Finite Group Databasebeta

← #35313640

Subgroups — #35313640

Order 21248.

398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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#24916156C211yesmaximal, characteristic
2C22⋊C16×D83C212yesmaximal, complemented
3#24905405C211yesmaximal, characteristic, complemented
4#24905388C212yesmaximal, complemented
5C83×#1323C211yesmaximal, characteristic, complemented
6C2×#14581800C411yescharacteristic
7C22×C8×D83C2211yescharacteristic
8#19128213C411yescharacteristic
9C2×C16×D83—22no—
10#19127771—22no—
11#19127766—22no—
12#19127667C2211yescharacteristic
13#19127664C411yescharacteristic
14#19127657C411yescharacteristic
15C22⋊(C83⋊C16)C2212yes—
16(C2×D83)⋊C16—22no—
17#424×C83C2211yescharacteristic
18C22⋊C16×C83C2212yes—
19C2×#13050590C2×C411yescharacteristic
20C22×C4×D83C2×C411yescharacteristic
21#14581800—42no—
22C2×#13050574C2×C411yescharacteristic
23C2×#13050573—21no—
24C22×C83⋊C8C2×C411yescharacteristic
25C2×C8×D83—21no—
26C2×C8×D83—42no—
27C2×C8×D83D412yes—
28C2×C8×D83D412yes—
29#14581776—21no—
30#14581772C812yes—
31#14581767C812yes—
32#14581762—21no—
33C4×D332—22no—
34C2×C83⋊C16—22no—
35C16×D83—44no—
36(C2×D83)⋊C8—22no—
37(C2×D83)⋊C8—22no—
38#14581703—21no—
39C4×C83⋊C8—21no—
40C2×M16×C83C2×C411yescharacteristic
41C22×C8×C83C2311yescharacteristic
42#117×C83C2×C411yescharacteristic
43C2×C16×C83—22no—
44C4⋊C8×C83—22no—
45C23×D83M1611yescharacteristic
46#13050590—41no—
47#13050590—41no—
48C2×Dic166C2×C811yescharacteristic
49C2×D332—22no—
50C2×D332C2×C811yescharacteristic
51C2×C22⋊D83—21no—
52C22×Dic83M1611yescharacteristic
53C2×C4×D83—21no—
54C2×C4×D83—41no—
55C2×C4×D83—41no—
56C2×C4×D83C22⋊C412yes—
57C2×C4×D83C2×C812yes—
58#13050574—41no—
59#13050573—42no—
60C2×C83⋊C8—22no—
61C2×C83⋊C8—21no—
62C2×C83⋊C8C22⋊C411yescharacteristic
63C2×C83⋊C8C22⋊C411yescharacteristic
64C8×D83—24no—
65C8×D83—42no—
66C8×D83—42no—
67C4⋊Dic83—22no—
68(C2×D83)⋊C4—22no—
69(C2×D83)⋊C4—22no—
70C83⋊C16—42no—
71C22×C4×C83C22×C411yescharacteristic
72M16×C83—41no—
73C2×C8×C83—21no—
74C2×C8×C83—41no—
75C2×C8×C83C2×D412yes—
76C4⋊C4×C83C2×C812yes—
77C22⋊C4×C83—21no—
78C42×C83—21no—
79C16×C83—42no—
80C23×C83C2×M1611yescharacteristic
81C22×D83—24no—
82C22×D83—21no—
83C22×D83—41no—
84C22×D83C22⋊C812yes—
85C2×C4×C83—21no—
86C2×C4×C83—21no—
87C2×C4×C83—22no—
88C2×C4×C83C2×C22⋊C411yescharacteristic
89C2×C4×C83C22×C811yescharacteristic
90C22⋊D83—42no—
91C2×Dic83—21no—
92C2×Dic83—41no—
93C2×Dic83C22⋊C812yes—
94D332—41no—
95D332—44no—
96C4×D83—22no—
97C4×D83—22no—
98C4×D83—42no—
99C4×D83—41no—
100C4×D83—41no—
101Dic166—41no—
102C8×C83—22no—
103C8×C83—41no—
104C83⋊C8—21no—
105C83⋊C8—41no—
106C83⋊C8#9912yes—
107C22×C83—22no—
108C22×C83—21no—
109C22×C83C2×C22⋊C811yescharacteristic
110C2×D83—22no—
111C2×D83—22no—
112C2×D83—44no—
113C2×D83—42no—
114C2×D83—41no—
115C2×D83#35014yes—
116C4×C83—21no—
117C4×C83—42no—
118C4×C83C2×#9911yescharacteristic
119C4×C83#41311yescharacteristic
120Dic83—22no—
121Dic83—41no—
122#11468—831nomaximal, Sylow
