Finite Group Databasebeta

← #35305394

Subgroups — #35305394

Order 21248.

528 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 103 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#24917987C211yesmaximal, characteristic, complemented
2#24917471C212yesmaximal
3#24905865C212yesmaximal, complemented
4#24905294C211yesmaximal, characteristic, complemented
5C83×#1955C211yesmaximal, characteristic
6#19128258C2212yes—
7#19128110—22no—
8#19128110—22no—
9#19128031—22no—
10#19127991—22no—
11#19127906—22no—
12#19127852—22no—
13C4×#13050578—24no—
14#19127754C2212yes—
15#19127739—22no—
16#19127431—24no—
17C2×C4×D4×C83C2211yescharacteristic
18C2×C4⋊C8×C83C2211yescharacteristic
19C2×C22⋊C8×C83—22no—
20C2×#97×C83C2211yescharacteristic
21C2×#13050578—24no—
22#14581792D412yes—
23#14581792D412yes—
24#14581784—22no—
25#14581771—22no—
26#14581771—22no—
27C4×Dic166—22no—
28C4×Dic166—22no—
29#14581751—22no—
30#14581726—22no—
31#14581726—22no—
32#14581724—24no—
33#14581723—24no—
34C4⋊(C83⋊C8)—22no—
35#14581715—24no—
36#14581713—24no—
37C22⋊(C83⋊C8)—22no—
38C4×C83⋊C8D414yes—
39C22×D4×C83D411yescharacteristic
40C23×C4×C83—21no—
41C22×C8×C83—21no—
42C22×C8×C83D412yes—
43C4×D4×C83—22no—
44C4×D4×C83—22no—
45C2×C4⋊C4×C83D411yescharacteristic
46C2×C22⋊C4×C83—21no—
47C2×C42×C83C2311yescharacteristic
48C4⋊C8×C83—22no—
49C22⋊C8×C83—44no—
50#97×C83—22no—
51C2×Dic166—22no—
52C2×Dic166—22no—
53#13050578—48no—
54C2×C83⋊C8—24no—
55C4⋊Dic83—22no—
56C4⋊Dic83—22no—
57C4⋊Dic83—22no—
58C4⋊Dic83—22no—
59Dic83⋊C4—42no—
60Dic83⋊C4—42no—
61C22⋊Dic83—42no—
62C4×Dic83—42no—
63C24×C83—21no—
64C2×D4×C83—22no—
65C2×D4×C83—42no—
66C22×C4×C83—21no—
67C22×C4×C83—41no—
68C22×C4×C83—41no—
69C22×C4×C83—42no—
70C22×C4×C83—42no—
71C22×C4×C83C2×D411yescharacteristic
72C22×C4×C83C2×D411yescharacteristic
73C22×C4×C83#4111yescharacteristic
74C2×C8×C83—22no—
75C2×C8×C83—22no—
76C2×C8×C83—41no—
77C2×C8×C83—42no—
78C2×C8×C83SD1614yescomplemented
79C4⋊C4×C83—22no—
80C22⋊C4×C83—42no—
81C42×C83C2×D412yes—
82C42×C83C2×D412yes—
83C23×C83—22no—
84C23×C83—41no—
85C23×C83—42no—
86C23×C83—41no—
87C23×C83—42no—
88C23×C83#12111yescharacteristic
89D4×C83—24no—
90D4×C83—42no—
91C2×C4×C83—41no—
92C2×C4×C83—41no—
93C2×C4×C83—41no—
94C2×C4×C83—42no—
95C2×C4×C83—82no—
96C2×C4×C83—81no—
97C2×C4×C83—81no—
98C2×C4×C83#12011yescharacteristic
99C2×C4×C83#12012yes—
100C2×C4×C83#12112yes—
101C2×C4×C83#12711yescharacteristic
102C2×C4×C83C2×SD1612yes—
103C2×C4×C83#13712yes—
104C2×Dic83—42no—
105C2×Dic83—42no—
106Dic166—44no—
107Dic166—44no—
108C8×C83—24no—
109C8×C83—81no—
110C83⋊C8—44no—
111C22×C83—21no—
112C22×C83—21no—
113C22×C83—44no—
114C22×C83—42no—
115C22×C83—82no—
116C22×C83—81no—
117C22×C83—81no—
118C22×C83#39211yescharacteristic
119C22×C83#46112yes—
120C4×C83—22no—
121C4×C83—22no—
122C4×C83—81no—
123C4×C83#44812yes—
124C4×C83#49211yescharacteristic
125C4×C83#49711yescharacteristic
126Dic83—82no—
127Dic83—82no—
128#10036—831nomaximal, Sylow
129C2×C83—22no—
130C2×C83—82no—
131C2×C83#201011yescharacteristic
132C2×C83#201311yescharacteristic
133C2×C83#201711yescharacteristic
