Finite Group Databasebeta

← #99941

Subgroups — #99941

Order 512.

405 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 405 conjugacy classes of subgroups — too many to draw. Only its 112 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#22307C211yesmaximal, characteristic
2#22218C211yesmaximal, characteristic
3#9641C211yesmaximal, characteristic
4#7590C211yesmaximal, characteristic
5#7588C211yesmaximal, characteristic
6#7018C211yesmaximal, characteristic
7#7014C211yesmaximal, characteristic
8C2×#487C411yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#1990C411yescharacteristic
12#1984—22no—
13#1956C411yescharacteristic
14#1939—21no—
15#1927—22no—
16#1916—22no—
17#1865—22no—
18#1844C411yescharacteristic
19#1831C2211yescharacteristic
20#1831C2211yescharacteristic
21C8×C4⋊C4—21no—
22#1744C2211yescharacteristic
23#1744C2211yescharacteristic
24#1744C2211yescharacteristic
25C2×Q8⋊C8—21no—
26C2×Q8⋊C8—21no—
27#1272—22no—
28#1271—22no—
29C2×C4⋊Q8C2×C411yescharacteristic
30C2×C4⋊Q8C2×C411yescharacteristic
31C2×C4×Q8—21no—
32C2×C4×Q8D412yes—
33#487—22no—
34#487C814yescomplemented
35C2×#106—22no—
36C2×C4⋊C8—21no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8—22no—
39C2×#103—22no—
40C2×#103—22no—
41C2×C4×C8—21no—
42C2×C4×C8—22no—
43C2×C4×C8C2×C411yescharacteristic
44C2×C4×C8C2×C411yescharacteristic
45C2×C4×C8D411yescharacteristic
46C2×C4×C8D411yescharacteristic
47#391—21no—
48#391D412yes—
49#389—21no—
50#389—21no—
51#389—21no—
52#389—21no—
53#384C2×C411yescharacteristic
54#384C2×C411yescharacteristic
55C4×C4⋊C4—21no—
56C4×C4⋊C4—21no—
57C4×C4⋊C4—21no—
58C4×C4⋊C4—21no—
59C43C2311yescharacteristic
60#340—22no—
61#336—22no—
62#336—22no—
63#336—21no—
64#336—21no—
65#336—21no—
66#336—21no—
67#336—21no—
68#336—21no—
69#336—21no—
70#336—21no—
71#336—21no—
72#336D412yes—
73Q8⋊C8—42no—
74Q8⋊C8—42no—
75C22×Q8—21no—
76C22×Q8C22⋊C412yes—
77C22×C8—21no—
78C22×C8—21no—
79C22×C8—21no—
80C22×C8—21no—
81C22×C8—22no—
82C22×C8—41no—
83C22×C8—41no—
84C4⋊Q8—21no—
85C4⋊Q8—21no—
86C4⋊Q8—21no—
87C4⋊Q8—21no—
88C4⋊Q8—21no—
89C4⋊Q8C2×C812yes—
90C4⋊Q8C2×C812yes—
91C4⋊Q8M1612yes—
92C4×Q8—41no—
93C4×Q8—41no—
94C4×Q8—41no—
95C4×Q8—41no—
96C4×Q8—82no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4C22⋊C412yes—
109C2×C42—22no—
110C2×C42—41no—
111C2×C42C22×C411yescharacteristic
112C2×C42C2×D411yescharacteristic
113C2×C42C2×D411yescharacteristic
114C2×C42C2×D411yescharacteristic
115C2×C42C2×D411yescharacteristic
116C2×C42#4111yescharacteristic
117C2×C42#4111yescharacteristic
118#106—82no—
119C4⋊C8—41no—
120C4⋊C8—41no—
121C4⋊C8—41no—
122C4⋊C8—41no—
123C4⋊C8—82no—
124#103—28no—
125#103—82no—
126C4×C8—22no—
127C4×C8—21no—
128C4×C8—21no—
129C4×C8—21no—
130C4×C8—21no—
131C4×C8—21no—
132C4×C8—21no—
133C4×C8—41no—
134C4×C8—82no—
135C4×C8C2×C812yes—
136C4×C8SD1612yes—
137#95—22no—
138#95—22no—
139#95—41no—
140#95—41no—
141C2×Q8—22no—
142C2×Q8—22no—
143C2×Q8—42no—
144C2×Q8—42no—
145C2×Q8—41no—
146C2×Q8—41no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×Q8C22⋊C814yes—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4C2×C22⋊C411yescharacteristic
156C22×C4C4×D411yescharacteristic
157C22×C4C4×D411yescharacteristic
158C22×C4#12011yescharacteristic
159C22×C4#12111yescharacteristic
160C22×C4#12111yescharacteristic
161C22×C4#12311yescharacteristic
162C2×C8—22no—
163C2×C8—22no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—42no—
169C2×C8—42no—
170C2×C8—41no—
171C2×C8—41no—
172C2×C8—41no—
173C2×C8—42no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—42no—
178C2×C8—81no—
179C2×C8—81no—
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—42no—
190C4⋊C4—42no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—81no—
198C4⋊C4—82no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C4⋊C4—81no—
202C42—21no—
203C42—21no—
204C42—41no—
205C42—41no—
206C42—41no—
207C42—41no—
208C42—42no—
209C42—42no—
210C42—81no—
211C42—81no—
212C42C22×C811yescharacteristic
213C42C2×M1611yescharacteristic
214C42#13111yescharacteristic
215C42#13111yescharacteristic
216C42C2×SD1611yescharacteristic
217C42#13511yescharacteristic
218C42AGL(1,ℤ/8)11yescharacteristic
219C42#13711yescharacteristic
220C23#38611yescharacteristic
221Q8—44no—
222Q8—42no—
223Q8—42no—
224Q8—82no—
225Q8—81no—
226Q8—81no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—24no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4C2×C22⋊C811yescharacteristic
254C2×C4#40811yescharacteristic
255C2×C4C8×D411yescharacteristic
256C2×C4C8×D411yescharacteristic
257C2×C4#43511yescharacteristic
258C2×C4#43511yescharacteristic
259C2×C4C4×SD1611yescharacteristic
260C2×C4#44011yescharacteristic
261C2×C4#44311yescharacteristic
262C2×C4#44411yescharacteristic
263C2×C4#44811yescharacteristic
264C2×C4#44911yescharacteristic
265C2×C4#46011yescharacteristic
266C2×C4#46411yescharacteristic
267C8—42no—
268C8—42no—
269C8—82no—
270C8—81no—
271C8—81no—
272C8—82no—
273C8—161no—
274C22#186911yescharacteristic
275C22#187611yescharacteristic
276C22#188011yescharacteristic
277C22#190211yescharacteristic
278C22#190511yescharacteristic
279C22#190911yescharacteristic
280C22#191111yescharacteristic
281C4—21no—
282C4—21no—
283C4—21no—
284C4—21no—
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—41no—
290C4—41no—
291C4—44no—
292C4—82no—
293C4—82no—
294C4—161no—
295C4C8×SD1611yescharacteristic
296C4SD16⋊C811yescharacteristic
297C4#158311yescharacteristic
298C4#158811yescharacteristic
299C2#894811yescharacteristic
300C2#908811yescharacteristic
301C2#909911yescharacteristic
302C2#928011yescharacteristic
303C2#928511yescharacteristic
304C2#929211yescharacteristic
305C2#930111yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC42C22×C8
Frattini, cosocleC43C23
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
34. #487C8semidirect

Maximal subgroups

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

subgroupindex
#223072
#222182
#96412
#75902
#75882
#70182
#70142