Finite Group Databasebeta

← #74356⋊C3 #11921156

Subgroups — #74356⋊C3 #11921156

Order 1152.

285 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 285 conjugacy classes of subgroups — too many to draw. Only its 32 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
1C3×#384⋊C3C211yesmaximal, characteristic
2Dic3×C42⋊C3C211yesmaximal, characteristic
3C3⋊(#384⋊C3)C211yesmaximal, characteristic
4#74356C311yesmaximal, characteristic, complemented
5#2868⋊C3—31nomaximal
6A4×Dic6—41nomaximal
7C2×C3×C42⋊C3C2211yescharacteristic
8C2×#888—31no—
9C2×#888—31no—
10C3×#384C2×C311yescharacteristic
11#4975—31no—
12#4975—31no—
13#4935C2×C311yescharacteristic
14C42×Dic3C2×C311yescharacteristic
15#384⋊C3—21no—
16#384⋊C3—31no—
17#384⋊C3D311yescharacteristic
18C4×C42⋊C3—31no—
19C3×C4×A4—41no—
20Dic3×A4—41no—
21Dic3×A4—41no—
22C3×C42⋊C3Q811yescharacteristic, complemented
23#2868—31noSylow
24C22×Dic6—31no—
25C22×Dic6A411yescharacteristic
26Q8×A4—121no—
27C2×C3×C4⋊C4—31no—
28C2×C3×C4⋊C4—31no—
29C2×C3×C42C22×C311yescharacteristic
30C2×C4⋊Dic3—31no—
31C2×C4⋊Dic3—31no—
32C2×Dic3⋊C4—32no—
33C2×Dic3⋊C4—31no—
34C2×Dic3⋊C4—31no—
35C2×C4×Dic3—31no—
36C2×C4×Dic3—31no—
37#888—62no—
38#888—62no—
39#888—62no—
40#888—62no—
41C2×C42⋊C3—21no—
42C2×C42⋊C3C2×D311yescharacteristic
43C2×C3×A4—41no—
44C3×Dic6—161no—
45C2×C4⋊Q8—91no—
46C2×C4⋊Q8—91no—
47#384—31no—
48#384—91no—
49#384—91no—
50#384C3×D311yescharacteristic
51C43—31no—
52C22×C3×C4—31no—
53C22×C3×C4—31no—
54C22×C3×C4C2×A411yescharacteristic
55C22×Dic3—31no—
56C22×Dic3—31no—
57C22×Dic3C2×A411yescharacteristic
58C22×Dic3C2×A411yescharacteristic
59C2×Dic6—61no—
60C2×Dic6—62no—
61C2×Dic6—61no—
62C2×Dic6—61no—
63C2×Dic6—62no—
64C2×Dic6—61no—
65C4×A4—41no—
66C4×A4—81no—
67C4×A4—121no—
68C4×A4—121no—
69C3×C4⋊C4—62no—
70C3×C4⋊C4—62no—
71C3×C42—31no—
72C3×C42C3×Q811yescharacteristic, complemented
73C4⋊Dic3—62no—
74C4⋊Dic3—62no—
75Dic3⋊C4—62no—
76Dic3⋊C4—62no—
77Dic3⋊C4—64no—
78C4×Dic3—32no—
79C4×Dic3—32no—
80C4×Dic3—34no—
81C42⋊C3—21no—
82C42⋊C3Dic611yescharacteristic, complemented
83C3×A4—41no—
84C32×C4—161no—
85C3×Dic3—161no—
86C3×Dic3—161no—
87C22×Q8—31no—
88C22×Q8—91no—
89C4⋊Q8—182no—
90C4⋊Q8—182no—
91C4⋊Q8—182no—
92C4⋊Q8—182no—
93C2×C4⋊C4—31no—
94C2×C4⋊C4—31no—
95C2×C4⋊C4—91no—
96C2×C4⋊C4—91no—
97C2×C4⋊C4—91no—
98C2×C4⋊C4—92no—
99C2×C4⋊C4—91no—
100C2×C42—91no—
101C2×C42—91no—
102C2×C42C2×C3×D311yescharacteristic
