Finite Group Databasebeta

← #9379

Subgroups — #9379

Order 256.

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

normal subgroups only

This group has 246 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#3215C211yesmaximal, characteristic
2#2337C211yesmaximal, characteristic
3#1986C211yesmaximal, characteristic, complemented
4#1527C211yesmaximal, characteristic
5#1515C211yesmaximal, characteristic, complemented
6#1288C211yesmaximal, characteristic, complemented
7#1285C211yesmaximal, characteristic, complemented
8#533C2211yescharacteristic
9C2×#124C2211yescharacteristic
10#497C412yescomplemented
11#489C412yescomplemented
12#464—22no—
13#451—21no—
14#450—21no—
15#432C2211yescharacteristic
16#432C2211yescharacteristic
17C4×M16C2211yescharacteristic
18#391—21no—
19#388—21no—
20#388—21no—
21#386—21no—
22#385—21no—
23#383C2211yescharacteristic
24C4×C4⋊C4C2211yescharacteristic
25C4×C22⋊C4—21no—
26#339—21no—
27#339—21no—
28#329—22no—
29#328—21no—
30#328—21no—
31C22×Q8D411yescharacteristic
32C22×D4D411yescharacteristic
33C23×C4—21no—
34C2×Q16—22no—
35C2×SD16—22no—
36C2×M16—21no—
37C4⋊Q8C2×C411yescharacteristic, complemented
38C4⋊Q8C2×C411yescharacteristic, complemented
39#125—21no—
40#124—21no—
41#124—21no—
42#124C2×C412yes—
43#124D412yes—
44C22⋊Q8—21no—
45C22⋊Q8—21no—
46C4×Q8—21no—
47C4×Q8—21no—
48#117—21no—
49C2×C4⋊C4—21no—
50C2×C4⋊C4—21no—
51C2×C22⋊C4—21no—
52C2×C22⋊C4—21no—
53C2×C22⋊C4—21no—
54C2×C22⋊C4—21no—
55C2×C22⋊C4—21no—
56C2×C42—21no—
57C2×C42D411yescharacteristic
58C2×C42D411yescharacteristic
59C2×C42C2311yescharacteristic
60C4⋊C8—21no—
61C4⋊C8—21no—
62#103—22no—
63#102—22no—
64C22⋊C8—21no—
65C22⋊C8—21no—
66#97—21no—
67#97—21no—
68#97C2×C412yescomplemented
69C4×C8—21no—
70#95—21no—
71#95—21no—
72#95—21no—
73#95—21no—
74#95—21no—
75#95D411yescharacteristic
76#95D411yescharacteristic
77C24—21no—
78C2×Q8—21no—
79C2×Q8—21no—
80C2×Q8—21no—
81C2×Q8—81no—
82C2×Q8C22⋊C412yes—
83C2×D4—21no—
84C2×D4—81no—
85C2×D4C22⋊C412yes—
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—21no—
91C22×C4—42no—
92C22×C4—81no—
93C22×C4—81no—
94C22×C4C2×D411yescharacteristic
95C22×C4C2×D411yescharacteristic
96C22×C4C2×D411yescharacteristic
97Q16—82no—
98SD16—82no—
99M16—22no—
100M16—41no—
101C2×C8—22no—
102C2×C8—41no—
103C2×C8—41no—
104C4⋊C4—21no—
105C4⋊C4—21no—
106C4⋊C4—21no—
107C4⋊C4—21no—
108C4⋊C4—42no—
109C4⋊C4—41no—
110C4⋊C4—41no—
111C4⋊C4—81no—
112C22⋊C4—22no—
113C22⋊C4—22no—
114C22⋊C4—22no—
115C22⋊C4—22no—
116C22⋊C4—42no—
117C22⋊C4—41no—
118C22⋊C4—81no—
119C22⋊C4—81no—
120C42—41no—
121C42—41no—
122C42—41no—
123C42—81no—
124C42C22×C411yescharacteristic
125C42C2×D411yescharacteristic
126C42#4111yescharacteristic
127C42#4111yescharacteristic
128C23—22no—
129C23—41no—
130C23—41no—
131C23—41no—
132C23—41no—
133C23—41no—
134C23—41no—
135C23#12011yescharacteristic
136Q8—42no—
137Q8—42no—
138Q8—81no—
139Q8—81no—
140D4—42no—
141D4—81no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—41no—
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—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—84no—
164C2×C4C2×C22⋊C411yescharacteristic
165C2×C4C4×D411yescharacteristic
166C2×C4C4×D411yescharacteristic
167C2×C4#12111yescharacteristic
168C2×C4#12111yescharacteristic
169C2×C4#12311yescharacteristic
170C8—42no—
171C8—42no—
172C8—81no—
173C22—21no—
174C22—21no—
175C22—42no—
176C22—42no—
177C22—42no—
178C22—81no—
179C22—81no—
180C22—81no—
181C22—81no—
182C22#38611yescharacteristic
183C22#45511yescharacteristic
184C22#45611yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—21no—
189C4—21no—
190C4—21no—
191C4—42no—
192C4—42no—
193C4—81no—
194C4—81no—
195C4—81no—
196C4—81no—
197C4—81no—
198C2—21no—
199C2—21no—
200C2—82no—
201C2#188211yescharacteristic
202C2#190611yescharacteristic
203C2#191111yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC42C22×C4
Frattini, cosocleC2×C42C23
prime radicalC22×D4D4
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
3. #1986C2semidirect
5. #1515C2semidirect
6. #1288C2semidirect
7. #1285C2semidirect
10. #497C4semidirect
11. #489C4semidirect
37. C4⋊Q8C2×C4semidirect
38. C4⋊Q8C2×C4semidirect
68. #97C2×C4semidirect

Maximal subgroups

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

subgroupindex
#32152
#23372
#19862
#15272
#15152
#12882
#12852