Finite Group Databasebeta

← #99322

Subgroups — #99322

Order 512.

460 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 116 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#21955C211yesmaximal, characteristic
2#11202C211yesmaximal, characteristic
3#8829C212yesmaximal
4C4×#324C211yesmaximal, characteristic
5#7029C212yesmaximal
6C2×#432—21no—
7C22×C4⋊C8C2211yescharacteristic
8C2×C4×C4⋊C4C2211yescharacteristic
9#1940—22no—
10#1940—22no—
11#1797—21no—
12#1797C2212yes—
13C4×C22⋊C8C2212yes—
14C2×#336—21no—
15C2×#336—21no—
16C2×#336C2211yescharacteristic
17C2×#335—22no—
18C2×#324C412yes—
19#1280C411yescharacteristic
20#1280C411yescharacteristic
21#1277—22no—
22C23×C8—21no—
23C23×C8—21no—
24C22×C4⋊C4C2×C411yescharacteristic
25C22×C4⋊C4Q811yescharacteristic
26C22×C42D411yescharacteristic
27C22×C42D411yescharacteristic
28C22×C42C2311yescharacteristic
29#432—42no—
30#432—42no—
31C2×C4⋊C8—22no—
32C2×C4⋊C8—21no—
33C2×C4⋊C8—21no—
34C2×C4⋊C8—21no—
35C2×C4⋊C8—21no—
36C2×C4⋊C8—42no—
37C2×C4⋊C8D412yes—
38C2×C4⋊C8D412yes—
39C2×C22⋊C8—22no—
40C2×C22⋊C8C2×C412yes—
41C2×C22⋊C8C2×C412yes—
42C2×#97—22no—
43C2×C4×C8—22no—
44C4×C4⋊C4—22no—
45C4×C4⋊C4—22no—
46C2×#95C2×C411yescharacteristic
47C2×#95Q811yescharacteristic
48#336—22no—
49#336—22no—
50#336—22no—
51#336—22no—
52#336—42no—
53#336—42no—
54#335—44no—
55#324—24no—
56C23×C4C4⋊C411yescharacteristic
57C23×C4C4⋊C411yescharacteristic
58C23×C4C4⋊C411yescharacteristic
59C23×C4C4⋊C411yescharacteristic
60C23×C4C22×C411yescharacteristic
61C23×C4C2×D411yescharacteristic
62C23×C4C2×Q811yescharacteristic
63C22×C8—22no—
64C22×C8—22no—
65C22×C8—22no—
66C22×C8—22no—
67C22×C8—22no—
68C22×C8—22no—
69C22×C8—41no—
70C22×C8—41no—
71C22×C8—41no—
72C22×C8—41no—
73C22×C8—41no—
74C22×C8—41no—
75C22×C8—41no—
76C22×C8—41no—
77C22×C8—41no—
78C22×C8—41no—
79C22×C8—41no—
80C22×C8—41no—
81C2×C4⋊C4—22no—
82C2×C4⋊C4—22no—
83C2×C4⋊C4—22no—
84C2×C4⋊C4—22no—
85C2×C4⋊C4—21no—
86C2×C4⋊C4—21no—
87C2×C4⋊C4—41no—
88C2×C42—21no—
89C2×C42—21no—
90C2×C42—21no—
91C2×C42—21no—
92C2×C42—21no—
93C2×C42—21no—
94C2×C42—41no—
95C2×C42—41no—
96C2×C42—41no—
97C2×C42—41no—
98C2×C42D812yes—
99C2×C42Q1612yes—
100C2×C42C2×D412yes—
101C2×C42#4112yes—
102C4⋊C8—24no—
103C4⋊C8—42no—
104C4⋊C8—42no—
105C4⋊C8—42no—
106C4⋊C8—42no—
107C4⋊C8—42no—
108C4⋊C8—81no—
109C4⋊C8—81no—
110C22⋊C8—22no—
111C22⋊C8—22no—
112C22⋊C8—22no—
113C22⋊C8—42no—
114C22⋊C8—42no—
115C22⋊C8M1614yes—
116#97—44no—
117C4×C8—42no—
118C4×C8—42no—
119#95—22no—
120#95—22no—
121C24C2×C4⋊C411yescharacteristic
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—21no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—41no—
142C22×C4—41no—
143C22×C4—41no—
144C22×C4—41no—
145C22×C4—41no—
146C22×C4—41no—
147C22×C4—41no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4#10712yes—
152C22×C4#10712yes—
153C22×C4#10812yes—
154C22×C4C4×D412yes—
155C22×C4#12011yescharacteristic
156C22×C4C22⋊Q812yes—
157C22×C4#12311yescharacteristic
158C22×C4C2×M1612yes—
159C22×C4#13111yescharacteristic
160C22×C4#13111yescharacteristic
161C22×C4C2×D811yescharacteristic
162C22×C4C2×Q1611yescharacteristic
163C22×C4AGL(1,ℤ/8)11yescharacteristic
164C22×C4#13711yescharacteristic
165C2×C8—24no—
166C2×C8—42no—
167C2×C8—42no—
168C2×C8—42no—
169C2×C8—42no—
170C2×C8—42no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—42no—
183C2×C8—81no—
184C2×C8—81no—
185C2×C8—81no—
186C2×C8—81no—
187C2×C8—81no—
188C2×C8—81no—
189C2×C8—81no—
190C2×C8—81no—
191C4⋊C4—44no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C42—22no—
195C42—22no—
196C42—22no—
197C42—22no—
198C42—22no—
199C42—22no—
200C42—42no—
201C42—41no—
202C42—41no—
203C42—81no—
204C23—21no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23#38511yescharacteristic
209C23#42311yescharacteristic
210C23#42411yescharacteristic
211C23C2×#10711yescharacteristic
212C23#42811yescharacteristic
213C23C2×#10811yescharacteristic
214C23#43011yescharacteristic
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—42no—
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—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4#43512yes—
258C2×C4#43612yes—
259C2×C4#44711yescharacteristic
260C2×C4#45111yescharacteristic
261C2×C4#45411yescharacteristic
262C2×C4#45611yescharacteristic
263C2×C4B(4,𝔽2)11yescharacteristic
264C2×C4#45811yescharacteristic
265C2×C4#48011yescharacteristic
266C2×C4#48411yescharacteristic
267C8—44no—
268C8—82no—
269C8—82no—
270C8—82no—
271C8—82no—
272C8—82no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22#156711yescharacteristic
286C22#156911yescharacteristic
287C22#157111yescharacteristic
288C22#157411yescharacteristic
289C22#185111yescharacteristic
290C22#185211yescharacteristic
291C22#185511yescharacteristic
292C22#185711yescharacteristic
293C22#185811yescharacteristic
294C22#186711yescharacteristic
295C22#186811yescharacteristic
296C4—22no—
297C4—22no—
298C4—21no—
299C4—21no—
300C4—42no—
301C4—42no—
302C4—42no—
303C4—42no—
304C4—81no—
305C4#159811yescharacteristic
306C4#160511yescharacteristic
307C4#161011yescharacteristic
308C4#161711yescharacteristic
309C2—21no—
310C2—21no—
311C2—21no—
312C2—21no—
313C2#883211yescharacteristic
314C2#883811yescharacteristic
315C2#885211yescharacteristic
316C2#885611yescharacteristic
317C2#885911yescharacteristic
318C2#886111yescharacteristic
319C2#886511yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
socleC23#385
prime radicalC24C2×C4⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#219552
#112022
#88292
C4×#3242
#70292