Finite Group Databasebeta

← #99542

Subgroups — #99542

Order 512.

384 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 92 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#23372C211yesmaximal, characteristic
2C4×#501C211yesmaximal, characteristic
3#9873C211yesmaximal, characteristic
4#9641C211yesmaximal, characteristic
5#7568C211yesmaximal, characteristic
6#7030C211yesmaximal, characteristic
7#7030C211yesmaximal, characteristic
8C2×#501C411yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10C4×#125C2211yescharacteristic
11#1993C411yescharacteristic
12#1992C411yescharacteristic
13#1944—21no—
14#1943—21no—
15#1940—21no—
16#1940—21no—
17#1917—21no—
18#1917—21no—
19#1917—21no—
20#1917—21no—
21#1847C411yescharacteristic
22#1831C2211yescharacteristic
23#1831C2211yescharacteristic
24C4×#107—21no—
25C4×#106—21no—
26#1744C2211yescharacteristic
27#1744C2211yescharacteristic
28C4×#97C2211yescharacteristic
29C2×Q8⋊C8—21no—
30C2×Q8⋊C8—21no—
31#1279—21no—
32#1279—21no—
33#1271—21no—
34#1271—21no—
35C2×C4⋊Q8C2×C411yescharacteristic
36C2×#125C2×C411yescharacteristic
37C2×C4×Q8—21no—
38#501—22no—
39#501—22no—
40C2×#107—21no—
41C2×#107—21no—
42C2×#106—21no—
43C2×#106—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8D411yescharacteristic
47C2×C4⋊C8D411yescharacteristic
48C2×C4⋊C8D411yescharacteristic
49C2×C4⋊C8D411yescharacteristic
50C2×#97—21no—
51C2×#97—21no—
52C2×#97—21no—
53C2×#97C2×C411yescharacteristic
54C2×#97C2×C411yescharacteristic
55C2×C4×C8—21no—
56C2×C4×C8—21no—
57C2×C4×C8—21no—
58#391—21no—
59#389—21no—
60#389—21no—
61#389D411yescharacteristic
62#389D411yescharacteristic
63#387—21no—
64#387—21no—
65#384C2×C411yescharacteristic
66#382C2×C411yescharacteristic
67C4×C4⋊C4—21no—
68C4×C4⋊C4—21no—
69C4×C4⋊C4—21no—
70C4×C4⋊C4—21no—
71C4×C4⋊C4D411yescharacteristic
72C4×C4⋊C4D411yescharacteristic
73C43C2311yescharacteristic
74#340—21no—
75#340—21no—
76#340—21no—
77#340—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336—21no—
85#336—21no—
86#336—21no—
87#336—21no—
88#336—21no—
89#336—21no—
90Q8⋊C8—42no—
91Q8⋊C8—42no—
92C22×Q8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—21no—
99C22×C8—41no—
100C22×C8—41no—
101C4⋊Q8—21no—
102C4⋊Q8—21no—
103C4⋊Q8—21no—
104C4⋊Q8M1612yes—
105#125—21no—
106#125—21no—
107#125—21no—
108#125—21no—
109C4×Q8—41no—
110C4×Q8—41no—
111C4×Q8—41no—
112C4×Q8—41no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4C22⋊C411yescharacteristic
124C2×C4⋊C4C22⋊C411yescharacteristic
125C2×C4⋊C4C22⋊C411yescharacteristic
126C2×C4⋊C4C22⋊C411yescharacteristic
127C2×C42—21no—
128C2×C42—21no—
129C2×C42—41no—
130C2×C42C22×C411yescharacteristic
131C2×C42C2×D411yescharacteristic
132C2×C42C2×D411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135C2×C42#4111yescharacteristic
136C2×C42#4111yescharacteristic
137#107—24no—
138#107—42no—
139#106—24no—
140#106—42no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143C4⋊C8—41no—
144C4⋊C8—41no—
145C4⋊C8—81no—
146C4⋊C8—81no—
147#97—21no—
148#97—21no—
149#97—21no—
150#97—42no—
151#97—81no—
152#97—81no—
153#97M1612yes—
154C4×C8—22no—
155C4×C8—22no—
156C4×C8—22no—
157C4×C8—22no—
158C4×C8—41no—
159C4×C8—41no—
160#95—21no—
161#95—21no—
162#95—21no—
163#95—21no—
164#95—21no—
165#95—21no—
166#95—41no—
167#95—41no—
168C2×Q8—22no—
169C2×Q8—41no—
170C2×Q8—41no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—41no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
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
186C22×C4#12311yescharacteristic
187C2×C8—22no—
188C2×C8—22no—
189C2×C8—22no—
190C2×C8—22no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—42no—
194C2×C8—42no—
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—41no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—81no—
208C2×C8—81no—
209C2×C8—81no—
210C2×C8—81no—
211C4⋊C4—21no—
212C4⋊C4—22no—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—22no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—42no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—81no—
231C4⋊C4—81no—
232C4⋊C4—81no—
233C4⋊C4—81no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—41no—
241C42—41no—
242C42—41no—
243C42—41no—
244C42—41no—
245C42—41no—
246C42—41no—
247C42—81no—
248C42—81no—
249C42C2×M1611yescharacteristic
250C42C2×M1611yescharacteristic
251C42#13111yescharacteristic
252C42#13111yescharacteristic
253C23#38611yescharacteristic
254Q8—42no—
255Q8—42no—
256Q8—81no—
257Q8—81no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
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—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4#40711yescharacteristic
292C2×C4#40811yescharacteristic
293C2×C4#43511yescharacteristic
294C2×C4#43511yescharacteristic
295C2×C4#43611yescharacteristic
296C2×C4#43611yescharacteristic
297C2×C4#45311yescharacteristic
298C2×C4#45411yescharacteristic
299C2×C4#45511yescharacteristic
300C2×C4#45611yescharacteristic
301C2×C4#45611yescharacteristic
302C2×C4#45611yescharacteristic
303C8—24no—
304C8—42no—
305C8—82no—
306C8—82no—
307C8—81no—
308C8—81no—
309C8—81no—
310C8—81no—
311C22#187011yescharacteristic
312C22#188111yescharacteristic
313C22#188111yescharacteristic
314C22#188211yescharacteristic
315C22#188311yescharacteristic
316C22#188411yescharacteristic
317C22#188611yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—81no—
331C4—82no—
332C4—161no—
333C4#166011yescharacteristic
334C4#166111yescharacteristic
335C4#166311yescharacteristic
336C4#166411yescharacteristic
337C2#895511yescharacteristic
338C2#895611yescharacteristic
339C2#896211yescharacteristic
340C2#899711yescharacteristic
341C2#899811yescharacteristic
342C2#900011yescharacteristic
343C2#900611yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
socle, prime radicalC23#386
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#233722
C4×#5012
#98732
#96412
#75682
#70302