Finite Group Databasebeta

← #150909

Subgroups — #150909

Order 512.

281 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 281 conjugacy classes of subgroups — too many to draw. Only its 62 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#29146C211yesmaximal, characteristic
2#12801C211yesmaximal, characteristic
3#11477C211yesmaximal, characteristic
4#7429C214yesmaximal, complemented
5#2859C411yescharacteristic
6C4×#124C2211yescharacteristic
7C2×#355—21no—
8#2026C2212yes—
9#2025C412yes—
10#1959—21no—
11#1836—21no—
12#1805—21no—
13#1804—21no—
14#1801—21no—
15#1767C411yescharacteristic
16#1459—21no—
17#1394C2212yes—
18#1324—21no—
19#1319C2212yes—
20C2×#125C2×C412yes—
21C2×#124D411yescharacteristic
22C2×C4×Q8D411yescharacteristic
23C2×C4×D4D411yescharacteristic
24#423—41no—
25C2×C4⋊C8—21no—
26C2×#103—22no—
27C2×#102—22no—
28C2×#101—22no—
29C2×C22⋊C8—41no—
30C2×#97—21no—
31#391C2311yescharacteristic
32#390C2×C411yescharacteristic
33#389—41no—
34#389—41no—
35#388—41no—
36#384—21no—
37#382—21no—
38#382D411yescharacteristic
39C4×C22⋊C4—41no—
40C43C2×C411yescharacteristic
41#355—42no—
42#343—41no—
43#340—22no—
44#340—22no—
45#336C2×C412yes—
46#324—22no—
47#323—41no—
48C22×Q8C2×D411yescharacteristic
49C22×D4C22⋊C411yescharacteristic
50C23×C4—21no—
51C2×M16—42no—
52C22×C8—22no—
53C22×C8—81no—
54#125—82no—
55#124—41no—
56#124SD1612yes—
57#124Q1612yes—
58C4×Q8—41no—
59C4×Q8—41no—
60C4×D4—41no—
61C4×D4—41no—
62C2×C4⋊C4—22no—
63C2×C4⋊C4—21no—
64C2×C4⋊C4—42no—
65C2×C4⋊C4—41no—
66C2×C4⋊C4—41no—
67C2×C4⋊C4C22⋊C411yescharacteristic
68C2×C4⋊C4C2×D411yescharacteristic
69C2×C22⋊C4—21no—
70C2×C22⋊C4—41no—
71C2×C22⋊C4—41no—
72C2×C42—21no—
73C2×C42—21no—
74C2×C42—21no—
75C2×C42C22⋊C411yescharacteristic
76C2×C42C22⋊C411yescharacteristic
77C2×C42C22×C411yescharacteristic
78C4⋊C8—41no—
79C4⋊C8—41no—
80C4⋊C8—81no—
81C4⋊C8—81no—
82#103—82no—
83#102—82no—
84#101—42no—
85#101—42no—
86C22⋊C8—42no—
87C22⋊C8—81no—
88#97—42no—
89#95—41no—
90#95—41no—
91#95—41no—
92#95—41no—
93C24—21no—
94C2×Q8—21no—
95C2×Q8—41no—
96C2×Q8—41no—
97C2×Q8C2×SD1611yescharacteristic
98C2×Q8C2×Q1611yescharacteristic
99C2×D4—21no—
100C2×D4—41no—
101C2×D4—41no—
102C2×D4#10312yes—
103C22×C4—21no—
104C22×C4—21no—
105C22×C4—21no—
106C22×C4—21no—
107C22×C4—21no—
108C22×C4—41no—
109C22×C4—41no—
110C22×C4—42no—
111C22×C4—82no—
112C22×C4#9911yescharacteristic
113C22×C4#9911yescharacteristic
114C22×C4C2×C22⋊C411yescharacteristic
115M16—82no—
116M16—82no—
117C2×C8—42no—
118C2×C8—42no—
119C2×C8—42no—
120C2×C8—82no—
121C2×C8—82no—
122C2×C8—162no—
123C4⋊C4—41no—
124C4⋊C4—41no—
125C4⋊C4—42no—
126C4⋊C4—42no—
127C4⋊C4—81no—
128C4⋊C4—84no—
129C4⋊C4—82no—
130C4⋊C4—82no—
131C22⋊C4—42no—
132C22⋊C4—42no—
133C22⋊C4—81no—
134C22⋊C4—82no—
135C42—21no—
136C42—21no—
137C42—21no—
138C42—41no—
139C42—41no—
140C42—41no—
141C42—81no—
142C42—81no—
143C42#10312yes—
144C23—22no—
145C23—41no—
146C23—41no—
147C23—81no—
148C23—81no—
149C23C2×#9911yescharacteristic
150Q8—41no—
151Q8—41no—
152Q8—81no—
153D4—42no—
154D4—81no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—82no—
173C2×C4—81no—
174C2×C4—81no—
175C2×C4—82no—
176C2×C4—82no—
177C2×C4—82no—
178C2×C4—161no—
179C2×C4#35411yescharacteristic
180C2×C4#35411yescharacteristic
181C2×C4C2×#10311yescharacteristic
182C2×C4#42111yescharacteristic
183C8—82no—
184C8—162no—
185C8—162no—
186C22—21no—
187C22—21no—
188C22—42no—
189C22—82no—
190C22—81no—
191C22—81no—
192C22—161no—
193C22#152011yescharacteristic
194C22#212211yescharacteristic
195C22C2×#35411yescharacteristic
196C4—21no—
197C4—21no—
198C4—21no—
199C4—21no—
200C4—42no—
201C4—41no—
202C4—41no—
203C4—41no—
204C4—81no—
205C4—81no—
206C4—81no—
207C4—162no—
208C2—21no—
209C2—21no—
210C2—82no—
211C2#1190011yescharacteristic
212C2#1359811yescharacteristic
213C2#1360311yescharacteristic
subgroupG/H
center, socleC22C2×#354
commutatorC2×C42C22×C4
Frattini, cosocle#391C23
prime radicalC22×D4C22⋊C4
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×#124 ◁ G
LECSG ▷ #391 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #7429C2semidirect

Maximal subgroups

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

subgroupindex
#291462
#128012
#114772
#74292