Finite Group Databasebeta

← #101717

Subgroups — #101717

Order 512.

443 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#28687C211yesmaximal, characteristic
2#23149C211yesmaximal, characteristic
3#9898C211yesmaximal, characteristic
4#9692C211yesmaximal, characteristic
5#8586C211yesmaximal, characteristic
6#7031C211yesmaximal, characteristic
7#7031C211yesmaximal, characteristic
8C2×#498—21no—
9C2×C8×Q8—21no—
10#2868C2211yescharacteristic
11C4×C4⋊Q8C2211yescharacteristic
12#2084C414yes—
13#1990—21no—
14#1984—21no—
15#1948—22no—
16#1939—21no—
17#1916—22no—
18#1842C2211yescharacteristic
19#1842C2211yescharacteristic
20C8×C4⋊C4—21no—
21C4×C4⋊C8C2211yescharacteristic
22C4×C4⋊C8C2211yescharacteristic
23C4×C4⋊C8C2211yescharacteristic
24C2×#332—21no—
25C2×#332—21no—
26C2×#332—21no—
27#1296—21no—
28#1296—21no—
29#1296—21no—
30C2×C4⋊Q8—21no—
31C2×C4⋊Q8—21no—
32C2×C4⋊Q8—21no—
33C2×C4⋊Q8D411yescharacteristic
34C2×C4×Q8—21no—
35#498—42no—
36#498—42no—
37C8×Q8—42no—
38C8×Q8—42no—
39C2×#106—24no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—22no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8D411yescharacteristic
49C2×C4⋊C8D411yescharacteristic
50C2×C4⋊C8D411yescharacteristic
51C2×C4⋊C8D411yescharacteristic
52C2×C4×C8—22no—
53C2×C4×C8—21no—
54C2×C4×C8—21no—
55C2×C4×C8—21no—
56#391—21no—
57#389—21no—
58#389C2×C412yes—
59#384—21no—
60#384—21no—
61#384—21no—
62#384C2×C412yes—
63#384D411yescharacteristic
64C4×C4⋊C4—21no—
65C4×C4⋊C4D412yes—
66C43C2311yescharacteristic
67#340—24no—
68#336—22no—
69#336—22no—
70#336—21no—
71#336—21no—
72#336C2×C412yes—
73#332—42no—
74#332—42no—
75#332—42no—
76C22×Q8—21no—
77C22×Q8—41no—
78C22×C8—22no—
79C22×C8—21no—
80C22×C8—21no—
81C22×C8—21no—
82C22×C8—21no—
83C22×C8—41no—
84C22×C8—41no—
85C4⋊Q8—21no—
86C4⋊Q8—21no—
87C4⋊Q8—41no—
88C4⋊Q8—41no—
89C4⋊Q8—41no—
90C4⋊Q8—41no—
91C4⋊Q8—41no—
92C4⋊Q8—41no—
93C4⋊Q8—41no—
94C4⋊Q8—41no—
95C4⋊Q8—81no—
96C4⋊Q8—81no—
97C4⋊Q8D812yes—
98C4⋊Q8SD1612yes—
99C4×Q8—41no—
100C4×Q8—41no—
101C4×Q8—41no—
102C4×Q8—41no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4C22⋊C412yes—
114C2×C4⋊C4C22⋊C412yes—
115C2×C42—22no—
116C2×C42C22×C411yescharacteristic
117C2×C42C2×D411yescharacteristic
118C2×C42C2×D411yescharacteristic
119C2×C42C2×D411yescharacteristic
120C2×C42C2×D411yescharacteristic
121C2×C42#4111yescharacteristic
122C2×C42#4111yescharacteristic
123#106—48no—
124C4⋊C8—22no—
125C4⋊C8—22no—
126C4⋊C8—21no—
127C4⋊C8—21no—
128C4⋊C8—21no—
129C4⋊C8—21no—
130C4⋊C8—21no—
131C4⋊C8—21no—
132C4⋊C8—44no—
133C4⋊C8—41no—
134C4⋊C8—41no—
135C4⋊C8—41no—
136C4⋊C8—41no—
137C4⋊C8—41no—
138C4⋊C8—41no—
139C4⋊C8—41no—
140C4⋊C8—41no—
141C4⋊C8—81no—
142C4⋊C8—81no—
143C4⋊C8SD1612yes—
144C4⋊C8SD1612yes—
145C4×C8—44no—
146C4×C8—41no—
147C4×C8—41no—
148C4×C8—41no—
149C4×C8—41no—
150C4×C8—41no—
151C4×C8—41no—
152#95—22no—
153#95—22no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8—81no—
161C2×Q8—81no—
162C2×Q8—81no—
163C2×Q8—81no—
164C2×Q8—81no—
165C2×Q8—81no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—42no—
169C22×C4C2×C22⋊C411yescharacteristic
170C22×C4C4×D411yescharacteristic
171C22×C4C4×D411yescharacteristic
