Finite Group Databasebeta

← C2×#14521232 #16855053

Subgroups — C2×#14521232 #16855053

Order 3968.

708 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 165 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×#11758528C212yesmaximal, complemented
2C2×#11758521C211yesmaximal, characteristic, complemented
3#14521232C218yesmaximal, direct product factor
4C2×#11758425C212yesmaximal, complemented
5C2×#11758424C211yesmaximal, characteristic, complemented
6C2×C31×2−1+4C211yesmaximal, characteristic
7C31×2−1+4—24no—
8C31×2−1+4—22no—
9C31×2−1+4C2214yes—
10C2×#41×C31—22no—
11C2×#41×C31—22no—
12C2×#41×C31C2212yes—
13C22×Q8×C31—22no—
14C22×Q8×C31C2211yescharacteristic
15C22×Dic62C2211yescharacteristic
16#11758528—24no—
17#11758528C2218yescomplemented
18#11758521—22no—
19#11758521C2214yescomplemented
20C2×#92482—22no—
21C2×#92480—22no—
22C2×Dic31⋊C4—22no—
23C2×C4×Dic31C2211yescharacteristic
24C2×#92474C2212yes—
25#11758425C2218yescomplemented
26#11758424C2214yescomplemented
27#41×C31—28no—
28#41×C31—28no—
29#41×C31—28no—
30#41×C31—28no—
31#41×C31—22no—
32#41×C31—22no—
33#41×C31D414yes—
34#41×C31C2314yes—
35C2×Q8×C31—22no—
36C2×Q8×C31—28no—
37C2×Q8×C31—28no—
38C2×Q8×C31—22no—
39C2×Q8×C31—22no—
40C2×Q8×C31D412yes—
41C2×Q8×C31D412yes—
42C2×Q8×C31C2312yes—
43C2×D4×C31—22no—
44C2×D4×C31—22no—
45C2×D4×C31D412yes—
46C22×C4×C31—24no—
47C22×C4×C31—22no—
48C22×C4×C31D412yes—
49C22×C4×C31C2311yescharacteristic
50C22×Dic31—21no—
51C22×Dic31—21no—
52C2×Dic62—22no—
53C2×Dic62—22no—
54C2×Dic62—21no—
55C2×Dic62C2312yes—
56#92482—28no—
57#92480—28no—
58Dic31⋊C4—28no—
59C4×Dic31—21no—
60C4×Dic31C2312yes—
61#92474—22no—
62#92474C2314yes—
63C2×C31⋊C8—22no—
64C23×C31—22no—
65C23×C31C2×D411yescharacteristic
66Q8×C31—28no—
67Q8×C31—22no—
68Q8×C31—24no—
69Q8×C31—24no—
70Q8×C31C2×D414yes—
71D4×C31—28no—
72D4×C31—24no—
73D4×C31—24no—
74D4×C31—22no—
75D4×C31C2×D414yes—
76C2×C4×C31—216no—
77C2×C4×C31—22no—
78C2×C4×C31—22no—
79C2×C4×C31—22no—
80C2×C4×C31—24no—
81C2×C4×C31—24no—
82C2×C4×C31C2×D414yes—
83C2×C4×C31C2×D411yescharacteristic
84C2×C4×C31C2×D412yes—
85C2×C4×C31C2×D412yes—
86C2×C4×C31C2411yescharacteristic
87C2×Dic31—24no—
88C2×Dic31—22no—
89C2×Dic31—22no—
90C2×Dic31—41no—
91C2×Dic31—41no—
92Dic62—24no—
93Dic62—42no—
94C31⋊C8—24no—
95C2×#456—311nomaximal, Sylow
96C22×C31—22no—
97C22×C31—24no—
98C22×C31—44no—
99C22×C31#12011yescharacteristic
100C22×C31#12011yescharacteristic
101C22×C31C22×D411yescharacteristic
102C4×C31—24no—
103C4×C31—24no—
104C4×C31#12012yes—
105C4×C31C22×D412yes—
106Dic31—24no—
107Dic31—42no—
108C2×2−1+4D3111yescharacteristic
109C2×#137—312no—
110C2×C4⋊Q8—311no—
111#456—318no—
112C2×#104—312no—
113C2×#101—311no—
114C2×C31—21no—
115C2×C31—21no—
