Finite Group Databasebeta

← #10210

Subgroups — #10210

Order 256.

220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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#3237C211yesmaximal, characteristic, complemented
2#3235C211yesmaximal, characteristic
3#3216C211yesmaximal, characteristic
4#1515C211yesmaximal, characteristic, complemented
5#1515C211yesmaximal, characteristic, complemented
6#1514C211yesmaximal, characteristic
7#1308C211yesmaximal, characteristic, complemented
8#533C2211yescharacteristic
9#533C2211yescharacteristic
10#532C2211yescharacteristic
11#501—21no—
12#501—21no—
13#497—21no—
14#491—21no—
15#490—21no—
16#489—21no—
17#485—22no—
18#482—22no—
19#477—21no—
20#476—21no—
21#475—21no—
22#474—21no—
23#462—21no—
24#460—21no—
25#452—22no—
26#432C2211yescharacteristic
27#432C2211yescharacteristic
28#432C2211yescharacteristic
29#383C2211yescharacteristic
30#328—22no—
31#328—22no—
32#327—22no—
33C2×#41—21no—
34C2×Q16—22no—
35C2×SD16—22no—
36C4⋊Q8D411yescharacteristic
37C4⋊Q8D411yescharacteristic
38C4⋊Q8D411yescharacteristic
39C4⋊Q8D411yescharacteristic
40C4⋊Q8D411yescharacteristic
41#127D411yescharacteristic
42#125—21no—
43#125—21no—
44#124—21no—
45C22⋊Q8—21no—
46C22⋊Q8—21no—
47C22⋊Q8—21no—
48C22⋊Q8—21no—
49#121—21no—
50#121—21no—
51C4×Q8—21no—
52C4×Q8—21no—
53C4×Q8—21no—
54C4×Q8—21no—
55C4×D4—21no—
56C4×D4—21no—
57#117—21no—
58#117—21no—
59C2×C42C2311yescharacteristic
60#107—22no—
61#107—22no—
62#106—22no—
63#106—22no—
64C4⋊C8—21no—
65C4⋊C8—21no—
66C4⋊C8—21no—
67#103—22no—
68#103—22no—
69#103—22no—
70#102—22no—
71#102—22no—
72#102—22no—
73C22⋊C8D412yes—
74C22⋊C8D412yes—
75C22⋊C8D412yes—
76#97—21no—
77#97—21no—
78#97—21no—
79#95—21no—
80#95—21no—
81#95—21no—
82#41—82no—
83C2×Q8—21no—
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—21no—
87C2×Q8—21no—
88C2×D4—21no—
89C2×D4—21no—
90C2×D4—21no—
91C2×D4—41no—
92C22×C4—41no—
93C22×C4—41no—
94C22×C4C2×D411yescharacteristic
95C22×C4C2×D411yescharacteristic
96C22×C4C2×D411yescharacteristic
97Q16—82no—
98SD16—82no—
99C2×C8—22no—
100C2×C8—22no—
101C2×C8—22no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—21no—
106C4⋊C4—21no—
107C4⋊C4—21no—
108C4⋊C4—21no—
109C4⋊C4—21no—
110C4⋊C4—21no—
111C4⋊C4—21no—
112C4⋊C4—41no—
113C4⋊C4—41no—
114C4⋊C4—41no—
115C4⋊C4—41no—
116C22⋊C4—41no—
117C22⋊C4—41no—
118C22⋊C4—41no—
119C22⋊C4—41no—
120C42—41no—
121C42—41no—
122C42C2×D411yescharacteristic
123C42C2×D411yescharacteristic
124C42C2×D411yescharacteristic
125C42#4111yescharacteristic
126C23—41no—
127C23#12711yescharacteristic
128Q8—41no—
129Q8—41no—
130Q8—42no—
131Q8—42no—
132Q8—81no—
133Q8—81no—
134D4—42no—
135D4—42no—
136D4—81no—
137D4—82no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—82no—
147C2×C4—81no—
148C2×C4—81no—
149C2×C4—81no—
150C2×C4#12011yescharacteristic
151C2×C4#12011yescharacteristic
152C2×C4#12011yescharacteristic
153C2×C4#12111yescharacteristic
154C2×C4#12111yescharacteristic
155C2×C4#12111yescharacteristic
156C8—42no—
157C8—42no—
158C8—42no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—81no—
163C22—81no—
164C22—81no—
165C22#39211yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—81no—
173C4—81no—
174C4—81no—
175C4—81no—
176C4—81no—
177C4—161no—
178C2—41no—
179C2—161no—
180C2#200811yescharacteristic
181C2#200911yescharacteristic
182C2#200911yescharacteristic
subgroupG/H
center, socleC22#392
commutator, Frattini, cosocleC2×C42C23
prime radical#532C22
LCSG ▷ C2×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
1. #3237C2semidirect
4. #1515C2semidirect
5. #1515C2semidirect
7. #1308C2semidirect

Maximal subgroups

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

subgroupindex
#32372
#32352
#32162
#15152
#15142
#13082