Finite Group Databasebeta

← #511198

Subgroups — #511198

Order 512.

379 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#28828C211yesmaximal, characteristic
2#27995C211yesmaximal, characteristic
3#13539C211yesmaximal, characteristic
4#13537C211yesmaximal, characteristic
5#13537C211yesmaximal, characteristic
6#13514C211yesmaximal, characteristic
7#13507C211yesmaximal, characteristic
8#13506C211yesmaximal, characteristic
9#13178C211yesmaximal, characteristic
10#13167C211yesmaximal, characteristic
11#13112C211yesmaximal, characteristic
12#13112C211yesmaximal, characteristic
13#13111C211yesmaximal, characteristic
14#13105C211yesmaximal, characteristic
15#12890C211yesmaximal, characteristic
16#2571—21no—
17#2507—21no—
18C2×#367C2211yescharacteristic
19C2×#367C2211yescharacteristic
20C2×#366C2211yescharacteristic
21C2×#366C2211yescharacteristic
22C2×C4⋊C16C2211yescharacteristic
23C2×#346C2211yescharacteristic
24#2100—21no—
25#2087—21no—
26#2085—21no—
27#2085—21no—
28#1948—21no—
29#1942C2211yescharacteristic
30#1942C2211yescharacteristic
31#1942C2211yescharacteristic
32#1942C2211yescharacteristic
33#1942C2211yescharacteristic
34#1942C2211yescharacteristic
35#1921—21no—
36#1846C2211yescharacteristic
37#1846C2211yescharacteristic
38#1845C2211yescharacteristic
39#1845C2211yescharacteristic
40C4×#107C2211yescharacteristic
41C4×#107C2211yescharacteristic
42C8×C4⋊C4C2211yescharacteristic
43#1380C2211yescharacteristic
44#1380C2211yescharacteristic
45#1380C2211yescharacteristic
46#1380C2211yescharacteristic
47#1380C2211yescharacteristic
48#1380C2211yescharacteristic
49#1380C2211yescharacteristic
50#1380C2211yescharacteristic
51#1380C2211yescharacteristic
52#1380C2211yescharacteristic
53#1380C2211yescharacteristic
54#1380C2211yescharacteristic
55#1374C2211yescharacteristic
56#1374C2211yescharacteristic
57#1374C2211yescharacteristic
58#1374C2211yescharacteristic
59C22×C16C2311yescharacteristic
60C22×C16C2311yescharacteristic
61C22×C16C2311yescharacteristic
62C22×C16C2311yescharacteristic
63C2×#107—21no—
64C2×#107—21no—
65C2×#107C2311yescharacteristic
66C2×#107C2311yescharacteristic
67C2×#107C2311yescharacteristic
68C2×#107C2311yescharacteristic
69C2×#107C2311yescharacteristic
70C2×#107C2311yescharacteristic
71C2×#107C2311yescharacteristic
72C2×#107C2311yescharacteristic
73C2×#106—21no—
74C2×#106—21no—
75C2×C4⋊C8D411yescharacteristic
76C2×C4×C8C2311yescharacteristic
77C2×C4×C8C2311yescharacteristic
78C2×C4×C8C2311yescharacteristic
79#400—41no—
80#400—41no—
81#398—41no—
82#398—41no—
83#389—21no—
84#389—21no—
85#389—21no—
86#389—21no—
87#389—21no—
88#389—21no—
89#389—41no—
90#389—41no—
91#387—41no—
92#384—21no—
93#384—21no—
94#382—21no—
95#382—21no—
96#382—41no—
97C4×C4⋊C4—21no—
98C4×C4⋊C4—21no—
99C4×C4⋊C4D411yescharacteristic
100#367—22no—
101#367—22no—
102#366—22no—
103#366—22no—
104C4⋊C16—22no—
105#346—22no—
106#340—21no—
107#340—21no—
108#340—21no—
109#340—21no—
110#340—21no—
111#340—21no—
112#340—21no—
113#340—21no—
114#336D411yescharacteristic
115#336D411yescharacteristic
116C22×C8C2×D411yescharacteristic
117C22×C8C2×D411yescharacteristic
118C22×C8C2×D411yescharacteristic
119C22×C8C2411yescharacteristic
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
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—41no—
129C2×C4⋊C4—41no—
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⋊C4D811yescharacteristic
