Finite Group Databasebeta

← C3×#67650 #11771835

Subgroups — C3×#67650 #11771835

Order 1152.

323 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 323 conjugacy classes of subgroups — too many to draw. Only its 74 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×#398C211yesmaximal, characteristic
2C3×#4530C211yesmaximal, characteristic
3C3×#4528C211yesmaximal, characteristic
4C3×#1346—31nomaximal
5#67650C311yesmaximal, characteristic, direct product factor
6C2×C32×C4⋊C4—21no—
7C2×C32×C4⋊C4C411yescharacteristic
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×C3×#208—21no—
10C32×#95—21no—
11C32×#95C411yescharacteristic
12C3×#830—21no—
13C3×#398—21no—
14C3×#398D311yescharacteristic
15C3×#398C2×C311yescharacteristic
16C3×#343—31no—
17C3×#324—31no—
18#4530C2×C311yescharacteristic
19#4528C2×C311yescharacteristic
20C22×C32×C4—21no—
21C22×C32×C4—21no—
22C22×C32×C4C2×C411yescharacteristic
23C22×C32×C4D411yescharacteristic
24C22×C32×C4D411yescharacteristic
25C32×C4⋊C4—41no—
26C32×C4⋊C4—41no—
27C32×C4⋊C4—41no—
28C32×C4⋊C4—41no—
29C3×#208—22no—
30C3×#208—41no—
31C2×C3×C3⋊C8—41no—
32C2×C3×C3⋊C8—41no—
33#1346—31noSylow
34C2×C3×M16—61no—
35C2×C3×C4⋊C4—22no—
36C2×C3×C4⋊C4—21no—
37C2×C3×C4⋊C4—21no—
38C2×C3×C4⋊C4—21no—
39C2×C3×C4⋊C4—21no—
40C2×C3×C4⋊C4Dic311yescharacteristic
41C2×C3×C4⋊C4C3×C411yescharacteristic
42C2×C3×C4⋊C4C2×D311yescharacteristic
43C2×C3×C4⋊C4C22×C311yescharacteristic
44C2×#208—21no—
45C3×C22⋊C8—61no—
46C3×#95—22no—
47C3×#95—21no—
48C3×#95—21no—
49C3×#95—21no—
50C3×#95Dic311yescharacteristic
51C3×#95C3×C411yescharacteristic
52#830—21no—
53C23×C32C22⋊C411yescharacteristic
54C2×C32×C4—22no—
55C2×C32×C4—21no—
56C2×C32×C4—21no—
57C2×C32×C4—21no—
58C2×C32×C4—21no—
59C2×C32×C4—41no—
60C2×C32×C4—41no—
61C2×C32×C4—41no—
62C2×C32×C4—41no—
63C2×C32×C4—41no—
64C2×C32×C4—41no—
65C2×C32×C4—41no—
66C2×C32×C4D811yescharacteristic
67C2×C32×C4SD1611yescharacteristic
68C3×C3⋊C8—42no—
69C3×C3⋊C8—81no—
70#398C3×D311yescharacteristic
71#343—31no—
72#324—31no—
73C22×C3×C4—22no—
74C22×C3×C4—21no—
75C22×C3×C4—21no—
76C22×C3×C4—22no—
77C22×C3×C4—21no—
78C22×C3×C4—21no—
79C22×C3×C4—21no—
80C22×C3×C4—21no—
81C22×C3×C4—21no—
82C22×C3×C4C2×Dic311yescharacteristic
83C22×C3×C4#6711yescharacteristic
84C22×C3×C4#6711yescharacteristic
85C22×C3×C4C2×C3×C411yescharacteristic
86C22×C3×C4C3×D411yescharacteristic
87C22×C3×C4C3×D411yescharacteristic
88C3×M16—62no—
89C3×M16—121no—
90C2×C3×C8—121no—
91C2×C3×C8—121no—
92C3×C4⋊C4—41no—
93C3×C4⋊C4—41no—
94C3×C4⋊C4—41no—
95C3×C4⋊C4—41no—
96C3×C4⋊C4—42no—
97C3×C4⋊C4—42no—
98C3×C4⋊C4—42no—
99C3×C4⋊C4—42no—
100C3×C4⋊C4—41no—
101C3×C4⋊C4—41no—
102C3×C4⋊C4—41no—
103C3×C4⋊C4—41no—
104#208—22no—
105#208—41no—
106C2×C3⋊C8—41no—
107C2×C3⋊C8—41no—
108C22×C32—21no—
109C22×C32—21no—
110C22×C32#9911yescharacteristic
111C22×C32#10211yescharacteristic
112C22×C32#10411yescharacteristic
113C32×C4—21no—
114C32×C4—21no—
115C32×C4—42no—
116C32×C4—41no—
117C32×C4—41no—
118C32×C4—81no—
119C2×M16—61no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4C3×Dic311yescharacteristic
122C2×C4⋊C4C2×C3×D311yescharacteristic
123C22⋊C8—61no—
124#95—21no—
125#95C3×Dic311yescharacteristic
126C23×C3—21no—
127C23×C3#21711yescharacteristic
128C23×C3C3×C22⋊C411yescharacteristic
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—22no—
134C2×C3×C4—24no—
135C2×C3×C4—22no—
