Finite Group Databasebeta

← #9687

Subgroups — #9687

Order 256.

263 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 263 conjugacy classes of subgroups — too many to draw. Only its 73 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#2861C211yesmaximal, characteristic
2#1767C211yesmaximal, characteristic, complemented
3C4×#97C211yesmaximal, characteristic, complemented
4C2×#330C212yesmaximal, complemented
5C2×#329C212yesmaximal
6C2×#125C2211yescharacteristic
7C2×#124C2211yescharacteristic
8C2×C4⋊C8—21no—
9C2×#97—21no—
10C2×#97C2212yes—
11C2×#97C2212yes—
12C2×C4×C8—21no—
13#391C411yescharacteristic
14#391C411yescharacteristic
15#390C411yescharacteristic
16#390C411yescharacteristic
17#388—21no—
18#388—21no—
19#388—21no—
20#388—21no—
21C43C2211yescharacteristic
22#336—21no—
23#330—24no—
24#329—24no—
25C22×Q8C2×C411yescharacteristic
26C22×D4C2×C411yescharacteristic
27C22×C8—22no—
28C22×C8—22no—
29#125—22no—
30#125—22no—
31#124—22no—
32#124—22no—
33C2×C4⋊C4—21no—
34C2×C4⋊C4—21no—
35C2×C4⋊C4C2×C411yescharacteristic
36C2×C4⋊C4C2×C411yescharacteristic
37C2×C22⋊C4—21no—
38C2×C22⋊C4—21no—
39C2×C22⋊C4—21no—
40C2×C22⋊C4—21no—
41C2×C22⋊C4—21no—
42C2×C22⋊C4—21no—
43C2×C42C2×C411yescharacteristic
44C2×C42C2×C411yescharacteristic
45C2×C42D411yescharacteristic
46C2×C42D411yescharacteristic
47C2×C42D411yescharacteristic
48C2×C42D411yescharacteristic
49C2×C42C2311yescharacteristic
50C4⋊C8—24no—
51#97—24no—
52#97—22no—
53#97—22no—
54#97—22no—
55#97D414yes—
56C4×C8—24no—
57#95—21no—
58#95—21no—
59#95—21no—
60#95—21no—
61C24—21no—
62C2×Q8—22no—
63C2×Q8—41no—
64C2×Q8—41no—
65C2×D4—22no—
66C2×D4—41no—
67C2×D4—41no—
68C22×C4—21no—
69C22×C4—21no—
70C22×C4—21no—
71C22×C4C22⋊C411yescharacteristic
72C22×C4C22⋊C411yescharacteristic
73C22×C4C22⋊C411yescharacteristic
74C22×C4C22⋊C411yescharacteristic
75C22×C4C22×C411yescharacteristic
76C22×C4C2×D411yescharacteristic
77C22×C4C2×D411yescharacteristic
78C2×C8—24no—
79C2×C8—24no—
80C2×C8—24no—
81C2×C8—24no—
82C2×C8—42no—
83C2×C8—42no—
84C4⋊C4—22no—
85C4⋊C4—22no—
86C4⋊C4—42no—
87C4⋊C4—41no—
88C4⋊C4—41no—
89C22⋊C4—42no—
90C22⋊C4—42no—
91C22⋊C4—42no—
92C22⋊C4—42no—
93C22⋊C4—42no—
94C22⋊C4—41no—
95C22⋊C4—41no—
96C42—22no—
97C42—22no—
98C42—22no—
99C42—41no—
100C42—41no—
101C42—41no—
102C42C2×D412yes—
103C42#4112yes—
104C23—41no—
105C23—41no—
106C23—41no—
107C23—41no—
108C23—41no—
109C23—41no—
110C23—41no—
111C23C2×C22⋊C411yescharacteristic
112Q8—82no—
113D4—82no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4#10412yes—
139C2×C4#10412yes—
140C2×C4#10412yes—
141C2×C4C4×D412yes—
142C2×C4#12112yes—
143C2×C4#12411yescharacteristic
144C2×C4#12711yescharacteristic
145C8—28no—
146C8—44no—
147C22—81no—
148C22—81no—
149C22—81no—
150C22—81no—
151C22—81no—
152C22—81no—
153C22—81no—
154C22#39011yescharacteristic
155C22#41311yescharacteristic
156C22#41311yescharacteristic
157C22C2×#10411yescharacteristic
158C22C2×#10411yescharacteristic
159C22C2×#10411yescharacteristic
160C22#42111yescharacteristic
161C4—22no—
162C4—22no—
163C4—21no—
164C4—21no—
165C4—22no—
166C4—22no—
167C4—22no—
168C4—41no—
169C4—81no—
170C4—81no—
171C4—81no—
172C2—161no—
173C2#152411yescharacteristic
174C2#152411yescharacteristic
175C2#152911yescharacteristic
176C2#153211yescharacteristic
177C2#196211yescharacteristic
178C2#196711yescharacteristic
179C2#198011yescharacteristic
subgroupG/H
center, socleC23C2×C22⋊C4
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
prime radicalC22×D4C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #1767C2semidirect
3. C4×#97C2semidirect
4. C2×#330C2semidirect

Maximal subgroups

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

subgroupindex
#28612
#17672
C4×#972
C2×#3302
C2×#3292