Finite Group Databasebeta

← #11780716

Subgroups — #11780716

Order 1152.

389 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 389 conjugacy classes of subgroups — too many to draw. Only its 76 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×C3⋊#564C211yesmaximal, characteristic
2#10592768C211yesmaximal, characteristic
3#10590306C212yesmaximal
4C3×#4543C211yesmaximal, characteristic
5#10589088C212yesmaximal
6#71961—31nomaximal
7#68377—31nomaximal
8C32×#125C2211yescharacteristic
9#64078C2211yescharacteristic
10C3×#890—22no—
11C3×#889—22no—
12C3×#889—22no—
13C3×#870C2212yes—
14#63637—22no—
15#63630C2211yescharacteristic
16C3×#803C2212yes—
17#63575—22no—
18#63573—22no—
19C3×#564—31no—
20C3⋊#564D311yescharacteristic
21#5069—31no—
22#5069—31no—
23#5069—61no—
24#5064—32no—
25#4702—32no—
26C3×#330—31no—
27#4543—32no—
28#4543D311yescharacteristic
29#4465—32no—
30C2×#634—21no—
31C32×C4⋊C4—22no—
32C32×C4⋊C4D412yes—
33C32×C42C2311yescharacteristic
34C4⋊(C3⋊Dic3)—22no—
35C2×C3⋊(C3⋊C8)—21no—
36C3×C4⋊Dic3—22no—
37C3×C4⋊Dic3D412yes—
38C3×C4⋊Dic3D412yes—
39C3×Dic3⋊C4—22no—
40C3×Dic3⋊C4—22no—
41C3×Dic3⋊C4—22no—
42C3×Dic3⋊C4—22no—
43C3×C4×Dic3—22no—
44C2×C3×C3⋊C8—22no—
45#1663—91noSylow
46C3×#125—21no—
47C3×#125—32no—
48C3×#125—62no—
49C3×#125—62no—
50C3×#125—62no—
51C3×#125C2×D311yescharacteristic
52C3×#125C2×D311yescharacteristic
53#890—22no—
54#889—22no—
55#889—22no—
56#870C2×D312yes—
57#869—31no—
58#869—31no—
59#869—61no—
60C3×#97—32no—
61#818—62no—
62#817—62no—
63#810—64no—
64#810—62no—
65#810—62no—
66#808—62no—
67#807—62no—
68#803—31no—
69#803—31no—
70#803—61no—
71#803C2×D312yes—
72C2×C32×C4—22no—
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4C2×D412yes—
75C2×C3⋊Dic3—41no—
76#634—42no—
77C2×C3×Dic3—22no—
78C2×C3×Dic3—22no—
79C3⋊(C3⋊C8)—41no—
80C3×C3⋊C8—24no—
81#564—31no—
82#501—92no—
83#491—91no—
84#330—31no—
85#330—92no—
86C2×Dic6—62no—
87C2×Dic6—61no—
88C2×Dic6—61no—
89C2×C3×C8—62no—
90C3×C4⋊C4—22no—
91C3×C4⋊C4—22no—
92C3×C4⋊C4—22no—
93C3×C4⋊C4—32no—
94C3×C4⋊C4—32no—
95C3×C4⋊C4—42no—
96C3×C4⋊C4—62no—
97C3×C4⋊C4—62no—
98C3×C4⋊C4—62no—
99C3×C4⋊C4—62no—
100C3×C4⋊C4—62no—
101C3×C4⋊C4D1212yes—
102C3×C4⋊C4#6712yes—
103C3×C42—21no—
104C3×C42—62no—
105C3×C42C22×D311yescharacteristic
106C3×C42C22×D311yescharacteristic
107C4⋊Dic3—22no—
108C4⋊Dic3—62no—
109C4⋊Dic3—62no—
110C4⋊Dic3—122no—
111C4⋊Dic3#6712yes—
112C4⋊Dic3#6712yes—
113Dic3⋊C4—22no—
114Dic3⋊C4—22no—
115Dic3⋊C4—22no—
116Dic3⋊C4—22no—
117C4×Dic3—22no—
118C2×C3⋊C8—22no—
