Finite Group Databasebeta

← #35307482

Subgroups — #35307482

Order 21248.

476 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 91 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#24915738C211yesmaximal, characteristic, complemented
2#24908288C212yesmaximal
3#24905345C212yesmaximal, complemented
4#24905344C211yesmaximal, characteristic, complemented
5C83×#1961C211yesmaximal, characteristic
6C2×#14581713—22no—
7C2×#14581713—22no—
8C2×#14581703C2212yes—
9#19127635—22no—
10#19127634—22no—
11#19127633—22no—
12#19127567C2212yes—
13C2×#127×C83C2211yescharacteristic
14C2×#102×C83—22no—
15C2×#97×C83C2211yescharacteristic
16#382×C83C2211yescharacteristic
17C22×C83⋊C8—22no—
18C2×C4⋊Dic83—22no—
19C2×C4⋊Dic83D412yes—
20C2×C4⋊Dic83D412yes—
21C2×Dic83⋊C4—22no—
22C2×Dic83⋊C4—22no—
23#14581713—44no—
24#14581713—44no—
25#14581703—22no—
26#14581703—22no—
27C83⋊#95—22no—
28C83⋊#95—22no—
29C83⋊#95—22no—
30C22×D4×C83—22no—
31C22×D4×C83—21no—
32C22×C8×C83—21no—
33#127×C83—22no—
34#127×C83—21no—
35#127×C83Q812yes—
36C2×C4⋊C4×C83D412yes—
37C2×C42×C83C2311yescharacteristic
38#102×C83—44no—
39#97×C83—22no—
40#95×C83—22no—
41C22×Dic83—22no—
42C22×Dic83—22no—
43C2×C83⋊C8—24no—
44C2×C83⋊C8—42no—
45C2×C83⋊C8—42no—
46C4⋊Dic83—42no—
47C4⋊Dic83—42no—
48C4⋊Dic83—82no—
49Dic83⋊C4—82no—
50Dic83⋊C4—82no—
51C24×C83—41no—
52C2×D4×C83—24no—
53C2×D4×C83—22no—
54C2×D4×C83—42no—
55C2×D4×C83—42no—
56C2×D4×C83—42no—
57C2×D4×C83—42no—
58C2×D4×C83—42no—
59C2×D4×C83—42no—
60C2×D4×C83—42no—
61C2×D4×C83—41no—
62C22×C4×C83—22no—
63C22×C4×C83C2×D412yes—
64C22×C4×C83C2×D411yescharacteristic
65C2×C8×C83—22no—
66C2×C8×C83—41no—
67C2×C8×C83—41no—
68C4⋊C4×C83—42no—
69C42×C83C2×Q811yescharacteristic
70C42×C83#4112yes—
71C42×C83#4111yescharacteristic
72C23×C83—42no—
73C23×C83—82no—
74C23×C83—81no—
75C23×C83—82no—
76C23×C83—81no—
77C23×C83#12011yescharacteristic
78D4×C83—44no—
79D4×C83—44no—
80D4×C83—44no—
81D4×C83—82no—
82D4×C83—82no—
83D4×C83—82no—
84C2×C4×C83—21no—
85C2×C4×C83—22no—
86C2×C4×C83—21no—
87C2×C4×C83—22no—
88C2×C4×C83—42no—
89C2×C4×C83—42no—
90C2×C4×C83—42no—
91C2×C4×C83C22⋊Q812yes—
92C2×C4×C83C22⋊Q811yescharacteristic
93C2×C4×C83#12412yes—
94C2×C4×C83#12411yescharacteristic
95C2×Dic83—42no—
96C2×Dic83—42no—
97C2×Dic83—42no—
98C2×Dic83—42no—
99C2×Dic83—42no—
100C2×Dic83—42no—
101C8×C83—42no—
102C83⋊C8—44no—
103C22×C83—84no—
104C22×C83—82no—
105C22×C83—162no—
106C22×C83—161no—
107C22×C83—161no—
108C22×C83#39311yescharacteristic
109C22×C83#45312yes—
110C22×C83#45311yescharacteristic
111C22×C83#45412yes—
112C22×C83#45411yescharacteristic
113C4×C83—22no—
114C4×C83—21no—
115C4×C83—22no—
116C4×C83—21no—
117C4×C83—82no—
118Dic83—82no—
119Dic83—82no—
120#10360—831nomaximal, Sylow
121C2×C83—162no—
122C2×C83#165612yes—
123C2×C83#165611yescharacteristic
124C2×C83#165811yescharacteristic
125C2×C83#202712yes—
126C2×C83#202711yescharacteristic
127#2845—831no—
