Finite Group Databasebeta

← #103643

Subgroups — #103643

Order 512.

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

normal subgroups only

This group has 568 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#29951C211yesmaximal, characteristic
2#27910C211yesmaximal, characteristic
3C2×#2096C211yesmaximal, characteristic
4#9878C211yesmaximal, characteristic
5#8724C211yesmaximal, characteristic
6#7665C211yesmaximal, characteristic
7#7029C211yesmaximal, characteristic
8C2×#484—22no—
9C22×#106—21no—
10C22×#103—21no—
11#2857C2211yescharacteristic
12C2×#391C2211yescharacteristic
13C2×#384C2211yescharacteristic
14#2096—22no—
15#2096—21no—
16#2096—22no—
17#2095—22no—
18#2066—22no—
19#2024—21no—
20#1956—21no—
21#1853—21no—
22#1845—21no—
23#1797C2211yescharacteristic
24#1797C2211yescharacteristic
25#1787—21no—
26C4×C22⋊C8C2211yescharacteristic
27C2×#336C2211yescharacteristic
28#1296—22no—
29#1280—22no—
30#1271—22no—
31C23×Q8D411yescharacteristic
32C23×C8—21no—
33C2×C4⋊Q8D411yescharacteristic
34C2×C22⋊Q8—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4—21no—
37C22×C4⋊C4—21no—
38C22×C4⋊C4D411yescharacteristic
39C22×C42C2311yescharacteristic
40#484—44no—
41#484—44no—
42C2×#107—24no—
43C2×#106—24no—
44C2×#106—22no—
45C2×#106—44no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8D412yes—
48C2×#103—24no—
49C2×#103—24no—
50C2×#103—22no—
51C2×#103—22no—
52C2×#103—44no—
53C2×C22⋊C8—21no—
54C2×C22⋊C8—21no—
55C2×C22⋊C8D412yes—
56C2×C4×C8—21no—
57#391—21no—
58#391—21no—
59#391—21no—
60#391—21no—
61#391—21no—
62#389—21no—
63#389—21no—
64#384—21no—
65#384—21no—
66#384—21no—
67#384D411yescharacteristic
68#384D412yes—
69#380—21no—
70#380—21no—
71C2×#95—21no—
72C2×#95—21no—
73#340—22no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336D412yes—
79C22×Q8—21no—
80C22×Q8—21no—
81C22×Q8—21no—
82C22×Q8—21no—
83C22×Q8—21no—
84C22×Q8—21no—
85C22×Q8—42no—
86C22×Q8—42no—
87C22×Q8Q1612yes—
88C23×C4—21no—
89C23×C4—21no—
90C23×C4—41no—
91C23×C4C2×D411yescharacteristic
92C23×C4C2×D411yescharacteristic
93C23×C4#4111yescharacteristic
94C22×C8—24no—
95C22×C8—22no—
96C22×C8—22no—
97C22×C8—22no—
98C22×C8—42no—
99C22×C8—41no—
100C22×C8—41no—
101C22×C8—41no—
102C4⋊Q8—42no—
103C22⋊Q8—42no—
104C22⋊Q8—42no—
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—42no—
117C2×C4⋊C4—42no—
118C2×C4⋊C4—42no—
119C2×C4⋊C4—42no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—82no—
125C2×C22⋊C4—41no—
126C2×C42—42no—
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42C2×D411yescharacteristic
130C2×C42C2×D411yescharacteristic
131#107—48no—
132#106—48no—
133#106—82no—
134C4⋊C8—42no—
135C4⋊C8—42no—
136#103—48no—
137#103—48no—
138#103—82no—
139#103—82no—
140C22⋊C8—22no—
141C22⋊C8—41no—
142C22⋊C8—41no—
143C22⋊C8—42no—
144C22⋊C8SD1614yes—
145C4×C8—42no—
146#95—41no—
147#95—41no—
148#95—41no—
149#95—41no—
150#95—41no—
151#95—41no—
152C24#12111yescharacteristic
153C2×Q8—22no—
154C2×Q8—22no—
155C2×Q8—44no—
156C2×Q8—42no—
157C2×Q8—42no—
158C2×Q8—44no—
159C2×Q8—42no—
160C2×Q8—42no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8—42no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8—82no—
167C2×Q8—82no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—42no—
182C22×C4—42no—
183C22×C4—81no—
184C22×C4—81no—
185C22×C4—82no—
186C22×C4—82no—
187C22×C4—82no—
188C22×C4—81no—
189C22×C4—81no—
190C22×C4#12011yescharacteristic
191C22×C4#12011yescharacteristic
192C22×C4#12011yescharacteristic
193C22×C4#12111yescharacteristic
194C22×C4#12111yescharacteristic
195C22×C4#12711yescharacteristic
196C22×C4C2×SD1612yes—
197C22×C4C2×Q1611yescharacteristic
198C22×C4#13511yescharacteristic
199C22×C4AGL(1,ℤ/8)12yes—
200C22×C4#13711yescharacteristic
201C22×C4#13711yescharacteristic
202C2×C8—24no—
203C2×C8—24no—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—44no—
208C2×C8—44no—
209C2×C8—42no—
210C2×C8—42no—
211C2×C8—42no—
212C2×C8—42no—
213C2×C8—81no—
214C2×C8—81no—
215C2×C8—81no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—44no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—82no—
226C4⋊C4—81no—
227C4⋊C4—82no—
228C4⋊C4—82no—
229C4⋊C4—81no—
230C4⋊C4—81no—
231C4⋊C4—81no—
232C4⋊C4—81no—
233C22⋊C4—82no—
234C42—22no—
235C42—22no—
236C42—41no—
237C42—41no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23#39211yescharacteristic
243C23#46012yes—
244C23#46711yescharacteristic
245C23#47011yescharacteristic
246C23#47312yes—
247Q8—44no—
248Q8—44no—
249Q8—82no—
250Q8—84no—
251Q8—82no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—44no—
270C2×C4—42no—
271C2×C4—82no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—82no—
275C2×C4—81no—
276C2×C4—82no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—82no—
283C2×C4—81no—
284C2×C4—82no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—164no—
288C2×C4—162no—
289C2×C4#45012yes—
290C2×C4#45111yescharacteristic
291C2×C4#45111yescharacteristic
292C2×C4#45211yescharacteristic
293C2×C4#45211yescharacteristic
294C2×C4#45312yes—
295C2×C4#45812yes—
296C2×C4#47112yes—
297C2×C4#49211yescharacteristic
298C2×C4#49611yescharacteristic
299C8—44no—
300C8—44no—
301C8—82no—
302C8—161no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—22no—
311C22#167012yes—
312C22#169012yes—
313C22#200111yescharacteristic
314C22#200211yescharacteristic
315C22#200911yescharacteristic
316C22#201411yescharacteristic
317C22#201911yescharacteristic
318C22#202011yescharacteristic
319C22#202211yescharacteristic
320C4—22no—
321C4—21no—
322C4—21no—
323C4—22no—
324C4—21no—
325C4—21no—
326C4—41no—
327C4—82no—
328C4—161no—
329C4—161no—
330C4—162no—
331C4—161no—
332C4#161412yes—
333C4#161812yes—
334C2—22no—
335C2—22no—
336C2#992811yescharacteristic
337C2#996011yescharacteristic
338C2#999511yescharacteristic
339C2#1013311yescharacteristic
340C2#1014611yescharacteristic
341C2#1019111yescharacteristic
342C2#1027611yescharacteristic
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
#299512
#279102
C2×#20962
#98782
#87242
#76652
#70292