Finite Group Databasebeta

← #9257

Subgroups — #9257

Order 256.

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

normal subgroups only

This group has 262 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×#484C211yesmaximal, characteristic
2#2345C211yesmaximal, characteristic
3#1996C211yesmaximal, characteristic
4#1824C211yesmaximal, characteristic
5#1520C211yesmaximal, characteristic
6#1289C211yesmaximal, characteristic
7#1282C211yesmaximal, characteristic
8C2×C22⋊Q8C2211yescharacteristic
9C22×C4⋊C4C2211yescharacteristic
10#484—22no—
11#484—21no—
12#484—21no—
13C2×#107C412yescomplemented
14C2×#103C412yescomplemented
15C2×C22⋊C8C2211yescharacteristic
16C2×C22⋊C8C2211yescharacteristic
17#389—21no—
18#387—22no—
19#380—21no—
20#380C2211yescharacteristic
21#380C2211yescharacteristic
22C4×C4⋊C4—21no—
23C4×C22⋊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—
38C2×C4⋊C4—21no—
39C2×C4⋊C4—21no—
40C2×C4⋊C4—21no—
41C2×C4⋊C4—21no—
42C2×C4⋊C4—21no—
43C2×C4⋊C4—21no—
44C2×C4⋊C4—22no—
45C2×C4⋊C4C2×C411yescharacteristic
46C2×C4⋊C4C2×C412yes—
47C2×C4⋊C4D412yes—
48C2×C4⋊C4D411yescharacteristic
49C2×C4⋊C4D411yescharacteristic
50C2×C22⋊C4—21no—
51C2×C22⋊C4—21no—
52C2×C22⋊C4—21no—
53C2×C22⋊C4D411yescharacteristic
54C2×C22⋊C4D411yescharacteristic
55C2×C42—21no—
56C2×C42—22no—
57#107—22no—
58#107—22no—
59#103—22no—
60#103—22no—
61C22⋊C8—21no—
62C22⋊C8—21no—
63C22⋊C8—21no—
64C22⋊C8—21no—
65#95—22no—
66#95—22no—
67#95—21no—
68#95—21no—
69#95D412yes—
70C24C2×D411yescharacteristic
71C2×Q8—21no—
72C2×Q8—21no—
73C2×Q8—42no—
74C22×C4—21no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—22no—
78C22×C4—22no—
79C22×C4—21no—
80C22×C4—22no—
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—42no—
84C22×C4—41no—
85C22×C4—82no—
86C22×C4C22×C411yescharacteristic
87C22×C4C2×D411yescharacteristic
88C22×C4C2×D411yescharacteristic
89C22×C4C2×D411yescharacteristic
90C22×C4#4111yescharacteristic
91C22×C4#4111yescharacteristic
92C2×C8—22no—
93C2×C8—42no—
94C2×C8—42no—
95C2×C8—41no—
96C4⋊C4—22no—
97C4⋊C4—22no—
98C4⋊C4—21no—
99C4⋊C4—21no—
100C4⋊C4—21no—
101C4⋊C4—21no—
102C4⋊C4—42no—
103C4⋊C4—42no—
104C4⋊C4—41no—
105C4⋊C4—41no—
106C4⋊C4—82no—
107C4⋊C4C22⋊C412yes—
108C4⋊C4C22⋊C412yes—
109C22⋊C4—21no—
110C22⋊C4—21no—
111C22⋊C4—21no—
112C22⋊C4—41no—
113C22⋊C4—41no—
114C22⋊C4—41no—
115C22⋊C4—41no—
116C22⋊C4—41no—
117C22⋊C4—41no—
118C22⋊C4Q1612yes—
119C42—42no—
120C42—82no—
121C23—41no—
122C23—41no—
123C23C4×D411yescharacteristic
124C23#12011yescharacteristic
125C23#12111yescharacteristic
126C23C2×Q1611yescharacteristic
127C23#13511yescharacteristic
128C23#13711yescharacteristic
129C23#13711yescharacteristic
130Q8—42no—
131Q8—81no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—42no—
144C2×C4—42no—
145C2×C4—41no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—82no—
154C2×C4—82no—
155C2×C4—81no—
156C2×C4—81no—
157C2×C4—81no—
158C2×C4—81no—
159C2×C4—81no—
160C2×C4C2×C22⋊C411yescharacteristic
161C2×C4C4×D411yescharacteristic
162C2×C4#12111yescharacteristic
163C2×C4#12311yescharacteristic
164C8—42no—
165C8—81no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—21no—
171C22—21no—
172C22—41no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22#38611yescharacteristic
177C22C4×Q1611yescharacteristic
178C22#44111yescharacteristic
179C22#45111yescharacteristic
180C22#45211yescharacteristic
181C22#46211yescharacteristic
182C22#46411yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—42no—
187C4—42no—
188C4—42no—
189C4—81no—
190C4—82no—
191C4—81no—
192C4—81no—
193C4—161no—
194C4#41012yes—
195C2—21no—
196C2—21no—
197C2—21no—
198C2—21no—
199C2—21no—
200C2—21no—
201C2#187811yescharacteristic
202C2#189911yescharacteristic
203C2#190411yescharacteristic
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
13. C2×#107C4semidirect
14. C2×#103C4semidirect

Maximal subgroups

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

subgroupindex
C2×#4842
#23452
#19962
#18242
#15202
#12892
#12822