Finite Group Databasebeta

← #35302877

Subgroups — #35302877

Order 21248.

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

normal subgroups only

This group has 326 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#24908439C211yesmaximal, characteristic
2#24907318C211yesmaximal, characteristic
3#24906118C211yesmaximal, characteristic
4#24905865C211yesmaximal, characteristic
5#24905358C211yesmaximal, characteristic
6#24905295C211yesmaximal, characteristic
7C83×#1571C211yesmaximal, characteristic
8#19128258C2211yescharacteristic
9#19127754C2211yescharacteristic
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11C2×#14581702—21no—
12C42×Dic83C2211yescharacteristic
13#19127462—21no—
14#19127462—21no—
15#19127455—21no—
16#19127449C412yescomplemented
17#19127448C412yescomplemented
18#19127431—22no—
19#431×C83C2211yescharacteristic
20#423×C83C2211yescharacteristic
21C2×C4⋊C8×C83C2211yescharacteristic
22#335×C83—22no—
23C22×C83⋊C8—21no—
24#14581792C2×C411yescharacteristic
25#14581792C2×C411yescharacteristic
26#14581784—21no—
27#14581771—21no—
28#14581771—21no—
29C4×Dic166—21no—
30C4×Dic166—21no—
31#14581751—21no—
32C2×C4×Dic83—21no—
33C2×C4×Dic83—21no—
34C2×C4×Dic83D411yescharacteristic
35C2×C4×Dic83D411yescharacteristic
36C4⋊(C83⋊C8)—21no—
37C4⋊(C83⋊C8)—21no—
38C4⋊(C83⋊C8)C2×C412yes—
39C22⋊(C83⋊C8)—21no—
40#14581702—42no—
41C4×C83⋊C8—21no—
42C2×M16×C83—21no—
43C22×C8×C83—21no—
44C2×C42×C83C2311yescharacteristic
45C4⋊C8×C83—21no—
46C4⋊C8×C83—21no—
47C4⋊C8×C83—21no—
48C4⋊C8×C83C2×C412yes—
49C4⋊C8×C83D412yes—
50C22⋊C8×C83—21no—
51C4×C8×C83—21no—
52C2×Dic166—21no—
53C2×Dic166—21no—
54C22×Dic83—21no—
55C22×Dic83—21no—
56C2×C83⋊C8—22no—
57C2×C83⋊C8—41no—
58C2×C83⋊C8—41no—
59C2×C83⋊C8—41no—
60C4⋊Dic83—21no—
61C4⋊Dic83—21no—
62C4⋊Dic83—21no—
63C4⋊Dic83—21no—
64Dic83⋊C4—41no—
65Dic83⋊C4—41no—
66C22⋊Dic83—41no—
67C4×Dic83—21no—
68C4×Dic83—21no—
69C4×Dic83—21no—
70C4×Dic83—42no—
71C4×Dic83—42no—
72C4×Dic83—41no—
73C4×Dic83Q1612yes—
74C22×C4×C83C2×D411yescharacteristic
75C22×C4×C83#4111yescharacteristic
76C22×C4×C83#4111yescharacteristic
77M16×C83—41no—
78M16×C83—41no—
79C2×C8×C83—22no—
80C2×C8×C83—22no—
81C2×C8×C83—41no—
82C2×C8×C83—41no—
83C2×C8×C83—41no—
84C42×C83C22×C411yescharacteristic
85C42×C83C2×D411yescharacteristic
86C42×C83#4111yescharacteristic
87C42×C83#4111yescharacteristic
88C23×C83#12311yescharacteristic
89C2×C4×C83—22no—
90C2×C4×C83—41no—
91C2×C4×C83#11711yescharacteristic
92C2×C4×C83C4×D411yescharacteristic
93C2×C4×C83C4×D411yescharacteristic
94C2×C4×C83#12111yescharacteristic
95C2×C4×C83#12411yescharacteristic
96C2×C4×C83#12611yescharacteristic
97C2×C4×C83C2×Q1611yescharacteristic
98C2×C4×C83#13511yescharacteristic
99C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
100C2×C4×C83#13711yescharacteristic
101C2×Dic83—22no—
102C2×Dic83—22no—
103C2×Dic83—41no—
104C2×Dic83—41no—
105C2×Dic83—41no—
106C2×Dic83—41no—
107C2×Dic83—41no—
108C2×Dic83—41no—
109Dic166—42no—
110Dic166—81no—
111C8×C83—42no—
112C8×C83—42no—
113C8×C83—81no—
114C83⋊C8—42no—
115C83⋊C8—81no—
116C22×C83—21no—
117C22×C83—21no—
118C22×C83#38811yescharacteristic
119C22×C83#48411yescharacteristic
120C22×C83#48511yescharacteristic
121C4×C83—21no—
122C4×C83—21no—
123C4×C83—21no—
124C4×C83C4×Q1611yescharacteristic
125C4×C83#44011yescharacteristic
126C4×C83#44412yes—
127C4×C83#46211yescharacteristic
128C4×C83#46311yescharacteristic
129Dic83—42no—
130Dic83—42no—
131Dic83—81no—
132Dic83—81no—
133#9584—831nomaximal, Sylow
134C2×C83—21no—
135C2×C83—21no—
