Finite Group Databasebeta

← #9250

Subgroups — #9250

Order 256.

217 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 217 conjugacy classes of subgroups — too many to draw. Only its 73 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×#477C211yesmaximal, characteristic
2Q8×M16C211yesmaximal, characteristic
3#1997C211yesmaximal, characteristic
4#1549C211yesmaximal, characteristic
5#1487C211yesmaximal, characteristic
6#1292C211yesmaximal, characteristic
7#1283C211yesmaximal, characteristic
8C2×C4⋊Q8C2211yescharacteristic
9C2×C4×Q8C2211yescharacteristic
10#477—21no—
11#477—21no—
12#477—21no—
13#477—21no—
14#446—21no—
15#446—22no—
16C8×Q8—21no—
17#431C2211yescharacteristic
18C2×#107C412yes—
19#423—21no—
20#423C2211yescharacteristic
21#423C2211yescharacteristic
22C2×C4⋊C8C2211yescharacteristic
23C2×#103C412yes—
24C4×M16—21no—
25C4×M16C2211yescharacteristic
26#343—21no—
27#343—21no—
28#332—22no—
29Q8⋊C8—21no—
30Q8⋊C8—21no—
31C22×Q8—21no—
32C22×Q8C2×C411yescharacteristic
33C2×M16—21no—
34C2×M16—21no—
35C2×M16D411yescharacteristic
36C2×M16D411yescharacteristic
37C22×C8C2×C412yes—
38C4⋊Q8—21no—
39C4⋊Q8—21no—
40C4⋊Q8—21no—
41C4⋊Q8—21no—
42C4×Q8—21no—
43C4×Q8—21no—
44C4×Q8D411yescharacteristic
45C4×Q8D411yescharacteristic
46C4×Q8D411yescharacteristic
47C4×Q8D411yescharacteristic
48C2×C4⋊C4—21no—
49C2×C4⋊C4—21no—
50C2×C4⋊C4C2×C412yes—
51C2×C4⋊C4C2×C411yescharacteristic
52C2×C42—21no—
53C2×C42C2311yescharacteristic
54#107—22no—
55#107—22no—
56C4⋊C8—22no—
57C4⋊C8—22no—
58C4⋊C8—21no—
59C4⋊C8—21no—
60C4⋊C8—21no—
61C4⋊C8—21no—
62C4⋊C8—21no—
63C4⋊C8—21no—
64C4⋊C8D412yes—
65#103—22no—
66#103—22no—
67C22⋊C8—21no—
68#97—22no—
69#97—21no—
70C4×C8—22no—
71C4×C8—21no—
72C4×C8—21no—
73C2×Q8—21no—
74C2×Q8—22no—
75C2×Q8—41no—
76C2×Q8—41no—
77C2×Q8—41no—
78C2×Q8—82no—
79C2×Q8C22⋊C411yescharacteristic
80C2×Q8C22⋊C411yescharacteristic
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—22no—
84C22×C4C22×C411yescharacteristic
85C22×C4C2×D411yescharacteristic
86C22×C4#4111yescharacteristic
87M16—21no—
88M16—21no—
89M16—21no—
90M16—41no—
91M16—41no—
92M16—41no—
93M16—41no—
94M16Q1612yes—
95C2×C8—21no—
96C2×C8—22no—
97C2×C8—21no—
98C2×C8—22no—
99C2×C8—42no—
100C2×C8—41no—
101C2×C8—41no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—21no—
106C4⋊C4—21no—
107C4⋊C4—22no—
108C4⋊C4—22no—
109C4⋊C4—41no—
110C4⋊C4—41no—
111C4⋊C4C22⋊C411yescharacteristic
112C4⋊C4C22⋊C411yescharacteristic
113C42—21no—
114C42—21no—
115C42—21no—
116C42—21no—
117C42C2×D411yescharacteristic
118C42C2×D411yescharacteristic
119C42C2×D411yescharacteristic
120C42#4111yescharacteristic
121C23C4×D411yescharacteristic
122Q8—21no—
123Q8—21no—
124Q8—21no—
125Q8—42no—
126Q8—82no—
127Q8—82no—
128Q8#10112yes—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—41no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4—81no—
139C2×C4—82no—
140C2×C4C2×C22⋊C411yescharacteristic
141C2×C4C4×D411yescharacteristic
142C2×C4#12011yescharacteristic
143C2×C4#12111yescharacteristic
144C2×C4#12111yescharacteristic
145C2×C4#12311yescharacteristic
146C2×C4C2×Q1611yescharacteristic
147C2×C4#13511yescharacteristic
148C2×C4#13711yescharacteristic
149C2×C4#13711yescharacteristic
150C8—22no—
151C8—42no—
152C8—41no—
153C8—42no—
154C8—81no—
155C8—81no—
156C22—21no—
157C22—21no—
158C22#38611yescharacteristic
159C22C4×Q1611yescharacteristic
160C22#44111yescharacteristic
161C4—21no—
162C4—22no—
163C4—21no—
164C4—21no—
165C4—41no—
166C4—41no—
167C4—41no—
168C4—82no—
169C4C2×#10111yescharacteristic
170C4#41311yescharacteristic
171C4#45111yescharacteristic
172C4#45211yescharacteristic
173C4#46211yescharacteristic
174C4#46411yescharacteristic
175C2—21no—
176C2—21no—
177C2#187811yescharacteristic
178C2#190111yescharacteristic
179C2#190311yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
prime radicalC23C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ 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×#4772
Q8×M162
#19972
#15492
#14872
#12922
#12832