Finite Group Databasebeta

← C3×#68504 #11779048

Subgroups — C3×#68504 #11779048

Order 1152.

488 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 114 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×#5722C211yesmaximal, characteristic, complemented
2C3×#5085C211yesmaximal, characteristic
3C3×#4848C212yesmaximal
4C32×#333C211yesmaximal, characteristic, complemented
5C3×#4484C212yesmaximal, complemented
6C3×#1623—31nomaximal
7#68504C311yesmaximal, characteristic, direct product factor
8C32×C4⋊Q8C2211yescharacteristic
9C3×#944—22no—
10C2×C3×#215—22no—
11C2×C3×#204—22no—
12C3×#888—22no—
13C3×#887—22no—
14C3×#874C2211yescharacteristic
15C3×C4×Dic6C2212yes—
16C32×C4⋊C8C2212yes—
17C3×#821—22no—
18C3×C4×C3⋊C8C2211yescharacteristic
19C3×Q82—31no—
20#5722C2×C311yescharacteristic, complemented
21C3×#492—31no—
22C3×#460—32no—
23#5085C2×C311yescharacteristic
24#4848C2×C312yes—
25C3×#333—21no—
26C3×#333D311yescharacteristic, complemented
27C3×#333C2×C311yescharacteristic, complemented
28C3×Q8⋊C8—32no—
29#4484C2×C312yescomplemented
30C2×C32×Q8D412yes—
31C2×C3×D12—22no—
32C2×C3×D12—21no—
33C2×C3×Dic6—22no—
34C2×C3×Dic6D412yes—
35C2×C32×C8—22no—
36C32×C4⋊C4—22no—
37C32×C42C2311yescharacteristic
38C3×#215—44no—
39C3×C4⋊Dic3D412yes—
40C3×Dic3⋊C4—24no—
41C3×Dic3⋊C4—22no—
42C3×C4×Dic3—22no—
43C3×C4×Dic3—22no—
44C2×C3×C3⋊C8—21no—
45C3×#204—44no—
46#1623—31noSylow
47C2×C3×SD16—62no—
48C2×C3×SD16—62no—
49C3×C4⋊Q8—21no—
50C3×C4⋊Q8—62no—
51C3×C4⋊Q8—62no—
52C3×C4⋊Q8C2×D311yescharacteristic
53C3×C4⋊Q8C22×C311yescharacteristic
54C3×#127—31no—
55C3×C4×Q8—32no—
56C3×C4×Q8—62no—
57#944—22no—
58C2×#215—22no—
59C2×#204—22no—
60#888—22no—
61#887—22no—
62#874C22×C311yescharacteristic
63C4×Dic6C22×C312yes—
64C3×C4⋊C8—22no—
65C3×C4⋊C8C2×D312yes—
66C3×C4⋊C8C22×C312yes—
67C3×#102—62no—
68C3×C4×C8—31no—
69#821—22no—
70C4×C3⋊C8C22×C311yescharacteristic
71C22×C3×D3—41no—
72C32×Q8—42no—
73C2×C32×C4—22no—
74C2×C32×C4C2×D411yescharacteristic
75C2×C32×C4C2×D412yes—
76C2×C3×Dic3—22no—
77C2×C3×Dic3—22no—
78C3×D12—42no—
79C3×D12—42no—
80C3×D12—42no—
81C3×Dic6—22no—
82C3×Dic6—82no—
83C3×Dic6SD1614yescomplemented
84C32×C8—42no—
85C3×C3⋊C8—22no—
86Q82—31no—
87#492—31no—
88#460—32no—
89#333C3×D311yescharacteristic, complemented
90Q8⋊C8—32no—
91C2×C3×Q8—22no—
92C2×C3×Q8—32no—
93C2×C3×Q8—62no—
94C2×C3×Q8D1212yes—
95C2×C3×Q8C3×D412yes—
96C2×C3×D4—61no—
97C2×C3×D4—62no—
98C2×D12—22no—
99C2×D12—21no—
100C2×Dic6—22no—
101C2×Dic6C3×D412yes—
102C3×SD16—124no—
103C3×SD16—124no—
104C2×C3×C8—22no—
105C2×C3×C8—22no—
106C2×C3×C8—42no—
107C2×C3×C8—61no—
108C3×C4⋊C4—22no—
109C3×C4⋊C4—22no—
110C3×C4⋊C4—32no—
111C3×C4⋊C4—42no—
112C3×C4⋊C4—64no—
113C3×C4⋊C4—62no—
114C3×C42—21no—
115C3×C42—62no—
116C3×C42—62no—
117C3×C42C22×D311yescharacteristic
118C3×C42C23×C311yescharacteristic
119#215—44no—
120C4⋊Dic3C3×D412yes—
121Dic3⋊C4—24no—
122Dic3⋊C4—22no—
123C4×Dic3—22no—
124C4×Dic3—22no—
125C2×C3⋊C8—21no—
126#204—44no—
127C22×C32#12011yescharacteristic
128C2×C3×D3—82no—
129C2×C3×D3—81no—
130C32×C4—21no—
131C32×C4—42no—
132C32×C4C2×SD1612yes—
133C32×C4#13712yes—
134C3×Dic3—24no—
135C3×Dic3—42no—
136C2×SD16—62no—
137C2×SD16—62no—
