Finite Group Databasebeta

← C2×#19151969 #26030657

Subgroups — C2×#19151969 #26030657

Order 11392.

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×#13083563C211yesmaximal, characteristic, complemented
2C22×#13083562C211yesmaximal, characteristic, complemented
3C22×#13083561C211yesmaximal, characteristic, complemented
4C2×#15668010C211yesmaximal, characteristic, complemented
5C2×#15668008C211yesmaximal, characteristic
6#19151969C218yesmaximal, direct product factor
7C2×C8×Dic89C211yesmaximal, characteristic, complemented
8C22×SD16×C89C211yesmaximal, characteristic, complemented
9C22×Dic178C2211yescharacteristic
10C22×D356C2211yescharacteristic
11C22×C22⋊D89—22no—
12C2×#13083563—24no—
13C2×#13083563C2214yescomplemented
14C2×#13083562—24no—
15C2×#13083562C2214yescomplemented
16C2×#13083561—24no—
17C2×#13083561C2214yescomplemented
18C22×#10623494C2211yescharacteristic
19#15668010—22no—
20#15668010C2214yescomplemented
21#15668008—22no—
22#15668008C2214yes—
23C2×#13083553—22no—
24C2×C4×Dic89C2211yescharacteristic
25C8×Dic89C2214yescomplemented
26C22×Q8×C89C2211yescharacteristic
27C22×D4×C89C2211yescharacteristic
28C2×SD16×C89—24no—
29C2×SD16×C89C2214yescomplemented
30C22×C8×C89C2211yescharacteristic
31C23×D89—21no—
32C2×Dic178—22no—
33C2×Dic178—22no—
34C2×Dic178—21no—
35C2×Dic178C2312yes—
36C2×D356—22no—
37C2×D356—22no—
38C2×D356—21no—
39C2×D356C2312yes—
40C2×C22⋊D89—28no—
41C2×C22⋊D89—48no—
42C22×Dic89—21no—
43C22×Dic89D412yes—
44#13083563—28no—
45#13083562—28no—
46#13083561—28no—
47C2×#10623494D414yescomplemented
48C2×#10623494C2312yes—
49#13083553—28no—
50C4×Dic89D412yes—
51C4×Dic89C2312yes—
52C24×C89—21no—
53C2×Q8×C89—21no—
54C2×Q8×C89—22no—
55C2×Q8×C89—22no—
56C2×Q8×C89C2312yes—
57C2×D4×C89—22no—
58C2×D4×C89—22no—
59C2×D4×C89—21no—
60C2×D4×C89C2312yes—
61C22×C4×C89—21no—
62C22×C4×C89C2311yescharacteristic
63SD16×C89—28no—
64C2×C8×C89D414yescomplemented
65C2×C8×C89C2312yes—
66C23×C89—22no—
67C23×C89—42no—
68C23×C89—44no—
69C23×C89C2×D411yescharacteristic
70C22×D89—22no—
71C22×D89—42no—
72C22×D89—44no—
73Q8×C89—22no—
74Q8×C89—22no—
75Q8×C89—42no—
76D4×C89—22no—
77D4×C89—22no—
78D4×C89—42no—
79C2×C4×C89—22no—
80C2×C4×C89—42no—
81C2×C4×C89C2×D411yescharacteristic
82C2×C4×C89C2×D412yes—
83C2×C4×C89C2×D412yes—
84C2×C4×C89C2411yescharacteristic
85C22⋊D89—416no—
86C2×Dic89—22no—
87C2×Dic89—42no—
88C2×Dic89SD1618yescomplemented
89C2×Dic89C2×D414yes—
90D356—22no—
91D356—22no—
92D356—42no—
93Dic178—22no—
94Dic178—22no—
95Dic178—42no—
96C8×C89C2×D414yescomplemented
97#10623494C2×D414yescomplemented
98C22×C89—42no—
99C22×C89—44no—
100C22×C89—84no—
101C22×C89#12712yes—
102C22×C89C2×SD1614yes—
103C22×C89C22×D411yescharacteristic
104C2×D89—42no—
105C2×D89—44no—
106C2×D89—84no—
107C4×C89—42no—
108C4×C89#12712yes—
109C4×C89C22×D411yescharacteristic
110C4×C89C22×D411yescharacteristic
111Dic89—42no—
112Dic89C2×SD1618yescomplemented
113C2×C89—82no—
114C2×C89#49214yescomplemented
115C2×C89C2×#12711yescharacteristic
116C2×C89C22×SD1612yes—
117D89—82no—
118C2×#492—891nomaximal, Sylow
119C89C2×#49211yescharacteristic, complemented, Sylow
120C22×SD16—891no—
121C22×SD16—891no—
122C22×SD16—891no—
123C22×SD16D8911yescharacteristic, complemented
124C2×C4⋊Q8—891no—
