Finite Group Databasebeta

← #35308538

Subgroups — #35308538

Order 21248.

382 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 95 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#24918808C211yesmaximal, characteristic
2#24908439C212yesmaximal
3#24907579C211yesmaximal, characteristic
4#24906154C212yesmaximal
5C83×#1292C211yesmaximal, characteristic
6#19128258C2212yes—
7#19127997—22no—
8#19127942—22no—
9#19127912—22no—
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11C42×Dic83C2211yescharacteristic
12#19127462—22no—
13#19127462—22no—
14#19127455—22no—
15#19127449—22no—
16#19127446—22no—
17#423×C83C2212yes—
18C2×C4⋊C8×C83C2211yescharacteristic
19C2×Dic332—22no—
20C22×C83⋊C8—21no—
21#14581792D412yes—
22#14581792D412yes—
23#14581784—22no—
24#14581771—22no—
25#14581771—22no—
26C4×Dic166—22no—
27C4×Dic166—22no—
28#14581751—22no—
29C2×C4×Dic83—21no—
30C2×C4×Dic83—21no—
31C2×C4×Dic83D411yescharacteristic
32C2×C4×Dic83D411yescharacteristic
33#14581726—22no—
34C4⋊(C83⋊C8)—22no—
35#14581717—24no—
36C2×M16×C83—22no—
37C22×C8×C83D412yes—
38C2×C42×C83C2311yescharacteristic
39C4⋊C8×C83—22no—
40C4⋊C8×C83—22no—
41C4⋊C8×C83—22no—
42C2×Dic166—22no—
43C2×Dic166—22no—
44C22×Dic83—21no—
45C22×Dic83—21no—
46Dic332—82no—
47C2×C83⋊C8—42no—
48C2×C83⋊C8—41no—
49C4⋊Dic83—22no—
50C4⋊Dic83—22no—
51C4⋊Dic83—22no—
52C4⋊Dic83—22no—
53Dic83⋊C4—42no—
54Dic83⋊C4—42no—
55C22⋊Dic83—42no—
56C4×Dic83—21no—
57C4×Dic83—22no—
58C4×Dic83—42no—
59C4×Dic83—41no—
60C4×Dic83—41no—
61C4×Dic83—42no—
62C4×Dic83Q1612yescomplemented
63C22×C4×C83C2×D411yescharacteristic
64C22×C4×C83C2×D411yescharacteristic
65C22×C4×C83#4111yescharacteristic
66M16×C83—42no—
67M16×C83—42no—
68C2×C8×C83—22no—
69C2×C8×C83—42no—
70C2×C8×C83—42no—
71C42×C83C2×D412yes—
72C42×C83#4112yes—
73C23×C83#12111yescharacteristic
74C2×C4×C83—21no—
75C2×C4×C83—21no—
76C2×C4×C83—41no—
77C2×C4×C83#12011yescharacteristic
78C2×C4×C83#12112yes—
79C2×C4×C83#12312yes—
80C2×C4×C83#12411yescharacteristic
81C2×C4×C83C2×Q1611yescharacteristic
82C2×C4×C83#13511yescharacteristic
83C2×C4×C83#13712yes—
84C2×Dic83—22no—
85C2×Dic83—22no—
86C2×Dic83—41no—
87C2×Dic83—41no—
88C2×Dic83—41no—
89C2×Dic83—41no—
90C2×Dic83—42no—
91C2×Dic83—42no—
92Dic166—42no—
93Dic166—42no—
94Dic166—82no—
95C8×C83—42no—
96C8×C83—82no—
97C83⋊C8—81no—
98C22×C83—21no—
99C22×C83—21no—
100C22×C83#39411yescharacteristic
101C22×C83#46711yescharacteristic
102C22×C83#47011yescharacteristic
103C4×C83—22no—
104C4×C83—21no—
105C4×C83#45411yescharacteristic
106C4×C83#45511yescharacteristic
107C4×C83#46212yes—
108C4×C83#46412yes—
109Dic83—42no—
110Dic83—42no—
111Dic83—82no—
112Dic83—82no—
113#10523—831nomaximal, Sylow
114C2×C83—21no—
115C2×C83—21no—
116C2×C83#204011yescharacteristic
117C2×C83#205011yescharacteristic
118C2×C83#205611yescharacteristic
