Finite Group Databasebeta

← #11777326

Subgroups — #11777326

Order 1152.

353 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 353 conjugacy classes of subgroups — too many to draw. Only its 126 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×C4×Dic12C211yesmaximal, characteristic
2#10590250C212yesmaximal
3#10589321C211yesmaximal, characteristic
4C3×#4457C211yesmaximal, characteristic
5#10589083C212yesmaximal
6#70902—31nomaximal
7#68517—31nomaximal
8C2×C3×Dic12C411yescharacteristic
9C3×C4×Dic6C2212yes—
10C32×C4×C8C2211yescharacteristic
11C4×C3⋊(C3⋊C8)C2211yescharacteristic
12C4×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×#818C411yescharacteristic
14C3×#816C412yes—
15C3×C4⋊(C3⋊C8)C2212yes—
16Dic3⋊(C3⋊C8)—22no—
17Dic3×C3⋊C8—22no—
18C3×C4×Q16—31no—
19Q8×C3⋊C8—32no—
20#4830—32no—
21C4×Dic12D311yescharacteristic
22C3×#334—31no—
23#4535—32no—
24#4484—32no—
25#4457D311yescharacteristic
26#4455—31no—
27#4455—31no—
28#4455—61no—
29C2×C3×Dic6C2×C412yes—
30C2×C32×C8C2×C411yescharacteristic
31C2×C32×C8C2×C411yescharacteristic
32C32×C42C2311yescharacteristic
33C2×C3⋊(C3⋊C8)—21no—
34C2×C3⋊(C3⋊C8)D412yes—
35C3×C4⋊Dic3C2×C412yes—
36C3×Dic3⋊C4—22no—
37C3×C4×Dic3—22no—
38C2×C3×C3⋊C8—22no—
39C3×Dic12C814yescomplemented
40#1579—91noSylow
41C2×C3×Q16—31no—
42C3×C4×Q8—32no—
43C2×Dic12Dic311yescharacteristic
44C4×Dic6C2×D312yes—
45C3×#107—31no—
46C3×C4⋊C8—32no—
47C3×#103—32no—
48C3×C4×C8—21no—
49C3×C4×C8C2×D311yescharacteristic
50C3×C4×C8C2×D311yescharacteristic
51#818Dic311yescharacteristic
52#816Dic312yes—
53Dic3⋊C8—62no—
54C8×Dic3—62no—
55C4⋊(C3⋊C8)—62no—
56C4⋊(C3⋊C8)C2×D312yes—
57C4×C3⋊C8—31no—
58C4×C3⋊C8—31no—
59C4×C3⋊C8—31no—
60C4×C3⋊C8—31no—
61C4×C3⋊C8—61no—
62C4×C3⋊C8—61no—
63C4×C3⋊C8—62no—
64C2×C32×C4C22×C411yescharacteristic
65C2×C32×C4C2×D411yescharacteristic
66C2×C32×C4#4111yescharacteristic
67C2×C3×Dic3—22no—
68C2×C3×Dic3—22no—
69C3×Dic6—22no—
70C3×Dic6C2×C814yes—
71C32×C8—21no—
72C32×C8C2×C812yes—
73C3⋊(C3⋊C8)—22no—
74C3⋊(C3⋊C8)—41no—
75C3×C3⋊C8—42no—
76C8×Q8—92no—
77C4×Q16—31no—
78#334—31no—
79Q8⋊C8—92no—
80#322—91no—
81C2×C3×Q8—32no—
82C2×Dic6C2×Dic312yes—
83C3×Q16—34no—
84C2×C3×C8—21no—
85C2×C3×C8—21no—
86C2×C3×C8—62no—
87C2×C3×C8C4×D311yescharacteristic
88C2×C3×C8C4×D311yescharacteristic
89C2×C3×C8C2×Dic311yescharacteristic
90C2×C3×C8C2×Dic311yescharacteristic
91C3×C4⋊C4—32no—
92C3×C4⋊C4—62no—
93C3×C42—21no—
94C3×C42—62no—
95C3×C42C22×D311yescharacteristic
96C3×C42C22×D311yescharacteristic
97C4⋊Dic3C2×Dic312yes—
98Dic3⋊C4—22no—
99C4×Dic3—22no—
100C2×C3⋊C8—22no—
101C2×C3⋊C8—32no—
102C2×C3⋊C8—32no—
103C2×C3⋊C8—62no—
104C2×C3⋊C8—62no—
105C2×C3⋊C8—61no—
106C2×C3⋊C8—61no—
107Dic12C3⋊C814yescomplemented
108C22×C32C4×D411yescharacteristic
109C32×C4—21no—
110C32×C4C22×C811yescharacteristic
111C32×C4#13111yescharacteristic
112C32×C4#13712yes—
113C3×Dic3—24no—
114C3×Dic3—42no—
115C2×Q16—31no—
116C4×Q8—32no—