138C4⋊Q8—62no—
139C4⋊Q8—62no—
140C4⋊Q8C2×C3×D311yescharacteristic
141#127—31no—
142C4×Q8—32no—
143C4×Q8—62no—
144C4⋊C8C2×C3×D312yes—
145#102—62no—
146C4×C8—31no—
147C23×C3—121no—
148C22×D3—41no—
149C3×Q8—34no—
150C3×Q8—42no—
151C3×Q8—42no—
152C3×Q8—62no—
153C3×Q8—82no—
154C3×Q8—242no—
155C3×D4—122no—
156C3×D4—122no—
157C3×D4—122no—
158C2×C3×C4—22no—
159C2×C3×C4—22no—
160C2×C3×C4—21no—
161C2×C3×C4—22no—
162C2×C3×C4—42no—
163C2×C3×C4—62no—
164C2×C3×C4—62no—
165C2×C3×C4C2×D1211yescharacteristic
166C2×C3×C4D3×D412yes—
167C2×C3×C4C2×C3×D411yescharacteristic
168C2×C3×C4C2×C3×D412yes—
169C2×Dic3—22no—
170C2×Dic3—22no—
171D12—42no—
172D12—42no—
173D12—42no—
174Dic6—22no—
175Dic6—82no—
176Dic6C3×SD1614yescomplemented
177C3×C8—42no—
178C3×C8—42no—
179C3×C8—62no—
180C3×C8—82no—
181C3⋊C8—22no—
182C2×C32#44812yes—
183C2×C32#45311yescharacteristic
184C3×D3—161no—
185C2×Q8—32no—
186C2×Q8—62no—
187C2×Q8C3×D1212yes—
188C2×D4—61no—
189C2×D4—62no—
190SD16—124no—
191SD16—124no—
192C2×C8—22no—
193C2×C8—61no—
194C4⋊C4—22no—
195C4⋊C4—32no—
196C4⋊C4—64no—
197C4⋊C4—62no—
198C42—62no—
199C42—62no—
200C42C22×C3×D311yescharacteristic
201C22×C3—21no—
202C22×C3—241no—
203C22×C3—242no—
204C22×C3#88211yescharacteristic
205C22×C3C3×#12011yescharacteristic
206C2×D3—82no—
207C2×D3—81no—
208C3×C4—21no—
209C3×C4—21no—
210C3×C4—22no—
211C3×C4—22no—
212C3×C4—41no—
213C3×C4—42no—
214C3×C4—42no—
215C3×C4—64no—
216C3×C4—82no—
217C3×C4—122no—
218C3×C4D3×SD1612yes—
219C3×C4#91812yes—
220C3×C4C2×C3×SD1612yes—
221C3×C4C3×#13712yes—
222Dic3—24no—
223Dic3—42no—
224C32#162311yescharacteristic, complemented, Sylow
225C23—121no—
226Q8—34no—
227Q8—42no—
228Q8—62no—
229Q8—242no—
230D4—122no—
231D4—122no—
232D4—122no—
233C2×C4—22no—
234C2×C4—62no—
235C2×C4—62no—
236C2×C4C2×C3×D1211yescharacteristic
237C2×C4C3×D3×D412yes—
238C8—42no—
239C8—62no—
240C2×C3—21no—
241C2×C3—22no—
242C2×C3—481no—
243C2×C3#474711yescharacteristic
244C2×C3#480612yes—
245C2×C3C3×#44812yes—
246C2×C3C3×#45311yescharacteristic
247D3—161no—
248C22—241no—
249C22—242no—
250C22C3×#88211yescharacteristic
251C4—21no—
252C4—42no—
253C4—64no—
254C4—122no—
255C4C3×D3×SD1612yes—
256C4C3×#91812yes—
257C3—21no—
258C3#6850411yescharacteristic, direct product factor
259C3C3×#162311yescharacteristic, complemented
260C2—481no—
261C2C3×#474711yescharacteristic
262C2C3×#480612yes—
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#333C2
socleC22×C32#120
prime radicalC3×#874C22
hypercenterC3×#333D3
hypocenterC3C3×#1623
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#333

Complements

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

NH ≅ G/Ntype
1. C3×#5722C2semidirect
4. C32×#333C2semidirect
5. C3×#4484C2semidirect
7. #68504C3direct (N × H)
20. #5722C2×C3semidirect
26. C3×#333D3semidirect
27. C3×#333C2×C3semidirect
29. #4484C2×C3semidirect
83. C3×Dic6SD16semidirect
89. #333C3×D3semidirect
176. Dic6C3×SD16semidirect
224. C32#1623semidirect
258. C3#68504direct (N × H)
259. C3C3×#1623semidirect

Maximal subgroups

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

subgroupindex
C3×#57222
C3×#50852
C3×#48482
C32×#3332
C3×#44842
C3×#16233
#685043