Finite Group Databasebeta

← #94299

Subgroups — #94299

Order 512.

480 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 62 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×#1320C211yesmaximal, characteristic
2#11100C211yesmaximal, characteristic
3C2×#1297C211yesmaximal, characteristic
4#2911C411yescharacteristic, complemented
5C2×#407C2211yescharacteristic
6#2280—21no—
7C2×C4×C22⋊C4—21no—
8C2×#349—21no—
9#1733—21no—
10C2×H(3,ℤ/4)C411yescharacteristic, complemented
11#1320—21no—
12#1320C412yescomplemented
13#1297—21no—
14#1297C412yescomplemented
15C24×C4D411yescharacteristic
16C22×M16C2×C411yescharacteristic
17C22×M16D411yescharacteristic
18C2×#117—21no—
19C2×#117—21no—
20C22×C22⋊C4—41no—
21C22×C42—41no—
22C2×M32—41no—
23#428—42no—
24#427—41no—
25#407—41no—
26#407C2×C411yescharacteristic
27#407C2×C411yescharacteristic
28#407D411yescharacteristic
29#407Q811yescharacteristic
30C2×C22⋊C8—41no—
31#381—41no—
32#380—42no—
33#379—41no—
34C4×C22⋊C4—22no—
35C4×C22⋊C4—22no—
36C4×C22⋊C4—42no—
37C4×C22⋊C4—41no—
38C4×C22⋊C4—41no—
39C2×#95—22no—
40#349—22no—
41#349—41no—
42#339—42no—
43H(3,ℤ/4)—41no—
44C25D811yescharacteristic
45C23×C4—21no—
46C23×C4—21no—
47C23×C4—21no—
48C23×C4—21no—
49C23×C4—41no—
50C23×C4—41no—
51C23×C4—41no—
52C23×C4—41no—
53C23×C4—42no—
54C23×C4C22⋊C411yescharacteristic
55C23×C4C22⋊C411yescharacteristic
56C23×C4C4⋊C411yescharacteristic
57C23×C4SD1611yescharacteristic
58C23×C4SD1611yescharacteristic
59C23×C4Q1611yescharacteristic
60C2×M16—21no—
61C2×M16—21no—
62C2×M16—41no—
63C2×M16—41no—
64C2×M16—41no—
65C2×M16—41no—
66C2×M16C4211yescharacteristic
67C2×M16C22⋊C411yescharacteristic
68C2×M16C4⋊C411yescharacteristic
69C2×M16C4⋊C411yescharacteristic
70C22×C8—21no—
71C22×C8—21no—
72#117—41no—
73#117—41no—
74#117—41no—
75#117—41no—
76#117—41no—
77#117—41no—
78#117—41no—
79#117—41no—
80C2×C4⋊C4—22no—
81C2×C4⋊C4—41no—
82C2×C22⋊C4—42no—
83C2×C22⋊C4—48no—
84C2×C22⋊C4—42no—
85C2×C22⋊C4—44no—
86C2×C22⋊C4—41no—
87C2×C22⋊C4—41no—
88C2×C42—22no—
89C2×C42—41no—
90C2×C42—42no—
91C2×C42—42no—
92C2×C42—81no—
93C2×C42—81no—
94C2×C42—81no—
95C2×C42—81no—
96M32—42no—
97M32—81no—
98C2×C16—81no—
99#107—42no—
100#106—42no—
101C22⋊C8—41no—
102C22⋊C8—41no—
103C22⋊C8—41no—
104C22⋊C8—41no—
105#95—24no—
106#95—42no—
107#95—44no—
108C24—21no—
109C24—21no—
110C24—41no—
111C24—44no—
112C24—41no—
113C24#10211yescharacteristic
114C24#10211yescharacteristic
115C24#10711yescharacteristic
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—41no—
131C22×C4—41no—
132C22×C4—41no—
133C22×C4—41no—
134C22×C4—41no—
135C22×C4—41no—
136C22×C4—41no—
137C22×C4—41no—
138C22×C4—41no—
139C22×C4—41no—
140C22×C4—41no—
141C22×C4—41no—
142C22×C4—41no—
143C22×C4—41no—
144C22×C4—44no—
145C22×C4—48no—
146C22×C4—42no—
147C22×C4—42no—
148C22×C4—81no—
149C22×C4—81no—
150C22×C4—81no—
151C22×C4—81no—
152C22×C4—81no—
153C22×C4—81no—
