Finite Group Databasebeta

← C2×#63944 #10595329

Subgroups — C2×#63944 #10595329

Order 576.

594 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 144 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×Q8×C3⋊D3C211yesmaximal, characteristic
2C2×#3797C211yesmaximal, characteristic
3C2×C3×#216C212yesmaximal, complemented
4#63944C218yesmaximal, direct product factor
5C2×#3719C212yesmaximal, complemented
6C2×#3710C211yesmaximal, characteristic
7C2×D3×Q16—32nomaximal
8C2×C32×Q8C2211yescharacteristic
9Q8×C3⋊D3—22no—
10Q8×C3⋊D3C2214yes—
11C2×C4×C3⋊D3—21no—
12C2×C4×C3⋊D3C2211yescharacteristic
13C2×#634—21no—
14C2×#634C2211yescharacteristic
15C2×C3×Dic6C2212yes—
16C2×#627—21no—
17C2×#624—21no—
18#3797—22no—
19#3797C2214yes—
20C3×#216C2218yescomplemented
21C2×C3×C3⋊C8C2212yes—
22#3719C2218yescomplemented
23#3710C2214yes—
24C2×D3×Q8—32no—
25C2×D3×Q8—32no—
26C2×D3×Q8—61no—
27C2×C3×Q16—32no—
28C2×#216—32no—
29C2×#216D312yescomplemented
30D3×Q16—316no—
31C2×Dic12—32no—
32C2×D3×C8—32no—
33C22×C3⋊D3D411yescharacteristic
34C32×Q8—21no—
35C32×Q8C2312yes—
36C2×C32×C4—21no—
37C2×C32×C4C2311yescharacteristic
38C2×C3⋊Dic3—21no—
39C2×C3⋊Dic3D411yescharacteristic
40C4×C3⋊D3—24no—
41C4×C3⋊D3D412yes—
42C4×C3⋊D3C2312yes—
43#634—21no—
44#634—24no—
45#634C2312yes—
46C2×C3×Dic3—22no—
47C3×Dic6—22no—
48C3×Dic6C2314yes—
49#627—24no—
50#624—24no—
51C3×C3⋊C8C2314yes—
52C22×Q16—91noSylow
53C2×C3×Q8—21no—
54C2×C3×Q8—32no—
55C2×C3×Q8C2×D312yes—
56D3×Q8—38no—
57D3×Q8—38no—
58D3×Q8—64no—
59D3×Q8—64no—
60D3×Q8—64no—
61D3×Q8—64no—
62C2×C4×D3—32no—
63C2×C4×D3—61no—
64C2×C4×D3—62no—
65C2×C4×D3—62no—
66C2×C4×D3—62no—
67C2×Dic6—32no—
68C2×Dic6—61no—
69C2×Dic6—62no—
70C2×Dic6—62no—
71C2×Dic6—62no—
72C2×Dic6C2×D312yes—
73C3×Q16—38no—
74C2×C3×C8—32no—
75#216—38no—
76#216C2×D318yescomplemented
77C2×C3⋊C8C2×D312yes—
78Dic12—38no—
79D3×C8—38no—
80C22×C32C2×D411yescharacteristic
81C2×C3⋊D3Q1614yescomplemented
82C2×C3⋊D3C2×D412yes—
83C32×C4—22no—
84C32×C4C2×D411yescharacteristic
85C32×C4C2411yescharacteristic
86C3⋊Dic3—22no—
87C3⋊Dic3C2×D412yes—
88C3×Dic3—24no—
89C22×Q8—91no—
90C22×Q8—91no—
91C2×Q16—32no—
92C2×Q16—92no—
93C2×Q16—98no—
94C22×C8—91no—
95C22×D3—32no—
96C22×D3—61no—
97C3×Q8—22no—
98C3×Q8—22no—
99C3×Q8—22no—
100C3×Q8—34no—
101C3×Q8—62no—
102C3×Q8C22×D314yes—
103C2×C3×C4—22no—
104C2×C3×C4—22no—
105C2×C3×C4—21no—
106C2×C3×C4—62no—
107C2×C3×C4C22×D312yes—
108C2×Dic3—22no—
109C2×Dic3—32no—
