Finite Group Databasebeta

← #35315356

Subgroups — #35315356

Order 21248.

314 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 79 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#24918044C211yesmaximal, characteristic
2#24909263C211yesmaximal, characteristic
3#24907592C211yesmaximal, characteristic
4#24905476C211yesmaximal, characteristic
5#24905475C211yesmaximal, characteristic
6#24905474C211yesmaximal, characteristic
7C83×#1348C211yesmaximal, characteristic
8#19128253—21no—
9#19128105C411yescharacteristic, complemented
10#19128079C411yescharacteristic, complemented
11#19128050—21no—
12#19127942C2211yescharacteristic
13#19127940—21no—
14Q16×Dic83C411yescharacteristic, complemented
15#19127795C411yescharacteristic, complemented
16#19127793—21no—
17C2×C8×Dic83C2211yescharacteristic
18#19127566—21no—
19Dic83⋊C16—21no—
20C22⋊(C83⋊C16)C2211yescharacteristic
21#19127476—21no—
22#19127464C2211yescharacteristic
23#19127463—21no—
24#467×C83C2211yescharacteristic
25C22⋊C16×C83C2211yescharacteristic
26#340×C83C2211yescharacteristic
27C2×Dic332C2×C411yescharacteristic
28C2×#13050580—21no—
29C22×C83⋊C8D411yescharacteristic
30#14581791—21no—
31#14581790—21no—
32#14581782—41no—
33#14581771—21no—
34#14581769—41no—
35Q8×Dic83—21no—
36#14581757—21no—
37#14581757—41no—
38#14581748—41no—
39C2×C4⋊Dic83—21no—
40C2×C4×Dic83D411yescharacteristic
41C2×C83⋊C16—21no—
42#14581726C2×C411yescharacteristic
43#14581725—21no—
44#14581717—21no—
45#14581716—21no—
46#14581715—21no—
47C8×Dic83C2×C411yescharacteristic
48C8×Dic83C2×C411yescharacteristic
49C8×Dic83D411yescharacteristic
50C8×Dic83D411yescharacteristic
51C83⋊#95—41no—
52C83⋊#95—41no—
53C2×Q16×C83C2×C411yescharacteristic
54C22×C8×C83C2311yescharacteristic
55C22⋊Q8×C83—21no—
56C2×C4⋊C4×C83—21no—
57C2×C16×C83—21no—
58#107×C83C2×C411yescharacteristic
59#103×C83—21no—
60C2×Dic166—21no—
61C2×Dic166—41no—
62C22×Dic83—41no—
63C22×Dic83D811yescharacteristic
64C22×Dic83D811yescharacteristic
65Dic332—41no—
66#13050580—42no—
67C2×C83⋊C8—41no—
68C2×C83⋊C8C22⋊C411yescharacteristic
69C2×C83⋊C8C22⋊C411yescharacteristic
70C4⋊Dic83—21no—
71C4⋊Dic83—41no—
72C4⋊Dic83—41no—
73C4⋊Dic83—41no—
74Dic83⋊C4—41no—
75Dic83⋊C4—41no—
76Dic83⋊C4—41no—
77Dic83⋊C4—41no—
78Dic83⋊C4—41no—
79C22⋊Dic83—41no—
80C4×Dic83—41no—
81C4×Dic83—41no—
82C4×Dic83C22⋊C411yescharacteristic
83C4×Dic83C22⋊C411yescharacteristic
84C4×Dic83SD1611yescharacteristic
85C4×Dic83SD1611yescharacteristic
86C83⋊C16—41no—
87C2×Q8×C83—21no—
88C22×C4×C83—41no—
89C22×C4×C83C2×D411yescharacteristic
90Q16×C83—41no—
91C2×C8×C83—41no—
92C2×C8×C83C22×C411yescharacteristic
93C2×C8×C83C2×D411yescharacteristic
94C4⋊C4×C83—21no—
95C4⋊C4×C83—41no—
96C4⋊C4×C83—41no—
97C4⋊C4×C83—41no—
98C22⋊C4×C83—41no—
99C16×C83—41no—
100C23×C83C2×D811yescharacteristic
101Q8×C83—41no—
102Q8×C83—41no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—41no—
106C2×C4×C83—41no—
107C2×C4×C83—81no—
108C2×C4×C83—81no—
109C2×C4×C83—81no—
110C2×C4×C83C2×C22⋊C411yescharacteristic
111C2×C4×C83C2×SD1611yescharacteristic
112C2×Dic83—21no—
113C2×Dic83—21no—
114C2×Dic83—41no—
115C2×Dic83—41no—
116C2×Dic83—41no—
117C2×Dic83—81no—
118C2×Dic83—81no—
119C2×Dic83—81no—
120C2×Dic83#10211yescharacteristic
121C2×Dic83#10211yescharacteristic
122C2×Dic83#10211yescharacteristic
123C2×Dic83#10211yescharacteristic
124Dic166—41no—
125Dic166—41no—
126Dic166—82no—
127C8×C83—21no—
128C8×C83—21no—
129C83⋊C8—21no—
130C83⋊C8—21no—
131C22×C83—21no—
132C22×C83—21no—
133C22×C83C2×#10211yescharacteristic
134C22×C83#51011yescharacteristic
135C22×C83#51011yescharacteristic
136C4×C83—21no—
137C4×C83—81no—
138C4×C83—81no—
139C4×C83—161no—
140C4×C83#41011yescharacteristic
141C4×C83#42111yescharacteristic
142Dic83—21no—
