Finite Group Databasebeta

← #35313683

Subgroups — #35313683

Order 21248.

428 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 89 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#24910032C211yesmaximal, characteristic
2#24905785C212yesmaximal
3#24905408C212yesmaximal
4#24905397C211yesmaximal, characteristic
5C83×#1319C211yesmaximal, characteristic
6C2×#14581790C411yescharacteristic
7C2×Q8×Dic83C411yescharacteristic
8C2×#14581757C2211yescharacteristic
9#19127751—22no—
10#19127607C411yescharacteristic
11#19127598—22no—
12#19127570C2211yescharacteristic
13#19127552—22no—
14C42×Dic83C411yescharacteristic
15#19127427C2212yes—
16#19127426—22no—
17#391×C83C2211yescharacteristic
18#324×C83C2212yes—
19C22×Dic166C2×C411yescharacteristic
20#14581790—22no—
21#14581790C814yescomplemented
22Q8×Dic83—41no—
23Q8×Dic83—41no—
24#14581757—41no—
25#14581757—41no—
26C2×C4⋊Dic83—21no—
27C2×C4⋊Dic83C2×C411yescharacteristic
28C2×Dic83⋊C4—22no—
29C2×Dic83⋊C4—22no—
30C2×Dic83⋊C4D412yes—
31C2×C4×Dic83—21no—
32C2×C4×Dic83—21no—
33C2×C4×Dic83—21no—
34C2×C4×Dic83C2×C411yescharacteristic
35C2×C4×Dic83C2×C411yescharacteristic
36C2×C4×Dic83D412yes—
37Dic83⋊C8—42no—
38C22⋊(C83⋊C8)—22no—
39C8×Dic83—42no—
40C83⋊#95—22no—
41C22×Q8×C83C2×C411yescharacteristic
42C2×C4⋊C4×C83C2311yescharacteristic
43C2×C42×C83C2×C411yescharacteristic
44C22⋊C8×C83—22no—
45#95×C83—22no—
46C2×Dic166—41no—
47C2×Dic166—41no—
48C2×Dic166C2×C812yes—
49C2×Dic166M1612yes—
50C22×Dic83—21no—
51C22×Dic83—21no—
52C22×Dic83C22⋊C412yes—
53C22×Dic83C22⋊C411yescharacteristic
54C22×Dic83C22⋊C411yescharacteristic
55C2×C83⋊C8—42no—
56C4⋊Dic83—42no—
57C4⋊Dic83—41no—
58Dic83⋊C4—28no—
59Dic83⋊C4—42no—
60Dic83⋊C4—44no—
61C4×Dic83—24no—
62C4×Dic83—21no—
63C4×Dic83—22no—
64C4×Dic83—22no—
65C4×Dic83—21no—
66C4×Dic83—21no—
67C4×Dic83—42no—
68C4×Dic83—41no—
69C4×Dic83—41no—
70C4×Dic83C2×C812yes—
71C2×Q8×C83—21no—
72C2×Q8×C83—41no—
73C2×Q8×C83—41no—
74C2×Q8×C83C2×C812yes—
75C22×C4×C83—21no—
76C22×C4×C83—21no—
77C22×C4×C83C22×C411yescharacteristic
78C22×C4×C83C2×D412yes—
79C2×C8×C83—42no—
80C4⋊C4×C83—41no—
81C42×C83—41no—
82C23×C83C2×C22⋊C411yescharacteristic
83Q8×C83—42no—
84Q8×C83—42no—
85C2×C4×C83—21no—
86C2×C4×C83—21no—
87C2×C4×C83—22no—
88C2×C4×C83—22no—
89C2×C4×C83—22no—
90C2×C4×C83—41no—
91C2×C4×C83—41no—
92C2×C4×C83—41no—
93C2×C4×C83—41no—
94C2×C4×C83—42no—
95C2×C4×C83C22×C811yescharacteristic
96C2×C4×C83C2×M1611yescharacteristic
97C2×Dic83—22no—
98C2×Dic83—22no—
99C2×Dic83—22no—
100C2×Dic83—22no—
101C2×Dic83—22no—
102C2×Dic83—22no—
103C2×Dic83—21no—
104C2×Dic83—41no—
105C2×Dic83—42no—
106C2×Dic83—41no—
107C2×Dic83C22⋊C814yes—
108C2×Dic83#9911yescharacteristic
109C2×Dic83#9911yescharacteristic
110Dic166—42no—
111Dic166—42no—
112C8×C83—82no—
113C83⋊C8—82no—
114C22×C83—21no—
115C22×C83—21no—
116C22×C83C2×C22⋊C811yescharacteristic
117C22×C83C2×#9911yescharacteristic
118C22×C83#41311yescharacteristic
119C4×C83—21no—
120C4×C83—21no—
121C4×C83—42no—
122C4×C83—42no—
123C4×C83—42no—
124Dic83—24no—
125Dic83—21no—
126Dic83—24no—
127Dic83—41no—
128Dic83—81no—
