Finite Group Databasebeta

← #8610

Subgroups — #8610

Order 256.

262 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 75 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×#435C211yesmaximal, characteristic
2#1808C211yesmaximal, characteristic, complemented
3#1807C211yesmaximal, characteristic, complemented
4#1799C212yesmaximal
5#1289C212yesmaximal, complemented
6C22×M16C411yescharacteristic, complemented
7C23×C8C2211yescharacteristic
8C2×C4×D4C2211yescharacteristic
9#435—21no—
10#435—21no—
11#435—21no—
12#435—21no—
13C2×#107—21no—
14C2×#106—21no—
15C2×C4⋊C8C411yescharacteristic, complemented
16C2×#99—22no—
17C2×C22⋊C8C411yescharacteristic, complemented
18C2×C22⋊C8C2211yescharacteristic
19C2×#97C411yescharacteristic, complemented
20#380C2212yes—
21#380C2212yes—
22#342—22no—
23#340—21no—
24#340—21no—
25C22×D4D411yescharacteristic
26C23×C4C2×C411yescharacteristic
27C23×C4C2311yescharacteristic
28C2×M16—21no—
29C2×M16—21no—
30C2×M16—42no—
31C22×C8—42no—
32C22×C8C2×C411yescharacteristic
33C22×C8C2×C411yescharacteristic
34C22×C8C2×C411yescharacteristic
35C22×C8C2×C411yescharacteristic
36C22×C8D411yescharacteristic
37C22×C8D411yescharacteristic
38C22×C8D411yescharacteristic
39C22×C8D411yescharacteristic
40C4×D4—21no—
41C4×D4—21no—
42C4×D4—21no—
43C4×D4—21no—
44C2×C4⋊C4—22no—
45C2×C4⋊C4—22no—
46C2×C4⋊C4Q811yescharacteristic
47C2×C22⋊C4—22no—
48C2×C22⋊C4—22no—
49C2×C22⋊C4D411yescharacteristic
50C2×C22⋊C4Q811yescharacteristic
51C2×C42C2×C411yescharacteristic
52#107—42no—
53#106—42no—
54C4⋊C8—21no—
55C4⋊C8—21no—
56#99—44no—
57C22⋊C8—21no—
58C22⋊C8—21no—
59C22⋊C8—21no—
60C22⋊C8—21no—
61#97—21no—
62#97—21no—
63#95—22no—
64#95—22no—
65C24C4⋊C411yescharacteristic
66C24C2×D411yescharacteristic
67C2×D4—21no—
68C2×D4—21no—
69C2×D4—22no—
70C2×D4—22no—
71C22×C4—21no—
72C22×C4—21no—
73C22×C4—41no—
74C22×C4—41no—
75C22×C4—41no—
76C22×C4—41no—
77C22×C4—42no—
78C22×C4—42no—
79C22×C4C4⋊C411yescharacteristic
80C22×C4C4⋊C411yescharacteristic
81C22×C4C4⋊C411yescharacteristic
82C22×C4C22×C411yescharacteristic
83C22×C4C2×D411yescharacteristic
84C22×C4C2×D411yescharacteristic
85C22×C4C2×Q811yescharacteristic
86C22×C4#4111yescharacteristic
87C22×C4#4111yescharacteristic
88M16—42no—
89M16—42no—
90C2×C8—22no—
91C2×C8—22no—
92C2×C8—22no—
93C2×C8—21no—
94C2×C8—21no—
95C2×C8—41no—
96C2×C8—41no—
97C2×C8—41no—
98C2×C8—41no—
99C2×C8—41no—
100C2×C8C22⋊C411yescharacteristic
101C2×C8C22⋊C411yescharacteristic
102C2×C8C22⋊C411yescharacteristic
103C2×C8C22⋊C411yescharacteristic
104C4⋊C4—21no—
105C4⋊C4—21no—
106C4⋊C4—42no—
107C4⋊C4—42no—
108C4⋊C4—42no—
109C4⋊C4—42no—
110C22⋊C4—21no—
111C22⋊C4—21no—
112C22⋊C4—21no—
113C22⋊C4—21no—
114C22⋊C4—42no—
115C22⋊C4—42no—
116C22⋊C4—42no—
117C22⋊C4—42no—
118C42—21no—
119C42—21no—
120C23—21no—
121C23—22no—
122C23—41no—
123C23—41no—
124C23—41no—
125C23—41no—
126C23C2×C4⋊C411yescharacteristic
127C23#12111yescharacteristic
128C23#12111yescharacteristic
129C23AGL(1,ℤ/8)12yes—
130C23#13712yes—
131D4—42no—
132D4—41no—
133D4—41no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—22no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—42no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—82no—
153C2×C4—82no—
154C2×C4—82no—
155C2×C4—82no—
156C2×C4—82no—
157C2×C4—82no—
158C2×C4C2×C22⋊C411yescharacteristic
159C2×C4#11711yescharacteristic
160C2×C4C22⋊Q811yescharacteristic
161C2×C4C22⋊Q811yescharacteristic
162C8—21no—
163C8—21no—
164C8—21no—
165C8—41no—
166C8—41no—
167C8#9912yescomplemented
168C22—21no—
169C22—21no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22—21no—
174C22—42no—
175C22—42no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—82no—
180C22#38011yescharacteristic
181C22#42812yes—
182C22#46812yes—
183C22#46911yescharacteristic
184C22#47011yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—41no—
189C4—41no—
190C4—41no—
191C4—162no—
192C4—162no—
193C4C2×#9911yescharacteristic
194C4#41011yescharacteristic
195C2—21no—
196C2—22no—
197C2—22no—
198C2—21no—
199C2—81no—
200C2#179911yescharacteristic
201C2#180911yescharacteristic
202C2#181211yescharacteristic
subgroupG/H
center, socleC22#380
commutatorC22×C4C22×C4
Frattini, cosocleC23×C4C23
prime radicalC22×D4D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #1808C2semidirect
3. #1807C2semidirect
5. #1289C2semidirect
6. C22×M16C4semidirect
15. C2×C4⋊C8C4semidirect
17. C2×C22⋊C8C4semidirect
19. C2×#97C4semidirect
167. C8#99semidirect

Maximal subgroups

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

subgroupindex
C2×#4352
#18082
#18072
#17992
#12892