Finite Group Databasebeta

← #93957

Subgroups — #93957

Order 512.

315 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 315 conjugacy classes of subgroups — too many to draw. Only its 56 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#11324C211yesmaximal, characteristic
2#7189C211yesmaximal, characteristic
3#7189C211yesmaximal, characteristic
4C22×#107—21no—
5C2×#384C411yescharacteristic
6C2×#340—21no—
7C2×#336C411yescharacteristic
8C2×#324—21no—
9C2×#324—21no—
10C4⋊#95C2211yescharacteristic
11C23×C8—21no—
12C22×C4⋊C4—21no—
13C22×C4⋊C4—41no—
14C22×C4⋊C4D411yescharacteristic
15C22×C4⋊C4D411yescharacteristic
16C22×C42C2×C411yescharacteristic
17C2×#107—42no—
18C2×#107—42no—
19C2×#107—41no—
20C2×#107—41no—
21C2×C22⋊C8—41no—
22C2×C22⋊C8—41no—
23#384—42no—
24C2×#95—41no—
25#340—42no—
26#336—21no—
27#336C812yescomplemented
28#324—22no—
29#324—22no—
30#324—41no—
31#324—41no—
32C23×C4—21no—
33C23×C4—21no—
34C23×C4—21no—
35C23×C4—41no—
36C23×C4C22⋊C411yescharacteristic
37C22×C8—22no—
38C22×C8—22no—
39C22×C8—22no—
40C22×C8—41no—
41C22×C8—41no—
42C22×C8—41no—
43C22×C8—41no—
44C22×C8—81no—
45C22×C8—81no—
46C2×C4⋊C4—22no—
47C2×C4⋊C4—21no—
48C2×C4⋊C4—21no—
49C2×C4⋊C4—41no—
50C2×C4⋊C4—41no—
51C2×C4⋊C4—41no—
52C2×C4⋊C4—41no—
53C2×C4⋊C4—41no—
54C2×C4⋊C4—41no—
55C2×C4⋊C4—41no—
56C2×C4⋊C4—41no—
57C2×C4⋊C4—41no—
58C2×C4⋊C4—42no—
59C2×C4⋊C4—42no—
60C2×C4⋊C4—82no—
61C2×C4⋊C4—82no—
62C2×C4⋊C4D811yescharacteristic
63C2×C4⋊C4SD1611yescharacteristic
64C2×C4⋊C4SD1611yescharacteristic
65C2×C4⋊C4Q1611yescharacteristic
66C2×C42—21no—
67C2×C42—41no—
68C2×C42—41no—
69C2×C42C2×C811yescharacteristic
70C2×C42M1611yescharacteristic
71#107—44no—
72#107—44no—
73C22⋊C8—42no—
74C22⋊C8—42no—
75C22⋊C8—81no—
76C22⋊C8—81no—
77#95—82no—
78C24#9911yescharacteristic
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—22no—
84C22×C4—22no—
85C22×C4—21no—
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—21no—
91C22×C4—41no—
92C22×C4—41no—
93C22×C4—41no—
94C22×C4—41no—
95C22×C4—41no—
96C22×C4—41no—
97C22×C4—41no—
98C22×C4—41no—
99C22×C4—42no—
100C22×C4—81no—
101C22×C4—81no—
102C22×C4—81no—
103C22×C4—81no—
104C22×C4—82no—
105C22×C4—82no—
106C22×C4—81no—
107C22×C4—81no—
108C22×C4C22⋊C811yescharacteristic
109C22×C4#10111yescharacteristic
110C22×C4#10211yescharacteristic
111C22×C4#10311yescharacteristic
112C22×C4#10411yescharacteristic
113C22×C4#10411yescharacteristic
114C2×C8—24no—
115C2×C8—42no—
116C2×C8—42no—
117C2×C8—42no—
118C2×C8—42no—
119C2×C8—42no—
120C2×C8—42no—
121C2×C8—82no—
122C2×C8—82no—
123C2×C8—161no—
124C2×C8—161no—
125C2×C8—161no—
126C2×C8—161no—
127C4⋊C4—41no—
128C4⋊C4—41no—
129C4⋊C4—41no—
130C4⋊C4—41no—
131C4⋊C4—42no—
132C4⋊C4—42no—
133C4⋊C4—81no—
134C4⋊C4—81no—
135C4⋊C4—81no—
136C4⋊C4—81no—
137C4⋊C4—84no—
138C4⋊C4—84no—
139C42—41no—
140C42—41no—
141C42—42no—
142C23—21no—
143C23—21no—
144C23—21no—
145C23—21no—
146C23#32411yescharacteristic
147C23#32711yescharacteristic
148C23#32811yescharacteristic
149C23AΣL(1,𝔽16)11yescharacteristic
150C23#35211yescharacteristic
151C23#35311yescharacteristic
152C23#35611yescharacteristic
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—42no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—81no—
180C2×C4—81no—
181C2×C4—81no—
182C2×C4—81no—
183C2×C4—81no—
184C2×C4—81no—
185C2×C4—81no—
186C2×C4—81no—
187C2×C4—84no—
188C2×C4—82no—
189C2×C4—161no—
190C2×C4—161no—
191C2×C4—162no—
192C2×C4—161no—
193C2×C4—161no—
194C2×C4D4⋊C811yescharacteristic
195C2×C4Q8⋊C811yescharacteristic
196C2×C4#33011yescharacteristic
197C2×C4#33211yescharacteristic
198C8—44no—
199C8—162no—
200C8—162no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22#127111yescharacteristic
214C22#132511yescharacteristic
215C22#132611yescharacteristic
216C22#134311yescharacteristic
217C22#134611yescharacteristic
218C22#135211yescharacteristic
219C22#135411yescharacteristic
220C22#140611yescharacteristic
221C22#140711yescharacteristic
222C22#140811yescharacteristic
223C22#141111yescharacteristic
224C4—21no—
225C4—21no—
226C4—21no—
227C4—21no—
228C4—42no—
229C4—42no—
230C4—81no—
231C4—81no—
232C4—81no—
233C4—81no—
234C4—162no—
235C2—21no—
236C2—21no—
237C2—21no—
238C2—21no—
239C2#712311yescharacteristic
240C2#737011yescharacteristic
241C2#737211yescharacteristic
242C2#740211yescharacteristic
243C2#740511yescharacteristic
244C2#743411yescharacteristic
245C2#743611yescharacteristic
subgroupG/H
center, socleC23#353
commutatorC2×C42C2×C8
Frattini, cosocleC4⋊#95C22
prime radicalC24#99
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C4⋊#95 ◁ G
LECSG ▷ C4⋊#95 ▷ C23×C4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
27. #336C8semidirect

Maximal subgroups

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

subgroupindex
#113242
#71892