Finite Group Databasebeta

← #10380

Subgroups — #10380

Order 256.

195 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 195 conjugacy classes of subgroups — too many to draw. Only its 45 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#2606C211yesmaximal, characteristic, complemented
2#1980C211yesmaximal, characteristic
3#1514C211yesmaximal, characteristic
4#1505C211yesmaximal, characteristic
5#1300C211yesmaximal, characteristic, complemented
6#1288C211yesmaximal, characteristic, complemented
7#1285C211yesmaximal, characteristic, complemented
8#532C2211yescharacteristic
9#432C2211yescharacteristic
10#432C2211yescharacteristic
11C2×#104—21no—
12C2×#104—21no—
13C4×M16C2211yescharacteristic
14#398—21no—
15#398—21no—
16#389—21no—
17#389—21no—
18#387—21no—
19#387—21no—
20#383C2211yescharacteristic
21C4×C4⋊C4C2211yescharacteristic
22#376C2211yescharacteristic
23#327—21no—
24#327—21no—
25#327—21no—
26#327—21no—
27C2×#41—21no—
28C2×M16—21no—
29C4⋊Q8Q811yescharacteristic
30#127Q811yescharacteristic
31#124—21no—
32#121—21no—
33#121—21no—
34C4×D4—21no—
35C4×D4—21no—
36C2×C4⋊C4—21no—
37C2×C4⋊C4—21no—
38C2×C4⋊C4—21no—
39C2×C4⋊C4—21no—
40C2×C4⋊C4—21no—
41C2×C4⋊C4—21no—
42C2×C4⋊C4—21no—
43C2×C42—21no—
44C2×C42D411yescharacteristic
45C2×C42D411yescharacteristic
46C2×C42C2311yescharacteristic
47C4⋊C8—21no—
48C4⋊C8—21no—
49#104—42no—
50#104—42no—
51C22⋊C8—21no—
52C22⋊C8—21no—
53#97—21no—
54#97—21no—
55#97—21no—
56C4×C8—21no—
57#95—21no—
58#95—21no—
59#95—21no—
60#95—21no—
61#95—21no—
62#95—21no—
63#95D411yescharacteristic
64#95D411yescharacteristic
65#95D411yescharacteristic
66#95D411yescharacteristic
67#41—41no—
68#41—41no—
69#41—41no—
70#41—41no—
71C2×Q8—21no—
72C2×D4—21no—
73C2×D4—21no—
74C2×D4—21no—
75C2×D4—41no—
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—41no—
83C22×C4C2×D411yescharacteristic
84C22×C4C2×D411yescharacteristic
85C22×C4C2×D411yescharacteristic
86M16—22no—
87M16—41no—
88C2×C8—41no—
89C2×C8—41no—
90C2×C8—41no—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—42no—
94C4⋊C4—42no—
95C4⋊C4—42no—
96C4⋊C4—42no—
97C4⋊C4—42no—
98C4⋊C4—81no—
99C4⋊C4—81no—
100C22⋊C4—41no—
101C22⋊C4—41no—
102C42—41no—
103C42—41no—
104C42—42no—
105C42C2×Q811yescharacteristic
106C42#4111yescharacteristic
107C42#4111yescharacteristic
108C42#4111yescharacteristic
109C23—41no—
110C23#12011yescharacteristic
111Q8—41no—
112Q8—41no—
113D4—41no—
114D4—41no—
115D4—81no—
116D4—81no—
117D4—81no—
118D4—81no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—22no—
122C2×C4—22no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—81no—
143C2×C4—81no—
144C2×C4C22⋊Q811yescharacteristic
145C2×C4C22⋊Q811yescharacteristic
146C2×C4C22⋊Q811yescharacteristic
147C2×C4#12411yescharacteristic
148C2×C4#12411yescharacteristic
149C2×C4#12411yescharacteristic
150C8—42no—
151C8—81no—
152C8—81no—
153C22—21no—
154C22—21no—
155C22—81no—
156C22—81no—
157C22—81no—
158C22#39311yescharacteristic
159C22#45311yescharacteristic
160C22#45411yescharacteristic
161C4—21no—
162C4—21no—
163C4—21no—
164C4—21no—
165C4—21no—
166C4—21no—
167C4—42no—
168C4—42no—
169C4—81no—
170C4—81no—
171C4—81no—
172C4—81no—
173C4—81no—
174C2—21no—
175C2—21no—
176C2—161no—
177C2#202711yescharacteristic
178C2#203111yescharacteristic
179C2#203111yescharacteristic
subgroupG/H
center, socleC22#393
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. #2606C2semidirect
5. #1300C2semidirect
6. #1288C2semidirect
7. #1285C2semidirect

Maximal subgroups

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

subgroupindex
#26062
#19802
#15142
#15052
#13002
#12882
#12852