Finite Group Databasebeta

← C3×#67635 #11771476

Subgroups — C3×#67635 #11771476

Order 1152.

361 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 361 conjugacy classes of subgroups — too many to draw. Only its 82 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×#384C211yesmaximal, characteristic
2C3×#4528C212yesmaximal
3C3×#1325—31nomaximal
4#67635C311yesmaximal, characteristic, direct product factor
5C2×C32×C4⋊C4—22no—
6C2×C32×C4⋊C4C411yescharacteristic
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×C32×C42C411yescharacteristic
9C3×#830—22no—
10C3×#384—21no—
11C3×#384D311yescharacteristic
12C3×#384C2×C311yescharacteristic
13C3×#324—32no—
14#4528C2×C312yes—
15C22×C32×C4—21no—
16C22×C32×C4—21no—
17C22×C32×C4C2×C411yescharacteristic
18C22×C32×C4D412yes—
19C32×C4⋊C4—41no—
20C32×C4⋊C4—44no—
21C32×C4⋊C4—41no—
22C32×C42—21no—
23C32×C42C812yescomplemented
24C2×C3×C3⋊C8—42no—
25#1325—31noSylow
26C2×C3×C4⋊C4—24no—
27C2×C3×C4⋊C4—22no—
28C2×C3×C4⋊C4—22no—
29C2×C3×C4⋊C4—21no—
30C2×C3×C4⋊C4—21no—
31C2×C3×C4⋊C4Dic311yescharacteristic
32C2×C3×C4⋊C4C3×C411yescharacteristic
33C2×C3×C4⋊C4C2×D311yescharacteristic
34C2×C3×C4⋊C4C22×C311yescharacteristic
35C2×C3×C42—21no—
36C2×C3×C42Dic311yescharacteristic
37C2×C3×C42C3×C411yescharacteristic
38C3×C22⋊C8—62no—
39#830—22no—
40C23×C32C22⋊C411yescharacteristic
41C2×C32×C4—22no—
42C2×C32×C4—22no—
43C2×C32×C4—22no—
44C2×C32×C4—21no—
45C2×C32×C4—21no—
46C2×C32×C4—22no—
47C2×C32×C4—42no—
48C2×C32×C4—42no—
49C2×C32×C4—41no—
50C2×C32×C4C2×C811yescharacteristic
51C2×C32×C4M1611yescharacteristic
52C3×C3⋊C8—82no—
53#384C3×D311yescharacteristic
54#324—32no—
55C22×C3×C4—22no—
56C22×C3×C4—21no—
57C22×C3×C4—21no—
58C22×C3×C4—22no—
59C22×C3×C4—21no—
60C22×C3×C4—21no—
61C22×C3×C4—21no—
62C22×C3×C4—22no—
63C22×C3×C4C2×Dic311yescharacteristic
64C22×C3×C4#6712yes—
65C22×C3×C4C2×C3×C411yescharacteristic
66C22×C3×C4C3×D412yes—
67C2×C3×C8—122no—
68C3×C4⋊C4—41no—
69C3×C4⋊C4—41no—
70C3×C4⋊C4—41no—
71C3×C4⋊C4—41no—
72C3×C4⋊C4—42no—
73C3×C4⋊C4—42no—
74C3×C4⋊C4—44no—
75C3×C4⋊C4—44no—
76C3×C4⋊C4—48no—
77C3×C42—22no—
78C3×C42—21no—
79C3×C42—21no—
80C3×C42—22no—
81C3×C42C3⋊C812yescomplemented
82C3×C42C3×C812yescomplemented
83C2×C3⋊C8—42no—
84C22×C32—21no—
85C22×C32—21no—
86C22×C32C22⋊C811yescharacteristic
87C22×C32#9911yescharacteristic
88C22×C32#10111yescharacteristic
89C32×C4—24no—
90C32×C4—21no—
91C32×C4—21no—
92C32×C4—42no—
93C32×C4—81no—
94C2×C4⋊C4—22no—
95C2×C4⋊C4C3×Dic311yescharacteristic
96C2×C4⋊C4C2×C3×D311yescharacteristic
97C2×C42C3×Dic311yescharacteristic
98C22⋊C8—62no—
99C23×C3—21no—
100C23×C3#21711yescharacteristic
101C23×C3C3×C22⋊C411yescharacteristic
102C2×C3×C4—24no—
103C2×C3×C4—24no—
104C2×C3×C4—22no—
105C2×C3×C4—22no—
106C2×C3×C4—22no—
107C2×C3×C4—24no—
108C2×C3×C4—22no—
109C2×C3×C4—22no—
110C2×C3×C4—22no—
111C2×C3×C4—22no—
112C2×C3×C4—21no—
113C2×C3×C4—21no—
114C2×C3×C4—22no—
115C2×C3×C4—21no—
116C2×C3×C4—21no—
117C2×C3×C4—22no—
118C2×C3×C4—22no—
119C2×C3×C4—21no—
120C2×C3×C4—21no—
