Finite Group Databasebeta

← #35293245

Subgroups — #35293245

Order 21248.

424 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 83 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#24915451C211yesmaximal, characteristic
2#24908793C212yesmaximal
3#24905289C211yesmaximal, characteristic
4#24905285C212yesmaximal
5C83×#2016C211yesmaximal, characteristic
6C2×#14581723—22no—
7#19127640—21no—
8#19127633—22no—
9#19127608—21no—
10#19127599C2212yes—
11#19127588—22no—
12#19127463—22no—
13#19127456C2212yes—
14C22×Q16×C83—21no—
15C2×C4⋊Q8×C83C2211yescharacteristic
16C2×#103×C83—21no—
17#391×C83C2211yescharacteristic
18#336×C83C2211yescharacteristic
19C22×C83⋊C8—22no—
20C2×C4⋊Dic83—21no—
21C2×C4⋊Dic83—21no—
22C2×C4⋊Dic83D412yes—
23C2×C4⋊Dic83D412yes—
24C2×Dic83⋊C4—22no—
25C2×C4×Dic83—21no—
26#14581723—44no—
27C83⋊#95—21no—
28C83⋊#95—22no—
29C83⋊#95—22no—
30C83⋊#95—22no—
31C22×Q8×C83—21no—
32C22×Q8×C83D411yescharacteristic
33C2×Q16×C83—42no—
34C2×Q16×C83—42no—
35C2×Q16×C83—42no—
36C22×C8×C83—21no—
37C4⋊Q8×C83—42no—
38C2×C4⋊C4×C83—22no—
39C2×C4⋊C4×C83D411yescharacteristic
40C2×C42×C83C2311yescharacteristic
41#103×C83—42no—
42#95×C83—22no—
43C22×Dic83—22no—
44C22×Dic83—22no—
45C2×C83⋊C8—24no—
46C2×C83⋊C8—42no—
47C2×C83⋊C8—42no—
48C4⋊Dic83—22no—
49C4⋊Dic83—22no—
50C4⋊Dic83—42no—
51C4⋊Dic83—81no—
52C4⋊Dic83—81no—
53Dic83⋊C4—42no—
54Dic83⋊C4—42no—
55C4×Dic83—81no—
56C2×Q8×C83—21no—
57C2×Q8×C83—22no—
58C2×Q8×C83—41no—
59C2×Q8×C83—41no—
60C2×Q8×C83—41no—
61C2×Q8×C83—41no—
62C2×Q8×C83—41no—
63C2×Q8×C83—41no—
64C2×Q8×C83—41no—
65C2×Q8×C83SD1612yes—
66C22×C4×C83—21no—
67C22×C4×C83—21no—
68C22×C4×C83—41no—
69C22×C4×C83C2×D412yes—
70C22×C4×C83C2×D411yescharacteristic
71Q16×C83—48no—
72C2×C8×C83—22no—
73C2×C8×C83—41no—
74C2×C8×C83—41no—
75C4⋊C4×C83—24no—
76C4⋊C4×C83—41no—
77C4⋊C4×C83—42no—
78C42×C83—41no—
79C23×C83#12011yescharacteristic
80Q8×C83—42no—
81Q8×C83—42no—
82Q8×C83—42no—
83Q8×C83—81no—
84Q8×C83—81no—
85Q8×C83—81no—
86C2×C4×C83—21no—
87C2×C4×C83—22no—
88C2×C4×C83—22no—
89C2×C4×C83—21no—
90C2×C4×C83—22no—
91C2×C4×C83—41no—
92C2×C4×C83—41no—
93C2×C4×C83—41no—
94C2×C4×C83—42no—
95C2×C4×C83—42no—
96C2×C4×C83—81no—
97C2×C4×C83—81no—
98C2×C4×C83C2×SD1611yescharacteristic
99C2×C4×C83#13512yes—
100C2×C4×C83#13711yescharacteristic
101C2×C4×C83#13712yes—
102C2×Dic83—42no—
103C2×Dic83—42no—
104C2×Dic83—42no—
105C2×Dic83—42no—
106C2×Dic83—42no—
107C2×Dic83—42no—
108C8×C83—42no—
109C83⋊C8—44no—
110C22×C83#44811yescharacteristic
111C22×C83#45212yes—
112C22×C83#45311yescharacteristic
113C22×C83#45612yes—
114C22×C83B(4,𝔽2)11yescharacteristic
115C4×C83—21no—
116C4×C83—21no—
117C4×C83—22no—
118C4×C83—22no—
119C4×C83—42no—
120C4×C83—82no—
121C4×C83—81no—
122Dic83—82no—
123Dic83—82no—
124#7760—831nomaximal, Sylow
125C2×C83#159611yescharacteristic
126C2×C83#160312yes—
127C2×C83#163411yescharacteristic
128C2×C83#165312yes—
