Finite Group Databasebeta

← #35302759

Subgroups — #35302759

Order 21248.

382 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24908424C211yesmaximal, characteristic
2#24908411C211yesmaximal, characteristic
3#24908226C211yesmaximal, characteristic
4C2×#19127449C211yesmaximal, characteristic
5#24905347C211yesmaximal, characteristic
6#24905298C211yesmaximal, characteristic
7C8×C4⋊C4×C83C211yesmaximal, characteristic
8C2×#14581792C2211yescharacteristic
9C2×#14581723—21no—
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11C2×C4⋊(C83⋊C8)C2211yescharacteristic
12#19127571C2211yescharacteristic
13#19127464—21no—
14#19127464—21no—
15#19127463—21no—
16#19127463—21no—
17#19127463—21no—
18#19127449C414yescomplemented
19C2×C4⋊C8×C83C2211yescharacteristic
20C2×C4×C8×C83—21no—
21C2×C4×C8×C83C2211yescharacteristic
22C4×C4⋊C4×C83C2211yescharacteristic
23#336×C83—21no—
24C22×Dic166—21no—
25C22×C83⋊C8—21no—
26C22×C83⋊C8—21no—
27#14581792—21no—
28#14581792—21no—
29#14581792—21no—
30#14581792C2×C412yes—
31C2×C4⋊Dic83—21no—
32C2×C4⋊Dic83—21no—
33C2×C4⋊Dic83—21no—
34C2×C4⋊Dic83—21no—
35C2×C4⋊Dic83—21no—
36#14581723—42no—
37C4⋊(C83⋊C8)—21no—
38C4⋊(C83⋊C8)—21no—
39C4⋊(C83⋊C8)—21no—
40C4⋊(C83⋊C8)C2×C412yes—
41C22×C8×C83—21no—
42C22×C8×C83D411yescharacteristic
43C22×C8×C83D411yescharacteristic
44C2×C4⋊C4×C83D411yescharacteristic
45C2×C4⋊C4×C83D411yescharacteristic
46C2×C42×C83—21no—
47C2×C42×C83C2311yescharacteristic
48C4⋊C8×C83—21no—
49C4⋊C8×C83C2×C412yes—
50C4×C8×C83—21no—
51C4×C8×C83—21no—
52C4×C8×C83—42no—
53#95×C83—21no—
54C2×Dic166—22no—
55C2×Dic166—41no—
56C2×Dic166—81no—
57C2×Dic166—81no—
58C22×Dic83—41no—
59C22×Dic83—41no—
60C2×C83⋊C8—22no—
61C2×C83⋊C8—41no—
62C2×C83⋊C8—41no—
63C2×C83⋊C8—41no—
64C2×C83⋊C8—41no—
65C2×C83⋊C8—41no—
66C4⋊Dic83—22no—
67C4⋊Dic83—22no—
68C4⋊Dic83—41no—
69C4⋊Dic83—41no—
70C4⋊Dic83—41no—
71C4⋊Dic83—41no—
72C4⋊Dic83—41no—
73C4⋊Dic83—41no—
74C4⋊Dic83—81no—
75C22×C4×C83—21no—
76C22×C4×C83—21no—
77C22×C4×C83C2×D411yescharacteristic
78C22×C4×C83C2×D411yescharacteristic
79C22×C4×C83#4111yescharacteristic
80C2×C8×C83—21no—
81C2×C8×C83—21no—
82C2×C8×C83—22no—
83C2×C8×C83—21no—
84C2×C8×C83—21no—
85C2×C8×C83—21no—
86C2×C8×C83—41no—
87C2×C8×C83—41no—
88C2×C8×C83SD1612yes—
89C4⋊C4×C83—21no—
90C4⋊C4×C83—21no—
91C4⋊C4×C83SD1612yes—
92C4⋊C4×C83Q1612yes—
93C42×C83—41no—
94C42×C83—41no—
95C42×C83C22×C411yescharacteristic
96C42×C83#4111yescharacteristic
97C42×C83#4111yescharacteristic
98C42×C83#4111yescharacteristic
99C23×C83#12111yescharacteristic
100C2×C4×C83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—22no—
103C2×C4×C83—22no—
104C2×C4×C83—41no—
105C2×C4×C83—41no—
106C2×C4×C83—41no—
107C2×C4×C83—41no—
108C2×C4×C83#11711yescharacteristic
109C2×C4×C83C4×D411yescharacteristic
110C2×C4×C83C4×D411yescharacteristic
111C2×C4×C83#12311yescharacteristic
