Finite Group Databasebeta

← #101839

Subgroups — #101839

Order 512.

524 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 102 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#28508C211yesmaximal, characteristic
2#23175C211yesmaximal, characteristic
3#9705C212yesmaximal, complemented
4#7651C211yesmaximal, characteristic
5#7022C212yesmaximal, complemented
6C2×#474—21no—
7C2×#474—21no—
8C2×#435—22no—
9#2868C2211yescharacteristic
10C4×#127C2211yescharacteristic
11#2093—21no—
12#2093—21no—
13#1957C412yes—
14#1955—22no—
15#1870—21no—
16#1869—21no—
17#1845C412yes—
18#1831C2212yes—
19#1767C2212yes—
20C4×C4⋊C8C2211yescharacteristic
21C2×#332—22no—
22C2×#332—22no—
23#1270—21no—
24#1270—21no—
25C22×M16—21no—
26C23×C8—21no—
27C2×C4⋊Q8—22no—
28C2×C4⋊Q8—21no—
29C2×#127C2×C411yescharacteristic
30C2×C4×D4—22no—
31C2×C4×D4D411yescharacteristic
32C2×C4×D4D411yescharacteristic
33#474—42no—
34#474—42no—
35#474—42no—
36#474—42no—
37#435—44no—
38#435—44no—
39C2×#107—22no—
40C2×#107—22no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—22no—
43C2×C4⋊C8D412yes—
44C2×C4⋊C8D412yes—
45C2×#102—22no—
46C2×#102—22no—
47C2×C22⋊C8—22no—
48C2×C22⋊C8—22no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8—21no—
51C2×#97—22no—
52C2×C4×C8C2×C412yes—
53#390—22no—
54#390D411yescharacteristic
55#390D411yescharacteristic
56#384—21no—
57#384—22no—
58#384C2×C412yes—
59#384C2×C411yescharacteristic
60C43C2311yescharacteristic
61#336—21no—
62#336—22no—
63#336—22no—
64#336—22no—
65#332—44no—
66#332—44no—
67C22×Q8—41no—
68C22×D4—22no—
69C22×D4C22⋊C411yescharacteristic
70C22×D4C22⋊C411yescharacteristic
71C23×C4—21no—
72C23×C4—21no—
73C2×M16—44no—
74C2×M16—81no—
75C22×C8—22no—
76C22×C8—22no—
77C22×C8—22no—
78C22×C8—44no—
79C22×C8—42no—
80C22×C8—81no—
81C4⋊Q8—41no—
82C4⋊Q8—41no—
83C4⋊Q8—41no—
84C4⋊Q8—41no—
85C4⋊Q8—42no—
86C4⋊Q8—42no—
87C4⋊Q8—42no—
88C4⋊Q8—42no—
89#127—22no—
90#127—41no—
91C4×D4—41no—
92C4×D4—41no—
93C4×D4—41no—
94C4×D4—41no—
95C4×D4—42no—
96C4×D4—42no—
97C4×D4—42no—
98C4×D4—42no—
99C2×C4⋊C4—22no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—24no—
102C2×C4⋊C4—42no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4C22⋊C411yescharacteristic
105C2×C4⋊C4C22⋊C411yescharacteristic
106C2×C22⋊C4—22no—
107C2×C22⋊C4—22no—
108C2×C22⋊C4—21no—
109C2×C22⋊C4—21no—
110C2×C42C22×C411yescharacteristic
111C2×C42C2×D411yescharacteristic
112C2×C42C2×D411yescharacteristic
113C2×C42C2×D412yes—
114C2×C42#4112yes—
115#107—44no—
116#107—44no—
117C4⋊C8—22no—
118C4⋊C8—22no—
119C4⋊C8—22no—
120C4⋊C8—22no—
121C4⋊C8—22no—
122C4⋊C8—42no—
123C4⋊C8—42no—
124C4⋊C8D814yes—
125#102—44no—
126#102—44no—
127C22⋊C8—44no—
128C22⋊C8—44no—
129C22⋊C8—81no—
130C22⋊C8—81no—
131#97—42no—
132#97—42no—
133C4×C8—42no—
134C24—21no—
135C24—21no—
136C2×Q8—82no—
137C2×Q8—82no—
138C2×Q8—81no—
139C2×Q8—81no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—41no—
144C2×D4—41no—
145C2×D4—41no—
146C2×D4—41no—
147C2×D4—44no—
148C2×D4—42no—
149C2×D4—42no—
150C2×D4—82no—
151C2×D4#10112yes—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—42no—
155C22×C4—42no—
156C22×C4—42no—
157C22×C4—42no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—42no—
163C22×C4C2×C22⋊C411yescharacteristic
164C22×C4C4×D412yes—
165C22×C4#12011yescharacteristic
166C22×C4#12112yes—
167C22×C4#12311yescharacteristic
168M16—84no—
169C2×C8—24no—
170C2×C8—24no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—84no—
179C2×C8—82no—
180C2×C8—82no—
181C2×C8—82no—
182C4⋊C4—41no—
183C4⋊C4—41no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—44no—
189C4⋊C4—44no—
190C4⋊C4—81no—
191C4⋊C4—81no—
192C4⋊C4—82no—
193C4⋊C4—82no—
194C22⋊C4—42no—
195C22⋊C4—42no—
196C22⋊C4—42no—
197C22⋊C4—42no—
198C22⋊C4—81no—
199C22⋊C4—81no—
200C42—21no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—41no—
205C42—42no—
206C42C2×D812yes—
207C42#13512yes—
208C42AGL(1,ℤ/8)12yes—
209C42AGL(1,ℤ/8)12yes—
210C23—22no—
211C23—42no—
212C23—41no—
213C23—42no—
214C23—41no—
215C23—42no—
216C23—41no—
217C23—41no—
218C23—42no—
219C23—41no—
220C23#38611yescharacteristic
221Q8—161no—
222Q8—161no—
223Q8—162no—
224D4—42no—
225D4—42no—
226D4—81no—
227D4—84no—
228D4—84no—
229D4—81no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—81no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—82no—
247C2×C4—82no—
248C2×C4—84no—
249C2×C4—82no—
250C2×C4C2×#10111yescharacteristic
251C2×C4#41311yescharacteristic
252C2×C4C4×D812yes—
253C2×C4#44212yes—
254C2×C4#44712yes—
255C2×C4#44912yes—
256C2×C4#45311yescharacteristic
257C2×C4#45311yescharacteristic
258C2×C4#45912yes—
259C2×C4#46312yes—
260C8—44no—
261C8—44no—
262C8—82no—
263C8—162no—
264C22—44no—
265C22—42no—
266C22—82no—
267C22—81no—
268C22—81no—
269C22—82no—
270C22—82no—
271C22—81no—
272C22—81no—
273C22—81no—
274C22#187912yes—
275C22#188711yescharacteristic
276C22#190111yescharacteristic
277C22#190212yes—
278C22#190911yescharacteristic
279C4—22no—
280C4—22no—
281C4—22no—
282C4—22no—
283C4—21no—
284C4—21no—
285C4—41no—
286C4—81no—
287C4—81no—
288C4—162no—
289C4#161911yescharacteristic
290C4#162011yescharacteristic
291C4#162112yes—
292C2—82no—
293C2—161no—
294C2#906111yescharacteristic
295C2#925112yes—
296C2#929112yes—
297C2#942111yescharacteristic
298C2#945511yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
prime radicalC2×#127C2×C4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #9705C2semidirect
5. #7022C2semidirect

Maximal subgroups

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

subgroupindex
#285082
#231752
#97052
#76512
#70222