Finite Group Databasebeta

← #10377

Subgroups — #10377

Order 256.

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

normal subgroups only

This group has 211 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#2569C211yesmaximal, characteristic
2#1996C211yesmaximal, characteristic
3#1520C211yesmaximal, characteristic
4C2×#328C211yesmaximal, characteristic
5#1294C211yesmaximal, characteristic
6#1289C211yesmaximal, characteristic
7#1282C211yesmaximal, characteristic
8C2×C22⋊Q8C2211yescharacteristic
9C2×C22⋊C8C2211yescharacteristic
10C2×C22⋊C8C2211yescharacteristic
11#400—21no—
12#398—21no—
13#387—21no—
14#387—21no—
15#385—21no—
16#380—21no—
17#380C2211yescharacteristic
18#380C2211yescharacteristic
19C4×C22⋊C4C2211yescharacteristic
20C2×#95C2211yescharacteristic
21#342—21no—
22#342—21no—
23#328—21no—
24#328—21no—
25#328—21no—
26#328—21no—
27C22×Q8Q811yescharacteristic
28C23×C4—21no—
29C23×C4C2311yescharacteristic
30C22×C8—21no—
31C22×C8—21no—
32C22⋊Q8—21no—
33C22⋊Q8—21no—
34C22⋊Q8—21no—
35C22⋊Q8—21no—
36C2×C4⋊C4—21no—
37C2×C4⋊C4—21no—
38C2×C4⋊C4—21no—
39C2×C4⋊C4—21no—
40C2×C4⋊C4—21no—
41C2×C4⋊C4—21no—
42C2×C4⋊C4—21no—
43C2×C4⋊C4Q811yescharacteristic
44C2×C22⋊C4—21no—
45C2×C22⋊C4—21no—
46C2×C22⋊C4—21no—
47C2×C22⋊C4D411yescharacteristic
48C2×C22⋊C4D411yescharacteristic
49C2×C42—21no—
50C22⋊C8—21no—
51C22⋊C8—21no—
52C22⋊C8—21no—
53C22⋊C8—21no—
54#95—21no—
55#95—21no—
56#95—21no—
57#95—21no—
58#95—21no—
59#95—21no—
60#95—21no—
61#95D411yescharacteristic
62#95D411yescharacteristic
63#95D411yescharacteristic
64#95D411yescharacteristic
65C24C2×D411yescharacteristic
66C2×Q8—21no—
67C2×Q8—21no—
68C2×Q8—81no—
69C22×C4—21no—
70C22×C4—21no—
71C22×C4—21no—
72C22×C4—21no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—42no—
78C22×C4—41no—
79C22×C4—41no—
80C22×C4—41no—
81C22×C4—81no—
82C22×C4—81no—
83C22×C4C2×D411yescharacteristic
84C22×C4C2×D411yescharacteristic
85C22×C4C2×Q811yescharacteristic
86C22×C4#4111yescharacteristic
87C22×C4#4111yescharacteristic
88C22×C4#4111yescharacteristic
89C2×C8—41no—
90C2×C8—41no—
91C2×C8—81no—
92C2×C8—81no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—42no—
96C4⋊C4—42no—
97C4⋊C4—41no—
98C4⋊C4—41no—
99C4⋊C4—81no—
100C4⋊C4—81no—
101C4⋊C4—81no—
102C4⋊C4—81no—
103C22⋊C4—21no—
104C22⋊C4—21no—
105C22⋊C4—21no—
106C22⋊C4—21no—
107C22⋊C4—41no—
108C22⋊C4—41no—
109C22⋊C4—41no—
110C22⋊C4—41no—
111C22⋊C4—41no—
112C22⋊C4—41no—
113C42—81no—
114C23—41no—
115C23—41no—
116C23#12011yescharacteristic
117C23C22⋊Q811yescharacteristic
118C23#12411yescharacteristic
119C23#13511yescharacteristic
120C23#13511yescharacteristic
121C23#13711yescharacteristic
122C23#13711yescharacteristic
123Q8—81no—
124Q8—81no—
125C2×C4—22no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
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—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—82no—
152C2×C4—82no—
153C2×C4—81no—
154C2×C4—81no—
155C2×C4—81no—
156C2×C4—81no—
157C2×C4—81no—
158C2×C4C22⋊Q811yescharacteristic
159C2×C4C22⋊Q811yescharacteristic
160C2×C4#12411yescharacteristic
161C2×C4#12411yescharacteristic
162C8—81no—
163C8—81no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22#39311yescharacteristic
175C22#45211yescharacteristic
176C22#45211yescharacteristic
177C22#47911yescharacteristic
178C22#47911yescharacteristic
179C22#48811yescharacteristic
180C22#49111yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—42no—
186C4—81no—
187C4—81no—
188C4—81no—
189C4—81no—
190C4—81no—
191C4—81no—
192C4—81no—
193C4—161no—
194C2—21no—
195C2—21no—
196C2—21no—
197C2—21no—
198C2—21no—
199C2—21no—
200C2#202611yescharacteristic
201C2#203111yescharacteristic
202C2#203211yescharacteristic
subgroupG/H
center, socleC22#393
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
#25692
#19962
#15202
C2×#3282
#12942
#12892
#12822