Finite Group Databasebeta

← #8433

Subgroups — #8433

Order 256.

336 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 87 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
1#3502C211yesmaximal, characteristic
2#1805C211yesmaximal, characteristic
3#1542C211yesmaximal, characteristic
4#1518C211yesmaximal, characteristic
5#1518C211yesmaximal, characteristic
6#1481C211yesmaximal, characteristic
7#1479C211yesmaximal, characteristic
8Q82—21no—
9Q82C412yescomplemented
10#557—21no—
11#557—22no—
12#557—22no—
13#557C412yescomplemented
14#544—22no—
15#544—21no—
16#533—22no—
17#533C2211yescharacteristic
18#533C2211yescharacteristic
19#519—21no—
20C2×C4×Q8C2211yescharacteristic
21#431C2211yescharacteristic
22#431C2211yescharacteristic
23C2×C4⋊C8C2211yescharacteristic
24C2×#103—21no—
25#382C2211yescharacteristic
26#340—21no—
27#333—21no—
28#332—21no—
29#328—22no—
30#328—22no—
31Q8⋊C8—22no—
32Q8⋊C8—22no—
33C22×Q8D411yescharacteristic
34C22×C8—21no—
35C4⋊Q8—24no—
36C4⋊Q8—22no—
37C4⋊Q8—22no—
38C4⋊Q8—24no—
39C4⋊Q8—22no—
40C4⋊Q8—22no—
41C4⋊Q8C2×C411yescharacteristic
42C4⋊Q8C2×C411yescharacteristic
43C4⋊Q8D411yescharacteristic
44C4⋊Q8D411yescharacteristic
45#125—24no—
46#125—24no—
47#125—22no—
48#125—24no—
49#125—22no—
50#125—21no—
51#125—21no—
52C22⋊Q8—24no—
53C22⋊Q8—21no—
54C22⋊Q8—21no—
55C22⋊Q8D412yes—
56C22⋊Q8D412yes—
57C4×Q8—22no—
58C4×Q8—22no—
59C4×Q8—24no—
60C4×Q8—22no—
61C4×Q8—22no—
62C4×Q8—22no—
63C4×Q8—22no—
64C4×Q8—21no—
65C4×Q8—21no—
66C4×Q8—21no—
67C4×Q8—21no—
68C4×Q8C2×C412yes—
69C4×Q8C2×C412yes—
70C4×Q8D412yes—
71C4×Q8D412yes—
72#117—24no—
73#117—21no—
74#117—21no—
75C2×C4⋊C4—21no—
76C2×C4⋊C4—21no—
77C2×C4⋊C4D411yescharacteristic
78C2×C42—21no—
79C2×C42C2311yescharacteristic
80C4⋊C8—21no—
81C4⋊C8—21no—
82C4⋊C8—21no—
83C4⋊C8—21no—
84#103—42no—
85C22⋊C8—21no—
86C22⋊C8—21no—
87C4×C8—21no—
88C4×C8—21no—
89#95—21no—
90#95—21no—
91C2×Q8—24no—
92C2×Q8—21no—
93C2×Q8—21no—
94C2×Q8—21no—
95C2×Q8—21no—
96C2×Q8—21no—
97C2×Q8C22⋊C412yes—
98C2×Q8C22⋊C412yes—
99C2×Q8C22⋊C412yes—
100C2×Q8SD1612yes—
101C2×Q8Q1612yes—
102C22×C4—21no—
103C22×C4—21no—
104C22×C4—41no—
105C22×C4C2×D411yescharacteristic
106C22×C4C2×D411yescharacteristic
107C22×C4C2×D411yescharacteristic
108C2×C8—41no—
109C2×C8—41no—
110C2×C8—41no—
111C2×C8—41no—
112C2×C8—41no—
113C4⋊C4—24no—
114C4⋊C4—24no—
115C4⋊C4—24no—
116C4⋊C4—24no—
117C4⋊C4—24no—
118C4⋊C4—22no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—22no—
123C4⋊C4—22no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—22no—
128C4⋊C4—22no—
129C4⋊C4—21no—
130C4⋊C4—22no—
131C4⋊C4—41no—
132C4⋊C4—41no—
133C4⋊C4C22⋊C412yes—
134C4⋊C4C22⋊C412yes—
135C4⋊C4C22⋊C412yes—
136C22⋊C4—22no—
137C22⋊C4—22no—
138C42—24no—
139C42—24no—
140C42—22no—
141C42—22no—
142C42—22no—
143C42—22no—
144C42C22×C411yescharacteristic
145C42C2×D411yescharacteristic
146C42C2×D411yescharacteristic
147C42C2×D411yescharacteristic
148C23#12011yescharacteristic
149Q8—22no—
150Q8—22no—
151Q8—22no—
152Q8—42no—
153Q8—42no—
154Q8—42no—
155Q8—81no—
156Q8—84no—
157Q8#10314yes—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—81no—
169C2×C4—81no—
170C2×C4—81no—
171C2×C4—81no—
172C2×C4C2×C22⋊C411yescharacteristic
173C2×C4C2×C22⋊C411yescharacteristic
174C2×C4C2×C22⋊C411yescharacteristic
175C2×C4#12011yescharacteristic
176C2×C4#12011yescharacteristic
177C2×C4#12011yescharacteristic
178C2×C4C2×SD1611yescharacteristic
179C2×C4C2×Q1611yescharacteristic
180C2×C4#13711yescharacteristic
181C2×C4#13711yescharacteristic
182C8—81no—
183C8—81no—
184C8—81no—
185C22—21no—
186C22—21no—
187C22#37911yescharacteristic
188C22#44811yescharacteristic
189C22#45111yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—24no—
195C4—42no—
196C4—42no—
197C4—42no—
198C4—42no—
199C4—42no—
200C4—161no—
201C4C2×#10311yescharacteristic
202C4#41911yescharacteristic
203C4#44811yescharacteristic
204C4#45111yescharacteristic
205C2—21no—
206C2—21no—
207C2#178711yescharacteristic
208C2#179411yescharacteristic
209C2#179611yescharacteristic
subgroupG/H
center, socleC22#379
commutatorC42C22×C4
Frattini, cosocleC2×C42C23
prime radicalC23#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
9. Q82C4semidirect
13. #557C4semidirect

Maximal subgroups

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

subgroupindex
#35022
#18052
#15422
#15182
#14812
#14792