119#3249—831no—
120#1994—832no—
121#1831—831no—
122#1550—832no—
123#1292D8311yescharacteristic
124C83#1052311yescharacteristic, complemented, Sylow
125#533—832no—
126#477—1662no—
127#467—1662no—
128#462—1662no—
129#423C2×D8312yes—
130C2×C4⋊C8—831no—
131C2×C4⋊C8C2×D8311yescharacteristic
132C43—831no—
133#339—1662no—
134#339—1662no—
135#336—1662no—
136#333—1662no—
137#332—1662no—
138C2×Q16—1662no—
139C2×M16—22no—
140C22×C8—1661no—
141C22×C8D33212yes—
142C4⋊Q8—832no—
143C4⋊Q8—832no—
144#125—1662no—
145C22⋊Q8—1662no—
146C22⋊Q8—1662no—
147C4×Q8—1662no—
148C4×Q8—1662no—
149#117—1662no—
150C2×C42—831no—
151C2×C42—831no—
152C2×C42—1661no—
153C2×C42—1661no—
154C2×C42C22×D8311yescharacteristic
155#107—1662no—
156C4⋊C8—22no—
157C4⋊C8—22no—
158C4⋊C8—22no—
159C4⋊C8—1662no—
160#103—1664no—
161C2×Q8—1662no—
162C2×Q8—1662no—
163C22×C4—1661no—
164C22×C4—1661no—
165C22×C4D4×D8311yescharacteristic
166C22×C4C2×D33211yescharacteristic
167C22×C4#1305059111yescharacteristic
168Q16—6642no—
169M16—42no—
170M16—42no—
171C2×C8—22no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—3322no—
175C2×C8—3321no—
176C4⋊C4—3322no—
177C4⋊C4—3322no—
178C4⋊C4—1662no—
179C4⋊C4—1662no—
180C4⋊C4—1662no—
181C4⋊C4—1662no—
182C22⋊C4—3322no—
183C42—3321no—
184C42—3321no—
185C42—3322no—
186C42—3322no—
187C42—832no—
188C42—1662no—
189C42—1661no—
190C42D4×D8312yes—
191C42#1305059012yes—
192C23#1458176711yescharacteristic
193Q8—3322no—
194Q8—3322no—
195Q8—6642no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—3321no—
200C2×C4—3321no—
201C2×C4—3321no—
202C2×C4—3321no—
203C2×C4—3322no—
204C2×C4—3322no—
205C2×C4—1662no—
206C2×C4—1662no—
207C2×C4#1458176211yescharacteristic
208C2×C4#1458176512yes—
209C2×C4#1458177712yes—
210C2×C4#1458178011yescharacteristic
211C2×C4Q16×D8311yescharacteristic
212C2×C4#1458181111yescharacteristic
213C2×C4#1458182112yes—
214C8—42no—
215C8—82no—
216C8—6641no—
217C22—21no—
218C22—21no—
219C22#1912761911yescharacteristic
220C22#1912794311yescharacteristic
221C22#1912796011yescharacteristic
222C4—21no—
223C4—22no—
224C4—3322no—
225C4—3322no—
226C4—6642no—
227C4—6642no—
228C4#1912787611yescharacteristic
229C4#1912788111yescharacteristic
230C4#1912791012yes—
231C4#1912792212yes—
232C2—21no—
233C2—21no—
234C2#2490869311yescharacteristic
235C2#2490875111yescharacteristic
236C2#2490878711yescharacteristic
subgroupG/H
centerC22#19127619
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1292C2
socleC22×C83#394
prime radicalC23×C83#121
hypercenter#1292D83
hypocenterC83#10523
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
62. C4×Dic83Q16semidirect
124. C83#10523semidirect

Maximal subgroups

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

subgroupindex
#249188082
#249084392
#249075792
#249061542
C83×#12922
#1052383