154C22×C4—84no—
155C22×C4—82no—
156C22×C4—82no—
157C22×C4#9511yescharacteristic
158C22×C4#9911yescharacteristic
159C22×C4#9911yescharacteristic
160C22×C4#10311yescharacteristic
161C22×C4#10311yescharacteristic
162C22×C4#10411yescharacteristic
163C22×C4#10411yescharacteristic
164C22×C4#10611yescharacteristic
165M16—42no—
166M16—41no—
167M16—41no—
168M16—41no—
169M16—41no—
170M16—81no—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—21no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—41no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—81no—
182C4⋊C4—81no—
183C22⋊C4—48no—
184C22⋊C4—48no—
185C22⋊C4—81no—
186C22⋊C4—81no—
187C22⋊C4—88no—
188C22⋊C4—81no—
189C22⋊C4—81no—
190C42—42no—
191C42—42no—
192C42—81no—
193C42—82no—
194C42—82no—
195C42—82no—
196C42—82no—
197C42—81no—
198C16—82no—
199C23—24no—
200C23—21no—
201C23—21no—
202C23—21no—
203C23—21no—
204C23—42no—
205C23—42no—
206C23—41no—
207C23—41no—
208C23—42no—
209C23—42no—
210C23—42no—
211C23—42no—
212C23—41no—
213C23—41no—
214C23—44no—
215C23—81no—
216C23—82no—
217C23—82no—
218C23—82no—
219C23#32711yescharacteristic
220C23#32711yescharacteristic
221C23#34011yescharacteristic
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—48no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—84no—
253C2×C4—84no—
254C2×C4—88no—
255C2×C4—88no—
256C2×C4—82no—
257C2×C4—84no—
258C2×C4—84no—
259C2×C4—82no—
260C2×C4#32811yescharacteristic
261C2×C4#32811yescharacteristic
262C2×C4#33911yescharacteristic
263C2×C4#34211yescharacteristic
264C2×C4AΣL(1,𝔽16)11yescharacteristic
265C2×C4#35211yescharacteristic
266C2×C4#35311yescharacteristic
267C2×C4#35411yescharacteristic
268C8—41no—
269C8—41no—
270C8—41no—
271C8—41no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—21no—
276C22—21no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—44no—
281C22—41no—
282C22—42no—
283C22—42no—
284C22—41no—
285C22—41no—
286C22—42no—
287C22—44no—
288C22—81no—
289C22—81no—
290C22—84no—
291C22—81no—
292C22#129411yescharacteristic
293C22#134311yescharacteristic
294C22#134411yescharacteristic
295C4—21no—
296C4—21no—
297C4—41no—
298C4—41no—
299C4—88no—
300C4—162no—
301C4—162no—
302C4#135111yescharacteristic
303C4#135211yescharacteristic
304C4#139011yescharacteristic
305C4#139311yescharacteristic
306C2—21no—
307C2—21no—
308C2—42no—
309C2—41no—
310C2—42no—
311C2—41no—
312C2#725011yescharacteristic
313C2#739612yes—
subgroupG/H
centerC2×C4#353
commutatorC2×M16C42
Frattini, cosocleC2×#407C22
socleC22#1343
prime radicalC25D8
LCSG ▷ C2×M16 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×#407 ◁ G
LECSG ▷ C2×#407 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #2911C4semidirect
10. C2×H(3,ℤ/4)C4semidirect
12. #1320C4semidirect
14. #1297C4semidirect

Maximal subgroups

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

subgroupindex
C2×#13202
#111002
C2×#12972