Finite Group Databasebeta

← #9531

Subgroups — #9531

Order 256.

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

normal subgroups only

This group has 206 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#3117C211yesmaximal, characteristic
2#2967C211yesmaximal, characteristic
3#1535C211yesmaximal, characteristic
4#1491C211yesmaximal, characteristic, complemented
5#1467C211yesmaximal, characteristic, complemented
6#1308C211yesmaximal, characteristic, complemented
7#1291C211yesmaximal, characteristic, complemented
8#529C2211yescharacteristic
9C2×C4×Q8C2211yescharacteristic
10#484C411yescharacteristic
11#481C411yescharacteristic
12#479—21no—
13#464—21no—
14#451C411yescharacteristic
15#448C411yescharacteristic
16#446—21no—
17#441—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—
31Q8⋊C8—21no—
32Q8⋊C8—21no—
33#324—21no—
34#324—21no—
35C22×Q8C2×C411yescharacteristic
36C2×Q16—21no—
37C2×SD16—21no—
38C2×M16—21no—
39C2×M16—21no—
40C22×C8—21no—
41#126—21no—
42#125D411yescharacteristic
43#124D411yescharacteristic
44#123—21no—
45C22⋊Q8C2×C411yescharacteristic
46#121C2×C411yescharacteristic
47C4×Q8—21no—
48C4×Q8—21no—
49C4×Q8—21no—
50C4×Q8—21no—
51C4×Q8D411yescharacteristic
52C4×D4—21no—
53C4×D4D411yescharacteristic
54#117—21no—
55C2×C4⋊C4—21no—
56C2×C4⋊C4C2×C411yescharacteristic
57C2×C42—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#103—21no—
69#103—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
88C2×Q8—21no—
89C2×Q8—21no—
90C2×Q8—42no—
91C2×Q8C22⋊C411yescharacteristic
92C2×D4—21no—
93C2×D4C22⋊C411yescharacteristic
94C22×C4—21no—
95C22×C4—21no—
96C22×C4—21no—
97C22×C4C22×C411yescharacteristic
98C22×C4C2×D411yescharacteristic
99C22×C4#4111yescharacteristic
100Q16—42no—
101SD16—42no—
102M16—42no—
103M16—42no—
104C2×C8—21no—
105C2×C8—21no—
106C2×C8—21no—
107C2×C8—21no—
108C2×C8—21no—
109C2×C8—21no—
110C2×C8—42no—
111C2×C8—41no—
112C2×C8—41no—
113C4⋊C4—21no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—41no—
120C4⋊C4—41no—
121C4⋊C4C22⋊C411yescharacteristic
122C4⋊C4C22⋊C411yescharacteristic
123C22⋊C4—21no—
124C22⋊C4—21no—
125C22⋊C4—21no—
126C22⋊C4—21no—
127C22⋊C4—21no—
128C42—21no—
129C42—41no—
130C42—41no—
131C42C2×D411yescharacteristic
132C42C2×D411yescharacteristic
133C42C2×D411yescharacteristic
134C42#4111yescharacteristic
135C23—21no—
136C23C4×D411yescharacteristic
137Q8—22no—
138Q8—22no—
139Q8—41no—
140Q8—41no—
141Q8—41no—
142D4—41no—
143D4—81no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—81no—
157C2×C4C2×C22⋊C411yescharacteristic
158C2×C4C4×D411yescharacteristic
159C2×C4#12011yescharacteristic
160C2×C4#12111yescharacteristic
161C2×C4#12111yescharacteristic
162C2×C4#12311yescharacteristic
163C8—22no—
164C8—41no—
165C8—41no—
166C8—41no—
167C8—41no—
168C8—41no—
169C8—81no—
170C8—81no—
171C22—21no—
172C22—21no—
173C22—21no—
174C22—41no—
175C22—41no—
176C22—41no—
177C22#38611yescharacteristic
178C4—21no—
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—42no—
185C4—41no—
186C4—41no—
187C4—41no—
188C4—81no—
189C2—41no—
190C2—81no—
191C2#189111yescharacteristic
192C2#190211yescharacteristic
193C2#190611yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
prime radical#121C2×C4
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
4. #1491C2semidirect
5. #1467C2semidirect
6. #1308C2semidirect
7. #1291C2semidirect

Maximal subgroups

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

subgroupindex
#31172
#29672
#15352
#14912
#14672
#13082
#12912