Finite Group Databasebeta

← #13300

Subgroups — #13300

Order 256.

246 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 61 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#2566C211yesmaximal, characteristic
2#1799C211yesmaximal, characteristic
3C4×#99C211yesmaximal, characteristic
4#1393C212yesmaximal
5#1393C212yesmaximal
6C2×#125C411yescharacteristic, complemented
7C2×C4×D4C2211yescharacteristic
8C2×#99C2212yes—
9C2×#99C2212yes—
10#396—21no—
11#396—21no—
12#390C2211yescharacteristic
13#390C2211yescharacteristic
14#385—21no—
15#385—21no—
16#384C411yescharacteristic, complemented
17#382C411yescharacteristic, complemented
18#380—21no—
19C4×C4⋊C4C411yescharacteristic, complemented
20C4×C22⋊C4—21no—
21#342—21no—
22#342—21no—
23C22×D4C2311yescharacteristic
24C23×C4D411yescharacteristic
25C23×C4D411yescharacteristic
26#125—41no—
27#125—41no—
28C4×D4—41no—
29C4×D4—41no—
30C2×C4⋊C4—21no—
31C2×C4⋊C4—21no—
32C2×C4⋊C4—21no—
33C2×C4⋊C4—21no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4—41no—
36C2×C4⋊C4C2×C411yescharacteristic
37C2×C4⋊C4C2×C411yescharacteristic
38C2×C4⋊C4C2×C411yescharacteristic
39C2×C22⋊C4—22no—
40C2×C22⋊C4—21no—
41C2×C22⋊C4—21no—
42C2×C22⋊C4—22no—
43C2×C22⋊C4—21no—
44C2×C22⋊C4—21no—
45C2×C22⋊C4D411yescharacteristic
46C2×C22⋊C4D411yescharacteristic
47C2×C42—41no—
48C2×C42C2×C411yescharacteristic
49C2×C42C2×C411yescharacteristic
50C2×C42C2×C411yescharacteristic
51#99—22no—
52#99—24no—
53#99Q814yes—
54#95—21no—
55#95—21no—
56#95—21no—
57#95—41no—
58#95—41no—
59C24C2×D411yescharacteristic
60C24C2×D411yescharacteristic
61C2×D4—41no—
62C2×D4—41no—
63C2×D4C2×Q812yes—
64C2×D4#4112yes—
65C22×C4—21no—
66C22×C4—21no—
67C22×C4—21no—
68C22×C4—21no—
69C22×C4—21no—
70C22×C4—21no—
71C22×C4—21no—
72C22×C4—21no—
73C22×C4—42no—
74C22×C4—42no—
75C22×C4—81no—
76C22×C4—81no—
77C22×C4C22⋊C411yescharacteristic
78C22×C4C22⋊C411yescharacteristic
79C22×C4C22⋊C411yescharacteristic
80C22×C4C22⋊C411yescharacteristic
81C22×C4C22×C411yescharacteristic
82C4⋊C4—41no—
83C4⋊C4—41no—
84C4⋊C4—41no—
85C4⋊C4—42no—
86C4⋊C4—42no—
87C4⋊C4—41no—
88C4⋊C4—41no—
89C4⋊C4—81no—
90C4⋊C4—81no—
91C4⋊C4—82no—
92C22⋊C4—24no—
93C22⋊C4—41no—
94C22⋊C4—41no—
95C22⋊C4—42no—
96C22⋊C4—42no—
97C22⋊C4—42no—
98C22⋊C4—42no—
99C22⋊C4—42no—
100C22⋊C4—81no—
101C22⋊C4—81no—
102C42—21no—
103C42—21no—
104C42—41no—
105C42—41no—
106C42—82no—
107C23—21no—
108C23—21no—
109C23—21no—
110C23—21no—
111C23—41no—
112C23—41no—
113C23—41no—
114C23—41no—
115C23C2×C22⋊C411yescharacteristic
116C23C22⋊Q812yes—
117C23#12411yescharacteristic
118C23C4⋊Q811yescharacteristic
119D4—42no—
120D4—42no—
121C2×C4—21no—
122C2×C4—21no—
123C2×C4—22no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—42no—
129C2×C4—42no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—44no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—81no—
146C2×C4—81no—
147C2×C4—82no—
148C2×C4—82no—
149C2×C4—82no—
150C2×C4—82no—
151C2×C4—82no—
152C2×C4#9911yescharacteristic
153C2×C4#9911yescharacteristic
154C2×C4C4×Q812yes—
155C22—21no—
156C22—21no—
157C22—22no—
158C22—21no—
159C22—21no—
160C22—42no—
161C22—41no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—81no—
168C22—81no—
169C22#39111yescharacteristic
170C22C2×#9911yescharacteristic
171C22#41011yescharacteristic
172C4—21no—
173C4—21no—
174C4—22no—
175C4—42no—
176C4—41no—
177C4—41no—
178C4—41no—
179C4—81no—
180C4—84no—
181C4—81no—
182C4—81no—
183C4—162no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—41no—
188C2—41no—
189C2#199611yescharacteristic
190C2#212611yescharacteristic
191C2#212711yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutatorC22×C4C22×C4
Frattini, prime radical, cosocleC22×D4C23
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ G
LECSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
6. C2×#125C4semidirect
16. #384C4semidirect
17. #382C4semidirect
19. C4×C4⋊C4C4semidirect

Maximal subgroups

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

subgroupindex
#25662
#17992
C4×#992
#13932