129C2×C83#166011yescharacteristic
130#2809—831no—
131#2058—832no—
132#2016D8311yescharacteristic
133#1272—831no—
134#1271—832no—
135C83#776011yescharacteristic, complemented, Sylow
136C22×Q16—21no—
137C2×C4⋊Q8C2×D8311yescharacteristic
138C2×#106—1662no—
139C2×#103—21no—
140#400—1661no—
141#398—1662no—
142#391—1661no—
143#391C2×D8311yescharacteristic
144#389—832no—
145#387—1662no—
146#340—1662no—
147#336—832no—
148#336C2×D8311yescharacteristic
149C22×Q8—21no—
150C22×Q8C22⋊D8311yescharacteristic
151C2×Q16—42no—
152C2×Q16—42no—
153C2×Q16—42no—
154C22×C8—21no—
155C22×C8—1662no—
156C4⋊Q8—42no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—832no—
159C2×C4⋊C4—832no—
160C2×C4⋊C4—1662no—
161C2×C4⋊C4—1661no—
162C2×C4⋊C4—1661no—
163C2×C4⋊C4C22⋊D8311yescharacteristic
164C2×C42—1661no—
165C2×C42C22×D8311yescharacteristic
166#106—3324no—
167#103—42no—
168#95—22no—
169#95—1661no—
170#95—1662no—
171#95—1662no—
172#95—1662no—
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8—41no—
182C2×Q8#1305057812yes—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—41no—
186C22×C4—1662no—
187C22×C4—1662no—
188C22×C4D4×D8312yes—
189C22×C4C2×C22⋊D8311yescharacteristic
190Q16—48no—
191C2×C8—22no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—3322no—
195C2×C8—3322no—
196C2×C8—1664no—
197C4⋊C4—24no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—3322no—
201C4⋊C4—3322no—
202C4⋊C4—3322no—
203C4⋊C4—6641no—
204C4⋊C4—6641no—
205C4⋊C4—1662no—
206C4⋊C4—1662no—
207C42—41no—
208C42—6641no—
209C23#1458176011yescharacteristic
210Q8—42no—
211Q8—42no—
212Q8—42no—
213Q8—81no—
214Q8—81no—
215Q8—81no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—81no—
227C2×C4—81no—
228C2×C4—3322no—
229C2×C4—3322no—
230C2×C4—3322no—
231C2×C4—3322no—
232C2×C4—3322no—
233C2×C4—3322no—
234C2×C4C2×#1305057811yescharacteristic
235C2×C4#1458181512yes—
236C2×C4#1458182211yescharacteristic
237C2×C4#1458182412yes—
238C8—42no—
239C8—3324no—
240C22#1912783911yescharacteristic
241C22#1912786212yes—
242C22#1912786811yescharacteristic
243C22#1912788212yes—
244C22#1912788711yescharacteristic
245C4—21no—
246C4—21no—
247C4—22no—
248C4—22no—
249C4—42no—
250C4—81no—
251C4—82no—
252C4—6642no—
253C4—6642no—
254C2#2490638511yescharacteristic
255C2#2490642512yes—
256C2#2490660611yescharacteristic
257C2#2490673812yes—
258C2#2490677211yescharacteristic
subgroupG/H
centerC23#14581760
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#2016C2
socle, prime radicalC23×C83#120
hypercenter#2016D83
hypocenterC83#7760
LCSG ▷ C2×C42×C83 ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2016

Complements

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

NH ≅ G/Ntype
135. C83#7760semidirect

Maximal subgroups

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

subgroupindex
#249154512
#249087932
#249052892
#249052852
C83×#20162
#776083