Finite Group Databasebeta

← #101708

Subgroups — #101708

Order 512.

346 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 86 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#29573C211yesmaximal, characteristic
2#21344C211yesmaximal, characteristic
3#9891C211yesmaximal, characteristic
4#7660C211yesmaximal, characteristic
5#7615C211yesmaximal, characteristic
6#7030C211yesmaximal, characteristic
7#7027C211yesmaximal, characteristic
8#2859C2211yescharacteristic
9#2295C2211yescharacteristic
10#2100C411yescharacteristic
11#2095C411yescharacteristic
12#2083C411yescharacteristic
13#2072C411yescharacteristic
14#1985—21no—
15#1942—21no—
16#1940—21no—
17#1933—21no—
18#1921—21no—
19#1916—22no—
20#1863—21no—
21#1831C2211yescharacteristic
22#1768—21no—
23#1767C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25#1746—21no—
26#1744C2211yescharacteristic
27C4×#97C2211yescharacteristic
28#1295—21no—
29#1295—21no—
30#1272—21no—
31#1271—21no—
32#1271—22no—
33C2×#125—21no—
34C2×C4×Q8D411yescharacteristic
35C2×#107—21no—
36C2×#107—21no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8—22no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×#103—21no—
42C2×#103—21no—
43C2×#97—21no—
44C2×#97—21no—
45C2×#97D411yescharacteristic
46C2×#97D411yescharacteristic
47C2×C4×C8—21no—
48C2×C4×C8—21no—
49C2×C4×C8—21no—
50#391C2×C411yescharacteristic
51#391D411yescharacteristic
52#389—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#389C2×C411yescharacteristic
57#389D411yescharacteristic
58#387—21no—
59#387—21no—
60#384C2×C411yescharacteristic
61#384C2×C411yescharacteristic
62#382—21no—
63C4×C4⋊C4—21no—
64C4×C4⋊C4D411yescharacteristic
65#376—21no—
66C43C2311yescharacteristic
67#340—21no—
68#340—21no—
69#340—21no—
70#340—21no—
71#336—22no—
72#336—22no—
73#336—22no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336C2×C411yescharacteristic
79#336C2×C411yescharacteristic
80#336D412yes—
81C22×Q8C22⋊C411yescharacteristic
82C22×C8—21no—
83C22×C8—21no—
84C22×C8—21no—
85C22×C8—21no—
86C22×C8—22no—
87C22×C8—41no—
88C22×C8—41no—
89#125—81no—
90#125—81no—
91C4×Q8—41no—
92C4×Q8—41no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—41no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4C22⋊C411yescharacteristic
105C2×C4⋊C4C22⋊C411yescharacteristic
106C2×C4⋊C4C22⋊C411yescharacteristic
107C2×C42—21no—
108C2×C42—21no—
109C2×C42C22×C411yescharacteristic
110C2×C42C2×D411yescharacteristic
111C2×C42C2×D411yescharacteristic
112C2×C42C2×D411yescharacteristic
113C2×C42C2×D411yescharacteristic
114C2×C42#4111yescharacteristic
115C2×C42#4111yescharacteristic
116#107—42no—
117#107—42no—
118C4⋊C8—22no—
119C4⋊C8—41no—
120C4⋊C8—41no—
121C4⋊C8—41no—
122C4⋊C8—44no—
123C4⋊C8—81no—
124#103—42no—
125#103—42no—
126#97—21no—
127#97—21no—
128#97—21no—
129#97—41no—
130#97—41no—
131#97—41no—
132#97—41no—
133#97Q1612yes—
134C4×C8—42no—
135C4×C8—42no—
136C4×C8—41no—
137C4×C8—41no—
138#95—21no—
139#95—21no—
140#95—21no—
141#95—21no—
142#95—21no—
143#95—21no—
144#95—21no—
145#95—41no—
146#95—41no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—41no—
150C2×Q8—41no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4C2×C22⋊C411yescharacteristic
158C22×C4C4×D411yescharacteristic
159C22×C4C4×D411yescharacteristic
160C22×C4#12011yescharacteristic
161C22×C4#12111yescharacteristic
162C22×C4#12111yescharacteristic
163C22×C4#12311yescharacteristic
164C2×C8—22no—
165C2×C8—22no—
166C2×C8—22no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—41no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—42no—
180C2×C8—81no—
181C2×C8—81no—
182C2×C8—81no—
183C2×C8—81no—
184C2×C8—81no—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—42no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—81no—
201C4⋊C4—81no—
202C4⋊C4—81no—
203C4⋊C4—82no—
204C4⋊C4—81no—
205C4⋊C4—81no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—41no—
213C42—41no—
214C42—41no—
215C42—42no—
216C42—42no—
217C42C2×Q1611yescharacteristic
218C42#13511yescharacteristic
219C42#13711yescharacteristic
220C42#13711yescharacteristic
221C23#38611yescharacteristic
222Q8—42no—
223Q8—81no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4#42111yescharacteristic
258C2×C4#42111yescharacteristic
259C2×C4C4×Q1611yescharacteristic
260C2×C4#44111yescharacteristic
261C2×C4#44311yescharacteristic
262C2×C4#44411yescharacteristic
263C2×C4#45111yescharacteristic
264C2×C4#45211yescharacteristic
265C2×C4#46211yescharacteristic
266C2×C4#46411yescharacteristic
267C2×C4#47111yescharacteristic
268C2×C4#47211yescharacteristic
269C8—42no—
270C8—42no—
271C8—42no—
272C8—82no—
273C8—81no—
274C8—82no—
275C8—161no—
276C22#187611yescharacteristic
277C22#187811yescharacteristic
278C22#188411yescharacteristic
279C22#189711yescharacteristic
280C22#190611yescharacteristic
281C22#190711yescharacteristic
282C22#191511yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—41no—
296C4—81no—
297C4—81no—
298C4—81no—
299C4—81no—
300C4—161no—
301C4—161no—
302C2#905611yescharacteristic
303C2#921311yescharacteristic
304C2#923611yescharacteristic
305C2#926611yescharacteristic
306C2#927011yescharacteristic
307C2#939011yescharacteristic
308C2#943211yescharacteristic
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
#295732
#213442
#98912
#76602
#76152
#70302
#70272