Finite Group Databasebeta

← #105102

Subgroups — #105102

Order 512.

375 conjugacy classes of subgroups.

The subgroup lattice has 313 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#29206C211yesmaximal, characteristic
2#9864C211yesmaximal, characteristic
3#9694C211yesmaximal, characteristic
4#9691C211yesmaximal, characteristic
5#9602C211yesmaximal, characteristic
6#8587C211yesmaximal, characteristic
7#7031C211yesmaximal, characteristic
8#2868C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10#2058—22no—
11#1990—21no—
12#1948—21no—
13#1948—21no—
14#1844—21no—
15#1842C2211yescharacteristic
16#1842C2211yescharacteristic
17C4×C4⋊C8C2211yescharacteristic
18C4×C4⋊C8C2211yescharacteristic
19C4×C4⋊C8C2211yescharacteristic
20C2×#334—21no—
21C2×#333—21no—
22C2×#333—21no—
23C2×#333—21no—
24C2×#332—22no—
25#1296—21no—
26#1279—21no—
27#1279—21no—
28#1277—21no—
29C2×C4⋊Q8—21no—
30C2×C4⋊Q8—21no—
31C2×C4⋊Q8D411yescharacteristic
32C2×C4⋊Q8D412yes—
33C2×C4×Q8—21no—
34C2×#106—22no—
35C2×#106—22no—
36C2×C4⋊C8—21no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8D411yescharacteristic
44C2×C4⋊C8D411yescharacteristic
45C2×C4⋊C8D411yescharacteristic
46C2×C4⋊C8D411yescharacteristic
47C2×C4×C8—21no—
48C2×C4×C8—21no—
49C2×C4×C8—21no—
50#391—21no—
51#389—21no—
52#389—21no—
53#384—21no—
54#384—21no—
55#384—21no—
56#384—21no—
57#384D411yescharacteristic
58C4×C4⋊C4—21no—
59C4×C4⋊C4—21no—
60C43C2311yescharacteristic
61#340—22no—
62#340—22no—
63#336—21no—
64#336—21no—
65#336—21no—
66#334—42no—
67#333—42no—
68#333—42no—
69#333—42no—
70#332—44no—
71C22×Q8—22no—
72C22×Q8—21no—
73C22×C8—21no—
74C22×C8—21no—
75C22×C8—21no—
76C22×C8—21no—
77C22×C8—41no—
78C22×C8—41no—
79C22×C8—41no—
80C4⋊Q8—21no—
81C4⋊Q8—21no—
82C4⋊Q8—21no—
83C4⋊Q8—42no—
84C4⋊Q8—42no—
85C4⋊Q8—41no—
86C4⋊Q8—41no—
87C4⋊Q8—41no—
88C4⋊Q8—41no—
89C4⋊Q8—82no—
90C4⋊Q8SD1612yes—
91C4×Q8—81no—
92C4×Q8—81no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—22no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—22no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4—41no—
102C2×C4⋊C4—41no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4—41no—
105C2×C42—41no—
106C2×C42C2×D411yescharacteristic
107C2×C42C2×D411yescharacteristic
108C2×C42C2×D411yescharacteristic
109C2×C42C2×D411yescharacteristic
110C2×C42#4111yescharacteristic
111C2×C42#4111yescharacteristic
112C2×C42#4111yescharacteristic
113#106—82no—
114#106—82no—
115C4⋊C8—22no—
116C4⋊C8—21no—
117C4⋊C8—21no—
118C4⋊C8—21no—
119C4⋊C8—21no—
120C4⋊C8—21no—
121C4⋊C8—41no—
122C4⋊C8—42no—
123C4⋊C8—41no—
124C4⋊C8—41no—
125C4⋊C8—41no—
126C4⋊C8—41no—
127C4⋊C8—41no—
128C4⋊C8—41no—
129C4⋊C8—41no—
130C4⋊C8—41no—
131C4⋊C8—81no—
132C4⋊C8SD1612yes—
133C4⋊C8SD1612yes—
134C4⋊C8Q1612yes—
135C4×C8—41no—
136C4×C8—41no—
137C4×C8—41no—
138C4×C8—41no—
139C4×C8—41no—
140C4×C8—41no—
141#95—41no—
142#95—41no—
143C2×Q8—22no—
144C2×Q8—41no—
145C2×Q8—42no—
146C2×Q8—42no—
147C2×Q8—81no—
148C2×Q8—81no—
149C2×Q8—82no—
150C2×Q8—82no—
151C22×C4—41no—
152C22×C4—41no—
153C22×C4—42no—
154C22×C4#12011yescharacteristic
155C22×C4#12111yescharacteristic
156C22×C4#12111yescharacteristic
157C22×C4#12111yescharacteristic
158C22×C4#12311yescharacteristic
159C22×C4#12311yescharacteristic
