Finite Group Databasebeta

← #10073

Subgroups — #10073

Order 256.

283 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 283 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C2×#487C211yesmaximal, characteristic
2C2×#475C211yesmaximal, characteristic
3#2567C211yesmaximal, characteristic
4#1981C211yesmaximal, characteristic
5C2×#333C211yesmaximal, characteristic
6C2×Q8⋊C8C211yesmaximal, characteristic
7#1279C211yesmaximal, characteristic
8C2×C4⋊Q8C2211yescharacteristic
9C2×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8C2211yescharacteristic
11#487—22no—
12#487—22no—
13#475—22no—
14#475—22no—
15C2×#106—21no—
16C2×C4⋊C8C2211yescharacteristic
17C2×C4⋊C8C2211yescharacteristic
18C2×#103—21no—
19C2×#103—22no—
20C2×#103—22no—
21C2×C4×C8C2211yescharacteristic
22#395—22no—
23#391—21no—
24#389—22no—
25#384—21no—
26C4×C4⋊C4C2211yescharacteristic
27#333—22no—
28Q8⋊C8—22no—
29C22×Q8—21no—
30C22×Q8D411yescharacteristic
31C22×Q8D412yes—
32C22×C8—21no—
33C22×C8—21no—
34C22×C8—21no—
35C4⋊Q8—21no—
36C4⋊Q8—21no—
37C4⋊Q8—21no—
38C4⋊Q8—21no—
39C4⋊Q8—21no—
40C4⋊Q8—21no—
41C4⋊Q8—21no—
42C4⋊Q8D412yes—
43C4×Q8—21no—
44C4×Q8—21no—
45C4×Q8—21no—
46C4×Q8—21no—
47C2×C4⋊C4—21no—
48C2×C4⋊C4—21no—
49C2×C4⋊C4—21no—
50C2×C4⋊C4—21no—
51C2×C4⋊C4—21no—
52C2×C4⋊C4—24no—
53C2×C4⋊C4D411yescharacteristic
54C2×C4⋊C4D412yes—
55C2×C42—21no—
56C2×C42—21no—
57C2×C42C2311yescharacteristic
58#106—24no—
59C4⋊C8—21no—
60C4⋊C8—21no—
61C4⋊C8—21no—
62C4⋊C8D412yes—
63#103—24no—
64#103—28no—
65#103—44no—
66C4×C8—21no—
67C4×C8D412yes—
68#95—24no—
69#95—21no—
70C2×Q8—21no—
71C2×Q8—21no—
72C2×Q8—22no—
73C2×Q8—21no—
74C2×Q8—22no—
75C2×Q8—22no—
76C2×Q8—21no—
77C2×Q8—21no—
78C2×Q8—44no—
79C2×Q8—41no—
80C2×Q8—42no—
81C2×Q8—42no—
82C2×Q8Q1612yes—
83C22×C4—21no—
84C22×C4—22no—
85C22×C4—22no—
86C22×C4—21no—
87C22×C4—41no—
88C22×C4C2×D411yescharacteristic
89C22×C4C2×D411yescharacteristic
90C22×C4C2×D411yescharacteristic
91C2×C8—22no—
92C2×C8—22no—
93C2×C8—42no—
94C2×C8—41no—
95C2×C8—41no—
96C2×C8—41no—
97C2×C8—42no—
98C4⋊C4—22no—
99C4⋊C4—22no—
100C4⋊C4—22no—
101C4⋊C4—21no—
102C4⋊C4—21no—
103C4⋊C4—41no—
104C4⋊C4—41no—
105C4⋊C4—41no—
106C4⋊C4—41no—
107C4⋊C4—41no—
108C4⋊C4—41no—
109C4⋊C4—41no—
110C4⋊C4—41no—
111C4⋊C4—84no—
112C4⋊C4SD1614yes—
113C42—41no—
114C42—41no—
115C42—41no—
116C42—41no—
117C42C2×D411yescharacteristic
118C42C2×D411yescharacteristic
119C42C2×D411yescharacteristic
120C42#4111yescharacteristic
121C23#12011yescharacteristic
122Q8—22no—
123Q8—22no—
124Q8—44no—
125Q8—41no—
126Q8—41no—
127Q8—44no—
128Q8—82no—
129Q8—81no—
130Q8—81no—
131C2×C4—22no—
132C2×C4—24no—
133C2×C4—22no—
134C2×C4—41no—
135C2×C4—42no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—41no—
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—44no—
143C2×C4—82no—
144C2×C4#12011yescharacteristic
145C2×C4#12011yescharacteristic
146C2×C4#12111yescharacteristic
147C2×C4#12111yescharacteristic
148C2×C4#12111yescharacteristic
149C2×C4#12711yescharacteristic
150C2×C4C2×SD1612yes—
151C2×C4C2×Q1611yescharacteristic
152C2×C4#13511yescharacteristic
153C2×C4#13711yescharacteristic
154C2×C4#13711yescharacteristic
155C2×C4#13712yes—
156C8—42no—
157C8—42no—
158C8—81no—
159C22#39211yescharacteristic
160C22#44812yes—
161C22#45111yescharacteristic
162C22#45211yescharacteristic
163C22#45512yes—
164C4—21no—
165C4—21no—
166C4—44no—
167C4—42no—
168C4—81no—
169C4—82no—
170C4—82no—
171C4#45111yescharacteristic
172C4#45211yescharacteristic
173C4#46112yes—
174C4#46711yescharacteristic
175C4#47011yescharacteristic
176C4#49211yescharacteristic
177C4#49711yescharacteristic
178C2#164312yes—
179C2#164512yes—
180C2#200111yescharacteristic
181C2#200411yescharacteristic
182C2#201311yescharacteristic
subgroupG/H
center, socle, prime radicalC23#120
commutator, Frattini, cosocleC2×C42C23
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ 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
C2×#4872
C2×#4752
#25672
#19812
C2×#3332
C2×Q8⋊C82
#12792