Finite Group Databasebeta

← #121152

Subgroups — #121152

Order 512.

483 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 483 conjugacy classes of subgroups — too many to draw. Only its 106 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#8112C211yesmaximal, characteristic
2#8112C211yesmaximal, characteristic
3#8104C211yesmaximal, characteristic
4#8104C211yesmaximal, characteristic
5#8104C211yesmaximal, characteristic
6#8104C211yesmaximal, characteristic
7#8100C211yesmaximal, characteristic
8C2×#407C2211yescharacteristic
9C2×#407C2211yescharacteristic
10C2×#407C2211yescharacteristic
11C2×#407C2211yescharacteristic
12#2280C2211yescharacteristic
13#2280C2211yescharacteristic
14#2280C2211yescharacteristic
15#1306—22no—
16#1306—22no—
17#1305—22no—
18#1305—22no—
19#1305—22no—
20#1305—22no—
21#1304C414yes—
22C24×C4C2311yescharacteristic
23C22×M16—21no—
24C22×M16—21no—
25C22×M16—21no—
26C22×M16—21no—
27C2×#117—21no—
28C2×#117—21no—
29C2×#117—21no—
30#407—21no—
31#407—21no—
32#407—21no—
33#407—21no—
34#407—21no—
35#407—21no—
36#407—21no—
37#407—21no—
38#407—21no—
39#407—21no—
40#407—21no—
41#407—21no—
42#407D412yes—
43#407D412yes—
44#407D412yes—
45#407Q812yes—
46C2×C22⋊C8—21no—
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8—21no—
51C2×C22⋊C8—21no—
52C2×C22⋊C8—21no—
53C2×C22⋊C8—21no—
54#381—21no—
55#381—21no—
56#381—21no—
57#380—21no—
58#380—21no—
59#380—21no—
60#380—21no—
61#380—21no—
62#380—21no—
63#379C2×C412yes—
64#379C2×C412yes—
65#379C2×C412yes—
66C4×C22⋊C4—21no—
67C4×C22⋊C4—21no—
68C4×C22⋊C4—21no—
69C4×C22⋊C4—21no—
70C4×C22⋊C4—21no—
71C4×C22⋊C4—21no—
72C25C22×C411yescharacteristic
73C23×C4—82no—
74C23×C4C2×D411yescharacteristic
75C23×C4C2×D411yescharacteristic
76C23×C4C2×D411yescharacteristic
77C23×C4C2×Q811yescharacteristic
78C23×C4#4111yescharacteristic
79C23×C4#4111yescharacteristic
80C23×C4#4111yescharacteristic
81C23×C4#4111yescharacteristic
82C23×C4#4111yescharacteristic
83C23×C4#4111yescharacteristic
84C23×C4#4111yescharacteristic
85C23×C4#4111yescharacteristic
86C23×C4#4111yescharacteristic
87C23×C4#4111yescharacteristic
88C2×M16—22no—
89C2×M16—22no—
90C2×M16—22no—
91C2×M16—22no—
92C2×M16—41no—
93C2×M16—41no—
94C2×M16—41no—
95C2×M16—41no—
96C2×M16—82no—
97C2×M16—82no—
98C2×M16—82no—
99C2×M16—82no—
100C22×C8—41no—
101C22×C8—41no—
102C22×C8—41no—
103C22×C8—41no—
104#117—82no—
105#117—82no—
106#117—82no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C22⋊C4—22no—
111C2×C22⋊C4—22no—
112C2×C22⋊C4—22no—
113C2×C22⋊C4—22no—
114C2×C22⋊C4—22no—
115C2×C22⋊C4—22no—
116C2×C22⋊C4—22no—
117C2×C22⋊C4—22no—
118C2×C22⋊C4—22no—
119C2×C42—41no—
120C2×C42—41no—
121C2×C42—41no—
122C22⋊C8—22no—
123C22⋊C8—22no—
124C22⋊C8—22no—
125C22⋊C8—22no—
126C22⋊C8—22no—
127C22⋊C8—22no—
128C22⋊C8—22no—
129C22⋊C8—22no—
130C22⋊C8—41no—
131C22⋊C8—41no—
132C22⋊C8—41no—
133C22⋊C8—41no—
134C22⋊C8—41no—
135C22⋊C8—41no—
136C22⋊C8—41no—
137C22⋊C8—41no—
138#95—41no—
139#95—41no—
140#95—41no—
141#95—41no—
142#95—41no—
143#95—41no—
144C24—81no—
145C24—81no—
146C24—81no—
147C24#11711yescharacteristic
148C24#11711yescharacteristic
149C24#11711yescharacteristic
150C24C4×D411yescharacteristic
151C24C4×D411yescharacteristic
152C24C4×D411yescharacteristic
153C24C4×Q811yescharacteristic
