Finite Group Databasebeta

← #35307898

Subgroups — #35307898

Order 21248.

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

normal subgroups only

This group has 386 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#24915531C211yesmaximal, characteristic
2#24908431C212yesmaximal
3C2×#19127442C212yesmaximal
4#24905344C211yesmaximal, characteristic
5C83×#1836C211yesmaximal, characteristic
6C2×#14581784C2212yes—
7C2×#14581703C2212yes—
8#19127641—22no—
9#19127633—22no—
10#19127631—22no—
11#19127463—22no—
12#19127463—22no—
13#19127442—24no—
14C2×#97×C83C2211yescharacteristic
15#384×C83C2211yescharacteristic
16#382×C83C2211yescharacteristic
17#340×C83—22no—
18C22×C83⋊C8—22no—
19#14581784—22no—
20#14581784—22no—
21#14581784—22no—
22#14581784—22no—
23C2×C4⋊Dic83—22no—
24C2×C4⋊Dic83D412yes—
25C2×C4⋊Dic83D412yes—
26C2×Dic83⋊C4—22no—
27C2×Dic83⋊C4—22no—
28#14581703—22no—
29#14581703—22no—
30C83⋊#95—24no—
31C83⋊#95—22no—
32C22×C8×C83—21no—
33C2×C4⋊C4×C83—21no—
34C2×C4⋊C4×C83—22no—
35C2×C4⋊C4×C83D412yes—
36C2×C42×C83C2311yescharacteristic
37#97×C83—21no—
38#97×C83D412yes—
39#95×C83—22no—
40C22×Dic83—22no—
41C22×Dic83—22no—
42C2×C83⋊C8—24no—
43C2×C83⋊C8—42no—
44C2×C83⋊C8—42no—
45C4⋊Dic83—22no—
46C4⋊Dic83—22no—
47C4⋊Dic83—22no—
48C4⋊Dic83—22no—
49C4⋊Dic83—82no—
50Dic83⋊C4—42no—
51Dic83⋊C4—42no—
52Dic83⋊C4—42no—
53Dic83⋊C4—42no—
54C22×C4×C83—22no—
55C22×C4×C83—41no—
56C22×C4×C83C2×D412yes—
57C22×C4×C83C2×D411yescharacteristic
58C2×C8×C83—22no—
59C2×C8×C83—41no—
60C2×C8×C83—41no—
61C4⋊C4×C83—42no—
62C4⋊C4×C83—42no—
63C4⋊C4×C83—44no—
64C42×C83C2×D411yescharacteristic
65C42×C83#4111yescharacteristic
66C42×C83#4112yes—
67C23×C83#12011yescharacteristic
68C2×C4×C83—21no—
69C2×C4×C83—22no—
70C2×C4×C83—21no—
71C2×C4×C83—22no—
72C2×C4×C83—42no—
73C2×C4×C83—42no—
74C2×C4×C83—42no—
75C2×C4×C83—82no—
76C2×C4×C83—81no—
77C2×C4×C83#12111yescharacteristic
78C2×C4×C83#12112yes—
79C2×C4×C83#12312yes—
80C2×C4×C83#12411yescharacteristic
81C2×Dic83—42no—
82C2×Dic83—42no—
83C2×Dic83—42no—
84C2×Dic83—42no—
85C2×Dic83—42no—
86C2×Dic83—42no—
87C8×C83—42no—
88C83⋊C8—44no—
89C22×C83#39411yescharacteristic
90C22×C83#45412yes—
91C22×C83#45411yescharacteristic
92C22×C83#45511yescharacteristic
93C22×C83#45612yes—
94C4×C83—22no—
95C4×C83—22no—
96C4×C83—21no—
97C4×C83—21no—
98C4×C83—82no—
99C4×C83—161no—
100Dic83—82no—
101Dic83—82no—
102#10428—831nomaximal, Sylow
103C2×C83#165811yescharacteristic
104C2×C83#166311yescharacteristic
105C2×C83#166412yes—
106C2×C83#203812yes—
107C2×C83#204011yescharacteristic
108#2822—831no—
109#1992—832no—
110#1836D8311yescharacteristic
111C2×#330—832no—
112#1295—831no—
113C83#1042811yescharacteristic, complemented, Sylow
114C2×#125—832no—
115C2×#97—832no—
116C2×#97C2×D8311yescharacteristic
117#400—1662no—
118#398—1662no—
119#398—1662no—
120#384C2×D8311yescharacteristic
121#382C2×D8311yescharacteristic
122#340—22no—
123#340—1662no—
124#340—1662no—
125#330—1664no—
126C22×C8—21no—
127C22×C8—1662no—
128#125—1662no—
129#125—1662no—
130#125—1662no—
131#125—1662no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—832no—
135C2×C4⋊C4—832no—
136C2×C4⋊C4—1662no—
137C2×C4⋊C4—1662no—
138C2×C4⋊C4—1662no—
139C2×C4⋊C4C22⋊D8312yes—
140C2×C42C22×D8311yescharacteristic
141#97—21no—
142#97—1662no—
143#97—1662no—
144#97D33212yes—
145#95—22no—
146#95—1664no—
147#95—1662no—
148C22×C4—22no—
149C22×C4—41no—
150C22×C4—1662no—
151C22×C4—1662no—
152C22×C4D4×D8312yes—
153C22×C4C2×C22⋊D8311yescharacteristic
154C2×C8—22no—
155C2×C8—41no—
156C2×C8—41no—
157C2×C8—3322no—
158C2×C8—3322no—
159C2×C8—1664no—
160C4⋊C4—42no—
161C4⋊C4—44no—
162C4⋊C4—42no—
163C4⋊C4—3322no—
164C4⋊C4—3322no—
165C4⋊C4—3322no—
166C4⋊C4—3322no—
167C4⋊C4—6642no—
168C4⋊C4—1662no—
169C4⋊C4—1662no—
170C4⋊C4—1662no—
171C4⋊C4—1662no—
172C42C2×D33211yescharacteristic
173C42#1305059011yescharacteristic
174C42#1305059112yes—
175C23#1458176011yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—82no—
184C2×C4—81no—
185C2×C4—3322no—
186C2×C4—3322no—
187C2×C4—3322no—
188C2×C4—3322no—
189C2×C4—3322no—
190C2×C4—3322no—
191C2×C4#1458176611yescharacteristic
192C2×C4#1458176712yes—
193C2×C4#1458177712yes—
194C2×C4#1458178111yescharacteristic
195C8—42no—
196C8—3324no—
197C22#1912761811yescharacteristic
198C22#1912787212yes—
199C22#1912787311yescharacteristic
200C22#1912787811yescharacteristic
201C22#1912788212yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—161no—
208C4—6642no—
209C4—6642no—
210C2#2490676411yescharacteristic
211C2#2490678911yescharacteristic
212C2#2490679612yes—
213C2#2490868212yes—
214C2#2490869211yescharacteristic
subgroupG/H
centerC23#14581760
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1836C2
socle, prime radicalC23×C83#120
hypercenter#1836D83
hypocenterC83#10428
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
113. C83#10428semidirect

Maximal subgroups

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

subgroupindex
#249155312
#249084312
C2×#191274422
#249053442
C83×#18362
#1042883