Finite Group Databasebeta

← #103571

Subgroups — #103571

Order 512.

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

normal subgroups only

This group has 504 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#29966C211yesmaximal, characteristic
2#27972C211yesmaximal, characteristic
3C2×#2084C211yesmaximal, characteristic
4#9650C211yesmaximal, characteristic
5#8724C211yesmaximal, characteristic
6#7665C211yesmaximal, characteristic
7#7029C211yesmaximal, characteristic
8C22×#106—21no—
9#2857C2211yescharacteristic
10C2×#389C2211yescharacteristic
11C2×#384C2211yescharacteristic
12#2099—21no—
13#2086—22no—
14#2084—22no—
15#2084—22no—
16#2072—22no—
17#2057—21no—
18#1956—21no—
19#1872—22no—
20#1852—21no—
21#1834—21no—
22#1823—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
41C2×#107—22no—
42C2×#106—24no—
43C2×#106—42no—
44C2×#106—42no—
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—
77#324—44no—
78C22×Q8—21no—
79C23×C4—21no—
80C23×C4—21no—
81C23×C4—41no—
82C23×C4C2×D411yescharacteristic
83C23×C4C2×D411yescharacteristic
84C23×C4#4111yescharacteristic
85C22×C8—24no—
86C22×C8—22no—
87C22×C8—22no—
88C22×C8—22no—
89C22×C8—42no—
90C22×C8—41no—
91C22×C8—41no—
92C22×C8—41no—
93C4⋊Q8—42no—
94C22⋊Q8—42no—
95C22⋊Q8—42no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—42no—
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—41no—
122C2×C4⋊C4—42no—
123C2×C4⋊C4—42no—
124C2×C4⋊C4—82no—
125C2×C4⋊C4—82no—
126C2×C4⋊C4SD1612yes—
127C2×C22⋊C4—41no—
128C2×C42—42no—
129C2×C42C2×D411yescharacteristic
130C2×C42C2×D411yescharacteristic
131C2×C42C2×D411yescharacteristic
132C2×C42C2×D411yescharacteristic
133#107—82no—
134#106—48no—
135C4⋊C8—42no—
136C4⋊C8—42no—
137#103—84no—
138C22⋊C8—22no—
139C22⋊C8—22no—
140C22⋊C8—41no—
141C22⋊C8—41no—
142C22⋊C8—42no—
143C4×C8—42no—
144#95—41no—
145#95—41no—
146#95—41no—
147#95—41no—
148C24#12111yescharacteristic
149C2×Q8—42no—
150C2×Q8—42no—
151C2×Q8—42no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—42no—
162C22×C4—41no—
163C22×C4—42no—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—42no—
168C22×C4—42no—
169C22×C4—82no—
170C22×C4—82no—
171C22×C4—81no—
172C22×C4—81no—
173C22×C4—81no—
174C22×C4—81no—
175C22×C4#12011yescharacteristic
176C22×C4#12011yescharacteristic
177C22×C4#12011yescharacteristic
178C22×C4#12111yescharacteristic
179C22×C4#12111yescharacteristic
180C22×C4#12711yescharacteristic
181C22×C4C2×SD1611yescharacteristic
182C22×C4#13511yescharacteristic
183C22×C4#13512yes—
184C22×C4AGL(1,ℤ/8)11yescharacteristic
185C22×C4AGL(1,ℤ/8)12yes—
186C22×C4#13711yescharacteristic
187C2×C8—24no—
188C2×C8—42no—
189C2×C8—44no—
190C2×C8—44no—
191C2×C8—42no—
192C2×C8—42no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—42no—
196C2×C8—42no—
197C2×C8—42no—
198C2×C8—81no—
199C2×C8—81no—
200C2×C8—81no—
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—44no—
204C4⋊C4—42no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—42no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—82no—
215C4⋊C4—81no—
216C4⋊C4—82no—
217C4⋊C4—81no—
218C4⋊C4—82no—
219C4⋊C4—81no—
220C4⋊C4—82no—
221C4⋊C4—81no—
222C4⋊C4—81no—
223C4⋊C4—81no—
224C4⋊C4—81no—
225C22⋊C4—82no—
226C42—22no—
227C42—22no—
228C42—41no—
229C42—41no—
230C23—21no—
231C23—21no—
232C23—21no—
233C23—21no—
234C23#39211yescharacteristic
235C23#46312yes—
236C23#46511yescharacteristic
237C23#46811yescharacteristic
238C23#47312yes—
239Q8—84no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—42no—
260C2×C4—82no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—82no—
264C2×C4—81no—
265C2×C4—82no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—82no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—162no—
276C2×C4—162no—
277C2×C4—162no—
278C2×C4#44811yescharacteristic
279C2×C4#44912yes—
280C2×C4#44911yescharacteristic
281C2×C4#45011yescharacteristic
282C2×C4#45211yescharacteristic
283C2×C4#45612yes—
284C2×C4#45812yes—
285C2×C4#47112yes—
286C2×C4#49511yescharacteristic
287C2×C4#49611yescharacteristic
288C8—44no—
289C8—82no—
290C8—82no—
291C8—161no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—22no—
300C22#167912yes—
301C22#169912yes—
302C22#200011yescharacteristic
303C22#200511yescharacteristic
304C22#200811yescharacteristic
305C22#201211yescharacteristic
306C22#201911yescharacteristic
307C22#202011yescharacteristic
308C22#202211yescharacteristic
309C4—22no—
310C4—21no—
311C4—21no—
312C4—22no—
313C4—21no—
314C4—21no—
315C4—41no—
316C4—82no—
317C4—161no—
318C4—162no—
319C4—161no—
320C4—161no—
321C4#160912yes—
322C4#161112yes—
323C2—22no—
324C2—22no—
325C2#992711yescharacteristic
326C2#995011yescharacteristic
327C2#999511yescharacteristic
328C2#1013911yescharacteristic
329C2#1016611yescharacteristic
330C2#1017911yescharacteristic
331C2#1027011yescharacteristic
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
#299662
#279722
C2×#20842
#96502
#87242
#76652
#70292