Finite Group Databasebeta

← #9532

Subgroups — #9532

Order 256.

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

normal subgroups only

This group has 222 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#3114C211yesmaximal, characteristic
2#2967C211yesmaximal, characteristic, complemented
3#1535C211yesmaximal, characteristic, complemented
4#1490C211yesmaximal, characteristic, complemented
5#1466C211yesmaximal, characteristic, complemented
6#1308C211yesmaximal, characteristic, complemented
7#1291C211yesmaximal, characteristic, complemented
8#529C2211yescharacteristic
9C2×C4×D4C2211yescharacteristic
10#483C411yescharacteristic
11#480C411yescharacteristic
12#478—21no—
13#463—21no—
14#450C411yescharacteristic
15#447C411yescharacteristic
16#446—21no—
17#442—21no—
18#440—21no—
19#436—21no—
20#435—21no—
21#435—21no—
22#433—21no—
23#432C2211yescharacteristic
24#432C2211yescharacteristic
25#432C2211yescharacteristic
26#432C2211yescharacteristic
27#405—21no—
28C4×M16C2211yescharacteristic
29#330—21no—
30#329—21no—
31D4⋊C8—21no—
32D4⋊C8—21no—
33#323—21no—
34#323—21no—
35C22×D4C2×C411yescharacteristic
36C23×C4—21no—
37C2×SD16—21no—
38C2×D8—21no—
39C2×M16—21no—
40C2×M16—21no—
41C22×C8—21no—
42#126—21no—
43#125D411yescharacteristic
44#124D411yescharacteristic
45#123—21no—
46C22⋊Q8C2×C411yescharacteristic
47#121C2×C411yescharacteristic
48C4×Q8D411yescharacteristic
49C4×D4—21no—
50C4×D4—21no—
51C4×D4—21no—
52C4×D4—21no—
53C4×D4—21no—
54C4×D4D411yescharacteristic
55#117—21no—
56C2×C4⋊C4C2×C411yescharacteristic
57C2×C22⋊C4—21no—
58C2×C42C2311yescharacteristic
59#107—21no—
60#106—21no—
61C4⋊C8—21no—
62C4⋊C8—21no—
63C4⋊C8—21no—
64C4⋊C8—21no—
65C4⋊C8—21no—
66C4⋊C8—21no—
67#103—21no—
68#102—21no—
69#102—21no—
70#102—21no—
71C22⋊C8—21no—
72C22⋊C8—21no—
73C22⋊C8—21no—
74C22⋊C8—21no—
75C22⋊C8C2×C411yescharacteristic
76C22⋊C8C2×C411yescharacteristic
77C22⋊C8D411yescharacteristic
78C22⋊C8D411yescharacteristic
79#97—21no—
80#97—21no—
81#97—21no—
82#97—21no—
83#97—21no—
84#97—21no—
85C4×C8—21no—
86C4×C8D411yescharacteristic
87C4×C8D411yescharacteristic
88C24—21no—
89C2×Q8C22⋊C411yescharacteristic
90C2×D4—21no—
91C2×D4—21no—
92C2×D4—21no—
93C2×D4—42no—
94C2×D4C22⋊C411yescharacteristic
95C22×C4—21no—
96C22×C4—21no—
97C22×C4—41no—
98C22×C4—41no—
99C22×C4—82no—
100C22×C4C22×C411yescharacteristic
101C22×C4C2×D411yescharacteristic
102C22×C4#4111yescharacteristic
103SD16—42no—
104D8—42no—
105M16—42no—
106M16—42no—
107C2×C8—21no—
108C2×C8—21no—
109C2×C8—21no—
110C2×C8—21no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—42no—
114C2×C8—41no—
115C2×C8—41no—
116C4⋊C4—21no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4C22⋊C411yescharacteristic
123C4⋊C4C22⋊C411yescharacteristic
124C22⋊C4—21no—
125C22⋊C4—21no—
126C22⋊C4—21no—
127C22⋊C4—21no—
128C22⋊C4—21no—
129C22⋊C4—41no—
130C22⋊C4—41no—
131C42—21no—
132C42C2×D411yescharacteristic
133C42C2×D411yescharacteristic
134C42C2×D411yescharacteristic
135C42#4111yescharacteristic
136C23—22no—
137C23—21no—
138C23—41no—
139C23—41no—
140C23—81no—
141C23—81no—
142C23C4×D411yescharacteristic
143Q8—41no—
144D4—22no—
145D4—22no—
146D4—41no—
147D4—41no—
148D4—41no—
149D4—81no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—82no—
160C2×C4—82no—
161C2×C4—81no—
162C2×C4C2×C22⋊C411yescharacteristic
163C2×C4C4×D411yescharacteristic
164C2×C4#12011yescharacteristic
165C2×C4#12111yescharacteristic
166C2×C4#12111yescharacteristic
167C2×C4#12311yescharacteristic
168C8—22no—
169C8—41no—
170C8—41no—
171C8—41no—
172C8—41no—
173C8—41no—
174C8—81no—
175C8—81no—
176C22—21no—
177C22—21no—
178C22—21no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—82no—
184C22—82no—
185C22—81no—
186C22—81no—
187C22#38611yescharacteristic
188C4—21no—
189C4—21no—
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—41no—
195C4—41no—
196C4—41no—
197C4—81no—
198C2—41no—
199C2—81no—
200C2—82no—
201C2#189111yescharacteristic
202C2#190311yescharacteristic
203C2#190611yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
prime radical#447C4
LCSG ▷ C22×C4 ▷ 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
2. #2967C2semidirect
3. #1535C2semidirect
4. #1490C2semidirect
5. #1466C2semidirect
6. #1308C2semidirect
7. #1291C2semidirect

Maximal subgroups

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

subgroupindex
#31142
#29672
#15352
#14902
#14662
#13082
#12912