136C2×C83#192811yescharacteristic
137C2×C83#193211yescharacteristic
138C2×C83#193811yescharacteristic
139#1994—831no—
140#1767—831no—
141#1571D8311yescharacteristic
142#1542—831no—
143#1481—831no—
144#1301—831no—
145#1276—831no—
146C83#958411yescharacteristic, complemented, Sylow
147#533—831no—
148#431—831no—
149#431C2×D8311yescharacteristic
150#423C2×D8311yescharacteristic
151C2×C4⋊C8—831no—
152C2×C4⋊C8C2×D8311yescharacteristic
153C2×#97—1661no—
154C43—831no—
155#339—1661no—
156#339—1661no—
157#336—1661no—
158#335—22no—
159#333—832no—
160#332—832no—
161Q8⋊C8—1662no—
162C2×M16—21no—
163C22×C8—21no—
164C22×C8—1661no—
165C4⋊Q8—831no—
166C4⋊Q8—831no—
167#125—1661no—
168C22⋊Q8—1661no—
169C22⋊Q8—1661no—
170C4×Q8—1661no—
171C4×Q8—1661no—
172#117—1661no—
173C2×C42—831no—
174C2×C42—831no—
175C2×C42—1661no—
176C2×C42—1661no—
177C2×C42C22×D8311yescharacteristic
178C4⋊C8—21no—
179C4⋊C8—21no—
180C4⋊C8—21no—
181C4⋊C8—832no—
182C4⋊C8—1661no—
183C4⋊C8—1661no—
184C4⋊C8C4×D8312yes—
185C4⋊C8C22⋊D8312yes—
186C22⋊C8—21no—
187C22⋊C8—1661no—
188#97—3322no—
189C4×C8—21no—
190C4×C8—1661no—
191C2×Q8—1661no—
192C2×Q8—1661no—
193C22×C4—1661no—
194C22×C4—1661no—
195C22×C4D4×D8311yescharacteristic
196C22×C4#1305059011yescharacteristic
197C22×C4#1305059111yescharacteristic
198M16—41no—
199M16—41no—
200C2×C8—22no—
201C2×C8—22no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—3321no—
206C2×C8—3321no—
207C2×C8—3321no—
208C2×C8—1662no—
209C4⋊C4—3321no—
210C4⋊C4—3321no—
211C4⋊C4—1661no—
212C4⋊C4—1661no—
213C4⋊C4—1661no—
214C4⋊C4—1661no—
215C22⋊C4—3321no—
216C42—3322no—
217C42—3322no—
218C42—3321no—
219C42—832no—
220C42—1661no—
221C42—1661no—
222C42—1661no—
223C42C2×C4×D8311yescharacteristic
224C42C2×C22⋊D8311yescharacteristic
225C42#1305058911yescharacteristic
226C42#1305059111yescharacteristic
227C23#1458177711yescharacteristic
228Q8—3322no—
229Q8—6641no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—3321no—
233C2×C4—3321no—
234C2×C4—3321no—
235C2×C4—3321no—
236C2×C4—3321no—
237C2×C4—3321no—
238C2×C4—1662no—
239C2×C4—1662no—
240C2×C4#1458175011yescharacteristic
241C2×C4C4×C22⋊D8311yescharacteristic
242C2×C4#1458175411yescharacteristic
243C2×C4#1458176411yescharacteristic
244C2×C4#1458178111yescharacteristic
245C2×C4#1458178711yescharacteristic
246C2×C4Q16×D8311yescharacteristic
247C2×C4#1458181111yescharacteristic
248C2×C4#1458181611yescharacteristic
249C2×C4#1458182411yescharacteristic
250C8—42no—
251C8—42no—
252C8—81no—
253C8—3322no—
254C8—6641no—
255C22—21no—
256C22—21no—
257C22#1912759111yescharacteristic
258C22#1912803811yescharacteristic
259C22#1912804411yescharacteristic
260C4—21no—
261C4—21no—
262C4—21no—
263C4—3322no—
264C4—3322no—
265C4—6641no—
266C4—6641no—
267C4#1912779511yescharacteristic
268C4#1912780011yescharacteristic
269C4#1912782112yes—
270C4#1912790911yescharacteristic
271C4#1912791411yescharacteristic
272C2—21no—
273C2—21no—
274C2#2490810311yescharacteristic
275C2#2490813111yescharacteristic
276C2#2490817311yescharacteristic
subgroupG/H
centerC2×C4#14581764
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1571C2
socleC22×C83#388
prime radicalC23×C83#123
cosocleC2×C42×C83C23
hypercenter#1571D83
hypocenterC83#9584
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
16. #19127449C4semidirect
17. #19127448C4semidirect
146. C83#9584semidirect

Maximal subgroups

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

subgroupindex
#249084392
#249073182
#249061182
#249058652
#249053582
#249052952
C83×#15712
#958483