Finite Group Databasebeta

← #9245

Subgroups — #9245

Order 256.

228 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#478C211yesmaximal, characteristic
2#2974C211yesmaximal, characteristic
3#1528C211yesmaximal, characteristic, complemented
4#1490C211yesmaximal, characteristic
5#1470C211yesmaximal, characteristic, complemented
6#1290C211yesmaximal, characteristic, complemented
7#1283C211yesmaximal, characteristic, complemented
8C2×#125C2211yescharacteristic
9C2×C4×D4C2211yescharacteristic
10#478—21no—
11#478—21no—
12#478—21no—
13#478—21no—
14#436—21no—
15#435—22no—
16C8×D4—21no—
17#432C2211yescharacteristic
18#432C2211yescharacteristic
19#431C2211yescharacteristic
20C2×#107C411yescharacteristic
21C2×#106C411yescharacteristic
22C2×C4⋊C8C2211yescharacteristic
23C2×#102C411yescharacteristic
24C2×#102C411yescharacteristic
25#407—21no—
26C2×C22⋊C8—21no—
27C4×M16C2211yescharacteristic
28#330—22no—
29D4⋊C8—21no—
30D4⋊C8—21no—
31#324—21no—
32#324—21no—
33C22×D4C2×C411yescharacteristic
34C23×C4—21no—
35C2×M16—22no—
36C2×M16—21no—
37C22×C8—22no—
38C22×C8C2×C411yescharacteristic
39C22×C8C2×C411yescharacteristic
40#125—21no—
41#125—21no—
42#125—21no—
43#125—21no—
44C4×D4—21no—
45C4×D4—21no—
46C4×D4D411yescharacteristic
47C4×D4D411yescharacteristic
48C4×D4D411yescharacteristic
49C4×D4D411yescharacteristic
50C2×C4⋊C4—21no—
51C2×C4⋊C4—21no—
52C2×C4⋊C4C2×C411yescharacteristic
53C2×C4⋊C4C2×C411yescharacteristic
54C2×C4⋊C4C2×C411yescharacteristic
55C2×C22⋊C4—21no—
56C2×C42C2311yescharacteristic
57#107—21no—
58#107—21no—
59#106—21no—
60#106—21no—
61C4⋊C8—21no—
62C4⋊C8—21no—
63C4⋊C8—21no—
64C4⋊C8—21no—
65C4⋊C8—21no—
66#102—21no—
67#102—21no—
68#102—21no—
69#102—21no—
70C22⋊C8—22no—
71C22⋊C8—22no—
72C22⋊C8—21no—
73C22⋊C8—21no—
74C22⋊C8D411yescharacteristic
75C22⋊C8D411yescharacteristic
76#97—21no—
77#97—21no—
78#97D412yes—
79C4×C8—21no—
80C4×C8—21no—
81C24—21no—
82C2×D4—22no—
83C2×D4—21no—
84C2×D4—41no—
85C2×D4C22⋊C411yescharacteristic
86C2×D4C22⋊C411yescharacteristic
87C22×C4—21no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—21no—
91C22×C4—21no—
92C22×C4—21no—
93C22×C4—21no—
94C22×C4—82no—
95C22×C4C22×C411yescharacteristic
96C22×C4C2×D411yescharacteristic
97C22×C4#4111yescharacteristic
98M16—22no—
99M16—41no—
100M16—82no—
101C2×C8—21no—
102C2×C8—21no—
103C2×C8—21no—
104C2×C8—21no—
105C2×C8—22no—
106C2×C8—41no—
107C2×C8—41no—
108C2×C8—41no—
109C2×C8—41no—
110C2×C8—82no—
111C4⋊C4—21no—
112C4⋊C4—21no—
113C4⋊C4—21no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—41no—
117C4⋊C4—41no—
118C4⋊C4—41no—
119C4⋊C4—41no—
120C4⋊C4C22⋊C411yescharacteristic
121C4⋊C4C22⋊C411yescharacteristic
122C22⋊C4—21no—
123C22⋊C4—21no—
124C22⋊C4—21no—
125C22⋊C4—21no—
126C42C2×D411yescharacteristic
127C42C2×D411yescharacteristic
128C42C2×D411yescharacteristic
129C42#4111yescharacteristic
130C23—21no—
131C23—21no—
132C23—42no—
133C23—41no—
134C23—41no—
135C23—81no—
136C23C4×D411yescharacteristic
137D4—21no—
138D4—21no—
139D4—21no—
140D4—42no—
141D4#10112yes—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—81no—
156C2×C4—81no—
157C2×C4—81no—
158C2×C4—81no—
159C2×C4C2×C22⋊C411yescharacteristic
160C2×C4C4×D411yescharacteristic
161C2×C4#12011yescharacteristic
162C2×C4#12111yescharacteristic
163C2×C4#12111yescharacteristic
164C2×C4#12311yescharacteristic
165C8—41no—
166C8—42no—
167C8—41no—
168C8—42no—
169C8—41no—
170C8—41no—
171C8—81no—
172C22—21no—
173C22—21no—
174C22—22no—
175C22—41no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22—82no—
181C22—82no—
182C22#38611yescharacteristic
183C22#44311yescharacteristic
184C22#44411yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—21no—
189C4—21no—
190C4—41no—
191C4—41no—
192C4—81no—
193C4—81no—
194C4C2×#10111yescharacteristic
195C4#41311yescharacteristic
196C2—21no—
197C2—21no—
198C2—42no—
199C2—81no—
200C2#187611yescharacteristic
201C2#190111yescharacteristic
202C2#190411yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
prime radicalC22×D4C2×C4
LCSG ▷ C22×C4 ▷ 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
3. #1528C2semidirect
5. #1470C2semidirect
6. #1290C2semidirect
7. #1283C2semidirect

Maximal subgroups

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

subgroupindex
C2×#4782
#29742
#15282
#14902
#14702
#12902
#12832