Finite Group Databasebeta

← #11777322

Subgroups — #11777322

Order 1152.

353 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 353 conjugacy classes of subgroups — too many to draw. Only its 112 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×C8×Dic6C212yesmaximal
2C4×#3718C211yesmaximal, characteristic
3#10589320C211yesmaximal, characteristic
4#10589098C211yesmaximal, characteristic
5#10589083C212yesmaximal
6#70932—32nomaximal
7C3×C4×Dic6C2212yes—
8C2×#3718C411yescharacteristic
9C32×C4×C8C2211yescharacteristic
10C4×C3⋊(C3⋊C8)C2211yescharacteristic
11C4×C3⋊(C3⋊C8)C2211yescharacteristic
12C3×Dic3⋊C8—22no—
13C3×C8×Dic3—22no—
14C3×C4⋊(C3⋊C8)C2212yes—
15#63576C411yescharacteristic
16#63565C412yes—
17C3×C8×Q8—32no—
18C4×#216—32no—
19C8×Dic6D312yes—
20#4535—32no—
21#4484—32no—
22#4480—32no—
23#4454—32no—
24#4454—61no—
25C2×C3×Dic6C2×C412yes—
26C2×C32×C8D412yes—
27C32×C42C2311yescharacteristic
28C2×C3⋊(C3⋊C8)—21no—
29C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
30C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
31C3×C4⋊Dic3C2×C412yes—
32C3×Dic3⋊C4—22no—
33C3×C4×Dic3—22no—
34C2×C3×C3⋊C8—22no—
35#3718C814yescomplemented
36#1579—91noSylow
37C3×C4×Q8—32no—
38C2×#216—32no—
39C4×Dic6C2×D312yes—
40C3×C4⋊C8—32no—
41C3×C4⋊C8—62no—
42C3×C4×C8—21no—
43C3×C4×C8—62no—
44C3×C4×C8C2×D312yes—
45#835—32no—
46Dic3⋊C8—22no—
47C8×Dic3—22no—
48#810—32no—
49#807—32no—
50C4⋊(C3⋊C8)C2×D312yes—
51C4×C3⋊C8—32no—
52C4×C3⋊C8—32no—
53C4×C3⋊C8—61no—
54C4×C3⋊C8—61no—
55C2×C32×C4C22×C411yescharacteristic
56C2×C32×C4C2×D411yescharacteristic
57C2×C32×C4#4111yescharacteristic
58C2×C3×Dic3—22no—
59C2×C3×Dic3—22no—
60C3×Dic6—22no—
61C3×Dic6C2×C814yes—
62C32×C8—22no—
63C3⋊(C3⋊C8)—21no—
64C3⋊(C3⋊C8)—41no—
65C3⋊(C3⋊C8)C2×C812yes—
66C3×C3⋊C8—42no—
67C8×Q8—32no—
68C4×Q16—91no—
69#334—91no—
70Q8⋊C8—92no—
71#322—91no—
72C2×C3×Q8—32no—
73C2×Dic6C4×D312yes—
74C2×C3×C8—22no—
75C2×C3×C8—62no—
76C2×C3×C8#6712yes—
77C2×C3×C8#6712yes—
78C3×C4⋊C4—32no—
79C3×C4⋊C4—62no—
80C3×C42—21no—
81C3×C42—62no—
82C3×C42C22×D312yes—
83#216—38no—
84C4⋊Dic3C4×D312yes—
85Dic3⋊C4—22no—
86C4×Dic3—22no—
87C2×C3⋊C8—22no—
88C2×C3⋊C8—32no—
89C2×C3⋊C8—32no—
90C2×C3⋊C8—61no—
91C2×C3⋊C8—61no—
92C2×C3⋊C8—62no—
93C2×C3⋊C8—62no—
94C22×C32C4×D411yescharacteristic
95C32×C4—21no—
96C32×C4C22×C811yescharacteristic
97C32×C4#13111yescharacteristic
98C32×C4#13712yes—
99C3×Dic3—24no—
100C3×Dic3—42no—
101C2×Q16—91no—
102C4×Q8—32no—
103#107—91no—
104C4⋊C8—32no—
105C4⋊C8—62no—
106#103—92no—
107C4×C8—62no—
108C4×C8—91no—
109C4×C8—91no—
110C4×C8D3211yescharacteristic
111C3×Q8—34no—
112C3×Q8—62no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—62no—
117C2×C3×C4—62no—
118C2×C3×C4C2×C4×D312yes—
119C2×C3×C4#23512yes—
120C2×C3×C4C2×#6712yes—
121C2×Dic3—22no—
122C2×Dic3—22no—
123Dic6—22no—
124Dic6D3×C814yes—
125C3×C8—22no—
126C3×C8—22no—
127C3×C8—42no—
128C3×C8—122no—
129C3⋊C8—34no—
130C3⋊C8—42no—
131C3⋊C8—62no—
132C3⋊C8—62no—
133C3⋊C8—62no—
134C3⋊C8—122no—
135C3⋊C8—122no—
136C2×C32C8×D411yescharacteristic
137C2×C32#44111yescharacteristic
138C2×C32#44411yescharacteristic
139C2×Q8—32no—
140Q16—94no—
141C2×C8—62no—
142C2×C8—91no—
143C2×C8—91no—
144C2×C8—181no—
145C2×C8#62512yes—
146C4⋊C4—32no—
147C4⋊C4—62no—
148C42—62no—
149C42C2×D3211yescharacteristic
150C22×C3—21no—
151C22×C3C4×#6712yes—
152C3×C4—22no—
153C3×C4—22no—
154C3×C4—21no—
155C3×C4—21no—
156C3×C4—22no—
157C3×C4—64no—
158C3×C4—122no—
159C3×C4C2×D3×C812yes—
160C3×C4#90112yes—
161C3×C4#94212yes—
162C3×C4#95112yes—
163Dic3—24no—
164Dic3—42no—
165C32#157911yescharacteristic, complemented, Sylow
166Q8—34no—
167Q8—62no—
168C2×C4—62no—
169C2×C4—62no—
170C2×C4#379811yescharacteristic
171C2×C4C4×D3211yescharacteristic
172C2×C4C2×#62511yescharacteristic
173C8—22no—
174C8—92no—
175C8—122no—
176C8—181no—
177C8—361no—
178C2×C3—21no—
179C2×C3—21no—
180C2×C3—21no—
181C2×C3#503012yes—
182C2×C3C8×#6712yes—
183C2×C3#514512yes—
184C22C4×#62511yescharacteristic
185C4—21no—
186C4—64no—
187C4—122no—
188C4D32×C811yescharacteristic
189C4#6380311yescharacteristic
190C4#6382712yes—
191C3—21no—
192C3#7093212yescomplemented
193C2#1059038111yescharacteristic
194C2C8×#62511yescharacteristic
195C2#1059092211yescharacteristic
subgroupG/H
centerC2×C4C2×#625
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 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
35. #3718C8semidirect
165. C32#1579semidirect
192. C3#70932semidirect

Maximal subgroups

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

subgroupindex
C3×C8×Dic62
C4×#37182
#105893202
#105890982
#105890832
#709323