Finite Group Databasebeta

← #24913587

Subgroups — #24913587

Order 10624.

448 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C2×#14581791C211yesmaximal, characteristic
2C2×#14581783C211yesmaximal, characteristic
3#19127635C214yesmaximal
4#19127622C214yesmaximal
5#19127571C211yesmaximal, characteristic
6#19127570C211yesmaximal, characteristic
7#19127566C211yesmaximal, characteristic
8#19127547C211yesmaximal, characteristic
9#382×C83C211yesmaximal, characteristic
10C22×Dic166C2212yes—
11#14581791—24no—
12#14581783—24no—
13C2×C4⋊Dic83C2211yescharacteristic
14C2×C4⋊Dic83C2211yescharacteristic
15C2×C4⋊Dic83C2212yes—
16C2×C4⋊Dic83C2214yes—
17C2×Dic83⋊C4C2212yes—
18C2×Dic83⋊C4C2212yes—
19C2×Dic83⋊C4C2214yes—
20C2×C4×Dic83C2211yescharacteristic
21C2×C4×Dic83C2211yescharacteristic
22C83⋊#95C2214yes—
23C83⋊#95C2212yes—
24C83⋊#95C2212yes—
25C2×C4⋊C4×C83C2211yescharacteristic
26C2×C4⋊C4×C83C2211yescharacteristic
27C2×C42×C83C2211yescharacteristic
28#95×C83C2214yes—
29C2×Dic166—24no—
30C2×Dic166—44no—
31C22×Dic83C2312yes—
32C22×Dic83C2312yes—
33C22×Dic83C2311yescharacteristic
34C22×Dic83C2311yescharacteristic
35C22×Dic83C2312yes—
36C4⋊Dic83—22no—
37C4⋊Dic83—22no—
38C4⋊Dic83—24no—
39C4⋊Dic83—44no—
40Dic83⋊C4—24no—
41Dic83⋊C4—24no—
42Dic83⋊C4—44no—
43C4×Dic83D414yes—
44C4×Dic83Q814yescomplemented
45C22×C4×C83C2312yes—
46C22×C4×C83C2312yes—
47C22×C4×C83C2312yes—
48C22×C4×C83C2311yescharacteristic
49C4⋊C4×C83—22no—
50C4⋊C4×C83—22no—
51C42×C83Q814yescomplemented
52C23×C83C2411yescharacteristic
53C2×C4×C83—22no—
54C2×C4×C83—22no—
55C2×C4×C83—22no—
56C2×C4×C83—22no—
57C2×C4×C83—24no—
58C2×C4×C83—24no—
59C2×C4×C83C2×D412yes—
60C2×C4×C83C2×Q812yes—
61C2×C4×C83C2×Q814yes—
62C2×C4×C83C2×Q812yes—
63C2×Dic83—22no—
64C2×Dic83—22no—
65C2×Dic83—22no—
66C2×Dic83—22no—
67C2×Dic83—22no—
68C2×Dic83—22no—
69C2×Dic83—24no—
70C2×Dic83—24no—
71C2×Dic83C2×D412yes—
72C2×Dic83C2×D412yes—
73C2×Dic83C2×Q814yes—
74Dic166—48no—
75C22×C83C22×D411yescharacteristic
76C22×C83C22×Q811yescharacteristic
77C22×C83C22×Q811yescharacteristic
78C22×C83H(5,𝔽2)12yes—
79C22×C832−1+412yes—
80C4×C83—24no—
81C4×C83—42no—
82C4×C83—42no—
83C4×C83C4⋊Q814yes—
84Dic83—22no—
85Dic83—22no—
86Dic83—24no—
87Dic83—42no—
88Dic83—42no—
89C2×C83C2×C4⋊Q811yescharacteristic
90C2×C83#53511yescharacteristic
91C2×C83#53611yescharacteristic
92C2×C83#54412yes—
93C2×C83#54412yes—
94#2660—831nomaximal, Sylow
95C83#266011yescharacteristic, complemented, Sylow
96C2×C4⋊Q8—831no—
97C2×#125—831no—
98#398—834no—
99#395—834no—
100#384—831no—
101#384—831no—
102#382—831no—
103#382D8311yescharacteristic
104#376—831no—
105C22×Q8—832no—
106C4⋊Q8—1664no—
107#125—1664no—
108C2×C4⋊C4—834no—
109C2×C4⋊C4—834no—
110C2×C4⋊C4—831no—
111C2×C4⋊C4—832no—
112C2×C4⋊C4—832no—
113C2×C4⋊C4—831no—
114C2×C4⋊C4—832no—
115C2×C4⋊C4C2×D8311yescharacteristic
116C2×C4⋊C4C2×D8311yescharacteristic
117C2×C42—831no—
118C2×C42—831no—
119C2×C42C2×D8311yescharacteristic
120#95—832no—
121#95—832no—
122#95—834no—
123#95C2×D8314yes—
124C2×Q8—3324no—
125C2×Q8—1664no—
126C22×C4—832no—
127C22×C4—831no—
128C22×C4—831no—
129C22×C4—832no—
130C22×C4—832no—
131C22×C4C22×D8312yes—
132C22×C4C22×D8312yes—
133C22×C4C22×D8312yes—
134C22×C4C22×D8311yescharacteristic
135C4⋊C4—22no—
136C4⋊C4—22no—
137C4⋊C4—3324no—
138C4⋊C4—3324no—
139C4⋊C4—1664no—
140C4⋊C4—1664no—
141C4⋊C4—1664no—
142C4⋊C4—1662no—
143C4⋊C4—1662no—
144C42—834no—
145C42—834no—
146C42Dic16614yescomplemented
147C23C23×D8311yescharacteristic
148Q8—3328no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—24no—
154C2×C4—24no—
155C2×C4—832no—
156C2×C4—832no—
157C2×C4—834no—
158C2×C4—1662no—
159C2×C4—1662no—
160C2×C4—1664no—
161C2×C4—1664no—
162C2×C4—1662no—
163C2×C4—1662no—
164C2×C4—1662no—
165C2×C4—1662no—
166C2×C4D4×D8312yes—
167C2×C4Q8×D8312yes—
168C2×C4C2×Dic16614yes—
169C2×C4C2×Dic16612yes—
170C22C2×D4×D8311yescharacteristic
171C22C2×Q8×D8311yescharacteristic
172C22C22×Dic16611yescharacteristic
173C22#1458183812yes—
174C22#1458183912yes—
175C4—24no—
176C4—42no—
177C4—42no—
178C4—3322no—
179C4—3322no—
180C4—1664no—
181C4—1662no—
182C4—1662no—
183C4#1458179114yes—
184C2C2×#1458179111yescharacteristic
185C2#1912826911yescharacteristic
186C2#1912827111yescharacteristic
187C2#1912832912yes—
188C2#1912833112yes—
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#382×C83C2
hypercenter#382D83
hypocenterC83#2660
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
44. C4×Dic83Q8semidirect
51. C42×C83Q8semidirect
95. C83#2660semidirect
146. C42Dic166semidirect

Maximal subgroups

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

subgroupindex
C2×#145817912
C2×#145817832
#191276352
#191276222
#191275712
#191275702
#191275662
#191275472
#382×C832
#266083