Finite Group Databasebeta

← #35307903

Subgroups — #35307903

Order 21248.

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

normal subgroups only

This group has 402 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#24915531C211yesmaximal, characteristic
2#24908431C212yesmaximal
3C2×#19127442C212yesmaximal
4#24905344C211yesmaximal, characteristic
5C83×#1847C211yesmaximal, characteristic
6C2×#14581784C2212yes—
7C2×#14581703C2212yes—
8#19127641—22no—
9#19127633—22no—
10#19127631—21no—
11#19127631—21no—
12#19127463—22no—
13#19127463—22no—
14#19127442—24no—
15C2×#107×C83—21no—
16C2×#106×C83—21no—
17C2×#97×C83C2211yescharacteristic
18#384×C83C2211yescharacteristic
19#382×C83C2211yescharacteristic
20C22×C83⋊C8—22no—
21#14581784—22no—
22#14581784—22no—
23#14581784—22no—
24#14581784—22no—
25C2×C4⋊Dic83—21no—
26C2×C4⋊Dic83—21no—
27C2×C4⋊Dic83D412yes—
28C2×C4⋊Dic83D412yes—
29C2×Dic83⋊C4—22no—
30C2×Dic83⋊C4—22no—
31#14581703—22no—
32#14581703—22no—
33C83⋊#95—22no—
34C83⋊#95—22no—
35C83⋊#95—21no—
36C83⋊#95—21no—
37C22×C8×C83—21no—
38C2×C4⋊C4×C83—22no—
39C2×C4⋊C4×C83—21no—
40C2×C4⋊C4×C83D411yescharacteristic
41C2×C4⋊C4×C83D411yescharacteristic
42C2×C42×C83C2311yescharacteristic
43#107×C83—42no—
44#106×C83—42no—
45#97×C83—21no—
46#97×C83D412yes—
47#95×C83—22no—
48C22×Dic83—22no—
49C22×Dic83—22no—
50C2×C83⋊C8—24no—
51C2×C83⋊C8—42no—
52C2×C83⋊C8—42no—
53C4⋊Dic83—22no—
54C4⋊Dic83—22no—
55C4⋊Dic83—22no—
56C4⋊Dic83—22no—
57C4⋊Dic83—81no—
58C4⋊Dic83—81no—
59Dic83⋊C4—42no—
60Dic83⋊C4—42no—
61Dic83⋊C4—42no—
62Dic83⋊C4—42no—
63C22×C4×C83—21no—
64C22×C4×C83—21no—
65C22×C4×C83—41no—
66C22×C4×C83C2×D412yes—
67C22×C4×C83C2×D411yescharacteristic
68C2×C8×C83—22no—
69C2×C8×C83—22no—
70C2×C8×C83—22no—
71C4⋊C4×C83—41no—
72C4⋊C4×C83—41no—
73C4⋊C4×C83—41no—
74C4⋊C4×C83—41no—
75C4⋊C4×C83—44no—
76C42×C83C2×D411yescharacteristic
77C42×C83#4111yescharacteristic
78C42×C83#4112yes—
79C23×C83#12011yescharacteristic
80C2×C4×C83—21no—
81C2×C4×C83—22no—
82C2×C4×C83—21no—
83C2×C4×C83—22no—
84C2×C4×C83—41no—
85C2×C4×C83—41no—
86C2×C4×C83—42no—
87C2×C4×C83—42no—
88C2×C4×C83—81no—
89C2×C4×C83—82no—
90C2×C4×C83#12111yescharacteristic
91C2×C4×C83#12112yes—
92C2×C4×C83#12312yes—
93C2×C4×C83#12411yescharacteristic
94C2×Dic83—42no—
95C2×Dic83—42no—
96C2×Dic83—42no—
97C2×Dic83—42no—
98C2×Dic83—42no—
99C2×Dic83—42no—
100C8×C83—24no—
101C83⋊C8—44no—
102C22×C83#39411yescharacteristic
103C22×C83#45311yescharacteristic
104C22×C83#45412yes—
105C22×C83#45612yes—
106C22×C83#45611yescharacteristic
107C4×C83—22no—
108C4×C83—22no—
109C4×C83—21no—
110C4×C83—21no—
111C4×C83—81no—
112C4×C83—81no—
113C4×C83—161no—
114Dic83—82no—
115Dic83—82no—
116#10429—831nomaximal, Sylow
117C2×C83#165711yescharacteristic
118C2×C83#166011yescharacteristic