119C2×C3⋊C8—62no—
120C2×C3⋊C8—61no—
121C2×C3⋊C8—61no—
122C22×C32#12011yescharacteristic
123C32×C4—21no—
124C32×C4—22no—
125C32×C4—42no—
126C3⋊Dic3—81no—
127C3×Dic3—42no—
128C3×Dic3—42no—
129C4⋊Q8—91no—
130#125—32no—
131#125—62no—
132#125—62no—
133#125—62no—
134#125D3211yescharacteristic
135#107—182no—
136#106—182no—
137#103—182no—
138#97—32no—
139#97—91no—
140C2×C3×C4—22no—
141C2×C3×C4—22no—
142C2×C3×C4—21no—
143C2×C3×C4—22no—
144C2×C3×C4—42no—
145C2×C3×C4—62no—
146C2×C3×C4—62no—
147C2×C3×C4C2×D1211yescharacteristic
148C2×C3×C4D3×D412yes—
149C2×C3×C4C2×#6711yescharacteristic
150C2×C3×C4C2×#6712yes—
151C2×Dic3—22no—
152C2×Dic3—22no—
153C2×Dic3—122no—
154C2×Dic3—121no—
155C2×Dic3—121no—
156Dic6—124no—
157Dic6—122no—
158Dic6—122no—
159C3×C8—64no—
160C3⋊C8—24no—
161C3⋊C8—122no—
162C3⋊C8—121no—
163C3⋊C8—121no—
164C2×C32#45411yescharacteristic
165C2×C32#45612yes—
166C2×Q8—181no—
167C2×C8—62no—
168C2×C8—181no—
169C4⋊C4—22no—
170C4⋊C4—32no—
171C4⋊C4—32no—
172C4⋊C4—62no—
173C4⋊C4—62no—
174C4⋊C4—62no—
175C4⋊C4—62no—
176C4⋊C4—62no—
177C4⋊C4—182no—
178C4⋊C4#62612yes—
179C42—62no—
180C42C2×D3211yescharacteristic
181C22×C3—21no—
182C22×C3#88211yescharacteristic
183C22×C3#95311yescharacteristic
184C3×C4—22no—
185C3×C4—21no—
186C3×C4—22no—
187C3×C4—21no—
188C3×C4—22no—
189C3×C4—42no—
190C3×C4—42no—
191C3×C4—42no—
192C3×C4—82no—
193C3×C4—122no—
194C3×C4—122no—
195Dic3—42no—
196Dic3—42no—
197Dic3—242no—
198Dic3—241no—
199Dic3—241no—
200C32#166311yescharacteristic, complemented, Sylow
201Q8—362no—
202C2×C4—22no—
203C2×C4—62no—
204C2×C4—62no—
205C2×C4—361no—
206C2×C4C2×#62611yescharacteristic
207C2×C4D3×#6712yes—
208C8—64no—
209C8—361no—
210C2×C3—21no—
211C2×C3—22no—
212C2×C3#475311yescharacteristic
213C2×C3#482612yes—
214C2×C3#524511yescharacteristic
215C2×C3#524612yes—
216C22#6397711yescharacteristic
217C4—21no—
218C4—22no—
219C4—42no—
220C4—122no—
221C4—122no—
222C4—721no—
223C3—21no—
224C3#6837711yescharacteristic, complemented
225C3#7196111yescharacteristic, complemented
226C2#1059164611yescharacteristic
227C2#1059168912yes—
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#125C22
socle, prime radicalC22×C32#120
hypercenter#125D32
hypocenterC32#1663
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
200. C32#1663semidirect
224. C3#68377semidirect
225. C3#71961semidirect

Maximal subgroups

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

subgroupindex
C3×C3⋊#5642
#105927682
#105903062
C3×#45432
#105890882
#719613
#683773