Finite Group Databasebeta

← #9927

Subgroups — #9927

Order 256.

327 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 327 conjugacy classes of subgroups — too many to draw. Only its 67 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#2627C211yesmaximal, characteristic
3C2×#398C211yesmaximal, characteristic
4#1823C211yesmaximal, characteristic
5C2×#328C211yesmaximal, characteristic
6C2×#324C211yesmaximal, characteristic
7#1294C211yesmaximal, characteristic
8C2×C22⋊Q8C2211yescharacteristic
9C22×C4⋊C4—21no—
10C22×C4⋊C4C2211yescharacteristic
11C22×C4⋊C4C2211yescharacteristic
12#483—22no—
13#483—22no—
14C2×#106—21no—
15C2×#103—21no—
16C2×C22⋊C8C2211yescharacteristic
17C2×C22⋊C8C2211yescharacteristic
18#400—21no—
19#398—22no—
20#398—22no—
21#398—22no—
22#395—21no—
23#385—21no—
24#381—21no—
25#380C2211yescharacteristic
26C2×#95—21no—
27C2×#95C2211yescharacteristic
28#340—22no—
29#328—22no—
30#324—22no—
31C22×Q8D411yescharacteristic
32C23×C4—21no—
33C23×C4—21no—
34C23×C4D411yescharacteristic
35C23×C4D411yescharacteristic
36C23×C4C2311yescharacteristic
37C22×C8—21no—
38C22×C8—21no—
39C22⋊Q8—21no—
40C22⋊Q8—21no—
41C22⋊Q8—21no—
42C22⋊Q8—21no—
43C2×C4⋊C4—21no—
44C2×C4⋊C4—21no—
45C2×C4⋊C4—21no—
46C2×C4⋊C4—21no—
47C2×C4⋊C4—24no—
48C2×C4⋊C4—21no—
49C2×C4⋊C4—21no—
50C2×C4⋊C4—21no—
51C2×C4⋊C4—21no—
52C2×C4⋊C4—21no—
53C2×C4⋊C4—21no—
54C2×C4⋊C4—21no—
55C2×C4⋊C4—21no—
56C2×C4⋊C4—22no—
57C2×C4⋊C4—42no—
58C2×C4⋊C4—42no—
59C2×C4⋊C4D412yes—
60C2×C4⋊C4D411yescharacteristic
61C2×C4⋊C4D412yes—
62C2×C22⋊C4—21no—
63C2×C22⋊C4—21no—
64#106—24no—
65#103—24no—
66C22⋊C8—21no—
67C22⋊C8—21no—
68C22⋊C8—21no—
69C22⋊C8D412yes—
70#95—24no—
71#95—22no—
72#95—22no—
73#95—22no—
74#95—21no—
75#95—21no—
76#95D412yes—
77C24C2×D411yescharacteristic
78C2×Q8—21no—
79C2×Q8—21no—
80C2×Q8—42no—
81C22×C4—24no—
82C22×C4—22no—
83C22×C4—21no—
84C22×C4—21no—
85C22×C4—21no—
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—22no—
91C22×C4—21no—
92C22×C4—22no—
93C22×C4—21no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4—42no—
97C22×C4—42no—
98C22×C4—41no—
99C22×C4—41no—
100C22×C4—42no—
101C22×C4—41no—
102C22×C4—41no—
103C22×C4—41no—
104C22×C4—41no—
105C22×C4—41no—
106C22×C4—41no—
107C22×C4SD1612yes—
108C22×C4C2×D411yescharacteristic
109C22×C4C2×D411yescharacteristic
110C22×C4C2×D411yescharacteristic
111C22×C4C2×D411yescharacteristic
112C22×C4C2×D411yescharacteristic
113C22×C4#4111yescharacteristic
114C2×C8—22no—
115C2×C8—42no—
116C2×C8—42no—
117C2×C8—41no—
118C4⋊C4—22no—
119C4⋊C4—21no—
120C4⋊C4—22no—
121C4⋊C4—21no—
122C4⋊C4—42no—
123C4⋊C4—48no—
124C4⋊C4—41no—
125C4⋊C4—41no—
126C4⋊C4—41no—
127C4⋊C4—41no—
128C4⋊C4—41no—
129C4⋊C4—41no—
130C4⋊C4—41no—
131C4⋊C4—41no—
132C4⋊C4—82no—
133C22⋊C4—41no—
134C22⋊C4—41no—
135C22⋊C4—41no—
136C22⋊C4—41no—
137C23—22no—
138C23—22no—
139C23#12011yescharacteristic
140C23#12011yescharacteristic
141C23#12111yescharacteristic
142C23C2×SD1611yescharacteristic
143C23#13511yescharacteristic
144C23AGL(1,ℤ/8)11yescharacteristic
145C23#13711yescharacteristic
146Q8—42no—
147Q8—81no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—24no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—44no—
159C2×C4—44no—
160C2×C4—42no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—42no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—42no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—81no—
180C2×C4—81no—
181C2×C4—81no—
182C2×C4—81no—
183C2×C4—81no—
184C2×C4#12011yescharacteristic
185C2×C4#12111yescharacteristic
186C2×C4#12111yescharacteristic
187C2×C4#12711yescharacteristic
188C8—42no—
189C8—81no—
190C22—22no—
191C22—22no—
192C22—22no—
193C22—22no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22#39211yescharacteristic
199C22#44811yescharacteristic
200C22#44911yescharacteristic
201C22#45011yescharacteristic
202C22#45211yescharacteristic
203C22#45612yes—
204C22#45812yes—
205C22#46511yescharacteristic
206C22#46811yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—21no—
211C4—44no—
212C4—42no—
213C4—82no—
214C4—82no—
215C4—81no—
216C4—81no—
217C4—81no—
218C2—21no—
219C2—21no—
220C2—21no—
221C2—21no—
222C2#160912yes—
223C2#161112yes—
224C2#200011yescharacteristic
225C2#200511yescharacteristic
226C2#202211yescharacteristic
subgroupG/H
center, socleC23#120
commutator, Frattini, cosocleC23×C4C23
prime radicalC24C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#4832
#26272
C2×#3982
#18232
C2×#3282
C2×#3242
#12942