Finite Group Databasebeta

← #103652

Subgroups — #103652

Order 512.

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

normal subgroups only

This group has 474 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#29968C211yesmaximal, characteristic
2#27961C211yesmaximal, characteristic
3C2×#2099C211yesmaximal, characteristic
4#9650C211yesmaximal, characteristic
5#8724C211yesmaximal, characteristic
6#7667C211yesmaximal, characteristic
7#7029C211yesmaximal, characteristic
8#2857C2211yescharacteristic
9C2×#389C2211yescharacteristic
10C2×#384C2211yescharacteristic
11#2100—21no—
12#2100—22no—
13#2099—22no—
14#2099—22no—
15#2088—22no—
16#2058—21no—
17#1990—21no—
18#1853—21no—
19#1834—21no—
20#1824—22no—
21#1823—21no—
22#1797C2211yescharacteristic
23#1797C2211yescharacteristic
24C4×C22⋊C8C2211yescharacteristic
25C2×#340—21no—
26C2×#340—21no—
27C2×#336C2211yescharacteristic
28C2×#324—22no—
29#1296—22no—
30#1272—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×#106—22no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8D412yes—
44C2×C22⋊C8—21no—
45C2×C22⋊C8—21no—
46C2×C22⋊C8D412yes—
47C2×C4×C8—21no—
48#391—21no—
49#389—21no—
50#389—21no—
51#389—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#384—21no—
56#384—21no—
57#384—21no—
58#384D411yescharacteristic
59#384D412yes—
60#380—21no—
61#380—21no—
62C2×#95—21no—
63#340—22no—
64#340—22no—
65#340—24no—
66#340—24no—
67#340—22no—
68#340—24no—
69#340—24no—
70#336—21no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336D412yes—
75#324—44no—
76C22×Q8—21no—
77C23×C4—21no—
78C23×C4—21no—
79C23×C4—41no—
80C23×C4C2×D411yescharacteristic
81C23×C4C2×D411yescharacteristic
82C23×C4#4111yescharacteristic
83C22×C8—22no—
84C22×C8—22no—
85C22×C8—22no—
86C22×C8—42no—
87C22×C8—42no—
88C22×C8—41no—
89C22×C8—41no—
90C22×C8—41no—
91C4⋊Q8—42no—
92C22⋊Q8—82no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—22no—
99C2×C4⋊C4—22no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—42no—
109C2×C4⋊C4—44no—
110C2×C4⋊C4—42no—
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—42no—
119C2×C4⋊C4—42no—
120C2×C4⋊C4—82no—
121C2×C4⋊C4Q1612yes—
122C2×C22⋊C4—41no—
123C2×C42—42no—
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128#106—82no—
129C4⋊C8—42no—
130C4⋊C8—42no—
131C22⋊C8—22no—
132C22⋊C8—22no—
133C22⋊C8—41no—
134C22⋊C8—41no—
135C22⋊C8—42no—
136C4×C8—42no—
137#95—41no—
138#95—41no—
139#95—41no—
140#95—41no—
141C24#12111yescharacteristic
142C2×Q8—42no—
143C2×Q8—81no—
144C2×Q8—81no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—41no—
151C22×C4—41no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—42no—
155C22×C4—41no—
156C22×C4—42no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—42no—
161C22×C4—42no—
162C22×C4—82no—
163C22×C4—82no—
164C22×C4—82no—
165C22×C4—81no—
166C22×C4—81no—
167C22×C4#12011yescharacteristic
168C22×C4#12011yescharacteristic
169C22×C4#12011yescharacteristic
170C22×C4#12111yescharacteristic
171C22×C4#12111yescharacteristic
172C22×C4#12711yescharacteristic
173C22×C4C2×Q1611yescharacteristic
174C22×C4#13511yescharacteristic
175C22×C4#13512yes—
176C22×C4AGL(1,ℤ/8)12yes—
177C22×C4#13711yescharacteristic
178C22×C4#13711yescharacteristic
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—42no—
183C2×C8—42no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—42no—
188C2×C8—82no—
189C2×C8—82no—
190C2×C8—81no—
191C2×C8—81no—
192C2×C8—81no—
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—42no—
196C4⋊C4—44no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—44no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—82no—
206C4⋊C4—81no—
207C4⋊C4—82no—
208C4⋊C4—82no—
209C4⋊C4—82no—
210C4⋊C4—82no—
211C4⋊C4—81no—
212C4⋊C4—81no—
213C4⋊C4—81no—
214C4⋊C4—81no—
215C22⋊C4—82no—
216C42—22no—
217C42—22no—
218C42—41no—
219C42—41no—
220C23—21no—
221C23—21no—
222C23—21no—
223C23—21no—
224C23#39211yescharacteristic
225C23#46312yes—
226C23#46711yescharacteristic
227C23#47011yescharacteristic
228C23#47112yes—
229Q8—162no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—44no—
248C2×C4—44no—
249C2×C4—42no—
250C2×C4—82no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—82no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—82no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—82no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4—164no—
266C2×C4—162no—
267C2×C4#44912yes—
268C2×C4#45111yescharacteristic
269C2×C4#45111yescharacteristic
270C2×C4#45211yescharacteristic
271C2×C4#45211yescharacteristic
272C2×C4#45412yes—
273C2×C4#45812yes—
274C2×C4#47112yes—
275C2×C4#49511yescharacteristic
276C2×C4#49611yescharacteristic
277C8—82no—
278C8—82no—
279C8—82no—
280C8—161no—
281C22—22no—
282C22—22no—
283C22—22no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—22no—
289C22#168312yes—
290C22#170312yes—
291C22#200111yescharacteristic
292C22#200311yescharacteristic
293C22#200911yescharacteristic
294C22#201211yescharacteristic
295C22#201911yescharacteristic
296C22#201911yescharacteristic
297C22#202211yescharacteristic
298C4—22no—
299C4—21no—
300C4—21no—
301C4—22no—
302C4—21no—
303C4—21no—
304C4—41no—
305C4—82no—
306C4—161no—
307C4—161no—
308C4—162no—
309C4—161no—
310C4#161512yes—
311C4#161712yes—
312C2—22no—
313C2—22no—
314C2#992911yescharacteristic
315C2#995311yescharacteristic
316C2#999311yescharacteristic
317C2#1013411yescharacteristic
318C2#1015111yescharacteristic
319C2#1019111yescharacteristic
320C2#1027511yescharacteristic
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
#299682
#279612
C2×#20992
#96502
#87242
#76672
#70292