Finite Group Databasebeta

← #35322948

Subgroups — #35322948

Order 21248.

308 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 115 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#24916401C211yesmaximal, characteristic
2#24909229C211yesmaximal, characteristic
3#24905548C212yesmaximal
4#24905542C212yesmaximal
5C83×#2110C211yesmaximal, characteristic
6#19128254C411yescharacteristic
7C2×#14581732C2212yes—
8#19127831—22no—
9#19127829—22no—
10#19127729C411yescharacteristic
11#19127728C411yescharacteristic
12#19127724C411yescharacteristic
13#19127656C2211yescharacteristic
14C2×#14581702C2211yescharacteristic
15#19127522—22no—
16C2×M32×C83C2212yes—
17#405×C83C2211yescharacteristic
18#347×C83—22no—
19C2×#13050574C2×C411yescharacteristic
20C22×C83⋊C8C2×C411yescharacteristic
21#14581791—21no—
22#14581783—21no—
23#14581769—22no—
24C4×Dic166—22no—
25#14581751C2×C411yescharacteristic
26C2×C4×Dic83C2×C411yescharacteristic
27#14581732—22no—
28#14581732—22no—
29C2×C83⋊C16—22no—
30C4⋊(C83⋊C8)—22no—
31Dic83⋊C8—22no—
32Dic83⋊C8—22no—
33#14581702—21no—
34#14581702—21no—
35#14581702—21no—
36C8×Dic83—21no—
37C2×M16×C83C2×C411yescharacteristic
38C22×C8×C83C2311yescharacteristic
39#117×C83C2×C411yescharacteristic
40M32×C83—22no—
41M32×C83—22no—
42C2×C16×C83Q814yescomplemented
43#97×C83D412yes—
44C4×C8×C83D412yes—
45C2×Dic166—22no—
46C22×Dic83—21no—
47#13050574—22no—
48C2×C83⋊C8—21no—
49C2×C83⋊C8—21no—
50C2×C83⋊C8—22no—
51C4⋊Dic83—22no—
52C4⋊Dic83—21no—
53Dic83⋊C4—22no—
54Dic83⋊C4—22no—
55C22⋊Dic83M1612yes—
56C4×Dic83—21no—
57C4×Dic83—21no—
58C4×Dic83M1611yescharacteristic
59C4×Dic83M1611yescharacteristic
60C83⋊C16—42no—
61C22×C4×C83C22×C411yescharacteristic
62M16×C83—22no—
63C2×C8×C83C22⋊C412yes—
64C2×C8×C83C2×D411yescharacteristic
65C2×C8×C83C2×D411yescharacteristic
66C2×C8×C83C2×Q812yes—
67C2×C8×C83#4112yes—
68C4⋊C4×C83—21no—
69C22⋊C4×C83—21no—
70C42×C83C22⋊C412yes—
71C16×C83—24no—
72C23×C83C2×M1611yescharacteristic
73C2×C4×C83—22no—
74C2×C4×C83C2×C22⋊C411yescharacteristic
75C2×C4×C83C4×Q812yes—
76C2×C4×C83C2×M1611yescharacteristic
77C2×C4×C83#13112yes—
78C2×Dic83—21no—
79C2×Dic83—21no—
80C2×Dic83—22no—
81C2×Dic83—81no—
82Dic166—82no—
83C8×C83—22no—
84C8×C83C22⋊Q812yes—
85C8×C83#12411yescharacteristic
86C8×C83C4⋊Q811yescharacteristic
87C83⋊C8—41no—
88C83⋊C8—41no—
89C22×C83—41no—
90C22×C83#40711yescharacteristic
91C22×C83#44612yes—
92C4×C83—42no—
93C4×C83#39111yescharacteristic
94C4×C83#40811yescharacteristic
95C4×C83#44612yes—
96Dic83—41no—
97Dic83—42no—
98Dic83—41no—
99#13269—831nomaximal, Sylow
100C2×C83—21no—
101C2×C83—22no—
102C2×C83#198511yescharacteristic
103#2961—831no—
