Finite Group Databasebeta

← #150853

Subgroups — #150853

Order 512.

278 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 64 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#28725C211yesmaximal, characteristic
2#12802C211yesmaximal, characteristic
3#11478C211yesmaximal, characteristic
4#7413C214yesmaximal
5C2×#491—21no—
6#2859C411yescharacteristic
7C4×C4⋊Q8C2211yescharacteristic
8C2×#356—21no—
9#2074C412yes—
10#2074C2212yes—
11#1992—21no—
12#1803—21no—
13#1803—21no—
14#1801—21no—
15#1767C411yescharacteristic
16#1461—21no—
17#1394C2212yes—
18#1325—21no—
19#1319C2212yes—
20C2×C4⋊Q8D411yescharacteristic
21C2×#125—21no—
22C2×C4×Q8D411yescharacteristic
23C2×C4×Q8D411yescharacteristic
24#491—42no—
25#491—42no—
26#431—41no—
27#423—41no—
28C2×C4⋊C8—21no—
29C2×#103—22no—
30C2×#103—22no—
31C2×#101—22no—
32C2×#97—21no—
33#391C2×C411yescharacteristic
34#391C2311yescharacteristic
35#389—41no—
36#389—41no—
37#389—41no—
38#384—21no—
39#384D411yescharacteristic
40#382C2×C412yes—
41C4×C4⋊C4—41no—
42C43C2×C411yescharacteristic
43#356—42no—
44#343—41no—
45#340—22no—
46#340—22no—
47#336C2×C412yes—
48#324—22no—
49#324—41no—
50C22×Q8C22⋊C411yescharacteristic
51C22×Q8C2×D411yescharacteristic
52C2×M16—42no—
53C22×C8—22no—
54C4⋊Q8—41no—
55C4⋊Q8D812yes—
56C4⋊Q8SD1612yes—
57#125—42no—
58#125—42no—
59C4×Q8—41no—
60C4×Q8—41no—
61C4×Q8—41no—
62C4×Q8—41no—
63C2×C4⋊C4—22no—
64C2×C4⋊C4—21no—
65C2×C4⋊C4—21no—
66C2×C4⋊C4—41no—
67C2×C4⋊C4—41no—
68C2×C4⋊C4—42no—
69C2×C4⋊C4—41no—
70C2×C4⋊C4—41no—
71C2×C4⋊C4C22⋊C411yescharacteristic
72C2×C4⋊C4C2×D411yescharacteristic
73C2×C42—21no—
74C2×C42—21no—
75C2×C42—21no—
76C2×C42—21no—
77C2×C42C22⋊C411yescharacteristic
78C2×C42C22⋊C411yescharacteristic
79C2×C42C22×C411yescharacteristic
80C4⋊C8—41no—
81C4⋊C8—41no—
82C4⋊C8—81no—
83C4⋊C8—81no—
84C4⋊C8—81no—
85#103—44no—
86#103—42no—
87#103—42no—
88#101—42no—
89#101—42no—
90C22⋊C8—42no—
91#97—42no—
92C4×C8—81no—
93#95—41no—
94#95—41no—
95#95—42no—
96C2×Q8—21no—
97C2×Q8—21no—
98C2×Q8—41no—
99C2×Q8—41no—
100C2×Q8—41no—
101C2×Q8—41no—
102C2×Q8#10212yes—
103C2×Q8C2×D811yescharacteristic
104C2×Q8C2×SD1611yescharacteristic
105C22×C4—21no—
106C22×C4—21no—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—42no—
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—
122C4⋊C4—42no—
123C4⋊C4—42no—
124C4⋊C4—41no—
125C4⋊C4—41no—
126C4⋊C4—42no—
127C4⋊C4—42no—
128C4⋊C4—81no—
129C4⋊C4—81no—
130C4⋊C4—82no—
131C4⋊C4—84no—
132C4⋊C4—82no—
133C4⋊C4—82no—
134C42—21no—
135C42—21no—
136C42—21no—
137C42—41no—
138C42—42no—
139C42—41no—
140C42—41no—
141C42—41no—
142C42—41no—
143C42—81no—
144C42#10212yes—
145C23C2×#9911yescharacteristic
146Q8—42no—
147Q8—41no—
148Q8—41no—
149Q8—81no—
150Q8—81no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
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—81no—
172C2×C4—81no—
173C2×C4—82no—
174C2×C4—82no—
175C2×C4—82no—
176C2×C4#35411yescharacteristic
177C2×C4#35411yescharacteristic
178C2×C4C2×#10211yescharacteristic
179C2×C4#42111yescharacteristic
180C8—82no—
181C8—162no—
182C8—162no—
183C22—21no—
184C22—21no—
185C22#151911yescharacteristic
186C22#212311yescharacteristic
187C22C2×#35411yescharacteristic
188C4—21no—
189C4—21no—
190C4—21no—
191C4—42no—
192C4—41no—
193C4—41no—
194C4—42no—
195C4—41no—
196C4—81no—
197C4—81no—
198C4—81no—
199C4—162no—
200C4#141312yes—
201C2—21no—
202C2—21no—
203C2#1187811yescharacteristic
204C2C2×#141311yescharacteristic
205C2#1360411yescharacteristic
subgroupG/H
center, socleC22C2×#354
commutatorC2×C42C22×C4
Frattini, cosocle#391C23
prime radicalC23C2×#99
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊Q8 ◁ G
LECSG ▷ #391 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#287252
#128022
#114782
#74132