Finite Group Databasebeta

← C3×#67494 #11771968

Subgroups — C3×#67494 #11771968

Order 1152.

329 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 329 conjugacy classes of subgroups — too many to draw. Only its 70 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×#4979C211yesmaximal, characteristic
2C32×#343C211yesmaximal, characteristic
3C3×#4528C211yesmaximal, characteristic
4C3×#1354—31nomaximal
5#67494C311yesmaximal, characteristic, direct product factor
6C22×C3×Dic6C411yescharacteristic
7C2×C32×M16—21no—
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×C3×Dic3⋊C4—21no—
10C3×C3⋊#95—21no—
11C3×C3⋊#95C411yescharacteristic
12C3×#830—21no—
13C3×#395—31no—
14#4979C2×C311yescharacteristic
15C3×#343—21no—
16C3×#343D311yescharacteristic
17C3×#343C2×C311yescharacteristic
18C3×#324—31no—
19#4528C2×C311yescharacteristic
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4D411yescharacteristic
22C22×C32×C4D411yescharacteristic
23C22×C3×Dic3—21no—
24C22×C3×Dic3—21no—
25C2×C3×Dic6—41no—
26C2×C3×Dic6—42no—
27C32×M16—22no—
28C32×M16—41no—
29C2×C32×C8—41no—
30C32×C4⋊C4—41no—
31C3×Dic3⋊C4—42no—
32C2×C3×C3⋊C8—41no—
33#1354—31noSylow
34C22×C3×Q8—31no—
35C22×Dic6C3×C411yescharacteristic
36C2×C3×M16—22no—
37C2×C3×M16—21no—
38C2×C3×M16—21no—
39C2×C3×C4⋊C4—21no—
40C2×C3×C4⋊C4—61no—
41C2×C3×C4⋊C4C2×D311yescharacteristic
42C2×C3×C4⋊C4C22×C311yescharacteristic
43C2×Dic3⋊C4—21no—
44C3×C22⋊C8—61no—
45C3×#95—31no—
46C3×#95—61no—
47C3⋊#95—21no—
48C3⋊#95C3×C411yescharacteristic
49#830—21no—
50C23×C32C22⋊C411yescharacteristic
51C2×C32×C4—21no—
52C2×C32×C4—21no—
53C2×C32×C4—21no—
54C2×C32×C4—21no—
55C2×C32×C4—41no—
56C2×C32×C4—41no—
57C2×C32×C4SD1611yescharacteristic
58C2×C32×C4Q1611yescharacteristic
59C2×C3×Dic3—22no—
60C2×C3×Dic3—22no—
61C2×C3×Dic3—41no—
62C2×C3×Dic3—41no—
63C2×C3×Dic3—41no—
64C2×C3×Dic3—41no—
65C3×Dic6—42no—
66C3×Dic6—42no—
67C32×C8—42no—
68C3×C3⋊C8—81no—
69#395—31no—
70#343C3×D311yescharacteristic
71#324—31no—
72C2×C3×Q8—121no—
73C2×C3×Q8—122no—
74C22×C3×C4—21no—
75C22×C3×C4—21no—
76C22×C3×C4—21no—
77C22×C3×C4—61no—
78C22×C3×C4—61no—
79C22×C3×C4C4×D311yescharacteristic
80C22×C3×C4D1211yescharacteristic
81C22×C3×C4#6711yescharacteristic
82C22×C3×C4C2×C3×C411yescharacteristic
83C22×C3×C4C3×D411yescharacteristic
84C22×C3×C4C3×D411yescharacteristic
85C22×Dic3—21no—
86C22×Dic3—21no—
87C2×Dic6—41no—
88C2×Dic6—42no—
89C3×M16—24no—
90C3×M16—22no—
91C3×M16—22no—
92C3×M16—42no—
93C3×M16—41no—
94C3×M16—41no—
95C2×C3×C8—42no—
96C2×C3×C8—41no—
97C2×C3×C8—41no—
98C2×C3×C8—121no—
99C3×C4⋊C4—41no—
100C3×C4⋊C4—41no—
101C3×C4⋊C4—42no—
102C3×C4⋊C4—122no—
103Dic3⋊C4—42no—
104C2×C3⋊C8—41no—
105C22×C32—21no—
106C22×C32—21no—
107C22×C32#9911yescharacteristic
108C22×C32#10311yescharacteristic
109C22×C32#10411yescharacteristic
110C32×C4—21no—
111C32×C4—21no—
112C32×C4—41no—
113C32×C4—41no—
114C3×Dic3—42no—
115C3×Dic3—42no—
116C22×Q8—31no—
117C2×M16—21no—
118C2×C4⋊C4—61no—
119C2×C4⋊C4C2×C3×D311yescharacteristic
120C22⋊C8—61no—
121#95—31no—
122#95—61no—
123C23×C3—21no—
124C23×C3(C2×D3)⋊C411yescharacteristic
125C23×C3C3×C22⋊C411yescharacteristic
126C3×Q8—122no—
127C3×Q8—122no—
128C2×C3×C4—22no—
129C2×C3×C4—22no—
130C2×C3×C4—21no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—41no—
141C2×C3×C4—41no—
