Finite Group Databasebeta

← #10084

Subgroups — #10084

Order 256.

242 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 57 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×#501C211yesmaximal, characteristic
2C2×#491C211yesmaximal, characteristic
3#2822C211yesmaximal, characteristic
4#1993C211yesmaximal, characteristic
5C2×#330C211yesmaximal, characteristic
6C2×#330C211yesmaximal, characteristic
7#1295C211yesmaximal, characteristic
8C2×C4⋊Q8C2211yescharacteristic
9C2×#125C2211yescharacteristic
10C2×#125C2211yescharacteristic
11#501—22no—
12#501—22no—
13#491—22no—
14#491—22no—
15C2×#107—21no—
16C2×#106—21no—
17C2×#103—21no—
18C2×#103—21no—
19C2×#97C2211yescharacteristic
20C2×#97C2211yescharacteristic
21C2×#97C2211yescharacteristic
22#400—21no—
23#400—21no—
24#398—22no—
25#398—21no—
26#398—21no—
27#382C2211yescharacteristic
28#340—22no—
29#330—22no—
30#330—22no—
31C22×Q8—21no—
32C22×C8—21no—
33C22×C8—21no—
34C22×C8—21no—
35C4⋊Q8—21no—
36C4⋊Q8—21no—
37C4⋊Q8—21no—
38C4⋊Q8D412yes—
39#125—21no—
40#125—21no—
41#125—21no—
42#125—21no—
43#125—21no—
44#125—21no—
45#125—21no—
46#125—21no—
47C2×C4⋊C4—21no—
48C2×C4⋊C4—21no—
49C2×C4⋊C4—21no—
50C2×C4⋊C4—21no—
51C2×C4⋊C4—21no—
52C2×C4⋊C4—21no—
53C2×C4⋊C4—22no—
54C2×C4⋊C4D411yescharacteristic
55C2×C4⋊C4D411yescharacteristic
56C2×C4⋊C4D411yescharacteristic
57C2×C4⋊C4D411yescharacteristic
58C2×C4⋊C4D412yes—
59C2×C42C2311yescharacteristic
60#107—24no—
61#106—24no—
62#103—24no—
63#103—24no—
64#97—21no—
65#97—21no—
66#97—21no—
67#97—21no—
68#97D412yes—
69#97D412yes—
70#95—22no—
71#95—22no—
72#95—22no—
73#95—21no—
74#95—21no—
75C2×Q8—22no—
76C2×Q8—44no—
77C2×Q8—41no—
78C22×C4—22no—
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—41no—
84C22×C4C2×D411yescharacteristic
85C22×C4C2×D411yescharacteristic
86C22×C4C2×D411yescharacteristic
87C2×C8—24no—
88C2×C8—22no—
89C2×C8—22no—
90C2×C8—22no—
91C2×C8—42no—
92C2×C8—41no—
93C2×C8—41no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—21no—
97C4⋊C4—22no—
98C4⋊C4—21no—
99C4⋊C4—22no—
100C4⋊C4—21no—
101C4⋊C4—21no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—42no—
105C4⋊C4—41no—
106C4⋊C4—41no—
107C4⋊C4—41no—
108C4⋊C4—41no—
109C4⋊C4—41no—
110C4⋊C4—41no—
111C4⋊C4—41no—
112C4⋊C4—41no—
113C4⋊C4—41no—
114C4⋊C4—41no—
115C4⋊C4—82no—
116C42C2×D411yescharacteristic
117C42C2×D411yescharacteristic
118C42C2×D411yescharacteristic
119C42#4111yescharacteristic
120C23#12011yescharacteristic
121Q8—44no—
122Q8—82no—
123C2×C4—22no—
124C2×C4—21no—
125C2×C4—22no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—42no—
132C2×C4—42no—
133C2×C4—42no—
134C2×C4—42no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—42no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—82no—
142C2×C4#12011yescharacteristic
143C2×C4#12011yescharacteristic
144C2×C4#12111yescharacteristic
145C2×C4#12111yescharacteristic
146C2×C4#12111yescharacteristic
147C2×C4#12711yescharacteristic
148C8—24no—
149C8—42no—
150C8—42no—
151C22#39211yescharacteristic
152C22#45412yes—
153C22#45511yescharacteristic
154C22#45611yescharacteristic
155C22#45612yes—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—21no—
160C4—21no—
161C4—21no—
162C4—82no—
163C4—81no—
164C4—82no—
165C4—81no—
166C4—81no—
167C4—81no—
168C2#166312yes—
169C2#166412yes—
170C2#200311yescharacteristic
171C2#200511yescharacteristic
172C2#200711yescharacteristic
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×#5012
C2×#4912
#28222
#19932
C2×#3302
#12952