Finite Group Databasebeta

← C2×#27133045 #37582939

Subgroups — C2×#27133045 #37582939

Order 24448.

592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×#15690277C211yesmaximal, characteristic, complemented
2C22×#15690275C211yesmaximal, characteristic, complemented
3C22×#15690274C211yesmaximal, characteristic, complemented
4C22×#15690272C211yesmaximal, characteristic
5C2×#20259310C211yesmaximal, characteristic, complemented
6#27133045C218yesmaximal, direct product factor
7C2×C4×C191⋊C8C211yesmaximal, characteristic, complemented
8C2×#124×C191C211yesmaximal, characteristic, complemented
9C22×Dic382C2211yescharacteristic
10C22×D764C2211yescharacteristic
11C2×#15690277—24no—
12C2×#15690277C2214yescomplemented
13C2×#15690275—24no—
14C2×#15690275C2214yescomplemented
15C2×#15690274—24no—
16C2×#15690274C2214yescomplemented
17C2×#15690272—24no—
18C2×#15690272C2214yes—
19C22×C191⋊C8C2211yescharacteristic
20C22×C191⋊C8C2211yescharacteristic
21#20259310—22no—
22#20259310C2214yescomplemented
23C2×(C2×D191)⋊C4—22no—
24C4×C191⋊C8C2214yescomplemented
25C22×Q8×C191C2211yescharacteristic
26C22×D4×C191C2211yescharacteristic
27#124×C191—22no—
28#124×C191C2214yescomplemented
29C2×C22⋊C4×C191—22no—
30C2×C42×C191C2211yescharacteristic
31C23×D191—21no—
32C2×Dic382—21no—
33C2×Dic382—22no—
34C2×Dic382—22no—
35C2×Dic382C2312yes—
36C2×D764—22no—
37C2×D764—22no—
38C2×D764—21no—
39C2×D764C2312yes—
40C22×Dic191—21no—
41#15690277—28no—
42#15690275—28no—
43#15690274—28no—
44#15690272—28no—
45C2×C191⋊C8D414yes—
46C2×C191⋊C8D414yes—
47C2×C191⋊C8C2312yes—
48C2×C191⋊C8C2312yes—
49(C2×D191)⋊C4—28no—
50C24×C191—21no—
51C2×Q8×C191—21no—
52C2×Q8×C191—22no—
53C2×Q8×C191—22no—
54C2×Q8×C191C2312yes—
55C2×D4×C191—22no—
56C2×D4×C191—22no—
57C2×D4×C191—21no—
58C2×D4×C191C2312yes—
59C22×C4×C191—21no—
60C22×C4×C191D412yes—
61C22×C4×C191C2311yescharacteristic
62C22⋊C4×C191—28no—
63C42×C191D412yes—
64C42×C191C2312yes—
65C22×D191—22no—
66C22×D191—42no—
67C22×D191—44no—
68Dic382—22no—
69Dic382—22no—
70Dic382—42no—
71D764—22no—
72D764—22no—
73D764—42no—
74C2×Dic191—22no—
75C2×Dic191—42no—
76C191⋊C8C2×D414yes—
77C191⋊C8C2×D414yes—
78C23×C191—22no—
79C23×C191—42no—
80C23×C191—44no—
81C23×C191C2×D411yescharacteristic
82Q8×C191—22no—
83Q8×C191—22no—
84Q8×C191—42no—
85D4×C191—22no—
86D4×C191—22no—
87D4×C191—42no—
88C2×C4×C191—24no—
89C2×C4×C191—22no—
90C2×C4×C191—42no—
91C2×C4×C191C2×D412yes—
92C2×C4×C191C2×D412yes—
93C2×C4×C191C2×D414yes—
94C2×C4×C191C2×D411yescharacteristic
95C2×C4×C191C2411yescharacteristic
96C22×C191—42no—
97C22×C191—44no—
98C22×C191—84no—
99C22×C191#12712yes—
100C22×C191#13514yes—
101C22×C191C22×D411yescharacteristic
102C2×D191—42no—
103C2×D191—44no—
104C2×D191—84no—
105C4×C191—24no—
106C4×C191—42no—
107C4×C191#12712yes—
108C4×C191C22×D411yescharacteristic
109C4×C191C22×D411yescharacteristic
110Dic191—42no—
111C2×C191—82no—
112C2×C191#49514yescomplemented
113C2×C191C2×#12711yescharacteristic
114C2×C191C2×#13512yes—
115D191—82no—
116C191C2×#49511yescharacteristic, complemented, Sylow
117C2×#495—1911nomaximal, Sylow
118C22×Q16—1911no—
119C22×SD16—1911no—