104#2153—831no—
105#2110D8311yescharacteristic
106#1378—832no—
107#1375—832no—
108C83#1326911yescharacteristic, complemented, Sylow
109#533—831no—
110C2×M32—832no—
111C2×M32C2×D8312yes—
112#446—1662no—
113#446—1662no—
114#424—831no—
115#424—831no—
116#423—831no—
117#405—831no—
118#405C2×D8311yescharacteristic
119C2×#97—831no—
120#364—1662no—
121#347—22no—
122C2×M16—831no—
123C2×M16C4×D8311yescharacteristic
124C22×C8—831no—
125C22×C8C22×D8311yescharacteristic
126C4⋊Q8—1661no—
127#125—1661no—
128C22⋊Q8—1662no—
129C4×Q8—1662no—
130#117—831no—
131#117C4×D8311yescharacteristic
132C2×C42—831no—
133M32—22no—
134M32—22no—
135M32—1662no—
136M32—1662no—
137C2×C16—1662no—
138C2×C16Dic16614yescomplemented
139C4⋊C8—1662no—
140C4⋊C8—1662no—
141C4⋊C8—1662no—
142#97—1661no—
143#97—1661no—
144#97—1661no—
145#97C22⋊D8312yes—
146C4×C8—1661no—
147C4×C8D33212yes—
148C2×Q8—1662no—
149C22×C4—1661no—
150C22×C4C2×C4×D8311yescharacteristic
151M16—22no—
152M16—1662no—
153C2×C8—1662no—
154C2×C8—1661no—
155C2×C8—1661no—
156C2×C8(C2×D83)⋊C412yes—
157C2×C8C2×C22⋊D8311yescharacteristic
158C2×C8C2×D33211yescharacteristic
159C2×C8C2×Dic16612yes—
160C2×C8#1305059012yes—
161C4⋊C4—21no—
162C4⋊C4—1662no—
163C4⋊C4—1662no—
164C4⋊C4—1662no—
165C4⋊C4—1661no—
166C22⋊C4—21no—
167C22⋊C4—832no—
168C42—831no—
169C42—831no—
170C42—1661no—
171C42—1661no—
172C42(C2×D83)⋊C412yes—
173C16—24no—
174C16—3322no—
175C23M16×D8311yescharacteristic
176Q8—6642no—
177C2×C4—22no—
178C2×C4—6641no—
179C2×C4—1661no—
180C2×C4—1661no—
181C2×C4—1662no—
182C2×C4C2×(C2×D83)⋊C411yescharacteristic
183C2×C4C4×Dic16612yes—
184C2×C4M16×D8311yescharacteristic
185C2×C4#1458180012yes—
186C8—22no—
187C8—3321no—
188C8—3321no—
189C8#1458177112yes—
190C8#1458178011yescharacteristic
191C8#1458179211yescharacteristic
192C22—41no—
193C22#1912766411yescharacteristic
194C22#1912782912yes—
195C4—42no—
196C4—3321no—
197C4—3321no—
198C4—3322no—
199C4#1912760711yescharacteristic
200C4#1912766911yescharacteristic
201C4#1912782912yes—
202C2—21no—
203C2—22no—
204C2#2490840311yescharacteristic
subgroupG/H
centerC4#19127607
commutatorC22×C4×C83C22×C4
FrattiniC22×C8C22×D83
FittingC83×#2110C2
socleC2×C83#1985
prime radicalC23×C83C2×M16
cosocleC22×C8×C83C23
hypercenter#2110D83
hypocenterC83#13269
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C4 ◁ C22×C8 ◁ #2110

Complements

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

NH ≅ G/Ntype
42. C2×C16×C83Q8semidirect
108. C83#13269semidirect
138. C2×C16Dic166semidirect

Maximal subgroups

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

subgroupindex
#249164012
#249092292
#249055482
#249055422
C83×#21102
#1326983