143Dic83—21no—
144Dic83—21no—
145Dic83—21no—
146Dic83—81no—
147Dic83—81no—
148Dic83—161no—
149#11859—831nomaximal, Sylow
150C2×C83—21no—
151C2×C83—21no—
152C2×C83#151711yescharacteristic
153C2×C83#214111yescharacteristic
154C2×C83#214511yescharacteristic
155#3170—831no—
156#2163—831no—
157#1835—831no—
158#1348—831no—
159#1348—831no—
160#1348—831no—
161#1348D8311yescharacteristic
162C83#1185911yescharacteristic, complemented, Sylow
163#533—1661no—
164#500—831no—
165#494—831no—
166#487—1661no—
167#467—831no—
168#467—1661no—
169#467C2×D8311yescharacteristic
170C4×Q16—831no—
171C4×Q16—831no—
172C4×Q16—1661no—
173C2×C4×C8—831no—
174#382—1661no—
175C4⋊C16—1661no—
176C22⋊C16—831no—
177C22⋊C16C2×D8311yescharacteristic
178#346—1661no—
179#340—831no—
180#340—1661no—
181#340C2×D8311yescharacteristic
182C2×Q16—831no—
183C2×Q16—1661no—
184C2×Q16C4×D8311yescharacteristic
185C22×C8—831no—
186C22×C8C22×D8311yescharacteristic
187C4⋊Q8—1661no—
188C4⋊Q8—1661no—
189#125—3321no—
190C22⋊Q8—21no—
191C22⋊Q8—3321no—
192C22⋊Q8—1661no—
193C4×Q8—3321no—
194C4×Q8—1661no—
195C4×Q8—1661no—
196#117—3321no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—1661no—
199C2×C42—831no—
200C2×C16—21no—
201C2×C16—1661no—
202#107—831no—
203#107—1661no—
204#107C4×D8311yescharacteristic
205#103—21no—
206#103—1661no—
207#103—1661no—
208#103—1661no—
209C4×C8—831no—
210C4×C8—831no—
211C4×C8—831no—
212C4×C8—831no—
213#95—3321no—
214#95—3321no—
215C2×Q8—21no—
216C2×Q8—3321no—
217C2×Q8—1661no—
218C22×C4—41no—
219C22×C4—3321no—
220C22×C4—831no—
221C22×C4—831no—
222C22×C4D4×D8311yescharacteristic
223Q16—41no—
224Q16—3321no—
225Q16—3322no—
226C2×C8—41no—
227C2×C8—3321no—
228C2×C8—831no—
229C2×C8—831no—
230C2×C8C2×C4×D8311yescharacteristic
231C2×C8D4×D8311yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—3321no—
237C4⋊C4—3321no—
238C4⋊C4—3321no—
239C4⋊C4—3321no—
240C4⋊C4—3321no—
241C4⋊C4—3321no—
242C4⋊C4—3321no—
243C4⋊C4—3321no—
244C4⋊C4—1661no—
245C22⋊C4—41no—
246C22⋊C4—3321no—
247C42—3321no—
248C42—3321no—
249C42—831no—
250C42—831no—
251C42—831no—
252C42—831no—
253C16—41no—
254C16—3321no—
255C23D8×D8311yescharacteristic
256Q8—41no—
257Q8—41no—
258Q8—3321no—
259Q8—3321no—
260Q8—6642no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—3321no—
269C2×C4—3321no—
270C2×C4—3321no—
271C2×C4—831no—
272C2×C4—831no—
273C2×C4—831no—
274C2×C4—831no—
275C2×C4—6641no—
276C2×C4—6641no—
277C2×C4—6641no—
278C2×C4—1661no—
279C2×C4—1661no—
280C2×C4C22⋊C4×D8311yescharacteristic
281C2×C4SD16×D8311yescharacteristic
282C8—21no—
283C8—21no—
284C8—1661no—
285C8—1661no—
286C22—21no—
287C22—21no—
288C22#102×D8311yescharacteristic
289C22#1912814011yescharacteristic
290C22#1912814311yescharacteristic
291C4—21no—
292C4—81no—
293C4—81no—
294C4—161no—
295C4—13281no—
296C4—6641no—
297C4—6641no—
298C4—1661no—
299C4—1661no—
300C4—1661no—
301C4—1661no—
302C4#1912767311yescharacteristic
303C4#1912771611yescharacteristic
304C2—21no—
305C2—21no—
306C2#2490602111yescharacteristic
307C2#2490918111yescharacteristic
308C2#2490919711yescharacteristic
subgroupG/H
centerC22#102×D83
commutatorC2×C8×C83C22×C4
FrattiniC22×C8C22×D83
FittingC83×#1348C2
socleC22×C83C2×#102
prime radicalC23×C83C2×D8
cosocleC22×C8×C83C23
hypercenter#1348D83
hypocenterC83#11859
LCSG ▷ C2×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1348

Complements

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

NH ≅ G/Ntype
9. #19128105C4semidirect
10. #19128079C4semidirect
14. Q16×Dic83C4semidirect
15. #19127795C4semidirect
162. C83#11859semidirect

Maximal subgroups

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

subgroupindex
#249180442
#249092632
#249075922
#249054762
#249054752
#249054742
C83×#13482
#1185983