110C2×Dic3—61no—
111C2×Dic3—62no—
112C2×Dic3—62no—
113C4×D3—34no—
114C4×D3—34no—
115C4×D3—62no—
116C4×D3—62no—
117C4×D3—68no—
118C4×D3—68no—
119C4×D3—68no—
120Dic6—22no—
121Dic6—34no—
122Dic6—62no—
123Dic6—68no—
124Dic6—68no—
125Dic6—68no—
126Dic6—62no—
127Dic6—62no—
128Dic6C22×D314yes—
129C3×C8—34no—
130C3⋊C8C22×D314yes—
131C2×C32C2×Q1612yescomplemented
132C2×C32C22×D411yescharacteristic
133C3⋊D3C2×Q1614yescomplemented
134C2×Q8—32no—
135C2×Q8—94no—
136C2×Q8—94no—
137C2×Q8—91no—
138C2×Q8—181no—
139C2×Q8—181no—
140C2×Q8—182no—
141C2×Q8—182no—
142C2×Q8D3211yescharacteristic
143C22×C4—91no—
144C22×C4—181no—
145C22×C4—181no—
146Q16—38no—
147Q16—98no—
148C2×C8—32no—
149C2×C8—94no—
150C22×C3—21no—
151C22×C3D3×D412yes—
152C2×D3—38no—
153C2×D3—34no—
154C2×D3—62no—
155C2×D3—64no—
156C3×C4—24no—
157C3×C4—24no—
158C3×C4—21no—
159C3×C4—21no—
160C3×C4—64no—
161C3×C4D3×D412yes—
162C3×C4C23×D312yes—
163Dic3—24no—
164Dic3—34no—
165Dic3—62no—
166Dic3—64no—
167Dic3—64no—
168C32C22×Q1611yescharacteristic, complemented, Sylow
169C23—91no—
170Q8—21no—
171Q8—34no—
172Q8—62no—
173Q8—92no—
174Q8—184no—
175Q8—184no—
176Q8—181no—
177Q8C2×D3212yes—
178C2×C4—21no—
179C2×C4—62no—
180C2×C4—91no—
181C2×C4—92no—
182C2×C4—92no—
183C2×C4—184no—
184C2×C4—184no—
185C2×C4—181no—
186C2×C4C2×D3211yescharacteristic
187C8—34no—
188C2×C3—21no—
189C2×C3—22no—
190C2×C3D3×Q1614yescomplemented
191C2×C3C2×D3×D412yes—
192D3—38no—
193D3—64no—
194C22—92no—
195C22—94no—
196C22#381111yescharacteristic
197C4—22no—
198C4—64no—
199C4—92no—
200C4—182no—
201C4#381111yescharacteristic
202C4C22×D3211yescharacteristic
203C3—21no—
204C3C2×D3×Q1612yescomplemented
205C2—94no—
206C2#6394412yesdirect product factor
207C2C2×#381111yescharacteristic
subgroupG/H
centerC22#3811
commutator, cosocleC32×C4C24
FrattiniC4C22×D32
FittingC2×C32×Q8C22
socleC22×C32C2×D4
prime radicalC22×C3⋊D3D4
hypercenterC2×Q8D32
hypocenterC32C22×Q16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
3. C2×C3×#216C2semidirect
4. #63944C2direct (N × H)
5. C2×#3719C2semidirect
20. C3×#216C22semidirect
22. #3719C22semidirect
29. C2×#216D3semidirect
76. #216C2×D3semidirect
81. C2×C3⋊D3Q16semidirect
131. C2×C32C2×Q16semidirect
133. C3⋊D3C2×Q16semidirect
168. C32C22×Q16semidirect
190. C2×C3D3×Q16semidirect
204. C3C2×D3×Q16semidirect
206. C2#63944direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊D32
C2×#37972
C2×C3×#2162
#639442
C2×#37192
C2×#37102
C2×D3×Q163