Finite Group Databasebeta

← C3×#71961 #11780707

Subgroups — C3×#71961 #11780707

Order 1152.

430 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 98 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×#564C211yesmaximal, characteristic
2C3×#5069C211yesmaximal, characteristic
3C3×#5064C212yesmaximal
4C3×#4543C211yesmaximal, characteristic
5C3×#4543C212yesmaximal
6C3×#1663—31nomaximal
7#71961C311yesmaximal, characteristic, direct product factor
8C32×#125—22no—
9C32×#125—22no—
10C32×#125—22no—
11C32×#125C2212yes—
12C32×#125C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×#810—22no—
15C3×#808—22no—
16C3×#807—22no—
17C3×#803C2212yes—
18C3×#803C2211yescharacteristic
19C3×#564—21no—
20C3×#564D311yescharacteristic
21C3×#564C2×C311yescharacteristic
22C3×#501—32no—
23C3×#491—31no—
24#5069C2×C311yescharacteristic
25#5064C2×C312yes—
26C3×#330—32no—
27C3×#330—31no—
28#4543C2×C311yescharacteristic
29#4543C2×C312yes—
30C2×C3×Dic6—21no—
31C32×C4⋊C4—22no—
32C32×C4⋊C4—22no—
33C32×C4⋊C4—22no—
34C32×C4⋊C4—22no—
35C32×C4⋊C4—22no—
36C32×C4⋊C4—22no—
37C32×C4⋊C4D412yes—
38C32×C4⋊C4D412yes—
39C32×C4⋊C4D412yes—
40C32×C42—22no—
41C32×C42C2311yescharacteristic
42C3×C4⋊Dic3—22no—
43C2×C3×C3⋊C8—22no—
44C2×C3×C3⋊C8—21no—
45#1663—31noSylow
46C3×C4⋊Q8—31no—
47C3×#125—24no—
48C3×#125—24no—
49C3×#125—24no—
50C3×#125—22no—
51C3×#125—22no—
52C3×#125—22no—
53C3×#125—22no—
54C3×#125—22no—
55C3×#125—22no—
56C3×#125—21no—
57C3×#125—22no—
58C3×#125C2×D311yescharacteristic
59C3×#125C2×D312yes—
60C3×#125C22×C312yes—
61C3×#125C22×C311yescharacteristic
62#869C22×C311yescharacteristic
63C3×#107—62no—
64C3×#106—62no—
65C3×#103—62no—
66C3×#97—31no—
67C3×#97—32no—
68#810—22no—
69#808—22no—
70#807—22no—
71#803C22×C312yes—
72#803C22×C311yescharacteristic
73C2×C32×C4—22no—
74C2×C32×C4—22no—
75C2×C32×C4—22no—
76C2×C32×C4C2×D412yes—
77C2×C32×C4C2×D411yescharacteristic
78C2×C3×Dic3—41no—
79C3×Dic6—42no—
80C3×C3⋊C8—24no—
81C3×C3⋊C8—41no—
82#564C3×D311yescharacteristic
83#501—32no—
84#491—31no—
85#330—32no—
86#330—31no—
87C2×C3×Q8—61no—
88C2×Dic6—21no—
89C2×C3×C8—62no—
90C2×C3×C8—61no—
91C3×C4⋊C4—24no—
92C3×C4⋊C4—24no—
93C3×C4⋊C4—24no—
94C3×C4⋊C4—22no—
95C3×C4⋊C4—22no—
96C3×C4⋊C4—22no—
97C3×C4⋊C4—22no—
98C3×C4⋊C4—22no—
99C3×C4⋊C4—22no—
100C3×C4⋊C4—24no—
101C3×C4⋊C4—24no—
102C3×C4⋊C4—24no—
103C3×C4⋊C4—22no—
104C3×C4⋊C4—22no—
105C3×C4⋊C4—22no—
106C3×C4⋊C4—22no—
107C3×C4⋊C4—22no—
108C3×C4⋊C4—22no—
109C3×C4⋊C4—22no—
110C3×C4⋊C4—22no—
111C3×C4⋊C4—22no—
112C3×C4⋊C4—62no—
113C3×C4⋊C4#6712yes—
114C3×C4⋊C4#6712yes—
115C3×C4⋊C4#6712yes—
116C3×C4⋊C4C3×D412yes—
117C3×C4⋊C4C3×D412yes—
118C3×C4⋊C4C3×D412yes—
119C3×C42—24no—
120C3×C42—22no—
121C3×C42—22no—
122C3×C42—21no—
