Finite Group Databasebeta

← #9266

Subgroups — #9266

Order 256.

200 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 59 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#3232C211yesmaximal, characteristic
2#2968C211yesmaximal, characteristic
3#1532C211yesmaximal, characteristic
4C2×#330C211yesmaximal, characteristic, complemented
5#1470C211yesmaximal, characteristic, complemented
6#1302C211yesmaximal, characteristic, complemented
7#1281C211yesmaximal, characteristic, complemented
8#529C2211yescharacteristic
9C2×#125C2211yescharacteristic
10#499—21no—
11#488—21no—
12#484C411yescharacteristic
13#483C411yescharacteristic
14#481C411yescharacteristic
15#480C411yescharacteristic
16#479—21no—
17#478—21no—
18#446—21no—
19#435—21no—
20#435—21no—
21C8×D4—21no—
22#433—21no—
23#432C2211yescharacteristic
24#431C2211yescharacteristic
25#431C2211yescharacteristic
26#405—21no—
27C2×#97C2211yescharacteristic
28C2×#97C2211yescharacteristic
29#330—21no—
30#330—21no—
31#330—21no—
32#329—21no—
33#324—21no—
34#324—21no—
35C2×M16—21no—
36C22×C8—21no—
37C22×C8—21no—
38C22×C8—21no—
39#126—21no—
40#125—21no—
41#125—21no—
42#125—21no—
43#125—21no—
44#125D411yescharacteristic
45#124D411yescharacteristic
46#123—21no—
47C22⋊Q8C2×C411yescharacteristic
48#121C2×C411yescharacteristic
49C4×Q8D411yescharacteristic
50C4×D4—21no—
51C4×D4D411yescharacteristic
52#117—21no—
53C2×C4⋊C4—21no—
54C2×C4⋊C4—21no—
55C2×C4⋊C4C2×C411yescharacteristic
56C2×C4⋊C4C2×C411yescharacteristic
57C2×C42C2311yescharacteristic
58#107—21no—
59#107—21no—
60#106—21no—
61#106—21no—
62C4⋊C8—21no—
63C4⋊C8—21no—
64C4⋊C8—21no—
65C4⋊C8—21no—
66C4⋊C8—21no—
67#103—21no—
68#103—21no—
69#102—21no—
70#102—21no—
71C22⋊C8—21no—
72C22⋊C8—21no—
73C22⋊C8—21no—
74C22⋊C8C2×C411yescharacteristic
75C22⋊C8C2×C411yescharacteristic
76C22⋊C8D411yescharacteristic
77C22⋊C8D411yescharacteristic
78#97—21no—
79#97—21no—
80#97—21no—
81#97—21no—
82#97—21no—
83#97D411yescharacteristic
84#97D411yescharacteristic
85C4×C8—21no—
86C4×C8—21no—
87C4×C8—21no—
88C2×Q8C22⋊C411yescharacteristic
89C2×D4—21no—
90C2×D4C22⋊C411yescharacteristic
91C22×C4—21no—
92C22×C4—21no—
93C22×C4—21no—
94C22×C4C22×C411yescharacteristic
95C22×C4C2×D411yescharacteristic
96C22×C4#4111yescharacteristic
97M16—42no—
98C2×C8—21no—
99C2×C8—22no—
100C2×C8—21no—
101C2×C8—21no—
102C2×C8—21no—
103C2×C8—21no—
104C2×C8—21no—
105C2×C8—42no—
106C2×C8—42no—
107C2×C8—41no—
108C2×C8—41no—
109C2×C8—41no—
110C4⋊C4—21no—
111C4⋊C4—21no—
112C4⋊C4—21no—
113C4⋊C4—21no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—21no—
118C4⋊C4—41no—
119C4⋊C4—41no—
120C4⋊C4—41no—
121C4⋊C4—41no—
122C4⋊C4C22⋊C411yescharacteristic
123C4⋊C4C22⋊C411yescharacteristic
124C22⋊C4—21no—
125C22⋊C4—21no—
126C22⋊C4—21no—
127C22⋊C4—21no—
128C22⋊C4—21no—
129C42—21no—
130C42C2×D411yescharacteristic
131C42C2×D411yescharacteristic
132C42C2×D411yescharacteristic
133C42#4111yescharacteristic
134C23—21no—
135C23C4×D411yescharacteristic
136Q8—41no—
137D4—41no—
138D4—41no—
139D4—41no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—81no—
154C2×C4C2×C22⋊C411yescharacteristic
155C2×C4C4×D411yescharacteristic
156C2×C4#12011yescharacteristic
157C2×C4#12111yescharacteristic
158C2×C4#12111yescharacteristic
159C2×C4#12311yescharacteristic
160C8—22no—
161C8—41no—
162C8—41no—
163C8—42no—
164C8—41no—
165C8—41no—
166C8—41no—
167C8—81no—
168C22—21no—
169C22—21no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22#38611yescharacteristic
174C22#44311yescharacteristic
175C22#44411yescharacteristic
176C4—21no—
177C4—21no—
178C4—21no—
179C4—21no—
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—41no—
185C4—81no—
186C4—81no—
187C2—21no—
188C2—21no—
189C2—81no—
190C2#187611yescharacteristic
191C2#190611yescharacteristic
192C2#191511yescharacteristic
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. C2×#330C2semidirect
5. #1470C2semidirect
6. #1302C2semidirect
7. #1281C2semidirect

Maximal subgroups

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

subgroupindex
#32322
#29682
#15322
C2×#3302
#14702
#13022
#12812