Finite Group Databasebeta

← #9370

Subgroups — #9370

Order 256.

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

normal subgroups only

This group has 212 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#3219C211yesmaximal, characteristic
2#2967C211yesmaximal, characteristic, complemented
3#1521C211yesmaximal, characteristic, complemented
4#1514C211yesmaximal, characteristic, complemented
5#1484C211yesmaximal, characteristic, complemented
6#1288C211yesmaximal, characteristic, complemented
7#1287C211yesmaximal, characteristic, complemented
8#532C2211yescharacteristic
9#529C2211yescharacteristic
10#497C411yescharacteristic, complemented
11#496C411yescharacteristic, complemented
12#491C411yescharacteristic, complemented
13#490C411yescharacteristic, complemented
14#464—21no—
15#463—21no—
16#452—21no—
17#449—21no—
18#446—21no—
19#436—21no—
20#435—21no—
21#435—21no—
22#433—21no—
23#432C2211yescharacteristic
24#432C2211yescharacteristic
25#431C2211yescharacteristic
26#405—21no—
27C4×M16C2211yescharacteristic
28#383C2211yescharacteristic
29#328—21no—
30#327—21no—
31#327—21no—
32#327—21no—
33D4⋊C8—21no—
34D4⋊C8—21no—
35C2×#41—21no—
36C2×Q16—21no—
37C2×SD16—21no—
38C2×SD16—21no—
39C2×D8—21no—
40C2×M16—21no—
41C2×M16—21no—
42C22×C8—21no—
43C4⋊Q8C2×C411yescharacteristic
44#127C2×C411yescharacteristic
45#126—21no—
46#125C2×C411yescharacteristic
47#124—21no—
48#124C2×C411yescharacteristic
49#123—21no—
50C22⋊Q8D411yescharacteristic
51#121—21no—
52#121—21no—
53#121D411yescharacteristic
54C4×Q8D411yescharacteristic
55C4×D4—21no—
56C4×D4—21no—
57C4×D4—21no—
58C4×D4D411yescharacteristic
59#117—21no—
60C2×C42C2311yescharacteristic
61C4⋊C8—21no—
62C4⋊C8—21no—
63C4⋊C8—21no—
64C4⋊C8—21no—
65C4⋊C8—21no—
66#103—21no—
67#103—21no—
68#102—21no—
69#102—21no—
70C22⋊C8—21no—
71C22⋊C8—21no—
72C22⋊C8—21no—
73C22⋊C8—21no—
74C22⋊C8D411yescharacteristic
75C22⋊C8D411yescharacteristic
76#97—21no—
77#97—21no—
78#97—21no—
79#97C2×C411yescharacteristic
80#97C2×C411yescharacteristic
81C4×C8—21no—
82C4×C8—21no—
83C4×C8D411yescharacteristic
84C4×C8D411yescharacteristic
85#95—21no—
86#95—21no—
87#95—21no—
88#41—81no—
89#41—81no—
90C2×Q8—21no—
91C2×Q8C22⋊C411yescharacteristic
92C2×D4—21no—
93C2×D4—21no—
94C2×D4—21no—
95C2×D4—21no—
96C2×D4—41no—
97C2×D4C22⋊C411yescharacteristic
98C22×C4—21no—
99C22×C4—41no—
100C22×C4—41no—
101C22×C4C2×D411yescharacteristic
102C22×C4C2×D411yescharacteristic
103C22×C4#4111yescharacteristic
104Q16—81no—
105SD16—81no—
106SD16—81no—
107D8—81no—
108M16—42no—
109M16—42no—
110C2×C8—21no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—21no—
114C2×C8—21no—
115C2×C8—21no—
116C2×C8—42no—
117C2×C8—41no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4C22⋊C411yescharacteristic
125C4⋊C4C22⋊C411yescharacteristic
126C22⋊C4—21no—
127C22⋊C4—21no—
128C22⋊C4—21no—
129C22⋊C4—21no—
130C22⋊C4—21no—
131C22⋊C4—41no—
132C22⋊C4—41no—
133C42—21no—
134C42C22×C411yescharacteristic
135C42C2×D411yescharacteristic
136C42C2×D411yescharacteristic
137C42#4111yescharacteristic
138C23—21no—
139C23—41no—
140C23#12111yescharacteristic
141Q8—41no—
142Q8—41no—
143Q8—41no—
144D4—41no—
145D4—41no—
146D4—41no—
147D4—42no—
148D4—81no—
149D4—81no—
150D4—82no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—82no—
161C2×C4—81no—
162C2×C4—81no—
163C2×C4—81no—
164C2×C4C2×C22⋊C411yescharacteristic
165C2×C4C4×D411yescharacteristic
166C2×C4C4×D411yescharacteristic
167C2×C4#12011yescharacteristic
168C2×C4#12111yescharacteristic
169C2×C4#12311yescharacteristic
170C8—22no—
171C8—41no—
172C8—41no—
173C8—41no—
174C8—41no—
175C8—41no—
176C8—81no—
177C22—21no—
178C22—21no—
179C22—21no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—81no—
184C22—81no—
185C22—81no—
186C22#38611yescharacteristic
187C4—21no—
188C4—21no—
189C4—21no—
190C4—21no—
191C4—21no—
192C4—21no—
193C4—41no—
194C4—41no—
195C4—41no—
196C4—81no—
197C4—161no—
198C2—41no—
199C2—81no—
200C2—161no—
201C2#188111yescharacteristic
202C2#190611yescharacteristic
203C2#191011yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC42C22×C4
Frattini, cosocleC2×C42C23
prime radical#3219C2
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
2. #2967C2semidirect
3. #1521C2semidirect
4. #1514C2semidirect
5. #1484C2semidirect
6. #1288C2semidirect
7. #1287C2semidirect
10. #497C4semidirect
11. #496C4semidirect
12. #491C4semidirect
13. #490C4semidirect

Maximal subgroups

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

subgroupindex
#32192
#29672
#15212
#15142
#14842
#12882
#12872