Finite Group Databasebeta

← #508750

Subgroups — #508750

Order 512.

397 conjugacy classes of subgroups.

The subgroup lattice has 361 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33261C211yesmaximal, characteristic
2#21723C211yesmaximal, characteristic
3#13538C211yesmaximal, characteristic
4#13538C211yesmaximal, characteristic
5#13537C211yesmaximal, characteristic
6#13537C211yesmaximal, characteristic
7#13507C211yesmaximal, characteristic
8#13507C211yesmaximal, characteristic
9#13453C211yesmaximal, characteristic
10#13453C211yesmaximal, characteristic
11#13112C211yesmaximal, characteristic
12#13111C211yesmaximal, characteristic
13#13110C211yesmaximal, characteristic
14#13109C211yesmaximal, characteristic
15#12895C211yesmaximal, characteristic
16C2×#499C2211yescharacteristic
17#2647—21no—
18#2330—21no—
19C2×#367C2211yescharacteristic
20C2×#367C2211yescharacteristic
21C2×#366C2211yescharacteristic
22C2×#366C2211yescharacteristic
23#1992—21no—
24#1944—21no—
25#1944—21no—
26#1943—21no—
27#1942C2211yescharacteristic
28#1942C2211yescharacteristic
29#1942C2211yescharacteristic
30#1942C2211yescharacteristic
31#1942C2211yescharacteristic
32#1942C2211yescharacteristic
33#1846C2211yescharacteristic
34#1845C2211yescharacteristic
35#1845C2211yescharacteristic
36#1836—21no—
37#1776—21no—
38C4×#107C2211yescharacteristic
39C4×#107C2211yescharacteristic
40#1726C2211yescharacteristic
41#1380C2211yescharacteristic
42#1380C2211yescharacteristic
43#1380C2211yescharacteristic
44#1380C2211yescharacteristic
45#1380C2211yescharacteristic
46#1380C2211yescharacteristic
47#1380C2211yescharacteristic
48#1380C2211yescharacteristic
49#1380C2211yescharacteristic
50#1380C2211yescharacteristic
51#1380C2211yescharacteristic
52#1380C2211yescharacteristic
53#1374C2211yescharacteristic
54#1374C2211yescharacteristic
55#1374C2211yescharacteristic
56#1374C2211yescharacteristic
57#1374C2211yescharacteristic
58#1374C2211yescharacteristic
59C2×#125—21no—
60C22×C16C2311yescharacteristic
61C22×C16C2311yescharacteristic
62C22×C16C2311yescharacteristic
63C22×C16C2311yescharacteristic
64#499—22no—
65#499—22no—
66C2×#107—21no—
67C2×#107—21no—
68C2×#107C2311yescharacteristic
69C2×#107C2311yescharacteristic
70C2×#107C2311yescharacteristic
71C2×#107C2311yescharacteristic
72C2×#107C2311yescharacteristic
73C2×#107C2311yescharacteristic
74C2×#107C2311yescharacteristic
75C2×#107C2311yescharacteristic
76C2×#106—21no—
77C2×#106—21no—
78C2×#97D411yescharacteristic
79C2×#97D411yescharacteristic
80C2×#97D411yescharacteristic
81C2×C4×C8C2311yescharacteristic
82C2×C4×C8C2311yescharacteristic
83C2×C4×C8C2311yescharacteristic
84#400—41no—
85#400—41no—
86#398—41no—
87#398—41no—
88#389—21no—
89#389—21no—
90#389—21no—
91#389—21no—
92#389—21no—
93#389—21no—
94#389—41no—
95#389—41no—
96#387—41no—
97#387—41no—
98#384—21no—
99#384—21no—
100#382—21no—
101C4×C4⋊C4—21no—
102C4×C4⋊C4—21no—
103#376D411yescharacteristic
104#367—22no—
105#367—22no—
106#366—22no—
107#366—22no—
108#340—21no—
109#340—21no—
110#340—21no—
111#340—21no—
112#340—21no—
113#340—21no—
114#340—21no—
115#340—21no—
116C22×C8C2×D411yescharacteristic
117C22×C8C2×D411yescharacteristic
118C22×C8C2×D411yescharacteristic
119C22×C8C2411yescharacteristic
120#125—24no—
121#125—42no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—41no—
131C2×C4⋊C4—41no—
132C2×C4⋊C4—41no—
133C2×C4⋊C4—41no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4—41no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—41no—
