Finite Group Databasebeta

← #35316402

Subgroups — #35316402

Order 21248.

220 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C4×#14581737C211yesmaximal, characteristic
2#24906361C211yesmaximal, characteristic, complemented
3#24906349C211yesmaximal, characteristic
4#24905535C211yesmaximal, characteristic, complemented
5#24905428C211yesmaximal, characteristic, complemented
6#24905425C211yesmaximal, characteristic
7C83×#1311C211yesmaximal, characteristic, complemented
8C2×#14581737C411yescharacteristic
9#19127831—21no—
10C4×Dic332C2211yescharacteristic
11C4×D664C2211yescharacteristic
12#19127780—21no—
13#19127529C411yescharacteristic
14#19127506C411yescharacteristic
15#19127503C411yescharacteristic
16#19127454C2211yescharacteristic
17#19127454C2211yescharacteristic
18#19127433—21no—
19#19127430—21no—
20C4×C16×C83C2211yescharacteristic
21C4×C16×C83C2211yescharacteristic
22C82×C83C2211yescharacteristic
23C2×Dic332C2×C411yescharacteristic
24C2×D664C2×C411yescharacteristic
25C2×#13050573—41no—
26C4×Dic166—21no—
27C4×D332—21no—
28#14581737—22no—
29#14581726C2×C411yescharacteristic
30#14581726C2×C411yescharacteristic
31C4⋊(C83⋊C8)—21no—
32C4⋊(C83⋊C8)—21no—
33Dic83⋊C8—41no—
34#14581717—21no—
35#14581714—21no—
36(C2×D83)⋊C8—41no—
37#14581702—41no—
38C2×C16×C83—21no—
39C2×C16×C83C2×C411yescharacteristic
40C2×C16×C83C2×C411yescharacteristic
41C4×C8×C83D411yescharacteristic
42C4×C8×C83D411yescharacteristic
43C4×C8×C83C2311yescharacteristic
44C2×Dic166—21no—
45C2×D332—21no—
46C2×C4×D83—41no—
47Dic332—21no—
48Dic332—21no—
49D664—21no—
50D664—21no—
51#13050573—82no—
52C2×C83⋊C8—41no—
53C2×C83⋊C8—41no—
54C4⋊Dic83—21no—
55C4⋊Dic83—21no—
56Dic83⋊C4—41no—
57(C2×D83)⋊C4—41no—
58C4×Dic83—41no—
59C2×C8×C83—21no—
60C2×C8×C83D811yescharacteristic
61C2×C8×C83D811yescharacteristic
62C2×C8×C83C22×C411yescharacteristic
63C2×C8×C83#4111yescharacteristic
64C42×C83C2×D411yescharacteristic
65C16×C83—22no—
66C16×C83—21no—
67C16×C83M1612yescomplemented
68C22×D83—41no—
69C2×C4×C83C4×D411yescharacteristic
70C2×C4×C83C2×D811yescharacteristic
71C2×C4×C83#13511yescharacteristic
72C2×Dic83—41no—
73C2×Dic83—41no—
74C2×Dic83—41no—
75D332—41no—
76D332—41no—
77C4×D83—81no—
78C4×D83—81no—
79Dic166—41no—
80Dic166—41no—
81C8×C83—21no—
82C8×C83—21no—
83C8×C83—21no—
84C8×C83—41no—
85C8×C83C2×M1611yescharacteristic
86C8×C83#13111yescharacteristic
87C83⋊C8—81no—
88C83⋊C8—81no—
89C22×C83C4×D811yescharacteristic
90C2×D83—81no—
91C2×D83—81no—
92C2×D83—81no—
93C4×C83—21no—
94C4×C83#43611yescharacteristic
95C4×C83#44311yescharacteristic
96C4×C83#50911yescharacteristic
97C4×C83#51011yescharacteristic
98Dic83—81no—
99Dic83—81no—
100Dic83—81no—
101#12084—831nomaximal, Sylow
102C2×C83#158911yescharacteristic
103C2×C83#217511yescharacteristic
104C2×C83#217911yescharacteristic
105D83—161no—
106C4×SD32—831no—
107#1591—831no—
108#1589—831no—
109#1371—831no—
