Finite Group Databasebeta

← #9432

Subgroups — #9432

Order 256.

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

normal subgroups only

This group has 218 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#3180C211yesmaximal, characteristic
2#2968C211yesmaximal, characteristic, complemented
3#1530C211yesmaximal, characteristic, complemented
4#1517C211yesmaximal, characteristic, complemented
5#1512C211yesmaximal, characteristic, complemented
6#1302C211yesmaximal, characteristic, complemented
7#1295C211yesmaximal, characteristic, complemented
8#532C2211yescharacteristic
9#529C2211yescharacteristic
10#501C411yescharacteristic, complemented
11#496C411yescharacteristic, complemented
12#490C411yescharacteristic, complemented
13#489C411yescharacteristic, complemented
14#466—21no—
15#465—21no—
16#446—21no—
17#442—21no—
18#440—21no—
19#435—21no—
20#435—21no—
21C8×D4—21no—
22#433—21no—
23#432C2211yescharacteristic
24#431C2211yescharacteristic
25#405—21no—
26C2×#97C2211yescharacteristic
27C2×#97C2211yescharacteristic
28#382C2211yescharacteristic
29#329—21no—
30#329—21no—
31#328—21no—
32#327—21no—
33#327—21no—
34#327—21no—
35C2×#41—21no—
36C2×SD16—21no—
37C2×D8—21no—
38C2×M16—21no—
39C22×C8—21no—
40C22×C8—21no—
41C22×C8—21no—
42C4⋊Q8C2×C411yescharacteristic
43#127C2×C411yescharacteristic
44#126—21no—
45#125C2×C411yescharacteristic
46#124—21no—
47#124C2×C411yescharacteristic
48#123—21no—
49C22⋊Q8D411yescharacteristic
50#121—21no—
51#121—21no—
52#121D411yescharacteristic
53C4×Q8D411yescharacteristic
54C4×D4—21no—
55C4×D4—21no—
56C4×D4—21no—
57C4×D4D411yescharacteristic
58#117—21no—
59C2×C4⋊C4—21no—
60C2×C42C2311yescharacteristic
61#107—21no—
62#106—21no—
63C4⋊C8—21no—
64C4⋊C8—21no—
65C4⋊C8—21no—
66C4⋊C8—21no—
67#103—21no—
68#102—21no—
69#102—21no—
70#102—21no—
71C22⋊C8—21no—
72C22⋊C8—21no—
73C22⋊C8—21no—
74C22⋊C8D411yescharacteristic
75C22⋊C8D411yescharacteristic
76#97—21no—
77#97—21no—
78#97—21no—
79#97—21no—
80#97C2×C411yescharacteristic
81#97C2×C411yescharacteristic
82#97D411yescharacteristic
83#97D411yescharacteristic
84C4×C8—21no—
85C4×C8—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
104SD16—42no—
105D8—42no—
106M16—42no—
107C2×C8—21no—
108C2×C8—21no—
109C2×C8—21no—
110C2×C8—21no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—42no—
114C2×C8—42no—
115C2×C8—42no—
116C2×C8—41no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—81no—
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—81no—
143D4—41no—
144D4—41no—
145D4—41no—
146D4—41no—
147D4—41no—
148D4—81no—
149D4—81no—
150D4—81no—
151D4—81no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—82no—
163C2×C4—81no—
164C2×C4—81no—
165C2×C4—81no—
166C2×C4C2×C22⋊C411yescharacteristic
167C2×C4C4×D411yescharacteristic
168C2×C4C4×D411yescharacteristic
169C2×C4#12011yescharacteristic
170C2×C4#12111yescharacteristic
171C2×C4#12311yescharacteristic
172C8—22no—
173C8—22no—
174C8—41no—
175C8—41no—
176C8—41no—
177C8—41no—
178C8—81no—
179C22—21no—
180C22—21no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—81no—
185C22—81no—
186C22—81no—
187C22#38611yescharacteristic
188C22#47111yescharacteristic
189C22#47211yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—41no—
199C4—81no—
200C4—161no—
201C2—21no—
202C2—21no—
203C2—81no—
204C2—161no—
205C2#188411yescharacteristic
206C2#190611yescharacteristic
207C2#190711yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC42C22×C4
Frattini, cosocleC2×C42C23
prime radical#3180C2
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. #2968C2semidirect
3. #1530C2semidirect
4. #1517C2semidirect
5. #1512C2semidirect
6. #1302C2semidirect
7. #1295C2semidirect
10. #501C4semidirect
11. #496C4semidirect
12. #490C4semidirect
13. #489C4semidirect

Maximal subgroups

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

subgroupindex
#31802
#29682
#15302
#15172
#15122
#13022
#12952