Finite Group Databasebeta

← #103567

Subgroups — #103567

Order 512.

494 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 96 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#29967C211yesmaximal, characteristic
2#27972C211yesmaximal, characteristic
3C2×#2083C211yesmaximal, characteristic
4#9879C211yesmaximal, characteristic
5#8724C211yesmaximal, characteristic
6#7665C211yesmaximal, characteristic
7#7029C211yesmaximal, characteristic
8C22×#107—21no—
9#2857C2211yescharacteristic
10C2×#389C2211yescharacteristic
11C2×#384C2211yescharacteristic
12#2099—21no—
13#2088—22no—
14#2083—22no—
15#2083—22no—
16#2072—22no—
17#2058—21no—
18#1956—21no—
19#1872—22no—
20#1853—21no—
21#1834—21no—
22#1824—21no—
23#1797C2211yescharacteristic
24#1797C2211yescharacteristic
25C4×C22⋊C8C2211yescharacteristic
26C2×#340—21no—
27C2×#336C2211yescharacteristic
28#1296—22no—
29#1280—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
41C2×#107—24no—
42C2×#107—42no—
43C2×#107—42no—
44C2×#106—22no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8D412yes—
47C2×#103—24no—
48C2×C22⋊C8—21no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8D412yes—
51C2×C4×C8—21no—
52#391—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#389—21no—
58#389—21no—
59#384—21no—
60#384—21no—
61#384—21no—
62#384D412yes—
63#384D411yescharacteristic
64#380—21no—
65#380—21no—
66C2×#95—21no—
67#340—22no—
68#340—24no—
69#340—22no—
70#340—24no—
71#340—22no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336D412yes—
77C22×Q8—21no—
78C23×C4—21no—
79C23×C4—21no—
80C23×C4—41no—
81C23×C4C2×D411yescharacteristic
82C23×C4C2×D411yescharacteristic
83C23×C4#4111yescharacteristic
84C22×C8—24no—
85C22×C8—22no—
86C22×C8—22no—
87C22×C8—22no—
88C22×C8—42no—
89C22×C8—41no—
90C22×C8—41no—
91C22×C8—41no—
92C4⋊Q8—42no—
93C22⋊Q8—42no—
94C22⋊Q8—42no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—42no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—82no—
122C2×C4⋊C4—82no—
123C2×C4⋊C4—82no—
124C2×C4⋊C4SD1612yes—
125C2×C22⋊C4—41no—
126C2×C42—42no—
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42C2×D411yescharacteristic
130C2×C42C2×D411yescharacteristic
131#107—48no—
132#106—82no—
133C4⋊C8—42no—
134C4⋊C8—42no—
135#103—84no—
136C22⋊C8—22no—
137C22⋊C8—22no—
138C22⋊C8—41no—
139C22⋊C8—41no—
140C22⋊C8—42no—
141C4×C8—42no—
142#95—41no—
143#95—41no—
144#95—41no—
145#95—41no—
146C24#12111yescharacteristic
147C2×Q8—42no—
148C2×Q8—42no—
149C2×Q8—42no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—42no—
164C22×C4—42no—
165C22×C4—81no—
166C22×C4—81no—
167C22×C4—82no—
168C22×C4—82no—
169C22×C4—81no—
170C22×C4—81no—
171C22×C4—81no—
172C22×C4—81no—
173C22×C4#12011yescharacteristic
174C22×C4#12011yescharacteristic
175C22×C4#12011yescharacteristic
176C22×C4#12111yescharacteristic
177C22×C4#12111yescharacteristic
178C22×C4#12711yescharacteristic
179C22×C4C2×SD1611yescharacteristic
180C22×C4#13511yescharacteristic
181C22×C4#13512yes—
182C22×C4AGL(1,ℤ/8)11yescharacteristic
183C22×C4#13711yescharacteristic
184C22×C4#13712yes—
185C2×C8—24no—
186C2×C8—42no—
187C2×C8—44no—
188C2×C8—44no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—42no—
192C2×C8—42no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—42no—
196C2×C8—81no—
197C2×C8—81no—
198C2×C8—81no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—44no—
202C4⋊C4—42no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—42no—
212C4⋊C4—82no—
213C4⋊C4—81no—
214C4⋊C4—82no—
215C4⋊C4—82no—
216C4⋊C4—81no—
217C4⋊C4—81no—
218C4⋊C4—82no—
219C4⋊C4—82no—
220C4⋊C4—81no—
221C4⋊C4—81no—
222C22⋊C4—82no—
223C42—22no—
224C42—22no—
225C42—41no—
226C42—41no—
227C23—21no—
228C23—21no—
229C23—21no—
230C23—21no—
231C23#39211yescharacteristic
232C23#46412yes—
233C23#46511yescharacteristic
234C23#46811yescharacteristic
235C23#47312yes—
236Q8—84no—
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—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—44no—
255C2×C4—42no—
256C2×C4—82no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4—81no—
262C2×C4—82no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—82no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—162no—
273C2×C4—162no—
274C2×C4—162no—
275C2×C4#44811yescharacteristic
276C2×C4#44911yescharacteristic
277C2×C4#45011yescharacteristic
278C2×C4#45211yescharacteristic
279C2×C4#45212yes—
280C2×C4#45612yes—
281C2×C4#45812yes—
282C2×C4#47212yes—
283C2×C4#49511yescharacteristic
284C2×C4#49711yescharacteristic
285C8—44no—
286C8—82no—
287C8—82no—
288C8—161no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22#168012yes—
298C22#170012yes—
299C22#200011yescharacteristic
300C22#200511yescharacteristic
301C22#200811yescharacteristic
302C22#201511yescharacteristic
303C22#201811yescharacteristic
304C22#202011yescharacteristic
305C22#202211yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—22no—
310C4—21no—
311C4—21no—
312C4—41no—
313C4—82no—
314C4—161no—
315C4—161no—
316C4—162no—
317C4—161no—
318C4#160912yes—
319C4#161112yes—
320C2—22no—
321C2—22no—
322C2#992711yescharacteristic
323C2#995811yescharacteristic
324C2#999411yescharacteristic
325C2#1013911yescharacteristic
326C2#1016411yescharacteristic
327C2#1017811yescharacteristic
328C2#1027211yescharacteristic
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
#299672
#279722
C2×#20832
#98792
#87242
#76652
#70292