110#1332—831no—
111#1331—831no—
112#1311D8311yescharacteristic, complemented
113C83#1208411yescharacteristic, complemented, Sylow
114C2×SD32—831no—
115#446—1661no—
116C4×Q16—831no—
117C4×D8—831no—
118#436—1661no—
119#367—831no—
120#358—831no—
121#357—831no—
122C4×C16C2×D8311yescharacteristic
123C4×C16C2×D8311yescharacteristic
124#335—831no—
125#335—831no—
126Q8⋊C8—1661no—
127D4⋊C8—1661no—
128C82C2×D8311yescharacteristic
129C2×Q16—831no—
130C2×D8—831no—
131C2×M16—3321no—
132C4×Q8—1661no—
133C4×D4—1661no—
134SD32—1662no—
135C2×C16—21no—
136C2×C16C4×D8311yescharacteristic
137C2×C16C4×D8311yescharacteristic
138#107—831no—
139#107—831no—
140C4⋊C8—3321no—
141C4⋊C8—1661no—
142C4⋊C8—1661no—
143#103—1661no—
144#102—1661no—
145C22⋊C8—3321no—
146#97—3321no—
147C4×C8D33211yescharacteristic
148C4×C8D33211yescharacteristic
149C4×C8C22×D8311yescharacteristic
150C2×Q8—1661no—
151C2×D4—1661no—
152C22×C4—3321no—
153Q16—1661no—
154Q16—1661no—
155D8—1661no—
156D8—1661no—
157M16—6642no—
158C2×C8—21no—
159C2×C8—3321no—
160C2×C8—3321no—
161C2×C8D66411yescharacteristic
162C2×C8D66411yescharacteristic
163C2×C8C2×C4×D8311yescharacteristic
164C2×C8#1305059011yescharacteristic
165C4⋊C4—3321no—
166C4⋊C4—1661no—
167C4⋊C4—1661no—
168C22⋊C4—3321no—
169C42—3321no—
170C42C2×D33211yescharacteristic
171C16—22no—
172C16—21no—
173C16#1305057312yescomplemented
174C23—3321no—
175Q8—3321no—
176Q8—3321no—
177D4—3321no—
178D4—3321no—
179C2×C4—3321no—
180C2×C4—3321no—
181C2×C4—3321no—
182C2×C4—6641no—
183C2×C4—6641no—
184C2×C4C4×D33211yescharacteristic
185C2×C4C2×D66411yescharacteristic
186C2×C4#1458181411yescharacteristic
187C8—21no—
188C8—21no—
189C8—21no—
190C8—41no—
191C8—6641no—
192C8—6641no—
193C8C2×#1305057311yescharacteristic
194C8#1458179811yescharacteristic
195C22—6641no—
196C22—6641no—
197C22—6641no—
198C22C4×D66411yescharacteristic
199C4—21no—
200C4—6641no—
201C4—6641no—
202C4—6641no—
203C4#1912778011yescharacteristic
204C4#1912781911yescharacteristic
205C4#1912813911yescharacteristic
206C4#1912814411yescharacteristic
207C2—13281no—
208C2#2490634911yescharacteristic
209C2#2490932911yescharacteristic
210C2#2490935011yescharacteristic
subgroupG/H
centerC2×C4C2×D664
commutatorC2×C8×C83C22×C4
FrattiniC4×C8C22×D83
FittingC83×#1311C2
socleC22×C83C4×D8
prime radicalC2×D664C2×C4
cosocleC4×C8×C83C23
hypercenter#1311D83
hypocenterC83#12084
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C82 ◁ #1311

Complements

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

NH ≅ G/Ntype
2. #24906361C2semidirect
4. #24905535C2semidirect
5. #24905428C2semidirect
7. C83×#1311C2semidirect
67. C16×C83M16semidirect
112. #1311D83semidirect
113. C83#12084semidirect
173. C16#13050573semidirect

Maximal subgroups

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

subgroupindex
C4×#145817372
#249063612
#249063492
#249055352
#249054282
#249054252
C83×#13112
#1208483