142C2×C42—41no—
143C2×C42—41no—
144C2×C42C2×D411yescharacteristic
145C2×C42C2×D411yescharacteristic
146C2×C42C2×D411yescharacteristic
147C2×C16—21no—
148C2×C16—21no—
149C2×C16—21no—
150C2×C16—21no—
151C2×C16—21no—
152C2×C16—21no—
153C2×C16—21no—
154C2×C16—21no—
155C2×C16—21no—
156C2×C16—21no—
157C2×C16—21no—
158C2×C16—21no—
159#107—21no—
160#107—21no—
161#107—21no—
162#107—21no—
163#107—21no—
164#107—21no—
165#107—21no—
166#107—21no—
167#107—21no—
168#107—21no—
169#107—21no—
170#107—21no—
171#107—21no—
172#107—21no—
173#107—42no—
174#107—42no—
175#107#4112yes—
176#107#4112yes—
177#106—24no—
178#106—42no—
179#97—22no—
180#97—22no—
181#97—41no—
182C4×C8—21no—
183C4×C8—21no—
184C4×C8—21no—
185C4×C8—21no—
186C4×C8—21no—
187C4×C8—21no—
188#95—41no—
189#95—41no—
190#95—41no—
191#95—41no—
192#95—41no—
193#95—41no—
194#95—41no—
195#95—41no—
196#95—41no—
197#95—41no—
198#95D811yescharacteristic
199#95D811yescharacteristic
200#95D811yescharacteristic
201#95D811yescharacteristic
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4C2×D811yescharacteristic
211C22×C4C2×D811yescharacteristic
212C22×C4C2×D811yescharacteristic
213C22×C4C2×D811yescharacteristic
214C22×C4C2×D811yescharacteristic
215C22×C4C2×D811yescharacteristic
216C22×C4C22×D411yescharacteristic
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8#13712yes—
225C2×C8#13712yes—
226C2×C8C2×#4111yescharacteristic
227C2×C8C2×#4111yescharacteristic
228C2×C82−1+411yescharacteristic
229C2×C82−1+411yescharacteristic
230C2×C82−1+411yescharacteristic
231C2×C82−1+411yescharacteristic
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—44no—
235C4⋊C4—44no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—161no—
251C4⋊C4—161no—
252C4⋊C4—161no—
253C4⋊C4—161no—
254C4⋊C4—161no—
255C4⋊C4—161no—
256C4⋊C4—161no—
257C4⋊C4—161no—
258C4⋊C4—161no—
259C4⋊C4—161no—
260C42—21no—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—21no—
266C42—161no—
267C42—161no—
268C16—41no—
269C16—41no—
270C16—41no—
271C16—41no—
272C23C22×D811yescharacteristic
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4#52511yescharacteristic
316C2×C4#53611yescharacteristic
317C2×C4#53611yescharacteristic
318C2×C4C2×#13711yescharacteristic
319C2×C4C2×#13711yescharacteristic
320C2×C4#57511yescharacteristic
321C8—22no—
322C8—22no—
323C8—41no—
324C8#54111yescharacteristic
325C8#54111yescharacteristic
326C8#54111yescharacteristic
327C8#54111yescharacteristic
328C22#310011yescharacteristic
329C22#322611yescharacteristic
330C22#322611yescharacteristic
331C22#341511yescharacteristic
332C22#341611yescharacteristic
333C22#341611yescharacteristic
334C22#341711yescharacteristic
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—82no—
342C4—82no—
343C4—161no—
344C4—161no—
345C4—161no—
346C4—161no—
347C4—161no—
348C4—161no—
349C4#263411yescharacteristic
350C4#311311yescharacteristic
351C4#323611yescharacteristic
352C4#323711yescharacteristic
353C2#3009111yescharacteristic
354C2#3368411yescharacteristic
355C2#3368511yescharacteristic
356C2#3380711yescharacteristic
357C2#3380711yescharacteristic
358C2#3380811yescharacteristic
359C2#3380811yescharacteristic
subgroupG/H
center, socle, prime radicalC23C22×D8
commutator, Frattini, cosocleC22×C8C24
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #376 ◁ #1726 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#332612
#217232
#135382
#135372
#135072
#134532
#131122
#131112
#131102
#131092
#128952