Finite Group Databasebeta

← #35319165

Subgroups — #35319165

Order 21248.

306 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 75 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#24909718C211yesmaximal, characteristic, complemented
2#24909691C211yesmaximal, characteristic, complemented
3#24909686C211yesmaximal, characteristic, complemented
4#24907068C211yesmaximal, characteristic, complemented
5#24907052C211yesmaximal, characteristic, complemented
6#24905382C211yesmaximal, characteristic, complemented
7C83×#2246C211yesmaximal, characteristic
8C2×#14581736—22no—
9#19128106C2211yescharacteristic
10#19128081C2211yescharacteristic
11#19128073—21no—
12#19128047—21no—
13#19128047—21no—
14#19128047—21no—
15#19127506—22no—
16#19127502—22no—
17C4×C83⋊C16C2211yescharacteristic
18C8×C83⋊C8C2211yescharacteristic
19C2×D16×C83—22no—
20#493×C83C2211yescharacteristic
21#493×C83C2211yescharacteristic
22C4×C16×C83C2211yescharacteristic
23C2×Dic332—21no—
24C2×Dic332—21no—
25C2×#13050578—42no—
26#14581792—21no—
27#14581792—21no—
28#14581736—44no—
29C2×C83⋊C16D412yes—
30#14581726—21no—
31#14581726—21no—
32#14581713—42no—
33#14581713—42no—
34#14581713—42no—
35C4×C83⋊C8D411yescharacteristic
36C4×C83⋊C8D411yescharacteristic
37C2×D8×C83—21no—
38C2×D8×C83—21no—
39C2×D8×C83—21no—
40C2×D8×C83—21no—
41#127×C83—21no—
42#127×C83—21no—
43D16×C83—44no—
44C2×C16×C83D412yes—
45C4×C8×C83C2311yescharacteristic
46C2×Dic166—41no—
47C2×Dic166—41no—
48Dic332—42no—
49Dic332—42no—
50#13050578—84no—
51C2×C83⋊C8D812yes—
52C2×C83⋊C8D812yes—
53C4⋊Dic83—41no—
54C4⋊Dic83—41no—
55C4⋊Dic83—41no—
56C4⋊Dic83—41no—
57C83⋊C16—22no—
58C2×D4×C83—41no—
59C2×D4×C83—41no—
60C2×D4×C83—41no—
61C2×D4×C83—41no—
62C2×D4×C83—41no—
63C2×D4×C83—41no—
64D8×C83—42no—
65D8×C83—42no—
66D8×C83—42no—
67D8×C83—42no—
68C2×C8×C83C2×D411yescharacteristic
69C2×C8×C83C2×D411yescharacteristic
70C42×C83C2×D411yescharacteristic
71C16×C83—22no—
72C23×C83—81no—
73C23×C83—81no—
74D4×C83—81no—
75D4×C83—81no—
76D4×C83—81no—
77D4×C83—81no—
78D4×C83—82no—
79D4×C83—82no—
80D4×C83—82no—
81D4×C83—82no—
82C2×C4×C83#12711yescharacteristic
83C2×C4×C83C2×D811yescharacteristic
84C2×C4×C83C2×D811yescharacteristic
85C2×Dic83—81no—
86C2×Dic83—81no—
87Dic166—81no—
88Dic166—81no—
89Dic166—82no—
90C8×C83AGL(1,ℤ/8)12yes—
91C8×C83AGL(1,ℤ/8)12yes—
92C83⋊C8—22no—
93C83⋊C8—22no—
94C22×C83—161no—
95C22×C83—161no—
96C22×C83—161no—
97C22×C83—161no—
98C22×C83—161no—
99C22×C83—161no—
100C22×C83#49311yescharacteristic
101C4×C83#49611yescharacteristic
102C4×C83#49611yescharacteristic
103C4×C83#50812yes—
104C4×C83#50912yes—
105Dic83—161no—
106Dic83—161no—
107#12527—831nomaximal, Sylow
108C2×C83—321no—
109C2×C83—321no—
110C2×C83#172111yescharacteristic
111C2×C83#224911yescharacteristic
112C2×C83#225011yescharacteristic
