Finite Group Databasebeta

← #11777241

Subgroups — #11777241

Order 1152.

365 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 365 conjugacy classes of subgroups — too many to draw. Only its 108 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
1C4×#3718C211yesmaximal, characteristic
2#10590250C212yesmaximal
3C8×C3⋊(C3⋊C8)C211yesmaximal, characteristic
4C3×#4456C212yesmaximal
5#10589100C211yesmaximal, characteristic
6#68213—32nomaximal
7C3×C4×Dic6C2212yes—
8C2×#3718C411yescharacteristic
9C32×C4×C8C2211yescharacteristic
10C4×C3⋊(C3⋊C8)C2211yescharacteristic
11C4×C3⋊(C3⋊C8)C2211yescharacteristic
12C3×C4⋊(C3⋊C8)C2212yes—
13#63576C411yescharacteristic
14Dic3⋊(C3⋊C8)—22no—
15#63565C412yes—
16Dic3×C3⋊C8—22no—
17C4×#216—32no—
18Q8×C3⋊C8—32no—
19#4830—32no—
20C3×Q8⋊C8—32no—
21#4479—32no—
22#4456D312yes—
23C8×C3⋊C8—32no—
24C8×C3⋊C8—61no—
25C2×C3×Dic6C2×C412yes—
26C2×C32×C8—21no—
27C32×C42C2311yescharacteristic
28C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
29C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
30C2×C3⋊(C3⋊C8)D411yescharacteristic
31C2×C3⋊(C3⋊C8)D411yescharacteristic
32C3×C4⋊Dic3C2×C412yes—
33C3×Dic3⋊C4—22no—
34C3×C4×Dic3—22no—
35C2×C3×C3⋊C8—22no—
36#3718C814yescomplemented
37C8×Q16—91noSylow
38C3×C4×Q8—32no—
39C2×#216—32no—
40C4×Dic6C2×D312yes—
41C3×C4⋊C8—32no—
42C3×C4×C8—21no—
43C3×C4×C8C2×D312yes—
44#835—32no—
45Dic3⋊C8—62no—
46C8×Dic3—62no—
47#810—32no—
48#807—32no—
49C4⋊(C3⋊C8)—62no—
50C4⋊(C3⋊C8)C2×D312yes—
51C4×C3⋊C8—32no—
52C4×C3⋊C8—32no—
53C4×C3⋊C8—61no—
54C4×C3⋊C8—61no—
55C4×C3⋊C8—62no—
56C2×C32×C4C22×C411yescharacteristic
57C2×C32×C4C2×D411yescharacteristic
58C2×C32×C4#4111yescharacteristic
59C2×C3×Dic3—22no—
60C2×C3×Dic3—22no—
61C3×Dic6—22no—
62C3×Dic6C2×C814yes—
63C32×C8—22no—
64C3⋊(C3⋊C8)—21no—
65C3⋊(C3⋊C8)—21no—
66C3⋊(C3⋊C8)C2×C812yes—
67C3⋊(C3⋊C8)Q1612yescomplemented
68C3×C3⋊C8—42no—
69C8×Q8—92no—
70C4×Q16—91no—
71#335—91no—
72Q8⋊C8—32no—
73C82—91no—
74C2×C3×Q8—32no—
75C2×Dic6C4×D312yes—
76C2×C3×C8—22no—
77C2×C3×C8—22no—
78C2×C3×C8—62no—
79C3×C4⋊C4—32no—
80C3×C4⋊C4—62no—
81C3×C42—21no—
82C3×C42—62no—
83C3×C42C22×D312yes—
84#216—38no—
85C4⋊Dic3C4×D312yes—
86Dic3⋊C4—22no—
87C4×Dic3—22no—
88C2×C3⋊C8—22no—
89C2×C3⋊C8—32no—
90C2×C3⋊C8—32no—
91C2×C3⋊C8—32no—
92C2×C3⋊C8—32no—
93C2×C3⋊C8—61no—
94C2×C3⋊C8—61no—
95C2×C3⋊C8—61no—
96C2×C3⋊C8—61no—
97C22×C32C4×D411yescharacteristic
98C32×C4—21no—
99C32×C4C22×C811yescharacteristic
100C32×C4#13111yescharacteristic
101C32×C4C2×Q1611yescharacteristic
