Finite Group Databasebeta

← #103570

Subgroups — #103570

Order 512.

522 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 100 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#29756C211yesmaximal, characteristic
2#27950C211yesmaximal, characteristic
3C2×#2084C211yesmaximal, characteristic
4#9650C211yesmaximal, characteristic
5#8724C211yesmaximal, characteristic
6#7668C211yesmaximal, characteristic
7#7029C211yesmaximal, characteristic
8C2×#483—21no—
9C22×#106—21no—
10#2857C2211yescharacteristic
11C2×#389C2211yescharacteristic
12C2×#384C2211yescharacteristic
13#2084—21no—
14#2084—22no—
15#2084—22no—
16#2083—22no—
17#2066—22no—
18#2043—21no—
19#1990—21no—
20#1872—21no—
21#1852—22no—
22#1845—21no—
23#1797C2211yescharacteristic
24#1797C2211yescharacteristic
25C4×C22⋊C8C2211yescharacteristic
26C2×#340—21no—
27C2×#336C2211yescharacteristic
28C2×#324—22no—
29#1296—22no—
30#1271—22no—
31C23×C8—21no—
32C2×C4⋊Q8D411yescharacteristic
33C2×C22⋊Q8—21no—
34C22×C4⋊C4—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4—21no—
37C22×C4⋊C4—21no—
38C22×C4⋊C4D411yescharacteristic
39C22×C4⋊C4D411yescharacteristic
40C22×C42C2311yescharacteristic
41#483—42no—
42#483—42no—
43C2×#107—24no—
44C2×#106—22no—
45C2×#106—24no—
46C2×#106—42no—
47C2×#106—42no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8D412yes—
50C2×#103—22no—
51C2×#103—22no—
52C2×C22⋊C8—21no—
53C2×C22⋊C8—21no—
54C2×C22⋊C8D412yes—
55C2×C4×C8—21no—
56#391—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#389—21no—
61#389—21no—
62#389—21no—
63#384—21no—
64#384—21no—
65#384—21no—
66#384D412yes—
67#384D411yescharacteristic
68#380—21no—
69#380—21no—
70C2×#95—21no—
71#340—22no—
72#340—24no—
73#340—24no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336D412yes—
79#324—44no—
80C22×Q8—21no—
81C23×C4—21no—
82C23×C4—21no—
83C23×C4—41no—
84C23×C4C2×D411yescharacteristic
85C23×C4C2×D411yescharacteristic
86C23×C4#4111yescharacteristic
87C22×C8—24no—
88C22×C8—22no—
89C22×C8—22no—
90C22×C8—22no—
91C22×C8—42no—
92C22×C8—41no—
93C22×C8—41no—
94C22×C8—41no—
95C4⋊Q8—42no—
96C22⋊Q8—41no—
97C22⋊Q8—41no—
98C22⋊Q8—41no—
99C22⋊Q8—41no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—22no—
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—22no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—42no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—42no—
127C2×C4⋊C4—42no—
128C2×C4⋊C4—82no—
129C2×C4⋊C4—82no—
130C2×C4⋊C4D812yes—
131C2×C22⋊C4—41no—
132C2×C42—42no—
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135C2×C42C2×D411yescharacteristic
136C2×C42C2×D411yescharacteristic
137#107—84no—
138#106—48no—
139#106—44no—
140C4⋊C8—42no—
141C4⋊C8—42no—
142#103—44no—
143#103—82no—
144C22⋊C8—22no—
145C22⋊C8—41no—
146C22⋊C8—41no—
147C22⋊C8—42no—
148C22⋊C8SD1614yes—
149C4×C8—42no—
150#95—41no—
151#95—41no—
152#95—41no—
153#95—41no—
154C24#12111yescharacteristic
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—42no—
158C2×Q8—42no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—42no—
169C22×C4—41no—
170C22×C4—42no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—42no—
175C22×C4—42no—
176C22×C4—82no—
177C22×C4—82no—
178C22×C4—81no—
179C22×C4—81no—
180C22×C4—81no—
181C22×C4—81no—
182C22×C4#12011yescharacteristic
183C22×C4#12011yescharacteristic
184C22×C4#12011yescharacteristic
185C22×C4#12111yescharacteristic
186C22×C4#12111yescharacteristic
187C22×C4#12711yescharacteristic
188C22×C4C2×D811yescharacteristic
189C22×C4C2×SD1612yes—
190C22×C4#13511yescharacteristic
191C22×C4AGL(1,ℤ/8)11yescharacteristic
192C22×C4AGL(1,ℤ/8)11yescharacteristic
193C22×C4#13712yes—
194C2×C8—24no—
195C2×C8—24no—
196C2×C8—42no—
197C2×C8—42no—
198C2×C8—42no—
199C2×C8—44no—
200C2×C8—44no—
201C2×C8—42no—
202C2×C8—42no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—81no—
206C2×C8—81no—
207C2×C8—81no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—42no—
211C4⋊C4—44no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—42no—
217C4⋊C4—41no—
218C4⋊C4—42no—
219C4⋊C4—41no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—82no—
223C4⋊C4—81no—
224C4⋊C4—82no—
225C4⋊C4—81no—
226C4⋊C4—81no—
227C4⋊C4—82no—
228C4⋊C4—81no—
229C4⋊C4—81no—
230C4⋊C4—82no—
231C4⋊C4—81no—
232C4⋊C4—81no—
233C22⋊C4—81no—
234C22⋊C4—81no—
235C42—22no—
236C42—22no—
237C42—41no—
238C42—41no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—21no—
243C23#39211yescharacteristic
244C23#46112yes—
245C23#46611yescharacteristic
246C23#46911yescharacteristic
247C23#47312yes—
248Q8—82no—
249Q8—82no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—44no—
268C2×C4—44no—
269C2×C4—42no—
270C2×C4—82no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—82no—
276C2×C4—81no—
277C2×C4—82no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—82no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—162no—
286C2×C4—162no—
287C2×C4—162no—
288C2×C4#44711yescharacteristic
289C2×C4#44711yescharacteristic
290C2×C4#44812yes—
291C2×C4#44911yescharacteristic
292C2×C4#44911yescharacteristic
293C2×C4#45612yes—
294C2×C4#45812yes—
295C2×C4#47112yes—
296C2×C4#49211yescharacteristic
297C2×C4#49711yescharacteristic
298C8—44no—
299C8—44no—
300C8—82no—
301C8—161no—
302C22—22no—
303C22—22no—
304C22—22no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—22no—
310C22#167312yes—
311C22#169312yes—
312C22#199911yescharacteristic
313C22#200511yescharacteristic
314C22#200811yescharacteristic
315C22#201311yescharacteristic
316C22#201911yescharacteristic
317C22#202011yescharacteristic
318C22#202211yescharacteristic
319C4—22no—
320C4—21no—
321C4—21no—
322C4—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—82no—
327C4—161no—
328C4—161no—
329C4—162no—
330C4—161no—
331C4#160912yes—
332C4#161012yes—
333C2—22no—
334C2—22no—
335C2#991911yescharacteristic
336C2#995111yescharacteristic
337C2#999511yescharacteristic
338C2#1013911yescharacteristic
339C2#1016711yescharacteristic
340C2#1017711yescharacteristic
341C2#1026411yescharacteristic
subgroupG/H
center, socleC23#392
commutator, Frattini, cosocleC22×C42C23
prime radicalC24#121
LCSG ▷ C22×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#297562
#279502
C2×#20842
#96502
#87242
#76682
#70292