Finite Group Databasebeta

← #102575

Subgroups — #102575

Order 512.

420 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 86 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#29276C211yesmaximal, characteristic
2#29272C211yesmaximal, characteristic
3#23816C211yesmaximal, characteristic
4#9641C211yesmaximal, characteristic
5#7653C211yesmaximal, characteristic
6#7652C211yesmaximal, characteristic
7#7018C211yesmaximal, characteristic
8C4×C4⋊Q8C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#2100—21no—
12#2100—21no—
13#2099—21no—
14#2072—21no—
15#2058—21no—
16#2057—21no—
17#2043—21no—
18#2024—21no—
19#1988—21no—
20#1988—21no—
21#1948—21no—
22#1947—21no—
23#1920—22no—
24#1918—22no—
25#1831C2211yescharacteristic
26#1831C2211yescharacteristic
27#1831C2211yescharacteristic
28C4×#103—22no—
29#1744C2211yescharacteristic
30C2×Q8⋊C8—22no—
31#1272—22no—
32#1271—22no—
33C2×C4⋊Q8D411yescharacteristic
34C2×C4⋊Q8D411yescharacteristic
35C2×C4⋊Q8D411yescharacteristic
36C2×C4×Q8—21no—
37C2×C4×Q8—21no—
38C2×C4×Q8—21no—
39C2×#107—22no—
40C2×#106—22no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×#103—22no—
45C2×#103—22no—
46C2×C4×C8D412yes—
47#391—21no—
48#391—21no—
49#391—21no—
50#389—21no—
51#389—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#384D411yescharacteristic
57#384D411yescharacteristic
58#384D411yescharacteristic
59C4×C4⋊C4—21no—
60C4×C4⋊C4—21no—
61C4×C4⋊C4—21no—
62C4×C4⋊C4—21no—
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C43C2311yescharacteristic
66#340—22no—
67#340—22no—
68#340—22no—
69#340—22no—
70#340—22no—
71#340—22no—
72#340—22no—
73#340—22no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336D412yes—
81#336D412yes—
82Q8⋊C8—44no—
83C22×Q8—21no—
84C22×Q8—21no—
85C22×Q8—21no—
86C22×C8—22no—
87C22×C8—22no—
88C22×C8—22no—
89C22×C8—41no—
90C4⋊Q8—21no—
91C4⋊Q8—21no—
92C4⋊Q8—21no—
93C4⋊Q8—42no—
94C4⋊Q8—42no—
95C4⋊Q8Q1612yes—
96C4×Q8—42no—
97C4×Q8—42no—
98C4×Q8—42no—
99C4×Q8—42no—
100C4×Q8—82no—
101C2×C4⋊C4—21no—
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—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C42—41no—
120C2×C42—41no—
121C2×C42—41no—
122C2×C42C2×D411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42#4111yescharacteristic
129#107—44no—
130#106—44no—
131C4⋊C8—41no—
132C4⋊C8—41no—
133C4⋊C8—42no—
134C4⋊C8—41no—
135C4⋊C8—41no—
136#103—44no—
137#103—44no—
138C4×C8—22no—
139C4×C8—22no—
140#95—41no—
141#95—41no—
142#95—41no—
143#95—41no—
144#95—41no—
145#95—41no—
146C2×Q8—22no—
147C2×Q8—22no—
148C2×Q8—22no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8—42no—
152C2×Q8—41no—
153C2×Q8—42no—
154C2×Q8—42no—
155C2×Q8—42no—
156C2×Q8—81no—
157C2×Q8—81no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4#12011yescharacteristic
165C22×C4#12011yescharacteristic
166C22×C4#12011yescharacteristic
167C22×C4#12111yescharacteristic
168C22×C4#12111yescharacteristic
169C22×C4#12111yescharacteristic
170C22×C4#12711yescharacteristic
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—81no—
181C2×C8—81no—
182C2×C8—81no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—81no—
203C4⋊C4—81no—
204C4⋊C4—82no—
205C4⋊C4—82no—
206C4⋊C4—81no—
207C4⋊C4—81no—
208C42—22no—
209C42—41no—
210C42—41no—
211C42—41no—
212C42—41no—
213C42—82no—
214C42—82no—
215C42—81no—
216C42—81no—
217C42C2×Q1611yescharacteristic
218C42#13512yes—
219C42#13511yescharacteristic
220C42AGL(1,ℤ/8)12yes—
221C42#13711yescharacteristic
222C42#13711yescharacteristic
223C23#39211yescharacteristic
224Q8—44no—
225Q8—44no—
226Q8—82no—
227Q8—82no—
228Q8—82no—
229Q8—82no—
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—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4#44912yes—
263C2×C4#45111yescharacteristic
264C2×C4#45111yescharacteristic
265C2×C4#45211yescharacteristic
266C2×C4#45211yescharacteristic
267C2×C4#46312yes—
268C2×C4#46711yescharacteristic
269C2×C4#47011yescharacteristic
270C2×C4#47112yes—
271C2×C4#49511yescharacteristic
272C2×C4#49611yescharacteristic
273C8—82no—
274C8—82no—
275C8—82no—
276C8—161no—
277C22#200111yescharacteristic
278C22#200911yescharacteristic
279C22#200911yescharacteristic
280C22#201011yescharacteristic
281C22#201011yescharacteristic
282C22#201211yescharacteristic
283C22#201911yescharacteristic
284C4—21no—
285C4—21no—
286C4—21no—
287C4—21no—
288C4—22no—
289C4—21no—
290C4—21no—
291C4—41no—
292C4—41no—
293C4—82no—
294C4—82no—
295C4—82no—
296C4—161no—
297C4—161no—
298C4—161no—
299C4#168312yes—
300C4#170312yes—
301C2#1000311yescharacteristic
302C2#1000311yescharacteristic
303C2#1001311yescharacteristic
304C2#1004311yescharacteristic
305C2#1004411yescharacteristic
306C2#1022611yescharacteristic
307C2#1027511yescharacteristic
subgroupG/H
center, socle, prime radicalC23#392
commutator, Frattini, cosocleC43C23
LCSG ▷ C43 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#292762
#292722
#238162
#96412
#76532
#76522
#70182