Finite Group Databasebeta

← #150010

Subgroups — #150010

Order 512.

319 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 319 conjugacy classes of subgroups — too many to draw. Only its 58 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#28519C211yesmaximal, characteristic
2#11530C211yesmaximal, characteristic
3#11477C211yesmaximal, characteristic
4#7372C214yesmaximal, complemented
5C2×#477—21no—
6C2×#476—21no—
7#2868C411yescharacteristic
8C4×#124C2211yescharacteristic
9#2096—21no—
10#2093—21no—
11#1959C412yes—
12#1847C2212yes—
13#1767C411yescharacteristic
14#1467—21no—
15#1459—21no—
16#1324C2212yes—
17#1324C2212yes—
18#1319—21no—
19#1318—21no—
20C2×C4⋊Q8—21no—
21C2×C4⋊Q8—41no—
22C2×#124C2×C411yescharacteristic
23C2×C4×Q8D411yescharacteristic
24C2×C4×D4D411yescharacteristic
25#477—42no—
26#477—42no—
27#476—42no—
28#476—42no—
29#432—41no—
30C2×#107—22no—
31C2×#106—22no—
32C2×C4⋊C8—21no—
33C2×#103—22no—
34C2×#102—22no—
35C2×C22⋊C8—41no—
36C2×#97C2×C412yes—
37#391D411yescharacteristic
38#390D411yescharacteristic
39#388—41no—
40#384—21no—
41#384—41no—
42#384C2×C412yes—
43#382C2311yescharacteristic
44C4×C22⋊C4—41no—
45C43C2×C411yescharacteristic
46#336—21no—
47#324—22no—
48#324—22no—
49#324—41no—
50#323—41no—
51C22×Q8—41no—
52C22×Q8C22⋊C411yescharacteristic
53C22×D4C22⋊C411yescharacteristic
54C23×C4—21no—
55C22×C8—22no—
56C22×C8—81no—
57C4⋊Q8—41no—
58C4⋊Q8—41no—
59C4⋊Q8—41no—
60C4⋊Q8—41no—
61C4⋊Q8—84no—
62#124—22no—
63#124—22no—
64C4×Q8—41no—
65C4×Q8—41no—
66C4×D4—41no—
67C4×D4—41no—
68C2×C4⋊C4—22no—
69C2×C4⋊C4—21no—
70C2×C4⋊C4—42no—
71C2×C4⋊C4—42no—
72C2×C4⋊C4—41no—
73C2×C4⋊C4C2×D411yescharacteristic
74C2×C4⋊C4C2×D411yescharacteristic
75C2×C22⋊C4—21no—
76C2×C22⋊C4—41no—
77C2×C22⋊C4—41no—
78C2×C42—21no—
79C2×C42—21no—
80C2×C42—21no—
81C2×C42C22⋊C411yescharacteristic
82C2×C42C22⋊C411yescharacteristic
83C2×C42C22×C411yescharacteristic
84#107—44no—
85#106—44no—
86C4⋊C8—22no—
87C4⋊C8—22no—
88C4⋊C8—81no—
89#103—44no—
90#102—44no—
91C22⋊C8—42no—
92C22⋊C8—42no—
93C22⋊C8—81no—
94#97—24no—
95#97—81no—
96#95—41no—
97#95—41no—
98C24—21no—
99C2×Q8—21no—
100C2×Q8—21no—
101C2×Q8—41no—
102C2×Q8—41no—
103C2×Q8—81no—
104C2×Q8—81no—
105C2×Q8—84no—
106C2×D4—21no—
107C2×D4—41no—
108C2×D4—41no—
109C2×D4#10112yes—
110C22×C4—21no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4—41no—
116C22×C4—41no—
117C22×C4—42no—
118C22×C4—82no—
119C22×C4#9911yescharacteristic
120C22×C4#9911yescharacteristic
121C22×C4C2×C22⋊C411yescharacteristic
122C2×C8—24no—
123C2×C8—42no—
124C2×C8—42no—
125C2×C8—82no—
126C2×C8—82no—
127C2×C8—162no—
128C4⋊C4—41no—
129C4⋊C4—41no—
130C4⋊C4—42no—
131C4⋊C4—42no—
132C4⋊C4—81no—
133C4⋊C4—84no—
134C4⋊C4—84no—
135C4⋊C4—81no—
136C4⋊C4—81no—
137C22⋊C4—44no—
138C22⋊C4—81no—
139C22⋊C4—82no—
140C42—21no—
141C42—21no—
142C42—21no—
143C42—41no—
144C42—42no—
145C42—42no—
146C42—41no—
147C42—41no—
148C42#13112yes—
149C23—22no—
150C23—41no—
151C23—41no—
152C23—81no—
153C23—81no—
154C23C2×#9911yescharacteristic
155Q8—42no—
156Q8—81no—
157Q8—162no—
158Q8—162no—
159D4—42no—
160D4—81no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—82no—
178C2×C4—81no—
179C2×C4—81no—
180C2×C4—84no—
181C2×C4—82no—
182C2×C4—161no—
183C2×C4#35311yescharacteristic
184C2×C4#35311yescharacteristic
185C2×C4#40811yescharacteristic
186C2×C4C2×#10111yescharacteristic
187C8—44no—
188C8—162no—
189C8—162no—
190C22—21no—
191C22—21no—
192C22—42no—
193C22—82no—
194C22—81no—
195C22—81no—
196C22—161no—
197C22#147211yescharacteristic
198C22C2×#35311yescharacteristic
199C22#213511yescharacteristic
200C4—21no—
201C4—21no—
202C4—21no—
203C4—42no—
204C4—42no—
205C4—41no—
206C4—81no—
207C4—81no—
208C4—81no—
209C4—162no—
210C4#140712yes—
211C2—21no—
212C2—21no—
213C2—82no—
214C2#1157011yescharacteristic
215C2C2×#140711yescharacteristic
216C2#1357911yescharacteristic
subgroupG/H
center, socleC22C2×#353
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. #7372C2semidirect

Maximal subgroups

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

subgroupindex
#285192
#115302
#114772
#73722