Finite Group Databasebeta

← #11775767

Subgroups — #11775767

Order 1152.

563 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 563 conjugacy classes of subgroups — too many to draw. Only its 132 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
1#10595941C211yesmaximal, characteristic
2C3×C4×#208C212yesmaximal
3#10589089C214yesmaximal, complemented
4#69862—32nomaximal
5C2×C32×C42C2211yescharacteristic
6#64135C412yes—
7#64133—22no—
8#64079C2212yes—
9#64078C412yes—
10C4×#634—22no—
11C2×C3×#208—22no—
12C3×#803C2214yes—
13C3×C4×C3⋊C8—22no—
14#5470—32no—
15#5470—61no—
16C3×C4×M16—32no—
17C4×#208D312yes—
18#4465—38no—
19C22×C32×C4C2×C411yescharacteristic
20C22×C32×C4D412yes—
21C2×#634—22no—
22C32×C42C2×C411yescharacteristic
23C32×C42D412yes—
24C32×C42C2311yescharacteristic
25#3757—22no—
26C4⋊(C3⋊Dic3)—22no—
27C4⋊(C3⋊Dic3)C2×C414yes—
28#3750—24no—
29C4×C3⋊Dic3—22no—
30C3×#208—28no—
31C2×C3×C3⋊C8—24no—
32#1526—91noSylow
33C2×C3×M16—62no—
34C2×C3×C42—21no—
35C2×C3×C42C2×D312yes—
36#926—34no—
37#926—62no—
38#924—64no—
39#924—62no—
40#924—62no—
41C2×#208—22no—
42#870—34no—
43#870—62no—
44#869—32no—
45#869—32no—
46#869—62no—
47C4×Dic6—64no—
48C4×Dic6—62no—
49C4×Dic6—62no—
50C3×#97—34no—
51C3×C4×C8—62no—
52#803C2×D314yes—
53C4×C3⋊C8—22no—
54C23×C32C22⋊C411yescharacteristic
55C2×C32×C4—22no—
56C2×C32×C4—24no—
57C2×C32×C4C22⋊C411yescharacteristic
58C2×C32×C4C22⋊C412yes—
59C2×C32×C4C22×C411yescharacteristic
60C2×C32×C4C2×D412yes—
61C2×C3⋊Dic3—24no—
62#634—44no—
63C3×C3⋊C8—28no—
64#533—91no—
65C4×M16—32no—
66#330—94no—
67C22×C3×C4—21no—
68C22×C3×C4—22no—
69C22×C3×C4C4×D312yes—
70C22×C3×C4D1212yes—
71C22×C3×C4#6712yes—
72C2×Dic6—64no—
73C2×Dic6—62no—
74C2×Dic6—62no—
75C3×M16—68no—
76C2×C3×C8—64no—
77C3×C42—21no—
78C3×C42—22no—
79C3×C42—21no—
80C3×C42C4×D312yes—
81C3×C42D1212yes—
82C3×C42#6712yes—
83C3×C42C22×D312yes—
84#217—64no—
85#217—64no—
86C4⋊Dic3—34no—
87C4⋊Dic3—34no—
88C4⋊Dic3—64no—
89C4⋊Dic3—64no—
90C4⋊Dic3—62no—
91C4⋊Dic3—62no—
92Dic3⋊C4—68no—
93Dic3⋊C4—64no—
94Dic3⋊C4—64no—
95C4×Dic3—64no—
96C4×Dic3—64no—
97#208—28no—
98C2×C3⋊C8—24no—
99C22×C32—21no—
100C22×C32—22no—
101C22×C32C2×C22⋊C411yescharacteristic
102C32×C4—21no—
103C32×C4—22no—
104C32×C4#10112yes—
105C32×C4#10414yes—
106C3⋊Dic3—44no—
107C2×M16—62no—
108C4⋊Q8—92no—
109#125—92no—
110C22⋊Q8—182no—
111C4×Q8—182no—
112#117—92no—
113C2×C42D3211yescharacteristic
114#97—34no—
115C4×C8—62no—
116C23×C3—21no—
117C23×C3(C2×D3)⋊C412yes—
118C2×C3×C4—24no—
119C2×C3×C4—24no—
120C2×C3×C4—24no—
121C2×C3×C4—24no—
122C2×C3×C4—22no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—22no—
126C2×C3×C4—44no—
127C2×C3×C4(C2×D3)⋊C412yes—
128C2×C3×C4(C2×D3)⋊C412yes—
129C2×C3×C4(C2×D3)⋊C412yes—
130C2×C3×C4C2×C4×D312yes—
131C2×C3×C4C2×D1212yes—
132C2×C3×C4C2×#6712yes—
133C2×Dic3—68no—
134C2×Dic3—64no—
135C2×Dic3—64no—
136Dic6—128no—
137Dic6—124no—
138Dic6—124no—
139C3×C8—68no—
140C3⋊C8—28no—
141C2×C32—41no—
142C2×C32C2×#10111yescharacteristic
143C2×C32C2×#10412yes—
144C2×Q8—182no—
145C22×C4#62411yescharacteristic
146C22×C4#62612yes—
147M16—68no—
148C2×C8—64no—
149C4⋊C4—94no—
150C4⋊C4—182no—
151C4⋊C4—184no—
152C22⋊C4—182no—
153C42—182no—
154C42#62411yescharacteristic
155C42#62612yes—
156C42C2×D3211yescharacteristic
157C22×C3—22no—
158C22×C3—22no—
159C22×C3—22no—
160C22×C3—22no—
161C22×C3—21no—
162C22×C3—42no—
163C22×C3C2×(C2×D3)⋊C412yes—
164C3×C4—22no—
165C3×C4—22no—
166C3×C4—22no—
167C3×C4—22no—
168C3×C4—22no—
169C3×C4—24no—
170C3×C4—42no—
171C3×C4#80514yes—
172C3×C4#82414yes—
173C3×C4#82514yes—
174Dic3—128no—
175Dic3—124no—
176Dic3—124no—
177C32#152611yescharacteristic, complemented, Sylow
178C23#372211yescharacteristic
179Q8—364no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—184no—
183C2×C4#372212yes—
184C2×C4#372211yescharacteristic
185C2×C4C2×#62411yescharacteristic
186C2×C4C2×#62612yes—
187C8—68no—
188C2×C3—21no—
189C2×C3—22no—
190C2×C3—42no—
191C2×C3—42no—
192C2×C3C2×#80512yes—
193C2×C3C2×#82412yes—
194C2×C3C2×#82512yes—
195C22—21no—
196C22—22no—
197C22C2×#372211yescharacteristic
198C4—21no—
199C4—22no—
200C4—364no—
201C4#6356112yes—
202C4#6357014yes—
203C3—21no—
204C3#6986212yescomplemented
205C2—41no—
206C2C2×#6356111yescharacteristic
207C2C2×#6357012yes—
subgroupG/H
centerC2×C4#3722
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC32×C42C23
hypercenterC2×C42D32
hypocenterC32#1526
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. #10589089C2semidirect
177. C32#1526semidirect
204. C3#69862semidirect

Maximal subgroups

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

subgroupindex
#105959412
C3×C4×#2082
#105890892
#698623