Finite Group Databasebeta

← C3×#67486 #11771866

Subgroups — C3×#67486 #11771866

Order 1152.

289 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 289 conjugacy classes of subgroups — too many to draw. Only its 78 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×#5116C211yesmaximal, characteristic
2C32×#340C211yesmaximal, characteristic
3C3×#4549C211yesmaximal, characteristic
4C3×#1348—31nomaximal
5#67486C311yesmaximal, characteristic, direct product factor
6C22×C32×C8C2211yescharacteristic
7C2×C32×C4⋊C4—21no—
8C3×#924—21no—
9C2×C3×Dic12C411yescharacteristic, complemented
10C3×#818C411yescharacteristic, complemented
11C3×#816—21no—
12C2×C3×C3⋊C16—21no—
13C3×#467—31no—
14#5116C2×C311yescharacteristic
15C3×C22⋊C16—31no—
16C3×#340—21no—
17C3×#340D311yescharacteristic
18C3×#340C2×C311yescharacteristic
19#4549C2×C311yescharacteristic
20C22×C32×C4—41no—
21C22×C32×C4D411yescharacteristic
22C2×C3×Dic6—21no—
23C2×C32×C8—41no—
24C2×C32×C8C2×C411yescharacteristic
25C2×C32×C8D411yescharacteristic
26C32×C4⋊C4—22no—
27C32×C4⋊C4—41no—
28C3×#217—41no—
29C3×C4⋊Dic3—21no—
30C3×Dic3⋊C4—41no—
31C3×Dic12—41no—
32C3×C3⋊C16—41no—
33#1348—31noSylow
34C2×C3×Q16—31no—
35C22×C3×C8—21no—
36C22×C3×C8C2×D311yescharacteristic
37C22×C3×C8C22×C311yescharacteristic
38C3×C22⋊Q8—61no—
39C2×C3×C4⋊C4—22no—
40C2×C3×C4⋊C4—21no—
41C2×C3×C4⋊C4—21no—
42#924—21no—
43C2×Dic12C3×C411yescharacteristic, complemented
44C2×C3×C16—61no—
45C3×#107—31no—
46C3×#103—61no—
47#818C3×C411yescharacteristic, complemented
48#816—21no—
49C2×C3⋊C16—21no—
50C23×C32D811yescharacteristic
51C2×C32×C4—21no—
52C2×C32×C4—21no—
53C2×C32×C4—42no—
54C2×C32×C4—81no—
55C2×C32×C4—81no—
56C2×C32×C4C22⋊C411yescharacteristic
57C2×C32×C4SD1611yescharacteristic
58C2×C3×Dic3—41no—
59C2×C3×Dic3—41no—
60C3×Dic6—41no—
61C3×Dic6—41no—
62C32×C8—21no—
63C32×C8—21no—
64#467—31no—
65C22⋊C16—31no—
66#340C3×D311yescharacteristic
67C2×C3×Q8—61no—
68C22×C3×C4—21no—
69C22×C3×C4—42no—
70C22×C3×C4—41no—
71C22×C3×C4—41no—
72C22×C3×C4#6711yescharacteristic
73C22×C3×C4C3×D411yescharacteristic
74C2×Dic6—21no—
75C3×Q16—121no—
76C2×C3×C8—21no—
77C2×C3×C8—21no—
78C2×C3×C8—41no—
79C2×C3×C8—41no—
80C2×C3×C8—42no—
81C2×C3×C8C4×D311yescharacteristic
82C2×C3×C8D1211yescharacteristic
83C2×C3×C8C2×C3×C411yescharacteristic
84C2×C3×C8C3×D411yescharacteristic
85C3×C4⋊C4—24no—
86C3×C4⋊C4—22no—
87C3×C4⋊C4—22no—
88C3×C4⋊C4—42no—
89C3×C4⋊C4—41no—
90C3×C4⋊C4—41no—
91C3×C4⋊C4—61no—
92C3×C4⋊C4—121no—
93C3×C22⋊C4—121no—
94#217—41no—
95C4⋊Dic3—21no—
96Dic3⋊C4—41no—
97Dic12—41no—
98C3×C16—121no—
99C3⋊C16—41no—
100C22×C32—21no—
101C22×C32—21no—
102C22×C32#10211yescharacteristic
103C22×C32SD3211yescharacteristic
104C22×C32Q3211yescharacteristic
105C32×C4—21no—
106C32×C4—82no—
107C32×C4#9911yescharacteristic
108C32×C4#10411yescharacteristic
109C3×Dic3—81no—
110C3×Dic3—81no—
111C2×Q16—31no—
112C22×C8C2×C3×D311yescharacteristic
113C22⋊Q8—61no—
114C2×C4⋊C4—21no—
115C2×C16—61no—
116#107—31no—
117#103—61no—
118C23×C3—21no—
119C23×C3#21311yescharacteristic
120C23×C3C3×D811yescharacteristic
121C3×Q8—121no—
122C3×Q8—121no—
123C2×C3×C4—22no—
124C2×C3×C4—22no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—44no—
132C2×C3×C4—42no—
133C2×C3×C4—42no—
134C2×C3×C4—82no—
135C2×C3×C4—81no—
136C2×C3×C4—81no—
137C2×C3×C4—82no—
138C2×C3×C4—81no—
