Finite Group Databasebeta

← C2×#27133034 #37582925

Subgroups — C2×#27133034 #37582925

Order 24448.

656 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 181 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×#15690276C211yesmaximal, characteristic, complemented
2C22×#15690275C211yesmaximal, characteristic, complemented
3C22×#15690274C211yesmaximal, characteristic, complemented
4C2×#20259320C211yesmaximal, characteristic, complemented
5C2×#20259318C211yesmaximal, characteristic
6#27133034C218yesmaximal, direct product factor
7C2×C8×Dic191C211yesmaximal, characteristic, complemented
8C22×SD16×C191C211yesmaximal, characteristic, complemented
9C22×Dic382C2211yescharacteristic
10C22×D764C2211yescharacteristic
11C22×C22⋊D191—22no—
12C2×#15690276—24no—
13C2×#15690276C2214yescomplemented
14C2×#15690275—24no—
15C2×#15690275C2214yescomplemented
16C2×#15690274—24no—
17C2×#15690274C2214yescomplemented
18C22×C191⋊C8C2211yescharacteristic
19#20259320—22no—
20#20259320C2214yescomplemented
21#20259318—22no—
22#20259318C2214yes—
23C2×Dic191⋊C4—22no—
24C2×C4×Dic191C2211yescharacteristic
25C8×Dic191C2214yescomplemented
26C22×Q8×C191C2211yescharacteristic
27C22×D4×C191C2211yescharacteristic
28C2×SD16×C191—24no—
29C2×SD16×C191C2214yescomplemented
30C22×C8×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—
40C2×C22⋊D191—28no—
41C2×C22⋊D191—48no—
42C22×Dic191—21no—
43C22×Dic191D412yes—
44#15690276—28no—
45#15690275—28no—
46#15690274—28no—
47C2×C191⋊C8D414yescomplemented
48C2×C191⋊C8C2312yes—
49Dic191⋊C4—28no—
50C4×Dic191D412yes—
51C4×Dic191C2312yes—
52C24×C191—21no—
53C2×Q8×C191—21no—
54C2×Q8×C191—22no—
55C2×Q8×C191—22no—
56C2×Q8×C191C2312yes—
57C2×D4×C191—22no—
58C2×D4×C191—22no—
59C2×D4×C191—21no—
60C2×D4×C191C2312yes—
61C22×C4×C191—21no—
62C22×C4×C191C2311yescharacteristic
63SD16×C191—28no—
64C2×C8×C191D414yescomplemented
65C2×C8×C191C2312yes—
66C22×D191—22no—
67C22×D191—42no—
68C22×D191—44no—
69Dic382—22no—
70Dic382—22no—
71Dic382—42no—
72D764—22no—
73D764—22no—
74D764—42no—
75C22⋊D191—416no—
76C2×Dic191—22no—
77C2×Dic191—42no—
78C2×Dic191SD1618yescomplemented
79C2×Dic191C2×D414yes—
80C191⋊C8C2×D414yescomplemented
81C23×C191—22no—
82C23×C191—42no—
83C23×C191—44no—
84C23×C191C2×D411yescharacteristic
85Q8×C191—22no—
86Q8×C191—22no—
87Q8×C191—42no—
88D4×C191—22no—
89D4×C191—22no—
90D4×C191—42no—
91C2×C4×C191—22no—
92C2×C4×C191—42no—
93C2×C4×C191C2×D411yescharacteristic
94C2×C4×C191C2×D412yes—
95C2×C4×C191C2×D412yes—
96C2×C4×C191C2411yescharacteristic
97C8×C191C2×D414yescomplemented
98C22×C191—42no—
99C22×C191—44no—
100C22×C191—84no—
101C22×C191#12712yes—
102C22×C191C2×SD1614yes—
103C22×C191C22×D411yescharacteristic
104C2×D191—42no—
105C2×D191—44no—
106C2×D191—84no—
107C4×C191—42no—
108C4×C191#12712yes—
109C4×C191C22×D411yescharacteristic
110C4×C191C22×D411yescharacteristic
111Dic191—42no—
112Dic191C2×SD1618yescomplemented
113C2×C191—82no—
114C2×C191#49214yescomplemented
115C2×C191C2×#12711yescharacteristic
116C2×C191C22×SD1612yes—
117D191—82no—
118C191C2×#49211yescharacteristic, complemented, Sylow
119C2×#492—1911nomaximal, Sylow
120C22×SD16—1911no—
121C22×SD16—1911no—
122C22×SD16—1911no—
123C22×SD16D19111yescharacteristic, complemented
124C2×C4⋊Q8—1911no—
125C2×#127—1911no—
126#492—1918no—
