Finite Group Databasebeta

← #11798918

Subgroups — #11798918

Order 1152.

399 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 399 conjugacy classes of subgroups — too many to draw. Only its 82 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
1D8×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#827C212yesmaximal
3#10590905C211yesmaximal, characteristic, complemented
4#10589133C211yesmaximal, characteristic, complemented
5#10589118C212yesmaximal, complemented
6#71476—32nomaximal
7C2×C32×D8C2211yescharacteristic
8D4×C3⋊Dic3—21no—
9C2×C3×Dic12C2212yes—
10#63873—21no—
11C2×#3718—21no—
12#63659—21no—
13#63645C2211yescharacteristic
14C8×C3⋊Dic3C2211yescharacteristic
15C3×#827—24no—
16C2×C3×C3⋊C16C2212yes—
17C2×C3×SD32—32no—
18#5183—32no—
19Dic3×D8—32no—
20Dic3×D8—61no—
21C2×#827D312yes—
22#4564—32no—
23#4503—32no—
24Dic3⋊C16—32no—
25C2×C32×D4—21no—
26C22×C3⋊Dic3—41no—
27C2×C3×Dic6—22no—
28C32×D8—21no—
29C32×D8D412yes—
30C2×C32×C8C2311yescharacteristic
31#3757—41no—
32C4⋊(C3⋊Dic3)—21no—
33C4×C3⋊Dic3D411yescharacteristic
34C2×C3⋊(C3⋊C8)D411yescharacteristic
35C3×Dic12—22no—
36C3×Dic12—22no—
37#3724—41no—
38#3724—41no—
39#3718—42no—
40C3×C3⋊C16—22no—
41#2208—91noSylow
42C2×C3×Q16—32no—
43C2×C3×D8—21no—
44C2×C3×D8C2×D312yes—
45#944—62no—
46C2×#216—62no—
47D4×Dic3—62no—
48D4×Dic3—62no—
49C2×Dic12C2×D312yes—
50C3×SD32—64no—
51C2×C3×C16—32no—
52#832—62no—
53#832—62no—
54#827—24no—
55#818—32no—
56#818—61no—
57C8×Dic3—32no—
58C8×Dic3—61no—
59C2×C3⋊C16C2×D312yes—
60C23×C32—41no—
61C32×D4—22no—
62C32×D4—41no—
63C2×C32×C4C2×D411yescharacteristic
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3—82no—
66C2×C3⋊Dic3D811yescharacteristic
67C2×C3⋊Dic3D811yescharacteristic
68C2×C3×Dic3—42no—
69C3×Dic6—42no—
70C3×Dic6—42no—
71C32×C8C2×D411yescharacteristic
72C32×C8#4111yescharacteristic
73C3⋊(C3⋊C8)—21no—
74C2×SD32—32no—
75#494—91no—
76C4×D8—91no—
77C4⋊C16—91no—
78#358—92no—
79C2×C3×Q8—62no—
80C2×C3×D4—22no—
81C2×C3×D4—22no—
82C22×Dic3—122no—
83C22×Dic3—122no—
84C2×Dic6—22no—
85C3×Q16—62no—
86C3×Q16—62no—
87C3×D8—22no—
88C3×D8—22no—
89C3×D8—22no—
90C3×D8#6714yes—
91C2×C3×C8—21no—
92C2×C3×C8C22×D312yes—
93#217—122no—
94#217—122no—
95#216—124no—
96C4⋊Dic3—62no—
97C4⋊Dic3—62no—
98Dic3⋊C4—122no—
99Dic3⋊C4—122no—
100C4×Dic3—32no—
101C4×Dic3—61no—
102C2×C3⋊C8—32no—
103C2×C3⋊C8—61no—
104Dic12—22no—
105Dic12—22no—
106C3×C16—62no—
107C3⋊C16—22no—
108C22×C32—42no—
109C22×C32—81no—
110C22×C32—81no—
111C22×C32C2×D811yescharacteristic
112C32×C4#12111yescharacteristic
113C32×C4AGL(1,ℤ/8)11yescharacteristic
114C3⋊Dic3—21no—
115C3⋊Dic3—81no—
116C3⋊Dic3SD3212yescomplemented
