Finite Group Databasebeta

← C3×#67679 #11771033

Subgroups — C3×#67679 #11771033

Order 1152.

469 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 469 conjugacy classes of subgroups — too many to draw. Only its 122 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×C32×C22⋊C8C211yesmaximal, characteristic
2C3×#5207C212yesmaximal
3C3×#1293—31nomaximal
4#67679C311yesmaximal, characteristic, direct product factor
5C23×C32×C4C2211yescharacteristic
6C22×C32×C8C412yes—
7C2×C3×#208—22no—
8C32×C22⋊C8—22no—
9C3×#830—22no—
10C3×#830C414yes—
11C3×#407—32no—
12C2×C3×C22⋊C8—21no—
13C2×C3×C22⋊C8D311yescharacteristic
14C2×C3×C22⋊C8C2×C311yescharacteristic
15#5207C2×C312yes—
16C24×C32Q811yescharacteristic
17C22×C32×C4—42no—
18C22×C32×C4C2×C411yescharacteristic
19C22×C32×C4C2×C412yes—
20C22×C32×C4D412yes—
21C22×C32×C4D411yescharacteristic
22C2×C32×C8—22no—
23C2×C32×C8—42no—
24C3×#208—44no—
25C2×C3×C3⋊C8—24no—
26#1293—31noSylow
27C23×C3×C4—21no—
28C23×C3×C4C2×D311yescharacteristic
29C23×C3×C4C22×C311yescharacteristic
30C2×C3×M16—62no—
31C22×C3×C8—22no—
32C22×C3×C8Dic312yes—
33C22×C3×C8C3×C412yes—
34C2×#208—22no—
35C3×C22⋊C8—24no—
36C3×C22⋊C8—22no—
37C3×C22⋊C8—22no—
38C3×C22⋊C8—34no—
39C3×C22⋊C8—62no—
40#830—22no—
41#830C3×C414yes—
42C23×C32—22no—
43C23×C32—41no—
44C23×C32—41no—
45C23×C32C4⋊C412yes—
46C23×C32C4⋊C411yescharacteristic
47C2×C32×C4—22no—
48C2×C32×C4—24no—
49C2×C32×C4—42no—
50C2×C32×C4—41no—
51C2×C32×C4C4211yescharacteristic
52C2×C32×C4C22⋊C412yes—
53C2×C32×C4C22⋊C411yescharacteristic
54C32×C8—42no—
55C3×C3⋊C8—44no—
56#407—32no—
57C2×C22⋊C8C3×D311yescharacteristic
58C24×C3—21no—
59C24×C3Dic611yescharacteristic
60C24×C3C3×Q811yescharacteristic
61C22×C3×C4—22no—
62C22×C3×C4—21no—
63C22×C3×C4—21no—
64C22×C3×C4—22no—
65C22×C3×C4—42no—
66C22×C3×C4—42no—
67C22×C3×C4—44no—
68C22×C3×C4C4×D312yes—
69C22×C3×C4D1211yescharacteristic
70C22×C3×C4C2×Dic311yescharacteristic
71C22×C3×C4#6712yes—
72C22×C3×C4C2×C3×C412yes—
73C22×C3×C4C2×C3×C411yescharacteristic
74C22×C3×C4C3×D411yescharacteristic
75C22×C3×C4C3×D412yes—
76C3×M16—124no—
77C2×C3×C8—24no—
78C2×C3×C8—22no—
79C2×C3×C8—22no—
80C2×C3×C8—44no—
81C2×C3×C8—42no—
82C2×C3×C8—42no—
83C2×C3×C8—64no—
84#208—44no—
85C2×C3⋊C8—24no—
86C22×C32—21no—
87C22×C32—21no—
88C22×C32—22no—
89C22×C32—22no—
90C22×C32—22no—
91C22×C32—44no—
92C22×C32#9511yescharacteristic
93C22×C32#10812yes—
94C32×C4—21no—
95C32×C4—22no—
96C32×C4#9912yes—
97C23×C4C2×C3×D311yescharacteristic
98C2×M16—62no—
99C22×C8C3×Dic312yes—
100C22⋊C8—22no—
101C22⋊C8—34no—
102C22⋊C8—62no—
103C23×C3—24no—
104C23×C3—22no—
105C23×C3—22no—
106C23×C3—22no—
107C23×C3—21no—
108C23×C3—41no—
109C23×C3—41no—
110C23×C3—41no—
111C23×C3—41no—
112C23×C3—42no—
113C23×C3—42no—
114C23×C3Dic3⋊C412yes—
115C23×C3C4⋊Dic311yescharacteristic
116C23×C3C3×C4⋊C412yes—
117C23×C3C3×C4⋊C411yescharacteristic
118C2×C3×C4—24no—
119C2×C3×C4—22no—
120C2×C3×C4—24no—
121C2×C3×C4—24no—
122C2×C3×C4—22no—
123C2×C3×C4—21no—
124C2×C3×C4—22no—