160C22×C4#12411yescharacteristic
161C2×C8—22no—
162C2×C8—22no—
163C2×C8—22no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—42no—
171C2×C8—41no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—81no—
175C2×C8—81no—
176C2×C8—81no—
177C2×C8—81no—
178C2×C8—81no—
179C2×C8—81no—
180C2×C8—81no—
181C2×C8—81no—
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—44no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—42no—
189C4⋊C4—41no—
190C4⋊C4—42no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—81no—
194C4⋊C4—82no—
195C4⋊C4—82no—
196C4⋊C4—82no—
197C4⋊C4—81no—
198C4⋊C4—81no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—41no—
208C42—81no—
209C42—81no—
210C42C2×SD1611yescharacteristic
211C42C2×SD1611yescharacteristic
212C42C2×SD1611yescharacteristic
213C42C2×Q1611yescharacteristic
214C42#13511yescharacteristic
215C42#13511yescharacteristic
216C42AGL(1,ℤ/8)11yescharacteristic
217C42#13711yescharacteristic
218C42#13711yescharacteristic
219C42#13711yescharacteristic
220C42#13711yescharacteristic
221C42#13711yescharacteristic
222C23#39411yescharacteristic
223Q8—82no—
224Q8—82no—
225Q8—162no—
226Q8—162no—
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—21no—
236C2×C4—42no—
237C2×C4—81no—
238C2×C4—81no—
239C2×C4—82no—
240C2×C4—81no—
241C2×C4—82no—
242C2×C4—82no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4#44811yescharacteristic
246C2×C4#44811yescharacteristic
247C2×C4#45111yescharacteristic
248C2×C4#45211yescharacteristic
249C2×C4#45311yescharacteristic
250C2×C4#45511yescharacteristic
251C2×C4#46011yescharacteristic
252C2×C4#46111yescharacteristic
253C2×C4#46111yescharacteristic
254C2×C4#46211yescharacteristic
255C2×C4#46311yescharacteristic
256C2×C4#46411yescharacteristic
257C2×C4#46511yescharacteristic
258C2×C4#46511yescharacteristic
259C2×C4#46811yescharacteristic
260C2×C4#47011yescharacteristic
261C2×C4#47111yescharacteristic
262C2×C4#47111yescharacteristic
263C2×C4#47111yescharacteristic
264C2×C4#47311yescharacteristic
265C2×C4#48311yescharacteristic
266C2×C4#48511yescharacteristic
267C2×C4#48711yescharacteristic
268C2×C4#49111yescharacteristic
269C8—42no—
270C8—42no—
271C8—42no—
272C8—82no—
273C8—81no—
274C8—161no—
275C8—161no—
276C22#203511yescharacteristic
277C22#203711yescharacteristic
278C22#204311yescharacteristic
279C22#204611yescharacteristic
280C22#204811yescharacteristic
281C22#205211yescharacteristic
282C22#205511yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—41no—
290C4—82no—
291C4—162no—
292C4—161no—
293C4#162311yescharacteristic
294C4#163211yescharacteristic
295C4#164311yescharacteristic
296C4#164511yescharacteristic
297C4#166611yescharacteristic
298C4#167111yescharacteristic
299C4#167211yescharacteristic
300C4#168011yescharacteristic
301C4#169011yescharacteristic
302C4#169111yescharacteristic
303C4#169211yescharacteristic
304C4#170411yescharacteristic
305C2#1041511yescharacteristic
306C2#1045211yescharacteristic
307C2#1048611yescharacteristic
308C2#1048911yescharacteristic
309C2#1050411yescharacteristic
310C2#1054411yescharacteristic
311C2#1055511yescharacteristic
subgroupG/H
center, socle, prime radicalC23#394
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
#292062
#98642
#96942
#96912
#96022
#85872
#70312