Finite Group Databasebeta

← C3×#71269 #11779039

Subgroups — C3×#71269 #11779039

Order 1152.

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

normal subgroups only

This group has 527 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
2C32×#492C211yesmaximal, characteristic
3C3×#5075C212yesmaximal
4C3×#4546C211yesmaximal, characteristic, complemented
5C3×#4456C212yesmaximal, complemented
6C3×#1623—31nomaximal
7#71269C311yesmaximal, characteristic, direct product factor
8C2×C32×SD16—22no—
9C32×C4⋊Q8C2211yescharacteristic
10C32×#127C2211yescharacteristic
11C3×#944—22no—
12C2×C3×#214—22no—
13C3×#888—22no—
14C3×#887—22no—
15C3×C4×Dic6C2212yes—
16C32×C4×C8C2211yescharacteristic
17C3×#832—22no—
18C3×C4⋊(C3⋊C8)C2212yes—
19C3×Q82—31no—
20#5722C2×C311yescharacteristic, complemented
21C3×#492—21no—
22C3×#492D311yescharacteristic
23C3×#492C2×C311yescharacteristic
24C3×#460—32no—
25#5075C2×C312yes—
26C3×#333—31no—
27C3×Q8⋊C8—32no—
28#4546C2×C311yescharacteristic, complemented
29#4456C2×C312yescomplemented
30C2×C32×Q8D412yes—
31C2×C32×D4—21no—
32C2×C32×D4—22no—
33C2×C3×Dic6—22no—
34C2×C3×Dic6D412yes—
35C32×SD16—44no—
36C2×C32×C8—21no—
37C32×C4⋊C4—22no—
38C32×C42C2311yescharacteristic
39C3×#214—44no—
40C3×C4⋊Dic3D412yes—
41C3×Dic3⋊C4—24no—
42C3×Dic3⋊C4—22no—
43C3×C4×Dic3—22no—
44C3×C4×Dic3—22no—
45C2×C3×C3⋊C8—22no—
46#1623—31noSylow
47C2×C3×SD16—24no—
48C2×C3×SD16—22no—
49C2×C3×SD16—22no—
50C2×C3×SD16—62no—
51C3×C4⋊Q8—21no—
52C3×C4⋊Q8—62no—
53C3×C4⋊Q8—62no—
54C3×C4⋊Q8C2×D311yescharacteristic
55C3×C4⋊Q8C22×C311yescharacteristic
56C3×#127—21no—
57C3×#127C2×D311yescharacteristic
58C3×#127C22×C311yescharacteristic
59C3×C4×Q8—32no—
60C3×C4×Q8—62no—
61#944—22no—
62C2×#214—22no—
63#888—22no—
64#887—22no—
65C4×Dic6C22×C312yes—
66C3×C4⋊C8—32no—
67C3×#102—62no—
68C3×C4×C8—21no—
69C3×C4×C8C2×D311yescharacteristic
70C3×C4×C8C22×C311yescharacteristic
71#832—22no—
72C4⋊(C3⋊C8)C22×C312yes—
73C23×C32—41no—
74C32×Q8—42no—
75C32×D4—42no—
76C32×D4—42no—
77C32×D4—42no—
78C2×C32×C4—22no—
79C2×C32×C4C2×D412yes—
80C2×C32×C4C2×D411yescharacteristic
81C2×C3×Dic3—22no—
82C2×C3×Dic3—22no—
83C3×Dic6—22no—
84C3×Dic6—82no—
85C3×Dic6SD1614yescomplemented
86C32×C8—22no—
87C3×C3⋊C8—42no—
88Q82—31no—
89#492C3×D311yescharacteristic
90#460—32no—
91#333—31no—
92Q8⋊C8—32no—
93C2×C3×Q8—22no—
94C2×C3×Q8—32no—
95C2×C3×Q8—62no—
96C2×C3×Q8#6712yes—
97C2×C3×Q8C3×D412yes—
98C2×C3×D4—22no—
99C2×C3×D4—22no—
100C2×C3×D4—21no—
101C2×C3×D4—22no—
102C2×C3×D4—21no—
103C2×C3×D4—42no—
104C2×Dic6—22no—
105C2×Dic6C3×D412yes—
106C3×SD16—44no—
107C3×SD16—44no—
108C3×SD16—48no—
109C3×SD16—124no—
110C2×C3×C8—22no—
111C2×C3×C8—21no—
112C2×C3×C8—21no—
113C2×C3×C8—62no—
114C3×C4⋊C4—22no—
115C3×C4⋊C4—22no—
116C3×C4⋊C4—32no—
117C3×C4⋊C4—42no—
118C3×C4⋊C4—64no—
119C3×C4⋊C4—62no—
120C3×C42—21no—
121C3×C42—62no—
122C3×C42—62no—
123C3×C42C22×D311yescharacteristic
124C3×C42C23×C311yescharacteristic
125#214—44no—
126C4⋊Dic3C3×D412yes—
127Dic3⋊C4—24no—
128Dic3⋊C4—22no—
129C4×Dic3—22no—
130C4×Dic3—22no—
131C2×C3⋊C8—22no—
132C22×C32—82no—
133C22×C32—81no—
134C22×C32#12011yescharacteristic
135C32×C4—21no—
136C32×C4—42no—
137C32×C4C2×SD1612yes—
138C32×C4#13712yes—
139C3×Dic3—24no—
140C3×Dic3—42no—
141C2×SD16—22no—
142C2×SD16—62no—
