Finite Group Databasebeta

← C2×#14521486 #16858835

Subgroups — C2×#14521486 #16858835

Order 3968.

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×#11758496C211yesmaximal, characteristic, complemented
2C2×D8×D31C211yesmaximal, characteristic, complemented
3#14521486C218yesmaximal, direct product factor
4C2×#11758416C211yesmaximal, characteristic, complemented
5C2×D496C211yesmaximal, characteristic, complemented
6C2×#11758414C211yesmaximal, characteristic, complemented
7C2×#11758386C211yesmaximal, characteristic, complemented
8C2×C31×SD32C211yesmaximal, characteristic, complemented
9C2×#92499—21no—
10C2×D4×D31—21no—
11C2×Q16×C31C2211yescharacteristic, complemented
12C2×D8×C31C2211yescharacteristic
13C2×#92481—21no—
14C2×#92479—21no—
15#11758496—22no—
16#11758496C2214yescomplemented
17D8×D31—22no—
18D8×D31C2214yescomplemented
19C2×D248C2211yescharacteristic
20C2×D248C2211yescharacteristic, complemented
21C2×C8×D31C2211yescharacteristic
22C31×SD32C2214yescomplemented
23C2×C16×C31C2211yescharacteristic, complemented
24#11758416C2214yescomplemented
25#11758414C2214yescomplemented
26C2×C31⋊C16C2211yescharacteristic, complemented
27D496C2214yescomplemented
28#11758386C2214yescomplemented
29C23×D31—41no—
30C2×Q8×C31—21no—
31C2×D4×C31—21no—
32C2×C22⋊D31—41no—
33#92499—24no—
34#92499—42no—
35D4×D31—24no—
36D4×D31—42no—
37C2×D124—21no—
38C2×D124—21no—
39C2×D124—41no—
40C2×C4×D31—41no—
41C2×C4×D31D411yescharacteristic
42Q16×C31—21no—
43Q16×C31C2312yescomplemented
44D8×C31—21no—
45D8×C31C2312yes—
46C2×C8×C31C2311yescharacteristic
47#92481—24no—
48#92479—24no—
49C2×C31⋊C8D411yescharacteristic
50D248—21no—
51D248—21no—
52D248C2312yes—
53D248C2312yescomplemented
54C8×D31D412yes—
55C8×D31C2312yes—
56C16×C31C2312yescomplemented
57C31⋊C16C2312yescomplemented
58C23×C31—41no—
59C22×D31—41no—
60C22×D31—41no—
61C22×D31—44no—
62C22×D31—84no—
63C22×D31D811yescharacteristic
64Q8×C31—22no—
65Q8×C31—41no—
66D4×C31—22no—
67D4×C31—41no—
68C2×C4×C31—41no—
69C2×C4×C31C2×D411yescharacteristic
70C22⋊D31—44no—
71C2×Dic31D811yescharacteristic
72D124—22no—
73D124—22no—
74D124—44no—
75D124—41no—
76D124—41no—
77C4×D31—44no—
78C4×D31D812yes—
79C4×D31C2×D412yes—
80C8×C31C2×D411yescharacteristic
81C8×C31C2411yescharacteristic
82C31⋊C8C2×D412yes—
83C2×#509—311nomaximal, Sylow
84C22×C31—42no—
85C22×C31—82no—
86C22×C31C2×D811yescharacteristic
87C2×D31—22no—
88C2×D31—42no—
89C2×D31—42no—
90C2×D31—88no—
91C2×D31—82no—
92C2×D31—82no—
93C2×D31C2×D812yes—
94C4×C31—42no—
95C4×C31C2×D811yescharacteristic
96C4×C31C22×D411yescharacteristic
97Dic31C2×D812yes—
98C2×#135—311no—
99C22×D8—311no—
100#509—318no—
101C2×SD32—311no—
102C2×SD32D3111yescharacteristic, complemented
103C2×D16—311no—
104C2×D16—311no—
105C2×M32—311no—
106C2×C31—82no—
107C2×C31#50912yescomplemented
108C2×C31C22×D811yescharacteristic
109D31—22no—
110D31—82no—
111D31—82no—
112C2×#41—621no—
113C22×D4—621no—
114#135—314no—
