Finite Group Databasebeta

← #8410

Subgroups — #8410

Order 256.

346 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 87 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#3458C211yesmaximal, characteristic
2#1798C211yesmaximal, characteristic
3#1542C212yesmaximal, complemented
4#1481C212yesmaximal, complemented
5#1458C211yesmaximal, characteristic
6#544—22no—
7#544—22no—
8#544—21no—
9#544C412yes—
10#543—21no—
11#543C412yes—
12#533—24no—
13#533—21no—
14#533C2212yes—
15C2×#117—21no—
16C2×#117C2211yescharacteristic
17#431C2212yes—
18C2×C4⋊C8C2211yescharacteristic
19C2×C4⋊C8C2211yescharacteristic
20C2×C22⋊C8—21no—
21#336—21no—
22#333—22no—
23#332—22no—
24Q8⋊C8—24no—
25#324—21no—
26#323—21no—
27C23×C4D411yescharacteristic
28C22×C8—21no—
29C22×C8—21no—
30C4⋊Q8—24no—
31C4⋊Q8—21no—
32C4⋊Q8—21no—
33C4⋊Q8—24no—
34C4⋊Q8D412yes—
35C4⋊Q8D412yes—
36#125—24no—
37#125—22no—
38#125—24no—
39#125—22no—
40C22⋊Q8—24no—
41C22⋊Q8—24no—
42C22⋊Q8—24no—
43C22⋊Q8—22no—
44C22⋊Q8—22no—
45C22⋊Q8—22no—
46C22⋊Q8—24no—
47C22⋊Q8C2×C414yes—
48C4×Q8—22no—
49C4×Q8—22no—
50C4×Q8—22no—
51C4×Q8D414yes—
52#117—22no—
53#117—22no—
54#117—22no—
55#117—22no—
56#117—22no—
57#117—22no—
58C2×C4⋊C4—21no—
59C2×C4⋊C4—21no—
60C2×C4⋊C4C2×C411yescharacteristic
61C2×C4⋊C4D411yescharacteristic
62C2×C22⋊C4—22no—
63C2×C22⋊C4C2×C411yescharacteristic
64C2×C22⋊C4D411yescharacteristic
65C2×C42—22no—
66C2×C42D411yescharacteristic
67C2×C42C2311yescharacteristic
68C4⋊C8—22no—
69C4⋊C8—22no—
70C4⋊C8—22no—
71C22⋊C8—22no—
72C22⋊C8—42no—
73C4×C8—22no—
74C24C22⋊C411yescharacteristic
75C2×Q8—22no—
76C2×Q8—22no—
77C2×Q8—22no—
78C2×Q8C22⋊C414yes—
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—22no—
84C22×C4—22no—
85C22×C4C22⋊C411yescharacteristic
86C22×C4C22⋊C411yescharacteristic
87C22×C4C22⋊C411yescharacteristic
88C22×C4SD1612yes—
89C22×C4Q1612yes—
90C22×C4C22×C411yescharacteristic
91C22×C4C2×D411yescharacteristic
92C22×C4C2×D411yescharacteristic
93C2×C8—42no—
94C2×C8—41no—
95C2×C8—41no—
96C2×C8—41no—
97C2×C8—41no—
98C2×C8—41no—
99C2×C8—41no—
100C4⋊C4—22no—
101C4⋊C4—22no—
102C4⋊C4—22no—
103C4⋊C4—24no—
104C4⋊C4—24no—
105C4⋊C4—22no—
106C4⋊C4—22no—
107C4⋊C4—24no—
108C4⋊C4—22no—
109C4⋊C4—22no—
110C4⋊C4—22no—
111C4⋊C4—22no—
112C4⋊C4—24no—
113C4⋊C4C22⋊C414yes—
114C22⋊C4—24no—
115C22⋊C4—24no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C42—24no—
119C42—21no—
120C42—24no—
121C42—21no—
122C42C2×D412yes—
123C42C2×D412yes—
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23#10312yes—
129C23C2×C22⋊C411yescharacteristic
130Q8—44no—
131Q8—82no—
132Q8—82no—
133Q8—82no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—24no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—24no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—82no—
149C2×C4—82no—
150C2×C4#10312yes—
151C2×C4C2×C22⋊C412yes—
152C2×C4#12012yes—
153C2×C4#12011yescharacteristic
154C2×C4#12011yescharacteristic
155C2×C4C2×SD1611yescharacteristic
156C2×C4C2×Q1611yescharacteristic
157C2×C4#13711yescharacteristic
158C2×C4#13711yescharacteristic
159C8—82no—
160C8—81no—
161C8—81no—
162C22—21no—
163C22—21no—
164C22—22no—
165C22—42no—
166C22—41no—
167C22—41no—
168C22—81no—
169C22#37911yescharacteristic
170C22C2×#10311yescharacteristic
171C22#41911yescharacteristic
172C4—22no—
173C4—22no—
174C4—22no—
175C4—41no—
176C4—44no—
177C4—41no—
178C4—44no—
179C4#44811yescharacteristic
180C4#44811yescharacteristic
181C4#45111yescharacteristic
182C4#45111yescharacteristic
183C2—21no—
184C2—21no—
185C2—42no—
186C2#178711yescharacteristic
187C2#179111yescharacteristic
188C2#179411yescharacteristic
subgroupG/H
centerC2×C4#120
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
socleC22#379
prime radicalC24C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #1542C2semidirect
4. #1481C2semidirect

Maximal subgroups

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

subgroupindex
#34582
#17982
#15422
#14812
#14582