Finite Group Databasebeta

← #35313561

Subgroups — #35313561

Order 21248.

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

normal subgroups only

This group has 462 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#24909868C211yesmaximal, characteristic
2#24905776C212yesmaximal
3#24905409C211yesmaximal, characteristic, complemented
4#24905406C212yesmaximal, complemented
5C83×#1325C211yesmaximal, characteristic, complemented
6C2×#14581750C411yescharacteristic
7C2×#14581750C2211yescharacteristic
8C2×C42×D83C411yescharacteristic
9#19127751—22no—
10#19127571C411yescharacteristic
11#19127566C411yescharacteristic
12#19127566C2211yescharacteristic
13#19127558—22no—
14C4⋊C4×Dic83—22no—
15#19127427C2212yes—
16#19127424—22no—
17#384×C83C2211yescharacteristic
18#324×C83C2212yes—
19C22×C4×D83—21no—
20C22×C4×D83C2×C411yescharacteristic
21#14581750—41no—
22#14581750—41no—
23#14581750—41no—
24#14581750—41no—
25C2×C4⋊Dic83—22no—
26C2×C4⋊Dic83C2×C411yescharacteristic
27C2×C4⋊Dic83C2×C411yescharacteristic
28C2×(C2×D83)⋊C4—21no—
29C2×(C2×D83)⋊C4D412yes—
30C2×C4×Dic83—21no—
31C2×C4×Dic83—21no—
32C2×C4×Dic83C2×C411yescharacteristic
33C2×C4×Dic83D412yes—
34C42×D83—22no—
35C42×D83C814yescomplemented
36Dic83⋊C8—42no—
37C22⋊(C83⋊C8)—22no—
38C8×Dic83—42no—
39C83⋊#95—22no—
40C83⋊#95—22no—
41C2×C4⋊C4×C83—22no—
42C2×C4⋊C4×C83C2×C411yescharacteristic
43C2×C4⋊C4×C83C2311yescharacteristic
44C2×C42×C83C2×C411yescharacteristic
45C22⋊C8×C83—22no—
46C23×D83C22⋊C411yescharacteristic
47C22×Dic83—21no—
48C22×Dic83—21no—
49C22×Dic83C22⋊C412yes—
50C22×Dic83C22⋊C411yescharacteristic
51C2×C4×D83—21no—
52C2×C4×D83—21no—
53C2×C4×D83—22no—
54C2×C4×D83—24no—
55C2×C4×D83—42no—
56C2×C4×D83—42no—
57C2×C4×D83C2×C812yes—
58C2×C4×D83M1612yes—
59C2×C83⋊C8—42no—
60C4⋊Dic83—41no—
61C4⋊Dic83—44no—
62C4⋊Dic83—41no—
63(C2×D83)⋊C4—42no—
64(C2×D83)⋊C4—42no—
65C4×Dic83—21no—
66C4×Dic83—24no—
67C4×Dic83—22no—
68C4×Dic83—22no—
69C4×Dic83—41no—
70C4×Dic83—41no—
71C4×Dic83C2×C812yes—
72C22×C4×C83—21no—
73C22×C4×C83—21no—
74C22×C4×C83C22×C411yescharacteristic
75C22×C4×C83C2×D412yes—
76C2×C8×C83—42no—
77C4⋊C4×C83—41no—
78C4⋊C4×C83—41no—
79C4⋊C4×C83—44no—
80C42×C83—21no—
81C42×C83C2×C812yes—
82C23×C83C2×C22⋊C411yescharacteristic
83C22×D83—21no—
84C22×D83—21no—
85C22×D83—41no—
86C22×D83—41no—
87C22×D83C22⋊C812yes—
88C2×C4×C83—22no—
89C2×C4×C83—22no—
90C2×C4×C83—22no—
91C2×C4×C83—21no—
92C2×C4×C83—21no—
93C2×C4×C83—22no—
94C2×C4×C83—42no—
95C2×C4×C83—42no—
96C2×C4×C83—41no—
97C2×C4×C83C22×C811yescharacteristic
98C2×C4×C83C2×M1611yescharacteristic
99C2×Dic83—22no—
100C2×Dic83—22no—
101C2×Dic83—41no—
102C2×Dic83—41no—
103C2×Dic83—42no—
104C2×Dic83—42no—
105C2×Dic83—41no—
106C2×Dic83C22⋊C812yes—
107C2×Dic83#9911yescharacteristic
108C2×Dic83#9911yescharacteristic
109C2×Dic83#10112yes—
110C4×D83—22no—
111C4×D83—22no—
112C4×D83—22no—
113C4×D83—22no—
114C4×D83—48no—
115C8×C83—82no—
116C83⋊C8—82no—
117C22×C83—21no—
118C22×C83—21no—
119C22×C83C2×C22⋊C811yescharacteristic
120C22×C83C2×#9911yescharacteristic
121C22×C83C2×#10111yescharacteristic
122C2×D83—22no—
123C2×D83—42no—
124C2×D83—41no—
125C2×D83—41no—
126C2×D83—42no—
127C4×C83—24no—
128C4×C83—21no—
129C4×C83—21no—
130C4×C83—42no—
131C4×C83—81no—
132Dic83—42no—
133Dic83—42no—
134Dic83—81no—
135Dic83#32412yes—
136Dic83#32412yes—
137#11447—831nomaximal, Sylow
