Finite Group Databasebeta

← #35314048

Subgroups — #35314048

Order 21248.

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

normal subgroups only

This group has 394 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#24912448C211yesmaximal, characteristic
2#24905787C211yesmaximal, characteristic
3#24905396C214yesmaximal
4C83×#1467C211yesmaximal, characteristic
5C2×#14581792C411yescharacteristic
6C2×#14581790C412yes—
7#19127754—21no—
8#19127631—21no—
9#19127631—21no—
10#19127606C2212yes—
11#19127599—21no—
12#19127599—21no—
13C4×C4⋊Dic83C411yescharacteristic
14#19127427—21no—
15#19127427C2212yes—
16C2×C4×Q8×C83C2211yescharacteristic
17#432×C83—21no—
18#324×C83—21no—
19#324×C83C2212yes—
20C22×Dic166C2×C412yes—
21#14581792—41no—
22#14581792—41no—
23#14581790—44no—
24C2×C4⋊Dic83—21no—
25C2×C4⋊Dic83—21no—
26C2×C4⋊Dic83—21no—
27C2×Dic83⋊C4—22no—
28C2×Dic83⋊C4—22no—
29C2×C4×Dic83C2×C412yes—
30C4⋊(C83⋊C8)—41no—
31C22⋊(C83⋊C8)—22no—
32C4×C83⋊C8—41no—
33C83⋊#95—21no—
34C83⋊#95—22no—
35C83⋊#95—22no—
36C22×Q8×C83C2×C411yescharacteristic
37C4×Q8×C83—41no—
38C4×Q8×C83—41no—
39C2×C4⋊C4×C83D411yescharacteristic
40C2×C4⋊C4×C83D411yescharacteristic
41C2×C4⋊C4×C83C2311yescharacteristic
42C2×C42×C83C2×C411yescharacteristic
43C2×C42×C83D411yescharacteristic
44C2×C42×C83D411yescharacteristic
45C4⋊C8×C83—41no—
46C22⋊C8×C83—22no—
47#97×C83—41no—
48C2×Dic166—24no—
49C2×Dic166—42no—
50C2×Dic166—42no—
51C22×Dic83—22no—
52C22×Dic83—22no—
53C2×C83⋊C8—42no—
54C4⋊Dic83—24no—
55C4⋊Dic83—42no—
56C4⋊Dic83—41no—
57C4⋊Dic83—41no—
58Dic83⋊C4—44no—
59Dic83⋊C4—44no—
60C4×Dic83—42no—
61C2×Q8×C83—22no—
62C2×Q8×C83—22no—
63C2×Q8×C83—41no—
64C22×C4×C83C22⋊C411yescharacteristic
65C22×C4×C83C22⋊C411yescharacteristic
66C22×C4×C83C22⋊C411yescharacteristic
67C22×C4×C83C22⋊C411yescharacteristic
68C22×C4×C83C22×C411yescharacteristic
69C22×C4×C83C2×D411yescharacteristic
70C22×C4×C83C2×D411yescharacteristic
71C2×C8×C83—42no—
72C4⋊C4×C83—41no—
73C4⋊C4×C83—41no—
74C4⋊C4×C83—41no—
75C42×C83—21no—
76C42×C83—21no—
77C42×C83—21no—
78C42×C83—21no—
79C42×C83—21no—
80C42×C83—21no—
81C23×C83C2×C22⋊C411yescharacteristic
82Q8×C83—44no—
83C2×C4×C83—21no—
84C2×C4×C83—21no—
85C2×C4×C83—21no—
86C2×C4×C83—21no—
87C2×C4×C83—22no—
88C2×C4×C83—21no—
89C2×C4×C83—21no—
90C2×C4×C83—21no—
91C2×C4×C83—21no—
92C2×C4×C83—21no—
93C2×C4×C83—21no—
94C2×C4×C83—41no—
95C2×C4×C83—41no—
96C2×C4×C83—41no—
97C2×C4×C83#9911yescharacteristic
98C2×C4×C83#9911yescharacteristic
99C2×C4×C83#10012yes—
100C2×C4×C83#13112yes—
101C2×Dic83—24no—
102C2×Dic83—42no—
103C2×Dic83—42no—
104C2×Dic83—42no—
105C2×Dic83—42no—
106C2×Dic83—42no—
107Dic166—84no—
108C8×C83—82no—
109C83⋊C8—82no—
110C22×C83—21no—
111C22×C83—21no—
112C22×C83#40811yescharacteristic
113C22×C83C2×#9911yescharacteristic
114C22×C83C2×#10011yescharacteristic
115C4×C83—21no—
116C4×C83—22no—
117C4×C83—22no—
118C4×C83—41no—
119C4×C83—41no—
120C4×C83—41no—
121C4×C83—41no—
122C4×C83#35612yes—
123Dic83—44no—
124Dic83—82no—
125#11568—831nomaximal, Sylow
126C2×C83—21no—
