Finite Group Databasebeta

← #149986

Subgroups — #149986

Order 512.

282 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 56 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#28720C211yesmaximal, characteristic
2#11530C211yesmaximal, characteristic
3#11477C211yesmaximal, characteristic
4#7359C214yesmaximal, complemented
5C2×#488C412yes—
6#2859C411yescharacteristic
7C4×#124C2211yescharacteristic
8#2072—21no—
9#2071—21no—
10#1991C2212yes—
11#1805—21no—
12#1804—21no—
13C4×C4⋊C8C411yescharacteristic
14#1467—21no—
15#1459—21no—
16#1324C2212yes—
17#1324C2212yes—
18#1319—21no—
19#1318—21no—
20C2×#125C2×C412yes—
21C2×#124C2×C411yescharacteristic
22C2×C4×Q8D411yescharacteristic
23C2×C4×D4D411yescharacteristic
24#488—44no—
25#432—41no—
26C2×C4⋊C8—21no—
27C2×#103—22no—
28C2×#102—22no—
29C2×C22⋊C8—41no—
30C2×C4×C8C2×C412yes—
31#391D411yescharacteristic
32#390D411yescharacteristic
33#389—41no—
34#389—41no—
35#388—41no—
36#384—21no—
37#382—21no—
38#382C2311yescharacteristic
39C4×C22⋊C4—41no—
40C43C2×C411yescharacteristic
41#340—22no—
42#340—22no—
43#336—21no—
44#324—22no—
45#324—22no—
46#324—41no—
47#323—41no—
48C22×Q8C22⋊C411yescharacteristic
49C22×D4C22⋊C411yescharacteristic
50C23×C4—21no—
51C22×C8—22no—
52C22×C8—81no—
53#125—24no—
54#125—42no—
55#124—22no—
56#124—22no—
57C4×Q8—41no—
58C4×Q8—41no—
59C4×D4—41no—
60C4×D4—41no—
61C2×C4⋊C4—22no—
62C2×C4⋊C4—21no—
63C2×C4⋊C4—42no—
64C2×C4⋊C4—41no—
65C2×C4⋊C4—41no—
66C2×C4⋊C4C2×D411yescharacteristic
67C2×C4⋊C4C2×D411yescharacteristic
68C2×C22⋊C4—21no—
69C2×C22⋊C4—41no—
70C2×C22⋊C4—41no—
71C2×C42—21no—
72C2×C42—21no—
73C2×C42—21no—
74C2×C42C22⋊C411yescharacteristic
75C2×C42C22⋊C411yescharacteristic
76C2×C42C22×C411yescharacteristic
77C4⋊C8—41no—
78C4⋊C8—41no—
79C4⋊C8—81no—
80#103—44no—
81#102—44no—
82C22⋊C8—42no—
83C22⋊C8—42no—
84C22⋊C8—81no—
85#97—81no—
86C4×C8—42no—
87#95—41no—
88#95—41no—
89#95—41no—
90#95—41no—
91C24—21no—
92C2×Q8—21no—
93C2×Q8—21no—
94C2×Q8—41no—
95C2×Q8—41no—
96C2×D4—21no—
97C2×D4—41no—
98C2×D4—41no—
99C2×D4#10012yes—
100C22×C4—21no—
101C22×C4—21no—
102C22×C4—21no—
103C22×C4—21no—
104C22×C4—21no—
105C22×C4—41no—
106C22×C4—41no—
107C22×C4—42no—
108C22×C4—82no—
109C22×C4#9911yescharacteristic
110C22×C4#9911yescharacteristic
111C22×C4C2×C22⋊C411yescharacteristic
112C2×C8—42no—
113C2×C8—42no—
114C2×C8—42no—
115C2×C8—82no—
116C2×C8—82no—
117C2×C8—162no—
118C4⋊C4—41no—
119C4⋊C4—41no—
120C4⋊C4—42no—
121C4⋊C4—42no—
122C4⋊C4—81no—
123C4⋊C4—84no—
124C4⋊C4—82no—
125C4⋊C4—82no—
126C22⋊C4—44no—
127C22⋊C4—81no—
128C22⋊C4—82no—
129C42—21no—
130C42—21no—
131C42—21no—
132C42—41no—
133C42—42no—
134C42—41no—
135C42—41no—
136C42—81no—
137C42#13112yes—
138C23—22no—
139C23—41no—
140C23—41no—
141C23—81no—
142C23—81no—
143C23C2×#9911yescharacteristic
144Q8—42no—
145Q8—81no—
146D4—42no—
147D4—81no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—22no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—82no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4—82no—
168C2×C4—82no—
169C2×C4—82no—
170C2×C4—161no—
171C2×C4#35411yescharacteristic
172C2×C4#35411yescharacteristic
173C2×C4#40811yescharacteristic
174C2×C4C2×#10011yescharacteristic
175C8—82no—
176C8—162no—
177C8—162no—
178C22—21no—
179C22—21no—
180C22—42no—
181C22—82no—
182C22—81no—
183C22—81no—
184C22—161no—
185C22#147111yescharacteristic
186C22C2×#35411yescharacteristic
187C22#213511yescharacteristic
188C4—21no—
189C4—21no—
190C4—21no—
191C4—21no—
192C4—42no—
193C4—42no—
194C4—41no—
195C4—81no—
196C4—81no—
197C4—81no—
198C4—162no—
199C2—21no—
200C2—21no—
201C2—82no—
202C2#1156411yescharacteristic
203C2#1360211yescharacteristic
204C2#1360311yescharacteristic
subgroupG/H
center, socleC22C2×#354
commutatorC2×C42C22×C4
Frattini, cosocle#382C23
prime radicalC22×D4C22⋊C4
LCSG ▷ C2×C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×#124 ◁ G
LECSG ▷ #382 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #7359C2semidirect

Maximal subgroups

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

subgroupindex
#287202
#115302
#114772
#73592