112C2×C4×C83#12411yescharacteristic
113C2×C4×C83#12611yescharacteristic
114C2×C4×C83C2×SD1611yescharacteristic
115C2×C4×C83C2×SD1611yescharacteristic
116C2×C4×C83C2×Q1611yescharacteristic
117C2×C4×C83#13511yescharacteristic
118C2×C4×C83#13511yescharacteristic
119C2×C4×C83#13511yescharacteristic
120C2×C4×C83#13711yescharacteristic
121C2×C4×C83#13711yescharacteristic
122C2×Dic83—42no—
123C2×Dic83—81no—
124C2×Dic83—81no—
125C2×Dic83—81no—
126C2×Dic83—81no—
127C2×Dic83—81no—
128Dic166—82no—
129Dic166—82no—
130C8×C83—22no—
131C8×C83—42no—
132C8×C83—41no—
133C83⋊C8—42no—
134C83⋊C8—81no—
135C22×C83#38811yescharacteristic
136C22×C83#46111yescharacteristic
137C22×C83#46411yescharacteristic
138C22×C83#46511yescharacteristic
139C22×C83#46711yescharacteristic
140C22×C83#47111yescharacteristic
141C22×C83#47211yescharacteristic
142C4×C83—21no—
143C4×C83—21no—
144C4×C83—42no—
145C4×C83—42no—
146C4×C83C4×SD1611yescharacteristic
147C4×C83C4×SD1611yescharacteristic
148C4×C83C4×Q1611yescharacteristic
149C4×C83#44111yescharacteristic
150C4×C83#48311yescharacteristic
151C4×C83#48511yescharacteristic
152C4×C83#48711yescharacteristic
153C4×C83#48811yescharacteristic
154Dic83—82no—
155Dic83—161no—
156#9567—831nomaximal, Sylow
157C2×C83#167111yescharacteristic
158C2×C83#167511yescharacteristic
159C2×C83#167811yescharacteristic
160C2×C83#168411yescharacteristic
161C2×C83#192711yescharacteristic
162C2×C83#193111yescharacteristic
163C2×C83#193311yescharacteristic
164#1990—831no—
165#1987—831no—
166#1948—831no—
167C8×C4⋊C4D8311yescharacteristic
168C2×#333—831no—
169#1296—831no—
170#1277—831no—
171C83#956711yescharacteristic, complemented, Sylow
172C2×C4⋊Q8—831no—
173C2×#106—1661no—
174C2×C4⋊C8—831no—
175C2×C4⋊C8—831no—
176C2×C4⋊C8C2×D8311yescharacteristic
177C2×C4×C8—21no—
178C2×C4×C8C2×D8311yescharacteristic
179#384—831no—
180C4×C4⋊C4C2×D8311yescharacteristic
181#340—1661no—
182#340—1661no—
183#340—1661no—
184#340—1661no—
185#340—1661no—
186#336—21no—
187#333—834no—
188C22×Q8—1661no—
189C22×C8—21no—
190C22×C8—1661no—
191C22×C8—1661no—
192C22×C8C22⋊D8311yescharacteristic
193C22×C8C22⋊D8311yescharacteristic
194C4⋊Q8—832no—
195C4⋊Q8—1661no—
196C4⋊Q8—1661no—
197C4⋊Q8—1661no—
198C2×C4⋊C4—1661no—
199C2×C4⋊C4—1661no—
200C2×C4⋊C4—1661no—
201C2×C4⋊C4—1661no—
202C2×C4⋊C4—1661no—
203C2×C4⋊C4D33211yescharacteristic
204C2×C4⋊C4D33211yescharacteristic
205C2×C42—21no—
206C2×C42C22×D8311yescharacteristic
207#106—3322no—
208C4⋊C8—21no—
209C4⋊C8—832no—
210C4⋊C8—1661no—
211C4⋊C8—1661no—
212C4⋊C8—1661no—
213C4⋊C8C4×D8312yes—
214C4×C8—21no—
215C4×C8—21no—
216C4×C8—42no—
217#95—21no—
218C2×Q8—3321no—
219C2×Q8—6641no—
220C2×Q8—6641no—
221C2×Q8—1662no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—3321no—
225C22×C4—3321no—
226C22×C4C2×C22⋊D8311yescharacteristic
227C22×C4C2×D33211yescharacteristic
