Finite Group Databasebeta

← #35308685

Subgroups — #35308685

Order 21248.

364 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 97 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#24917987C211yesmaximal, characteristic
2#24908186C211yesmaximal, characteristic
3#24906118C212yesmaximal
4#24905963C212yesmaximal
5C83×#1275C211yesmaximal, characteristic
6#19128258C2212yes—
7#19128110—22no—
8#19128110—22no—
9#19127739—21no—
10#19127739—21no—
11C2×C4⋊(C83⋊C8)C2211yescharacteristic
12C2×Dic83⋊C8—21no—
13C4×C4⋊Dic83C2211yescharacteristic
14#19127455—21no—
15#19127449—22no—
16#19127448—22no—
17#19127439—22no—
18#19127439—22no—
19#431×C83C2212yes—
20C2×#97×C83C2211yescharacteristic
21C22×C83⋊C8—21no—
22#14581792D412yes—
23#14581792D412yes—
24#14581784—22no—
25#14581771—22no—
26#14581771—22no—
27C4×Dic166—22no—
28C4×Dic166—22no—
29#14581751—22no—
30C2×C4⋊Dic83—21no—
31C2×C4×Dic83—21no—
32#14581726—21no—
33#14581726—21no—
34#14581726—21no—
35#14581726—21no—
36#14581724—22no—
37#14581724—22no—
38C4⋊(C83⋊C8)—22no—
39Dic83⋊C8—42no—
40C83⋊#95D411yescharacteristic
41C83⋊#95D411yescharacteristic
42C22×C8×C83D411yescharacteristic
43C22×C8×C83D411yescharacteristic
44C2×C42×C83C2311yescharacteristic
45C4⋊C8×C83—22no—
46C22⋊C8×C83—22no—
47#97×C83—22no—
48C4×C8×C83—22no—
49C2×Dic166—22no—
50C2×Dic166—22no—
51C22×Dic83—21no—
52C22×Dic83—21no—
53C2×C83⋊C8—41no—
54C2×C83⋊C8—41no—
55C2×C83⋊C8—41no—
56C4⋊Dic83—22no—
57C4⋊Dic83—22no—
58C4⋊Dic83—22no—
59C4⋊Dic83—22no—
60C4⋊Dic83—42no—
61Dic83⋊C4—42no—
62Dic83⋊C4—42no—
63C22⋊Dic83—42no—
64C4×Dic83—42no—
65C4×Dic83—41no—
66C4×Dic83—41no—
67C22×C4×C83C2×D411yescharacteristic
68C22×C4×C83C2×D411yescharacteristic
69C22×C4×C83#4111yescharacteristic
70C2×C8×C83—21no—
71C2×C8×C83—21no—
72C2×C8×C83—21no—
73C2×C8×C83—21no—
74C2×C8×C83—42no—
75C2×C8×C83SD1612yes—
76C2×C8×C83Q1612yes—
77C42×C83C2×D412yes—
78C42×C83#4112yes—
79C23×C83#12111yescharacteristic
80C2×C4×C83—41no—
81C2×C4×C83—41no—
82C2×C4×C83#12011yescharacteristic
83C2×C4×C83#12112yes—
84C2×C4×C83#12312yes—
85C2×C4×C83#12411yescharacteristic
86C2×C4×C83C2×SD1611yescharacteristic
87C2×C4×C83C2×Q1611yescharacteristic
88C2×C4×C83#13711yescharacteristic
89C2×C4×C83#13711yescharacteristic
90C2×Dic83—22no—
91C2×Dic83—41no—
92C2×Dic83—41no—
93C2×Dic83—41no—
94C2×Dic83—41no—
95C2×Dic83—42no—
96C2×Dic83—42no—
97C2×Dic83—41no—
98Dic166—82no—
99Dic166—82no—
100C8×C83—22no—
101C8×C83—22no—
102C8×C83—82no—
103C83⋊C8—81no—
104C22×C83—21no—
105C22×C83—21no—
106C22×C83#39411yescharacteristic
107C22×C83#46111yescharacteristic
108C22×C83#46211yescharacteristic
109C4×C83—22no—
110C4×C83—22no—
111C4×C83#44811yescharacteristic
112C4×C83#45111yescharacteristic
113C4×C83#48711yescharacteristic
114C4×C83#49111yescharacteristic
115Dic83—42no—
116Dic83—81no—
117Dic83—82no—
118Dic83—82no—
119#10548—831nomaximal, Sylow
120C2×C83—21no—
121C2×C83—21no—
122C2×C83#204311yescharacteristic
123C2×C83#205011yescharacteristic
124C2×C83#205311yescharacteristic