172C22×C4#12011yescharacteristic
173C22×C4#12111yescharacteristic
174C22×C4#12111yescharacteristic
175C22×C4#12311yescharacteristic
176C2×C8—24no—
177C2×C8—22no—
178C2×C8—22no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—81no—
192C2×C8—81no—
193C2×C8—81no—
194C2×C8—81no—
195C2×C8—81no—
196C2×C8—81no—
197C4⋊C4—22no—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—82no—
212C4⋊C4—82no—
213C4⋊C4—81no—
214C4⋊C4—81no—
215C4⋊C4—81no—
216C4⋊C4—81no—
217C4⋊C4#10214yes—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—41no—
225C42—42no—
226C42—42no—
227C42C2×D811yescharacteristic
228C42C2×SD1611yescharacteristic
229C42C2×SD1611yescharacteristic
230C42C2×SD1611yescharacteristic
231C42#13511yescharacteristic
232C42#13511yescharacteristic
233C42#13511yescharacteristic
234C42#13511yescharacteristic
235C42AGL(1,ℤ/8)11yescharacteristic
236C42AGL(1,ℤ/8)11yescharacteristic
237C42#13711yescharacteristic
238C42#13711yescharacteristic
239C23#38611yescharacteristic
240Q8—42no—
241Q8—42no—
242Q8—42no—
243Q8—42no—
244Q8—161no—
245Q8—161no—
246Q8—161no—
247Q8—161no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—24no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—82no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4C2×#10211yescharacteristic
267C2×C4#41611yescharacteristic
268C2×C4C4×SD1611yescharacteristic
269C2×C4C4×SD1611yescharacteristic
270C2×C4#44011yescharacteristic
271C2×C4#44011yescharacteristic
272C2×C4#44811yescharacteristic
273C2×C4#44911yescharacteristic
274C2×C4#45011yescharacteristic
275C2×C4#45211yescharacteristic
276C2×C4#45611yescharacteristic
277C2×C4#45611yescharacteristic
278C2×C4#46011yescharacteristic
279C2×C4#46111yescharacteristic
280C2×C4#46311yescharacteristic
281C2×C4#46411yescharacteristic
282C2×C4#46511yescharacteristic
283C2×C4#46511yescharacteristic
284C2×C4#46611yescharacteristic
285C2×C4#46611yescharacteristic
286C2×C4#47111yescharacteristic
287C2×C4#47111yescharacteristic
288C2×C4#47211yescharacteristic
289C2×C4#47311yescharacteristic
290C8—44no—
291C8—42no—
292C8—42no—
293C8—81no—
294C8—81no—
295C8—161no—
296C8—161no—
297C22#187711yescharacteristic
298C22#188011yescharacteristic
299C22#188611yescharacteristic
300C22#189311yescharacteristic
301C22#190711yescharacteristic
302C22#190811yescharacteristic
303C22#191511yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—44no—
311C4—41no—
312C4—82no—
313C4—162no—
314C4#165111yescharacteristic
315C4#165211yescharacteristic
316C4#165311yescharacteristic
317C4#165411yescharacteristic
318C4#166611yescharacteristic
319C4#166811yescharacteristic
320C4#167111yescharacteristic
321C4#167311yescharacteristic
322C4#167811yescharacteristic
323C4#167911yescharacteristic
324C4#168111yescharacteristic
325C4#168211yescharacteristic
326C2#905911yescharacteristic
327C2#921711yescharacteristic
328C2#922211yescharacteristic
329C2#926911yescharacteristic
330C2#927211yescharacteristic
331C2#939411yescharacteristic
332C2#943411yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ 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
#286872
#231492
#98982
#96922
#85862
#70312