Finite Group Databasebeta

← #93034

Subgroups — #93034

Order 512.

352 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 86 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
1C2×#1322C211yesmaximal, characteristic
2#11232C211yesmaximal, characteristic
3C2×#1292C211yesmaximal, characteristic
4C22×#107C411yescharacteristic
5C2×#423—21no—
6C22×C4⋊C8C2211yescharacteristic
7C2×C22⋊C16—21no—
8C2×#340—21no—
9C2×#340C411yescharacteristic
10C4⋊#95—21no—
11#1322—21no—
12#1322C412yescomplemented
13#1292—21no—
14#1292C412yescomplemented
15C22×M16—41no—
16C23×C8C2×C411yescharacteristic
17C23×C8D411yescharacteristic
18C22×C4⋊C4—21no—
19C22×C4⋊C4—21no—
20C22×C42D411yescharacteristic
21C22×C16—41no—
22C2×#107—41no—
23C2×#107—42no—
24#423—22no—
25#423—22no—
26#423—41no—
27#423—41no—
28C2×C4⋊C8—22no—
29C2×C4⋊C8—41no—
30C2×C4⋊C8—41no—
31C2×C4⋊C8—41no—
32C2×C4⋊C8C2×C411yescharacteristic
33C2×C4⋊C8C2×C411yescharacteristic
34C2×C4⋊C8D411yescharacteristic
35C2×C4⋊C8Q811yescharacteristic
36C2×#95—41no—
37C2×#95—41no—
38C22⋊C16—22no—
39C22⋊C16—41no—
40#340—42no—
41#340—41no—
42C23×C4—41no—
43C23×C4—41no—
44C23×C4C22⋊C411yescharacteristic
45C23×C4D811yescharacteristic
46C23×C4SD1611yescharacteristic
47C2×M16—42no—
48C2×M16—42no—
49C2×M16—81no—
50C2×M16—81no—
51C2×M16—81no—
52C2×M16—81no—
53C22×C8—21no—
54C22×C8—21no—
55C22×C8—21no—
56C22×C8—21no—
57C22×C8—41no—
58C22×C8—41no—
59C22×C8—41no—
60C22×C8—41no—
61C22×C8—42no—
62C22×C8C4211yescharacteristic
63C22×C8C22⋊C411yescharacteristic
64C22×C8C4⋊C411yescharacteristic
65C22×C8C4⋊C411yescharacteristic
66C2×C4⋊C4—22no—
67C2×C4⋊C4—22no—
68C2×C4⋊C4—41no—
69C2×C4⋊C4—41no—
70C2×C4⋊C4—41no—
71C2×C4⋊C4—41no—
72C2×C4⋊C4—41no—
73C2×C4⋊C4—41no—
74C2×C4⋊C4—41no—
75C2×C4⋊C4—41no—
76C2×C4⋊C4—41no—
77C2×C4⋊C4—41no—
78C2×C42—21no—
79C2×C42—21no—
80C2×C42—21no—
81C2×C42—21no—
82C2×C42C22⋊C411yescharacteristic
83C2×C42C4⋊C411yescharacteristic
84C2×C42SD1611yescharacteristic
85C2×C42Q1611yescharacteristic
86C2×C16—42no—
87C2×C16—81no—
88C2×C16—81no—
89#107—42no—
90#107—42no—
91C4⋊C8—24no—
92C4⋊C8—41no—
93C4⋊C8—41no—
94C4⋊C8—41no—
95C4⋊C8—41no—
96C4⋊C8—42no—
97C4⋊C8—42no—
98C4⋊C8—42no—
99#95—82no—
100#95—81no—
101#95—81no—
102C24#10211yescharacteristic
103C22×C4—21no—
104C22×C4—21no—
105C22×C4—21no—
106C22×C4—21no—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—41no—
114C22×C4—41no—
115C22×C4—42no—
116C22×C4—42no—
117C22×C4—81no—
118C22×C4—81no—
119C22×C4—81no—
120C22×C4—81no—
121C22×C4—81no—
122C22×C4—81no—
123C22×C4—81no—
124C22×C4—81no—
125C22×C4—81no—
126C22×C4—81no—
127C22×C4—81no—
128C22×C4—81no—
129C22×C4#9511yescharacteristic
130C22×C4#9911yescharacteristic
131C22×C4#9911yescharacteristic
132C22×C4#10211yescharacteristic
133C22×C4#10311yescharacteristic
134C22×C4#10311yescharacteristic
135C22×C4#10411yescharacteristic
136C22×C4#10411yescharacteristic
137C22×C4#10611yescharacteristic
138C22×C4#10711yescharacteristic
139C22×C4D1611yescharacteristic
