Finite Group Databasebeta

← #150493

Subgroups — #150493

Order 512.

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

normal subgroups only

This group has 367 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#28440C211yesmaximal, characteristic
2C4×#356C211yesmaximal, characteristic
3#11532C211yesmaximal, characteristic
4#7405C214yesmaximal
5C2×#494—21no—
6C2×#462—21no—
7C2×#462—21no—
8#2868C411yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10C2×#356—21no—
11#2016C412yes—
12#2016C2212yes—
13#1956—21no—
14C4×C4⋊C8C411yescharacteristic
15C4×#101—21no—
16#1467—21no—
17#1394C2212yes—
18#1325—21no—
19#1319C2212yes—
20C22×Q16—22no—
21C22×Q16—22no—
22C2×C4⋊Q8—21no—
23C2×C4⋊Q8—21no—
24C2×C4⋊Q8C2×C412yes—
25C2×C4⋊Q8D411yescharacteristic
26C2×C4×Q8D411yescharacteristic
27C2×C4×Q8D411yescharacteristic
28#494—44no—
29#462—42no—
30#462—42no—
31#462—42no—
32#462—42no—
33#432—41no—
34C2×C4⋊C8—21no—
35C2×#103—22no—
36C2×#103—22no—
37C2×#101—22no—
38C4×M16—41no—
39C2×C4×C8—21no—
40#391C2×C411yescharacteristic
41#391C2311yescharacteristic
42#389—41no—
43#384—41no—
44#384—41no—
45#384D411yescharacteristic
46C4×C4⋊C4—41no—
47C43C2×C411yescharacteristic
48#356—24no—
49#343—41no—
50#336C2×C412yes—
51#324—22no—
52#324—41no—
53C22×Q8—22no—
54C22×Q8C22⋊C411yescharacteristic
55C22×Q8C2×D411yescharacteristic
56C2×Q16—44no—
57C2×Q16—44no—
58C2×Q16—44no—
59C2×Q16—44no—
60C2×Q16—82no—
61C2×Q16—82no—
62C2×M16—42no—
63C22×C8—22no—
64C4⋊Q8—22no—
65C4⋊Q8—22no—
66C4⋊Q8—41no—
67C4⋊Q8—41no—
68C4⋊Q8—41no—
69C4⋊Q8—41no—
70C4⋊Q8—42no—
71C4⋊Q8—42no—
72C4⋊Q8—82no—
73C4×Q8—41no—
74C4×Q8—41no—
75C4×Q8—41no—
76C4×Q8—41no—
77C2×C4⋊C4—21no—
78C2×C4⋊C4—21no—
79C2×C4⋊C4—41no—
80C2×C4⋊C4—41no—
81C2×C4⋊C4—42no—
82C2×C4⋊C4—42no—
83C2×C4⋊C4—41no—
84C2×C4⋊C4—41no—
85C2×C4⋊C4C22⋊C411yescharacteristic
86C2×C4⋊C4C2×D411yescharacteristic
87C2×C42—21no—
88C2×C42—21no—
89C2×C42—21no—
90C2×C42—21no—
91C2×C42C22⋊C411yescharacteristic
92C2×C42C22⋊C411yescharacteristic
93C2×C42C22×C411yescharacteristic
94C4⋊C8—22no—
95C4⋊C8—22no—
96C4⋊C8—81no—
97#103—44no—
98#103—44no—
99#101—24no—
100#101—42no—
101C22⋊C8—42no—
102#97—81no—
103#97—81no—
104C4×C8—42no—
105C4×C8—81no—
106#95—41no—
107#95—41no—
108C2×Q8—21no—
109C2×Q8—21no—
110C2×Q8—21no—
111C2×Q8—41no—
112C2×Q8—41no—
113C2×Q8—41no—
114C2×Q8—41no—
115C2×Q8—42no—
116C2×Q8—42no—
117C2×Q8—42no—
118C2×Q8—42no—
119C2×Q8—42no—
120C2×Q8—42no—
121C2×Q8AGL(1,ℤ/8)12yes—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—42no—
129C22×C4#9911yescharacteristic
130C22×C4#9911yescharacteristic
131C22×C4C2×C22⋊C411yescharacteristic
132Q16—88no—
133Q16—88no—
134M16—44no—
135M16—82no—
136C2×C8—24no—
137C2×C8—42no—
138C2×C8—42no—
139C2×C8—82no—
140C2×C8—82no—
141C4⋊C4—44no—
142C4⋊C4—41no—
143C4⋊C4—41no—
144C4⋊C4—81no—
145C4⋊C4—81no—
146C4⋊C4—82no—
147C4⋊C4—84no—
148C4⋊C4—81no—
149C4⋊C4—81no—
150C4⋊C4—84no—
151C4⋊C4—81no—
152C4⋊C4—81no—
153C42—24no—
154C42—21no—
155C42—21no—
156C42—21no—
157C42—41no—
158C42—42no—
159C42—41no—
160C42—41no—
161C42—41no—
162C42—41no—
163C42#10412yes—
164C23C2×#9911yescharacteristic
165Q8—42no—
166Q8—42no—
167Q8—81no—
168Q8—81no—
169Q8—82no—
170Q8—82no—
171Q8—82no—
172Q8—82no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—81no—
193C2×C4—81no—
194C2×C4—82no—
195C2×C4—82no—
196C2×C4—82no—
197C2×C4#35311yescharacteristic
198C2×C4#35311yescharacteristic
199C2×C4#41811yescharacteristic
200C2×C4C2×#10411yescharacteristic
201C8—44no—
202C8—84no—
203C8—162no—
204C22—21no—
205C22—21no—
206C22#150711yescharacteristic
207C22#212211yescharacteristic
208C22C2×#35311yescharacteristic
209C4—24no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—42no—
214C4—42no—
215C4—41no—
216C4—81no—
217C4—81no—
218C4—81no—
219C4—162no—
220C4#141112yes—
221C2—21no—
222C2—21no—
223C2#1177611yescharacteristic
224C2#1358011yescharacteristic
225C2C2×#141111yescharacteristic
subgroupG/H
center, socleC22C2×#353
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
#284402
C4×#3562
#115322
#74052