Finite Group Databasebeta

← #9240

Subgroups — #9240

Order 256.

226 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 61 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×#485C211yesmaximal, characteristic
2#2924C211yesmaximal, characteristic
3#1826C211yesmaximal, characteristic
4#1508C211yesmaximal, characteristic
5#1472C211yesmaximal, characteristic
6#1293C211yesmaximal, characteristic
7#1282C211yesmaximal, characteristic
8C2×C22⋊Q8C2211yescharacteristic
9C2×#117C2211yescharacteristic
10#485—21no—
11#485—21no—
12#485—21no—
13#485—21no—
14#433—22no—
15#432—21no—
16#431—21no—
17C2×#107C411yescharacteristic, complemented
18C2×#106C411yescharacteristic, complemented
19#424—21no—
20C2×#103C411yescharacteristic, complemented
21C2×#103C411yescharacteristic, complemented
22#407C2211yescharacteristic
23#407C2211yescharacteristic
24C2×C22⋊C8C2211yescharacteristic
25C2×C22⋊C8C2211yescharacteristic
26#405—21no—
27C4×C22⋊C4C2211yescharacteristic
28#339—21no—
29#339—21no—
30#328—22no—
31#324—21no—
32#324—21no—
33C22×Q8C2×C411yescharacteristic
34C23×C4C2311yescharacteristic
35C2×M16—21no—
36C2×M16—21no—
37C22×C8—21no—
38C22×C8C2×C411yescharacteristic
39C22×C8C2×C411yescharacteristic
40C22⋊Q8—21no—
41C22⋊Q8—21no—
42C22⋊Q8—21no—
43C22⋊Q8—21no—
44#117—21no—
45#117—21no—
46#117D411yescharacteristic
47#117D411yescharacteristic
48#117D411yescharacteristic
49#117D411yescharacteristic
50C2×C4⋊C4—21no—
51C2×C4⋊C4C2×C411yescharacteristic
52C2×C4⋊C4C2×C411yescharacteristic
53C2×C4⋊C4C2×C411yescharacteristic
54C2×C22⋊C4—21no—
55C2×C22⋊C4—21no—
56C2×C22⋊C4—21no—
57C2×C42—21no—
58C2×C42—21no—
59#107—21no—
60#107—21no—
61#106—21no—
62#106—21no—
63C4⋊C8—22no—
64C4⋊C8—22no—
65#103—21no—
66#103—21no—
67#103—21no—
68#103—21no—
69C22⋊C8—21no—
70C22⋊C8—21no—
71C22⋊C8—21no—
72C22⋊C8—21no—
73C22⋊C8—21no—
74C22⋊C8—21no—
75C22⋊C8D411yescharacteristic
76C22⋊C8D411yescharacteristic
77C22⋊C8D412yes—
78#97—22no—
79C4×C8—22no—
80#95—21no—
81C24#4111yescharacteristic
82C2×Q8—21no—
83C2×Q8—21no—
84C2×Q8—41no—
85C2×Q8—41no—
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—41no—
91C22×C4—41no—
92C22×C4—41no—
93C22×C4C22×C411yescharacteristic
94C22×C4C2×D411yescharacteristic
95C22×C4C2×D411yescharacteristic
96C22×C4C2×D411yescharacteristic
97C22×C4C2×D411yescharacteristic
98C22×C4#4111yescharacteristic
99M16—41no—
100M16—41no—
101M16—41no—
102M16—41no—
103C2×C8—21no—
104C2×C8—21no—
105C2×C8—21no—
106C2×C8—22no—
107C2×C8—21no—
108C2×C8—41no—
109C2×C8—41no—
110C2×C8—41no—
111C2×C8—41no—
112C2×C8—41no—
113C4⋊C4—21no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—41no—
118C4⋊C4—41no—
119C4⋊C4C22⋊C411yescharacteristic
120C4⋊C4C22⋊C411yescharacteristic
121C4⋊C4C22⋊C411yescharacteristic
122C4⋊C4C22⋊C411yescharacteristic
123C22⋊C4—21no—
124C22⋊C4—21no—
125C22⋊C4—21no—
126C22⋊C4—21no—
127C22⋊C4—22no—
128C22⋊C4—41no—
129C22⋊C4—41no—
130C22⋊C4—41no—
131C42—21no—
132C42—21no—
133C42—21no—
134C42—21no—
135C42—41no—
136C42—41no—
137C23—21no—
138C23—21no—
139C23—41no—
140C23—41no—
141C23C4×D411yescharacteristic
142C23#12111yescharacteristic
143C23#12311yescharacteristic
144Q8—41no—
145Q8—41no—
146Q8—81no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—42no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—81no—
168C2×C4—81no—
169C2×C4—81no—
170C2×C4—81no—
171C2×C4C2×C22⋊C411yescharacteristic
172C2×C4C4×D411yescharacteristic
173C2×C4#12011yescharacteristic
174C2×C4#12111yescharacteristic
175C8—41no—
176C8—41no—
177C8—42no—
178C8—41no—
179C8—41no—
180C8—81no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22—81no—
190C22—81no—
191C22#38611yescharacteristic
192C22#44311yescharacteristic
193C22#44411yescharacteristic
194C4—21no—
195C4—21no—
196C4—21no—
197C4—41no—
198C4—41no—
199C4—41no—
200C4—41no—
201C4—82no—
202C4—81no—
203C4—81no—
204C4#41011yescharacteristic
205C4#41011yescharacteristic
206C2—21no—
207C2—21no—
208C2—41no—
209C2—41no—
210C2#187611yescharacteristic
211C2#189911yescharacteristic
212C2#190211yescharacteristic
subgroupG/H
center, socleC22#386
commutatorC22×C4C22×C4
Frattini, cosocleC23×C4C23
prime radicalC24#41
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
17. C2×#107C4semidirect
18. C2×#106C4semidirect
20. C2×#103C4semidirect
21. C2×#103C4semidirect

Maximal subgroups

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

subgroupindex
C2×#4852
#29242
#18262
#15082
#14722
#12932
#12822