Finite Group Databasebeta

← #10075

Subgroups — #10075

Order 256.

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

normal subgroups only

This group has 293 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×#498C211yesmaximal, characteristic
2C2×#475C211yesmaximal, characteristic
3#2546C211yesmaximal, characteristic
4#1981C211yesmaximal, characteristic
5C2×#332C211yesmaximal, characteristic
6C2×Q8⋊C8C211yesmaximal, characteristic
7#1279C211yesmaximal, characteristic
8C2×C4⋊Q8—21no—
9C2×C4⋊Q8C2211yescharacteristic
10C2×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8C2211yescharacteristic
12#498—22no—
13#498—22no—
14#475—22no—
15#475—22no—
16C2×#106—21no—
17C2×#106—22no—
18C2×C4⋊C8C2211yescharacteristic
19C2×C4⋊C8C2211yescharacteristic
20C2×#103—21no—
21C2×#103—22no—
22C2×C4×C8C2211yescharacteristic
23#398—22no—
24#391—21no—
25#389—22no—
26C4×C4⋊C4C2211yescharacteristic
27#332—22no—
28Q8⋊C8—22no—
29C22×Q8—21no—
30C22×Q8—21no—
31C22×Q8D411yescharacteristic
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⋊Q8—42no—
43C4⋊Q8—42no—
44C4⋊Q8D412yes—
45C4×Q8—21no—
46C4×Q8—21no—
47C4×Q8—21no—
48C4×Q8—21no—
49C2×C4⋊C4—21no—
50C2×C4⋊C4—21no—
51C2×C4⋊C4—24no—
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—24no—
61#106—28no—
62C4⋊C8—21no—
63C4⋊C8—21no—
64C4⋊C8—21no—
65C4⋊C8D412yes—
66#103—24no—
67#103—44no—
68C4×C8—21no—
69C4×C8D412yes—
70#95—24no—
71#95—21no—
72C2×Q8—21no—
73C2×Q8—21no—
74C2×Q8—21no—
75C2×Q8—22no—
76C2×Q8—21no—
77C2×Q8—21no—
78C2×Q8—41no—
79C2×Q8—41no—
80C2×Q8—41no—
81C2×Q8—41no—
82C2×Q8—41no—
83C2×Q8—41no—
84C2×Q8—41no—
85C2×Q8—42no—
86C2×Q8—42no—
87C2×Q8SD1612yes—
88C22×C4—22no—
89C22×C4—21no—
90C22×C4—21no—
91C22×C4—22no—
92C22×C4—41no—
93C22×C4C2×D411yescharacteristic
94C22×C4C2×D411yescharacteristic
95C22×C4C2×D411yescharacteristic
96C2×C8—24no—
97C2×C8—22no—
98C2×C8—22no—
99C2×C8—41no—
100C2×C8—41no—
101C2×C8—41no—
102C2×C8—42no—
103C4⋊C4—22no—
104C4⋊C4—22no—
105C4⋊C4—22no—
106C4⋊C4—21no—
107C4⋊C4—22no—
108C4⋊C4—21no—
109C4⋊C4—22no—
110C4⋊C4—48no—
111C4⋊C4—41no—
112C4⋊C4—41no—
113C4⋊C4—41no—
114C4⋊C4—41no—
115C4⋊C4—41no—
116C4⋊C4—41no—
117C4⋊C4SD1614yes—
118C42—41no—
119C42—41no—
120C42—41no—
121C42—41no—
122C42C2×D411yescharacteristic
123C42C2×D411yescharacteristic
124C42C2×D411yescharacteristic
125C42#4111yescharacteristic
126C23#12011yescharacteristic
127Q8—22no—
128Q8—22no—
129Q8—41no—
130Q8—41no—
131Q8—44no—
132Q8—81no—
133Q8—81no—
134Q8—81no—
135Q8—81no—
136Q8—81no—
137Q8—81no—
138C2×C4—22no—
139C2×C4—24no—
140C2×C4—22no—
141C2×C4—41no—
142C2×C4—42no—
143C2×C4—41no—
144C2×C4—42no—
145C2×C4—41no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—42no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—82no—
152C2×C4#12011yescharacteristic
153C2×C4#12011yescharacteristic
154C2×C4#12111yescharacteristic
155C2×C4#12111yescharacteristic
156C2×C4#12111yescharacteristic
157C2×C4#12711yescharacteristic
158C2×C4C2×SD1611yescharacteristic
159C2×C4C2×SD1612yes—
160C2×C4#13511yescharacteristic
161C2×C4AGL(1,ℤ/8)11yescharacteristic
162C2×C4#13711yescharacteristic
163C2×C4#13712yes—
164C8—24no—
165C8—42no—
166C8—81no—
167C22#39211yescharacteristic
168C22#44812yes—
169C22#45011yescharacteristic
170C22#45211yescharacteristic
171C22#45612yes—
172C4—21no—
173C4—21no—
174C4—44no—
175C4—42no—
176C4—82no—
177C4—81no—
178C4—82no—
179C4#44811yescharacteristic
180C4#44911yescharacteristic
181C4#46112yes—
182C4#46511yescharacteristic
183C4#46811yescharacteristic
184C4#49211yescharacteristic
185C4#49711yescharacteristic
186C2#165112yes—
187C2#165312yes—
188C2#200011yescharacteristic
189C2#200511yescharacteristic
190C2#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×#4982
C2×#4752
#25462
#19812
C2×#3322
C2×Q8⋊C82
#12792