Finite Group Databasebeta

← #101330

Subgroups — #101330

Order 512.

341 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 341 conjugacy classes of subgroups — too many to draw. Only its 80 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#23783C211yesmaximal, characteristic
2#22831C211yesmaximal, characteristic
3#7653C211yesmaximal, characteristic
4#7622C211yesmaximal, characteristic
5#7596C211yesmaximal, characteristic
6#7049C211yesmaximal, characteristic
7#7041C211yesmaximal, characteristic
8C4×C4⋊Q8C2211yescharacteristic
9#2295C2211yescharacteristic
10#2099C411yescharacteristic
11#2096C411yescharacteristic
12#2088—21no—
13#2068—21no—
14#2057C411yescharacteristic
15#2024C411yescharacteristic
16#1985—21no—
17#1917—21no—
18#1916—21no—
19#1840—21no—
20#1839C2211yescharacteristic
21#1831C2211yescharacteristic
22#1831C2211yescharacteristic
23#1776—21no—
24#1771—21no—
25#1767C2211yescharacteristic
26#1767C2211yescharacteristic
27#1763—21no—
28#1746—21no—
29#1272—21no—
30#1272—21no—
31#1272—21no—
32#1271—21no—
33#1271—21no—
34#1271—21no—
35C2×C4⋊Q8C2×C411yescharacteristic
36C2×C4×Q8—21no—
37C2×C4×Q8D411yescharacteristic
38C2×#107—21no—
39C2×#106—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×#103—21no—
45C2×#103—21no—
46C2×#97—21no—
47C2×#97—21no—
48C2×#97—21no—
49C2×C4×C8—21no—
50#391—21no—
51#391C2×C411yescharacteristic
52#391D411yescharacteristic
53#389—21no—
54#389—21no—
55#389C2×C411yescharacteristic
56#389D411yescharacteristic
57#387—21no—
58#387—21no—
59#384C2×C411yescharacteristic
60C4×C4⋊C4—21no—
61C4×C4⋊C4—21no—
62C4×C4⋊C4—21no—
63C4×C4⋊C4D411yescharacteristic
64#376—21no—
65C43C2311yescharacteristic
66#340—21no—
67#340—21no—
68#340—21no—
69#340—21no—
70#336—21no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336C2×C411yescharacteristic
83#336C2×C411yescharacteristic
84#336D411yescharacteristic
85#336D411yescharacteristic
86#336D411yescharacteristic
87#336D411yescharacteristic
88C22×Q8—21no—
89C22×Q8C22⋊C411yescharacteristic
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—41no—
97C22×C8—41no—
98C4⋊Q8—42no—
99C4×Q8—21no—
100C4×Q8—21no—
101C4×Q8—21no—
102C4×Q8—21no—
103C4×Q8—82no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4C22⋊C411yescharacteristic
114C2×C4⋊C4C22⋊C411yescharacteristic
115C2×C4⋊C4C22⋊C411yescharacteristic
116C2×C42—21no—
117C2×C42—21no—
118C2×C42—41no—
119C2×C42C22×C411yescharacteristic
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42C2×D411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42#4111yescharacteristic
125C2×C42#4111yescharacteristic
126#107—42no—
127#106—42no—
128C4⋊C8—42no—
129C4⋊C8—42no—
130C4⋊C8—41no—
131C4⋊C8—41no—
132C4⋊C8—81no—
133#103—42no—
134#103—42no—
135#97—42no—
136#97—41no—
137#97—41no—
138#97—41no—
139#97—41no—
140C4×C8—42no—
141#95—21no—
142#95—21no—
143#95—21no—
144#95—21no—
145#95—21no—
146#95—21no—
147#95—21no—
148#95—41no—
149#95—41no—
150C2×Q8—22no—
151C2×Q8—21no—
152C2×Q8—21no—
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8—81no—
157C2×Q8—81no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4C2×C22⋊C411yescharacteristic
165C22×C4C4×D411yescharacteristic
166C22×C4C4×D411yescharacteristic
167C22×C4#12011yescharacteristic
168C22×C4#12111yescharacteristic
169C22×C4#12111yescharacteristic
170C22×C4#12311yescharacteristic
171C2×C8—22no—
172C2×C8—22no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—81no—
190C2×C8—81no—
191C2×C8—81no—
192C2×C8—81no—
193C2×C8—81no—
194C2×C8—81no—
195C4⋊C4—22no—
196C4⋊C4—22no—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—81no—
210C4⋊C4—81no—
211C4⋊C4—81no—
212C4⋊C4—82no—
213C42—21no—
214C42—21no—
215C42—41no—
216C42—41no—
217C42—41no—
218C42—41no—
219C42—41no—
220C42—41no—
221C42—41no—
222C42—41no—
223C42—41no—
224C42—82no—
225C42#13511yescharacteristic
226C42#13511yescharacteristic
227C42#13711yescharacteristic
228C42#13711yescharacteristic
229C23#38611yescharacteristic
230Q8—42no—
231Q8—81no—
232Q8—82no—
233Q8—82no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4#41611yescharacteristic
270C2×C4#41911yescharacteristic
271C2×C4#45211yescharacteristic
272C2×C4#45211yescharacteristic
273C2×C4#47111yescharacteristic
274C2×C4#47311yescharacteristic
275C2×C4#48511yescharacteristic
276C2×C4#48511yescharacteristic
277C8—42no—
278C8—42no—
279C8—81no—
280C8—81no—
281C8—81no—
282C8—81no—
283C8—161no—
284C8—161no—
285C22#187311yescharacteristic
286C22#188411yescharacteristic
287C22#189111yescharacteristic
288C22#190311yescharacteristic
289C22#190511yescharacteristic
290C22#190611yescharacteristic
291C22#190811yescharacteristic
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—81no—
304C4—82no—
305C4—81no—
306C4—81no—
307C4—81no—
308C4—161no—
309C2#903411yescharacteristic
310C2#917011yescharacteristic
311C2#917811yescharacteristic
312C2#941811yescharacteristic
313C2#943111yescharacteristic
314C2#952811yescharacteristic
315C2#953211yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ 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
#237832
#228312
#76532
#76222
#75962
#70492
#70412