Finite Group Databasebeta

← #35307477

Subgroups — #35307477

Order 21248.

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

normal subgroups only

This group has 400 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#24915735C211yesmaximal, characteristic
2#24908437C212yesmaximal
3#24905345C212yesmaximal
4#24905344C211yesmaximal, characteristic
5C83×#1960C211yesmaximal, characteristic
6C2×#14581703C2212yes—
7#19127643—22no—
8#19127640—21no—
9#19127622—22no—
10#19127621—21no—
11#19127567C2212yes—
12#19127463—22no—
13#19127463—22no—
14C2×C4⋊Q8×C83C2211yescharacteristic
15C2×#103×C83—21no—
16C2×#103×C83—21no—
17C2×#97×C83C2211yescharacteristic
18#382×C83C2211yescharacteristic
19C22×Dic166—21no—
20C22×C83⋊C8—22no—
21C2×C4⋊Dic83—21no—
22C2×C4⋊Dic83D412yes—
23C2×C4⋊Dic83D412yes—
24C2×Dic83⋊C4—22no—
25#14581703—22no—
26#14581703—22no—
27C83⋊#95—21no—
28C83⋊#95—22no—
29C83⋊#95—21no—
30C83⋊#95—22no—
31C83⋊#95—22no—
32C22×Q8×C83—21no—
33C22×C8×C83—21no—
34C4⋊Q8×C83—22no—
35C4⋊Q8×C83—21no—
36C4⋊Q8×C83Q812yescomplemented
37C2×C4⋊C4×C83—22no—
38C2×C4⋊C4×C83D411yescharacteristic
39C2×C4⋊C4×C83D411yescharacteristic
40C2×C42×C83C2311yescharacteristic
41#103×C83—42no—
42#103×C83—42no—
43#97×C83—22no—
44#95×C83—22no—
45C2×Dic166—81no—
46C2×Dic166—82no—
47C22×Dic83—22no—
48C22×Dic83—22no—
49C2×C83⋊C8—24no—
50C2×C83⋊C8—42no—
51C2×C83⋊C8—42no—
52C4⋊Dic83—42no—
53C4⋊Dic83—42no—
54C4⋊Dic83—81no—
55Dic83⋊C4—82no—
56C2×Q8×C83—22no—
57C2×Q8×C83—41no—
58C2×Q8×C83—41no—
59C2×Q8×C83—41no—
60C2×Q8×C83—41no—
61C2×Q8×C83—41no—
62C22×C4×C83—21no—
63C22×C4×C83—21no—
64C22×C4×C83—41no—
65C22×C4×C83C2×D412yes—
66C22×C4×C83C2×D411yescharacteristic
67C2×C8×C83—22no—
68C2×C8×C83—41no—
69C2×C8×C83—41no—
70C4⋊C4×C83—24no—
71C4⋊C4×C83—41no—
72C4⋊C4×C83—41no—
73C4⋊C4×C83—42no—
74C42×C83C2×Q811yescharacteristic
75C42×C83#4112yes—
76C42×C83#4111yescharacteristic
77C23×C83#12011yescharacteristic
78Q8×C83—42no—
79Q8×C83—42no—
80Q8×C83—81no—
81Q8×C83—81no—
82C2×C4×C83—21no—
83C2×C4×C83—21no—
84C2×C4×C83—22no—
85C2×C4×C83—22no—
86C2×C4×C83—42no—
87C2×C4×C83—41no—
88C2×C4×C83—41no—
89C2×C4×C83—42no—
90C2×C4×C83—42no—
91C2×C4×C83—81no—
92C2×C4×C83—81no—
93C2×C4×C83C22⋊Q812yes—
94C2×C4×C83C22⋊Q811yescharacteristic
95C2×C4×C83#12412yes—
96C2×C4×C83#12411yescharacteristic
97C2×Dic83—42no—
98C2×Dic83—42no—
99C2×Dic83—42no—
100C2×Dic83—42no—
101C2×Dic83—42no—
102C2×Dic83—42no—
103Dic166—84no—
104C8×C83—42no—
105C83⋊C8—44no—
106C22×C83#39311yescharacteristic
107C22×C83#45311yescharacteristic
108C22×C83#45411yescharacteristic
109C22×C83#45512yes—
110C22×C83#45612yes—
111C4×C83—21no—
112C4×C83—21no—
113C4×C83—22no—
114C4×C83—22no—
115C4×C83—81no—
116C4×C83—81no—
117C4×C83—82no—
118Dic83—82no—
119Dic83—82no—
120#10359—831nomaximal, Sylow
121C2×C83#165911yescharacteristic
122C2×C83#166011yescharacteristic
