Finite Group Databasebeta

← #35307899

Subgroups — #35307899

Order 21248.

386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 89 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#24908432C212yesmaximal
3#24907596C211yesmaximal, characteristic
4C2×#19127442C212yesmaximal
5C83×#1295C211yesmaximal, characteristic
6C2×#14581784C2212yes—
7C2×#14581703C2211yescharacteristic
8#19127641—22no—
9#19127633—22no—
10#19127631—22no—
11#19127571C2211yescharacteristic
12#19127464—22no—
13#19127464—22no—
14#19127463—22no—
15#19127442—24no—
16C2×#97×C83C2212yes—
17#382×C83C2211yescharacteristic
18C22×C83⋊C8—21no—
19#14581784—22no—
20#14581784—22no—
21#14581784—22no—
22#14581784—22no—
23C2×C4⋊Dic83—22no—
24C2×C4⋊Dic83—21no—
25C2×C4⋊Dic83—22no—
26C2×C4⋊Dic83D412yes—
27C2×C4⋊Dic83D412yes—
28C2×Dic83⋊C4—22no—
29C2×Dic83⋊C4—22no—
30#14581703—21no—
31#14581703D412yes—
32C83⋊#95—24no—
33C83⋊#95—22no—
34C22×C8×C83—22no—
35C2×C4⋊C4×C83D412yes—
36C2×C42×C83C2311yescharacteristic
37#97×C83—22no—
38#97×C83—22no—
39#95×C83—22no—
40C22×Dic83—22no—
41C22×Dic83—22no—
42C22×Dic83—41no—
43C2×C83⋊C8—22no—
44C2×C83⋊C8—41no—
45C2×C83⋊C8—41no—
46C4⋊Dic83—22no—
47C4⋊Dic83—22no—
48C4⋊Dic83—22no—
49C4⋊Dic83—22no—
50C4⋊Dic83—44no—
51C4⋊Dic83—42no—
52C4⋊Dic83—82no—
53Dic83⋊C4—42no—
54Dic83⋊C4—42no—
55Dic83⋊C4—42no—
56Dic83⋊C4—42no—
57C22×C4×C83—22no—
58C22×C4×C83C2×D412yes—
59C22×C4×C83C2×D411yescharacteristic
60C2×C8×C83—24no—
61C2×C8×C83—42no—
62C2×C8×C83—42no—
63C4⋊C4×C83—42no—
64C42×C83C2×D411yescharacteristic
65C42×C83#4112yes—
66C42×C83#4111yescharacteristic
67C23×C83#12011yescharacteristic
68C2×C4×C83—22no—
69C2×C4×C83—21no—
70C2×C4×C83—21no—
71C2×C4×C83—22no—
72C2×C4×C83—42no—
73C2×C4×C83—42no—
74C2×C4×C83—42no—
75C2×C4×C83#12112yes—
76C2×C4×C83#12111yescharacteristic
77C2×C4×C83#12312yes—
78C2×C4×C83#12411yescharacteristic
79C2×Dic83—42no—
80C2×Dic83—42no—
81C2×Dic83—42no—
82C2×Dic83—42no—
83C2×Dic83—42no—
84C2×Dic83—42no—
85C2×Dic83—82no—
86C2×Dic83—81no—
87C8×C83—44no—
88C83⋊C8—42no—
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—
99Dic83—82no—
100Dic83—82no—
101Dic83—161no—
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#1836—831no—
111C2×#330—832no—
112#1295D8311yescharacteristic
113C83#1042811yescharacteristic, complemented, Sylow
114C2×#125—832no—
115C2×#97—831no—
116C2×#97C2×D8312yes—
117#400—1662no—
118#398—1662no—
119#398—1662no—
120#384—831no—
121#382C2×D8311yescharacteristic
122#340—1662no—
123#340—1662no—
124#340—1662no—
125#330—1664no—
126C22×C8—22no—
127C22×C8—1661no—
128#125—1662no—
129#125—1662no—
130#125—1662no—
131#125—1662no—
132C2×C4⋊C4—832no—
133C2×C4⋊C4—832no—
134C2×C4⋊C4—1662no—
135C2×C4⋊C4—1661no—
136C2×C4⋊C4—1662no—
137C2×C4⋊C4—1662no—
138C2×C4⋊C4—1662no—
139C2×C4⋊C4D33212yes—
140C2×C42C22×D8311yescharacteristic
141#97—22no—
142#97—22no—
143#97—832no—
144#97—1661no—
145#95—22no—
146#95—1664no—
147#95—1662no—
148C22×C4—22no—
149C22×C4—3321no—
150C22×C4—1662no—
151C22×C4—1662no—
152C22×C4D4×D8312yes—
153C22×C4C2×D33211yescharacteristic
154C2×C8—24no—
155C2×C8—42no—
156C2×C8—42no—
157C2×C8—3321no—
158C2×C8—3321no—
159C2×C8—1662no—
160C4⋊C4—42no—
161C4⋊C4—3324no—
162C4⋊C4—3322no—
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—
172C42D4×D8311yescharacteristic
173C42#1305059012yes—
174C42#1305059111yescharacteristic
175C23#1458176211yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—3322no—
184C2×C4—3322no—
185C2×C4—3322no—
186C2×C4—3322no—
187C2×C4—3322no—
188C2×C4—3322no—
189C2×C4—6642no—
190C2×C4—6641no—
191C2×C4#1458176512yes—
192C2×C4#1458176711yescharacteristic
193C2×C4#1458177712yes—
194C2×C4#1458178011yescharacteristic
195C8—44no—
196C8—3322no—
197C22#1912761911yescharacteristic
198C22#1912787512yes—
199C22#1912787611yescharacteristic
200C22#1912788111yescharacteristic
201C22#1912788512yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—13281no—
208C4—6642no—
209C4—6642no—
210C2#2490676611yescharacteristic
211C2#2490679211yescharacteristic
212C2#2490680012yes—
213C2#2490868312yes—
214C2#2490869311yescharacteristic
subgroupG/H
centerC23#14581762
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1295C2
socle, prime radicalC23×C83#120
hypercenter#1295D83
hypocenterC83#10428
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

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
#249084322
#249075962
C2×#191274422
C83×#12952
#1042883