120C22×SD16—1911no—
121C22×D8—1911no—
122C2×#124—1911no—
123C2×#124D19111yescharacteristic, complemented
124#495—1918no—
125C2×C4×C8—1911no—
126C22×Q8—1911no—
127C22×Q8C2×D19111yescharacteristic
128C22×D4—1911no—
129C22×D4C2×D19111yescharacteristic
130C2×Q16—3824no—
131C2×Q16—1914no—
132C2×SD16—3824no—
133C2×SD16—3824no—
134C2×SD16—1914no—
135C2×SD16—1914no—
136C2×D8—3824no—
137C2×D8—1914no—
138C22×C8—1911no—
139C22×C8—1911no—
140#124—22no—
141#124—3822no—
142#124—1914no—
143#124C2×D19114yescomplemented
144C2×C22⋊C4—22no—
145C2×C22⋊C4—3822no—
146C2×C42C2×D19111yescharacteristic
147C4×C8—1914no—
148C24—21no—
149C24—3821no—
150C2×Q8—21no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—3821no—
154C2×Q8—3822no—
155C2×Q8—3822no—
156C2×Q8—1912no—
157C2×Q8C22×D19112yes—
158C2×D4—22no—
159C2×D4—22no—
160C2×D4—21no—
161C2×D4—3822no—
162C2×D4—3822no—
163C2×D4—3821no—
164C2×D4—1912no—
165C2×D4C22×D19112yes—
166C22×C4—21no—
167C22×C4—3821no—
168C22×C4C22⋊D19112yes—
169C22×C4C22×D19111yescharacteristic
170Q16—3828no—
171SD16—3828no—
172SD16—3828no—
173D8—3828no—
174C2×C8—1914no—
175C2×C8—1914no—
176C2×C8—1912no—
177C2×C8—1912no—
178C22⋊C4—28no—
179C22⋊C4—3828no—
180C42C22⋊D19112yes—
181C42C22×D19112yes—
182C23—22no—
183C23—44no—
184C23—42no—
185C23—3822no—
186C23—7644no—
187C23—7642no—
188C23C2×C22⋊D19111yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—3822no—
193Q8—3822no—
194Q8—7642no—
195D4—22no—
196D4—22no—
197D4—42no—
198D4—3822no—
199D4—3822no—
200D4—7642no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—42no—
204C2×C4—3822no—
205C2×C4—7642no—
206C2×C4D4×D19112yes—
207C2×C4D4×D19112yes—
208C2×C4C2×C22⋊D19114yes—
209C2×C4C2×C22⋊D19111yescharacteristic
210C2×C4C23×D19111yescharacteristic
211C8—1914no—
212C8—1914no—
213C22—44no—
214C22—42no—
215C22—84no—
216C22—15284no—
217C22—7644no—
218C22—7642no—
219C22#2025931812yes—
220C22#2025934214yes—
221C22C22×C22⋊D19111yescharacteristic
222C4—24no—
223C4—42no—
224C4—7642no—
225C4#2025931812yes—
226C4C2×D4×D19111yescharacteristic
227C4C2×D4×D19111yescharacteristic
228C2—82no—
229C2—15282no—
230C2#2713304514yesdirect product factor
231C2C2×#2025931811yescharacteristic
232C2C2×#2025934212yes—
subgroupG/H
centerC23C2×C22⋊D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC2×#124×C191C2
socleC23×C191C2×D4
prime radicalC22×#15690272C2
hypercenterC2×#124D191
hypocenterC191C2×#495
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C22×#15690277C2semidirect
2. C22×#15690275C2semidirect
3. C22×#15690274C2semidirect
5. C2×#20259310C2semidirect
6. #27133045C2direct (N × H)
7. C2×C4×C191⋊C8C2semidirect
8. C2×#124×C191C2semidirect
12. C2×#15690277C22semidirect
14. C2×#15690275C22semidirect
16. C2×#15690274C22semidirect
22. #20259310C22semidirect
24. C4×C191⋊C8C22semidirect
28. #124×C191C22semidirect
112. C2×C191#495semidirect
116. C191C2×#495semidirect
123. C2×#124D191semidirect
143. #124C2×D191semidirect
230. C2#27133045direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156902772
C22×#156902752
C22×#156902742
C22×#156902722
C2×#202593102
#271330452
C2×C4×C191⋊C82
C2×#124×C1912
C2×#495191