140C22×C4SD3211yescharacteristic
141C22×C4SD3211yescharacteristic
142C22×C4Q3211yescharacteristic
143M16—82no—
144M16—82no—
145M16—82no—
146M16—82no—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—21no—
151C2×C8—42no—
152C2×C8—41no—
153C2×C8—41no—
154C2×C8—41no—
155C2×C8—41no—
156C2×C8—41no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—41no—
160C2×C8—44no—
161C2×C8—81no—
162C2×C8—82no—
163C2×C8—82no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—81no—
169C4⋊C4—81no—
170C4⋊C4—81no—
171C4⋊C4—81no—
172C42—21no—
173C42—21no—
174C42—21no—
175C42—21no—
176C42—21no—
177C42—21no—
178C42—21no—
179C42—21no—
180C16—82no—
181C23—21no—
182C23—21no—
183C23—21no—
184C23—21no—
185C23#32711yescharacteristic
186C23#32711yescharacteristic
187C23#34011yescharacteristic
188C23#35711yescharacteristic
189C23#35811yescharacteristic
190C23#36011yescharacteristic
191C23#36011yescharacteristic
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—81no—
221C2×C4—82no—
222C2×C4—82no—
223C2×C4—82no—
224C2×C4—82no—
225C2×C4—82no—
226C2×C4—82no—
227C2×C4—161no—
228C2×C4—161no—
229C2×C4—161no—
230C2×C4—161no—
231C2×C4—161no—
232C2×C4—161no—
233C2×C4—161no—
234C2×C4—161no—
235C2×C4#32811yescharacteristic
236C2×C4#32811yescharacteristic
237C2×C4#33911yescharacteristic
238C2×C4#34211yescharacteristic
239C2×C4AΣL(1,𝔽16)11yescharacteristic
240C2×C4#35211yescharacteristic
241C2×C4#35511yescharacteristic
242C2×C4#35611yescharacteristic
243C2×C4#35711yescharacteristic
244C2×C4#35811yescharacteristic
245C2×C4#36611yescharacteristic
246C2×C4#36711yescharacteristic
247C8—41no—
248C8—41no—
249C8—41no—
250C8—41no—
251C8—84no—
252C22—21no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22#129411yescharacteristic
265C22#134111yescharacteristic
266C22#134211yescharacteristic
267C22#134511yescharacteristic
268C22#134611yescharacteristic
269C22#134711yescharacteristic
270C22#134711yescharacteristic
271C22#134811yescharacteristic
272C22#134811yescharacteristic
273C22#138011yescharacteristic
274C22#138611yescharacteristic
275C4—21no—
276C4—21no—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—41no—
282C4—41no—
283C4—162no—
284C4—162no—
285C4#135311yescharacteristic
286C4#135411yescharacteristic
287C4#139011yescharacteristic
288C4#139411yescharacteristic
289C2—21no—
290C2—21no—
291C2—21no—
292C2—21no—
293C2#708811yescharacteristic
294C2#708911yescharacteristic
295C2#709011yescharacteristic
296C2#709111yescharacteristic
297C2#725111yescharacteristic
298C2#725511yescharacteristic
299C2#725811yescharacteristic
subgroupG/H
center, socleC23#327
commutatorC22×C8C42
Frattini, cosocleC22×C4⋊C8C22
prime radicalC24#102
LCSG ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C8 ◁ G
LECSG ▷ C22×C4⋊C8 ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
12. #1322C4semidirect
14. #1292C4semidirect

Maximal subgroups

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

subgroupindex
C2×#13222
#112322
C2×#12922