Finite Group Databasebeta

← #100617

Subgroups — #100617

Order 512.

392 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 106 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#29869C211yesmaximal, characteristic
2#22723C211yesmaximal, characteristic
3#9905C211yesmaximal, characteristic
4#9898C211yesmaximal, characteristic
5#7577C211yesmaximal, characteristic
6#7040C211yesmaximal, characteristic
7#7022C211yesmaximal, characteristic
8C2×#477—21no—
9C2×#446—21no—
10#2868C2211yescharacteristic
11#2295C2211yescharacteristic
12#2083—21no—
13#2083C412yes—
14#2072—21no—
15#2072C412yes—
16#1987—21no—
17#1940—21no—
18#1940—21no—
19#1939—21no—
20#1843—21no—
21#1842C2211yescharacteristic
22#1831C2211yescharacteristic
23#1831C2211yescharacteristic
24#1768—21no—
25#1767C2211yescharacteristic
26C4×C4⋊C8C2211yescharacteristic
27#1296—21no—
28#1296—21no—
29#1296—21no—
30#1296—21no—
31#1272—21no—
32#1271—21no—
33C2×C4⋊Q8—21no—
34C2×C4⋊Q8—21no—
35C2×C4⋊Q8—21no—
36C2×C4×Q8D411yescharacteristic
37#477—42no—
38#477—42no—
39#446—42no—
40#446—42no—
41C2×#107—22no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8—21no—
50C2×C4⋊C8—21no—
51C2×C4⋊C8D411yescharacteristic
52C2×C4⋊C8D411yescharacteristic
53C2×C4⋊C8D411yescharacteristic
54C2×C4⋊C8D411yescharacteristic
55C2×#103—22no—
56C2×#97—21no—
57C2×#97—21no—
58C2×C4×C8—21no—
59C2×C4×C8—21no—
60#391C2×C411yescharacteristic
61#391D411yescharacteristic
62#389C2×C411yescharacteristic
63#389D411yescharacteristic
64#387—21no—
65#387—21no—
66#384—21no—
67#384—21no—
68#384—21no—
69#384C2×C412yes—
70C4×C4⋊C4—21no—
71C4×C4⋊C4D411yescharacteristic
72#376—21no—
73C43C2311yescharacteristic
74#340—22no—
75#340—22no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336C2×C412yes—
84C22×Q8—41no—
85C22×Q8C22⋊C411yescharacteristic
86C22×C8—21no—
87C22×C8—22no—
88C22×C8—21no—
89C22×C8—21no—
90C22×C8—21no—
91C22×C8—41no—
92C22×C8—41no—
93C4⋊Q8—41no—
94C4⋊Q8—41no—
95C4⋊Q8—41no—
96C4⋊Q8—41no—
97C4⋊Q8—81no—
98C4⋊Q8—81no—
99C4⋊Q8—82no—
100C4×Q8—21no—
101C4×Q8—21no—
102C4×Q8D812yes—
103C4×Q8SD1612yes—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4C22⋊C411yescharacteristic
114C2×C4⋊C4C22⋊C411yescharacteristic
115C2×C4⋊C4C22⋊C411yescharacteristic
116C2×C42—21no—
117C2×C42—21no—
118C2×C42C22×C411yescharacteristic
119C2×C42C2×D411yescharacteristic
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42C2×D411yescharacteristic
123C2×C42#4111yescharacteristic
124C2×C42#4111yescharacteristic
125#107—44no—
126C4⋊C8—22no—
127C4⋊C8—21no—
128C4⋊C8—21no—
129C4⋊C8—21no—
130C4⋊C8—41no—
131C4⋊C8—41no—
132C4⋊C8—41no—
133C4⋊C8—42no—
134C4⋊C8—42no—
135C4⋊C8—41no—
136C4⋊C8—41no—
137C4⋊C8—41no—
138C4⋊C8—41no—
139C4⋊C8—41no—
140C4⋊C8—41no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143C4⋊C8—81no—
144C4⋊C8—81no—
145C4⋊C8Q1612yes—
146#103—44no—
147#97—42no—
148#97—41no—
149#97—41no—
150C4×C8—42no—
151C4×C8—81no—
152#95—21no—
153#95—21no—
154#95—21no—
155#95—21no—
156#95—21no—
157#95—21no—
158#95—21no—
159C2×Q8—21no—
160C2×Q8—41no—
161C2×Q8—41no—
162C2×Q8—82no—
163C2×Q8—82no—
164C2×Q8—81no—
165C2×Q8—81no—
166C2×Q8#10212yes—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—42no—
172C22×C4C2×C22⋊C411yescharacteristic
173C22×C4C4×D411yescharacteristic
174C22×C4C4×D411yescharacteristic
175C22×C4#12011yescharacteristic
176C22×C4#12111yescharacteristic
177C22×C4#12111yescharacteristic
178C22×C4#12311yescharacteristic
179C2×C8—22no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—42no—
183C2×C8—42no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—81no—
196C2×C8—81no—
197C2×C8—81no—
198C2×C8—81no—
199C2×C8—81no—
200C4⋊C4—21no—
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—81no—
210C4⋊C4—82no—
211C4⋊C4—82no—
212C4⋊C4—82no—
213C4⋊C4—81no—
214C4⋊C4—81no—
215C4⋊C4—81no—
216C4⋊C4—81no—
217C4⋊C4#10212yes—
218C42—22no—
219C42—22no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—41no—
225C42—41no—
226C42—41no—
227C42—41no—
228C42—41no—
229C42C2×D811yescharacteristic
230C42C2×SD1611yescharacteristic
231C42C2×Q1611yescharacteristic
232C42#13511yescharacteristic
233C42AGL(1,ℤ/8)11yescharacteristic
234C42#13711yescharacteristic
235C42#13711yescharacteristic
236C42#13711yescharacteristic
237C23#38611yescharacteristic
238Q8—42no—
239Q8—81no—
240Q8—162no—
241Q8—162no—
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—21no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—82no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4C2×#10211yescharacteristic
271C2×C4#41711yescharacteristic
272C2×C4C4×Q1611yescharacteristic
273C2×C4#44111yescharacteristic
274C2×C4#44711yescharacteristic
275C2×C4#44811yescharacteristic
276C2×C4#45111yescharacteristic
277C2×C4#45211yescharacteristic
278C2×C4#45511yescharacteristic
279C2×C4#45611yescharacteristic
280C2×C4#46211yescharacteristic
281C2×C4#46411yescharacteristic
282C2×C4#47111yescharacteristic
283C2×C4#47211yescharacteristic
284C2×C4#48011yescharacteristic
285C2×C4#48111yescharacteristic
286C8—42no—
287C8—82no—
288C8—82no—
289C8—81no—
290C8—81no—
291C8—81no—
292C8—161no—
293C22#187411yescharacteristic
294C22#187811yescharacteristic
295C22#188211yescharacteristic
296C22#190311yescharacteristic
297C22#190711yescharacteristic
298C22#190911yescharacteristic
299C22#191511yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—41no—
311C4—42no—
312C4—42no—
313C4—81no—
314C4—81no—
315C4—162no—
316C4#164111yescharacteristic
317C4#164511yescharacteristic
318C4#164911yescharacteristic
319C4#165311yescharacteristic
320C2#898711yescharacteristic
321C2#917311yescharacteristic
322C2#919511yescharacteristic
323C2#927011yescharacteristic
324C2#928811yescharacteristic
325C2#933811yescharacteristic
326C2#937511yescharacteristic
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
#298692
#227232
#99052
#98982
#75772
#70402
#70222