Finite Group Databasebeta

← C2×#14521390 #16855603

Subgroups — C2×#14521390 #16855603

Order 3968.

416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11758501C211yesmaximal, characteristic
2#14521390C218yesmaximal, direct product factor
3C2×#11758395C211yesmaximal, characteristic, complemented
4C2×#11758396C211yesmaximal, characteristic, complemented
5C2×#11758398C211yesmaximal, characteristic, complemented
6C2×#11758398C211yesmaximal, characteristic, complemented
7C2×C22⋊(C31⋊C8)C211yesmaximal, characteristic
8C2×C31×#117C211yesmaximal, characteristic
9C23×C4×C31C2211yescharacteristic
10C22×Dic62C2211yescharacteristic
11C31×#117—22no—
12C31×#117C2214yes—
13C2×C4⋊C4×C31C2211yescharacteristic
14C2×C4⋊C4×C31C2211yescharacteristic
15C2×C22⋊C4×C31—21no—
16C2×C42×C31—21no—
17C2×C22⋊Dic31—21no—
18C2×C4⋊Dic31C2211yescharacteristic
19#11758501—22no—
20#11758501C2214yes—
21C2×Dic31⋊C4—21no—
22C22×C31⋊C8C2211yescharacteristic
23C22×C31⋊C8C2211yescharacteristic
24C22⋊(C31⋊C8)C2214yes—
25#11758398C2214yescomplemented
26#11758398C2214yescomplemented
27#11758396C2214yescomplemented
28#11758395C2214yescomplemented
29C24×C31D411yescharacteristic
30C22×C4×C31—22no—
31C22×C4×C31—22no—
32C22×C4×C31—21no—
33C22×C4×C31—21no—
34C22×C4×C31D411yescharacteristic
35C22×C4×C31D412yes—
36C22×C4×C31C2312yes—
37C22×C4×C31C2311yescharacteristic
38C22×Dic31—21no—
39C22×Dic31—21no—
40C2×Dic62—22no—
41C2×Dic62—22no—
42C2×Dic62—21no—
43C2×Dic62C2312yes—
44C4⋊C4×C31—21no—
45C4⋊C4×C31—21no—
46C4⋊C4×C31C2312yes—
47C4⋊C4×C31C2312yes—
48C22⋊C4×C31—24no—
49C42×C31—24no—
50C22⋊Dic31—24no—
51C4⋊Dic31—21no—
52C4⋊Dic31C2312yes—
53Dic31⋊C4—24no—
54C2×C31⋊C8—22no—
55C2×C31⋊C8—22no—
56C2×C31⋊C8C2312yes—
57C2×C31⋊C8C2312yes—
58C23×C31—22no—
59C23×C31—22no—
60C23×C31—22no—
61C23×C31C2×D412yes—
62C23×C31C2×D411yescharacteristic
63C2×C4×C31—22no—
64C2×C4×C31—24no—
65C2×C4×C31—22no—
66C2×C4×C31—22no—
67C2×C4×C31—22no—
68C2×C4×C31—22no—
69C2×C4×C31—42no—
70C2×C4×C31—42no—
71C2×C4×C31C2×D412yes—
72C2×C4×C31C2×D411yescharacteristic
73C2×C4×C31#4112yes—
74C2×C4×C31#4112yes—
75C2×C4×C31C2411yescharacteristic
76C2×Dic31—22no—
77C2×Dic31—22no—
78C2×Dic31—42no—
79C2×Dic31—42no—
80Dic62—22no—
81Dic62—22no—
82Dic62—42no—
83C31⋊C8—22no—
84C31⋊C8—22no—
85C2×#485—311nomaximal, Sylow
86C22×C31—22no—
87C22×C31—22no—
88C22×C31—22no—
89C22×C31—44no—
90C22×C31#12312yes—
91C22×C31#13512yes—
92C22×C31#13712yes—
93C22×C31C22×D411yescharacteristic
94C4×C31—22no—
95C4×C31—42no—
96C4×C31—42no—
97C4×C31#12312yes—
98C4×C31C2×#4111yescharacteristic
99C4×C31C2×#4111yescharacteristic
100Dic31—42no—
101Dic31—42no—
102C2×C22⋊Q8—311no—
103C2×#117D3111yescharacteristic
104#485—318no—
105C2×#107—311no—
106C2×#106—311no—
107C2×#103—311no—
108C2×#103—311no—
