Finite Group Databasebeta

← C2×#10593743 #11858276

Subgroups — C2×#10593743 #11858276

Order 1152.

842 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 842 conjugacy classes of subgroups — too many to draw. Only its 218 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×#3792C211yesmaximal, characteristic
2C23×#622C211yesmaximal, characteristic
3C2×#64086C211yesmaximal, characteristic
4C2×#63779C212yesmaximal, complemented
5C2×C4⋊#622C212yesmaximal, complemented
6#10593743C218yesmaximal, direct product factor
7C23×C3⋊Dic3C2211yescharacteristic
8C2×#3792—24no—
9C2×#3792C2214yes—
10C22×#622—24no—
11C22×#622C2211yescharacteristic
12C22×#622C2212yes—
13C22×#622C2211yescharacteristic
14C22×#622C2214yes—
15C2×C32×C22⋊C4C411yescharacteristic
16C2×#3757C411yescharacteristic
17C2×#3750C412yes—
18C2×C4×C3⋊Dic3C2212yes—
19#64086C414yes—
20#64086C2214yes—
21#63779C2218yescomplemented
22C4⋊#622C2218yescomplemented
23C2×#877—62no—
24C24×C32C2×C411yescharacteristic
25C22×C32×C4C2×C412yes—
26C22×C3⋊Dic3C2×C412yes—
27C22×C3⋊Dic3C2×C412yes—
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3D414yes—
30C22×C3⋊Dic3Q814yes—
31C22×C3⋊Dic3C2311yescharacteristic
32C22×C3⋊Dic3C2312yes—
33#3792—28no—
34C2×#622—24no—
35C2×#622—28no—
36C2×#622—22no—
37C2×#622—22no—
38C2×#622C2312yes—
39C2×#622C2314yes—
40C2×#622C2312yes—
41C32×C22⋊C4C2×C414yes—
42#3757C2×C414yes—
43#3750C2×C418yes—
44C4×C3⋊Dic3C2×C414yes—
45C4×C3⋊Dic3C2314yes—
46C2×#424—91nomaximal, Sylow
47C23×Dic3—62no—
48C2×C3×C22⋊C4—22no—
49C2×#217—62no—
50C2×Dic3⋊C4—64no—
51C2×C4×Dic3—64no—
52#877—68no—
53#877—68no—
54C23×C32—24no—
55C23×C32C4⋊C414yes—
56C23×C32C22×C412yes—
57C23×C32C22×C411yescharacteristic
58C2×C32×C4—24no—
59C2×C32×C4C22×C414yes—
60C2×C3⋊Dic3—24no—
61C2×C3⋊Dic3C4⋊C418yes—
62C2×C3⋊Dic3C4⋊C414yes—
63C2×C3⋊Dic3C22×C414yes—
64C2×C3⋊Dic3C22×C411yescharacteristic
65C2×C3⋊Dic3C22×C412yes—
66C2×C3⋊Dic3C2×D412yes—
67C2×C3⋊Dic3C2×D414yes—
68C2×C3⋊Dic3C2×Q814yes—
69C2×C3⋊Dic3C2×Q812yes—
70C2×C3⋊Dic3C2411yescharacteristic
71#622—24no—
72#622—22no—
73#622—22no—
74C22×M16—91no—
75C23×C8—91no—
76C2×#117—91no—
77#424—98no—
78C2×C4⋊C8—92no—
79C2×C4⋊C8—92no—
80C24×C3—22no—
81C22×C3×C4—24no—
82C22×Dic3—64no—
83C22×Dic3—64no—
84C22×Dic3—62no—
85C22×Dic3—62no—
86C22×Dic3—68no—
87C22×Dic3—68no—
88C22×Dic3—64no—
89C3×C22⋊C4—28no—
90#217—68no—
91Dic3⋊C4—616no—
92C4×Dic3—68no—
93C4×Dic3—68no—
94C22×C32—24no—
95C22×C32—28no—
96C22×C32C2×C4⋊C414yes—
97C22×C32C2×C4⋊C412yes—
98C22×C32#13114yes—
99C22×C32C23×C411yescharacteristic
100C32×C4—24no—
101C3⋊Dic3—24no—
102C3⋊Dic3C2×C4⋊C412yes—
103C3⋊Dic3C2×C4⋊C414yes—
104C3⋊Dic3C22×D411yescharacteristic