125C2×C3×C4—21no—
126C2×C3×C4—44no—
127C2×C3×C4—42no—
128C2×C3×C4—41no—
129C2×C3×C4—42no—
130C2×C3×C4—41no—
131C2×C3×C4—44no—
132C2×C3×C4—42no—
133C2×C3×C4C4×Dic311yescharacteristic
134C2×C3×C4(C2×D3)⋊C412yes—
135C2×C3×C4#21711yescharacteristic
136C2×C3×C4C3×C4211yescharacteristic
137C2×C3×C4C3×C22⋊C412yes—
138C2×C3×C4C3×C22⋊C411yescharacteristic
139C3×C8—44no—
140C3×C8—42no—
141C3×C8—42no—
142C3×C8—124no—
143C3⋊C8—44no—
144C2×C32—22no—
145C2×C32—42no—
146C2×C32#33811yescharacteristic
147C2×C32#34111yescharacteristic
148C2×C32#34211yescharacteristic
149C24C3×Dic611yescharacteristic
150C22×C4—42no—
151C22×C4C3×C4×D312yes—
152C22×C4C3×D1211yescharacteristic
153C22×C4C2×C3×Dic311yescharacteristic
154C22×C4C3×#6712yes—
155M16—124no—
156C2×C8—22no—
157C2×C8—42no—
158C2×C8—64no—
159C22×C3—22no—
160C22×C3—22no—
161C22×C3—21no—
162C22×C3—21no—
163C22×C3—21no—
164C22×C3—21no—
165C22×C3—24no—
166C22×C3—22no—
167C22×C3—22no—
168C22×C3—22no—
169C22×C3—22no—
170C22×C3—22no—
171C22×C3—22no—
172C22×C3—22no—
173C22×C3—21no—
174C22×C3—42no—
175C22×C3—42no—
176C22×C3—48no—
177C22×C3—44no—
178C22×C3—44no—
179C22×C3#81912yes—
180C22×C3C3⋊#9511yescharacteristic
181C22×C3C3×#9511yescharacteristic
182C22×C3C3×#10812yes—
183C3×C4—22no—
184C3×C4—22no—
185C3×C4—21no—
186C3×C4—22no—
187C3×C4—21no—
188C3×C4—22no—
189C3×C4—42no—
190C3×C4#83412yes—
191C3×C4C3×#9912yes—
192C32#129311yescharacteristic, complemented, Sylow
193C23—22no—
194C23—41no—
195C23—41no—
196C23C3×Dic3⋊C412yes—
197C23C3×C4⋊Dic311yescharacteristic
198C2×C4—22no—
199C2×C4—24no—
200C2×C4—42no—
201C2×C4—41no—
202C2×C4C3×C4×Dic311yescharacteristic
203C2×C4C3×(C2×D3)⋊C412yes—
204C2×C4C3×#21711yescharacteristic
205C8—42no—
206C8—124no—
207C2×C3—24no—
208C2×C3—22no—
209C2×C3—22no—
210C2×C3—21no—
211C2×C3—21no—
212C2×C3—21no—
213C2×C3—44no—
214C2×C3—42no—
215C2×C3—42no—
216C2×C3#452611yescharacteristic
217C2×C3#455211yescharacteristic
218C2×C3C3⋊#33811yescharacteristic
219C2×C3C3×#33811yescharacteristic
220C2×C3C3×#34111yescharacteristic
221C2×C3C3×#34211yescharacteristic
222C22—21no—
223C22—21no—
224C22—22no—
225C22—22no—
226C22—22no—
227C22—44no—
228C22C3×#81912yes—
229C22C3×C3⋊#9511yescharacteristic
230C4—22no—
231C4—21no—
232C4C3×#83412yes—
233C3—21no—
234C3#6767911yescharacteristic, direct product factor
235C3C3×#129311yescharacteristic, complemented
236C2—22no—
237C2—42no—
238C2C3×#452611yescharacteristic
239C2C3×#455211yescharacteristic
240C2C3×C3⋊#33811yescharacteristic
subgroupG/H
centerC22×C3C3⋊#95
commutatorC2×C3×C4C3×C42
FrattiniC23×C4C2×C3×D3
FittingC2×C32×C22⋊C8C2
socleC22×C32#95
prime radicalC24×C32Q8
cosocleC23×C3×C4C22×C3
hypercenterC2×C3×C22⋊C8D3
hypocenterC3C3×#1293
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C2×C3×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. #67679C3direct (N × H)
192. C32#1293semidirect
234. C3#67679direct (N × H)
235. C3C3×#1293semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊C82
C3×#52072
C3×#12933
#676793