115#135—622no—
116C2×Q16C2×D3111yescharacteristic, complemented
117C2×SD16—621no—
118C2×D8—314no—
119C2×D8—311no—
120C2×D8—311no—
121C2×D8—622no—
122C2×D8—621no—
123C2×D8C2×D3111yescharacteristic
124C22×C8—311no—
125SD32—314no—
126SD32C2×D3114yescomplemented
127D16—314no—
128D16—314no—
129M32—314no—
130C2×C16—311no—
131C2×C16C2×D3111yescharacteristic, complemented
132C31C2×#50911yescharacteristic, complemented, Sylow
133C24—1241no—
134#41—624no—
135#41—1242no—
136C2×Q8—21no—
137C2×D4—21no—
138C2×D4—624no—
139C2×D4—621no—
140C2×D4—621no—
141C2×D4—1241no—
142C2×D4—1242no—
143C2×D4—1241no—
144C22×C4—311no—
145C22×C4—1241no—
146Q16—21no—
147Q16C22×D3112yescomplemented
148SD16—624no—
149D8—21no—
150D8—312no—
151D8—312no—
152D8—624no—
153D8—621no—
154D8—621no—
155D8C22×D3112yes—
156C2×C8—311no—
157C2×C8—312no—
158C2×C8—312no—
159C2×C8C22×D3111yescharacteristic
160C16—312no—
161C16C22×D3112yescomplemented
162C23—41no—
163C23—311no—
164C23—1244no—
165C23—1241no—
166C23—1241no—
167C23—2484no—
168Q8—22no—
169Q8—41no—
170D4—22no—
171D4—41no—
172D4—622no—
173D4—622no—
174D4—1244no—
175D4—1244no—
176D4—1241no—
177D4—1241no—
178C2×C4—41no—
179C2×C4—311no—
180C2×C4—312no—
181C2×C4—312no—
182C2×C4—1244no—
183C2×C4D4×D3111yescharacteristic
184C8—312no—
185C8D4×D3111yescharacteristic
186C8C23×D3111yescharacteristic
187C22—42no—
188C22—82no—
189C22—312no—
190C22—622no—
191C22—1242no—
192C22—1242no—
193C22—2488no—
194C22—2482no—
195C22—2482no—
196C22D8×D3111yescharacteristic
197C4—42no—
198C4—312no—
199C4D8×D3111yescharacteristic
200C4C2×D4×D3111yescharacteristic
201C2—82no—
202C2—622no—
203C2—2482no—
204C2—2482no—
205C2#1452148612yesdirect product factor
206C2C2×D8×D3111yescharacteristic
subgroupG/H
centerC22D8×D31
commutator, cosocleC8×C31C24
FrattiniC8C23×D31
FittingC2×C31×SD32C2
socleC22×C31C2×D8
hypercenterC2×SD32D31
hypocenterC31C2×#509
LCSG ▷ C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#11758496C2semidirect
2. C2×D8×D31C2semidirect
3. #14521486C2direct (N × H)
4. C2×#11758416C2semidirect
5. C2×D496C2semidirect
6. C2×#11758414C2semidirect
7. C2×#11758386C2semidirect
8. C2×C31×SD32C2semidirect
11. C2×Q16×C31C22semidirect
16. #11758496C22semidirect
18. D8×D31C22semidirect
20. C2×D248C22semidirect
22. C31×SD32C22semidirect
23. C2×C16×C31C22semidirect
24. #11758416C22semidirect
25. #11758414C22semidirect
26. C2×C31⋊C16C22semidirect
27. D496C22semidirect
28. #11758386C22semidirect
43. Q16×C31C23semidirect
53. D248C23semidirect
56. C16×C31C23semidirect
57. C31⋊C16C23semidirect
102. C2×SD32D31semidirect
107. C2×C31#509semidirect
116. C2×Q16C2×D31semidirect
126. SD32C2×D31semidirect
131. C2×C16C2×D31semidirect
132. C31C2×#509semidirect
147. Q16C22×D31semidirect
161. C16C22×D31semidirect
205. C2#14521486direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117584962
C2×D8×D312
#145214862
C2×#117584162
C2×D4962
C2×#117584142
C2×#117583862
C2×C31×SD322
C2×#50931