Finite Group Databasebeta

← #100900

Subgroups — #100900

Order 512.

350 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 76 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#27968C211yesmaximal, characteristic
2#21920C211yesmaximal, characteristic
3#8728C211yesmaximal, characteristic
4#7728C211yesmaximal, characteristic
5#7727C211yesmaximal, characteristic
6#7038C211yesmaximal, characteristic
7#7038C211yesmaximal, characteristic
8#2857C2211yescharacteristic
9#2285C2211yescharacteristic
10#2100—21no—
11#2099—21no—
12#1993C411yescharacteristic
13#1993C411yescharacteristic
14#1917—21no—
15#1917—21no—
16#1916—21no—
17#1916—21no—
18#1836C411yescharacteristic
19#1836C411yescharacteristic
20#1825—21no—
21#1825—21no—
22#1817C2211yescharacteristic
23#1817C2211yescharacteristic
24#1798—21no—
25#1797C2211yescharacteristic
26#1797C2211yescharacteristic
27#1750—21no—
28#1749C2211yescharacteristic
29#1296—21no—
30#1296—21no—
31#1272—21no—
32#1272—21no—
33#1271—21no—
34#1271—21no—
35C2×C4⋊Q8C2×C411yescharacteristic
36C2×C22⋊Q8—21no—
37C2×#117D411yescharacteristic
38C2×#117D411yescharacteristic
39C22×C42C2311yescharacteristic
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C22⋊C8—21no—
45C2×C22⋊C8—21no—
46C2×C22⋊C8—21no—
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×#97—21no—
50C2×#97C2×C411yescharacteristic
51C2×#97C2×C411yescharacteristic
52C2×C4×C8—21no—
53#391—21no—
54#389—21no—
55#389—21no—
56#384C2×C411yescharacteristic
57#384D411yescharacteristic
58#384D411yescharacteristic
59#382C2×C411yescharacteristic
60#382C2×C411yescharacteristic
61#380—21no—
62#380—21no—
63#380—21no—
64#380—21no—
65C4×C4⋊C4—21no—
66C4×C4⋊C4—21no—
67#340—21no—
68#340—21no—
69#340—21no—
70#340—21no—
71#340—21no—
72#340—21no—
73#340—21no—
74#340—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336D411yescharacteristic
85#336D411yescharacteristic
86#336D411yescharacteristic
87#336D411yescharacteristic
88C22×Q8—21no—
89C23×C4C2×D411yescharacteristic
90C23×C4#4111yescharacteristic
91C23×C4#4111yescharacteristic
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—41no—
99C22×C8—41no—
100C4⋊Q8—41no—
101C4⋊Q8—41no—
102C22⋊Q8—81no—
103C22⋊Q8—81no—
104#117—41no—
105#117—41no—
106#117—41no—
107#117—41no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4C22⋊C411yescharacteristic
119C2×C4⋊C4C22⋊C411yescharacteristic
120C2×C4⋊C4C22⋊C411yescharacteristic
121C2×C4⋊C4C22⋊C411yescharacteristic
122C2×C22⋊C4—21no—
123C2×C22⋊C4—21no—
124C2×C22⋊C4—41no—
125C2×C42—21no—
126C2×C42—21no—
127C2×C42—41no—
128C2×C42—41no—
129C2×C42C22×C411yescharacteristic
130C2×C42C2×D411yescharacteristic
131C2×C42C2×D411yescharacteristic
132C2×C42C2×D411yescharacteristic
133C4⋊C8—41no—
134C4⋊C8—41no—
135C4⋊C8—41no—
136C4⋊C8—41no—
137C4⋊C8—81no—
138C4⋊C8—81no—
139C22⋊C8—41no—
140C22⋊C8—41no—
141C22⋊C8—41no—
142C22⋊C8—41no—
143C22⋊C8—41no—
144C22⋊C8—41no—
145C22⋊C8—81no—
146C22⋊C8—81no—
147#97—41no—
148#97—41no—
149#97—81no—
150C4×C8—81no—
151#95—21no—
152#95—21no—
153#95—21no—
154#95—21no—
155#95—41no—
156#95—41no—
157C24#12311yescharacteristic
158C2×Q8—42no—
159C2×Q8—81no—
160C2×Q8—81no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4C2×C22⋊C411yescharacteristic
181C22×C4C4×D411yescharacteristic
182C22×C4C4×D411yescharacteristic
183C22×C4#12011yescharacteristic
184C22×C4#12111yescharacteristic
185C22×C4#12111yescharacteristic
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—81no—
205C2×C8—81no—
206C2×C8—81no—
207C2×C8—81no—
208C2×C8—81no—
209C2×C8—81no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—81no—
223C4⋊C4—81no—
224C4⋊C4—81no—
225C4⋊C4—81no—
226C4⋊C4—81no—
227C4⋊C4—81no—
228C22⋊C4—81no—
229C22⋊C4—81no—
230C22⋊C4—82no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—41no—
236C42—41no—
237C42—41no—
238C42—41no—
239C42—41no—
240C42—41no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23#38611yescharacteristic
249Q8—162no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
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—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4#41011yescharacteristic
291C2×C4#41011yescharacteristic
292C2×C4#45511yescharacteristic
293C2×C4#45511yescharacteristic
294C2×C4#47111yescharacteristic
295C2×C4#47111yescharacteristic
296C2×C4#47211yescharacteristic
297C2×C4#47311yescharacteristic
298C8—81no—
299C8—81no—
300C8—81no—
301C8—81no—
302C8—81no—
303C8—81no—
304C8—161no—
305C8—161no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22#188111yescharacteristic
314C22#188111yescharacteristic
315C22#188511yescharacteristic
316C22#189911yescharacteristic
317C22#190711yescharacteristic
318C22#190811yescharacteristic
319C22#191211yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—81no—
331C4—81no—
332C4—81no—
333C4—81no—
334C4—161no—
335C4—161no—
336C2—81no—
337C2#900511yescharacteristic
338C2#934611yescharacteristic
339C2#934811yescharacteristic
340C2#937211yescharacteristic
341C2#937411yescharacteristic
342C2#943311yescharacteristic
343C2#946011yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#123
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ 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
#279682
#219202
#87282
#77282
#77272
#70382