143C4⋊Q8—62no—
144C4⋊Q8—62no—
145C4⋊Q8C2×C3×D311yescharacteristic
146#127C2×C3×D311yescharacteristic
147C4×Q8—32no—
148C4×Q8—62no—
149C4⋊C8—32no—
150#102—62no—
151C4×C8C2×C3×D311yescharacteristic
152C23×C3—42no—
153C23×C3—41no—
154C23×C3—41no—
155C3×Q8—34no—
156C3×Q8—42no—
157C3×Q8—42no—
158C3×Q8—44no—
159C3×Q8—62no—
160C3×Q8—242no—
161C3×D4—44no—
162C3×D4—42no—
163C3×D4—42no—
164C3×D4—42no—
165C3×D4—42no—
166C3×D4—42no—
167C3×D4—42no—
168C3×D4—82no—
169C3×D4—82no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—22no—
173C2×C3×C4—21no—
174C2×C3×C4—42no—
175C2×C3×C4—62no—
176C2×C3×C4—62no—
177C2×C3×C4D3×D412yes—
178C2×C3×C4C2×#6711yescharacteristic
179C2×C3×C4C2×C3×D412yes—
180C2×C3×C4C2×C3×D411yescharacteristic
181C2×Dic3—22no—
182C2×Dic3—22no—
183Dic6—22no—
184Dic6—82no—
185Dic6C3×SD1614yescomplemented
186C3×C8—24no—
187C3×C8—22no—
188C3×C8—22no—
189C3×C8—122no—
190C3⋊C8—42no—
191C2×C32—161no—
192C2×C32#44812yes—
193C2×C32#45311yescharacteristic
194C2×Q8—32no—
195C2×Q8—62no—
196C2×Q8C3×#6712yes—
197C2×D4—22no—
198C2×D4—21no—
199SD16—44no—
200SD16—124no—
201C2×C8—21no—
202C2×C8—62no—
203C4⋊C4—22no—
204C4⋊C4—32no—
205C4⋊C4—64no—
206C4⋊C4—62no—
207C42—62no—
208C42—62no—
209C42C22×C3×D311yescharacteristic
210C22×C3—21no—
211C22×C3—82no—
212C22×C3—84no—
213C22×C3—82no—
214C22×C3—82no—
215C22×C3—81no—
216C22×C3—81no—
217C22×C3#93711yescharacteristic
218C22×C3C3×#12011yescharacteristic
219C3×C4—22no—
220C3×C4—21no—
221C3×C4—21no—
222C3×C4—22no—
223C3×C4—22no—
224C3×C4—42no—
225C3×C4—42no—
226C3×C4—64no—
227C3×C4—82no—
228C3×C4—122no—
229C3×C4D3×SD1612yes—
230C3×C4#91512yes—
231C3×C4C2×C3×SD1612yes—
232C3×C4C3×#13712yes—
233Dic3—24no—
234Dic3—42no—
235C32#162311yescharacteristic, complemented, Sylow
236C23—41no—
237Q8—34no—
238Q8—42no—
239Q8—62no—
240Q8—242no—
241D4—42no—
242D4—42no—
243D4—42no—
244C2×C4—22no—
245C2×C4—62no—
246C2×C4—62no—
247C2×C4C3×D3×D412yes—
248C2×C4C2×C3×#6711yescharacteristic
249C8—22no—
250C8—122no—
251C2×C3—22no—
252C2×C3—21no—
253C2×C3—162no—
254C2×C3—161no—
255C2×C3—161no—
256C2×C3#507711yescharacteristic
257C2×C3#517012yes—
258C2×C3C3×#44812yes—
259C2×C3C3×#45311yescharacteristic
260C22—82no—
261C22—81no—
262C22C3×#93711yescharacteristic
263C4—21no—
264C4—42no—
265C4—64no—
266C4—122no—
267C4C3×D3×SD1612yes—
268C4C3×#91512yes—
269C3—21no—
270C3#7126911yescharacteristic, direct product factor
271C3C3×#162311yescharacteristic, complemented
272C2—161no—
273C2C3×#507711yescharacteristic
274C2C3×#517012yes—
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#492C2
socleC22×C32#120
prime radicalC32×#127C22
hypercenterC3×#492D3
hypocenterC3C3×#1623
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#492

Complements

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

NH ≅ G/Ntype
1. C3×#5722C2semidirect
4. C3×#4546C2semidirect
5. C3×#4456C2semidirect
7. #71269C3direct (N × H)
20. #5722C2×C3semidirect
28. #4546C2×C3semidirect
29. #4456C2×C3semidirect
85. C3×Dic6SD16semidirect
185. Dic6C3×SD16semidirect
235. C32#1623semidirect
270. C3#71269direct (N × H)
271. C3C3×#1623semidirect

Maximal subgroups

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

subgroupindex
C3×#57222
C32×#4922
C3×#50752
C3×#45462
C3×#44562
C3×#16233
#712693