Finite Group Databasebeta

← #103647

Subgroups — #103647

Order 512.

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

normal subgroups only

This group has 500 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#29967C211yesmaximal, characteristic
2#27910C211yesmaximal, characteristic
3C2×#2099C211yesmaximal, characteristic
4#9879C211yesmaximal, characteristic
5#8724C211yesmaximal, characteristic
6#7665C211yesmaximal, characteristic
7#7029C211yesmaximal, characteristic
8C2×#484—22no—
9#2857C2211yescharacteristic
10C2×#389C2211yescharacteristic
11C2×#384C2211yescharacteristic
12#2099—21no—
13#2099—22no—
14#2099—22no—
15#2095—22no—
16#2088—22no—
17#2058—21no—
18#1956—21no—
19#1853—21no—
20#1845—21no—
21#1824—21no—
22#1797C2211yescharacteristic
23#1797C2211yescharacteristic
24C4×C22⋊C8C2211yescharacteristic
25C2×#340—21no—
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
41#484—44no—
42#484—44no—
43C2×#107—24no—
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#384D411yescharacteristic
63#384D412yes—
64#380—21no—
65#380—21no—
66C2×#95—21no—
67#340—22no—
68#340—22no—
69#340—22no—
70#340—24no—
71#340—24no—
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—22no—
85C22×C8—22no—
86C22×C8—22no—
87C22×C8—42no—
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—44no—
112C2×C4⋊C4—42no—
113C2×C4⋊C4—42no—
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—82no—
121C2×C4⋊C4—82no—
122C2×C4⋊C4Q1612yes—
123C2×C22⋊C4—41no—
124C2×C42—42no—
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129#107—48no—
130#106—82no—
131C4⋊C8—42no—
132C4⋊C8—42no—
133#103—48no—
134C22⋊C8—22no—
135C22⋊C8—41no—
136C22⋊C8—41no—
137C22⋊C8—42no—
138C22⋊C8SD1614yes—
139C4×C8—42no—
140#95—41no—
141#95—41no—
142#95—41no—
143#95—41no—
144C24#12111yescharacteristic
145C2×Q8—42no—
146C2×Q8—42no—
147C2×Q8—42no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—42no—
162C22×C4—42no—
163C22×C4—81no—
164C22×C4—81no—
165C22×C4—82no—
166C22×C4—82no—
167C22×C4—82no—
168C22×C4—81no—
169C22×C4—81no—
170C22×C4#12011yescharacteristic
171C22×C4#12011yescharacteristic
172C22×C4#12011yescharacteristic
173C22×C4#12111yescharacteristic
174C22×C4#12111yescharacteristic
175C22×C4#12711yescharacteristic
176C22×C4C2×SD1612yes—
177C22×C4C2×Q1611yescharacteristic
178C22×C4#13511yescharacteristic
179C22×C4AGL(1,ℤ/8)12yes—
180C22×C4#13711yescharacteristic
181C22×C4#13711yescharacteristic
182C2×C8—24no—
183C2×C8—42no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—42no—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—82no—
192C2×C8—82no—
193C2×C8—81no—
194C2×C8—81no—
195C2×C8—81no—
196C4⋊C4—22no—
197C4⋊C4—22no—
198C4⋊C4—44no—
199C4⋊C4—42no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—44no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—82no—
209C4⋊C4—81no—
210C4⋊C4—82no—
211C4⋊C4—82no—
212C4⋊C4—82no—
213C4⋊C4—82no—
214C4⋊C4—81no—
215C4⋊C4—81no—
216C4⋊C4—81no—
217C4⋊C4—81no—
218C22⋊C4—82no—
219C42—22no—
220C42—22no—
221C42—41no—
222C42—41no—
223C23—21no—
224C23—21no—
225C23—21no—
226C23—21no—
227C23#39211yescharacteristic
228C23#46012yes—
229C23#46711yescharacteristic
230C23#47011yescharacteristic
231C23#47312yes—
232Q8—84no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—44no—
251C2×C4—42no—
252C2×C4—82no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—82no—
256C2×C4—82no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—82no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—82no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—164no—
269C2×C4—162no—
270C2×C4#45012yes—
271C2×C4#45111yescharacteristic
272C2×C4#45111yescharacteristic
273C2×C4#45211yescharacteristic
274C2×C4#45211yescharacteristic
275C2×C4#45412yes—
276C2×C4#45812yes—
277C2×C4#47212yes—
278C2×C4#49211yescharacteristic
279C2×C4#49611yescharacteristic
280C8—44no—
281C8—82no—
282C8—82no—
283C8—161no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—22no—
292C22#167012yes—
293C22#169012yes—
294C22#200111yescharacteristic
295C22#200311yescharacteristic
296C22#200911yescharacteristic
297C22#201411yescharacteristic
298C22#201811yescharacteristic
299C22#202011yescharacteristic
300C22#202211yescharacteristic
301C4—22no—
302C4—21no—
303C4—21no—
304C4—22no—
305C4—21no—
306C4—21no—
307C4—41no—
308C4—82no—
309C4—161no—
310C4—161no—
311C4—162no—
312C4—161no—
313C4#161512yes—
314C4#161712yes—
315C2—22no—
316C2—22no—
317C2#992911yescharacteristic
318C2#996011yescharacteristic
319C2#999411yescharacteristic
320C2#1013511yescharacteristic
321C2#1014811yescharacteristic
322C2#1019011yescharacteristic
323C2#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
#299672
#279102
C2×#20992
#98792
#87242
#76652
#70292