Finite Group Databasebeta

← #10383

Subgroups — #10383

Order 256.

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

normal subgroups only

This group has 202 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#2665C211yesmaximal, characteristic
2#1996C211yesmaximal, characteristic
3#1511C211yesmaximal, characteristic
4#1508C211yesmaximal, characteristic
5#1305C211yesmaximal, characteristic
6#1297C211yesmaximal, characteristic
7#1284C211yesmaximal, characteristic
8C2×C22⋊Q8C2211yescharacteristic
9#407C2211yescharacteristic
10#407C2211yescharacteristic
11#400—21no—
12#396—21no—
13#395—21no—
14#393—21no—
15#391—21no—
16#387—21no—
17#381C2211yescharacteristic
18#380C2211yescharacteristic
19C4×C22⋊C4C2211yescharacteristic
20C4×C22⋊C4C2211yescharacteristic
21#342—21no—
22#342—21no—
23#328—21no—
24#328—21no—
25#328—21no—
26#328—21no—
27C22×Q8—21no—
28C22×Q8Q811yescharacteristic, complemented
29C23×C4C2311yescharacteristic
30C2×M16—21no—
31C2×M16—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⋊C4Q811yescharacteristic, complemented
42C2×C22⋊C4—21no—
43C2×C22⋊C4—21no—
44C2×C22⋊C4—21no—
45C2×C22⋊C4—21no—
46C2×C22⋊C4D411yescharacteristic
47C2×C22⋊C4D411yescharacteristic
48C2×C42—21no—
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—42no—
69C2×Q8—81no—
70C2×Q8—81no—
71C2×Q8—81no—
72C22×C4—21no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—21no—
80C22×C4—41no—
81C22×C4—81no—
82C22×C4C2×D411yescharacteristic
83C22×C4C2×D411yescharacteristic
84C22×C4C2×Q811yescharacteristic
85C22×C4#4111yescharacteristic
86C22×C4#4111yescharacteristic
87C22×C4#4111yescharacteristic
88M16—81no—
89M16—81no—
90C2×C8—41no—
91C2×C8—41no—
92C4⋊C4—21no—
93C4⋊C4—21no—
94C4⋊C4—42no—
95C4⋊C4—41no—
96C4⋊C4—41no—
97C4⋊C4—81no—
98C4⋊C4—81no—
99C4⋊C4—81no—
100C22⋊C4—22no—
101C22⋊C4—42no—
102C22⋊C4—41no—
103C22⋊C4—41no—
104C22⋊C4—41no—
105C22⋊C4—41no—
106C22⋊C4—41no—
107C22⋊C4—81no—
108C42—81no—
109C42—81no—
110C23—21no—
111C23—21no—
112C23—41no—
113C23—41no—
114C23#12011yescharacteristic
115C23C22⋊Q811yescharacteristic
116C23#12411yescharacteristic
117Q8—81no—
118Q8—81no—
119Q8—84no—
120C2×C4—22no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—42no—
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—81no—
148C2×C4—81no—
149C2×C4—81no—
150C2×C4—81no—
151C2×C4C22⋊Q811yescharacteristic
152C2×C4C22⋊Q811yescharacteristic
153C2×C4#12411yescharacteristic
154C2×C4#12411yescharacteristic
155C8—81no—
156C8—81no—
157C22—21no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—21no—
164C22—21no—
165C22—81no—
166C22—81no—
167C22#39311yescharacteristic
168C22#45511yescharacteristic
169C22#45611yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—42no—
175C4—81no—
176C4—81no—
177C4—81no—
178C4—81no—
179C4—81no—
180C4—82no—
181C4—81no—
182C4—81no—
183C2—21no—
184C2—21no—
185C2—41no—
186C2—41no—
187C2#202811yescharacteristic
188C2#203111yescharacteristic
189C2#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

Complements

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

NH ≅ G/Ntype
28. C22×Q8Q8semidirect
41. C2×C4⋊C4Q8semidirect

Maximal subgroups

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

subgroupindex
#26652
#19962
#15112
#15082
#13052
#12972
#12842