Finite Group Databasebeta

← #9256

Subgroups — #9256

Order 256.

276 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 71 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×#483C211yesmaximal, characteristic
2#2344C211yesmaximal, characteristic
3#1996C211yesmaximal, characteristic
4#1823C211yesmaximal, characteristic
5#1520C211yesmaximal, characteristic
6#1289C211yesmaximal, characteristic
7#1282C211yesmaximal, characteristic
8C2×C22⋊Q8C2211yescharacteristic
9C2×#117—21no—
10C22×C4⋊C4C2211yescharacteristic
11#483—22no—
12#483—21no—
13#483—21no—
14C2×#106C412yescomplemented
15C2×#103C412yescomplemented
16C2×C22⋊C8C2211yescharacteristic
17C2×C22⋊C8C2211yescharacteristic
18#389—21no—
19#387—22no—
20#381—21no—
21#380C2211yescharacteristic
22#380C2211yescharacteristic
23C4×C4⋊C4—21no—
24C4×C22⋊C4C2211yescharacteristic
25#342—21no—
26#342—21no—
27#340—22no—
28#328—22no—
29C22×Q8C2×C411yescharacteristic
30C23×C4—21no—
31C23×C4C2311yescharacteristic
32C22×C8—21no—
33C22×C8C2×C412yes—
34C22⋊Q8—21no—
35C22⋊Q8—21no—
36C22⋊Q8—21no—
37C22⋊Q8—21no—
38#117—42no—
39#117—42no—
40C2×C4⋊C4—21no—
41C2×C4⋊C4—21no—
42C2×C4⋊C4—21no—
43C2×C4⋊C4—22no—
44C2×C4⋊C4—21no—
45C2×C4⋊C4—21no—
46C2×C4⋊C4—21no—
47C2×C4⋊C4C2×C411yescharacteristic
48C2×C4⋊C4C2×C412yes—
49C2×C4⋊C4D412yes—
50C2×C4⋊C4D411yescharacteristic
51C2×C4⋊C4D411yescharacteristic
52C2×C22⋊C4—21no—
53C2×C22⋊C4—21no—
54C2×C22⋊C4—21no—
55C2×C22⋊C4D411yescharacteristic
56C2×C22⋊C4D411yescharacteristic
57C2×C42—22no—
58C2×C42—21no—
59#106—22no—
60#106—22no—
61#103—22no—
62#103—22no—
63C22⋊C8—21no—
64C22⋊C8—21no—
65C22⋊C8—21no—
66C22⋊C8—21no—
67#95—22no—
68#95—22no—
69#95—21no—
70#95—21no—
71#95D412yes—
72C24C2×D411yescharacteristic
73C2×Q8—21no—
74C2×Q8—21no—
75C2×Q8—42no—
76C22×C4—22no—
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—21no—
80C22×C4—22no—
81C22×C4—21no—
82C22×C4—22no—
83C22×C4—21no—
84C22×C4—21no—
85C22×C4—42no—
86C22×C4—41no—
87C22×C4—41no—
88C22×C4—41no—
89C22×C4—41no—
90C22×C4—41no—
91C22×C4C22×C411yescharacteristic
92C22×C4C2×D411yescharacteristic
93C22×C4C2×D411yescharacteristic
94C22×C4C2×D411yescharacteristic
95C22×C4#4111yescharacteristic
96C22×C4#4111yescharacteristic
97C2×C8—22no—
98C2×C8—42no—
99C2×C8—42no—
100C2×C8—41no—
101C4⋊C4—22no—
102C4⋊C4—22no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—21no—
106C4⋊C4—21no—
107C4⋊C4—42no—
108C4⋊C4—44no—
109C4⋊C4—42no—
110C4⋊C4—41no—
111C4⋊C4—41no—
112C4⋊C4C22⋊C412yes—
113C4⋊C4C22⋊C412yes—
114C22⋊C4—21no—
115C22⋊C4—21no—
116C22⋊C4—21no—
117C22⋊C4—41no—
118C22⋊C4—41no—
119C22⋊C4—41no—
120C22⋊C4—41no—
121C22⋊C4—41no—
122C22⋊C4—41no—
123C22⋊C4SD1612yes—
124C42—42no—
125C42—44no—
126C23—41no—
127C23—41no—
128C23C4×D411yescharacteristic
129C23#12011yescharacteristic
130C23#12111yescharacteristic
131C23C2×SD1611yescharacteristic
132C23#13511yescharacteristic
133C23AGL(1,ℤ/8)11yescharacteristic
134C23#13711yescharacteristic
135Q8—42no—
136Q8—81no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—22no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—42no—
149C2×C4—42no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—42no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—42no—
163C2×C4—41no—
164C2×C4—81no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4—81no—
168C2×C4—81no—
169C2×C4C2×C22⋊C411yescharacteristic
170C2×C4C4×D411yescharacteristic
171C2×C4#12111yescharacteristic
172C2×C4#12311yescharacteristic
173C8—42no—
174C8—81no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—21no—
179C22—21no—
180C22—21no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—41no—
185C22#38611yescharacteristic
186C22C4×SD1611yescharacteristic
187C22#44011yescharacteristic
188C22#45011yescharacteristic
189C22#45211yescharacteristic
190C22#46111yescharacteristic
191C22#46311yescharacteristic
192C4—21no—
193C4—21no—
194C4—21no—
195C4—42no—
196C4—42no—
197C4—42no—
198C4—82no—
199C4—81no—
200C4—81no—
201C4—81no—
202C4—161no—
203C4#41012yes—
204C2—21no—
205C2—21no—
206C2—21no—
207C2—21no—
208C2—21no—
209C2—21no—
210C2#187711yescharacteristic
211C2#189911yescharacteristic
212C2#190511yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC22×C4C22×C4
Frattini, cosocleC23×C4C23
prime radicalC24C2×D4
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
14. C2×#106C4semidirect
15. C2×#103C4semidirect

Maximal subgroups

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

subgroupindex
C2×#4832
#23442
#19962
#18232
#15202
#12892
#12822