116C2×C31—44no—
117C2×C31#45612yescomplemented
118C2×C31C2×#12011yescharacteristic
1192−1+4—24no—
1202−1+4—22no—
1212−1+4C2×D3114yes—
122C2×#41—22no—
123C2×#41—22no—
124C2×#41C2×D3112yes—
125C22×Q8—22no—
126C22×Q8—311no—
127C22×Q8C2×D3111yescharacteristic
128#137—318no—
129#137—624no—
130C2×Q16—622no—
131C2×SD16—622no—
132C2×M16—312no—
133C4⋊Q8—314no—
134C4⋊Q8—622no—
135C2×C4⋊C4—622no—
136C2×C42—311no—
137#104—318no—
138#101—314no—
139C31C2×#45611yescharacteristic, complemented, Sylow
140#41—28no—
141#41—28no—
142#41—28no—
143#41—28no—
144#41—22no—
145#41—22no—
146#41C22⋊D3114yes—
147#41C22×D3114yes—
148C2×Q8—22no—
149C2×Q8—28no—
150C2×Q8—28no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—312no—
154C2×Q8—621no—
155C2×Q8—622no—
156C2×Q8—622no—
157C2×Q8C22⋊D3112yes—
158C2×Q8C22⋊D3112yes—
159C2×Q8C22×D3112yes—
160C2×D4—22no—
161C2×D4—22no—
162C2×D4C22⋊D3112yes—
163C22×C4—24no—
164C22×C4—22no—
165C22×C4—621no—
166C22×C4—621no—
167C22×C4C22⋊D3112yes—
168C22×C4C22×D3111yescharacteristic
169Q16—628no—
170SD16—628no—
171M16—314no—
172M16—622no—
173C2×C8—622no—
174C4⋊C4—628no—
175C42—312no—
176C42—621no—
177C23—22no—
178C23C2×C22⋊D3111yescharacteristic
179Q8—28no—
180Q8—22no—
181Q8—24no—
182Q8—24no—
183Q8—624no—
184Q8—1242no—
185Q8C2×C22⋊D3114yes—
186D4—28no—
187D4—24no—
188D4—24no—
189D4—22no—
190D4C2×C22⋊D3114yes—
191C2×C4—216no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—624no—
198C2×C4—622no—
199C2×C4—622no—
200C2×C4—1241no—
201C2×C4—1241no—
202C2×C4C2×C22⋊D3114yes—
203C2×C4C2×C22⋊D3111yescharacteristic
204C2×C4C2×C22⋊D3112yes—
205C2×C4C2×C22⋊D3112yes—
206C2×C4C23×D3111yescharacteristic
207C8—624no—
208C22—22no—
209C22—24no—
210C22—44no—
211C22#1175853011yescharacteristic
212C22#1175853011yescharacteristic
213C22C22×C22⋊D3111yescharacteristic
214C4—24no—
215C4—24no—
216C4—624no—
217C4—1242no—
218C4#1175853012yes—
219C4C22×C22⋊D3112yes—
220C2—21no—
221C2—21no—
222C2—44no—
223C2#1452123212yesdirect product factor
224C2C2×#1175853011yescharacteristic
subgroupG/H
centerC22#11758530
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
Fitting, prime radicalC2×C31×2−1+4C2
socleC22×C31#120
hypercenterC2×2−1+4D31
hypocenterC31C2×#456
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×#11758528C2semidirect
2. C2×#11758521C2semidirect
3. #14521232C2direct (N × H)
4. C2×#11758425C2semidirect
5. C2×#11758424C2semidirect
17. #11758528C22semidirect
19. #11758521C22semidirect
25. #11758425C22semidirect
26. #11758424C22semidirect
117. C2×C31#456semidirect
139. C31C2×#456semidirect
223. C2#14521232direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117585282
C2×#117585212
#145212322
C2×#117584252
C2×#117584242
C2×C31×2−1+42
C2×#45631