102C32×C4#13511yescharacteristic
103C3×Dic3—24no—
104C3×Dic3—42no—
105C2×Q16—91no—
106C4×Q8—32no—
107#107—91no—
108C4⋊C8—32no—
109C4⋊C8—182no—
110#103—92no—
111C4×C8—91no—
112C4×C8—91no—
113C4×C8—182no—
114C4×C8D3211yescharacteristic
115C3×Q8—34no—
116C3×Q8—62no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—21no—
120C2×C3×C4—62no—
121C2×C3×C4—62no—
122C2×C3×C4C2×C4×D312yes—
123C2×C3×C4D3×D412yes—
124C2×C3×C4#23712yes—
125C2×Dic3—22no—
126C2×Dic3—22no—
127Dic6—22no—
128Dic6D3×C814yes—
129C3×C8—24no—
130C3×C8—24no—
131C3×C8—122no—
132C3⋊C8—34no—
133C3⋊C8—34no—
134C3⋊C8—42no—
135C3⋊C8—62no—
136C3⋊C8—62no—
137C3⋊C8—62no—
138C3⋊C8—62no—
139C3⋊C8—62no—
140C3⋊C8—62no—
141C2×C32C8×D411yescharacteristic
142C2×C32C4×Q1611yescharacteristic
143C2×C32#44311yescharacteristic
144C2×Q8—32no—
145Q16—94no—
146C2×C8—21no—
147C2×C8—62no—
148C2×C8—91no—
149C2×C8—91no—
150C2×C8—91no—
151C2×C8—91no—
152C4⋊C4—32no—
153C4⋊C4—62no—
154C42—62no—
155C42C2×D3211yescharacteristic
156C22×C3—21no—
157C22×C3#67⋊C412yes—
158C3×C4—22no—
159C3×C4—22no—
160C3×C4—21no—
161C3×C4—21no—
162C3×C4—21no—
163C3×C4—21no—
164C3×C4—64no—
165C3×C4—122no—
166C3×C4C2×D3×C812yes—
167C3×C4#90712yes—
168C3×C4#91612yes—
169C3×C4D3×Q1612yes—
170Dic3—24no—
171Dic3—42no—
172C32C8×Q1611yescharacteristic, complemented, Sylow
173Q8—34no—
174Q8—62no—
175C2×C4—62no—
176C2×C4—62no—
177C2×C4C4×D3211yescharacteristic
178C2×C4#380211yescharacteristic
179C2×C4#380511yescharacteristic
180C8—22no—
181C8—92no—
182C8—92no—
183C8—122no—
184C8—181no—
185C8—181no—
186C2×C3—21no—
187C2×C3—21no—
188C2×C3—21no—
189C2×C3#67⋊C812yes—
190C2×C3#479012yes—
191C2×C3#482412yes—
192C22#6390211yescharacteristic
193C4—21no—
194C4—64no—
195C4—122no—
196C4D32×C811yescharacteristic
197C4#6380211yescharacteristic
198C4#6380511yescharacteristic
199C4#6380911yescharacteristic
200C3—21no—
201C3#6821312yescomplemented
202C2#1059038911yescharacteristic
203C2#1059071811yescharacteristic
204C2#1059079011yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC32×C4C22×C8
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32C4×D4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32C8×Q16
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
36. #3718C8semidirect
67. C3⋊(C3⋊C8)Q16semidirect
172. C32C8×Q16semidirect
201. C3#68213semidirect

Maximal subgroups

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

subgroupindex
C4×#37182
#105902502
C8×C3⋊(C3⋊C8)2
C3×#44562
#105891002
#682133