123C3×C42C22×D311yescharacteristic
124C3×C42C23×C311yescharacteristic
125C4⋊Dic3—22no—
126C2×C3⋊C8—22no—
127C2×C3⋊C8—21no—
128C22×C32#12011yescharacteristic
129C32×C4—21no—
130C32×C4—22no—
131C32×C4—42no—
132C32×C4—42no—
133C32×C4—42no—
134C3×Dic3—81no—
135C4⋊Q8—31no—
136#125—22no—
137#125—22no—
138#125—22no—
139#125C2×C3×D311yescharacteristic
140#125C2×C3×D312yes—
141#107—62no—
142#106—62no—
143#103—62no—
144#97—31no—
145#97—32no—
146C3×Q8—122no—
147C2×C3×C4—24no—
148C2×C3×C4—24no—
149C2×C3×C4—24no—
150C2×C3×C4—22no—
151C2×C3×C4—22no—
152C2×C3×C4—22no—
153C2×C3×C4—22no—
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×C3×C4—22no—
157C2×C3×C4—21no—
158C2×C3×C4—121no—
159C2×C3×C4C2×#6712yes—
160C2×C3×C4C2×#6711yescharacteristic
161C2×C3×C4C2×C3×D412yes—
162C2×C3×C4C2×C3×D411yescharacteristic
163C2×Dic3—41no—
164Dic6—42no—
165C3×C8—64no—
166C3×C8—121no—
167C3⋊C8—24no—
168C3⋊C8—41no—
169C2×C32#45411yescharacteristic
170C2×C32#45612yes—
171C2×Q8—61no—
172C2×C8—62no—
173C2×C8—61no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—62no—
181C4⋊C4C3×#6712yes—
182C4⋊C4C3×#6712yes—
183C4⋊C4C3×#6712yes—
184C42—22no—
185C42C22×C3×D311yescharacteristic
186C22×C3—21no—
187C22×C3#95311yescharacteristic
188C22×C3C3×#12011yescharacteristic
189C3×C4—21no—
190C3×C4—22no—
191C3×C4—21no—
192C3×C4—22no—
193C3×C4—41no—
194C3×C4—42no—
195C3×C4—44no—
196C3×C4—44no—
197C3×C4—44no—
198C3×C4—42no—
199C3×C4—42no—
200C3×C4—42no—
201C3×C4—42no—
202C3×C4—42no—
203C3×C4—42no—
204C3×C4—241no—
205Dic3—81no—
206C32#166311yescharacteristic, complemented, Sylow
207Q8—122no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—121no—
212C2×C4C2×C3×#6712yes—
213C2×C4C2×C3×#6711yescharacteristic
214C8—64no—
215C8—121no—
216C2×C3—21no—
217C2×C3—22no—
218C2×C3#524511yescharacteristic
219C2×C3#524612yes—
220C2×C3C3×#45411yescharacteristic
221C2×C3C3×#45612yes—
222C22C3×#95311yescharacteristic
223C4—21no—
224C4—22no—
225C4—42no—
226C4—42no—
227C4—42no—
228C4—241no—
229C3—21no—
230C3#7196111yescharacteristic, direct product factor
231C3C3×#166311yescharacteristic, complemented
232C2C3×#524511yescharacteristic
233C2C3×#524612yes—
subgroupG/H
centerC22×C3#953
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#564C2
socle, prime radicalC22×C32#120
hypercenterC3×#564D3
hypocenterC3C3×#1663
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#564

Complements

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

NH ≅ G/Ntype
7. #71961C3direct (N × H)
206. C32#1663semidirect
230. C3#71961direct (N × H)
231. C3C3×#1663semidirect

Maximal subgroups

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

subgroupindex
C32×#5642
C3×#50692
C3×#50642
C3×#45432
C3×#16633
#719613