Finite Group Databasebeta

← #11770869

Subgroups — #11770869

Order 1152.

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

normal subgroups only

This group has 300 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
1#10593727C211yesmaximal, characteristic
2C4×#3712C211yesmaximal, characteristic
3#10590331C211yesmaximal, characteristic
4C42×C3⋊D3C2211yescharacteristic
5C2×#3712C412yes—
6C2×#3710C412yes—
7#63778C412yes—
8C4⋊#622—21no—
9C4×#622—21no—
10C3×C4⋊(C3⋊C8)—21no—
11C3×C4×C3⋊C8—21no—
12#63572—21no—
13#63555—21no—
14D3×C4⋊C8—61no—
15C4×ΓL(1,𝔽25)—61no—
16C2×C4×C3⋊D3C2×C411yescharacteristic
17C2×C4×C3⋊D3C2×C411yescharacteristic
18C2×C4×C3⋊D3C2×C411yescharacteristic
19C2×#622—22no—
20C32×C42D411yescharacteristic
21C4×C3⋊Dic3D411yescharacteristic
22C4×C3⋊Dic3D411yescharacteristic
23C4×C3⋊Dic3Q811yescharacteristic
24C2×C3×C3⋊C8—22no—
25C2×C3×C3⋊C8—22no—
26#3712—22no—
27#3712C814yescomplemented
28#3710—42no—
29#1283—91nomaximal, Sylow
30C2×ΓL(1,𝔽25)—62no—
31C2×D3×C8—62no—
32C42×D3—61no—
33C42×D3—61no—
34C3×C4⋊C8—61no—
35C3×C4×C8—61no—
36#815—62no—
37Dic3⋊C8—62no—
38C4⋊(C3⋊C8)—21no—
39C4×C3⋊C8—21no—
40C22×C3⋊D3C4211yescharacteristic
41C2×C32×C4C22⋊C411yescharacteristic
42C2×C32×C4C22⋊C411yescharacteristic
43C2×C32×C4C4⋊C411yescharacteristic
44C2×C3⋊Dic3C22⋊C411yescharacteristic
45C2×C3⋊Dic3C4⋊C411yescharacteristic
46C2×C3⋊Dic3C4⋊C411yescharacteristic
47C4×C3⋊D3—21no—
48C4×C3⋊D3—21no—
49C4×C3⋊D3—41no—
50C4×C3⋊D3C2×C812yes—
51C4×C3⋊D3M1612yes—
52#622—42no—
53C3×C3⋊C8—24no—
54C3×C3⋊C8—42no—
55#431—91no—
56C2×C4⋊C8—91no—
57C4×M16—91no—
58C2×C4×D3—61no—
59C2×C4×D3—61no—
60C2×C4×D3—61no—
61C2×C4×D3—61no—
62C2×C4×D3—61no—
63C2×C4×D3—61no—
64C2×C3×C8—62no—
65C2×C3×C8—62no—
66C3×C42—21no—
67C3×C42—21no—
68C4×Dic3—61no—
69C4×Dic3—61no—
70C4×Dic3—61no—
71C4×Dic3—61no—
72C4×Dic3—61no—
73C4×Dic3—61no—
74C2×C3⋊C8—22no—
75C2×C3⋊C8—22no—
76ΓL(1,𝔽25)—64no—
77ΓL(1,𝔽25)—64no—
78D3×C8—124no—
79C22×C32#9511yescharacteristic
80C2×C3⋊D3—21no—
81C2×C3⋊D3—21no—
82C2×C3⋊D3C4×C811yescharacteristic
83C2×C3⋊D3#9711yescharacteristic
84C32×C4—21no—
85C32×C4C22⋊C812yes—
86C32×C4#10011yescharacteristic
87C32×C4#10111yescharacteristic
88C3⋊Dic3—21no—
89C3⋊Dic3—21no—
90C3⋊Dic3C4⋊C812yes—
91C2×M16—92no—
92C22×C8—92no—
93C2×C42—91no—
94C4⋊C8—61no—
95C4⋊C8—181no—
96C4⋊C8—181no—
97C22⋊C8—92no—
98#97—181no—
99C4×C8—61no—
100C4×C8—181no—
101C22×D3—61no—
102C22×D3—61no—
