Finite Group Databasebeta

← #10035

Subgroups — #10035

Order 256.

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

normal subgroups only

This group has 249 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#3135C211yesmaximal, characteristic
2#3104C211yesmaximal, characteristic, complemented
3#3103C211yesmaximal, characteristic
4#1985C211yesmaximal, characteristic, complemented
5#1481C211yesmaximal, characteristic, complemented
6#1480C211yesmaximal, characteristic
7#1275C211yesmaximal, characteristic, complemented
8#533C2211yescharacteristic
9#532C2211yescharacteristic
10C2×C4×Q8C2211yescharacteristic
11#491—21no—
12#490—21no—
13#489—21no—
14#489—21no—
15#484—21no—
16#481—21no—
17#477—21no—
18#475—21no—
19#462—21no—
20#460—21no—
21#451—21no—
22#448—21no—
23C4×Q16—22no—
24C4×SD16—22no—
25#431C2211yescharacteristic
26#431C2211yescharacteristic
27C2×C4⋊C8C2211yescharacteristic
28#416—22no—
29C2×#97C2211yescharacteristic
30#336—22no—
31Q8⋊C8—22no—
32D4⋊C8—22no—
33C2×#41—21no—
34C22×Q8D411yescharacteristic
35C2×Q16—22no—
36C2×SD16—22no—
37C22×C8—21no—
38C22×C8D412yes—
39C4⋊Q8D411yescharacteristic
40C4⋊Q8D411yescharacteristic
41C4⋊Q8D411yescharacteristic
42#127D411yescharacteristic
43#125—21no—
44#124—21no—
45C22⋊Q8—21no—
46C22⋊Q8—21no—
47#121—21no—
48#121—21no—
49C4×Q8—21no—
50C4×Q8—21no—
51C4×Q8—21no—
52C4×Q8—21no—
53C4×Q8—21no—
54C4×Q8—21no—
55C4×D4—21no—
56C4×D4—21no—
57#117—21no—
58C2×C4⋊C4—21no—
59C2×C4⋊C4D411yescharacteristic
60C2×C42—21no—
61C2×C42C2311yescharacteristic
62#107—22no—
63#106—22no—
64C4⋊C8—21no—
65C4⋊C8—21no—
66C4⋊C8—21no—
67C4⋊C8—21no—
68#103—22no—
69#103—22no—
70#103—22no—
71#103—22no—
72#103—22no—
73#102—22no—
74#102—22no—
75#102—22no—
76C22⋊C8—21no—
77C22⋊C8—21no—
78#97—21no—
79#97—21no—
80C4×C8D412yes—
81C4×C8D412yes—
82#41—42no—
83#41—42no—
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—21no—
87C2×Q8—21no—
88C2×Q8—21no—
89C2×Q8—42no—
90C2×D4—21no—
91C2×D4—21no—
92C2×D4—21no—
93C2×D4—41no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4—41no—
97C22×C4C2×D411yescharacteristic
98C22×C4C2×D411yescharacteristic
99C22×C4#4111yescharacteristic
100Q16—44no—
101SD16—44no—
102C2×C8—22no—
103C2×C8—22no—
104C2×C8—22no—
105C2×C8—22no—
106C2×C8—22no—
107C2×C8—41no—
108C2×C8—42no—
109C4⋊C4—21no—
110C4⋊C4—21no—
111C4⋊C4—21no—
112C4⋊C4—21no—
113C4⋊C4—21no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—41no—
118C4⋊C4—41no—
119C4⋊C4—41no—
120C4⋊C4—41no—
121C22⋊C4—41no—
122C22⋊C4—41no—
123C22⋊C4—41no—
124C42—41no—
125C42—41no—
126C42—41no—
127C42C2×D411yescharacteristic
128C42C2×D411yescharacteristic
129C42C2×D411yescharacteristic
130C42C2×D411yescharacteristic
131C23—41no—
132C23#12111yescharacteristic
133Q8—22no—
134Q8—22no—
135Q8—41no—
136Q8—41no—
137Q8—42no—
138Q8—42no—
139Q8—42no—
140D4—42no—
141D4—42no—
142D4—42no—
143D4—82no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—81no—
155C2×C4—81no—
156C2×C4#12011yescharacteristic
157C2×C4#12011yescharacteristic
158C2×C4#12011yescharacteristic
159C2×C4#12111yescharacteristic
160C2×C4#12111yescharacteristic
161C2×C4#12711yescharacteristic
162C2×C4#13512yes—
163C2×C4#13712yes—
164C8—42no—
165C8—42no—
166C8—42no—
167C8—81no—
168C22—21no—
169C22—21no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22#39211yescharacteristic
174C22#46412yes—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—21no—
179C4—42no—
180C4—81no—
181C4—81no—
182C4—81no—
183C4—81no—
184C4#45212yes—
185C4#49511yescharacteristic
186C4#49711yescharacteristic
187C2—22no—
188C2—161no—
189C2#201011yescharacteristic
190C2#201511yescharacteristic
191C2#201711yescharacteristic
subgroupG/H
centerC2×C4#127
commutator, Frattini, cosocleC2×C42C23
socleC22#392
prime radical#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #3104C2semidirect
4. #1985C2semidirect
5. #1481C2semidirect
7. #1275C2semidirect

Maximal subgroups

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

subgroupindex
#31352
#31042
#31032
#19852
#14812
#14802
#12752