Finite Group Databasebeta

← #11799504

Subgroups — #11799504

Order 1152.

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

normal subgroups only

This group has 351 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
2#10590902C211yesmaximal, characteristic, complemented
3C3×#4562C212yesmaximal
4#10589139C212yesmaximal, complemented
5#10589133C211yesmaximal, characteristic, complemented
6#69178—32nomaximal
7C2×C32×D8C2211yescharacteristic
8D4×C3⋊Dic3—21no—
9#63919—21no—
10#63659—21no—
11#63645C2211yescharacteristic
12C8×C3⋊Dic3C2211yescharacteristic
13C3×#818C2212yes—
14C2×C3×C3⋊C16C2212yes—
15#63576—21no—
16Dic3×D8—32no—
17Dic3×D8—61no—
18#4874—32no—
19C3×#357—32no—
20#4562D312yes—
21#4504—32no—
22Dic3⋊C16—32no—
23#4489—32no—
24C2×C32×D4—21no—
25C22×C3⋊Dic3—41no—
26C2×#627—41no—
27C32×D8—21no—
28C32×D8Q812yescomplemented
29C2×C32×C8C2311yescharacteristic
30#3757—41no—
31C4⋊(C3⋊Dic3)—21no—
32C4×C3⋊Dic3D411yescharacteristic
33C2×C3⋊(C3⋊C8)D411yescharacteristic
34C3×C4⋊Dic3—22no—
35#3724—41no—
36C3×C3⋊C16—22no—
37#2224—91noSylow
38C2×C3×D8—21no—
39C2×C3×D8C2×D312yes—
40D4×Dic3—62no—
41D4×Dic3—62no—
42#888—62no—
43C2×C3×C16—32no—
44C3×#107—32no—
45#832—62no—
46#832—62no—
47#818—32no—
48#818—61no—
49#818C2×D312yes—
50C8×Dic3—32no—
51C8×Dic3—61no—
52C2×C3⋊C16C2×D312yes—
53#807—62no—
54C23×C32—41no—
55C32×D4—22no—
56C32×D4—41no—
57C2×C32×C4C2×D411yescharacteristic
58C2×C3⋊Dic3—41no—
59C2×C3⋊Dic3—82no—
60C2×C3⋊Dic3D811yescharacteristic
61C2×C3⋊Dic3D811yescharacteristic
62C2×C3×Dic3—42no—
63#627—82no—
64C32×C8C2×Q811yescharacteristic
65C32×C8#4111yescharacteristic
66C3⋊(C3⋊C8)—21no—
67#500—91no—
68C4×D8—91no—
69#366—92no—
70C4⋊C16—91no—
71#357—32no—
72C2×C3×D4—22no—
73C2×C3×D4—22no—
74C22×Dic3—122no—
75C22×Dic3—122no—
76C2×Dic6—122no—
77C3×D8—22no—
78C3×D8—22no—
79C3×D8—22no—
80C3×D8Dic614yescomplemented
81C2×C3×C8—21no—
82C2×C3×C8C22×D312yes—
83C3×C4⋊C4—62no—
84#217—122no—
85#217—122no—
86C4⋊Dic3—22no—
87C4⋊Dic3—62no—
88C4⋊Dic3—62no—
89Dic3⋊C4—122no—
90C4×Dic3—32no—
91C4×Dic3—61no—
92C2×C3⋊C8—32no—
93C2×C3⋊C8—61no—
94C3×C16—62no—
95C3⋊C16—22no—
96C22×C32—42no—
97C22×C32—81no—
98C22×C32—81no—
99C22×C32C2×D811yescharacteristic
100C32×C4C22⋊Q811yescharacteristic
101C32×C4#13711yescharacteristic
102C3⋊Dic3—21no—
103C3⋊Dic3—81no—
104C3⋊Dic3D1612yes—
105C3×Dic3—82no—
106C2×D8D3211yescharacteristic
107C4⋊Q8—181no—
108C4×D4—181no—
109C2×C16—32no—
110#107—32no—
111#107—91no—
112#107—181no—
113#102—181no—
114C4×C8—91no—
115C23×C3—42no—
116C23×C3—42no—
117C3×D4—24no—
118C3×D4—24no—
119C3×D4—42no—
120C3×D4—42no—
121C2×C3×C4—21no—
122C2×C3×C4—122no—
123C2×C3×C4D3×D412yes—
124C2×Dic3—32no—
125C2×Dic3—32no—
126C2×Dic3—42no—
127C2×Dic3—61no—
128C2×Dic3—61no—
129C2×Dic3—122no—
130C2×Dic3—122no—
131C2×Dic3—244no—
132C2×Dic3—244no—
133Dic6—244no—
134C3×C8—21no—
135C3×C8—21no—
136C3×C8C2×Dic612yes—
137C3×C8#23712yes—
138C3⋊C8—62no—
139C3⋊C8—121no—
140C2×C32—82no—
141C2×C32#47411yescharacteristic
142C2×C32C2×D1611yescharacteristic
143C2×C32#51011yescharacteristic
144C2×Q8—361no—
145C2×D4—21no—
146C22×C4—361no—
147D8—21no—
148D8#62712yescomplemented
149C2×C8—91no—
150C2×C8C2×D3211yescharacteristic
151C4⋊C4—62no—
152C4⋊C4—181no—
153C4⋊C4—361no—
154C22⋊C4—361no—
155C42—91no—
156C16—62no—
157C22×C3—21no—
158C22×C3—44no—
159C22×C3—44no—
160C22×C3—82no—
161C22×C3—82no—
162C22×C3—82no—
163C22×C3—82no—
164C22×C3D3×D812yes—
165C3×C4—21no—
166C3×C4—21no—
167C3×C4—242no—
168C3×C4#87812yes—
169C3×C4#91512yes—
170Dic3—34no—
171Dic3—62no—
172Dic3—62no—
173Dic3—82no—
174Dic3—121no—
175Dic3—242no—
176Dic3—242no—
177C32#222411yescharacteristic, complemented, Sylow
178C23—41no—
179Q8—722no—
180D4—22no—
181D4—41no—
182C2×C4—91no—
183C2×C4—91no—
184C2×C4—122no—
185C2×C4—361no—
186C2×C4—722no—
187C2×C4#381111yescharacteristic
188C8—181no—
189C8#380511yescharacteristic
190C8C2×#62711yescharacteristic
191C2×C3—21no—
192C2×C3—21no—
193C2×C3—21no—
194C2×C3—84no—
195C2×C3—84no—
196C2×C3#475912yes—
197C2×C3D3×D1612yes—
198C2×C3#491512yes—
199C22—42no—
200C22—81no—
201C22—81no—
202C22#6392611yescharacteristic
203C4—92no—
204C4—181no—
205C4—242no—
206C4—721no—
207C4#6393111yescharacteristic
208C4#6398211yescharacteristic
209C3—21no—
210C3#6917812yescomplemented
211C2—82no—
212C2#1059102511yescharacteristic
213C2#1059103011yescharacteristic
214C2#1059149411yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
Fitting, prime radicalC2×C32×D8C22
socleC22×C32C2×D8
hypercenterC2×D8D32
hypocenterC32#2224
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
2. #10590902C2semidirect
4. #10589139C2semidirect
5. #10589133C2semidirect
28. C32×D8Q8semidirect
80. C3×D8Dic6semidirect
148. D8#627semidirect
177. C32#2224semidirect
210. C3#69178semidirect

Maximal subgroups

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

subgroupindex
D8×C3⋊Dic32
#105909022
C3×#45622
#105891392
#105891332
#691783