138C2×C83—21no—
139C2×C83—21no—
140C2×C83C2×#32411yescharacteristic
141C2×C83#212611yescharacteristic
142C2×C83#213211yescharacteristic
143D83—42no—
144#2285—831no—
145#1458—832no—
146#1325—831no—
147#1325D8311yescharacteristic, complemented
148#1324—832no—
149C83#1144711yescharacteristic, complemented, Sylow
150C2×#117—831no—
151C2×#117—831no—
152C22×C42—831no—
153#431—1662no—
154#384—831no—
155#384C2×D8311yescharacteristic
156#382—831no—
157#382—831no—
158#380—1662no—
159C4×C4⋊C4—1662no—
160#324—832no—
161#324C2×D8312yes—
162#323—1662no—
163C23×C4—831no—
164C23×C4—1661no—
165#117—3321no—
166#117—3321no—
167#117—3321no—
168#117—3321no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—831no—
171C2×C4⋊C4—831no—
172C2×C4⋊C4—1662no—
173C2×C4⋊C4C4×D8311yescharacteristic
174C2×C4⋊C4C22×D8311yescharacteristic
175C2×C22⋊C4—832no—
176C2×C22⋊C4—1661no—
177C2×C42—831no—
178C2×C42—834no—
179C2×C42—832no—
180C2×C42—1662no—
181C2×C42—1661no—
182C2×C42—1661no—
183C2×C42C4×D8311yescharacteristic
184C4⋊C8—3322no—
185C22⋊C8—22no—
186C22⋊C8—1662no—
187C4×C8—3322no—
188#95—1662no—
189#95—1662no—
190C24—831no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—3322no—
194C22×C4—3322no—
195C22×C4—832no—
196C22×C4—831no—
197C22×C4—832no—
198C22×C4—832no—
199C22×C4—1664no—
200C22×C4—1661no—
201C22×C4—1661no—
202C22×C4—1662no—
203C22×C4—1661no—
204C22×C4—1661no—
205C22×C4C2×C4×D8311yescharacteristic
206C22×C4D4×D8312yes—
207C2×C8—42no—
208C2×C8—3322no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—44no—
212C4⋊C4—3321no—
213C4⋊C4—3324no—
214C4⋊C4—3321no—
215C22⋊C4—3322no—
216C22⋊C4—3322no—
217C42—21no—
218C42—3321no—
219C42—3321no—
220C42—832no—
221C42—1662no—
222C42—1662no—
223C42—1664no—
224C42—1661no—
225C42C8×D8312yes—
226C23—3321no—
227C23—3321no—
228C23—832no—
229C23—1661no—
230C23—1661no—
231C23C22⋊C4×D8311yescharacteristic
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—3328no—
242C2×C4—3321no—
243C2×C4—3321no—
244C2×C4—3322no—
245C2×C4—3322no—
246C2×C4—3321no—
247C2×C4—832no—
248C2×C4—831no—
249C2×C4—831no—
250C2×C4—832no—
251C2×C4—1662no—
252C2×C4—1662no—
253C2×C4—1662no—
254C2×C4—1662no—
255C2×C4—1662no—
256C2×C4—1662no—
257C2×C4C2×C8×D8311yescharacteristic
258C2×C4M16×D8311yescharacteristic
259C8—82no—
260C8—6642no—
261C22—21no—
262C22—21no—
263C22—3322no—
264C22—3322no—
265C22—3321no—
266C22—3321no—
267C22—1662no—
268C22C22⋊C8×D8311yescharacteristic
269C22#99×D8311yescharacteristic
270C22#101×D8311yescharacteristic
271C4—24no—
272C4—21no—
273C4—21no—
274C4—42no—
275C4—81no—
276C4—3322no—
277C4—3322no—
278C4—832no—
279C4—832no—
280C4—6641no—
281C2—21no—
282C2—21no—
283C2—3322no—
284C2#324×D8311yescharacteristic
285C2#2490912511yescharacteristic
286C2#2490914711yescharacteristic
subgroupG/H
centerC22#99×D83
commutatorC2×C4×C83C22×C8
FrattiniC2×C4⋊C4C22×D83
FittingC83×#1325C2
socleC22×C83C2×#99
prime radicalC23×D83C22⋊C4
cosocleC2×C4⋊C4×C83C23
hypercenter#1325D83
hypocenterC83#11447
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
3. #24905409C2semidirect
4. #24905406C2semidirect
5. C83×#1325C2semidirect
35. C42×D83C8semidirect
147. #1325D83semidirect
149. C83#11447semidirect

Maximal subgroups

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

subgroupindex
#249098682
#249057762
#249054092
#249054062
C83×#13252
#1144783