109C2×C22⋊C8—311no—
110C2×C31—42no—
111C2×C31#48514yescomplemented
112C2×C31C2×#12311yescharacteristic
113C2×C31C2×#13511yescharacteristic
114C2×C31C2×#13711yescharacteristic
115C22×Q8—311no—
116C23×C4C2×D3111yescharacteristic
117C22×C8—311no—
118C22×C8—311no—
119C22⋊Q8—314no—
120C22⋊Q8—622no—
121#117—22no—
122#117C2×D3114yes—
123C2×C4⋊C4—311no—
124C2×C4⋊C4—621no—
125C2×C4⋊C4C2×D3111yescharacteristic
126C2×C4⋊C4C2×D3111yescharacteristic
127C2×C22⋊C4—21no—
128C2×C22⋊C4—621no—
129C2×C42—21no—
130#107—314no—
131#106—314no—
132#103—314no—
133#103—314no—
134C22⋊C8—314no—
135C31C2×#48511yescharacteristic, complemented, Sylow
136C24C22⋊D3111yescharacteristic
137C2×Q8—312no—
138C2×Q8—621no—
139C2×Q8—622no—
140C2×Q8—622no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—621no—
146C22×C4—621no—
147C22×C4C22⋊D3112yes—
148C22×C4C22⋊D3111yescharacteristic
149C22×C4C22×D3112yes—
150C22×C4C22×D3111yescharacteristic
151C2×C8—312no—
152C2×C8—312no—
153C2×C8—622no—
154C2×C8—622no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—312no—
158C4⋊C4—624no—
159C4⋊C4—621no—
160C4⋊C4C22×D3112yes—
161C4⋊C4C22×D3112yes—
162C22⋊C4—24no—
163C22⋊C4—624no—
164C42—24no—
165C23—22no—
166C23—22no—
167C23—22no—
168C23C2×C22⋊D3112yes—
169C23C2×C22⋊D3111yescharacteristic
170Q8—622no—
171Q8—622no—
172Q8—1242no—
173C2×C4—22no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—622no—
182C2×C4—622no—
183C2×C4—1242no—
184C2×C4—1242no—
185C2×C4#9249512yes—
186C2×C4#9249512yes—
187C2×C4C2×C22⋊D3112yes—
188C2×C4C2×C22⋊D3111yescharacteristic
189C2×C4C23×D3111yescharacteristic
190C8—622no—
191C8—622no—
192C22—22no—
193C22—22no—
194C22—22no—
195C22—44no—
196C22#1175850612yes—
197C22#1175852712yes—
198C22#1175852812yes—
199C22C22×C22⋊D3111yescharacteristic
200C4—22no—
201C4—42no—
202C4—42no—
203C4—1242no—
204C4—1242no—
205C4#1175850612yes—
206C4C2×#9249511yescharacteristic
207C4C2×#9249511yescharacteristic
208C2—42no—
209C2#1452139014yesdirect product factor
210C2C2×#1175850611yescharacteristic
211C2C2×#1175852711yescharacteristic
212C2C2×#1175852811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#117C2
socleC23×C31C2×D4
prime radicalC24×C31D4
hypercenterC2×#117D31
hypocenterC31C2×#485
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #14521390C2direct (N × H)
3. C2×#11758395C2semidirect
4. C2×#11758396C2semidirect
5. C2×#11758398C2semidirect
6. C2×#11758398C2semidirect
25. #11758398C22semidirect
26. #11758398C22semidirect
27. #11758396C22semidirect
28. #11758395C22semidirect
111. C2×C31#485semidirect
135. C31C2×#485semidirect
209. C2#14521390direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117585012
#145213902
C2×#117583952
C2×#117583962
C2×#117583982
C2×C22⋊(C31⋊C8)2
C2×C31×#1172
C2×#48531