Finite Group Databasebeta

← #8876

Subgroups — #8876

Order 256.

190 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 61 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#2992C211yesmaximal, characteristic
2#1843C211yesmaximal, characteristic, complemented
3#1573C211yesmaximal, characteristic, complemented
4#1500C211yesmaximal, characteristic
5#1483C211yesmaximal, characteristic
6#1300C211yesmaximal, characteristic, complemented
7#1283C211yesmaximal, characteristic, complemented
8#529C2211yescharacteristic
9#446—21no—
10#435—21no—
11#435—21no—
12C8×D4—21no—
13#433—21no—
14#432C2211yescharacteristic
15#431C2211yescharacteristic
16#424—21no—
17C2×C4⋊C8—21no—
18C2×C4⋊C8—21no—
19C2×C4⋊C8C2211yescharacteristic
20C2×C4⋊C8C2211yescharacteristic
21C4×M16C2211yescharacteristic
22#376C2211yescharacteristic
23#335—21no—
24#334—21no—
25#328C411yescharacteristic
26#328C411yescharacteristic
27#327C411yescharacteristic
28#327C411yescharacteristic
29Q8⋊C8—21no—
30D4⋊C8—21no—
31C2×M16—21no—
32C2×M16—21no—
33C22×C8—21no—
34C22×C8—21no—
35C22×C8D411yescharacteristic
36C22×C8D411yescharacteristic
37#126—21no—
38#125Q811yescharacteristic
39#124Q811yescharacteristic
40#123—21no—
41C22⋊Q8C2×C411yescharacteristic
42#121C2×C411yescharacteristic
43C4×Q8D411yescharacteristic
44C4×D4—21no—
45C4×D4D411yescharacteristic
46#117—21no—
47C2×C42—21no—
48C2×C42C2311yescharacteristic
49C4⋊C8—21no—
50C4⋊C8—21no—
51C4⋊C8—21no—
52C4⋊C8—21no—
53C4⋊C8—21no—
54C4⋊C8—21no—
55C4⋊C8—21no—
56C4⋊C8—42no—
57C4⋊C8—42no—
58C4⋊C8D411yescharacteristic
59C4⋊C8D411yescharacteristic
60C22⋊C8—21no—
61C22⋊C8—21no—
62C22⋊C8—21no—
63C22⋊C8C2×C411yescharacteristic
64C22⋊C8C2×C411yescharacteristic
65#97—21no—
66#97—21no—
67#97—21no—
68C4×C8—21no—
69C4×C8—21no—
70C4×C8—21no—
71#95—21no—
72#95C2×C411yescharacteristic
73#95C2×C411yescharacteristic
74C2×Q8C4⋊C411yescharacteristic
75C2×D4—21no—
76C2×D4C4⋊C411yescharacteristic
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—21no—
80C22×C4C22×C411yescharacteristic
81C22×C4C2×D411yescharacteristic
82C22×C4#4111yescharacteristic
83M16—22no—
84M16—41no—
85M16—81no—
86C2×C8—21no—
87C2×C8—21no—
88C2×C8—21no—
89C2×C8—21no—
90C2×C8—21no—
91C2×C8—21no—
92C2×C8—41no—
93C2×C8—41no—
94C2×C8—41no—
95C2×C8—41no—
96C2×C8—41no—
97C2×C8—41no—
98C2×C8—81no—
99C4⋊C4—21no—
100C4⋊C4—21no—
101C4⋊C4—21no—
102C4⋊C4—21no—
103C4⋊C4C4⋊C411yescharacteristic
104C4⋊C4C4⋊C411yescharacteristic
105C22⋊C4—21no—
106C22⋊C4—21no—
107C22⋊C4—21no—
108C22⋊C4—21no—
109C22⋊C4—21no—
110C42—22no—
111C42—22no—
112C42—21no—
113C42C2×D411yescharacteristic
114C42C2×D411yescharacteristic
115C42C2×Q811yescharacteristic
116C42#4111yescharacteristic
117C23—21no—
118C23C4×D411yescharacteristic
119Q8—41no—
120D4—41no—
121D4—41no—
122D4—41no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—22no—
128C2×C4—22no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4C2×C4⋊C411yescharacteristic
140C2×C4C4×D411yescharacteristic
141C2×C4#12011yescharacteristic
142C2×C4C22⋊Q811yescharacteristic
143C2×C4C22⋊Q811yescharacteristic
144C2×C4#12311yescharacteristic
145C8—41no—
146C8—41no—
147C8—42no—
148C8—41no—
149C8—41no—
150C8—41no—
151C8—41no—
152C8—81no—
153C22—21no—
154C22—21no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#38511yescharacteristic
159C22#44311yescharacteristic
160C22#44411yescharacteristic
161C4—21no—
162C4—21no—
163C4—21no—
164C4—21no—
165C4—21no—
166C4—42no—
167C4—42no—
168C4—41no—
169C4—41no—
170C4—41no—
171C4#45311yescharacteristic
172C4#45611yescharacteristic
173C2—21no—
174C2—21no—
175C2—81no—
176C2#185911yescharacteristic
177C2#186611yescharacteristic
178C2#186811yescharacteristic
subgroupG/H
centerC2×C4#120
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
socleC22#385
prime radical#121C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #1843C2semidirect
3. #1573C2semidirect
6. #1300C2semidirect
7. #1283C2semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#29922
#18432
#15732
#15002
#14832
#13002
#12832