Finite Group Databasebeta

← #35307900

Subgroups — #35307900

Order 21248.

402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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#24908433C212yesmaximal
2#24907632C211yesmaximal, characteristic
3C2×#19127443C212yesmaximal
4#24905344C211yesmaximal, characteristic
5C83×#2822C211yesmaximal, characteristic
6C2×#14581725—21no—
7C2×#14581723—21no—
8C2×#14581703C2212yes—
9C2×#14581703C2211yescharacteristic
10#19127571C2211yescharacteristic
11#19127463—22no—
12#19127463—22no—
13#19127443—24no—
14C2×#125×C83C2212yes—
15#400×C83—22no—
16#398×C83—21no—
17#398×C83—21no—
18#398×C83—22no—
19#382×C83C2211yescharacteristic
20C22×C83⋊C8—21no—
21C22×C83⋊C8—22no—
22C2×C4⋊Dic83—22no—
23C2×C4⋊Dic83—21no—
24#14581725—42no—
25#14581723—42no—
26#14581703—22no—
27#14581703—21no—
28#14581703—22no—
29#14581703D412yes—
30#125×C83—22no—
31#125×C83—22no—
32#125×C83—22no—
33#125×C83—22no—
34C2×C4⋊C4×C83—22no—
35C2×C4⋊C4×C83—22no—
36C2×C4⋊C4×C83—21no—
37C2×C4⋊C4×C83—21no—
38C2×C4⋊C4×C83D412yes—
39C2×C4⋊C4×C83D412yes—
40C2×C4⋊C4×C83D411yescharacteristic
41C2×C4⋊C4×C83D411yescharacteristic
42C2×C42×C83C2311yescharacteristic
43#95×C83—22no—
44#95×C83—22no—
45#95×C83—21no—
46#95×C83—21no—
47#95×C83—22no—
48C22×Dic83—41no—
49C2×C83⋊C8—22no—
50C2×C83⋊C8—22no—
51C2×C83⋊C8—22no—
52C2×C83⋊C8—24no—
53C2×C83⋊C8—42no—
54C2×C83⋊C8—42no—
55C4⋊Dic83—41no—
56C4⋊Dic83—41no—
57C4⋊Dic83—44no—
58C22×C4×C83—21no—
59C22×C4×C83—21no—
60C22×C4×C83—22no—
61C22×C4×C83—22no—
62C22×C4×C83C2×D412yes—
63C22×C4×C83C2×D411yescharacteristic
64C4⋊C4×C83—22no—
65C4⋊C4×C83—22no—
66C4⋊C4×C83—22no—
67C4⋊C4×C83—22no—
68C4⋊C4×C83—41no—
69C4⋊C4×C83—41no—
70C4⋊C4×C83—42no—
71C4⋊C4×C83—42no—
72C4⋊C4×C83—42no—
73C4⋊C4×C83—42no—
74C4⋊C4×C83—81no—
75C4⋊C4×C83—81no—
76C42×C83C2×D411yescharacteristic
77C42×C83#4111yescharacteristic
78C42×C83#4112yes—
79C23×C83#12011yescharacteristic
80C2×C4×C83—21no—
81C2×C4×C83—22no—
82C2×C4×C83—22no—
83C2×C4×C83—21no—
84C2×C4×C83—42no—
85C2×C4×C83—42no—
86C2×C4×C83—41no—
87C2×C4×C83—41no—
88C2×C4×C83—42no—
89C2×C4×C83—42no—
90C2×C4×C83—42no—
91C2×C4×C83—42no—
92C2×C4×C83—42no—
93C2×C4×C83—42no—
94C2×C4×C83#12111yescharacteristic
95C2×C4×C83#12112yes—
96C2×C4×C83#12312yes—
97C2×C4×C83#12411yescharacteristic
98C2×Dic83—81no—
99C2×Dic83—82no—
100C83⋊C8—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—82no—
114C4×C83—82no—
115Dic83—161no—
116#10429—831nomaximal, Sylow
117C2×C83#165711yescharacteristic
118C2×C83#166011yescharacteristic
119C2×C83#166312yes—
120C2×C83#203812yes—
121C2×C83#203911yescharacteristic
122#2822D8311yescharacteristic
123#1992—832no—
124#1847—831no—
125C2×#330—832no—
126#1295—831no—
127C83#1042911yescharacteristic, complemented, Sylow
128C2×#125C2×D8312yes—
129C2×#107—1661no—
130C2×#106—1661no—
131C2×#97—831no—
132C2×#97—832no—
133#400—22no—
134#398—21no—
135#398—21no—
136#398—22no—
137#384—831no—
138#382C2×D8311yescharacteristic
139#340—1662no—
140#340—1662no—
141#330—1664no—
142C22×C8—1662no—
143C22×C8—1661no—
144#125—22no—
145#125—22no—
146#125—22no—
147#125—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—1662no—
153C2×C4⋊C4—1661no—
154C2×C4⋊C4C22⋊D8312yes—
155C2×C4⋊C4C22⋊D8312yes—
156C2×C4⋊C4C22⋊D8311yescharacteristic
157C2×C4⋊C4C22⋊D8311yescharacteristic
158C2×C42C22×D8311yescharacteristic
159#107—3322no—
160#106—3322no—
161#97—832no—
162#97—1662no—
163#97—1662no—
164#97—1661no—
165#95—22no—
166#95—22no—
167#95—21no—
168#95—21no—
169#95—22no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—3321no—
175C22×C4C2×C22⋊D8311yescharacteristic
176C22×C4C2×C22⋊D8312yes—
177C2×C8—3322no—
178C2×C8—3322no—
179C2×C8—1664no—
180C2×C8—1662no—
181C2×C8—1662no—
182C2×C8—1662no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—81no—
194C4⋊C4—81no—
195C4⋊C4—3321no—
196C4⋊C4—3321no—
197C4⋊C4—3324no—
198C42D4×D8311yescharacteristic
199C42#1305058911yescharacteristic
200C42#1305058912yes—
201C23#1458176111yescharacteristic
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—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—6641no—
217C2×C4—6642no—
218C2×C4#1458176311yescharacteristic
219C2×C4#1458176412yes—
220C2×C4#1458177312yes—
221C2×C4#1458177911yescharacteristic
222C8—3324no—
223C8—1664no—
224C22#1912761511yescharacteristic
225C22#1912786911yescharacteristic
226C22#1912787412yes—
227C22#1912788412yes—
228C22#1912788411yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—81no—
234C4—81no—
235C4—82no—
236C4—82no—
237C4—13281no—
238C2#2490676111yescharacteristic
239C2#2490677411yescharacteristic
240C2#2490679112yes—
241C2#2490867712yes—
242C2#2490868411yescharacteristic
subgroupG/H
centerC23#14581761
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#2822C2
socle, prime radicalC23×C83#120
hypercenter#2822D83
hypocenterC83#10429
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

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
#249084332
#249076322
C2×#191274432
#249053442
C83×#28222
#1042983