Finite Group Databasebeta

← #35308915

Subgroups — #35308915

Order 21248.

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

normal subgroups only

This group has 350 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#24915738C211yesmaximal, characteristic
2#24907597C212yesmaximal
3#24907596C211yesmaximal, characteristic
4#24905345C212yesmaximal
5C83×#1295C211yesmaximal, characteristic
6C2×#14581703C2211yescharacteristic
7#19127635—22no—
8#19127634—22no—
9#19127633—22no—
10#19127571C2211yescharacteristic
11#19127567C2212yes—
12#19127464—22no—
13#19127464—22no—
14#19127463—22no—
15C2×#97×C83C2212yes—
16#382×C83C2211yescharacteristic
17C22×C83⋊C8—21no—
18C2×C4⋊Dic83—22no—
19C2×C4⋊Dic83—21no—
20C2×C4⋊Dic83—22no—
21C2×C4⋊Dic83D412yes—
22C2×C4⋊Dic83D412yes—
23C2×Dic83⋊C4—22no—
24C2×Dic83⋊C4—22no—
25#14581703—21no—
26#14581703Q812yes—
27C83⋊#95—22no—
28C83⋊#95—22no—
29C83⋊#95—22no—
30C22×C8×C83—22no—
31C2×C4⋊C4×C83D412yes—
32C2×C42×C83C2311yescharacteristic
33#97×C83—22no—
34#97×C83Q814yes—
35#95×C83—22no—
36C22×Dic83—22no—
37C22×Dic83—22no—
38C22×Dic83—41no—
39C2×C83⋊C8—22no—
40C2×C83⋊C8—41no—
41C2×C83⋊C8—41no—
42C4⋊Dic83—42no—
43C4⋊Dic83—42no—
44C4⋊Dic83—44no—
45C4⋊Dic83—42no—
46C4⋊Dic83—82no—
47Dic83⋊C4—82no—
48Dic83⋊C4—82no—
49C22×C4×C83—22no—
50C22×C4×C83C2×D412yes—
51C22×C4×C83C2×D411yescharacteristic
52C2×C8×C83—24no—
53C2×C8×C83—42no—
54C2×C8×C83—42no—
55C4⋊C4×C83—42no—
56C42×C83C2×Q811yescharacteristic
57C42×C83C2×Q812yes—
58C42×C83#4111yescharacteristic
59C23×C83#12011yescharacteristic
60C2×C4×C83—22no—
61C2×C4×C83—21no—
62C2×C4×C83—21no—
63C2×C4×C83—22no—
64C2×C4×C83—42no—
65C2×C4×C83—42no—
66C2×C4×C83—42no—
67C2×C4×C83C22⋊Q812yes—
68C2×C4×C83C22⋊Q811yescharacteristic
69C2×C4×C83C4⋊Q812yes—
70C2×C4×C83C4⋊Q811yescharacteristic
71C2×Dic83—42no—
72C2×Dic83—42no—
73C2×Dic83—42no—
74C2×Dic83—42no—
75C2×Dic83—42no—
76C2×Dic83—42no—
77C2×Dic83—82no—
78C2×Dic83—81no—
79C8×C83—44no—
80C83⋊C8—42no—
81C22×C83#39511yescharacteristic
82C22×C83#45412yes—
83C22×C83#45411yescharacteristic
84C22×C83#45512yes—
85C22×C83#45511yescharacteristic
86C4×C83—21no—
87C4×C83—22no—
88C4×C83—22no—
89C4×C83—21no—
90C4×C83—82no—
91Dic83—82no—
92Dic83—82no—
93Dic83—161no—
94#10586—831nomaximal, Sylow
95C2×C83#165811yescharacteristic
96C2×C83#166211yescharacteristic
97C2×C83#166212yes—
98C2×C83#206112yes—
99C2×C83#206111yescharacteristic
100#2845—831no—
101#1836—832no—
102#1836—831no—
103#1295—832no—
104#1295D8311yescharacteristic
105C83#1058611yescharacteristic, complemented, Sylow
106C2×#97—831no—
107C2×#97C2×D8312yes—
108#398—1662no—
109#398—1662no—
110#398—1662no—
111#384—831no—
112#382—832no—
113#382C2×D8311yescharacteristic
114#340—1662no—
115#340—1662no—
116#340—1662no—
117C22×C8—22no—
118C22×C8—1661no—
119C2×C4⋊C4—832no—
120C2×C4⋊C4—832no—
121C2×C4⋊C4—1662no—
122C2×C4⋊C4—1661no—
123C2×C4⋊C4—1662no—
124C2×C4⋊C4—1662no—
125C2×C4⋊C4—1662no—
126C2×C4⋊C4D33212yes—
127C2×C42C22×D8311yescharacteristic
128#97—22no—
129#97—832no—
130#97—1661no—
131#97Dic16614yes—
132#95—22no—
133#95—1662no—
134#95—1662no—
135#95—1662no—
136C22×C4—22no—
137C22×C4—3321no—
138C22×C4—1662no—
139C22×C4—1662no—
140C22×C4D4×D8312yes—
141C22×C4C2×D33211yescharacteristic
142C2×C8—24no—
143C2×C8—42no—
144C2×C8—42no—
145C2×C8—3321no—
146C2×C8—3321no—
147C2×C8—1662no—
148C4⋊C4—42no—
149C4⋊C4—3322no—
150C4⋊C4—3322no—
151C4⋊C4—3324no—
152C4⋊C4—3322no—
153C4⋊C4—6642no—
154C4⋊C4—6642no—
155C4⋊C4—6642no—
156C42Q8×D8311yescharacteristic
157C42C2×Dic16612yes—
158C42#1305058911yescharacteristic
159C23#1458176211yescharacteristic
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—3322no—
168C2×C4—3322no—
169C2×C4—3322no—
170C2×C4—3322no—
171C2×C4—3322no—
172C2×C4—3322no—
173C2×C4—6642no—
174C2×C4—6641no—
175C2×C4#1458176912yes—
176C2×C4#1458177211yescharacteristic
177C2×C4#1458179112yes—
178C2×C4#1458179211yescharacteristic
179C8—44no—
180C8—3322no—
181C22#1912762211yescharacteristic
182C22#1912787512yes—
183C22#1912787611yescharacteristic
184C22#1912788012yes—
185C22#1912788111yescharacteristic
186C4—22no—
187C4—22no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—13281no—
192C4—6642no—
193C4—6642no—
194C2#2490676611yescharacteristic
195C2#2490678711yescharacteristic
196C2#2490678812yes—
197C2#2490881212yes—
198C2#2490881411yescharacteristic
subgroupG/H
centerC23#14581762
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1295C2
socle, prime radicalC23×C83#120
hypercenter#1295D83
hypocenterC83#10586
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
105. C83#10586semidirect

Maximal subgroups

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

subgroupindex
#249157382
#249075972
#249075962
#249053452
C83×#12952
#1058683