128#1961—832no—
129#1961D8311yescharacteristic
130#1295—832no—
131#1295—831no—
132C83#1036011yescharacteristic, complemented, Sylow
133C2×#127C2×D8311yescharacteristic
134C2×#102—22no—
135C2×#102—1662no—
136C2×#102—1662no—
137C2×#97—832no—
138C2×#97C2×D8311yescharacteristic
139#398—1662no—
140#398—1662no—
141#398—1662no—
142#382—832no—
143#382C2×D8311yescharacteristic
144C22×D4—22no—
145C22×D4—21no—
146C22×C8—21no—
147C22×C8—1662no—
148#127—22no—
149#127—21no—
150#127Dic16612yes—
151C2×C4⋊C4—832no—
152C2×C4⋊C4—832no—
153C2×C4⋊C4—1662no—
154C2×C4⋊C4—1662no—
155C2×C4⋊C4—1662no—
156C2×C4⋊C4C22⋊D8312yes—
157C2×C42C22×D8311yescharacteristic
158#102—44no—
159#102—3324no—
160#102—3324no—
161#97—22no—
162#97—1662no—
163#97—1662no—
164#95—22no—
165#95—1662no—
166#95—1662no—
167#95—1662no—
168C24—41no—
169C2×D4—24no—
170C2×D4—22no—
171C2×D4—42no—
172C2×D4—42no—
173C2×D4—42no—
174C2×D4—42no—
175C2×D4—42no—
176C2×D4—42no—
177C2×D4—42no—
178C2×D4—41no—
179C22×C4—22no—
180C22×C4—1662no—
181C22×C4—1662no—
182C22×C4D4×D8312yes—
183C22×C4C2×C22⋊D8311yescharacteristic
184C2×C8—22no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—3322no—
188C2×C8—3322no—
189C2×C8—1664no—
190C4⋊C4—42no—
191C4⋊C4—3322no—
192C4⋊C4—3322no—
193C4⋊C4—6642no—
194C4⋊C4—6642no—
195C4⋊C4—6642no—
196C42C2×Dic16611yescharacteristic
197C42#1305058912yes—
198C42#1305059011yescharacteristic
199C23—42no—
200C23—82no—
201C23—81no—
202C23—82no—
203C23—81no—
204C23#1458176011yescharacteristic
205D4—44no—
206D4—44no—
207D4—44no—
208D4—82no—
209D4—82no—
210D4—82no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—3322no—
219C2×C4—3322no—
220C2×C4—3322no—
221C2×C4—3322no—
222C2×C4—3322no—
223C2×C4—3322no—
224C2×C4#1458176912yes—
225C2×C4#1458177111yescharacteristic
226C2×C4#1458177812yes—
227C2×C4#1458177911yescharacteristic
228C8—42no—
229C8—3324no—
230C22—84no—
231C22—82no—
232C22—162no—
233C22—161no—
234C22—161no—
235C22#1912761311yescharacteristic
236C22#1912786712yes—
237C22#1912786811yescharacteristic
238C22#1912787212yes—
239C22#1912787311yescharacteristic
240C4—22no—
241C4—22no—
242C4—21no—
243C4—21no—
244C4—82no—
245C4—6642no—
246C4—6642no—
247C2—162no—
248C2#2490675412yes—
249C2#2490675511yescharacteristic
250C2#2490676411yescharacteristic
251C2#2490861712yes—
252C2#2490861911yescharacteristic
subgroupG/H
centerC23#14581760
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1961C2
socleC23×C83#120
prime radicalC2×#127×C83C22
hypercenter#1961D83
hypocenterC83#10360
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1961

Complements

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

NH ≅ G/Ntype
1. #24915738C2semidirect
3. #24905345C2semidirect
4. #24905344C2semidirect
132. C83#10360semidirect

Maximal subgroups

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

subgroupindex
#249157382
#249082882
#249053452
#249053442
C83×#19612
#1036083