Finite Group Databasebeta

← #24906503

Subgroups — #24906503

Order 10624.

202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 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#19128330C211yesmaximal, characteristic
2#19128036C211yesmaximal, characteristic
3#19127639C211yesmaximal, characteristic
4#19127439C211yesmaximal, characteristic
5#19127438C211yesmaximal, characteristic
6#19127426C211yesmaximal, characteristic
7#484×C83C211yesmaximal, characteristic
8#14581791—21no—
9#14581790—21no—
10#14581782—21no—
11#14581782—21no—
12#14581771C2211yescharacteristic
13#14581769—21no—
14#14581748—21no—
15C2×Dic83⋊C4C2211yescharacteristic
16#14581725—21no—
17#14581715—21no—
18C22⋊(C83⋊C8)C2211yescharacteristic
19C83⋊#95—21no—
20C83⋊#95—21no—
21C83⋊#95C2211yescharacteristic
22C22⋊Q8×C83C2211yescharacteristic
23C2×C4⋊C4×C83C2211yescharacteristic
24#107×C83—21no—
25#103×C83—21no—
26C22⋊C8×C83C2211yescharacteristic
27C2×Dic166—21no—
28C2×Dic166D411yescharacteristic
29C22×Dic83—21no—
30C22×Dic83D411yescharacteristic
31C22×Dic83D411yescharacteristic
32C2×C83⋊C8—21no—
33C4⋊Dic83—21no—
34C4⋊Dic83D411yescharacteristic
35Dic83⋊C4—21no—
36Dic83⋊C4—21no—
37Dic83⋊C4—21no—
38Dic83⋊C4—21no—
39Dic83⋊C4—21no—
40Dic83⋊C4—21no—
41Dic83⋊C4—21no—
42C22⋊Dic83—21no—
43C4×Dic83—21no—
44C4×Dic83—21no—
45C2×Q8×C83D411yescharacteristic
46C22×C4×C83—21no—
47C22×C4×C83C2311yescharacteristic
48C2×C8×C83—21no—
49C4⋊C4×C83—21no—
50C4⋊C4×C83—21no—
51C4⋊C4×C83—21no—
52C4⋊C4×C83D411yescharacteristic
53C22⋊C4×C83—21no—
54C23×C83C2×D411yescharacteristic
55Q8×C83—41no—
56C2×C4×C83—21no—
57C2×C4×C83—21no—
58C2×C4×C83—41no—
59C2×C4×C83—42no—
60C2×C4×C83—41no—
61C2×C4×C83C2×D411yescharacteristic
62C2×C4×C83C2×D411yescharacteristic
63C2×Dic83—21no—
64C2×Dic83—21no—
65C2×Dic83—21no—
66C2×Dic83—21no—
67C2×Dic83—21no—
68C2×Dic83—41no—
69C2×Dic83—41no—
70C2×Dic83—41no—
71C2×Dic83—41no—
72C2×Dic83Q1612yes—
73Dic166—41no—
74Dic166—81no—
75C8×C83—41no—
76C83⋊C8—41no—
77C22×C83—21no—
78C22×C83—21no—
79C22×C83#12011yescharacteristic
80C22×C83C2×Q1611yescharacteristic
81C22×C83#13711yescharacteristic
82C4×C83—21no—
83C4×C83—21no—
84C4×C83—41no—
85C4×C83—41no—
86C4×C83—81no—
87Dic83—22no—
88Dic83—41no—
89Dic83—41no—
90Dic83—41no—
91Dic83—81no—
92C2×C83—21no—
93C2×C83—21no—
94C2×C83#45111yescharacteristic
95C2×C83#45411yescharacteristic
96C2×C83#45811yescharacteristic
97#1617—831nomaximal, Sylow
98C83#161711yescharacteristic, complemented, Sylow
99#544—831no—
100#484—831no—
101#484D8311yescharacteristic
102#400—831no—
103#328—831no—
104#328—831no—
105#324—831no—
106C4⋊Q8—1661no—
107C4⋊Q8—1661no—
108#125—1661no—
109#125—1661no—
110C22⋊Q8—831no—
111C22⋊Q8—1661no—
112C22⋊Q8C2×D8311yescharacteristic
113#117—1661no—
114C2×C4⋊C4—831no—
115C2×C4⋊C4C2×D8311yescharacteristic
116#107—21no—
117#107—1661no—
118#103—21no—
119#103—1661no—
120C22⋊C8—831no—
121C22⋊C8C2×D8311yescharacteristic
122#95—831no—
123#95—1661no—
124#95—1661no—
125C2×Q8—831no—
126C2×Q8—1661no—
127C2×Q8C22⋊D8311yescharacteristic
128C22×C4—21no—
129C22×C4—831no—
130C22×C4—831no—
131C22×C4—1661no—
132C22×C4C22×D8311yescharacteristic
133C2×C8—21no—
134C2×C8—1661no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—831no—
139C4⋊C4—1661no—
140C4⋊C4—1661no—
141C4⋊C4—1661no—
142C4⋊C4—1661no—
143C4⋊C4—1661no—
144C4⋊C4—1661no—
145C4⋊C4—1661no—
146C4⋊C4—1661no—
147C4⋊C4C22⋊D8311yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—1661no—
150C42—1661no—
151C42—1661no—
152C23D4×D8311yescharacteristic
153Q8—41no—
154Q8—3321no—
155Q8—6641no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—3321no—
162C2×C4—3321no—
163C2×C4—3321no—
164C2×C4—3321no—
165C2×C4—832no—
166C2×C4—1661no—
167C2×C4—1661no—
168C2×C4—1661no—
169C2×C4—1661no—
170C2×C4—1661no—
171C2×C4D4×D8311yescharacteristic
172C2×C4C2×C22⋊D8311yescharacteristic
173C8—41no—
174C8—3321no—
175C22—21no—
176C22—21no—
177C22#1458176011yescharacteristic
178C22Q16×D8311yescharacteristic
179C22#1458182411yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—3321no—
186C4—3321no—
187C4—3321no—
188C4—6641no—
189C4—1662no—
190C2—21no—
191C2—21no—
192C2#1912785511yescharacteristic
193C2#1912787211yescharacteristic
194C2#1912789011yescharacteristic
subgroupG/H
centerC22#14581760
commutator, cosocleC22×C4×C83C23
FrattiniC22×C4C22×D83
Fitting#484×C83C2
socleC22×C83#120
prime radicalC23×C83C2×D4
hypercenter#484D83
hypocenterC83#1617
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
98. C83#1617semidirect

Maximal subgroups

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

subgroupindex
#191283302
#191280362
#191276392
#191274392
#191274382
#191274262
#484×C832
#161783