125C2×#127—891no—
126#492—898no—
127C2×C4×C8—891no—
128C22×Q8—891no—
129C22×Q8C2×D8911yescharacteristic
130C22×D4—891no—
131C22×D4—1782no—
132C22×D4C2×D8911yescharacteristic
133C2×SD16—24no—
134C2×SD16—894no—
135C2×SD16—894no—
136C2×SD16—894no—
137C2×SD16—1784no—
138C2×SD16—1784no—
139C2×SD16—1784no—
140C2×SD16C2×D8914yescomplemented
141C22×C8—891no—
142C22×C8C2×D8911yescharacteristic
143C4⋊Q8—894no—
144C4⋊Q8—1782no—
145#127—894no—
146#127—1782no—
147C2×C4⋊C4—1782no—
148C2×C42—891no—
149C4×C8—894no—
150C24—21no—
151C24—1781no—
152C2×Q8—21no—
153C2×Q8—22no—
154C2×Q8—22no—
155C2×Q8—892no—
156C2×Q8—1782no—
157C2×Q8—1782no—
158C2×Q8—1781no—
159C2×Q8C22×D8912yes—
160C2×D4—22no—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—892no—
164C2×D4—3568no—
165C2×D4—1788no—
166C2×D4—1781no—
167C2×D4—1782no—
168C2×D4—1782no—
169C2×D4C22×D8912yes—
170C22×C4—21no—
171C22×C4—892no—
172C22×C4—1781no—
173C22×C4C22×D8911yescharacteristic
174SD16—28no—
175SD16—1788no—
176SD16—1788no—
177SD16—1788no—
178C2×C8—894no—
179C2×C8—892no—
180C2×C8C22⋊D8914yescomplemented
181C2×C8C22×D8912yes—
182C4⋊C4—1788no—
183C42—892no—
184C42—892no—
185C23—22no—
186C23—42no—
187C23—44no—
188C23—3562no—
189C23—3564no—
190C23—1782no—
191C23D4×D8911yescharacteristic
192Q8—22no—
193Q8—22no—
194Q8—42no—
195Q8—3562no—
196Q8—1782no—
197Q8—1782no—
198D4—22no—
199D4—22no—
200D4—42no—
201D4—35616no—
202D4—3562no—
203D4—1782no—
204D4—1782no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—898no—
208C2×C4—894no—
209C2×C4—3562no—
210C2×C4—1782no—
211C2×C4D4×D8911yescharacteristic
212C2×C4D4×D8912yes—
213C2×C4C2×C22⋊D8912yes—
214C2×C4C23×D8911yescharacteristic
215C8—894no—
216C8C2×C22⋊D8914yescomplemented
217C22—42no—
218C22—44no—
219C22—84no—
220C22—3562no—
221C22—3564no—
222C22—7124no—
223C22#1566800812yes—
224C22SD16×D8914yes—
225C22C2×D4×D8911yescharacteristic
226C4—42no—
227C4—898no—
228C4—3562no—
229C4#1566800812yes—
230C4C2×D4×D8911yescharacteristic
231C4C22×C22⋊D8911yescharacteristic
232C2—82no—
233C2—7122no—
234C2#1915196914yesdirect product factor
235C2C2×#1566800811yescharacteristic
236C2C2×SD16×D8912yes—
subgroupG/H
centerC23D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC22×SD16×C89C2
socleC23×C89C2×D4
prime radicalC2×#15668008C2
hypercenterC22×SD16D89
hypocenterC89C2×#492
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#13083563C2semidirect
2. C22×#13083562C2semidirect
3. C22×#13083561C2semidirect
4. C2×#15668010C2semidirect
6. #19151969C2direct (N × H)
7. C2×C8×Dic89C2semidirect
8. C22×SD16×C89C2semidirect
13. C2×#13083563C22semidirect
15. C2×#13083562C22semidirect
17. C2×#13083561C22semidirect
20. #15668010C22semidirect
25. C8×Dic89C22semidirect
29. C2×SD16×C89C22semidirect
47. C2×#10623494D4semidirect
64. C2×C8×C89D4semidirect
88. C2×Dic89SD16semidirect
96. C8×C89C2×D4semidirect
97. #10623494C2×D4semidirect
112. Dic89C2×SD16semidirect
114. C2×C89#492semidirect
119. C89C2×#492semidirect
123. C22×SD16D89semidirect
140. C2×SD16C2×D89semidirect
180. C2×C8C22⋊D89semidirect
216. C8C2×C22⋊D89semidirect
234. C2#19151969direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130835632
C22×#130835622
C22×#130835612
C2×#156680102
C2×#156680082
#191519692
C2×C8×Dic892
C22×SD16×C892
C2×#49289