127C2×C4×C8—1911no—
128C22×Q8—1911no—
129C22×Q8C2×D19111yescharacteristic
130C22×D4—3822no—
131C22×D4—1911no—
132C22×D4C2×D19111yescharacteristic
133C2×SD16—24no—
134C2×SD16—3824no—
135C2×SD16—3824no—
136C2×SD16—3824no—
137C2×SD16—1914no—
138C2×SD16—1914no—
139C2×SD16—1914no—
140C2×SD16C2×D19114yescomplemented
141C22×C8—1911no—
142C22×C8C2×D19111yescharacteristic
143C4⋊Q8—3822no—
144C4⋊Q8—1914no—
145#127—3822no—
146#127—1914no—
147C2×C4⋊C4—3822no—
148C2×C42—1911no—
149C4×C8—1914no—
150C24—21no—
151C24—3821no—
152C2×Q8—21no—
153C2×Q8—22no—
154C2×Q8—22no—
155C2×Q8—3821no—
156C2×Q8—3822no—
157C2×Q8—3822no—
158C2×Q8—1912no—
159C2×Q8C22×D19112yes—
160C2×D4—22no—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—3828no—
164C2×D4—3822no—
165C2×D4—3821no—
166C2×D4—3822no—
167C2×D4—1912no—
168C2×D4—7648no—
169C2×D4C22×D19112yes—
170C22×C4—21no—
171C22×C4—3821no—
172C22×C4—1912no—
173C22×C4C22×D19111yescharacteristic
174SD16—28no—
175SD16—3828no—
176SD16—3828no—
177SD16—3828no—
178C2×C8—1914no—
179C2×C8—1912no—
180C2×C8C22⋊D19114yescomplemented
181C2×C8C22×D19112yes—
182C4⋊C4—3828no—
183C42—1912no—
184C42—1912no—
185C23—22no—
186C23—44no—
187C23—42no—
188C23—3822no—
189C23—7644no—
190C23—7642no—
191C23D4×D19111yescharacteristic
192Q8—22no—
193Q8—22no—
194Q8—42no—
195Q8—3822no—
196Q8—3822no—
197Q8—7642no—
198D4—22no—
199D4—22no—
200D4—42no—
201D4—3822no—
202D4—3822no—
203D4—76416no—
204D4—7642no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—3822no—
208C2×C4—1918no—
209C2×C4—1914no—
210C2×C4—7642no—
211C2×C4D4×D19112yes—
212C2×C4D4×D19111yescharacteristic
213C2×C4C2×C22⋊D19112yes—
214C2×C4C23×D19111yescharacteristic
215C8—1914no—
216C8C2×C22⋊D19114yescomplemented
217C22—42no—
218C22—44no—
219C22—84no—
220C22—15284no—
221C22—7642no—
222C22—7644no—
223C22#2025931812yes—
224C22SD16×D19114yes—
225C22C2×D4×D19111yescharacteristic
226C4—42no—
227C4—1918no—
228C4—7642no—
229C4#2025931812yes—
230C4C2×D4×D19111yescharacteristic
231C4C22×C22⋊D19111yescharacteristic
232C2—82no—
233C2—15282no—
234C2#2713303414yesdirect product factor
235C2C2×#2025931811yescharacteristic
236C2C2×SD16×D19112yes—
subgroupG/H
centerC23D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC22×SD16×C191C2
socleC23×C191C2×D4
prime radicalC2×#20259318C2
hypercenterC22×SD16D191
hypocenterC191C2×#492
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#15690276C2semidirect
2. C22×#15690275C2semidirect
3. C22×#15690274C2semidirect
4. C2×#20259320C2semidirect
6. #27133034C2direct (N × H)
7. C2×C8×Dic191C2semidirect
8. C22×SD16×C191C2semidirect
13. C2×#15690276C22semidirect
15. C2×#15690275C22semidirect
17. C2×#15690274C22semidirect
20. #20259320C22semidirect
25. C8×Dic191C22semidirect
29. C2×SD16×C191C22semidirect
47. C2×C191⋊C8D4semidirect
64. C2×C8×C191D4semidirect
78. C2×Dic191SD16semidirect
80. C191⋊C8C2×D4semidirect
97. C8×C191C2×D4semidirect
112. Dic191C2×SD16semidirect
114. C2×C191#492semidirect
118. C191C2×#492semidirect
123. C22×SD16D191semidirect
140. C2×SD16C2×D191semidirect
180. C2×C8C22⋊D191semidirect
216. C8C2×C22⋊D191semidirect
234. C2#27133034direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156902762
C22×#156902752
C22×#156902742
C2×#202593202
C2×#202593182
#271330342
C2×C8×Dic1912
C22×SD16×C1912
C2×#492191