103C2×C3×C4—21no—
104C2×C3×C4—21no—
105C2×C3×C4—21no—
106C2×C3×C4—21no—
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×Dic3—61no—
110C2×Dic3—61no—
111C2×Dic3—61no—
112C2×Dic3—61no—
113C2×Dic3—61no—
114C2×Dic3—61no—
115C4×D3—62no—
116C4×D3—62no—
117C4×D3—62no—
118C4×D3—62no—
119C4×D3—62no—
120C4×D3—62no—
121C4×D3—121no—
122C4×D3—121no—
123C4×D3—122no—
124C4×D3—122no—
125C3×C8—64no—
126C3×C8—122no—
127C3⋊C8—24no—
128C3⋊C8—42no—
129C2×C32#33611yescharacteristic
130C2×C32#34311yescharacteristic
131C2×C32#34411yescharacteristic
132C3⋊D3—21no—
133C3⋊D3—21no—
134C22×C4—91no—
135C22×C4—91no—
136C22×C4—91no—
137M16—94no—
138M16—182no—
139C2×C8—62no—
140C2×C8—62no—
141C2×C8—182no—
142C2×C8—362no—
143C42—91no—
144C42—91no—
145C42—91no—
146C42GO+(4,𝔽2)11yescharacteristic
147C22×C3—21no—
148C22×C3—21no—
149C2×D3—61no—
150C2×D3—61no—
151C2×D3—61no—
152C2×D3—61no—
153C2×D3—62no—
154C2×D3—62no—
155C2×D3—121no—
156C2×D3—121no—
157C3×C4—22no—
158C3×C4—22no—
159C3×C4—22no—
160C3×C4—21no—
161C3×C4—21no—
162C3×C4—21no—
163C3×C4—21no—
164C3×C4—41no—
165Dic3—62no—
166Dic3—62no—
167Dic3—62no—
168Dic3—121no—
169Dic3—121no—
170Dic3—121no—
171C32#128311yescharacteristic, complemented, Sylow
172C23—91no—
173C2×C4—91no—
174C2×C4—92no—
175C2×C4—92no—
176C2×C4—91no—
177C2×C4—91no—
178C2×C4—181no—
179C2×C4—181no—
180C2×C4—361no—
181C2×C4D32⋊C411yescharacteristic
182C2×C4D32⋊C411yescharacteristic
183C2×C4#377311yescharacteristic
184C8—64no—
185C8—122no—
186C8—362no—
187C2×C3—21no—
188C2×C3—21no—
189C2×C3—21no—
190C2×C3—21no—
191C2×C3—21no—
192C2×C3—21no—
193D3—62no—
194D3—62no—
195D3—121no—
196D3—121no—
197C22—91no—
198C22—91no—
199C22—181no—
200C22—181no—
201C22#6373711yescharacteristic
202C4—21no—
203C4—92no—
204C4—181no—
205C4—181no—
206C4D32⋊C812yes—
207C4#6372711yescharacteristic
208C4#6372811yescharacteristic
209C3—21no—
210C3—21no—
211C2—181no—
212C2—181no—
213C2#1059004311yescharacteristic
214C2#1059005211yescharacteristic
215C2#1059005511yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊D3C4×C8
Frattini, hypercenterC42GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32#95
prime radicalC22×C3⋊D3C42
cosocleC42×C3⋊D3C22
hypocenterC32#1283
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
27. #3712C8semidirect
171. C32#1283semidirect

Maximal subgroups

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

subgroupindex
#105937272
C4×#37122
#105903312
#12839