Finite Group Databasebeta

← #100658

Subgroups — #100658

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#30095C211yesmaximal, characteristic
2#22313C211yesmaximal, characteristic
3#9894C211yesmaximal, characteristic
4#8237C211yesmaximal, characteristic
5#7663C211yesmaximal, characteristic
6#7041C211yesmaximal, characteristic
7#7023C211yesmaximal, characteristic
8#2859C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10#2100—21no—
11#2100C411yescharacteristic
12#2100C411yescharacteristic
13#2083C411yescharacteristic
14#2083C411yescharacteristic
15#2057—21no—
16#1985—21no—
17#1984—21no—
18#1940—21no—
19#1921—21no—
20#1921—21no—
21#1917—21no—
22#1916—21no—
23#1839C2211yescharacteristic
24#1831C2211yescharacteristic
25#1771—21no—
26#1767C2211yescharacteristic
27C4×C4⋊C8C2211yescharacteristic
28#1745C2211yescharacteristic
29C2×#332—21no—
30#1296—21no—
31#1295—21no—
32#1295—21no—
33#1271—21no—
34#1271—21no—
35C2×C4⋊Q8D411yescharacteristic
36C2×#125—21no—
37C2×C4×Q8—21no—
38C2×#107—21no—
39C2×#107—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×#97—21no—
46C2×#97—21no—
47C2×#97D411yescharacteristic
48C2×#97D411yescharacteristic
49C2×C4×C8—21no—
50C2×C4×C8—21no—
51#391—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#389C2×C411yescharacteristic
58#389C2×C411yescharacteristic
59#384C2×C411yescharacteristic
60#384C2×C411yescharacteristic
61#384D411yescharacteristic
62#382—21no—
63C4×C4⋊C4—21no—
64C4×C4⋊C4D411yescharacteristic
65C4×C4⋊C4D411yescharacteristic
66C43C2311yescharacteristic
67#340—21no—
68#340—21no—
69#340—21no—
70#340—21no—
71#340—21no—
72#340—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#336—21no—
83#336—21no—
84#336C2×C411yescharacteristic
85#336C2×C411yescharacteristic
86#336D411yescharacteristic
87#336D411yescharacteristic
88#332—24no—
89C22×Q8—21no—
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—22no—
99C4⋊Q8—41no—
100#125—81no—
101#125—81no—
102C4×Q8—81no—
103C4×Q8—81no—
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—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4C22⋊C411yescharacteristic
118C2×C4⋊C4C22⋊C411yescharacteristic
119C2×C4⋊C4C22⋊C411yescharacteristic
120C2×C4⋊C4C22⋊C411yescharacteristic
121C2×C42—21no—
122C2×C42—21no—
123C2×C42C22×C411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42#4111yescharacteristic
129C2×C42#4111yescharacteristic
130#107—42no—
131#107—42no—
132C4⋊C8—22no—
133C4⋊C8—22no—
134C4⋊C8—41no—
135C4⋊C8—41no—
136C4⋊C8—41no—
137C4⋊C8—41no—
138C4⋊C8—81no—
139C4⋊C8—81no—
140#97—21no—
141#97—21no—
142#97—21no—
143#97—41no—
144#97—41no—
145#97—81no—
146#97Q1612yes—
147C4×C8—81no—
148C4×C8—81no—
149#95—21no—
150#95—21no—
151#95—21no—
152#95—21no—
153#95—41no—
154#95—41no—
155C2×Q8—42no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8—81no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4C2×C22⋊C411yescharacteristic
166C22×C4C4×D411yescharacteristic
167C22×C4C4×D411yescharacteristic
168C22×C4#12011yescharacteristic
169C22×C4#12111yescharacteristic
170C22×C4#12111yescharacteristic
171C22×C4#12311yescharacteristic
172C2×C8—22no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—42no—
178C2×C8—42no—
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—41no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—81no—
193C2×C8—81no—
194C2×C8—81no—
195C2×C8—81no—
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—42no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—81no—
207C4⋊C4—81no—
208C4⋊C4—81no—
209C4⋊C4—81no—
210C4⋊C4—81no—
211C4⋊C4—81no—
212C4⋊C4—81no—
213C4⋊C4—82no—
214C4⋊C4—81no—
215C4⋊C4—81no—
216C4⋊C4#10412yes—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—41no—
222C42—41no—
223C42—41no—
224C42—41no—
225C42—41no—
226C42—41no—
227C42—41no—
228C42—41no—
229C42C2×Q1611yescharacteristic
230C42#13511yescharacteristic
231C42#13711yescharacteristic
232C42#13711yescharacteristic
233C23#38611yescharacteristic
234Q8—82no—
235Q8—82no—
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—22no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
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—81no—
270C2×C4C2×#10411yescharacteristic
271C2×C4#42111yescharacteristic
272C2×C4C4×Q1611yescharacteristic
273C2×C4#44111yescharacteristic
274C2×C4#45111yescharacteristic
275C2×C4#45211yescharacteristic
276C2×C4#46211yescharacteristic
277C2×C4#46411yescharacteristic
278C2×C4#47111yescharacteristic
279C2×C4#47211yescharacteristic
280C8—42no—
281C8—81no—
282C8—81no—
283C8—81no—
284C8—81no—
285C8—81no—
286C8—82no—
287C8—82no—
288C22#187111yescharacteristic
289C22#187811yescharacteristic
290C22#188111yescharacteristic
291C22#190411yescharacteristic
292C22#190711yescharacteristic
293C22#191211yescharacteristic
294C22#191511yescharacteristic
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—42no—
308C4—81no—
309C4—81no—
310C4—81no—
311C4—161no—
312C4—161no—
313C2#899011yescharacteristic
314C2#916311yescharacteristic
315C2#919011yescharacteristic
316C2#927011yescharacteristic
317C2#929811yescharacteristic
318C2#933511yescharacteristic
319C2#937211yescharacteristic
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
#300952
#223132
#98942
#82372
#76632
#70412
#70232