103C23×C3C22×A411yescharacteristic
104C2×A4—41no—
105C2×A4—81no—
106C3×Q8—481no—
107C2×C3×C4—32no—
108C2×C3×C4—32no—
109C2×C3×C4—31no—
110C2×C3×C4—31no—
111C2×C3×C4—61no—
112C2×C3×C4—61no—
113C2×C3×C4—62no—
114C2×Dic3—32no—
115C2×Dic3—34no—
116C2×Dic3—31no—
117C2×Dic3—31no—
118C2×Dic3—61no—
119C2×Dic3—61no—
120C2×Dic3—62no—
121Dic6—41no—
122Dic6—121no—
123Dic6—121no—
124Dic6—122no—
125Dic6—121no—
126C2×C32—161no—
127C2×Q8—181no—
128C2×Q8—181no—
129C2×Q8—181no—
130C2×Q8—182no—
131C2×Q8—181no—
132C2×Q8—182no—
133C22×C4—31no—
134C22×C4—31no—
135C22×C4—31no—
136C22×C4—31no—
137C22×C4—91no—
138C22×C4—91no—
139C22×C4D3×A411yescharacteristic
140C4⋊C4—62no—
141C4⋊C4—62no—
142C4⋊C4—182no—
143C4⋊C4—182no—
144C4⋊C4—182no—
145C4⋊C4—182no—
146C4⋊C4—184no—
147C42—31no—
148C42—92no—
149C42—92no—
150C42—94no—
151C42C3×Dic611yescharacteristic, complemented
152C22×C3—31no—
153C22×C3—31no—
154C22×C3Q8×A411yescharacteristic
155A4—41no—
156A4—81no—
157C3×C4—32no—
158C3×C4—32no—
159C3×C4—41no—
160C3×C4—121no—
161C3×C4—161no—
162C3×C4—321no—
163C3×C4—481no—
164C3×C4—481no—
165Dic3—34no—
166Dic3—31no—
167Dic3—41no—
168Dic3—121no—
169Dic3#127⋊C311yescharacteristic
170C32—161noSylow
171C23C2×D3×A411yescharacteristic
172Q8—121no—
173Q8—361no—
174Q8—361no—
175Q8—361no—
176Q8—362no—
177C2×C4—32no—
178C2×C4—32no—
179C2×C4—31no—
180C2×C4—31no—
181C2×C4—61no—
182C2×C4—61no—
183C2×C4—62no—
184C2×C4—91no—
185C2×C4—92no—
186C2×C4—94no—
187C2×C4—91no—
188C2×C4—181no—
189C2×C4—181no—
190C2×C4—182no—
191C2×C3—31no—
192C2×C3—31no—
193C2×C3—161no—
194C2×C3—321no—
195C2×C3C2×#127⋊C311yescharacteristic
196C22—31no—
197C22—31no—
198C22A4×Dic611yescharacteristic
199C4—32no—
200C4—32no—
201C4—31no—
202C4—41no—
203C4—94no—
204C4—91no—
205C4—121no—
206C4—121no—
207C4—361no—
208C3—161no—
209C3—321no—
210C3#2868⋊C311yescharacteristic, complemented
211C2—31no—
212C2—31no—
213C2D3×#127⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#127⋊C3
commutator, cosocleC2×C3×C42C22×C3
FrattiniC23C2×D3×A4
FittingC3×#384C2×C3
socleC23×C3C22×A4
prime radicalC2×C3×C42⋊C3C22
hypocenterC3×C42C3×Q8
LCSG ▷ C2×C3×C42 ▷ C3×C42
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
4. #74356C3semidirect
22. C3×C42⋊C3Q8semidirect
72. C3×C42C3×Q8semidirect
82. C42⋊C3Dic6semidirect
151. C42C3×Dic6semidirect
210. C3#2868⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×#384⋊C32
Dic3×C42⋊C32
C3⋊(#384⋊C3)2
#743563
#2868⋊C33
A4×Dic64