Finite Group Databasebeta

← #35313707

Subgroups — #35313707

Order 21248.

368 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 83 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#24916162C211yesmaximal, characteristic
2#24909082C212yesmaximal, complemented
3#24905415C212yesmaximal, complemented
4#24905399C211yesmaximal, characteristic, complemented
5C83×#1320C211yesmaximal, characteristic, complemented
6C2×#14581800C2211yescharacteristic
7C22×#13050574C411yescharacteristic
8#19128212C411yescharacteristic
9M32×D83—22no—
10#19127776—22no—
11#19127775—22no—
12#19127729C2211yescharacteristic
13#19127669C411yescharacteristic
14#19127659C411yescharacteristic
15#19127483C2212yes—
16#19127482—22no—
17#407×C83C2211yescharacteristic
18#349×C83C2212yes—
19C2×#13050590C2×C411yescharacteristic
20#14581800—42no—
21C2×#13050574—21no—
22C2×#13050574—21no—
23C2×#13050574—42no—
24C2×#13050573D412yes—
25C22×C83⋊C8C2×C411yescharacteristic
26C22×C83⋊C8C2×C411yescharacteristic
27C2×C8×D83D412yes—
28#14581775C812yes—
29#14581771—21no—
30#14581766—21no—
31#14581761C812yes—
32C4×C22⋊D83—22no—
33#14581751C2×C411yescharacteristic
34#14581732—22no—
35#14581731—42no—
36C16×D83—42no—
37Dic83⋊C8—22no—
38(C2×D83)⋊C8—22no—
39#14581702—21no—
40C8×Dic83—21no—
41C23×C4×C83C2×C411yescharacteristic
42C2×M16×C83C2×C411yescharacteristic
43C2×M16×C83C2311yescharacteristic
44M32×C83—22no—
45C22⋊C8×C83—22no—
46#13050590—41no—
47#13050590—41no—
48C2×Dic166M1611yescharacteristic
49C2×D332M1611yescharacteristic
50C2×C22⋊D83—22no—
51C2×C22⋊D83C2×C812yes—
52C2×C4×D83C22⋊C412yes—
53#13050574—42no—
54#13050574—42no—
55#13050573—42no—
56C2×C83⋊C8—22no—
57C2×C83⋊C8—21no—
58C2×C83⋊C8—41no—
59C2×C83⋊C8C22⋊C411yescharacteristic
60C2×C83⋊C8C22⋊C411yescharacteristic
61C8×D83—22no—
62C8×D83—22no—
63C4⋊Dic83—21no—
64Dic83⋊C4—22no—
65C22⋊Dic83—22no—
66C22⋊Dic83C2×C812yes—
67(C2×D83)⋊C4—22no—
68C4×Dic83—21no—
69C83⋊C16—42no—
70C24×C83C2×C811yescharacteristic
71C22×C4×C83—21no—
72C22×C4×C83—21no—
73C22×C4×C83—41no—
74C22×C4×C83—41no—
75C22×C4×C83C2×C811yescharacteristic
76C22×C4×C83C22×C411yescharacteristic
77M16×C83—41no—
78M16×C83—41no—
79C2×C8×C83—21no—
80C2×C8×C83C2×D412yes—
81C16×C83—42no—
82C23×C83—21no—
83C23×C83—41no—
84C23×C83—81no—
85C23×C83C22×C811yescharacteristic
86C22×D83C22⋊C812yes—
87C2×C4×C83—21no—
88C2×C4×C83—21no—
89C2×C4×C83—21no—
90C2×C4×C83—42no—
91C2×C4×C83—41no—
92C2×C4×C83—41no—
93C2×C4×C83—41no—
94C2×C4×C83C2×C22⋊C411yescharacteristic
95C2×C4×C83C2×M1611yescharacteristic
96C22⋊D83—42no—
97C22⋊D83—82no—
98C2×Dic83—22no—
99C2×Dic83C22⋊C812yes—
100D332—41no—
101C4×D83—22no—
102C4×D83—22no—
103Dic166—41no—
104C8×C83—22no—
105C8×C83—41no—
106C83⋊C8—21no—
107C83⋊C8—41no—
108C83⋊C8#9912yes—
109C22×C83—21no—
110C22×C83—41no—
111C22×C83—41no—
112C22×C83—41no—
113C22×C83—41no—
114C22×C83—82no—
115C22×C83C2×C22⋊C811yescharacteristic
116C2×D83—22no—
117C2×D83—42no—
118C4×C83—21no—
119C4×C83—41no—
120C4×C83C2×#9911yescharacteristic
121C4×C83#41311yescharacteristic