228C22×C4#1305059011yescharacteristic
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—22no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—3321no—
238C2×C8—3321no—
239C2×C8—3321no—
240C2×C8—3321no—
241C2×C8—3321no—
242C2×C8—1662no—
243C2×C8#1305057812yes—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—3321no—
247C4⋊C4—3321no—
248C4⋊C4—3321no—
249C4⋊C4—3321no—
250C4⋊C4—3321no—
251C4⋊C4—3321no—
252C4⋊C4—6641no—
253C4⋊C4—1662no—
254C4⋊C4—1662no—
255C4⋊C4#1305057912yes—
256C4⋊C4Dic33212yes—
257C42—41no—
258C42—41no—
259C42C2×C4×D8311yescharacteristic
260C42#1305059011yescharacteristic
261C42#1305059011yescharacteristic
262C42#1305059011yescharacteristic
263C23#1458176611yescharacteristic
264Q8—6642no—
265Q8—6642no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—3322no—
275C2×C4—6641no—
276C2×C4—6641no—
277C2×C4—6641no—
278C2×C4—6641no—
279C2×C4—6641no—
280C2×C4#1458174911yescharacteristic
281C2×C4C4×C22⋊D8311yescharacteristic
282C2×C4C4×D33211yescharacteristic
283C2×C4#1458177511yescharacteristic
284C2×C4#1458178011yescharacteristic
285C2×C4#1458178611yescharacteristic
286C2×C4C2×#1305057811yescharacteristic
287C2×C4C2×#1305057911yescharacteristic
288C2×C4C2×Dic33211yescharacteristic
289C2×C4#1458181211yescharacteristic
290C2×C4#1458181411yescharacteristic
291C2×C4#1458181411yescharacteristic
292C2×C4#1458182211yescharacteristic
293C2×C4#1458182311yescharacteristic
294C8—22no—
295C8—41no—
296C8—42no—
297C8—3322no—
298C8—6641no—
299C22#1912759211yescharacteristic
300C22#1912790611yescharacteristic
301C22#1912792311yescharacteristic
302C22#1912793011yescharacteristic
303C22#1912794211yescharacteristic
304C22#1912796411yescharacteristic
305C22#1912797111yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—42no—
310C4—13281no—
311C4—6642no—
312C4C4×#1305057811yescharacteristic
313C4C4×#1305057911yescharacteristic
314C4C4×Dic33211yescharacteristic
315C4#1912780611yescharacteristic
316C4#1912803111yescharacteristic
317C4#1912804211yescharacteristic
318C4#1912805211yescharacteristic
319C4#1912805611yescharacteristic
320C2#2490683811yescharacteristic
321C2#2490686211yescharacteristic
322C2#2490687911yescharacteristic
323C2#2490692111yescharacteristic
324C2#2490809711yescharacteristic
325C2#2490812511yescharacteristic
326C2#2490813911yescharacteristic
subgroupG/H
centerC23#14581766
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC8×C4⋊C4×C83C2
socle, prime radicalC23×C83#121
cosocleC2×C42×C83C23
hypercenterC8×C4⋊C4D83
hypocenterC83#9567
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
18. #19127449C4semidirect
171. C83#9567semidirect

Maximal subgroups

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

subgroupindex
#249084242
#249084112
#249082262
C2×#191274492
#249053472
#249052982
C8×C4⋊C4×C832
#956783