Finite Group Databasebeta

← #35302821

Subgroups — #35302821

Order 21248.

370 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#24908423C211yesmaximal, characteristic
2#24908411C211yesmaximal, characteristic
3#24907332C211yesmaximal, characteristic
4C2×#19127449C211yesmaximal, characteristic
5#24905346C211yesmaximal, characteristic
6#24905297C211yesmaximal, characteristic
7C83×#1947C211yesmaximal, characteristic
8C2×#14581792C2211yescharacteristic
9C2×C4⋊(C83⋊C8)C2211yescharacteristic
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11C2×#14581703—21no—
12C2×C4×C83⋊C8C2211yescharacteristic
13#19127463—21no—
14#19127463—21no—
15#19127463—21no—
16#19127463—21no—
17#19127456—21no—
18#19127449C414yescomplemented
19C2×#107×C83—21no—
20C2×C4⋊C8×C83C2211yescharacteristic
21#384×C83C2211yescharacteristic
22C4×C4⋊C4×C83C2211yescharacteristic
23#340×C83—21no—
24C22×Dic166—21no—
25C22×C83⋊C8—21no—
26C22×C83⋊C8—21no—
27C22×C83⋊C8D411yescharacteristic
28C22×C83⋊C8D411yescharacteristic
29#14581792—21no—
30#14581792—21no—
31#14581792—21no—
32#14581792C2×C412yes—
33C2×C4⋊Dic83—21no—
34C2×C4⋊Dic83—21no—
35C4⋊(C83⋊C8)—21no—
36C4⋊(C83⋊C8)—21no—
37C4⋊(C83⋊C8)—21no—
38C4⋊(C83⋊C8)C2×C412yes—
39#14581703—42no—
40C4×C83⋊C8—21no—
41C4×C83⋊C8—21no—
42C22×C8×C83—21no—
43C2×C4⋊C4×C83—21no—
44C2×C4⋊C4×C83—21no—
45C2×C4⋊C4×C83—21no—
46C2×C4⋊C4×C83D411yescharacteristic
47C2×C4⋊C4×C83D411yescharacteristic
48C2×C42×C83—21no—
49C2×C42×C83C2311yescharacteristic
50#107×C83—42no—
51C4⋊C8×C83—21no—
52C4⋊C8×C83C2×C412yes—
53#95×C83—21no—
54C2×Dic166—22no—
55C2×Dic166—41no—
56C2×Dic166—81no—
57C2×Dic166—81no—
58C22×Dic83—41no—
59C2×C83⋊C8—21no—
60C2×C83⋊C8—21no—
61C2×C83⋊C8—22no—
62C2×C83⋊C8—21no—
63C2×C83⋊C8—21no—
64C2×C83⋊C8—21no—
65C2×C83⋊C8—41no—
66C2×C83⋊C8—41no—
67C2×C83⋊C8—41no—
68C2×C83⋊C8—41no—
69C2×C83⋊C8—41no—
70C2×C83⋊C8Q1612yes—
71C4⋊Dic83—22no—
72C4⋊Dic83—22no—
73C4⋊Dic83—41no—
74C4⋊Dic83—41no—
75C22×C4×C83—21no—
76C22×C4×C83—21no—
77C22×C4×C83—41no—
78C22×C4×C83C2×D411yescharacteristic
79C22×C4×C83C2×D411yescharacteristic
80C22×C4×C83#4111yescharacteristic
81C2×C8×C83—22no—
82C2×C8×C83—41no—
83C2×C8×C83—41no—
84C4⋊C4×C83—21no—
85C4⋊C4×C83—21no—
86C4⋊C4×C83—21no—
87C4⋊C4×C83—21no—
88C4⋊C4×C83—41no—
89C4⋊C4×C83—41no—
90C4⋊C4×C83—41no—
91C4⋊C4×C83—41no—
92C4⋊C4×C83—81no—
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—41no—
103C2×C4×C83—41no—
104C2×C4×C83—41no—
105C2×C4×C83—41no—
106C2×C4×C83—41no—
107C2×C4×C83—41no—
108C2×C4×C83—81no—
109C2×C4×C83—81no—
110C2×C4×C83—81no—
111C2×C4×C83#11711yescharacteristic
112C2×C4×C83C4×D411yescharacteristic
113C2×C4×C83C4×D411yescharacteristic
114C2×C4×C83#12311yescharacteristic
115C2×C4×C83#12411yescharacteristic
116C2×C4×C83#12611yescharacteristic
117C2×C4×C83C2×Q1611yescharacteristic
118C2×C4×C83#13511yescharacteristic
119C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C83#13711yescharacteristic
122C2×C4×C83#13711yescharacteristic
123C2×C4×C83#13711yescharacteristic
124C2×C4×C83#13711yescharacteristic
125C2×Dic83—42no—
126C2×Dic83—81no—
127C2×Dic83—81no—
128Dic166—82no—
129Dic166—82no—
130C8×C83—42no—
131C83⋊C8—22no—
132C83⋊C8—42no—
133C83⋊C8—41no—
134C83⋊C8—81no—
135C22×C83#38811yescharacteristic
136C22×C83#46211yescharacteristic
137C22×C83#46311yescharacteristic
138C22×C83#46811yescharacteristic
139C22×C83#47011yescharacteristic
140C22×C83#47111yescharacteristic
141C22×C83#47211yescharacteristic
142C4×C83—21no—
143C4×C83—21no—
144C4×C83—81no—
145C4×C83—81no—
146C4×C83—161no—
147C4×C83C4×Q1611yescharacteristic
148C4×C83#44011yescharacteristic
149C4×C83#44011yescharacteristic
150C4×C83#44111yescharacteristic
151C4×C83#48411yescharacteristic
152C4×C83#48511yescharacteristic
153C4×C83#48911yescharacteristic
154C4×C83#49111yescharacteristic
155Dic83—82no—
156#9576—831nomaximal, Sylow
157C2×C83#169211yescharacteristic
158C2×C83#169611yescharacteristic
159C2×C83#169711yescharacteristic
160C2×C83#170311yescharacteristic
161C2×C83#192811yescharacteristic
