Finite Group Databasebeta

← #10253

Subgroups — #10253

Order 256.

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

normal subgroups only

This group has 252 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#3230C211yesmaximal, characteristic
2#3078C211yesmaximal, characteristic
3#2567C211yesmaximal, characteristic
4#1549C211yesmaximal, characteristic
5#1503C211yesmaximal, characteristic
6#1479C211yesmaximal, characteristic
7#1303C211yesmaximal, characteristic
8#533C2211yescharacteristic
9C2×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8C2211yescharacteristic
11#500—21no—
12#487—21no—
13#484—22no—
14#479—22no—
15#477—21no—
16#477—22no—
17#475—21no—
18#431C2211yescharacteristic
19#431C2211yescharacteristic
20#428—21no—
21#423C2211yescharacteristic
22#419—21no—
23#395—22no—
24#391—21no—
25#389—22no—
26#384—21no—
27C4×C4⋊C4C2211yescharacteristic
28#332—22no—
29#328—22no—
30Q8⋊C8—22no—
31C22×Q8—21no—
32C22×Q8D411yescharacteristic
33C2×M16—21no—
34C4⋊Q8—21no—
35C4⋊Q8—21no—
36C4⋊Q8—21no—
37C4⋊Q8—21no—
38C4⋊Q8D411yescharacteristic
39C4⋊Q8D411yescharacteristic
40#125—21no—
41C22⋊Q8—21no—
42C22⋊Q8—21no—
43C4×Q8—21no—
44C4×Q8—21no—
45C4×Q8—21no—
46C4×Q8—21no—
47C4×Q8—21no—
48C4×Q8—21no—
49#117—21no—
50C2×C4⋊C4—21no—
51C2×C4⋊C4—21no—
52C2×C4⋊C4—21no—
53C2×C4⋊C4—24no—
54C2×C4⋊C4D411yescharacteristic
55C2×C4⋊C4D412yes—
56C2×C42—21no—
57C2×C42—21no—
58C2×C42C2311yescharacteristic
59#107—22no—
60#107—24no—
61#106—22no—
62C4⋊C8—21no—
63C4⋊C8—21no—
64C4⋊C8D412yes—
65C4⋊C8D412yes—
66#103—22no—
67#103—22no—
68#103—24no—
69C22⋊C8—21no—
70C22⋊C8—21no—
71C4×C8—21no—
72C4×C8—21no—
73#95—24no—
74#95D412yes—
75C2×Q8—21no—
76C2×Q8—21no—
77C2×Q8—21no—
78C2×Q8—21no—
79C2×Q8—21no—
80C2×Q8—21no—
81C2×Q8—21no—
82C2×Q8—41no—
83C2×Q8—41no—
84C2×Q8—82no—
85C2×Q8Q1612yes—
86C22×C4—21no—
87C22×C4—22no—
88C22×C4—22no—
89C22×C4—21no—
90C22×C4C2×D411yescharacteristic
91C22×C4C2×D411yescharacteristic
92C22×C4C2×D411yescharacteristic
93M16—41no—
94M16—41no—
95C2×C8—22no—
96C2×C8—22no—
97C2×C8—41no—
98C4⋊C4—24no—
99C4⋊C4—21no—
100C4⋊C4—22no—
101C4⋊C4—21no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—22no—
106C4⋊C4—21no—
107C4⋊C4—41no—
108C4⋊C4—41no—
109C4⋊C4—41no—
110C4⋊C4—41no—
111C4⋊C4—41no—
112C4⋊C4—41no—
113C4⋊C4—84no—
114C22⋊C4—41no—
115C42—41no—
116C42—41no—
117C42—41no—
118C42—41no—
119C42—41no—
120C42C2×D411yescharacteristic
121C42C2×D411yescharacteristic
122C42C2×D411yescharacteristic
123C42#4111yescharacteristic
124C23#12011yescharacteristic
125Q8—22no—
126Q8—22no—
127Q8—41no—
128Q8—41no—
129Q8—42no—
130Q8—81no—
131Q8—82no—
132Q8—82no—
133C2×C4—22no—
134C2×C4—24no—
135C2×C4—22no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—41no—
139C2×C4—42no—
140C2×C4—41no—
141C2×C4—42no—
142C2×C4—44no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—42no—
147C2×C4#12011yescharacteristic
148C2×C4#12011yescharacteristic
149C2×C4#12111yescharacteristic
150C2×C4#12111yescharacteristic
151C2×C4#12111yescharacteristic
152C2×C4#12711yescharacteristic
153C2×C4C2×Q1611yescharacteristic
154C2×C4#13511yescharacteristic
155C2×C4#13711yescharacteristic
156C2×C4#13711yescharacteristic
157C8—42no—
158C8—42no—
159C8—81no—
160C22—21no—
161C22—21no—
162C22#39211yescharacteristic
163C22#45111yescharacteristic
164C22#45211yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—44no—
169C4—42no—
170C4—81no—
171C4—81no—
172C4—82no—
173C4—81no—
174C4#45111yescharacteristic
175C4#45211yescharacteristic
176C4#45612yes—
177C4#46711yescharacteristic
178C4#47011yescharacteristic
179C2—21no—
180C2—21no—
181C2#200111yescharacteristic
182C2#200511yescharacteristic
183C2#200811yescharacteristic
subgroupG/H
center, socleC22#392
commutator, Frattini, cosocleC2×C42C23
prime radicalC23#120
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#32302
#30782
#25672
#15492
#15032
#14792
#13032