Finite Group Databasebeta

← #103631

Subgroups — #103631

Order 512.

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

normal subgroups only

This group has 472 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×#2100C211yesmaximal, characteristic
4#9879C211yesmaximal, characteristic
5#8725C211yesmaximal, characteristic
6#7665C211yesmaximal, characteristic
7#7029C211yesmaximal, characteristic
8#2857C2211yescharacteristic
9C2×#389C2211yescharacteristic
10C2×#384C2211yescharacteristic
11#2100—22no—
12#2100—22no—
13#2099—21no—
14#2088—22no—
15#2072—22no—
16#2058—21no—
17#1956—21no—
18#1872—22no—
19#1853—21no—
20#1834—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
41C2×#106—22no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8D412yes—
44C2×#103—24no—
45C2×C22⋊C8—21no—
46C2×C22⋊C8—21no—
47C2×C22⋊C8D412yes—
48C2×C4×C8—21no—
49#391—21no—
50#389—21no—
51#389—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#384—21no—
57#384—21no—
58#384—21no—
59#384D412yes—
60#384D411yescharacteristic
61#380—21no—
62#380—21no—
63C2×#95—21no—
64#340—22no—
65#340—24no—
66#340—22no—
67#340—22no—
68#340—24no—
69#340—24no—
70#336—21no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336D412yes—
75C22×Q8—21no—
76C23×C4—21no—
77C23×C4—21no—
78C23×C4—41no—
79C23×C4C2×D411yescharacteristic
80C23×C4C2×D411yescharacteristic
81C23×C4#4111yescharacteristic
82C22×C8—22no—
83C22×C8—22no—
84C22×C8—22no—
85C22×C8—42no—
86C22×C8—42no—
87C22×C8—41no—
88C22×C8—41no—
89C22×C8—41no—
90C4⋊Q8—42no—
91C22⋊Q8—42no—
92C22⋊Q8—42no—
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—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—82no—
117C2×C4⋊C4—82no—
118C2×C4⋊C4—82no—
119C2×C4⋊C4Q1612yes—
120C2×C22⋊C4—41no—
121C2×C42—42no—
122C2×C42C2×D411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126#106—82no—
127C4⋊C8—42no—
128C4⋊C8—42no—
129#103—84no—
130C22⋊C8—22no—
131C22⋊C8—22no—
132C22⋊C8—41no—
133C22⋊C8—41no—
134C22⋊C8—42no—
135C4×C8—42no—
136#95—41no—
137#95—41no—
138#95—41no—
139#95—41no—
140C24#12111yescharacteristic
141C2×Q8—42no—
142C2×Q8—42no—
143C2×Q8—42no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4—41no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—42no—
158C22×C4—42no—
159C22×C4—81no—
160C22×C4—81no—
161C22×C4—82no—
162C22×C4—82no—
163C22×C4—82no—
164C22×C4—81no—
165C22×C4—81no—
166C22×C4#12011yescharacteristic
167C22×C4#12011yescharacteristic
168C22×C4#12011yescharacteristic
169C22×C4#12111yescharacteristic
170C22×C4#12111yescharacteristic
171C22×C4#12711yescharacteristic
172C22×C4C2×Q1611yescharacteristic
173C22×C4#13511yescharacteristic
174C22×C4#13512yes—
175C22×C4#13711yescharacteristic
176C22×C4#13711yescharacteristic
177C22×C4#13712yes—
178C2×C8—42no—
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—82no—
188C2×C8—82no—
189C2×C8—81no—
190C2×C8—81no—
191C2×C8—81no—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—44no—
195C4⋊C4—44no—
196C4⋊C4—42no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—82no—
205C4⋊C4—81no—
206C4⋊C4—82no—
207C4⋊C4—82no—
208C4⋊C4—82no—
209C4⋊C4—82no—
210C4⋊C4—82no—
211C4⋊C4—81no—
212C4⋊C4—81no—
213C22⋊C4—82no—
214C42—22no—
215C42—22no—
216C42—41no—
217C42—41no—
218C23—21no—
219C23—21no—
220C23—21no—
221C23—21no—
222C23#39211yescharacteristic
223C23#46412yes—
224C23#46711yescharacteristic
225C23#47011yescharacteristic
226C23#47112yes—
227Q8—84no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—44no—
246C2×C4—42no—
247C2×C4—82no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—82no—
251C2×C4—82no—
252C2×C4—81no—
253C2×C4—82no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—82no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—164no—
264C2×C4—162no—
265C2×C4#45111yescharacteristic
266C2×C4#45111yescharacteristic
267C2×C4#45211yescharacteristic
268C2×C4#45212yes—
269C2×C4#45211yescharacteristic
270C2×C4#45412yes—
271C2×C4#45812yes—
272C2×C4#47112yes—
273C2×C4#49511yescharacteristic
274C2×C4#49711yescharacteristic
275C8—82no—
276C8—82no—
277C8—82no—
278C8—161no—
279C22—22no—
280C22—22no—
281C22—22no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—22no—
287C22#168412yes—
288C22#170412yes—
289C22#200111yescharacteristic
290C22#200311yescharacteristic
291C22#200811yescharacteristic
292C22#201511yescharacteristic
293C22#201911yescharacteristic
294C22#201911yescharacteristic
295C22#202211yescharacteristic
296C4—22no—
297C4—21no—
298C4—21no—
299C4—22no—
300C4—21no—
301C4—21no—
302C4—41no—
303C4—82no—
304C4—161no—
305C4—162no—
306C4—161no—
307C4—161no—
308C4#161512yes—
309C4#161712yes—
310C2—22no—
311C2—22no—
312C2#992911yescharacteristic
313C2#995811yescharacteristic
314C2#999311yescharacteristic
315C2#1013111yescharacteristic
316C2#1015611yescharacteristic
317C2#1018211yescharacteristic
318C2#1027711yescharacteristic
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×#21002
#98792
#87252
#76652
#70292