162C2×C83#193111yescharacteristic
163C2×C83#193511yescharacteristic
164#1990—831no—
165#1987—831no—
166#1947D8311yescharacteristic
167#1770—831no—
168C2×#333—831no—
169#1296—831no—
170#1277—831no—
171C83#957611yescharacteristic, complemented, Sylow
172C2×C4⋊Q8—831no—
173C2×#107—21no—
174C2×C4⋊C8—831no—
175C2×C4⋊C8—831no—
176C2×C4⋊C8C2×D8311yescharacteristic
177C2×#97—1661no—
178C2×C4×C8—831no—
179#384C2×D8311yescharacteristic
180C4×C4⋊C4C2×D8311yescharacteristic
181#340—21no—
182#340—1661no—
183#340—1661no—
184#340—1661no—
185#340—1661no—
186#336—1661no—
187#333—834no—
188C22×Q8—1661no—
189C22×C8—21no—
190C22×C8—831no—
191C22×C8—831no—
192C22×C8—1661no—
193C22×C8—1661no—
194C4⋊Q8—832no—
195C4⋊Q8—1661no—
196C4⋊Q8—1661no—
197C4⋊Q8—1661no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—1661no—
202C2×C4⋊C4—1661no—
203C2×C4⋊C4C22⋊D8311yescharacteristic
204C2×C4⋊C4C22⋊D8311yescharacteristic
205C2×C42—21no—
206C2×C42C22×D8311yescharacteristic
207#107—42no—
208C4⋊C8—21no—
209C4⋊C8—832no—
210C4⋊C8—1661no—
211C4⋊C8—1661no—
212C4⋊C8—1661no—
213C4⋊C8C4×D8312yes—
214#97—3322no—
215C4×C8—1661no—
216C4×C8—1661no—
217#95—21no—
218C2×Q8—3321no—
219C2×Q8—6641no—
220C2×Q8—6641no—
221C2×Q8—1662no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—3321no—
226C22×C4D4×D8311yescharacteristic
227C22×C4C2×C22⋊D8311yescharacteristic
228C22×C4#1305058911yescharacteristic
229C2×C8—22no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—3321no—
233C2×C8—3321no—
234C2×C8—3321no—
235C2×C8—3321no—
236C2×C8—3321no—
237C2×C8—832no—
238C2×C8—1661no—
239C2×C8—1661no—
240C2×C8—1661no—
241C2×C8—1662no—
242C2×C8—1661no—
243C2×C8—1661no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—81no—
253C4⋊C4—3321no—
254C4⋊C4—3321no—
255C4⋊C4—1662no—
256C4⋊C4—1662no—
257C42—41no—
258C42—41no—
259C42C2×C4×D8311yescharacteristic
260C42#1305059011yescharacteristic
261C42#1305059111yescharacteristic
262C42#1305059111yescharacteristic
263C23#1458176411yescharacteristic
264Q8—6642no—
265Q8—6642no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—3322no—
278C2×C4—6641no—
279C2×C4—6641no—
280C2×C4#1458175011yescharacteristic
281C2×C4C4×C22⋊D8311yescharacteristic
282C2×C4#1458175411yescharacteristic
283C2×C4#1458177711yescharacteristic
284C2×C4#1458178111yescharacteristic
285C2×C4#1458178711yescharacteristic
286C2×C4Q16×D8311yescharacteristic
287C2×C4#1458181111yescharacteristic
288C2×C4#1458181611yescharacteristic
289C2×C4#1458181811yescharacteristic
290C2×C4#1458182211yescharacteristic
291C2×C4#1458182211yescharacteristic
292C2×C4#1458182311yescharacteristic
293C2×C4#1458182411yescharacteristic
294C8—42no—
295C8—3321no—
296C8—3322no—
297C8—6641no—
298C8—1662no—
299C22#1912759111yescharacteristic
300C22#1912790911yescharacteristic
301C22#1912791411yescharacteristic
302C22#1912794511yescharacteristic
303C22#1912795711yescharacteristic
304C22#1912796611yescharacteristic
305C22#1912796911yescharacteristic
306C4—21no—
307C4—21no—
308C4—81no—
309C4—81no—
310C4—161no—
311C4—6642no—
312C4#1912779511yescharacteristic
313C4#1912780011yescharacteristic
314C4#1912780111yescharacteristic
315C4#1912780611yescharacteristic
316C4#1912803811yescharacteristic
317C4#1912804411yescharacteristic
318C4#1912806311yescharacteristic
319C4#1912807111yescharacteristic
320C2#2490696711yescharacteristic
321C2#2490698911yescharacteristic
322C2#2490699411yescharacteristic
323C2#2490703611yescharacteristic
324C2#2490810311yescharacteristic
325C2#2490812411yescharacteristic
326C2#2490815211yescharacteristic
subgroupG/H
centerC23#14581764
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1947C2
socle, prime radicalC23×C83#121
cosocleC2×C42×C83C23
hypercenter#1947D83
hypocenterC83#9576
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
18. #19127449C4semidirect
171. C83#9576semidirect

Maximal subgroups

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

subgroupindex
#249084232
#249084112
#249073322
C2×#191274492
#249053462
#249052972
C83×#19472
#957683