Finite Group Databasebeta

← #9929

Subgroups — #9929

Order 256.

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

normal subgroups only

This group has 305 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×#484C211yesmaximal, characteristic
2#2627C211yesmaximal, characteristic
3C2×#400C211yesmaximal, characteristic
4#1824C211yesmaximal, characteristic
5C2×#328C211yesmaximal, characteristic
6C2×#324C211yesmaximal, characteristic
7#1294C211yesmaximal, characteristic
8C2×C22⋊Q8C2211yescharacteristic
9C22×C4⋊C4C2211yescharacteristic
10C22×C4⋊C4C2211yescharacteristic
11#484—22no—
12#484—22no—
13C2×#107—21no—
14C2×#103—21no—
15C2×C22⋊C8C2211yescharacteristic
16C2×C22⋊C8C2211yescharacteristic
17#400—21no—
18#400—22no—
19#400—22no—
20#398—22no—
21#395—21no—
22#385—21no—
23#381—21no—
24#380C2211yescharacteristic
25C2×#95—21no—
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—21no—
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—22no—
56C2×C4⋊C4D412yes—
57C2×C4⋊C4D411yescharacteristic
58C2×C4⋊C4D412yes—
59C2×C22⋊C4—21no—
60C2×C22⋊C4—21no—
61#107—24no—
62#103—24no—
63C22⋊C8—21no—
64C22⋊C8—21no—
65C22⋊C8—21no—
66C22⋊C8D412yes—
67#95—24no—
68#95—24no—
69#95—22no—
70#95—22no—
71#95—22no—
72#95—21no—
73#95—21no—
74#95D412yes—
75C24C2×D411yescharacteristic
76C2×Q8—21no—
77C2×Q8—21no—
78C2×Q8—42no—
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—21no—
84C22×C4—21no—
85C22×C4—22no—
86C22×C4—21no—
87C22×C4—22no—
88C22×C4—21no—
89C22×C4—22no—
90C22×C4—21no—
91C22×C4—21no—
92C22×C4—21no—
93C22×C4—42no—
94C22×C4—42no—
95C22×C4—42no—
96C22×C4—42no—
97C22×C4—44no—
98C22×C4—41no—
99C22×C4—41no—
100C22×C4—41no—
101C22×C4—41no—
102C22×C4Q1612yes—
103C22×C4C2×D411yescharacteristic
104C22×C4C2×D411yescharacteristic
105C22×C4C2×D411yescharacteristic
106C22×C4C2×D411yescharacteristic
107C22×C4C2×D411yescharacteristic
108C22×C4#4111yescharacteristic
109C2×C8—22no—
110C2×C8—42no—
111C2×C8—42no—
112C2×C8—41no—
113C4⋊C4—22no—
114C4⋊C4—21no—
115C4⋊C4—22no—
116C4⋊C4—21no—
117C4⋊C4—42no—
118C4⋊C4—41no—
119C4⋊C4—41no—
120C4⋊C4—41no—
121C4⋊C4—41no—
122C4⋊C4—41no—
123C4⋊C4—41no—
124C4⋊C4—41no—
125C4⋊C4—41no—
126C4⋊C4—82no—
127C22⋊C4—41no—
128C22⋊C4—41no—
129C22⋊C4—41no—
130C22⋊C4—41no—
131C23—22no—
132C23—22no—
133C23#12011yescharacteristic
134C23#12011yescharacteristic
135C23#12111yescharacteristic
136C23C2×Q1611yescharacteristic
137C23#13511yescharacteristic
138C23#13711yescharacteristic
139C23#13711yescharacteristic
140Q8—42no—
141Q8—81no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—44no—
158C2×C4—42no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—42no—
162C2×C4—41no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—82no—
171C2×C4—82no—
172C2×C4—82no—
173C2×C4—82no—
174C2×C4—81no—
175C2×C4#12011yescharacteristic
176C2×C4#12111yescharacteristic
177C2×C4#12111yescharacteristic
178C2×C4#12711yescharacteristic
179C8—42no—
180C8—81no—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—22no—
185C22—21no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22#39211yescharacteristic
190C22#45111yescharacteristic
191C22#45111yescharacteristic
192C22#45211yescharacteristic
193C22#45211yescharacteristic
194C22#45412yes—
195C22#45812yes—
196C22#46711yescharacteristic
197C22#47011yescharacteristic
198C4—21no—
199C4—21no—
200C4—21no—
201C4—21no—
202C4—42no—
203C4—82no—
204C4—82no—
205C4—81no—
206C4—82no—
207C4—81no—
208C4—81no—
209C2—21no—
210C2—21no—
211C2—21no—
212C2—21no—
213C2#161512yes—
214C2#161712yes—
215C2#200111yescharacteristic
216C2#200311yescharacteristic
217C2#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×#4842
#26272
C2×#4002
#18242
C2×#3282
C2×#3242
#12942