Finite Group Databasebeta

← C2×#11926981 #14576759

Subgroups — C2×#11926981 #14576759

Order 2432.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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×#10597365C211yesmaximal, characteristic, complemented
2C2×D8×D19C211yesmaximal, characteristic, complemented
3#11926981C218yesmaximal, direct product factor
4C2×#10597285C211yesmaximal, characteristic, complemented
5C2×D304C211yesmaximal, characteristic, complemented
6C2×#10597283C211yesmaximal, characteristic, complemented
7C2×#10597255C211yesmaximal, characteristic, complemented
8C2×C19×SD32C211yesmaximal, characteristic, complemented
9C2×#64545—21no—
10C2×D4×D19—21no—
11C2×Q16×C19C2211yescharacteristic, complemented
12C2×D8×C19C2211yescharacteristic
13C2×#64527—21no—
14C2×#64525—21no—
15#10597365—22no—
16#10597365C2214yescomplemented
17D8×D19—22no—
18D8×D19C2214yescomplemented
19C2×D152C2211yescharacteristic
20C2×D152C2211yescharacteristic, complemented
21C2×C8×D19C2211yescharacteristic
22C19×SD32C2214yescomplemented
23C2×C16×C19C2211yescharacteristic, complemented
24#10597285C2214yescomplemented
25#10597283C2214yescomplemented
26C2×C19⋊C16C2211yescharacteristic, complemented
27D304C2214yescomplemented
28#10597255C2214yescomplemented
29C23×D19—41no—
30C2×Q8×C19—21no—
31C2×D4×C19—21no—
32C2×C22⋊D19—41no—
33#64545—24no—
34#64545—42no—
35D4×D19—24no—
36D4×D19—42no—
37C2×D76—21no—
38C2×D76—21no—
39C2×D76—41no—
40C2×C4×D19—41no—
41C2×C4×D19D411yescharacteristic
42Q16×C19—21no—
43Q16×C19C2312yescomplemented
44D8×C19—21no—
45D8×C19C2312yes—
46C2×C8×C19C2311yescharacteristic
47#64527—24no—
48#64525—24no—
49C2×C19⋊C8D411yescharacteristic
50D152—21no—
51D152—21no—
52D152C2312yes—
53D152C2312yescomplemented
54C8×D19D412yes—
55C8×D19C2312yes—
56C16×C19C2312yescomplemented
57C19⋊C16C2312yescomplemented
58C23×C19—41no—
59C22×D19—41no—
60C22×D19—41no—
61C22×D19—44no—
62C22×D19—84no—
63C22×D19D811yescharacteristic
64Q8×C19—22no—
65Q8×C19—41no—
66D4×C19—22no—
67D4×C19—41no—
68C2×C4×C19—41no—
69C2×C4×C19C2×D411yescharacteristic
70C22⋊D19—44no—
71C2×Dic19D811yescharacteristic
72D76—22no—
73D76—22no—
74D76—44no—
75D76—41no—
76D76—41no—
77C4×D19—44no—
78C4×D19D812yes—
79C4×D19C2×D412yes—
80C8×C19C2×D411yescharacteristic
81C8×C19C2411yescharacteristic
82C19⋊C8C2×D412yes—
83C2×#509—191nomaximal, Sylow
84C22×C19—42no—
85C22×C19—82no—
86C22×C19C2×D811yescharacteristic
87C2×D19—22no—
88C2×D19—42no—
89C2×D19—42no—
90C2×D19—88no—
91C2×D19—82no—
92C2×D19—82no—
93C2×D19C2×D812yes—
94C4×C19—42no—
95C4×C19C2×D811yescharacteristic
96C4×C19C22×D411yescharacteristic
97Dic19C2×D812yes—
98C2×#135—191no—
99C22×D8—191no—
100#509—198no—
101C2×SD32—191no—
102C2×SD32D1911yescharacteristic, complemented
103C2×D16—191no—
104C2×D16—191no—
105C2×M32—191no—
106C2×C19—82no—
107C2×C19#50912yescomplemented
108C2×C19C22×D811yescharacteristic
109D19—22no—
110D19—82no—
111D19—82no—
112C2×#41—381no—