117C3×Dic3—82no—
118C2×Q16—32no—
119C2×Q16—181no—
120C2×D8D3211yescharacteristic
121C4⋊Q8—181no—
122C4×D4—181no—
123SD32—64no—
124C2×C16—32no—
125#107—91no—
126#102—181no—
127C4×C8—91no—
128C23×C3—42no—
129C23×C3—42no—
130C3×Q8—122no—
131C3×Q8—122no—
132C3×D4—24no—
133C3×D4—24no—
134C3×D4—42no—
135C3×D4—42no—
136C2×C3×C4—21no—
137C2×C3×C4—122no—
138C2×C3×C4D3×D412yes—
139C2×Dic3—32no—
140C2×Dic3—32no—
141C2×Dic3—42no—
142C2×Dic3—61no—
143C2×Dic3—61no—
144C2×Dic3—122no—
145C2×Dic3—122no—
146C2×Dic3—244no—
147C2×Dic3—244no—
148Dic6—42no—
149Dic6—42no—
150C3×C8—21no—
151C3×C8—21no—
152C3×C8#23712yes—
153C3×C8C2×#6712yes—
154C3⋊C8—62no—
155C3⋊C8—121no—
156C2×C32—82no—
157C2×C32#45911yescharacteristic
158C2×C32C2×SD3211yescharacteristic
159C2×C32#51011yescharacteristic
160C2×Q8—62no—
161C2×D4—21no—
162C22×C4—361no—
163Q16—62no—
164Q16—62no—
165Q16—362no—
166D8—21no—
167D8#62512yes—
168C2×C8—91no—
169C2×C8C2×D3211yescharacteristic
170C4⋊C4—181no—
171C4⋊C4—361no—
172C4⋊C4—361no—
173C22⋊C4—361no—
174C42—91no—
175C16—62no—
176C22×C3—21no—
177C22×C3—44no—
178C22×C3—44no—
179C22×C3—82no—
180C22×C3—82no—
181C22×C3—82no—
182C22×C3—82no—
183C22×C3D3×D812yes—
184C3×C4—21no—
185C3×C4—21no—
186C3×C4—242no—
187C3×C4#91112yes—
188C3×C4#93912yes—
189Dic3—34no—
190Dic3—62no—
191Dic3—62no—
192Dic3—82no—
193Dic3—121no—
194Dic3—242no—
195Dic3—242no—
196C32#220811yescharacteristic, complemented, Sylow
197C23—41no—
198Q8—122no—
199Q8—122no—
200D4—22no—
201D4—41no—
202C2×C4—91no—
203C2×C4—91no—
204C2×C4—122no—
205C2×C4—361no—
206C2×C4—722no—
207C2×C4#381111yescharacteristic
208C8—181no—
209C8#380511yescharacteristic
210C8C2×#62511yescharacteristic
211C2×C3—21no—
212C2×C3—21no—
213C2×C3—21no—
214C2×C3—84no—
215C2×C3—84no—
216C2×C3D3×SD3212yes—
217C2×C3#491512yes—
218C2×C3#515012yes—
219C22—42no—
220C22—81no—
221C22—81no—
222C22#6392611yescharacteristic
223C4—92no—
224C4—181no—
225C4—242no—
226C4—721no—
227C4#6392711yescharacteristic
228C4#6398011yescharacteristic
229C3—21no—
230C3#7147612yescomplemented
231C2—82no—
232C2#1059102911yescharacteristic
233C2#1059103011yescharacteristic
234C2#1059148611yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
Fitting, prime radicalC2×C32×D8C22
socleC22×C32C2×D8
hypercenterC2×D8D32
hypocenterC32#2208
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
3. #10590905C2semidirect
4. #10589133C2semidirect
5. #10589118C2semidirect
116. C3⋊Dic3SD32semidirect
196. C32#2208semidirect
230. C3#71476semidirect

Maximal subgroups

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

subgroupindex
D8×C3⋊Dic32
C2×C3×#8272
#105909052
#105891332
#105891182
#714763