122Dic83—22no—
123Dic83—42no—
124#11484—831nomaximal, Sylow
125C2×C83—21no—
126C2×C83—41no—
127C2×C83—81no—
128C2×C83#145911yescharacteristic
129D83—42no—
130#2930—831no—
131#2115—832no—
132#1328—832no—
133#1320—831no—
134#1320D8311yescharacteristic, complemented
135C83#1148411yescharacteristic, complemented, Sylow
136C2×#131—831no—
137C22×M16—831no—
138#525—831no—
139C2×M32—1662no—
140#436—1662no—
141#435—1662no—
142#424—831no—
143#408—831no—
144#407C2×D8311yescharacteristic
145#405—831no—
146#349—832no—
147#349—1662no—
148#349C2×D8312yes—
149C2×#41—831no—
150C23×C4C4×D8311yescharacteristic
151#131—3322no—
152C2×M16—3322no—
153C2×M16—832no—
154C2×M16—1661no—
155C2×M16—1661no—
156C2×M16C4×D8311yescharacteristic
157C2×M16C22×D8311yescharacteristic
158C22×C8—831no—
159C22×C8—831no—
160C22×C8—832no—
161#123—832no—
162C22⋊Q8—1661no—
163#121—1661no—
164#120—832no—
165C4×D4—1662no—
166#117—831no—
167M32—22no—
168M32—3322no—
169M32—1662no—
170C2×C16—3322no—
171C4⋊C8—1662no—
172C22⋊C8—22no—
173C22⋊C8—1662no—
174#97—1661no—
175C4×C8—1661no—
176C24C8×D8311yescharacteristic
177#41—3321no—
178#41—3321no—
179C2×Q8—831no—
180C2×D4—832no—
181C2×D4—831no—
182C2×D4—1662no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—832no—
188C22×C4C8×D8311yescharacteristic
189C22×C4C2×C4×D8311yescharacteristic
190M16—41no—
191M16—41no—
192M16—3322no—
193M16—3322no—
194M16—3322no—
195C2×C8—21no—
196C2×C8—3321no—
197C2×C8—831no—
198C2×C8—831no—
199C2×C8—1662no—
200C2×C8—1662no—
201C2×C8—1661no—
202C2×C8—1662no—
203C2×C8D4×D8312yes—
204C4⋊C4—1662no—
205C4⋊C4—1661no—
206C22⋊C4—832no—
207C22⋊C4—1662no—
208C22⋊C4—1662no—
209C42—1661no—
210C16—42no—
211C16—3322no—
212C23—21no—
213C23—41no—
214C23—81no—
215C23—832no—
216C23C2×C8×D8311yescharacteristic
217Q8—3321no—
218D4—3321no—
219D4—3322no—
220D4—6642no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—832no—
229C2×C4—1662no—
230C2×C4—1662no—
231C2×C4—1662no—
232C2×C4C22⋊C4×D8311yescharacteristic
233C2×C4M16×D8311yescharacteristic
234C8—22no—
235C8—41no—
236C8—3321no—
237C8—832no—
238C8—1661no—
239C22—21no—
240C22—41no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—82no—
245C22—3322no—
246C22—1662no—
247C22C22⋊C8×D8311yescharacteristic
248C4—21no—
249C4—41no—
250C4—3322no—
251C4—1662no—
252C4#99×D8311yescharacteristic
253C4#1912768211yescharacteristic
254C2—21no—
255C2—41no—
256C2—81no—
257C2—3322no—
258C2#2490577811yescharacteristic
subgroupG/H
centerC4#99×D83
commutatorC23×C83C22×C8
FrattiniC2×M16C22×D83
FittingC83×#1320C2
socleC2×C83#1459
prime radical#19128212C4
cosocleC2×M16×C83C23
hypercenter#1320D83
hypocenterC83#11484
LCSG ▷ C23×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #24909082C2semidirect
3. #24905415C2semidirect
4. #24905399C2semidirect
5. C83×#1320C2semidirect
134. #1320D83semidirect
135. C83#11484semidirect

Maximal subgroups

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

subgroupindex
#249161622
#249090822
#249054152
#249053992
C83×#13202
#1148483