Finite Group Databasebeta

← #35314072

Subgroups — #35314072

Order 21248.

374 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 87 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#24912668C211yesmaximal, characteristic
2#24905807C211yesmaximal, characteristic
3#24905408C214yesmaximal
4C83×#1461C211yesmaximal, characteristic
5C2×#14581792C411yescharacteristic
6#19127758—21no—
7#19127621—21no—
8#19127621—21no—
9#19127608C412yes—
10#19127599—21no—
11#19127599—21no—
12#19127570C2212yes—
13C4×C4⋊Dic83C411yescharacteristic
14#19127427—21no—
15#19127427C2212yes—
16C2×C4×Q8×C83C2211yescharacteristic
17#431×C83—21no—
18#324×C83—21no—
19#324×C83C2212yes—
20C22×Dic166—21no—
21#14581792—41no—
22#14581792—41no—
23C2×C4⋊Dic83—21no—
24C2×C4⋊Dic83—21no—
25C2×C4⋊Dic83C2×C412yes—
26C2×Dic83⋊C4—22no—
27C2×Dic83⋊C4—22no—
28C2×C4×Dic83C2×C412yes—
29C4⋊(C83⋊C8)—41no—
30C22⋊(C83⋊C8)—22no—
31#14581703—41no—
32C83⋊#95—21no—
33C83⋊#95—22no—
34C83⋊#95—22no—
35C22×Q8×C83C2×C411yescharacteristic
36C4×Q8×C83—41no—
37C4×Q8×C83—41no—
38C2×C4⋊C4×C83D411yescharacteristic
39C2×C4⋊C4×C83D411yescharacteristic
40C2×C4⋊C4×C83C2311yescharacteristic
41C2×C42×C83C2×C411yescharacteristic
42C2×C42×C83D411yescharacteristic
43C2×C42×C83D411yescharacteristic
44C4⋊C8×C83—41no—
45C22⋊C8×C83—22no—
46C4×C8×C83—41no—
47C2×Dic166—42no—
48C2×Dic166—82no—
49C22×Dic83—22no—
50C22×Dic83—22no—
51C2×C83⋊C8—42no—
52C4⋊Dic83—24no—
53C4⋊Dic83—41no—
54C4⋊Dic83—41no—
55C4⋊Dic83—42no—
56Dic83⋊C4—82no—
57Dic83⋊C4—82no—
58C4×Dic83—24no—
59C2×Q8×C83—22no—
60C2×Q8×C83—22no—
61C2×Q8×C83—41no—
62C22×C4×C83C22⋊C411yescharacteristic
63C22×C4×C83C22⋊C411yescharacteristic
64C22×C4×C83C22⋊C411yescharacteristic
65C22×C4×C83C22⋊C411yescharacteristic
66C22×C4×C83C22×C411yescharacteristic
67C22×C4×C83C2×D411yescharacteristic
68C22×C4×C83C2×D411yescharacteristic
69C2×C8×C83—42no—
70C4⋊C4×C83—41no—
71C4⋊C4×C83—41no—
72C4⋊C4×C83—41no—
73C42×C83—21no—
74C42×C83—21no—
75C42×C83—21no—
76C42×C83—21no—
77C42×C83—21no—
78C42×C83—21no—
79C23×C83C2×C22⋊C411yescharacteristic
80Q8×C83—44no—
81C2×C4×C83—21no—
82C2×C4×C83—21no—
83C2×C4×C83—21no—
84C2×C4×C83—21no—
85C2×C4×C83—22no—
86C2×C4×C83—21no—
87C2×C4×C83—21no—
88C2×C4×C83—21no—
89C2×C4×C83—21no—
90C2×C4×C83—21no—
91C2×C4×C83—21no—
92C2×C4×C83—41no—
93C2×C4×C83—41no—
94C2×C4×C83—41no—
95C2×C4×C83#9911yescharacteristic
96C2×C4×C83#9911yescharacteristic
97C2×C4×C83#10112yes—
98C2×C4×C83#13112yes—
99C2×Dic83—24no—
100C2×Dic83—42no—
101C2×Dic83—42no—
102C2×Dic83—42no—
103C2×Dic83—42no—
104C2×Dic83—42no—
105Dic166—84no—
106C8×C83—82no—
107C83⋊C8—82no—
108C22×C83—21no—
109C22×C83—21no—
110C22×C83#40811yescharacteristic
111C22×C83C2×#9911yescharacteristic
112C22×C83C2×#10111yescharacteristic
113C4×C83—21no—
114C4×C83—22no—
115C4×C83—22no—
116C4×C83—41no—
117C4×C83—41no—
118C4×C83—41no—
119C4×C83—41no—
120C4×C83#35612yes—
121Dic83—44no—
122Dic83—82no—
123#11574—831nomaximal, Sylow
124C2×C83—21no—
125C2×C83—21no—