121C2×C3×C4—42no—
122C2×C3×C4—42no—
123C2×C3×C4—42no—
124C2×C3×C4—44no—
125C2×C3×C4—44no—
126C2×C3×C4—42no—
127C2×C3×C4—42no—
128C2×C3×C4—42no—
129C2×C3×C4—41no—
130C2×C3×C4—41no—
131C2×C3×C4C2×C3⋊C811yescharacteristic
132C2×C3×C4#20811yescharacteristic
133C2×C3×C4C2×C3×C811yescharacteristic
134C2×C3×C4C3×M1611yescharacteristic
135C3×C8—242no—
136C3⋊C8—82no—
137C2×C32—21no—
138C2×C32—21no—
139C2×C32#32411yescharacteristic
140C2×C32#35311yescharacteristic
141C2×C32#35611yescharacteristic
142C22×C4—21no—
143C22×C4—21no—
144C22×C4C2×C3×Dic311yescharacteristic
145C22×C4C3×#6712yes—
146C2×C8—122no—
147C4⋊C4—41no—
148C4⋊C4—41no—
149C4⋊C4—44no—
150C42—21no—
151C42C3×C3⋊C812yescomplemented
152C22×C3—22no—
153C22×C3—22no—
154C22×C3—21no—
155C22×C3—21no—
156C22×C3—21no—
157C22×C3—21no—
158C22×C3—21no—
159C22×C3—21no—
160C22×C3—21no—
161C22×C3#83011yescharacteristic
162C22×C3#83411yescharacteristic
163C22×C3#83611yescharacteristic
164C22×C3C3×C22⋊C811yescharacteristic
165C22×C3C3×#9911yescharacteristic
166C22×C3C3×#10111yescharacteristic
167C3×C4—28no—
168C3×C4—24no—
169C3×C4—24no—
170C3×C4—22no—
171C3×C4—22no—
172C3×C4—21no—
173C3×C4—21no—
174C3×C4—21no—
175C3×C4—21no—
176C3×C4—42no—
177C3×C4—42no—
178C3×C4—82no—
179C3×C4—82no—
180C3×C4—81no—
181C3×C4—81no—
182C32#132511yescharacteristic, complemented, Sylow
183C23C3×#21711yescharacteristic
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—41no—
193C2×C4C2×C3×C3⋊C811yescharacteristic
194C2×C4C3×#20811yescharacteristic
195C8—242no—
196C2×C3—22no—
197C2×C3—22no—
198C2×C3—21no—
199C2×C3—21no—
200C2×C3—21no—
201C2×C3—21no—
202C2×C3—21no—
203C2×C3—21no—
204C2×C3—21no—
205C2×C3#452811yescharacteristic
206C2×C3#454511yescharacteristic
207C2×C3#454811yescharacteristic
208C2×C3C3×#32411yescharacteristic
209C2×C3C3×#35311yescharacteristic
210C2×C3C3×#35611yescharacteristic
211C22—21no—
212C22—21no—
213C22C3×#83011yescharacteristic
214C22C3×#83411yescharacteristic
215C22C3×#83611yescharacteristic
216C4—24no—
217C4—21no—
218C4—21no—
219C4—42no—
220C4—81no—
221C3—21no—
222C3#6763511yescharacteristic, direct product factor
223C3C3×#132511yescharacteristic, complemented
224C2—21no—
225C2—21no—
226C2C3×#452811yescharacteristic
227C2C3×#454511yescharacteristic
228C2C3×#454811yescharacteristic
subgroupG/H
centerC22×C3#834
commutatorC2×C3×C4C2×C3×C8
FrattiniC2×C4⋊C4C2×C3×D3
FittingC32×#384C2
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×C3×C4⋊C4C22×C3
hypercenterC3×#384D3
hypocenterC3C3×#1325
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C4⋊C4 ◁ C3×#384

Complements

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

NH ≅ G/Ntype
4. #67635C3direct (N × H)
23. C32×C42C8semidirect
81. C3×C42C3⋊C8semidirect
82. C3×C42C3×C8semidirect
151. C42C3×C3⋊C8semidirect
182. C32#1325semidirect
222. C3#67635direct (N × H)
223. C3C3×#1325semidirect

Maximal subgroups

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

subgroupindex
C32×#3842
C3×#45282
C3×#13253
#676353