117#107—31no—
118C4⋊C8—32no—
119C4⋊C8—182no—
120#103—32no—
121C4×C8—91no—
122C4×C8—91no—
123C4×C8—182no—
124C4×C8D3211yescharacteristic
125C3×Q8—34no—
126C3×Q8—62no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—62no—
131C2×C3×C4—62no—
132C2×C3×C4C2×C4×D311yescharacteristic
133C2×C3×C4D3×D411yescharacteristic
134C2×C3×C4D3×D411yescharacteristic
135C2×C3×C4#23711yescharacteristic
136C2×C3×C4#23911yescharacteristic
137C2×C3×C4C22×Dic311yescharacteristic
138C2×Dic3—22no—
139C2×Dic3—22no—
140Dic6—22no—
141Dic6C2×C3⋊C814yes—
142C3×C8—22no—
143C3×C8—21no—
144C3×C8—21no—
145C3×C8—22no—
146C3×C8—122no—
147C3×C8D3×C812yes—
148C3×C8C2×C3⋊C812yes—
149C3⋊C8—42no—
150C3⋊C8—62no—
151C3⋊C8—62no—
152C3⋊C8—122no—
153C3⋊C8—122no—
154C3⋊C8—121no—
155C3⋊C8—121no—
156C2×C32C8×D411yescharacteristic
157C2×C32#44111yescharacteristic
158C2×C32#44411yescharacteristic
159C2×Q8—32no—
160Q16—34no—
161C2×C8—62no—
162C2×C8—92no—
163C2×C8—181no—
164C2×C8D3×Dic311yescharacteristic
165C2×C8D3×Dic311yescharacteristic
166C4⋊C4—32no—
167C4⋊C4—62no—
168C42—62no—
169C42C2×D3211yescharacteristic
170C22×C3—21no—
171C22×C3#89311yescharacteristic
172C22×C3D4×Dic311yescharacteristic
173C3×C4—22no—
174C3×C4—21no—
175C3×C4—21no—
176C3×C4—22no—
177C3×C4—21no—
178C3×C4—21no—
179C3×C4—64no—
180C3×C4—122no—
181C3×C4C2×D3×C811yescharacteristic
182C3×C4#90711yescharacteristic
183C3×C4#91512yes—
184C3×C4#91812yes—
185C3×C4C22×C3⋊C811yescharacteristic
186C3×C4#94811yescharacteristic
187Dic3—24no—
188Dic3—42no—
189C32#157911yescharacteristic, complemented, Sylow
190Q8—34no—
191Q8—62no—
192C2×C4—62no—
193C2×C4—62no—
194C2×C4#379611yescharacteristic
195C2×C4#380211yescharacteristic
196C2×C4C2×D3×Dic311yescharacteristic
197C8—21no—
198C8—122no—
199C8—182no—
200C8—361no—
201C8D3×C3⋊C812yes—
202C2×C3—21no—
203C2×C3—21no—
204C2×C3—21no—
205C2×C3#483411yescharacteristic
206C2×C3#485311yescharacteristic
207C2×C3#489411yescharacteristic
208C2×C3D4×C3⋊C811yescharacteristic
209C2×C3#518411yescharacteristic
210C2×C3#519711yescharacteristic
211C22#6389811yescharacteristic
212C4—21no—
213C4—64no—
214C4—122no—
215C4#6381112yes—
216C4C2×D3×C3⋊C811yescharacteristic
217C4#6381511yescharacteristic
218C3—21no—
219C3#6851711yescharacteristic, complemented
220C3#7090211yescharacteristic, complemented
221C2#1059032911yescharacteristic
222C2#1059081911yescharacteristic
223C2#1059092011yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC32×C4C22×C8
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32C4×D4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1579
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
39. C3×Dic12C8semidirect
107. Dic12C3⋊C8semidirect
189. C32#1579semidirect
219. C3#68517semidirect
220. C3#70902semidirect

Maximal subgroups

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

subgroupindex
C3×C4×Dic122
#105902502
#105893212
C3×#44572
#105890832
#709023
#685173