113#2248—831no—
114#2246D8311yescharacteristic
115#2241—831no—
116#2240—831no—
117#1709—831no—
118#1706—831no—
119#1312—831no—
120C83#1252711yescharacteristic, complemented, Sylow
121C2×SD32—1662no—
122C2×D16—22no—
123#500—831no—
124#494—831no—
125#493C2×D8311yescharacteristic
126#493C2×D8311yescharacteristic
127#492—1661no—
128#486—1661no—
129#486—1661no—
130#486—1661no—
131#358—1662no—
132#357—1662no—
133C4×C16—831no—
134C4×C16C2×D8311yescharacteristic
135C82—831no—
136C2×Q16—1661no—
137C2×Q16—1661no—
138C2×SD16—3322no—
139C2×D8—21no—
140C2×D8—21no—
141C2×D8—21no—
142C2×D8—21no—
143C4⋊Q8—1661no—
144C4⋊Q8—1661no—
145#127—21no—
146#127—21no—
147SD32—3324no—
148D16—44no—
149C2×C16—832no—
150C2×C16C22⋊D8312yes—
151#107—1661no—
152#107—1661no—
153#102—3322no—
154#102—3322no—
155#102—3322no—
156C4×C8—831no—
157C4×C8—831no—
158C4×C8C22×D8311yescharacteristic
159C2×Q8—3321no—
160C2×Q8—3321no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—41no—
164C2×D4—41no—
165C2×D4—41no—
166C2×D4—41no—
167Q16—3322no—
168Q16—3322no—
169SD16—6644no—
170D8—42no—
171D8—42no—
172D8—42no—
173D8—42no—
174C2×C8—832no—
175C2×C8—832no—
176C2×C8D4×D8311yescharacteristic
177C2×C8C2×C22⋊D8311yescharacteristic
178C4⋊C4—3321no—
179C4⋊C4—3321no—
180C4⋊C4—3321no—
181C4⋊C4—3321no—
182C42D4×D8311yescharacteristic
183C16—22no—
184C16—1662no—
185C23—81no—
186C23—81no—
187Q8—6641no—
188Q8—6641no—
189Q8—6642no—
190D4—81no—
191D4—81no—
192D4—81no—
193D4—81no—
194D4—82no—
195D4—82no—
196D4—82no—
197D4—82no—
198C2×C4—6641no—
199C2×C4—6641no—
200C2×C4#1458178811yescharacteristic
201C2×C4D8×D8311yescharacteristic
202C2×C4D8×D8311yescharacteristic
203C8—1662no—
204C8—1662no—
205C8#1458181612yes—
206C8#1458181812yes—
207C22—161no—
208C22—161no—
209C22—161no—
210C22—161no—
211C22—161no—
212C22—161no—
213C22#1912807611yescharacteristic
214C4—13281no—
215C4—13281no—
216C4#1912808811yescharacteristic
217C4#1912808911yescharacteristic
218C4#1912813012yes—
219C4#1912813512yes—
220C2—321no—
221C2—321no—
222C2#2490712811yescharacteristic
223C2#2490972111yescharacteristic
224C2#2490972611yescharacteristic
subgroupG/H
centerC22#19128076
commutator, cosocleC4×C8×C83C23
FrattiniC4×C8C22×D83
Fitting, prime radicalC83×#2246C2
socleC22×C83#493
hypercenter#2246D83
hypocenterC83#12527
LCSG ▷ C4×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2246

Complements

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

NH ≅ G/Ntype
1. #24909718C2semidirect
2. #24909691C2semidirect
3. #24909686C2semidirect
4. #24907068C2semidirect
5. #24907052C2semidirect
6. #24905382C2semidirect
120. C83#12527semidirect

Maximal subgroups

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

subgroupindex
#249097182
#249096912
#249096862
#249070682
#249070522
#249053822
C83×#22462
#1252783