Finite Group Databasebeta

← #10069

Subgroups — #10069

Order 256.

283 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 283 conjugacy classes of subgroups — too many to draw. Only its 75 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×#498C211yesmaximal, characteristic
2C2×#462C211yesmaximal, characteristic
3#2568C211yesmaximal, characteristic
4#1988C211yesmaximal, characteristic
5C2×#332C211yesmaximal, characteristic
6C2×Q8⋊C8C211yesmaximal, characteristic
7#1279C211yesmaximal, characteristic
8C22×Q16—21no—
9C2×C4⋊Q8C2211yescharacteristic
10C2×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8C2211yescharacteristic
12#498—22no—
13#498—22no—
14#462—22no—
15#462—22no—
16C2×#106—22no—
17C2×C4⋊C8C2211yescharacteristic
18C2×C4⋊C8C2211yescharacteristic
19C2×#103—21no—
20C2×C4×C8C2211yescharacteristic
21#400—22no—
22#391—21no—
23#391—22no—
24#382—21no—
25C4×C4⋊C4C2211yescharacteristic
26#340—22no—
27#332—22no—
28Q8⋊C8—22no—
29C22×Q8—21no—
30C22×Q8—21no—
31C22×Q8D411yescharacteristic
32C2×Q16—24no—
33C2×Q16—42no—
34C2×Q16—42no—
35C22×C8—21no—
36C22×C8—21no—
37C22×C8—21no—
38C4⋊Q8—21no—
39C4⋊Q8—21no—
40C4⋊Q8—21no—
41C4⋊Q8—21no—
42C4⋊Q8—21no—
43C4⋊Q8—21no—
44C4⋊Q8—21no—
45C4⋊Q8D412yes—
46C4×Q8—21no—
47C4×Q8—21no—
48C4×Q8—21no—
49C4×Q8—21no—
50C2×C4⋊C4—21no—
51C2×C4⋊C4—21no—
52C2×C4⋊C4—21no—
53C2×C4⋊C4—21no—
54C2×C4⋊C4D411yescharacteristic
55C2×C4⋊C4D412yes—
56C2×C4⋊C4D412yes—
57C2×C42—21no—
58C2×C42—21no—
59C2×C42C2311yescharacteristic
60#106—28no—
61C4⋊C8—21no—
62C4⋊C8—21no—
63C4⋊C8—21no—
64C4⋊C8D412yes—
65#103—24no—
66C4×C8—21no—
67C4×C8D412yes—
68#95—24no—
69#95—24no—
70#95—21no—
71C2×Q8—21no—
72C2×Q8—21no—
73C2×Q8—22no—
74C2×Q8—21no—
75C2×Q8—21no—
76C2×Q8—21no—
77C2×Q8—41no—
78C2×Q8—41no—
79C2×Q8—41no—
80C2×Q8—42no—
81C2×Q8—42no—
82C2×Q8—41no—
83C2×Q8—41no—
84C2×Q8—41no—
85C2×Q8—41no—
86C2×Q8SD1612yes—
87C22×C4—21no—
88C22×C4—22no—
89C22×C4—21no—
90C22×C4—22no—
91C22×C4—41no—
92C22×C4C2×D411yescharacteristic
93C22×C4C2×D411yescharacteristic
94C22×C4C2×D411yescharacteristic
95Q16—48no—
96C2×C8—24no—
97C2×C8—22no—
98C2×C8—22no—
99C2×C8—41no—
100C2×C8—41no—
101C2×C8—41no—
102C2×C8—42no—
103C4⋊C4—21no—
104C4⋊C4—22no—
105C4⋊C4—22no—
106C4⋊C4—22no—
107C4⋊C4—21no—
108C4⋊C4—22no—
109C4⋊C4—22no—
110C4⋊C4—22no—
111C4⋊C4—41no—
112C4⋊C4—41no—
113C4⋊C4—41no—
114C4⋊C4—41no—
115C4⋊C4—41no—
116C4⋊C4—41no—
117C42—41no—
118C42—41no—
119C42—41no—
120C42—41no—
121C42C2×D411yescharacteristic
122C42C2×D411yescharacteristic
123C42C2×D411yescharacteristic
124C42#4111yescharacteristic
125C23#12011yescharacteristic
126Q8—22no—
127Q8—22no—
128Q8—41no—
129Q8—41no—
130Q8—42no—
131Q8—42no—
132Q8—82no—
133Q8—81no—
134Q8—81no—
135Q8—81no—
136Q8—81no—
137C2×C4—22no—
138C2×C4—22no—
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—81no—
150C2×C4—81no—
151C2×C4#12011yescharacteristic
152C2×C4#12011yescharacteristic
153C2×C4#12111yescharacteristic
154C2×C4#12111yescharacteristic
155C2×C4#12111yescharacteristic
156C2×C4#12711yescharacteristic
157C2×C4C2×SD1611yescharacteristic
158C2×C4#13511yescharacteristic
159C2×C4#13512yes—
160C2×C4AGL(1,ℤ/8)11yescharacteristic
161C2×C4#13711yescharacteristic
162C2×C4#13712yes—
163C8—24no—
164C8—42no—
165C8—81no—
166C22#39211yescharacteristic
167C22#44811yescharacteristic
168C22#44911yescharacteristic
169C22#45212yes—
170C22#45612yes—
171C4—21no—
172C4—21no—
173C4—42no—
174C4—82no—
175C4—82no—
176C4—81no—
177C4—82no—
178C4#45011yescharacteristic
179C4#45211yescharacteristic
180C4#46412yes—
181C4#46511yescharacteristic
182C4#46811yescharacteristic
183C4#49511yescharacteristic
184C4#49711yescharacteristic
185C2#165212yes—
186C2#165312yes—
187C2#200011yescharacteristic
188C2#200511yescharacteristic
189C2#201511yescharacteristic
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×#4982
C2×#4622
#25682
#19882
C2×#3322
C2×Q8⋊C82
#12792