Finite Group Databasebeta

← #10422

Subgroups — #10422

Order 256.

226 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 71 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#2568C211yesmaximal, characteristic
2#1990C211yesmaximal, characteristic
3#1947C211yesmaximal, characteristic
4#1803C211yesmaximal, characteristic
5C2×#332C211yesmaximal, characteristic
6C2×Q8⋊C8C211yesmaximal, characteristic
7#1279C211yesmaximal, characteristic
8C2×C4⋊Q8C2211yescharacteristic
9C2×C4×Q8C2211yescharacteristic
10C2×#107—21no—
11C2×C4⋊C8C2211yescharacteristic
12C2×C4⋊C8C2211yescharacteristic
13C2×#103—21no—
14C2×C4×C8C2211yescharacteristic
15#400—22no—
16#391—21no—
17#391—21no—
18#391—21no—
19#384C2211yescharacteristic
20#382—21no—
21C4×C4⋊C4C2211yescharacteristic
22#340—21no—
23#340—21no—
24#340—22no—
25#332—22no—
26Q8⋊C8—22no—
27C22×Q8—21no—
28C22×Q8D411yescharacteristic
29C22×C8—21no—
30C22×C8—21no—
31C22×C8—21no—
32C4⋊Q8—21no—
33C4⋊Q8—21no—
34C4⋊Q8—21no—
35C4⋊Q8—21no—
36C4×Q8—21no—
37C4×Q8—21no—
38C4×Q8—21no—
39C4×Q8—21no—
40C2×C4⋊C4—21no—
41C2×C4⋊C4—21no—
42C2×C4⋊C4—21no—
43C2×C4⋊C4—21no—
44C2×C4⋊C4—21no—
45C2×C4⋊C4D411yescharacteristic
46C2×C4⋊C4D412yes—
47C2×C4⋊C4D411yescharacteristic
48C2×C4⋊C4D411yescharacteristic
49C2×C42—21no—
50C2×C42—21no—
51C2×C42C2311yescharacteristic
52#107—42no—
53C4⋊C8—21no—
54C4⋊C8—21no—
55C4⋊C8—21no—
56C4⋊C8D412yes—
57#103—42no—
58C4×C8—21no—
59C4×C8—21no—
60#95—22no—
61#95—22no—
62#95—22no—
63#95—22no—
64#95—21no—
65C2×Q8—21no—
66C2×Q8—21no—
67C2×Q8—21no—
68C2×Q8—21no—
69C2×Q8—21no—
70C2×Q8—41no—
71C2×Q8—41no—
72C2×Q8—41no—
73C2×Q8—41no—
74C2×Q8—41no—
75C2×Q8—41no—
76C2×Q8Q1612yes—
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—22no—
82C22×C4—41no—
83C22×C4C2×D411yescharacteristic
84C22×C4C2×D411yescharacteristic
85C22×C4C2×D411yescharacteristic
86C2×C8—22no—
87C2×C8—22no—
88C2×C8—41no—
89C2×C8—41no—
90C2×C8—41no—
91C2×C8—41no—
92C2×C8—41no—
93C2×C8—41no—
94C2×C8—41no—
95C4⋊C4—21no—
96C4⋊C4—22no—
97C4⋊C4—21no—
98C4⋊C4—22no—
99C4⋊C4—21no—
100C4⋊C4—21no—
101C4⋊C4—21no—
102C4⋊C4—21no—
103C4⋊C4—42no—
104C4⋊C4—41no—
105C4⋊C4—41no—
106C4⋊C4—41no—
107C4⋊C4—41no—
108C4⋊C4—41no—
109C4⋊C4—41no—
110C4⋊C4—41no—
111C4⋊C4—41no—
112C42—41no—
113C42—41no—
114C42—41no—
115C42—41no—
116C42C2×D411yescharacteristic
117C42#4111yescharacteristic
118C42#4111yescharacteristic
119C42#4111yescharacteristic
120C23#12011yescharacteristic
121Q8—22no—
122Q8—22no—
123Q8—41no—
124Q8—41no—
125Q8—81no—
126Q8—81no—
127Q8—81no—
128Q8—81no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—22no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—42no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—42no—
140C2×C4—41no—
141C2×C4—42no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—81no—
147C2×C4—81no—
148C2×C4—81no—
149C2×C4#12111yescharacteristic
150C2×C4#12111yescharacteristic
151C2×C4#12111yescharacteristic
152C2×C4#12311yescharacteristic
153C2×C4#12311yescharacteristic
154C2×C4#12411yescharacteristic
155C2×C4C2×Q1611yescharacteristic
156C2×C4#13511yescharacteristic
157C2×C4#13511yescharacteristic
158C2×C4#13511yescharacteristic
159C2×C4AGL(1,ℤ/8)11yescharacteristic
160C2×C4AGL(1,ℤ/8)11yescharacteristic
161C2×C4#13711yescharacteristic
162C2×C4#13711yescharacteristic
163C8—42no—
164C8—42no—
165C8—81no—
166C22#39411yescharacteristic
167C22#44911yescharacteristic
168C22#44911yescharacteristic
169C22#45111yescharacteristic
170C22#45211yescharacteristic
171C22#45411yescharacteristic
172C22#45611yescharacteristic
173C4—21no—
174C4—21no—
175C4—42no—
176C4—81no—
177C4—81no—
178C4—81no—
179C4—82no—
180C4—161no—
181C4#46311yescharacteristic
182C4#46411yescharacteristic
183C4#46711yescharacteristic
184C4#46811yescharacteristic
185C4#48411yescharacteristic
186C4#48511yescharacteristic
187C4#48811yescharacteristic
188C4#48911yescharacteristic
189C2#162811yescharacteristic
190C2#163611yescharacteristic
191C2#164811yescharacteristic
192C2#165211yescharacteristic
193C2#203611yescharacteristic
194C2#203811yescharacteristic
195C2#204211yescharacteristic
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
#25682
#19902
#19472
#18032
C2×#3322
C2×Q8⋊C82
#12792