Finite Group Databasebeta

← #99401

Subgroups — #99401

Order 512.

338 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 102 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#23249C211yesmaximal, characteristic
2#9643C211yesmaximal, characteristic
3#9605C212yesmaximal
4#7571C211yesmaximal, characteristic
5#7027C212yesmaximal
6C4×C4⋊Q8C2211yescharacteristic
7#1985—21no—
8#1984—21no—
9#1940—22no—
10#1842C2211yescharacteristic
11#1771—22no—
12#1767C2212yes—
13C4×C4⋊C8C2212yes—
14#1744C2211yescharacteristic
15C2×#334—22no—
16C2×Q8⋊C8—21no—
17C2×Q8⋊C8—21no—
18#1277—22no—
19#1272C411yescharacteristic
20#1272C412yes—
21#1272C411yescharacteristic
22C2×C4⋊Q8Q811yescharacteristic
23C2×C4×Q8D411yescharacteristic
24C2×C4×Q8D411yescharacteristic
25C2×C4⋊C8—22no—
26C2×C4⋊C8—21no—
27C2×C4⋊C8—22no—
28C2×C4⋊C8—21no—
29C2×C4⋊C8—21no—
30C2×C4⋊C8D412yes—
31C2×C4⋊C8D412yes—
32C2×#97—22no—
33C2×#97—21no—
34C2×C4×C8—21no—
35C2×C4×C8—22no—
36C2×C4×C8—21no—
37#391C2×C411yescharacteristic
38#391C2×C411yescharacteristic
39#389—22no—
40#384Q811yescharacteristic
41C4×C4⋊C4—22no—
42C43C2311yescharacteristic
43#336—22no—
44#336—22no—
45#336—22no—
46#336—22no—
47#336C2×C412yes—
48#336C2×C412yes—
49#334—44no—
50Q8⋊C8—42no—
51Q8⋊C8—42no—
52C22×Q8C4⋊C411yescharacteristic
53C22×Q8C4⋊C411yescharacteristic
54C22×C8—22no—
55C22×C8—22no—
56C22×C8—22no—
57C22×C8—22no—
58C22×C8—41no—
59C22×C8—41no—
60C4⋊Q8—22no—
61C4⋊Q8—41no—
62C4×Q8—41no—
63C4×Q8—41no—
64C4×Q8—41no—
65C4×Q8—41no—
66C2×C4⋊C4—22no—
67C2×C4⋊C4—22no—
68C2×C4⋊C4—21no—
69C2×C4⋊C4—21no—
70C2×C4⋊C4C4⋊C411yescharacteristic
71C2×C4⋊C4C4⋊C411yescharacteristic
72C2×C42—21no—
73C2×C42—21no—
74C2×C42C22×C411yescharacteristic
75C2×C42C2×D411yescharacteristic
76C2×C42C2×D412yes—
77C2×C42C2×Q811yescharacteristic
78C2×C42#4112yes—
79C4⋊C8—22no—
80C4⋊C8—22no—
81C4⋊C8—22no—
82C4⋊C8—41no—
83C4⋊C8—41no—
84C4⋊C8—44no—
85C4⋊C8—42no—
86C4⋊C8—42no—
87C4⋊C8—81no—
88C4⋊C8—81no—
89C4⋊C8SD1614yes—
90#97—42no—
91#97—42no—
92#97—81no—
93C4×C8—22no—
94C4×C8—41no—
95C4×C8—42no—
96C4×C8—42no—
97C4×C8—81no—
98#95—22no—
99#95—22no—
100C2×Q8—21no—
101C2×Q8—21no—
102C2×Q8—21no—
103C2×Q8—41no—
104C2×Q8—41no—
105C2×Q8—41no—
106C2×Q8—41no—
107C2×Q8#10812yes—
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—21no—
112C22×C4C2×C4⋊C411yescharacteristic
113C22×C4C4×D412yes—
114C22×C4#12011yescharacteristic
115C22×C4C22⋊Q812yes—
116C22×C4#12311yescharacteristic
117C2×C8—24no—
118C2×C8—24no—
119C2×C8—42no—
120C2×C8—42no—
121C2×C8—42no—
122C2×C8—42no—
123C2×C8—42no—
124C2×C8—42no—
125C2×C8—42no—
126C2×C8—42no—
127C2×C8—42no—
128C2×C8—42no—
129C2×C8—42no—
130C2×C8—82no—
131C2×C8—82no—
132C2×C8—81no—
133C4⋊C4—44no—
134C4⋊C4—41no—
135C4⋊C4—41no—
136C4⋊C4—82no—
137C4⋊C4—81no—
138C4⋊C4—81no—
139C42—21no—
140C42—21no—
141C42—21no—
142C42—21no—
143C42—42no—
144C42—41no—
145C42—41no—
146C42—41no—
147C42—41no—
148C42—41no—
149C42C2×SD1612yes—
150C42#13512yes—
151C42#13712yes—
152C42#13712yes—
153C23#38511yescharacteristic
154Q8—42no—
155Q8—42no—
156Q8—81no—
157Q8—81no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—21no—
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—42no—
174C2×C4—42no—
175C2×C4—41no—
176C2×C4C2×#10811yescharacteristic
177C2×C4#43011yescharacteristic
178C2×C4C4×SD1612yes—
179C2×C4#44112yes—
180C2×C4#44812yes—
181C2×C4#45212yes—
182C2×C4#45311yescharacteristic
183C2×C4#45511yescharacteristic
184C2×C4#47512yes—
185C2×C4#47912yes—
186C8—44no—
187C8—44no—
188C8—82no—
189C8—82no—
190C8—82no—
191C8—161no—
192C22#185511yescharacteristic
193C22#185611yescharacteristic
194C22#186112yes—
195C22#186512yes—
196C22#186811yescharacteristic
197C4—21no—
198C4—21no—
199C4—22no—
200C4—22no—
201C4—22no—
202C4—22no—
203C4—42no—
204C4—41no—
205C4—81no—
206C4—81no—
207C4—81no—
208C4#162311yescharacteristic
209C4#163411yescharacteristic
210C4#164312yes—
211C2#886411yescharacteristic
212C2#888112yes—
213C2#890912yes—
214C2#891811yescharacteristic
215C2#892811yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
socle, prime radicalC23#385
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#232492
#96432
#96052
#75712
#70272