125#3162—831no—
126#1940—831no—
127#1542—832no—
128#1503—832no—
129#1275D8311yescharacteristic
130C83#1054811yescharacteristic, complemented, Sylow
131#533—832no—
132#501—1662no—
133#501—1662no—
134#431C2×D8312yes—
135#427—1661no—
136#427—1661no—
137C2×C4⋊C8—831no—
138C2×C4⋊C8—1661no—
139C2×#97C2×D8311yescharacteristic
140C4×C4⋊C4—831no—
141#336—1661no—
142#333—1662no—
143#332—1662no—
144#328—1662no—
145#328—1662no—
146C22×C8—1661no—
147C22×C8D33211yescharacteristic
148C22×C8D33211yescharacteristic
149C4⋊Q8—832no—
150C4⋊Q8—832no—
151#125—1662no—
152C22⋊Q8—1662no—
153C22⋊Q8—1662no—
154C4×Q8—1662no—
155C4×Q8—1662no—
156#117—1662no—
157C2×C4⋊C4—1661no—
158C2×C42—1661no—
159C2×C42C22×D8311yescharacteristic
160#107—1661no—
161#107—1661no—
162#107—1661no—
163#107—1661no—
164#106—1662no—
165#106—1662no—
166C4⋊C8—22no—
167C4⋊C8—3322no—
168C4⋊C8—1662no—
169C22⋊C8—22no—
170#97—22no—
171C4×C8—22no—
172#95—831no—
173#95—831no—
174C2×Q8—1662no—
175C2×Q8—1662no—
176C22×C4—1661no—
177C22×C4—1661no—
178C22×C4D4×D8311yescharacteristic
179C22×C4C2×D33211yescharacteristic
180C22×C4#1305059111yescharacteristic
181C2×C8—21no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—42no—
186C2×C8—3321no—
187C2×C8—3321no—
188C2×C8—3321no—
189C2×C8#1305057912yes—
190C2×C8Dic33212yes—
191C4⋊C4—3322no—
192C4⋊C4—3322no—
193C4⋊C4—3322no—
194C4⋊C4—1662no—
195C4⋊C4—1662no—
196C4⋊C4—1662no—
197C4⋊C4—1662no—
198C22⋊C4—3322no—
199C42—3322no—
200C42—3321no—
201C42—3321no—
202C42D4×D8312yes—
203C42#1305059012yes—
204C23#1458176711yescharacteristic
205Q8—6642no—
206Q8—6642no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—3321no—
210C2×C4—3321no—
211C2×C4—3321no—
212C2×C4—3321no—
213C2×C4—3322no—
214C2×C4—3322no—
215C2×C4—3321no—
216C2×C4—1662no—
217C2×C4#1458176211yescharacteristic
218C2×C4#1458176512yes—
219C2×C4#1458177712yes—
220C2×C4#1458178011yescharacteristic
221C2×C4C2×#1305057911yescharacteristic
222C2×C4C2×Dic33211yescharacteristic
223C2×C4#1458182511yescharacteristic
224C2×C4#1458182511yescharacteristic
225C8—22no—
226C8—22no—
227C8—82no—
228C8—6641no—
229C22—21no—
230C22—21no—
231C22#1912761911yescharacteristic
232C22#1912790711yescharacteristic
233C22#1912791211yescharacteristic
234C4—22no—
235C4—22no—
236C4—3322no—
237C4—6641no—
238C4—6642no—
239C4—6642no—
240C4#1912784211yescharacteristic
241C4#1912785911yescharacteristic
242C4#1912805211yescharacteristic
243C4#1912807011yescharacteristic
244C2—21no—
245C2—21no—
246C2#2490871011yescharacteristic
247C2#2490875111yescharacteristic
248C2#2490877011yescharacteristic
subgroupG/H
centerC2×C4#14581780
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1275C2
socleC22×C83#394
prime radicalC23×C83#121
hypercenter#1275D83
hypocenterC83#10548
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
130. C83#10548semidirect

Maximal subgroups

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

subgroupindex
#249179872
#249081862
#249061182
#249059632
C83×#12752
#1054883