154C22×C4—42no—
155C22×C4—42no—
156C22×C4—42no—
157C22×C4—42no—
158C22×C4—42no—
159C22×C4—42no—
160C22×C4—42no—
161C22×C4—42no—
162C22×C4—42no—
163C22×C4—42no—
164C22×C4—81no—
165C22×C4—81no—
166C22×C4—81no—
167C22×C4—81no—
168C22×C4—81no—
169C22×C4—81no—
170C22×C4—81no—
171C22×C4#12111yescharacteristic
172C22×C4#12111yescharacteristic
173C22×C4#12111yescharacteristic
174C22×C4C22⋊Q811yescharacteristic
175C22×C4C22⋊Q811yescharacteristic
176C22×C4C22⋊Q811yescharacteristic
177C22×C4#12311yescharacteristic
178C22×C4#12311yescharacteristic
179C22×C4#12311yescharacteristic
180C22×C4#12311yescharacteristic
181C22×C4#12311yescharacteristic
182C22×C4#12311yescharacteristic
183C22×C4#12411yescharacteristic
184C22×C4#12411yescharacteristic
185C22×C4#12411yescharacteristic
186C22×C4#12511yescharacteristic
187C22×C4#12511yescharacteristic
188C22×C4#12511yescharacteristic
189C22×C4#12611yescharacteristic
190C22×C4#12611yescharacteristic
191C22×C4#12611yescharacteristic
192C22×C4#12611yescharacteristic
193C22×C4#12611yescharacteristic
194C22×C4#12611yescharacteristic
195C22×C4#12611yescharacteristic
196C22×C4#12611yescharacteristic
197C22×C4#12611yescharacteristic
198C22×C4#12611yescharacteristic
199M16—82no—
200M16—82no—
201M16—82no—
202M16—82no—
203M16—82no—
204M16—82no—
205M16—82no—
206M16—82no—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8—42no—
211C2×C8—82no—
212C2×C8—82no—
213C2×C8—82no—
214C2×C8—82no—
215C4⋊C4—82no—
216C4⋊C4—82no—
217C4⋊C4—82no—
218C22⋊C4—82no—
219C22⋊C4—82no—
220C22⋊C4—82no—
221C22⋊C4—82no—
222C22⋊C4—82no—
223C22⋊C4—82no—
224C22⋊C4—82no—
225C22⋊C4—82no—
226C22⋊C4—82no—
227C42—82no—
228C42—82no—
229C42—82no—
230C23—41no—
231C23—41no—
232C23—41no—
233C23—41no—
234C23—41no—
235C23—41no—
236C23—41no—
237C23—41no—
238C23—41no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23—41no—
246C23—41no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23—88no—
252C23#38311yescharacteristic
253C23#38711yescharacteristic
254C23#38711yescharacteristic
255C23#38711yescharacteristic
256C23#38811yescharacteristic
257C23#38811yescharacteristic
258C23#38811yescharacteristic
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—82no—
288C2×C4—82no—
289C2×C4—82no—
290C2×C4—82no—
291C2×C4—82no—
292C2×C4—82no—
293C2×C4—82no—
294C2×C4—82no—
295C2×C4—82no—
296C2×C4#39611yescharacteristic
297C2×C4#39711yescharacteristic
298C2×C4#39711yescharacteristic
299C2×C4#39711yescharacteristic
300C2×C4#40011yescharacteristic
301C2×C4#40011yescharacteristic
302C2×C4#40011yescharacteristic
303C2×C4#40111yescharacteristic
304C8—82no—
305C8—82no—
306C8—82no—
307C8—82no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—82no—
330C22—82no—
331C22—82no—
332C22—82no—
333C22—82no—
334C22—82no—
335C22—82no—
336C22#144311yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—162no—
345C4—162no—
346C4—162no—
347C4#210412yes—
348C2—41no—
349C2—41no—
350C2—41no—
351C2—41no—
352C2—41no—
353C2—41no—
354C2—41no—
355C2#1131811yescharacteristic
356C2#1131911yescharacteristic
357C2#1131911yescharacteristic
subgroupG/H
centerC2×C4#401
commutator, prime radicalC25C22×C4
Frattini, cosocleC24×C4C23
socleC22#1443
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#81122
#81042
#81002