126C2×C83#147211yescharacteristic
127C2×C83#212811yescharacteristic
128C2×C83C2×#35611yescharacteristic
129#2567—831no—
130#1467—831no—
131#1461D8311yescharacteristic
132#1325—834no—
133C83#1157411yescharacteristic, complemented, Sylow
134C2×C4⋊Q8—831no—
135C2×C4×Q8C2×D8311yescharacteristic
136#432—1661no—
137#431—21no—
138#395—1661no—
139#395—1661no—
140#391—832no—
141#389—1661no—
142#389—1661no—
143#384—832no—
144C4×C4⋊C4—831no—
145#324—21no—
146#324—832no—
147#324—1661no—
148#324C2×D8312yes—
149C22×Q8—1661no—
150C22×Q8C4×D8311yescharacteristic
151C4⋊Q8—3321no—
152C4⋊Q8—3321no—
153C4×Q8—41no—
154C4×Q8—41no—
155C2×C4⋊C4—832no—
156C2×C4⋊C4—1661no—
157C2×C4⋊C4—1662no—
158C2×C4⋊C4—1662no—
159C2×C4⋊C4—1661no—
160C2×C4⋊C4D33211yescharacteristic
161C2×C4⋊C4C22⋊D8311yescharacteristic
162C2×C4⋊C4C22×D8311yescharacteristic
163C2×C42—832no—
164C2×C42C4×D8311yescharacteristic
165C2×C42D33211yescharacteristic
166C2×C42C22⋊D8311yescharacteristic
167C4⋊C8—41no—
168C4⋊C8—3321no—
169C22⋊C8—22no—
170C22⋊C8—1662no—
171#97—3321no—
172C4×C8—41no—
173#95—1661no—
174#95—1662no—
175#95—1662no—
176C2×Q8—22no—
177C2×Q8—22no—
178C2×Q8—41no—
179C2×Q8—3322no—
180C2×Q8—6642no—
181C22×C4—1662no—
182C22×C4—1662no—
183C22×C4(C2×D83)⋊C411yescharacteristic
184C22×C4(C2×D83)⋊C411yescharacteristic
185C22×C4(C2×D83)⋊C411yescharacteristic
186C22×C4(C2×D83)⋊C411yescharacteristic
187C22×C4C2×C4×D8311yescharacteristic
188C22×C4C2×C22⋊D8311yescharacteristic
189C22×C4C2×D33211yescharacteristic
190C2×C8—42no—
191C2×C8—3322no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—3322no—
196C4⋊C4—3321no—
197C4⋊C4—3321no—
198C4⋊C4—6642no—
199C4⋊C4—6642no—
200C4⋊C4—1664no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—1664no—
208C23C2×(C2×D83)⋊C411yescharacteristic
209Q8—44no—
210Q8—6644no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—3322no—
226C2×C4—3322no—
227C2×C4—3322no—
228C2×C4—3322no—
229C2×C4—3322no—
230C2×C4—1664no—
231C2×C4#1458170611yescharacteristic
232C2×C4#1458170611yescharacteristic
233C2×C4#1458171012yes—
234C2×C4#1458179812yes—
235C8—82no—
236C8—6642no—
237C22—21no—
238C22—21no—
239C22#1912766711yescharacteristic
240C22C2×#1458170611yescharacteristic
241C22C2×#1458171011yescharacteristic
242C4—21no—
243C4—22no—
244C4—22no—
245C4—41no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—3324no—
250C4—6642no—
251C4#1912749912yes—
252C2—21no—
253C2—21no—
254C2#2490582611yescharacteristic
255C2#2490913411yescharacteristic
256C2C2×#1912749911yescharacteristic
subgroupG/H
centerC22C2×#14581706
commutatorC22×C4×C83C22×C4
FrattiniC2×C4⋊C4C22×D83
FittingC83×#1461C2
socleC22×C83C2×#99
prime radicalC23×C83C2×C22⋊C4
cosocleC2×C4⋊C4×C83C23
hypercenter#1461D83
hypocenterC83#11574
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
133. C83#11574semidirect

Maximal subgroups

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

subgroupindex
#249126682
#249058072
#249054082
C83×#14612
#1157483