
230C22—21no—
231C22—21no—
232C22—21no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—44no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—84no—
242C22#2025934812yes—
243C22#2025935212yes—
244C22C22×C22⋊D19111yescharacteristic
245C4—21no—
246C4—21no—
247C4—21no—
248C4—42no—
249C4—7642no—
250C4—7642no—
251C4#2025936712yes—
252C2—22no—
253C2—22no—
254C2—41no—
255C2—82no—
256C2#2713322211yescharacteristic
257C2C2×#2025934811yescharacteristic
258C2C2×#2025935211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting, prime radicalC2×#121×C191C2
socleC22×C191C22×D4
hypercenterC2×#121D191
hypocenterC191#3193
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#20259301C2semidirect
2. #27132998C2semidirect
3. #27132974C2semidirect
4. #27132907C2semidirect
5. #27132814C2semidirect
6. #27132801C2semidirect
7. #27132627C2semidirect
9. C22×Dic382C22semidirect
10. C2×#15690275C22semidirect
11. C2×#15690271C22semidirect
15. #20259301C22semidirect
16. C2×C4⋊Dic191C22semidirect
19. #20259255C22semidirect
20. #20259245C22semidirect
21. #20259243C22semidirect
23. C22⋊(C191⋊C8)C22semidirect
129. C191#3193semidirect

Maximal subgroups

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

subgroupindex
C2×#202593012
#271329982
#271329742
#271329072
#271328142
#271328012
#271326272
C2×#121×C1912
#3193191