123C2×C83#166412yes—
124C2×C83#202711yescharacteristic
125C2×C83#202812yes—
126#2844—831no—
127#1993—832no—
128#1960D8311yescharacteristic
129#1295—832no—
130#1295—831no—
131C83#1035911yescharacteristic, complemented, Sylow
132C2×C4⋊Q8C2×D8311yescharacteristic
133C2×#103—21no—
134C2×#103—21no—
135C2×#97—832no—
136C2×#97C2×D8311yescharacteristic
137#400—1662no—
138#400—1661no—
139#395—1662no—
140#395—1661no—
141#382—832no—
142#382C2×D8311yescharacteristic
143#340—1662no—
144#340—1662no—
145C22×Q8—21no—
146C22×Q8—1661no—
147C22×C8—21no—
148C22×C8—1662no—
149C4⋊Q8—22no—
150C4⋊Q8—21no—
151C4⋊Q8Dic16612yescomplemented
152C2×C4⋊C4—22no—
153C2×C4⋊C4—832no—
154C2×C4⋊C4—832no—
155C2×C4⋊C4—1662no—
156C2×C4⋊C4—1661no—
157C2×C4⋊C4C22⋊D8311yescharacteristic
158C2×C4⋊C4C22⋊D8311yescharacteristic
159C2×C42C22×D8311yescharacteristic
160#103—42no—
161#103—42no—
162#97—22no—
163#97—1662no—
164#97—1662no—
165#95—22no—
166#95—1662no—
167#95—1661no—
168#95—1661no—
169#95—1662no—
170#95—1662no—
171C2×Q8—22no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—6641no—
178C2×Q8—6642no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—1662no—
183C22×C4—1662no—
184C22×C4D4×D8312yes—
185C22×C4C2×C22⋊D8311yescharacteristic
186C2×C8—22no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—3322no—
190C2×C8—3322no—
191C2×C8—1664no—
192C4⋊C4—24no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C4⋊C4—3322no—
197C4⋊C4—3322no—
198C4⋊C4—6642no—
199C4⋊C4—6641no—
200C42C2×Dic16611yescharacteristic
201C42#1305058912yes—
202C42#1305059011yescharacteristic
203C23#1458176011yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—81no—
207Q8—81no—
208Q8—6644no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—3322no—
221C2×C4—3322no—
222C2×C4—3322no—
223C2×C4—3322no—
224C2×C4—3322no—
225C2×C4—3322no—
226C2×C4#1458176912yes—
227C2×C4#1458177111yescharacteristic
228C2×C4#1458177812yes—
229C2×C4#1458177911yescharacteristic
230C8—42no—
231C8—3324no—
232C22#1912761311yescharacteristic
233C22#1912786811yescharacteristic
234C22#1912787311yescharacteristic
235C22#1912787712yes—
236C22#1912788212yes—
237C4—21no—
238C4—21no—
239C4—22no—
240C4—22no—
241C4—81no—
242C4—81no—
243C4—82no—
244C4—6642no—
245C4—6642no—
246C2#2490676711yescharacteristic
247C2#2490677211yescharacteristic
248C2#2490679412yes—
249C2#2490861911yescharacteristic
250C2#2490862212yes—
subgroupG/H
centerC23#14581760
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1960C2
socle, prime radicalC23×C83#120
hypercenter#1960D83
hypocenterC83#10359
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
36. C4⋊Q8×C83Q8semidirect
131. C83#10359semidirect
151. C4⋊Q8Dic166semidirect

Maximal subgroups

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

subgroupindex
#249157352
#249084372
#249053452
#249053442
C83×#19602
#1035983