142C2×C3×C4—41no—
143C2×C3×C4—41no—
144C2×C3×C4—41no—
145C2×C3×C4—41no—
146C2×C3×C4—62no—
147C2×C3×C4—62no—
148C2×C3×C4—81no—
149C2×C3×C4—81no—
150C2×C3×C4—121no—
151C2×C3×C4—121no—
152C2×C3×C4—121no—
153C2×C3×C4—121no—
154C2×C3×C4#21411yescharacteristic
155C2×C3×C4#21611yescharacteristic
156C2×C3×C4C3×SD1611yescharacteristic
157C2×C3×C4C3×Q1611yescharacteristic
158C2×Dic3—22no—
159C2×Dic3—22no—
160C2×Dic3—41no—
161C2×Dic3—41no—
162C2×Dic3—41no—
163C2×Dic3—41no—
164Dic6—42no—
165Dic6—42no—
166C3×C8—44no—
167C3×C8—42no—
168C3×C8—42no—
169C3×C8—241no—
170C3⋊C8—81no—
171C2×C32—21no—
172C2×C32—21no—
173C2×C32#32811yescharacteristic
174C2×C32AΣL(1,𝔽16)11yescharacteristic
175C2×C32#35611yescharacteristic
176C2×Q8—121no—
177C2×Q8—122no—
178C22×C4—61no—
179C22×C4—61no—
180C22×C4C3×C4×D311yescharacteristic
181C22×C4C3×D1211yescharacteristic
182C22×C4C3×#6711yescharacteristic
183M16—22no—
184M16—41no—
185C2×C8—41no—
186C2×C8—121no—
187C4⋊C4—41no—
188C4⋊C4—122no—
189C22×C3—21no—
190C22×C3—21no—
191C22×C3—21no—
192C22×C3—21no—
193C22×C3—21no—
194C22×C3—21no—
195C22×C3—21no—
196C22×C3—41no—
197C22×C3—41no—
198C22×C3#80511yescharacteristic
199C22×C3#80611yescharacteristic
200C22×C3#81011yescharacteristic
201C22×C3C3×#9911yescharacteristic
202C22×C3C3×#10311yescharacteristic
203C22×C3C3×#10411yescharacteristic
204C3×C4—22no—
205C3×C4—22no—
206C3×C4—21no—
207C3×C4—21no—
208C3×C4—21no—
209C3×C4—21no—
210C3×C4—41no—
211C3×C4—41no—
212C3×C4—41no—
213C3×C4—41no—
214C3×C4—81no—
215C3×C4—81no—
216C3×C4—122no—
217C3×C4—122no—
218Dic3—42no—
219Dic3—42no—
220C32#135411yescharacteristic, complemented, Sylow
221C23C3×(C2×D3)⋊C411yescharacteristic
222Q8—122no—
223Q8—122no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—62no—
231C2×C4—62no—
232C2×C4—121no—
233C2×C4—121no—
234C2×C4—121no—
235C2×C4—121no—
236C2×C4C3×#21411yescharacteristic
237C2×C4C3×#21611yescharacteristic
238C8—42no—
239C8—241no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3—41no—
248C2×C3—41no—
249C2×C3#445211yescharacteristic
250C2×C3#447511yescharacteristic
251C2×C3#447811yescharacteristic
252C2×C3C3×#32811yescharacteristic
253C2×C3C3×AΣL(1,𝔽16)11yescharacteristic
254C2×C3C3×#35611yescharacteristic
255C22—21no—
256C22—21no—
257C22C3×#80511yescharacteristic
258C22C3×#80611yescharacteristic
259C22C3×#81011yescharacteristic
260C4—21no—
261C4—21no—
262C4—41no—
263C4—41no—
264C4—122no—
265C4—122no—
266C3—21no—
267C3#6749411yescharacteristic, direct product factor
268C3C3×#135411yescharacteristic, complemented
269C2—21no—
270C2—21no—
271C2C3×#445211yescharacteristic
272C2C3×#447511yescharacteristic
273C2C3×#447811yescharacteristic
subgroupG/H
centerC22×C3#806
commutatorC22×C3×C4C2×C3×C4
FrattiniC2×C4⋊C4C2×C3×D3
FittingC32×#343C2
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×C3×C4⋊C4C22×C3
hypercenterC3×#343D3
hypocenterC3C3×#1354
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C2×C3×C4⋊C4 ◁ C3×#343

Complements

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

NH ≅ G/Ntype
5. #67494C3direct (N × H)
220. C32#1354semidirect
267. C3#67494direct (N × H)
268. C3C3×#1354semidirect

Maximal subgroups

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

subgroupindex
C3×#49792
C32×#3432
C3×#45282
C3×#13543
#674943