Finite Group Databasebeta

← #35315341

Subgroups — #35315341

Order 21248.

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

normal subgroups only

This group has 324 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#24918034C211yesmaximal, characteristic
2#24909259C211yesmaximal, characteristic, complemented
3#24907592C211yesmaximal, characteristic, complemented
4#24905475C211yesmaximal, characteristic, complemented
5#24905473C211yesmaximal, characteristic
6#24905471C211yesmaximal, characteristic
7C83×#1348C211yesmaximal, characteristic, complemented
8#19128237—21no—
9#19128102C411yescharacteristic, complemented
10#19128086C411yescharacteristic, complemented
11#19128057—21no—
12#19127937C2211yescharacteristic
13#19127932—21no—
14Q16×Dic83C411yescharacteristic, complemented
15#19127786—21no—
16#19127783C411yescharacteristic, complemented
17C2×C8×Dic83C2211yescharacteristic
18#19127566—21no—
19Dic83⋊C16—21no—
20C22⋊(C83⋊C16)C2211yescharacteristic
21C16×Dic83—21no—
22#19127464C2211yescharacteristic
23#19127463—21no—
24#467×C83C2211yescharacteristic
25C22⋊C16×C83C2211yescharacteristic
26#340×C83C2211yescharacteristic
27C2×#13050577—21no—
28C2×D664C2×C411yescharacteristic
29C22×C83⋊C8D411yescharacteristic
30#14581787—41no—
31#14581783—21no—
32#14581781—21no—
33#14581776—41no—
34#14581766—21no—
35Q8×Dic83—21no—
36#14581754—21no—
37(C22⋊D83)⋊C4—41no—
38#14581750—41no—
39C2×C4⋊Dic83—21no—
40C2×C4×Dic83D411yescharacteristic
41C2×C83⋊C16—21no—
42#14581726C2×C411yescharacteristic
43#14581723—21no—
44#14581716—21no—
45#14581714—21no—
46#14581712—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×D332—21no—
61C2×C22⋊D83—41no—
62C22×Dic83—41no—
63C22×Dic83D811yescharacteristic
64C22×Dic83D811yescharacteristic
65C2×C4×D83—41no—
66#13050577—42no—
67D664—41no—
68C2×C83⋊C8—41no—
69C2×C83⋊C8C22⋊C411yescharacteristic
70C2×C83⋊C8C22⋊C411yescharacteristic
71C4⋊Dic83—21no—
72C4⋊Dic83—41no—
73C4⋊Dic83—41no—
74C4⋊Dic83—41no—
75C4⋊Dic83—41no—
76Dic83⋊C4—41no—
77(C2×D83)⋊C4—41no—
78(C2×D83)⋊C4—41no—
79(C2×D83)⋊C4—41no—
80(C2×D83)⋊C4—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
101C22×D83—41no—
102Q8×C83—41no—
103Q8×C83—41no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—41no—
107C2×C4×C83—41no—
108C2×C4×C83—81no—
109C2×C4×C83—81no—
110C2×C4×C83—81no—
111C2×C4×C83C2×C22⋊C411yescharacteristic
112C2×C4×C83C2×SD1611yescharacteristic
113C22⋊D83—81no—
114C22⋊D83—81no—
115C2×Dic83—21no—
116C2×Dic83—21no—
117C2×Dic83—41no—
118C2×Dic83—41no—
119C2×Dic83—81no—
120C2×Dic83—81no—
121C2×Dic83—81no—
122C2×Dic83#10211yescharacteristic
123C2×Dic83#10211yescharacteristic
124C2×Dic83#10211yescharacteristic
125C2×Dic83#10211yescharacteristic
126D332—41no—
127D332—41no—
128C4×D83—82no—
129C8×C83—21no—
130C8×C83—21no—
131C83⋊C8—21no—
132C83⋊C8—21no—
133C22×C83—21no—
134C22×C83—21no—
135C22×C83C2×#10211yescharacteristic
136C22×C83#50811yescharacteristic
137C22×C83#50811yescharacteristic
138C2×D83—81no—
139C2×D83—81no—
140C2×D83—81no—
141C4×C83—21no—
142C4×C83—81no—
143C4×C83—81no—
144C4×C83—161no—
145C4×C83#41011yescharacteristic
146C4×C83#42111yescharacteristic
147Dic83—21no—
148Dic83—21no—
149Dic83—21no—
150Dic83—21no—
151Dic83—81no—
152Dic83—161no—
153#11855—831nomaximal, Sylow
154C2×C83—21no—
155C2×C83—21no—
156C2×C83#151711yescharacteristic
157C2×C83#213811yescharacteristic
158C2×C83#214511yescharacteristic
159D83—161no—
160#3168—831no—
161#2162—831no—
162#1835—831no—
163#1348—831no—
164#1348D8311yescharacteristic, complemented
