Finite Group Databasebeta

← C3×#29659 #10648266

Subgroups — C3×#29659 #10648266

Order 768.

974 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 974 conjugacy classes of subgroups — too many to draw. Only its 238 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×#3458C211yesmaximal, characteristic
2C3×#2484C213yesmaximal
3C3×#2062C214yesmaximal
4C3×#2030C214yesmaximal
5C3×#1820C213yesmaximal
6#29659C311yesmaximal, characteristic, direct product factor, Sylow
7C3×#544—23no—
8C3×#544—23no—
9C3×#543C2214yes—
10C3×#533—26no—
11C2×C3×#117C2213yes—
12C22×C3×C4⋊C4C2211yescharacteristic
13C3×#400—23no—
14C3×#398—23no—
15C3×#387—26no—
16C3×#385C2216yes—
17C3×#381C2216yes—
18C3×#381C2213yes—
19C3×#342C22112yes—
20#3458C2×C311yescharacteristic
21#2484C2×C313yes—
22#2062C2×C314yes—
23#2030C2×C314yes—
24#1820C2×C313yes—
25C23×C3×C4C2311yescharacteristic
26C23×C3×C4C2311yescharacteristic
27C23×C3×C4C2311yescharacteristic
28C3×C4⋊Q8—26no—
29C3×C4⋊Q8—26no—
30C3×#125—212no—
31C3×C22⋊Q8—212no—
32C3×C22⋊Q8—212no—
33C3×C4×Q8—24no—
34C3×C4×Q8—24no—
35C3×#117—26no—
36C3×#117—26no—
37C2×C3×C4⋊C4—26no—
38C2×C3×C4⋊C4—23no—
39C2×C3×C4⋊C4—23no—
40C2×C3×C4⋊C4D413yes—
41C2×C3×C4⋊C4D413yes—
42C2×C3×C22⋊C4C2316yes—
43C2×C3×C22⋊C4C2316yes—
44C2×C3×C42D416yes—
45C3×#95—23no—
46C3×#95—26no—
47C3×#95—26no—
48C3×#95—23no—
49C3×#95—26no—
50#544—23no—
51#544—23no—
52#543C22×C314yes—
53#533—26no—
54C2×#117C22×C313yes—
55C22×C4⋊C4C22×C311yescharacteristic
56#400—23no—
57#398—23no—
58#387—26no—
59#385C22×C316yes—
60#381C22×C313yes—
61#381C22×C316yes—
62#342C22×C3112yes—
63C24×C3C2411yescharacteristic
64C2×C3×Q8—24no—
65C2×C3×Q8—24no—
66C22×C3×C4—24no—
67C22×C3×C4—23no—
68C22×C3×C4—26no—
69C22×C3×C4—23no—
70C22×C3×C4—24no—
71C22×C3×C4—42no—
72C22×C3×C4C2×D413yes—
73C22×C3×C4C2×D413yes—
74C22×C3×C4C2×D416yes—
75C22×C3×C4C2×D416yes—
76C3×C4⋊C4—212no—
77C3×C4⋊C4—212no—
78C3×C4⋊C4—26no—
79C3×C4⋊C4—26no—
80C3×C4⋊C4—412no—
81C3×C4⋊C4—41no—
82C3×C4⋊C4—43no—
83C3×C22⋊C4—212no—
84C3×C22⋊C4—212no—
85C3×C42—26no—
86C3×C42—26no—
87C23×C4C23×C311yescharacteristic
88C23×C4C23×C311yescharacteristic
89C23×C4C23×C311yescharacteristic
90C4⋊Q8—26no—
91C4⋊Q8—26no—
92#125—212no—
93C22⋊Q8—212no—
94C22⋊Q8—212no—
95C4×Q8—24no—
96C4×Q8—24no—
97#117—26no—
98#117—26no—
99C2×C4⋊C4—23no—
100C2×C4⋊C4—23no—
101C2×C4⋊C4—26no—
102C2×C4⋊C4C3×D413yes—
103C2×C4⋊C4C3×D413yes—
104C2×C22⋊C4C23×C316yes—
105C2×C22⋊C4C23×C316yes—
106C2×C42C3×D416yes—
107#95—23no—
108#95—26no—
109#95—26no—
110#95—23no—
111#95—26no—
112C23×C3—41no—
113C23×C3—41no—
114C23×C3C22×D413yes—
115C23×C32−1+414yes—
116C3×Q8—84no—
117C3×Q8—84no—
118C2×C3×C4—26no—
119C2×C3×C4—26no—
120C2×C3×C4—26no—
121C2×C3×C4—26no—
122C2×C3×C4—26no—
123C2×C3×C4—43no—
124C2×C3×C4—41no—
125C2×C3×C4—46no—
126C2×C3×C4—46no—
127C2×C3×C4—46no—
128C2×C3×C4—46no—
129C2×C3×C4—41no—
130C2×C3×C4—46no—
131C2×C3×C4—46no—
132C2×C3×C4#12011yescharacteristic
133C2×C3×C4#12013yes—
134C24C24×C311yescharacteristic
135C2×Q8—24no—
136C2×Q8—24no—
137C22×C4—24no—
138C22×C4—23no—
139C22×C4—26no—
140C22×C4—23no—
141C22×C4—24no—
142C22×C4—42no—
143C22×C4C2×C3×D413yes—
144C22×C4C2×C3×D413yes—
145C22×C4C2×C3×D416yes—
146C22×C4C2×C3×D416yes—
147C4⋊C4—212no—
148C4⋊C4—212no—
149C4⋊C4—26no—
150C4⋊C4—26no—
151C4⋊C4—412no—
152C4⋊C4—41no—
153C4⋊C4—43no—
154C22⋊C4—212no—
155C22⋊C4—212no—
156C42—26no—
157C42—26no—
158C22×C3—23no—
159C22×C3—23no—
160C22×C3—44no—
161C22×C3C2×#12011yescharacteristic
162C22×C3#53616yes—
163C3×C4—21no—
164C3×C4—23no—
165C3×C4—42no—
166C3×C4—46no—
167C3×C4—46no—
168C3×C4—86no—
169C3×C4—81no—
170C23—41no—
171C23—41no—
172C23C22×C3×D413yes—
173C23C3×2−1+414yes—
174Q8—84no—
175Q8—84no—
176C2×C4—26no—
177C2×C4—26no—
178C2×C4—26no—
179C2×C4—26no—
180C2×C4—26no—
181C2×C4—43no—
182C2×C4—41no—
183C2×C4—46no—
184C2×C4—46no—
185C2×C4—46no—
186C2×C4—46no—
187C2×C4—41no—
188C2×C4—46no—
189C2×C4—46no—
190C2×C4C3×#12011yescharacteristic
191C2×C4C3×#12013yes—
192C2×C3—26no—
193C2×C3#261411yescharacteristic
194C2×C3#302511yescharacteristic
195C2×C3#302811yescharacteristic
196C22—23no—
197C22—23no—
198C22—44no—
199C22C2×C3×#12011yescharacteristic
200C22C3×#53616yes—
201C4—21no—
202C4—23no—
203C4—42no—
204C4—46no—
205C4—46no—
206C4—86no—
207C4—81no—
208C3#2965911yescharacteristic, direct product factor, Sylow
209C2—26no—
210C2C3×#261411yescharacteristic
211C2C3×#302511yescharacteristic
212C2C3×#302811yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC24C24×C3
prime radicalC24×C3C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
6. #29659C3direct (N × H)
208. C3#29659direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#34582
C3×#24842
C3×#20622
C3×#20302
C3×#18202
#296593