Finite Group Databasebeta

← #10335

Subgroups — #10335

Order 256.

287 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 287 conjugacy classes of subgroups — too many to draw. Only its 53 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#3195C211yesmaximal, characteristic
2#2503C211yesmaximal, characteristic
3#2502C211yesmaximal, characteristic
4#1821C211yesmaximal, characteristic
5#1508C211yesmaximal, characteristic
6#1508C211yesmaximal, characteristic
7#1297C211yesmaximal, characteristic
8C2×C22⋊Q8C2211yescharacteristic
9C2×C22⋊Q8C2211yescharacteristic
10C22×C4⋊C4C2211yescharacteristic
11#483—21no—
12#483—21no—
13#470—22no—
14#451—21no—
15#451—21no—
16#407C2211yescharacteristic
17#407C2211yescharacteristic
18#400—22no—
19#398—22no—
20#391—21no—
21#391—21no—
22#385—22no—
23#384—21no—
24#382—21no—
25#381—22no—
26C4×C22⋊C4C2211yescharacteristic
27C4×C22⋊C4C2211yescharacteristic
28#343—22no—
29#328—22no—
30#328—22no—
31C22×Q8D411yescharacteristic
32C22×Q8D411yescharacteristic
33C23×C4D412yes—
34C23×C4C2311yescharacteristic
35C2×Q16—22no—
36C2×M16—21no—
37C2×M16D412yes—
38C22⋊Q8—21no—
39C22⋊Q8—21no—
40C22⋊Q8—21no—
41C22⋊Q8—21no—
42C22⋊Q8—21no—
43C22⋊Q8—21no—
44C22⋊Q8—21no—
45C22⋊Q8—21no—
46C2×C4⋊C4—21no—
47C2×C4⋊C4—21no—
48C2×C4⋊C4—21no—
49C2×C4⋊C4—21no—
50C2×C4⋊C4—21no—
51C2×C4⋊C4—21no—
52C2×C4⋊C4—21no—
53C2×C4⋊C4—21no—
54C2×C4⋊C4—24no—
55C2×C4⋊C4D411yescharacteristic
56C2×C4⋊C4D411yescharacteristic
57C2×C22⋊C4—21no—
58C2×C22⋊C4—21no—
59C2×C22⋊C4—21no—
60C2×C22⋊C4—21no—
61C2×C42—21no—
62C2×C42—21no—
63#106—22no—
64#103—22no—
65#103—22no—
66C22⋊C8—21no—
67C22⋊C8—21no—
68C22⋊C8—21no—
69C22⋊C8—21no—
70#95—24no—
71#95—24no—
72#95—24no—
73#95D412yes—
74#95D412yes—
75C24C2×D411yescharacteristic
76C2×Q8—21no—
77C2×Q8—21no—
78C2×Q8—21no—
79C2×Q8—21no—
80C2×Q8—42no—
81C2×Q8—42no—
82C22×C4—22no—
83C22×C4—22no—
84C22×C4—21no—
85C22×C4—21no—
86C22×C4—21no—
87C22×C4—22no—
88C22×C4—22no—
89C22×C4—21no—
90C22×C4—22no—
91C22×C4—42no—
92C22×C4—44no—
93C22×C4C2×D411yescharacteristic
94C22×C4C2×D411yescharacteristic
95C22×C4C2×D411yescharacteristic
96C22×C4C2×D411yescharacteristic
97C22×C4C2×D411yescharacteristic
98C22×C4#4111yescharacteristic
99Q16—82no—
100M16—42no—
101M16—42no—
102C2×C8—22no—
103C2×C8—41no—
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—
114C4⋊C4—41no—
115C4⋊C4—41no—
116C4⋊C4—84no—
117C22⋊C4—24no—
118C22⋊C4—42no—
119C22⋊C4—41no—
120C22⋊C4—41no—
121C22⋊C4—41no—
122C22⋊C4—41no—
123C42—42no—
124C42—42no—
125C23—22no—
126C23—22no—
127C23—41no—
128C23#12011yescharacteristic
129C23#12011yescharacteristic
130C23#12111yescharacteristic
131Q8—42no—
132Q8—42no—
133Q8—81no—
134Q8—81no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—24no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4—44no—
147C2×C4—42no—
148C2×C4—42no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—44no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—82no—
159C2×C4#12011yescharacteristic
160C2×C4#12111yescharacteristic
161C2×C4#12111yescharacteristic
162C2×C4#12711yescharacteristic
163C8—42no—
164C8—81no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—21no—
171C22—21no—
172C22—44no—
173C22#39211yescharacteristic
174C22#45512yes—
175C22#45612yes—
176C4—21no—
177C4—21no—
178C4—21no—
179C4—44no—
180C4—82no—
181C4—81no—
182C4—82no—
183C4—81no—
184C4—81no—
185C4—81no—
186C4#45812yes—
187C2—22no—
188C2—22no—
189C2—41no—
190C2#200411yescharacteristic
191C2#200511yescharacteristic
192C2#202211yescharacteristic
subgroupG/H
center, socleC22#392
commutator, Frattini, cosocleC23×C4C23
prime radicalC24C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#31952
#25032
#25022
#18212
#15082
#12972