105C3⋊Dic3C22×Q811yescharacteristic
106C23×C4—91no—
107C2×M16—94no—
108C2×M16—184no—
109C22×C8—92no—
110C22×C8—94no—
111C22×C8—91no—
112C22×C8—91no—
113C22×C8—184no—
114#117—94no—
115#117—94no—
116C2×C4⋊C4—92no—
117C2×C22⋊C4—91no—
118C2×C22⋊C4#15711yescharacteristic
119C2×C42—92no—
120C4⋊C8—98no—
121C4⋊C8—98no—
122C23×C3—24no—
123C23×C3—22no—
124C23×C3—28no—
125C23×C3—48no—
126C2×C3×C4—28no—
127C2×C3×C4—48no—
128C2×Dic3—68no—
129C2×Dic3—616no—
130C2×Dic3—62no—
131C2×Dic3—64no—
132C2×Dic3—64no—
133C2×Dic3—68no—
134C2×Dic3—64no—
135C2×Dic3—68no—
136C2×Dic3—62no—
137C2×Dic3—68no—
138C2×Dic3—128no—
139C2×C32—24no—
140C2×C32#42414yescomplemented
141C2×C32C22×C4⋊C411yescharacteristic
142C2×C32C2×#13112yes—
143C24C2×#15711yescharacteristic
144C22×C4—92no—
145C22×C4—92no—
146C22×C4—91no—
147C22×C4—91no—
148C22×C4—94no—
149C22×C4—94no—
150C22×C4—92no—
151C22×C4C2×#15712yes—
152M16—188no—
153C2×C8—94no—
154C2×C8—92no—
155C2×C8—92no—
156C2×C8—184no—
157C2×C8—188no—
158C2×C8—182no—
159C2×C8—182no—
160C4⋊C4—98no—
161C22⋊C4—94no—
162C22⋊C4C2×#15714yes—
163C42—94no—
164C42—94no—
165C22×C3—24no—
166C22×C3—28no—
167C22×C3—28no—
168C22×C3—22no—
169C22×C3—48no—
170C22×C3—416no—
171C3×C4—48no—
172Dic3—64no—
173Dic3—68no—
174Dic3—62no—
175Dic3—62no—
176Dic3—128no—
177C32C2×#42411yescharacteristic, complemented, Sylow
178C23—24no—
179C23C4⋊#15714yes—
180C23C22×#15712yes—
181C23C22×#15711yescharacteristic
182C2×C4—24no—
183C2×C4—92no—
184C2×C4—94no—
185C2×C4—94no—
186C2×C4—98no—
187C2×C4—92no—
188C2×C4—94no—
189C2×C4—91no—
190C2×C4—91no—
191C2×C4—92no—
192C2×C4—94no—
193C2×C4—184no—
194C2×C4C22×#15714yes—
195C8—184no—
196C8—182no—
197C8—182no—
198C2×C3—22no—
199C2×C3—24no—
200C2×C3—28no—
201C2×C3—48no—
202C22—24no—
203C22—28no—
204C22C2×C4⋊#15714yes—
205C22C2×C4⋊#15712yes—
206C22#6428714yes—
207C22C23×#15711yescharacteristic
208C4—24no—
209C4—91no—
210C4—92no—
211C4—94no—
212C4—91no—
213C4—184no—
214C3—22no—
215C2—24no—
216C2#1059374314yesdirect product factor
217C2C22×C4⋊#15711yescharacteristic
218C2C2×#6428712yes—
subgroupG/H
centerC23C22×#157
commutatorC22×C32C23×C4
FrattiniC22C23×#157
FittingC2×C32×C22⋊C4C4
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC2×C3⋊Dic3C24
hypercenterC2×C22⋊C4#157
hypocenterC32C2×#424
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#63779C2semidirect
5. C2×C4⋊#622C2semidirect
6. #10593743C2direct (N × H)
21. #63779C22semidirect
22. C4⋊#622C22semidirect
140. C2×C32#424semidirect
177. C32C2×#424semidirect
216. C2#10593743direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37922
C23×#6222
C2×#640862
C2×#637792
C2×C4⋊#6222
#105937432
C2×#4249