113C22×D4—381no—
114#135—194no—
115#135—382no—
116C2×Q16C2×D1911yescharacteristic, complemented
117C2×SD16—381no—
118C2×D8—194no—
119C2×D8—191no—
120C2×D8—191no—
121C2×D8—382no—
122C2×D8—381no—
123C2×D8C2×D1911yescharacteristic
124C22×C8—191no—
125SD32—194no—
126SD32C2×D1914yescomplemented
127D16—194no—
128D16—194no—
129M32—194no—
130C2×C16—191no—
131C2×C16C2×D1911yescharacteristic, complemented
132C19C2×#50911yescharacteristic, complemented, Sylow
133C24—761no—
134#41—384no—
135#41—762no—
136C2×Q8—21no—
137C2×D4—21no—
138C2×D4—384no—
139C2×D4—381no—
140C2×D4—381no—
141C2×D4—761no—
142C2×D4—762no—
143C2×D4—761no—
144C22×C4—191no—
145C22×C4—761no—
146Q16—21no—
147Q16C22×D1912yescomplemented
148SD16—384no—
149D8—21no—
150D8—192no—
151D8—192no—
152D8—384no—
153D8—381no—
154D8—381no—
155D8C22×D1912yes—
156C2×C8—191no—
157C2×C8—192no—
158C2×C8—192no—
159C2×C8C22×D1911yescharacteristic
160C16—192no—
161C16C22×D1912yescomplemented
162C23—41no—
163C23—191no—
164C23—764no—
165C23—761no—
166C23—761no—
167C23—1524no—
168Q8—22no—
169Q8—41no—
170D4—22no—
171D4—41no—
172D4—382no—
173D4—382no—
174D4—764no—
175D4—764no—
176D4—761no—
177D4—761no—
178C2×C4—41no—
179C2×C4—191no—
180C2×C4—192no—
181C2×C4—192no—
182C2×C4—764no—
183C2×C4D4×D1911yescharacteristic
184C8—192no—
185C8D4×D1911yescharacteristic
186C8C23×D1911yescharacteristic
187C22—42no—
188C22—82no—
189C22—192no—
190C22—382no—
191C22—762no—
192C22—762no—
193C22—1528no—
194C22—1522no—
195C22—1522no—
196C22D8×D1911yescharacteristic
197C4—42no—
198C4—192no—
199C4D8×D1911yescharacteristic
200C4C2×D4×D1911yescharacteristic
201C2—82no—
202C2—382no—
203C2—1522no—
204C2—1522no—
205C2#1192698112yesdirect product factor
206C2C2×D8×D1911yescharacteristic
subgroupG/H
centerC22D8×D19
commutator, cosocleC8×C19C24
FrattiniC8C23×D19
FittingC2×C19×SD32C2
socleC22×C19C2×D8
hypercenterC2×SD32D19
hypocenterC19C2×#509
LCSG ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#10597365C2semidirect
2. C2×D8×D19C2semidirect
3. #11926981C2direct (N × H)
4. C2×#10597285C2semidirect
5. C2×D304C2semidirect
6. C2×#10597283C2semidirect
7. C2×#10597255C2semidirect
8. C2×C19×SD32C2semidirect
11. C2×Q16×C19C22semidirect
16. #10597365C22semidirect
18. D8×D19C22semidirect
20. C2×D152C22semidirect
22. C19×SD32C22semidirect
23. C2×C16×C19C22semidirect
24. #10597285C22semidirect
25. #10597283C22semidirect
26. C2×C19⋊C16C22semidirect
27. D304C22semidirect
28. #10597255C22semidirect
43. Q16×C19C23semidirect
53. D152C23semidirect
56. C16×C19C23semidirect
57. C19⋊C16C23semidirect
102. C2×SD32D19semidirect
107. C2×C19#509semidirect
116. C2×Q16C2×D19semidirect
126. SD32C2×D19semidirect
131. C2×C16C2×D19semidirect
132. C19C2×#509semidirect
147. Q16C22×D19semidirect
161. C16C22×D19semidirect
205. C2#11926981direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#105973652
C2×D8×D192
#119269812
C2×#105972852
C2×D3042
C2×#105972832
C2×#105972552
C2×C19×SD322
C2×#50919