Finite Group Databasebeta

← #9369

Subgroups — #9369

Order 256.

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

normal subgroups only

This group has 195 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
1#3240C211yesmaximal, characteristic
2#2967C211yesmaximal, characteristic
3#1521C211yesmaximal, characteristic
4#1515C211yesmaximal, characteristic, complemented
5#1485C211yesmaximal, characteristic, complemented
6#1288C211yesmaximal, characteristic, complemented
7#1287C211yesmaximal, characteristic, complemented
8#533C2211yescharacteristic
9#529C2211yescharacteristic
10#501C411yescharacteristic, complemented
11#501C411yescharacteristic, complemented
12#489C411yescharacteristic, complemented
13#489C411yescharacteristic, complemented
14#485—21no—
15#482—21no—
16#479—21no—
17#478—21no—
18#446—21no—
19#436—21no—
20#435—21no—
21#435—21no—
22#433—21no—
23#432C2211yescharacteristic
24#432C2211yescharacteristic
25#431C2211yescharacteristic
26#405—21no—
27C4×M16C2211yescharacteristic
28#383C2211yescharacteristic
29#328—21no—
30#328—21no—
31#328—21no—
32#327—21no—
33Q8⋊C8—21no—
34Q8⋊C8—21no—
35C2×M16—21no—
36C2×M16—21no—
37C22×C8—21no—
38C4⋊Q8C2×C411yescharacteristic
39C4⋊Q8C2×C411yescharacteristic
40#126—21no—
41#125—21no—
42#125C2×C411yescharacteristic
43#124C2×C411yescharacteristic
44#123—21no—
45C22⋊Q8—21no—
46C22⋊Q8—21no—
47C22⋊Q8D411yescharacteristic
48#121D411yescharacteristic
49C4×Q8—21no—
50C4×Q8—21no—
51C4×Q8D411yescharacteristic
52C4×D4—21no—
53C4×D4D411yescharacteristic
54#117—21no—
55#117—21no—
56C2×C42C2311yescharacteristic
57#107—21no—
58#107—21no—
59#106—21no—
60#106—21no—
61C4⋊C8—21no—
62C4⋊C8—21no—
63C4⋊C8—21no—
64C4⋊C8—21no—
65C4⋊C8—21no—
66#103—21no—
67#103—21no—
68#102—21no—
69#102—21no—
70C22⋊C8—21no—
71C22⋊C8—21no—
72C22⋊C8—21no—
73C22⋊C8—21no—
74C22⋊C8D411yescharacteristic
75C22⋊C8D411yescharacteristic
76#97—21no—
77#97—21no—
78#97—21no—
79#97C2×C411yescharacteristic
80#97C2×C411yescharacteristic
81C4×C8—21no—
82C4×C8—21no—
83C4×C8D411yescharacteristic
84C4×C8D411yescharacteristic
85#95—21no—
86#95—21no—
87#95—21no—
88C2×Q8—21no—
89C2×Q8—21no—
90C2×Q8C22⋊C411yescharacteristic
91C2×D4—21no—
92C2×D4C22⋊C411yescharacteristic
93C22×C4—21no—
94C22×C4—41no—
95C22×C4C2×D411yescharacteristic
96C22×C4C2×D411yescharacteristic
97C22×C4#4111yescharacteristic
98M16—42no—
99M16—42no—
100C2×C8—21no—
101C2×C8—21no—
102C2×C8—21no—
103C2×C8—21no—
104C2×C8—21no—
105C2×C8—21no—
106C2×C8—42no—
107C2×C8—41no—
108C4⋊C4—21no—
109C4⋊C4—21no—
110C4⋊C4—21no—
111C4⋊C4—21no—
112C4⋊C4—21no—
113C4⋊C4—21no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—41no—
117C4⋊C4—41no—
118C4⋊C4C22⋊C411yescharacteristic
119C4⋊C4C22⋊C411yescharacteristic
120C22⋊C4—21no—
121C22⋊C4—21no—
122C22⋊C4—21no—
123C22⋊C4—21no—
124C22⋊C4—21no—
125C22⋊C4—41no—
126C42—21no—
127C42—41no—
128C42C22×C411yescharacteristic
129C42C2×D411yescharacteristic
130C42C2×D411yescharacteristic
131C42#4111yescharacteristic
132C23—21no—
133C23#12111yescharacteristic
134Q8—41no—
135Q8—42no—
136Q8—81no—
137D4—41no—
138D4—81no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—81no—
150C2×C4—81no—
151C2×C4—81no—
152C2×C4C2×C22⋊C411yescharacteristic
153C2×C4C4×D411yescharacteristic
154C2×C4C4×D411yescharacteristic
155C2×C4#12011yescharacteristic
156C2×C4#12111yescharacteristic
157C2×C4#12311yescharacteristic
158C8—22no—
159C8—41no—
160C8—41no—
161C8—41no—
162C8—41no—
163C8—41no—
164C8—81no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22#38611yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—41no—
179C4—41no—
180C4—41no—
181C4—81no—
182C4—81no—
183C4—161no—
184C2—41no—
185C2—81no—
186C2#188111yescharacteristic
187C2#190611yescharacteristic
188C2#190911yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC42C22×C4
Frattini, cosocleC2×C42C23
prime radical#121D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #1515C2semidirect
5. #1485C2semidirect
6. #1288C2semidirect
7. #1287C2semidirect
10. #501C4semidirect
11. #501C4semidirect
12. #489C4semidirect
13. #489C4semidirect

Maximal subgroups

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

subgroupindex
#32402
#29672
#15212
#15152
#14852
#12882
#12872