139C2×C4⋊C4D811yescharacteristic
140C2×C42—41no—
141C2×C42—41no—
142C2×C42C2×D411yescharacteristic
143C2×C42C2×D411yescharacteristic
144C2×C42C2×D411yescharacteristic
145C2×C16—21no—
146C2×C16—21no—
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#4112yes—
157#107—21no—
158#107—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—42no—
173#107—81no—
174#107#4112yes—
175#106—81no—
176#106—81no—
177C4⋊C8—22no—
178C4×C8—21no—
179C4×C8—21no—
180C4×C8—21no—
181C4×C8—21no—
182C4×C8—21no—
183C4×C8—21no—
184#95—41no—
185#95—41no—
186#95—41no—
187#95—41no—
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#95D811yescharacteristic
197#95D811yescharacteristic
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4C2×D811yescharacteristic
207C22×C4C2×D811yescharacteristic
208C22×C4C2×D811yescharacteristic
209C22×C4C2×D811yescharacteristic
210C22×C4C2×D811yescharacteristic
211C22×C4C2×D811yescharacteristic
212C22×C4C22×D411yescharacteristic
213C2×C8—21no—
214C2×C8—21no—
215C2×C8—21no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—21no—
221C2×C8#13712yes—
222C2×C8C2×#4111yescharacteristic
223C2×C8C2×#4111yescharacteristic
224C2×C82−1+411yescharacteristic
225C2×C82−1+411yescharacteristic
226C2×C82−1+411yescharacteristic
227C2×C82−1+411yescharacteristic
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
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—82no—
247C4⋊C4—82no—
248C4⋊C4—161no—
249C4⋊C4—161no—
250C4⋊C4—161no—
251C4⋊C4—161no—
252C4⋊C4—161no—
253C4⋊C4—161no—
254C4⋊C4—161no—
255C4⋊C4—161no—
256C42—21no—
257C42—21no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—21no—
262C42—82no—
263C42—161no—
264C16—22no—
265C16—41no—
266C16—41no—
267C16—41no—
268C23C22×D811yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
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—42no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
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#51012yes—
311C2×C4#53611yescharacteristic
312C2×C4#54711yescharacteristic
313C2×C4#54811yescharacteristic
314C2×C4C2×#13711yescharacteristic
315C2×C4#57711yescharacteristic
316C2×C4#57811yescharacteristic
317C8—22no—
318C8—41no—
319C8—41no—
320C8#54111yescharacteristic
321C8#54111yescharacteristic
322C8#55211yescharacteristic
323C8#56411yescharacteristic
324C22#322611yescharacteristic
325C22#333411yescharacteristic
326C22#335811yescharacteristic
327C22C2×#51011yescharacteristic
328C22#341411yescharacteristic
329C22#341511yescharacteristic
330C22#341611yescharacteristic
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—82no—
338C4—161no—
339C4—161no—
340C4—161no—
341C4—161no—
342C4—161no—
343C4—161no—
344C4—161no—
345C4#271911yescharacteristic
346C4#324211yescharacteristic
347C4#334411yescharacteristic
348C4#337411yescharacteristic
349C2#3231011yescharacteristic
350C2#3380211yescharacteristic
351C2#3380711yescharacteristic
352C2#3391411yescharacteristic
353C2#3392311yescharacteristic
354C2#3394211yescharacteristic
355C2#3394311yescharacteristic
subgroupG/H
center, socle, prime radicalC23C22×D8
commutator, Frattini, cosocleC22×C8C24
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ C8×C4⋊C4 ◁ 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
#288282
#279952
#135392
#135372
#135142
#135072
#135062
#131782
#131672
#131122
#131112
#131052
#128902