Finite Group Databasebeta

← #10384

Subgroups — #10384

Order 256.

219 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 219 conjugacy classes of subgroups — too many to draw. Only its 45 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#2667C211yesmaximal, characteristic, complemented
2#1964C211yesmaximal, characteristic
3#1510C211yesmaximal, characteristic
4#1507C211yesmaximal, characteristic
5#1305C211yesmaximal, characteristic, complemented
6#1297C211yesmaximal, characteristic, complemented
7#1284C211yesmaximal, characteristic, complemented
8C2×#121C2211yescharacteristic
9C2×#99—21no—
10C2×#99—21no—
11#407C2211yescharacteristic
12#407C2211yescharacteristic
13#399—21no—
14#398—21no—
15#398—21no—
16#396—21no—
17#389—21no—
18#387—21no—
19#381C2211yescharacteristic
20#380C2211yescharacteristic
21C4×C22⋊C4C2211yescharacteristic
22C4×C22⋊C4C2211yescharacteristic
23#327—21no—
24#327—21no—
25#327—21no—
26#327—21no—
27C22×D4—21no—
28C22×D4Q811yescharacteristic
29C23×C4C2311yescharacteristic
30C2×M16—21no—
31C2×M16—21no—
32#121—21no—
33#121—21no—
34#121—21no—
35#121—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⋊C4—21no—
48C2×C22⋊C4D411yescharacteristic
49C2×C22⋊C4D411yescharacteristic
50C2×C42—21no—
51C2×C42—21no—
52#99—42no—
53#99—42no—
54C22⋊C8—21no—
55C22⋊C8—21no—
56C22⋊C8—21no—
57C22⋊C8—21no—
58#95—21no—
59#95—21no—
60#95—21no—
61#95—21no—
62#95—21no—
63#95D411yescharacteristic
64#95D411yescharacteristic
65#95D411yescharacteristic
66#95D411yescharacteristic
67C24—21no—
68C24C2×D411yescharacteristic
69C2×D4—21no—
70C2×D4—21no—
71C2×D4—41no—
72C2×D4—41no—
73C2×D4—41no—
74C2×D4—41no—
75C2×D4—41no—
76C2×D4—41no—
77C2×D4—81no—
78C22×C4—21no—
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—21no—
84C22×C4—21no—
85C22×C4—41no—
86C22×C4—81no—
87C22×C4C2×D411yescharacteristic
88C22×C4C2×D411yescharacteristic
89C22×C4C2×Q811yescharacteristic
90C22×C4#4111yescharacteristic
91C22×C4#4111yescharacteristic
92C22×C4#4111yescharacteristic
93M16—81no—
94M16—81no—
95C2×C8—41no—
96C2×C8—41no—
97C4⋊C4—21no—
98C4⋊C4—21no—
99C4⋊C4—42no—
100C4⋊C4—42no—
101C4⋊C4—81no—
102C4⋊C4—81no—
103C4⋊C4—81no—
104C4⋊C4—81no—
105C4⋊C4—81no—
106C22⋊C4—22no—
107C22⋊C4—42no—
108C22⋊C4—41no—
109C22⋊C4—41no—
110C22⋊C4—41no—
111C22⋊C4—41no—
112C22⋊C4—41no—
113C22⋊C4—81no—
114C42—81no—
115C42—81no—
116C23—21no—
117C23—21no—
118C23—41no—
119C23—41no—
120C23—41no—
121C23—41no—
122C23—41no—
123C23—81no—
124C23—81no—
125C23#12011yescharacteristic
126C23C22⋊Q811yescharacteristic
127C23#12411yescharacteristic
128D4—81no—
129D4—81no—
130D4—81no—
131D4—81no—
132D4—81no—
133D4—81no—
134C2×C4—22no—
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—42no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—81no—
163C2×C4—81no—
164C2×C4C22⋊Q811yescharacteristic
165C2×C4C22⋊Q811yescharacteristic
166C2×C4#12411yescharacteristic
167C2×C4#12411yescharacteristic
168C8—81no—
169C8—81no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—81no—
179C22—81no—
180C22—81no—
181C22—81no—
182C22—81no—
183C22—161no—
184C22—161no—
185C22#39311yescharacteristic
186C22#45311yescharacteristic
187C22#45411yescharacteristic
188C4—21no—
189C4—21no—
190C4—21no—
191C4—21no—
192C4—42no—
193C4—81no—
194C4—81no—
195C4—81no—
196C4—81no—
197C4—81no—
198C4—82no—
199C4—81no—
200C2—21no—
201C2—21no—
202C2—41no—
203C2—41no—
204C2—161no—
205C2#202711yescharacteristic
206C2#203111yescharacteristic
207C2#203211yescharacteristic
subgroupG/H
center, socleC22#393
commutator, Frattini, cosocleC23×C4C23
prime radicalC2×#121C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #2667C2semidirect
5. #1305C2semidirect
6. #1297C2semidirect
7. #1284C2semidirect

Maximal subgroups

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

subgroupindex
#26672
#19642
#15102
#15072
#13052
#12972
#12842