119C2×C83#166312yes—
120C2×C83#203812yes—
121C2×C83#203911yescharacteristic
122#2822—831no—
123#1992—832no—
124#1847D8311yescharacteristic
125C2×#330—832no—
126#1295—831no—
127C83#1042911yescharacteristic, complemented, Sylow
128C2×#125—832no—
129C2×#107—21no—
130C2×#106—21no—
131C2×#97—832no—
132C2×#97C2×D8311yescharacteristic
133#400—1662no—
134#398—1662no—
135#398—1661no—
136#398—1661no—
137#384C2×D8311yescharacteristic
138#382C2×D8311yescharacteristic
139#340—1662no—
140#340—1662no—
141#330—1664no—
142C22×C8—21no—
143C22×C8—1662no—
144#125—1662no—
145#125—1662no—
146#125—1662no—
147#125—1662no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—832no—
151C2×C4⋊C4—832no—
152C2×C4⋊C4—1662no—
153C2×C4⋊C4—1662no—
154C2×C4⋊C4—1661no—
155C2×C4⋊C4—1661no—
156C2×C4⋊C4C22⋊D8311yescharacteristic
157C2×C4⋊C4C22⋊D8311yescharacteristic
158C2×C42C22×D8311yescharacteristic
159#107—42no—
160#106—42no—
161#97—21no—
162#97—1662no—
163#97—1662no—
164#97D33212yes—
165#95—22no—
166#95—1662no—
167#95—1662no—
168#95—1661no—
169#95—1661no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—41no—
173C22×C4—1662no—
174C22×C4—1662no—
175C22×C4D4×D8312yes—
176C22×C4C2×C22⋊D8311yescharacteristic
177C2×C8—22no—
178C2×C8—22no—
179C2×C8—22no—
180C2×C8—3322no—
181C2×C8—3322no—
182C2×C8—1664no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—44no—
188C4⋊C4—3322no—
189C4⋊C4—3322no—
190C4⋊C4—3322no—
191C4⋊C4—3322no—
192C4⋊C4—6641no—
193C4⋊C4—6641no—
194C4⋊C4—1662no—
195C4⋊C4—1662no—
196C4⋊C4—1662no—
197C4⋊C4—1662no—
198C42C2×D33211yescharacteristic
199C42#1305059011yescharacteristic
200C42#1305059112yes—
201C23#1458176011yescharacteristic
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—81no—
211C2×C4—82no—
212C2×C4—3322no—
213C2×C4—3322no—
214C2×C4—3322no—
215C2×C4—3322no—
216C2×C4—3322no—
217C2×C4—3322no—
218C2×C4#1458176611yescharacteristic
219C2×C4#1458176712yes—
220C2×C4#1458177712yes—
221C2×C4#1458178111yescharacteristic
222C8—24no—
223C8—3324no—
224C22#1912761811yescharacteristic
225C22#1912786811yescharacteristic
226C22#1912787212yes—
227C22#1912788212yes—
228C22#1912788311yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—81no—
234C4—81no—
235C4—161no—
236C4—6642no—
237C4—6642no—
238C2#2490675911yescharacteristic
239C2#2490677211yescharacteristic
240C2#2490679012yes—
241C2#2490868212yes—
242C2#2490868711yescharacteristic
subgroupG/H
centerC23#14581760
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1847C2
socle, prime radicalC23×C83#120
hypercenter#1847D83
hypocenterC83#10429
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
127. C83#10429semidirect

Maximal subgroups

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

subgroupindex
#249155312
#249084312
C2×#191274422
#249053442
C83×#18472
#1042983