129Dic83#35612yes—
130#11478—831nomaximal, Sylow
131C2×C83—21no—
132C2×C83—21no—
133C2×C83#145911yescharacteristic
134C2×C83#212611yescharacteristic
135C2×C83C2×#35611yescharacteristic
136C4×C4⋊Q8—831no—
137#1461—832no—
138#1325—832no—
139#1319—831no—
140#1319D8311yescharacteristic
141C83#1147811yescharacteristic, complemented, Sylow
142C2×C4⋊Q8—831no—
143C2×C4×Q8—831no—
144C2×C4×Q8—831no—
145#431—1662no—
146#391—831no—
147#391C2×D8311yescharacteristic
148#389—1662no—
149#384—831no—
150C4×C4⋊C4—1662no—
151C43—831no—
152#324—832no—
153#324—1662no—
154#324C2×D8312yes—
155C22×Q8—831no—
156C22×Q8C4×D8311yescharacteristic
157C4⋊Q8—834no—
158C4⋊Q8—1662no—
159C4×Q8—3321no—
160C4×Q8—3321no—
161C4×Q8—3321no—
162C4×Q8—3321no—
163C2×C4⋊C4—832no—
164C2×C4⋊C4—831no—
165C2×C4⋊C4—1661no—
166C2×C4⋊C4—1662no—
167C2×C4⋊C4—1662no—
168C2×C4⋊C4C22×D8311yescharacteristic
169C2×C42—831no—
170C2×C42—831no—
171C2×C42—832no—
172C2×C42—1661no—
173C2×C42—1661no—
174C2×C42—1661no—
175C2×C42C4×D8311yescharacteristic
176C4⋊C8—3322no—
177C22⋊C8—22no—
178C22⋊C8—1662no—
179C4×C8—3322no—
180#95—22no—
181#95—1662no—
182C2×Q8—21no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—3321no—
186C2×Q8—3321no—
187C2×Q8—832no—
188C2×Q8—832no—
189C2×Q8C8×D8312yes—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—831no—
193C22×C4—832no—
194C22×C4—831no—
195C22×C4—1661no—
196C22×C4—1661no—
197C22×C4C2×C4×D8311yescharacteristic
198C22×C4D4×D8312yes—
199C2×C8—42no—
200C2×C8—3322no—
201C4⋊C4—41no—
202C4⋊C4—3321no—
203C4⋊C4—3322no—
204C4⋊C4—3322no—
205C4⋊C4—3324no—
206C4⋊C4—1668no—
207C42—41no—
208C42—3321no—
209C42—3321no—
210C42—3322no—
211C42—832no—
212C42—1662no—
213C42—1662no—
214C42—1661no—
215C42—1661no—
216C42—1664no—
217C42—1661no—
218C23C22⋊C4×D8311yescharacteristic
219Q8—42no—
220Q8—42no—
221Q8—3322no—
222Q8—3322no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—3321no—
234C2×C4—3322no—
235C2×C4—3321no—
236C2×C4—831no—
237C2×C4—834no—
238C2×C4—831no—
239C2×C4—1661no—
240C2×C4—1662no—
241C2×C4—1662no—
242C2×C4—1662no—
243C2×C4—1662no—
244C2×C4—1662no—
245C2×C4—1662no—
246C2×C4C2×C8×D8311yescharacteristic
247C2×C4M16×D8311yescharacteristic
248C8—82no—
249C8—6642no—
250C22—21no—
251C22—21no—
252C22C22⋊C8×D8311yescharacteristic
253C22#99×D8311yescharacteristic
254C22#1912768211yescharacteristic
255C4—21no—
256C4—21no—
257C4—42no—
258C4—42no—
259C4—42no—
260C4—3321no—
261C4—832no—
262C4—6641no—
263C4—1664no—
264C4—1664no—
265C4—1661no—
266C2—21no—
267C2—21no—
268C2#2490577811yescharacteristic
269C2#2490912711yescharacteristic
270C2#356×D8311yescharacteristic
subgroupG/H
centerC22#99×D83
commutatorC2×C4×C83C22×C8
FrattiniC2×C4⋊C4C22×D83
FittingC83×#1319C2
socleC22×C83C2×#99
prime radicalC23×C83C2×C22⋊C4
cosocleC2×C4⋊C4×C83C23
hypercenter#1319D83
hypocenterC83#11478
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
21. #14581790C8semidirect
141. C83#11478semidirect

Maximal subgroups

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

subgroupindex
#249100322
#249057852
#249054082
#249053972
C83×#13192
#1147883