127C2×C83—21no—
128C2×C83#147111yescharacteristic
129C2×C83#212911yescharacteristic
130C2×C83C2×#35611yescharacteristic
131#2546—831no—
132#1467D8311yescharacteristic
133#1461—831no—
134#1319—834no—
135C83#1156811yescharacteristic, complemented, Sylow
136C2×C4⋊Q8—832no—
137C2×C4⋊Q8—831no—
138C2×C4×Q8C2×D8311yescharacteristic
139#432—21no—
140#431—1661no—
141#398—1661no—
142#398—1661no—
143#391—832no—
144#389—1661no—
145#389—1661no—
146C4×C4⋊C4—831no—
147#324—21no—
148#324—832no—
149#324—1661no—
150#324C2×D8312yes—
151C22×Q8—832no—
152C22×Q8C4×D8311yescharacteristic
153C4⋊Q8—3321no—
154C4⋊Q8—3321no—
155C4⋊Q8—3324no—
156C4×Q8—41no—
157C4×Q8—41no—
158C2×C4⋊C4—1662no—
159C2×C4⋊C4—1662no—
160C2×C4⋊C4—1661no—
161C2×C4⋊C4—1661no—
162C2×C4⋊C4—1661no—
163C2×C4⋊C4D33211yescharacteristic
164C2×C4⋊C4C22⋊D8311yescharacteristic
165C2×C4⋊C4C22×D8311yescharacteristic
166C2×C42—832no—
167C2×C42C4×D8311yescharacteristic
168C2×C42D33211yescharacteristic
169C2×C42C22⋊D8311yescharacteristic
170C4⋊C8—41no—
171C4⋊C8—3321no—
172C22⋊C8—22no—
173C22⋊C8—1662no—
174#97—41no—
175C4×C8—3321no—
176#95—1661no—
177#95—1662no—
178#95—1662no—
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—41no—
182C2×Q8—3322no—
183C2×Q8—3322no—
184C2×Q8—1664no—
185C22×C4—1662no—
186C22×C4—1662no—
187C22×C4(C2×D83)⋊C411yescharacteristic
188C22×C4(C2×D83)⋊C411yescharacteristic
189C22×C4(C2×D83)⋊C411yescharacteristic
190C22×C4(C2×D83)⋊C411yescharacteristic
191C22×C4C2×C4×D8311yescharacteristic
192C22×C4C2×C22⋊D8311yescharacteristic
193C22×C4C2×D33211yescharacteristic
194C2×C8—42no—
195C2×C8—3322no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—3324no—
200C4⋊C4—3322no—
201C4⋊C4—3321no—
202C4⋊C4—3321no—
203C4⋊C4—3324no—
204C4⋊C4—1664no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—3322no—
212C23C2×(C2×D83)⋊C411yescharacteristic
213Q8—44no—
214Q8—6644no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—3322no—
230C2×C4—3322no—
231C2×C4—3322no—
232C2×C4—3322no—
233C2×C4—3322no—
234C2×C4—1664no—
235C2×C4#1458170611yescharacteristic
236C2×C4#1458170611yescharacteristic
237C2×C4#1458170812yes—
238C2×C4#1458180012yes—
239C8—82no—
240C8—6642no—
241C22—21no—
242C22—21no—
243C22#1912766911yescharacteristic
244C22C2×#1458170611yescharacteristic
245C22C2×#1458170811yescharacteristic
246C4—21no—
247C4—22no—
248C4—22no—
249C4—41no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—3324no—
254C4—6642no—
255C4#1912749912yes—
256C2—21no—
257C2—21no—
258C2#2490582411yescharacteristic
259C2#2490913711yescharacteristic
260C2C2×#1912749911yescharacteristic
subgroupG/H
centerC22C2×#14581706
commutatorC22×C4×C83C22×C4
FrattiniC2×C4⋊C4C22×D83
FittingC83×#1467C2
socleC22×C83C2×#99
prime radicalC23×C83C2×C22⋊C4
cosocleC2×C4⋊C4×C83C23
hypercenter#1467D83
hypocenterC83#11568
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
135. C83#11568semidirect

Maximal subgroups

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

subgroupindex
#249124482
#249057872
#249053962
C83×#14672
#1156883