136C2×C3×C4—22no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—21no—
141C2×C3×C4—21no—
142C2×C3×C4—21no—
143C2×C3×C4—41no—
144C2×C3×C4—41no—
145C2×C3×C4—41no—
146C2×C3×C4—42no—
147C2×C3×C4—42no—
148C2×C3×C4—41no—
149C2×C3×C4—41no—
150C2×C3×C4—42no—
151C2×C3×C4—41no—
152C2×C3×C4—41no—
153C2×C3×C4—41no—
154C2×C3×C4—41no—
155C2×C3×C4—41no—
156C2×C3×C4—41no—
157C2×C3×C4—42no—
158C2×C3×C4—42no—
159C2×C3×C4—42no—
160C2×C3×C4—42no—
161C2×C3×C4—41no—
162C2×C3×C4—41no—
163C2×C3×C4—41no—
164C2×C3×C4—41no—
165C2×C3×C4—41no—
166C2×C3×C4—41no—
167C2×C3×C4#21311yescharacteristic
168C2×C3×C4#21411yescharacteristic
169C2×C3×C4C3×D811yescharacteristic
170C2×C3×C4C3×SD1611yescharacteristic
171C3×C8—122no—
172C3×C8—241no—
173C3⋊C8—42no—
174C3⋊C8—81no—
175C2×C32—21no—
176C2×C32—21no—
177C2×C32#32711yescharacteristic
178C2×C32#35211yescharacteristic
179C2×C32#35611yescharacteristic
180C22×C4—21no—
181C22×C4—21no—
182C22×C4C2×C3×Dic311yescharacteristic
183C22×C4C3×#6711yescharacteristic
184C22×C4C3×#6711yescharacteristic
185M16—62no—
186M16—121no—
187C2×C8—121no—
188C2×C8—121no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C22×C3—22no—
194C22×C3—22no—
195C22×C3—21no—
196C22×C3—21no—
197C22×C3—21no—
198C22×C3—21no—
199C22×C3—21no—
200C22×C3—21no—
201C22×C3—21no—
202C22×C3#83211yescharacteristic
203C22×C3#83411yescharacteristic
204C22×C3#83711yescharacteristic
205C22×C3C3×#9911yescharacteristic
206C22×C3C3×#10211yescharacteristic
207C22×C3C3×#10411yescharacteristic
208C3×C4—21no—
209C3×C4—21no—
210C3×C4—21no—
211C3×C4—21no—
212C3×C4—41no—
213C3×C4—41no—
214C3×C4—44no—
215C3×C4—42no—
216C3×C4—42no—
217C3×C4—42no—
218C3×C4—41no—
219C3×C4—41no—
220C3×C4—41no—
221C3×C4—41no—
222C3×C4—81no—
223C3×C4—82no—
224C3×C4—81no—
225C3×C4—81no—
226C32#134611yescharacteristic, complemented, Sylow
227C23C3×#21711yescharacteristic
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4C3×#21311yescharacteristic
241C2×C4C3×#21411yescharacteristic
242C8—122no—
243C8—241no—
244C2×C3—22no—
245C2×C3—22no—
246C2×C3—21no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3#453711yescharacteristic
254C2×C3#453911yescharacteristic
255C2×C3#454811yescharacteristic
256C2×C3C3×#32711yescharacteristic
257C2×C3C3×#35211yescharacteristic
258C2×C3C3×#35611yescharacteristic
259C22—21no—
260C22—21no—
261C22C3×#83211yescharacteristic
262C22C3×#83411yescharacteristic
263C22C3×#83711yescharacteristic
264C4—21no—
265C4—21no—
266C4—42no—
267C4—41no—
268C4—41no—
269C4—81no—
270C3—21no—
271C3#6765011yescharacteristic, direct product factor
272C3C3×#134611yescharacteristic, complemented
273C2—21no—
274C2—21no—
275C2C3×#453711yescharacteristic
276C2C3×#453911yescharacteristic
277C2C3×#454811yescharacteristic
subgroupG/H
centerC22×C3#834
commutatorC22×C3×C4C2×C3×C4
FrattiniC2×C4⋊C4C2×C3×D3
FittingC32×#398C2
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×C3×C4⋊C4C22×C3
hypercenterC3×#398D3
hypocenterC3C3×#1346
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C4⋊C4 ◁ C3×#398

Complements

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

NH ≅ G/Ntype
5. #67650C3direct (N × H)
226. C32#1346semidirect
271. C3#67650direct (N × H)
272. C3C3×#1346semidirect

Maximal subgroups

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

subgroupindex
C32×#3982
C3×#45302
C3×#45282
C3×#13463
#676503