139C2×C3×C4—81no—
140C2×C3×C4—121no—
141C2×C3×C4—121no—
142C2×C3×C4(C2×D3)⋊C411yescharacteristic
143C2×C3×C4#21511yescharacteristic
144C2×C3×C4C3×C22⋊C411yescharacteristic
145C2×C3×C4C3×SD1611yescharacteristic
146C2×Dic3—41no—
147C2×Dic3—41no—
148Dic6—41no—
149Dic6—41no—
150C3×C8—21no—
151C3×C8—21no—
152C3×C8—21no—
153C3×C8—21no—
154C3×C8—41no—
155C3×C8—41no—
156C2×C32—21no—
157C2×C32—21no—
158C2×C32#32711yescharacteristic
159C2×C32#35811yescharacteristic
160C2×C32#36011yescharacteristic
161C2×Q8—61no—
162C22×C4—41no—
163C22×C4C3×#6711yescharacteristic
164Q16—121no—
165C2×C8—41no—
166C2×C8C3×C4×D311yescharacteristic
167C2×C8C3×D1211yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—41no—
170C4⋊C4—61no—
171C4⋊C4—121no—
172C22⋊C4—121no—
173C16—121no—
174C22×C3—22no—
175C22×C3—22no—
176C22×C3—21no—
177C22×C3—21no—
178C22×C3—21no—
179C22×C3—21no—
180C22×C3—21no—
181C22×C3—21no—
182C22×C3—21no—
183C22×C3#80911yescharacteristic
184C22×C3#82711yescharacteristic
185C22×C3#82911yescharacteristic
186C22×C3C3×#10211yescharacteristic
187C22×C3C3×SD3211yescharacteristic
188C22×C3C3×Q3211yescharacteristic
189C3×C4—22no—
190C3×C4—21no—
191C3×C4—21no—
192C3×C4—21no—
193C3×C4—21no—
194C3×C4—84no—
195C3×C4—82no—
196C3×C4—82no—
197C3×C4—241no—
198C3×C4—241no—
199C3×C4#80511yescharacteristic
200C3×C4#80611yescharacteristic
201C3×C4C3×#9911yescharacteristic
202C3×C4C3×#10411yescharacteristic
203Dic3—81no—
204Dic3—81no—
205C32#134811yescharacteristic, complemented, Sylow
206C23C3×#21311yescharacteristic
207Q8—121no—
208Q8—121no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—42no—
212C2×C4—81no—
213C2×C4—81no—
214C2×C4—121no—
215C2×C4—121no—
216C2×C4C3×(C2×D3)⋊C411yescharacteristic
217C2×C4C3×#21511yescharacteristic
218C8—21no—
219C8—21no—
220C2×C3—22no—
221C2×C3—22no—
222C2×C3—21no—
223C2×C3—21no—
224C2×C3—21no—
225C2×C3—21no—
226C2×C3—21no—
227C2×C3—21no—
228C2×C3—21no—
229C2×C3#445111yescharacteristic
230C2×C3#448811yescharacteristic
231C2×C3#449211yescharacteristic
232C2×C3C3×#32711yescharacteristic
233C2×C3C3×#35811yescharacteristic
234C2×C3C3×#36011yescharacteristic
235C22—21no—
236C22—21no—
237C22C3×#80911yescharacteristic
238C22C3×#82711yescharacteristic
239C22C3×#82911yescharacteristic
240C4—21no—
241C4—82no—
242C4—241no—
243C4—241no—
244C4C3×#80511yescharacteristic
245C4C3×#80611yescharacteristic
246C3—21no—
247C3#6748611yescharacteristic, direct product factor
248C3C3×#134811yescharacteristic, complemented
249C2—21no—
250C2—21no—
251C2C3×#445111yescharacteristic
252C2C3×#448811yescharacteristic
253C2C3×#449211yescharacteristic
subgroupG/H
centerC22×C3#809
commutatorC2×C3×C8C2×C3×C4
FrattiniC22×C8C2×C3×D3
FittingC32×#340C2
socleC22×C32#102
prime radicalC23×C32D8
cosocleC22×C3×C8C22×C3
hypercenterC3×#340D3
hypocenterC3C3×#1348
LCSG ▷ C2×C3×C8 ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C3×#340

Complements

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

NH ≅ G/Ntype
5. #67486C3direct (N × H)
9. C2×C3×Dic12C4semidirect
10. C3×#818C4semidirect
43. C2×Dic12C3×C4semidirect
47. #818C3×C4semidirect
205. C32#1348semidirect
247. C3#67486direct (N × H)
248. C3C3×#1348semidirect

Maximal subgroups

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

subgroupindex
C3×#51162
C32×#3402
C3×#45492
C3×#13483
#674863