Finite Group Databasebeta

← C3×#67782 #11772896

Subgroups — C3×#67782 #11772896

Order 1152.

216 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C32×#488C211yesmaximal, characteristic
2C3×#4542C211yesmaximal, characteristic
3C3×#4541C211yesmaximal, characteristic
4C3×#1414—31nomaximal
5#67782C311yesmaximal, characteristic, direct product factor
6C32×#125C411yescharacteristic, complemented
7C32×#124C2211yescharacteristic
8C32×#103—21no—
9C32×#102—21no—
10C32×C4×C8C411yescharacteristic, complemented
11C3×#836—21no—
12C3×#834—21no—
13C3×#488—21no—
14C3×#488D311yescharacteristic
15C3×#488C2×C311yescharacteristic
16C3×#355—31no—
17C3×#354—31no—
18#4542C2×C311yescharacteristic
19#4541C2×C311yescharacteristic
20C2×C32×Q8D411yescharacteristic
21C2×C32×D4D411yescharacteristic
22C2×C32×C8—21no—
23C32×C4⋊C4—21no—
24C32×C4⋊C4—41no—
25C32×C22⋊C4—41no—
26C32×C42C2×C411yescharacteristic
27C3×#217—41no—
28C3×#208—41no—
29#1414—31noSylow
30C3×#125—21no—
31C3×#125Dic311yescharacteristic, complemented
32C3×#125C3×C411yescharacteristic, complemented
33C3×#124—21no—
34C3×#124C2×D311yescharacteristic
35C3×#124C22×C311yescharacteristic
36C3×#103—22no—
37C3×#103—21no—
38C3×#103—21no—
39C3×#102—22no—
40C3×#102—21no—
41C3×#102—21no—
42C3×#101—61no—
43C3×#99—61no—
44C3×C4×C8—21no—
45C3×C4×C8Dic311yescharacteristic, complemented
46C3×C4×C8C3×C411yescharacteristic, complemented
47#836—21no—
48#834—21no—
49C23×C32—21no—
50C32×Q8—41no—
51C32×D4—41no—
52C2×C32×C4—21no—
53C2×C32×C4—21no—
54C2×C32×C4—41no—
55C2×C32×C4C22⋊C411yescharacteristic
56C2×C3×Dic3—81no—
57C32×C8—41no—
58C3×C3⋊C8—81no—
59#488C3×D311yescharacteristic
60#355—31no—
61#354—31no—
62C2×C3×Q8—21no—
63C2×C3×Q8#6711yescharacteristic
64C2×C3×Q8C3×D411yescharacteristic
65C2×C3×D4—21no—
66C2×C3×D4#6711yescharacteristic
67C2×C3×D4C3×D411yescharacteristic
68C3×M16—121no—
69C2×C3×C8—22no—
70C2×C3×C8—21no—
71C2×C3×C8—21no—
72C3×C4⋊C4—22no—
73C3×C4⋊C4—21no—
74C3×C4⋊C4—21no—
75C3×C4⋊C4—41no—
76C3×C4⋊C4—41no—
77C3×C4⋊C4—42no—
78C3×C22⋊C4—41no—
79C3×C22⋊C4—41no—
80C3×C22⋊C4—42no—
81C3×C22⋊C4—121no—
82C3×C42—21no—
83C3×C42C2×Dic311yescharacteristic
84C3×C42C2×C3×C411yescharacteristic
85#217—41no—
86#208—41no—
87C22×C32—41no—
88C22×C32—81no—
89C22×C32#9911yescharacteristic
90C32×C4—21no—
91C32×C4—41no—
92C32×C4—41no—
93C32×C4—81no—
94C3×Dic3—161no—
95#125C3×Dic311yescharacteristic, complemented
96#124C2×C3×D311yescharacteristic
97#103—21no—
98#102—21no—
99#101—61no—
100#99—61no—
101C4×C8C3×Dic311yescharacteristic, complemented
102C23×C3—21no—
103C23×C3—21no—
104C23×C3—41no—
105C3×Q8—41no—
