Finite Group Databasebeta

← #10191

Subgroups — #10191

Order 256.

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

normal subgroups only

This group has 232 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
3C2×#475C211yesmaximal, characteristic
4#1548C211yesmaximal, characteristic
5#1481C211yesmaximal, characteristic
6#1461C211yesmaximal, characteristic
7#1301C211yesmaximal, 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—22no—
18#475—21no—
19#475—22no—
20#431C2211yescharacteristic
21#431C2211yescharacteristic
22#428—21no—
23C2×#106—21no—
24#423C2211yescharacteristic
25C2×C4⋊C8C2211yescharacteristic
26#419—21no—
27C2×#103—21no—
28#333—22no—
29Q8⋊C8—22no—
30#324—22no—
31C22×Q8—21no—
32C22×Q8D411yescharacteristic
33C2×M16—21no—
34C22×C8—21no—
35C4⋊Q8—21no—
36C4⋊Q8—21no—
37C4⋊Q8—21no—
38C4⋊Q8D412yes—
39C4⋊Q8D411yescharacteristic
40C4⋊Q8D411yescharacteristic
41#125—21no—
42C22⋊Q8—21no—
43C22⋊Q8—21no—
44C4×Q8—21no—
45C4×Q8—21no—
46C4×Q8—21no—
47C4×Q8—21no—
48C4×Q8—21no—
49C4×Q8—21no—
50#117—21no—
51C2×C4⋊C4—21no—
52C2×C4⋊C4—21no—
53C2×C4⋊C4—21no—
54C2×C4⋊C4D411yescharacteristic
55C2×C42—21no—
56C2×C42C2311yescharacteristic
57#107—22no—
58#107—24no—
59#106—24no—
60#106—22no—
61C4⋊C8—21no—
62C4⋊C8—21no—
63C4⋊C8—21no—
64C4⋊C8—21no—
65C4⋊C8D412yes—
66C4⋊C8D412yes—
67#103—24no—
68#103—22no—
69#103—22no—
70#103—24no—
71C22⋊C8—21no—
72C22⋊C8D412yes—
73C4×C8—21no—
74C4×C8—21no—
75C2×Q8—21no—
76C2×Q8—21no—
77C2×Q8—21no—
78C2×Q8—21no—
79C2×Q8—21no—
80C2×Q8—22no—
81C2×Q8—21no—
82C2×Q8—21no—
83C2×Q8—41no—
84C2×Q8—82no—
85C2×Q8Q1612yes—
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—41no—
89C22×C4C2×D411yescharacteristic
90C22×C4C2×D411yescharacteristic
91C22×C4#4111yescharacteristic
92M16—41no—
93M16—41no—
94C2×C8—22no—
95C2×C8—22no—
96C2×C8—22no—
97C2×C8—41no—
98C2×C8—41no—
99C2×C8—41no—
100C4⋊C4—22no—
101C4⋊C4—21no—
102C4⋊C4—22no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—21no—
106C4⋊C4—21no—
107C4⋊C4—21no—
108C4⋊C4—41no—
109C4⋊C4—41no—
110C4⋊C4—41no—
111C4⋊C4—41no—
112C4⋊C4—41no—
113C4⋊C4—41no—
114C22⋊C4—41no—
115C42—41no—
116C42—41no—
117C42—41no—
118C42C2×D411yescharacteristic
119C42C2×D411yescharacteristic
120C42C2×D411yescharacteristic
121C42C2×D411yescharacteristic
122C23#12111yescharacteristic
123Q8—22no—
124Q8—22no—
125Q8—42no—
126Q8—41no—
127Q8—41no—
128Q8—42no—
129Q8—82no—
130Q8—82no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—42no—
140C2×C4—82no—
141C2×C4—81no—
142C2×C4#12011yescharacteristic
143C2×C4#12011yescharacteristic
144C2×C4#12011yescharacteristic
145C2×C4#12111yescharacteristic
146C2×C4#12111yescharacteristic
147C2×C4#12711yescharacteristic
148C2×C4C2×Q1611yescharacteristic
149C2×C4#13511yescharacteristic
150C2×C4#13711yescharacteristic
151C2×C4#13711yescharacteristic
152C8—42no—
153C8—42no—
154C8—42no—
155C8—81no—
156C22—21no—
157C22—21no—
158C22#39211yescharacteristic
159C22#46711yescharacteristic
160C22#47011yescharacteristic
161C4—21no—
162C4—21no—
163C4—21no—
164C4—42no—
165C4—81no—
166C4—81no—
167C4—82no—
168C4—81no—
169C4#45111yescharacteristic
170C4#45111yescharacteristic
171C4#45211yescharacteristic
172C4#45211yescharacteristic
173C4#47112yes—
174C2—21no—
175C2—21no—
176C2#200111yescharacteristic
177C2#200911yescharacteristic
178C2#201911yescharacteristic
subgroupG/H
center, socleC22#392
commutator, Frattini, cosocleC2×C42C23
prime radicalC23#121
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
C2×#4752
#15482
#14812
#14612
#13012