Finite Group Databasebeta

← C2×C4×#3776 #11859957

Subgroups — C2×C4×#3776 #11859957

Order 1152.

786 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 183 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×#3776C211yesmaximal, characteristic
2C2×C4×#627C212yesmaximal
3C2×C4×#622C211yesmaximal, characteristic
4C2×#63743C211yesmaximal, characteristic
5C2×#63740C212yesmaximal
6C4×#3776C218yesmaximal, direct product factor
7C22×#627C2212yes—
8C22×#622C2211yescharacteristic
9C22×#622C2211yescharacteristic
10C2×#3776C418yesdirect product factor
11C2×#3776C2214yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C3×C4×Dic3—22no—
14C2×#3724C2212yes—
15C2×Dic3⋊Dic3—22no—
16C4×#627—24no—
17C4×#627C2218yes—
18C4×#622C2214yes—
19#63743C2214yes—
20#63740C2218yes—
21C2×C4×Dic6—62no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3D411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C22×C3×Dic3—22no—
26C22×C3×Dic3—22no—
27C2×#627—22no—
28C2×#627—24no—
29C2×#627C2×C418yes—
30C2×#627C2314yes—
31C2×#622—22no—
32C2×#622C2×C414yes—
33C2×#622C2312yes—
34C2×#622C2312yes—
35#3776C2×C4116yesdirect product factor
36C4×C3⋊Dic3D412yes—
37C4×C3⋊Dic3C2312yes—
38C3×C4×Dic3—28no—
39#3724—22no—
40#3724C2314yes—
41Dic3⋊Dic3—28no—
42C2×C4×Q16—91nomaximal, Sylow
43C22×Dic6—62no—
44C2×C3×C42—62no—
45C2×C4⋊Dic3—62no—
46C2×Dic3⋊C4—62no—
47C2×Dic3⋊C4—62no—
48C2×C4×Dic3—22no—
49C2×C4×Dic3—62no—
50C4×Dic6—68no—
51C4×Dic6—68no—
52C23×C32C2×D411yescharacteristic
53C2×C32×C4Q1614yescomplemented
54C2×C32×C4C2×D412yes—
55C2×C3⋊Dic3—22no—
56C2×C3⋊Dic3C22×C412yes—
57C2×C3⋊Dic3C2×D412yes—
58C2×C3⋊Dic3C2×D411yescharacteristic
59C2×C3⋊Dic3#4112yes—
60C2×C3⋊Dic3C2411yescharacteristic
61C2×C3×Dic3—28no—
62C2×C3×Dic3—24no—
63C2×C3×Dic3—24no—
64C2×C3×Dic3—44no—
65#627—28no—
66#627—24no—
67#627C22×C418yes—
68#622—22no—
69#622C22×C414yes—
70C22×Q16—91no—
71C2×C4×Q8—92no—
72C4×Q16—98no—
73C2×#107—91no—
74C2×#103—92no—
75C2×C4×C8—91no—
76C22×C3×C4—22no—
77C22×C3×C4—62no—
78C22×C3×C4—62no—
79C22×Dic3—22no—
80C22×Dic3—22no—
81C22×Dic3—62no—
82C22×Dic3—62no—
83C2×Dic6—64no—
84C2×Dic6—68no—
85C2×Dic6—64no—
86C2×Dic6—68no—
87C3×C42—68no—
88C4⋊Dic3—68no—
89Dic3⋊C4—64no—
90Dic3⋊C4—68no—
91Dic3⋊C4—64no—
92C4×Dic3—28no—
93C4×Dic3—64no—
94C4×Dic3—64no—
95C22×C32C4×D412yes—
96C22×C32C2×Q1612yes—
97C22×C32#13512yes—
98C22×C32C22×D411yescharacteristic
99C32×C4C2×Q1614yescomplemented
100C3⋊Dic3—22no—
101C3⋊Dic3C4×D412yes—
102C3⋊Dic3C23×C411yescharacteristic
103C3⋊Dic3C2×#4111yescharacteristic
104C3×Dic3—28no—
105C3×Dic3—44no—
106C22×Q8—92no—
107C2×Q16—94no—
108C2×Q16—98no—
