Finite Group Databasebeta

← #11777939

Subgroups — #11777939

Order 1152.

329 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 329 conjugacy classes of subgroups — too many to draw. Only its 94 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#10590259C212yesmaximal
3#10589320C211yesmaximal, characteristic
4C3×#4456C212yesmaximal
5#10589098C211yesmaximal, characteristic
6#68227—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—
16#63554—22no—
17C4×#216—32no—
18#5024—32no—
19#4831—32no—
20C3×Q8⋊C8—32no—
21#4480—32no—
22#4456D312yes—
23#4454—32no—
24#4454—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)D412yes—
31C3×C4⋊Dic3C2×C412yes—
32C3×Dic3⋊C4—22no—
33C3×C4×Dic3—22no—
34C2×C3×C3⋊C8—22no—
35#3718—22no—
36#1593—91noSylow
37C3×C4×Q8—32no—
38C2×#216—32no—
39C4×Dic6C2×D312yes—
40C3×C4⋊C8—32no—
41C3×C4×C8—21no—
42C3×C4×C8C2×D312yes—
43#835—32no—
44#815—62no—
45Dic3⋊C8—62no—
46#810—32no—
47#807—32no—
48C4⋊(C3⋊C8)—62no—
49C4⋊(C3⋊C8)C2×D312yes—
50#803—62no—
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×Dic6—22no—
62C32×C8—41no—
63C3⋊(C3⋊C8)—21no—
64C3⋊(C3⋊C8)—22no—
65C3⋊(C3⋊C8)M1612yes—
66C3×C3⋊C8—42no—
67#446—92no—
68C4×Q16—91no—
69#334—91no—
70Q8⋊C8—32no—
71#322—91no—
72C2×C3×Q8—32no—
73C2×Dic6C4×D312yes—
74C2×C3×C8—22no—
75C2×C3×C8—22no—
76C2×C3×C8—62no—
77C3×C4⋊C4—32no—
78C3×C4⋊C4—62no—
79C3×C42—21no—
80C3×C42—62no—
81C3×C42C22×D312yes—
82#216—64no—
83C4⋊Dic3C4×D312yes—
84Dic3⋊C4—22no—
85C4×Dic3—22no—
86C2×C3⋊C8—22no—
87C2×C3⋊C8—32no—
88C2×C3⋊C8—32no—
89C2×C3⋊C8—32no—
90C2×C3⋊C8—32no—
91C2×C3⋊C8—61no—
92C2×C3⋊C8—61no—
93C2×C3⋊C8—62no—
94C22×C32C4×D411yescharacteristic
95C32×C4—21no—
96C32×C4C2×M1611yescharacteristic
97C32×C4#13111yescharacteristic
98C32×C4#13712yes—
99C3×Dic3—42no—
100C3×Dic3—42no—
101C2×Q16—91no—
102C4×Q8—32no—
103#107—91no—
104C4⋊C8—32no—
105C4⋊C8—182no—
106#103—92no—
107#97—182no—
108C4×C8—91no—
109C4×C8—91no—
110C4×C8D3211yescharacteristic
111C3×Q8—62no—
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×C4D3×D412yes—
120C2×C3×C4#23712yes—
121C2×Dic3—22no—
122C2×Dic3—22no—
123Dic6—22no—
124Dic6—22no—
125C3×C8—42no—
126C3×C8—42no—
127C3×C8—122no—
128C3⋊C8—34no—
129C3⋊C8—42no—
130C3⋊C8—62no—
131C3⋊C8—62no—
132C3⋊C8—62no—
133C3⋊C8—62no—
134C3⋊C8—62no—
135C3⋊C8—122no—
136C2×C32#43611yescharacteristic
137C2×C32#44111yescharacteristic
138C2×C32#44411yescharacteristic
139C2×Q8—32no—
140Q16—182no—
141C2×C8—21no—
142C2×C8—62no—
143C2×C8—91no—
144C2×C8—91no—
145C2×C8—92no—
146C4⋊C4—32no—
147C4⋊C4—62no—
148C42—62no—
149C42C2×D3211yescharacteristic
150C22×C3—21no—
151C22×C3#67⋊C412yes—
152C3×C4—22no—
153C3×C4—22no—
154C3×C4—21no—
155C3×C4—21no—
156C3×C4—22no—
157C3×C4—122no—
158C3×C4—122no—
159C3×C4#90112yes—
160C3×C4D3×M1612yes—
161C3×C4#91512yes—
162C3×C4#91812yes—
163Dic3—42no—
164Dic3—42no—
165C32#159311yescharacteristic, complemented, Sylow
166Q8—62no—
167Q8—62no—
168C2×C4—62no—
169C2×C4—62no—
170C2×C4C4×D3211yescharacteristic
171C2×C4#380211yescharacteristic
172C2×C4#380511yescharacteristic
173C8—41no—
174C8—92no—
175C8—122no—
176C8—181no—
177C8—182no—
178C2×C3—21no—
179C2×C3—21no—
180C2×C3—21no—
181C2×C3#472912yes—
182C2×C3#478912yes—
183C2×C3#482312yes—
184C22#6390211yescharacteristic
185C4—21no—
186C4—122no—
187C4—122no—
188C4#6379111yescharacteristic
189C4#6380311yescharacteristic
190C4#6381112yes—
191C3—21no—
192C3#6822712yescomplemented
193C2#1059039011yescharacteristic
194C2#1059073411yescharacteristic
195C2#1059079111yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32C4×D4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1593
LCSG ▷ C2×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
165. C32#1593semidirect
192. C3#68227semidirect

Maximal subgroups

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

subgroupindex
C4×#37182
#105902592
#105893202
C3×#44562
#105890982
#682273