Finite Group Databasebeta

← #11772499

Subgroups — #11772499

Order 1152.

254 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 59 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
1C2×#63773C211yesmaximal, characteristic
2C2×#63578C211yesmaximal, characteristic
3C2×#63576C211yesmaximal, characteristic
4C22×C3⋊(C3⋊C8)C2211yescharacteristic
5C2×C3×C4⋊Dic3—21no—
6C2×C3×#208—21no—
7#63773—21no—
8#63773C412yescomplemented
9C2×#3708—21no—
10#63578—21no—
11#63578C412yescomplemented
12#63576—21no—
13#63576C412yes—
14C2×#822—61no—
15C2×#807—61no—
16C22×C32×C4D411yescharacteristic
17C22×C3×Dic3—41no—
18C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
19C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
20C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
21C2×C3⋊(C3⋊C8)D411yescharacteristic
22C2×C3⋊(C3⋊C8)D411yescharacteristic
23C2×C3⋊(C3⋊C8)Q811yescharacteristic
24C3×C4⋊Dic3—22no—
25C3×C4⋊Dic3—41no—
26C3×#208—22no—
27C3×#208—41no—
28C2×C3×C3⋊C8—41no—
29#3708—22no—
30#1387—91nomaximal, Sylow
31C2×C3×M16—61no—
32C2×C3×C4⋊C4—61no—
33C2×C4⋊Dic3—21no—
34C2×#208—21no—
35C22×C3⋊C8—61no—
36C22×C3⋊C8—61no—
37#822—62no—
38#822—62no—
39#807—62no—
40#807—62no—
41C23×C32SD1611yescharacteristic
42C2×C32×C4C22⋊C411yescharacteristic
43C2×C32×C4C22⋊C411yescharacteristic
44C2×C32×C4C4⋊C411yescharacteristic
45C2×C32×C4D811yescharacteristic
46C2×C32×C4SD1611yescharacteristic
47C2×C32×C4Q1611yescharacteristic
48C2×C3×Dic3—42no—
49C2×C3×Dic3—82no—
50C3⋊(C3⋊C8)C4211yescharacteristic
51C3⋊(C3⋊C8)C22⋊C411yescharacteristic
52C3⋊(C3⋊C8)C4⋊C411yescharacteristic
53C3⋊(C3⋊C8)C4⋊C411yescharacteristic
54C3×C3⋊C8—42no—
55C2×M32—91no—
56C2×#108—91no—
57C2×#107—91no—
58C22×C3×C4—21no—
59C22×C3×C4—21no—
60C22×C3×C4—121no—
61C22×Dic3—41no—
62C3×M16—62no—
63C3×M16—121no—
64C2×C3×C8—121no—
65C3×C4⋊C4—62no—
66C3×C4⋊C4—121no—
67C4⋊Dic3—22no—
68C4⋊Dic3—41no—
69#208—22no—
70#208—41no—
71C2×C3⋊C8—41no—
72C2×C3⋊C8—61no—
73C2×C3⋊C8—61no—
74C2×C3⋊C8—61no—
75C2×C3⋊C8—61no—
76C2×C3⋊C8—61no—
77C2×C3⋊C8—61no—
78C2×C3⋊C8—61no—
79C2×C3⋊C8—61no—
80C2×C3⋊C8—61no—
81C2×C3⋊C8—61no—
82C2×C3⋊C8—61no—
83C2×C3⋊C8—61no—
84C22×C32—21no—
85C22×C32—21no—
86C22×C32#10211yescharacteristic
87C22×C32#10311yescharacteristic
88C22×C32#10611yescharacteristic
89C32×C4#9511yescharacteristic
90C32×C4#10211yescharacteristic
91C32×C4#10311yescharacteristic
92C32×C4#10711yescharacteristic
93C3×Dic3—82no—
94C2×M16—61no—
95C22×C8—91no—
96C2×C4⋊C4—61no—
97M32—92no—
98M32—181no—
99C2×C16—181no—
100#108—92no—
101#108—181no—
102#107—92no—
103#107—181no—
104C23×C3—21no—
105C23×C3—21no—
106C2×C3×C4—21no—
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×C3×C4—21no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—21no—
117C2×C3×C4—21no—
118C2×C3×C4—122no—
119C2×C3×C4—242no—
120C2×Dic3—42no—
121C2×Dic3—82no—
122C3×C8—122no—
123C3⋊C8—42no—
124C3⋊C8—61no—
125C3⋊C8—61no—
126C3⋊C8—61no—
127C3⋊C8—61no—
128C3⋊C8—61no—
129C3⋊C8—61no—
130C3⋊C8—61no—
131C3⋊C8—61no—
132C2×C32—21no—
133C2×C32—21no—
134C2×C32#34011yescharacteristic
135C2×C32#36111yescharacteristic
136C2×C32#36211yescharacteristic
137C22×C4—121no—
138C22×C4GO+(4,𝔽2)11yescharacteristic
139M16—62no—
140M16—121no—
141C2×C8—91no—
142C2×C8—91no—
143C2×C8—91no—
144C2×C8—91no—
145C2×C8—91no—
146C2×C8—91no—
147C2×C8—121no—
148C4⋊C4—62no—
149C4⋊C4—121no—
150C16—182no—
151C22×C3—22no—
152C22×C3—22no—
153C22×C3—21no—
154C22×C3—21no—
155C22×C3—21no—
156C22×C3—21no—
157C22×C3—21no—
158C22×C3—21no—
159C22×C3—41no—
160C22×C3—41no—
161C3×C4—21no—
162C3×C4—21no—
163C3×C4—21no—
164C3×C4—21no—
165C3×C4—21no—
166C3×C4—21no—
167C3×C4—21no—
168C3×C4—21no—
169C3×C4—242no—
170Dic3—82no—
171C32#138711yescharacteristic, complemented, Sylow
172C23#377511yescharacteristic
173C2×C4—122no—
174C2×C4—242no—
175C2×C4D32⋊C411yescharacteristic
176C2×C4D32⋊C411yescharacteristic
177C2×C4#377311yescharacteristic
178C2×C4#377411yescharacteristic
179C2×C4#377511yescharacteristic
180C2×C4#377611yescharacteristic
181C8—91no—
182C8—91no—
183C8—91no—
184C8—91no—
185C8—122no—
186C2×C3—22no—
187C2×C3—22no—
188C2×C3—21no—
189C2×C3—21no—
190C2×C3—21no—
191C2×C3—21no—
192C2×C3—21no—
193C2×C3—21no—
194C2×C3—41no—
195C2×C3—41no—
196C22—21no—
197C22—21no—
198C22#6373911yescharacteristic
199C22#6374011yescharacteristic
200C22#6374211yescharacteristic
201C4—242no—
202C4#6373711yescharacteristic
203C4#6373911yescharacteristic
204C4#6374011yescharacteristic
205C4#6374311yescharacteristic
206C3—21no—
207C3—21no—
208C2—21no—
209C2—21no—
210C2#1059006511yescharacteristic
211C2#1059006611yescharacteristic
212C2#1059007511yescharacteristic
subgroupG/H
centerC22#63739
commutatorC3⋊(C3⋊C8)C42
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#102
prime radicalC23×C32SD16
cosocleC22×C3⋊(C3⋊C8)C22
hypocenterC32#1387
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. #63773C4semidirect
11. #63578C4semidirect
171. C32#1387semidirect

Maximal subgroups

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

subgroupindex
C2×#637732
C2×#635782
C2×#635762
#13879