134#3162—831no—
135#3101—832no—
136#1955D8311yescharacteristic
137#1481—832no—
138#1275—831no—
139C83#1003611yescharacteristic, complemented, Sylow
140#533—832no—
141C2×C4×D4C2×D8311yescharacteristic
142#501—1662no—
143#501—1662no—
144#483—1662no—
145#476—1662no—
146#461—1662no—
147#450—1662no—
148C4×SD16—1664no—
149#431—832no—
150#427—1662no—
151C2×C4⋊C8C2×D8311yescharacteristic
152C2×C22⋊C8—22no—
153C2×#97C2×D8311yescharacteristic
154Q8⋊C8—1664no—
155C22×D4D33211yescharacteristic
156C23×C4—21no—
157C2×SD16—1664no—
158C22×C8—21no—
159C22×C8C22⋊D8312yes—
160C4⋊Q8—832no—
161C4⋊Q8—832no—
162#125—1662no—
163C22⋊Q8—1662no—
164C22⋊Q8—1662no—
165C4×Q8—1662no—
166C4×Q8—1662no—
167C4×D4—22no—
168C4×D4—22no—
169#117—1662no—
170C2×C4⋊C4D33211yescharacteristic
171C2×C22⋊C4—21no—
172C2×C42C22×D8311yescharacteristic
173#107—1662no—
174#107—1662no—
175#106—1664no—
176#106—1664no—
177C4⋊C8—22no—
178C4⋊C8—1662no—
179#103—1664no—
180#102—1664no—
181C22⋊C8—44no—
182C22⋊C8—1662no—
183#97—22no—
184C4×C8—834no—
185C24—21no—
186C2×Q8—1662no—
187C2×Q8—1662no—
188C2×D4—22no—
189C2×D4—42no—
190C22×C4—21no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4C2×C22⋊D8311yescharacteristic
196C22×C4C2×D33211yescharacteristic
197C22×C4#1305059011yescharacteristic
198SD16—3328no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—41no—
202C2×C8—42no—
203C2×C8—1664no—
204C2×C8#1305057814yescomplemented
205C4⋊C4—22no—
206C4⋊C4—3322no—
207C4⋊C4—3322no—
208C4⋊C4—1662no—
209C4⋊C4—1662no—
210C4⋊C4—1662no—
211C4⋊C4—1662no—
212C22⋊C4—42no—
213C22⋊C4—3322no—
214C42—3322no—
215C42D4×D8312yes—
216C42D4×D8312yes—
217C23—22no—
218C23—41no—
219C23—42no—
220C23—41no—
221C23—42no—
222C23#1458176611yescharacteristic
223Q8—3324no—
224Q8—3324no—
225D4—24no—
226D4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—42no—
231C2×C4—81no—
232C2×C4—82no—
233C2×C4—81no—
234C2×C4—3322no—
235C2×C4—3322no—
236C2×C4#1458176011yescharacteristic
237C2×C4#1458176212yes—
238C2×C4#1458176512yes—
239C2×C4#1458178811yescharacteristic
240C2×C4C2×#1305057812yes—
241C2×C4#1458182212yes—
242C8—24no—
243C8—81no—
244C8—3324no—
245C22—21no—
246C22—21no—
247C22—44no—
248C22—42no—
249C22—82no—
250C22—81no—
251C22—81no—
252C22#1912761011yescharacteristic
253C22#1912790612yes—
254C4—22no—
255C4—22no—
256C4—81no—
257C4—6642no—
258C4—6642no—
259C4#1912783912yes—
260C4#1912807311yescharacteristic
261C4#1912809611yescharacteristic
262C2—22no—
263C2—82no—
264C2#2490853011yescharacteristic
265C2#2490854511yescharacteristic
266C2#2490856711yescharacteristic
subgroupG/H
centerC2×C4#14581788
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1955C2
socleC22×C83#392
prime radicalC22×D4×C83D4
hypercenter#1955D83
hypocenterC83#10036
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. #24917987C2semidirect
3. #24905865C2semidirect
4. #24905294C2semidirect
78. C2×C8×C83SD16semidirect
139. C83#10036semidirect
204. C2×C8#13050578semidirect

Maximal subgroups

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

subgroupindex
#249179872
#249174712
#249058652
#249052942
C83×#19552
#1003683