165#1347—831no—
166#1347—831no—
167C83#1185511yescharacteristic, complemented, Sylow
168#529—1661no—
169#499—831no—
170#495—831no—
171#488—1661no—
172#467C2×D8311yescharacteristic
173#466—831no—
174#465—1661no—
175C4×Q16—831no—
176C4×SD16—1661no—
177C4×D8—831no—
178C2×C4×C8—831no—
179#382—1661no—
180C4⋊C16—1661no—
181C22⋊C16—831no—
182C22⋊C16C2×D8311yescharacteristic
183C4×C16—1661no—
184#340—831no—
185#340—1661no—
186#340C2×D8311yescharacteristic
187C2×Q16C4×D8311yescharacteristic
188C2×SD16—1661no—
189C2×D8—831no—
190C22×C8—831no—
191C22×C8C22×D8311yescharacteristic
192#126—3321no—
193#125—1661no—
194#124—1661no—
195#123—3321no—
196C22⋊Q8—21no—
197#121—1661no—
198C4×Q8—1661no—
199C4×D4—3321no—
200C4×D4—1661no—
201#117—3321no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—1661no—
204C2×C42—831no—
205C2×C16—21no—
206C2×C16—1661no—
207#107—831no—
208#107C4×D8311yescharacteristic
209#106—1661no—
210#103—21no—
211#103—1661no—
212#102—1661no—
213#102—1661no—
214C4×C8—831no—
215C4×C8—831no—
216C4×C8—831no—
217C4×C8—831no—
218#95—3321no—
219#95—3321no—
220C2×Q8—21no—
221C2×D4—3321no—
222C2×D4—1661no—
223C22×C4—41no—
224C22×C4—3321no—
225C22×C4—3321no—
226C22×C4—831no—
227C22×C4—831no—
228C22×C4D4×D8311yescharacteristic
229Q16—41no—
230SD16—3322no—
231D8—3321no—
232C2×C8—41no—
233C2×C8—3321no—
234C2×C8—831no—
235C2×C8—831no—
236C2×C8C2×C4×D8311yescharacteristic
237C2×C8D4×D8311yescharacteristic
238C4⋊C4—21no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—3321no—
243C4⋊C4—3321no—
244C4⋊C4—3321no—
245C4⋊C4—3321no—
246C4⋊C4—3321no—
247C4⋊C4—1661no—
248C22⋊C4—41no—
249C22⋊C4—3321no—
250C22⋊C4—3321no—
251C22⋊C4—3321no—
252C22⋊C4—3321no—
253C42—3321no—
254C42—831no—
255C42—831no—
256C42—831no—
257C42—831no—
258C16—41no—
259C16—3321no—
260C23—3321no—
261C23D8×D8311yescharacteristic
262Q8—41no—
263Q8—41no—
264D4—3321no—
265D4—3321no—
266D4—6641no—
267D4—6641no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—3321no—
276C2×C4—3321no—
277C2×C4—831no—
278C2×C4—831no—
279C2×C4—831no—
280C2×C4—831no—
281C2×C4—6642no—
282C2×C4—6641no—
283C2×C4—6641no—
284C2×C4—6641no—
285C2×C4—1661no—
286C2×C4—1661no—
287C2×C4C22⋊C4×D8311yescharacteristic
288C2×C4SD16×D8311yescharacteristic
289C8—21no—
290C8—21no—
291C8—1661no—
292C8—1661no—
293C22—21no—
294C22—21no—
295C22—6641no—
296C22—6641no—
297C22—6641no—
298C22#102×D8311yescharacteristic
299C22#1912813211yescharacteristic
300C22#1912813411yescharacteristic
301C4—21no—
302C4—81no—
303C4—81no—
304C4—161no—
305C4—13281no—
306C4—6641no—
307C4—1661no—
308C4—1661no—
309C4—1661no—
310C4—1661no—
311C4#1912767311yescharacteristic
312C4#1912771611yescharacteristic
313C2—21no—
314C2—21no—
315C2—13281no—
316C2#2490602111yescharacteristic
317C2#2490916911yescharacteristic
318C2#2490919711yescharacteristic
subgroupG/H
centerC22#102×D83
commutatorC2×C8×C83C22×C4
FrattiniC22×C8C22×D83
FittingC83×#1348C2
socleC22×C83C2×#102
prime radical#19127937C22
cosocleC22×C8×C83C23
hypercenter#1348D83
hypocenterC83#11855
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
2. #24909259C2semidirect
3. #24907592C2semidirect
4. #24905475C2semidirect
7. C83×#1348C2semidirect
9. #19128102C4semidirect
10. #19128086C4semidirect
14. Q16×Dic83C4semidirect
16. #19127783C4semidirect
164. #1348D83semidirect
167. C83#11855semidirect

Maximal subgroups

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

subgroupindex
#249180342
#249092592
#249075922
#249054752
#249054732
#249054712
C83×#13482
#1185583