109C22×C8—91no—
110C22×C8—91no—
111C4×Q8—98no—
112C4×Q8—184no—
113C2×C4⋊C4—92no—
114C2×C4⋊C4—182no—
115C2×C42—62no—
116C2×C42—91no—
117#107—94no—
118#103—98no—
119C4×C8—94no—
120C23×C3—22no—
121C2×C3×C4—24no—
122C2×C3×C4—28no—
123C2×C3×C4—64no—
124C2×C3×C4—68no—
125C2×C3×C4—64no—
126C2×C3×C4—124no—
127C2×Dic3—24no—
128C2×Dic3—28no—
129C2×Dic3—24no—
130C2×Dic3—44no—
131C2×Dic3—64no—
132C2×Dic3—62no—
133C2×Dic3—64no—
134C2×Dic3—62no—
135C2×Dic3—64no—
136C2×Dic3—124no—
137Dic6—68no—
138Dic6—616no—
139Dic6—68no—
140C2×C32C4×Q1614yescomplemented
141C2×C32C2×C4×D411yescharacteristic
142C2×C32C22×Q1611yescharacteristic
143C2×C32C2×#13511yescharacteristic
144C2×Q8—94no—
145C2×Q8—98no—
146C2×Q8—182no—
147C2×Q8—184no—
148C22×C4—62no—
149C22×C4—62no—
150C22×C4—91no—
151C22×C4—91no—
152C22×C4GO+(4,𝔽2)11yescharacteristic
153Q16—916no—
154C2×C8—92no—
155C2×C8—94no—
156C2×C8—92no—
157C2×C8—182no—
158C4⋊C4—94no—
159C4⋊C4—182no—
160C4⋊C4—188no—
161C42—68no—
162C42—92no—
163C42—92no—
164C22×C3—22no—
165C22×C3—24no—
166C22×C3—24no—
167C22×C3—24no—
168C3×C4—28no—
169C3×C4—68no—
170C3×C4—124no—
171Dic3—28no—
172Dic3—44no—
173Dic3—64no—
174Dic3—62no—
175Dic3—62no—
176Dic3—124no—
177C32C2×C4×Q1611yescharacteristic, complemented, Sylow
178C23C2×GO+(4,𝔽2)11yescharacteristic
179Q8—98no—
180Q8—184no—
181Q8—188no—
182C2×C4—64no—
183C2×C4—68no—
184C2×C4—64no—
185C2×C4—91no—
186C2×C4—91no—
187C2×C4—92no—
188C2×C4—92no—
189C2×C4—92no—
190C2×C4—124no—
191C2×C4—182no—
192C2×C4#377614yesdirect product factor
193C2×C4C2×GO+(4,𝔽2)12yes—
194C8—94no—
195C8—182no—
196C2×C3—22no—
197C2×C3—22no—
198C2×C3—28no—
199C2×C3—22no—
200C22#6422312yes—
201C22C4×GO+(4,𝔽2)12yes—
202C22C2×#377612yes—
203C22C22×GO+(4,𝔽2)11yescharacteristic
204C4—68no—
205C4—91no—
206C4—91no—
207C4—92no—
208C4—124no—
209C4—182no—
210C4C2×#377614yesdirect product factor
211C3—22no—
212C2C4×#377614yesdirect product factor
213C2C2×#6422311yescharacteristic
214C2C2×C4×GO+(4,𝔽2)11yescharacteristic
215C2C22×#377611yescharacteristic
subgroupG/H
center, hypercenterC22×C4GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC2×C3⋊Dic3C24
hypocenterC32C2×C4×Q16
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. C4×#3776C2direct (N × H)
10. C2×#3776C4direct (N × H)
35. #3776C2×C4direct (N × H)
53. C2×C32×C4Q16semidirect
99. C32×C4C2×Q16semidirect
140. C2×C32C4×Q16semidirect
177. C32C2×C4×Q16semidirect
192. C2×C4#3776direct (N × H)
210. C4C2×#3776direct (N × H)
212. C2C4×#3776direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37762
C2×C4×#6272
C2×C4×#6222
C2×#637432
C2×#637402
C4×#37762
C2×C4×Q169