106C3×Q8—41no—
107C3×Q8—42no—
108C3×D4—41no—
109C3×D4—41no—
110C3×D4—42no—
111C2×C3×C4—22no—
112C2×C3×C4—21no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—21no—
117C2×C3×C4—41no—
118C2×C3×C4—42no—
119C2×C3×C4—41no—
120C2×C3×C4—41no—
121C2×C3×C4—241no—
122C2×C3×C4#21711yescharacteristic
123C2×C3×C4C3×C22⋊C411yescharacteristic
124C2×Dic3—81no—
125C3×C8—42no—
126C3×C8—41no—
127C3×C8—41no—
128C3×C8—241no—
129C3⋊C8—81no—
130C2×C32—21no—
131C2×C32—81no—
132C2×C32#35411yescharacteristic
133C2×Q8C3×#6711yescharacteristic
134C2×D4C3×#6711yescharacteristic
135M16—121no—
136C2×C8—21no—
137C4⋊C4—21no—
138C4⋊C4—41no—
139C22⋊C4—41no—
140C22⋊C4—121no—
141C42C2×C3×Dic311yescharacteristic
142C22×C3—21no—
143C22×C3—41no—
144C22×C3—41no—
145C22×C3—81no—
146C22×C3—81no—
147C22×C3—81no—
148C22×C3—82no—
149C22×C3#83411yescharacteristic
150C22×C3C3×#9911yescharacteristic
151C3×C4—22no—
152C3×C4—21no—
153C3×C4—21no—
154C3×C4—42no—
155C3×C4—41no—
156C3×C4—41no—
157C3×C4—41no—
158C3×C4—41no—
159C3×C4—81no—
160C3×C4—82no—
161C3×C4—81no—
162C3×C4—81no—
163C3×C4—481no—
164Dic3—161no—
165C32#141411yescharacteristic, complemented, Sylow
166C23—21no—
167Q8—41no—
168D4—41no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—241no—
173C2×C4C3×#21711yescharacteristic
174C8—41no—
175C8—241no—
176C2×C3—22no—
177C2×C3—21no—
178C2×C3—21no—
179C2×C3—21no—
180C2×C3—81no—
181C2×C3—81no—
182C2×C3—161no—
183C2×C3#454111yescharacteristic
184C2×C3C3×#35411yescharacteristic
185C22—41no—
186C22—81no—
187C22C3×#83411yescharacteristic
188C4—21no—
189C4—41no—
190C4—41no—
191C4—81no—
192C4—481no—
193C3—21no—
194C3#6778211yescharacteristic, direct product factor
195C3C3×#141411yescharacteristic, complemented
196C2—21no—
197C2—81no—
198C2C3×#454111yescharacteristic
subgroupG/H
centerC2×C3#4541
commutatorC3×C42C2×C3×C4
Frattini#124C2×C3×D3
FittingC32×#488C2
socleC2×C32#354
prime radicalC2×C32×D4D4
cosocleC3×#124C22×C3
hypercenterC3×#488D3
hypocenterC3C3×#1414
LCSG ▷ C3×C42 ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#124 ◁ C3×#488

Complements

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

NH ≅ G/Ntype
5. #67782C3direct (N × H)
6. C32×#125C4semidirect
10. C32×C4×C8C4semidirect
31. C3×#125Dic3semidirect
32. C3×#125C3×C4semidirect
45. C3×C4×C8Dic3semidirect
46. C3×C4×C8C3×C4semidirect
95. #125C3×Dic3semidirect
101. C4×C8C3×Dic3semidirect
165. C32#1414semidirect
194. C3#67782direct (N × H)
195. C3C3×#1414semidirect

Maximal subgroups

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

subgroupindex
C32×#4882
C3×#45422
C3×#45412
C3×#14143
#677823