123C2×C83—41no—
124C2×C83#145911yescharacteristic
125C2×C83C2×#35012yes—
126D83—24no—
127D83—81no—
128#2929—831no—
129C2×C22⋊C16—832no—
130#1323—831no—
131#1323D8311yescharacteristic, complemented
132#1315—832no—
133C83#1146811yescharacteristic, complemented, Sylow
134C2×#131—831no—
135C23×C8—831no—
136#525—831no—
137C22×C16—1662no—
138#435—1662no—
139C8×D4—1662no—
140#424C2×D8311yescharacteristic
141#408—831no—
142#407—831no—
143#405—831no—
144C22⋊C16—832no—
145C22⋊C16—1662no—
146C22⋊C16C2×D8312yes—
147C2×#41—831no—
148C23×C4—831no—
149#131—3322no—
150C2×M16—831no—
151C2×M16—1661no—
152C2×M16C4×D8311yescharacteristic
153C22×C8—3322no—
154C22×C8—832no—
155C22×C8—831no—
156C22×C8—832no—
157C22×C8—1661no—
158C22×C8C22×D8311yescharacteristic
159#123—1661no—
160C22⋊Q8—832no—
161#121—832no—
162#120—1661no—
163C4×D4—1662no—
164#117C4×D8311yescharacteristic
165C2×C16—22no—
166C2×C16—3324no—
167C2×C16—1662no—
168C4⋊C8—22no—
169C22⋊C8—1662no—
170C22⋊C8—1662no—
171#97—1661no—
172C4×C8—1661no—
173C24—831no—
174#41—3321no—
175#41—3321no—
176C2×Q8—831no—
177C2×D4—831no—
178C2×D4—1662no—
179C2×D4—1661no—
180C22×C4—3321no—
181C22×C4—3321no—
182C22×C4—831no—
183C22×C4—832no—
184C22×C4—832no—
185C22×C4—1661no—
186C22×C4C2×C4×D8311yescharacteristic
187M16—41no—
188M16—3322no—
189M16—3321no—
190C2×C8—21no—
191C2×C8—41no—
192C2×C8—3322no—
193C2×C8—3322no—
194C2×C8—831no—
195C2×C8—831no—
196C2×C8—1664no—
197C2×C8—1661no—
198C2×C8—1662no—
199C2×C8D4×D8312yes—
200C4⋊C4—1662no—
201C4⋊C4C8×D8312yes—
202C22⋊C4—21no—
203C22⋊C4—1662no—
204C22⋊C4—1662no—
205C42—21no—
206C16—42no—
207C16—3322no—
208C23—3321no—
209C23—832no—
210C23—1664no—
211C23—1661no—
212C23M16×D8311yescharacteristic
213Q8—3321no—
214D4—3321no—
215D4—3324no—
216D4—3322no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—3322no—
221C2×C4—3321no—
222C2×C4—3321no—
223C2×C4—3321no—
224C2×C4—832no—
225C2×C4—1661no—
226C2×C4—1662no—
227C2×C4—1662no—
228C2×C4C22⋊C4×D8311yescharacteristic
229C2×C4C2×C8×D8311yescharacteristic
230C8—22no—
231C8—41no—
232C8—3321no—
233C8—832no—
234C8—1661no—
235C22—22no—
236C22—21no—
237C22—3324no—
238C22—3322no—
239C22—3321no—
240C22—834no—
241C22—1662no—
242C22—1662no—
243C22C22⋊C8×D8311yescharacteristic
244C4—21no—
245C4—42no—
246C4—3321no—
247C4—1662no—
248C4#99×D8311yescharacteristic
249C4#1912768411yescharacteristic
250C2—41no—
251C2—6641no—
252C2—1664no—
253C2#2490578011yescharacteristic
254C2#350×D8312yes—
subgroupG/H
centerC2×C4C22⋊C4×D83
commutatorC2×C4×C83C22×C8
FrattiniC22×C8C22×D83
FittingC83×#1323C2
socleC22×C83C2×C22⋊C8
prime radical#19128213C4
cosocleC22×C8×C83C23
hypercenter#1323D83
hypocenterC83#11468
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
2. C22⋊C16×D83C2semidirect
3. #24905405C2semidirect
4. #24905388C2semidirect
5. C83×#1323C2semidirect
131. #1323D83semidirect
133. C83#11468semidirect

Maximal subgroups

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

subgroupindex
#249161562
C22⋊C16×D832
#249054052
#249053882
C83×#13232
#1146883