Finite Group Databasebeta

← #24915736

Subgroups — #24915736

Order 10624.

356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 125 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#19127642C212yesmaximal
2#19127641C212yesmaximal
3#19127640C211yesmaximal, characteristic
4#19127622C212yesmaximal
5#19127622C212yesmaximal
6#19127621C212yesmaximal
7#19127566C211yesmaximal, characteristic
8#19127565C212yesmaximal
9#400×C83C211yesmaximal, characteristic
10C22×Dic166C2212yes—
11C2×C4⋊Dic83C2211yescharacteristic
12C2×C4⋊Dic83C2211yescharacteristic
13C2×C4⋊Dic83C2212yes—
14C2×Dic83⋊C4C2212yes—
15C2×Dic83⋊C4C2212yes—
16C2×Dic83⋊C4C2212yes—
17C2×C4×Dic83C2211yescharacteristic
18C83⋊#95C2212yes—
19C83⋊#95C2212yes—
20C83⋊#95C2212yes—
21C83⋊#95C2212yes—
22C83⋊#95C2212yes—
23C83⋊#95C2212yes—
24C83⋊#95C2212yes—
25C83⋊#95C2211yescharacteristic
26C2×C4⋊C4×C83C2211yescharacteristic
27C2×C4⋊C4×C83C2211yescharacteristic
28#95×C83C2212yes—
29#95×C83C2212yes—
30#95×C83C2211yescharacteristic
31C2×Dic166—42no—
32C2×Dic166—42no—
33C2×Dic166—42no—
34C22×Dic83C2312yes—
35C22×Dic83C2312yes—
36C22×Dic83C2312yes—
37C22×Dic83C2312yes—
38C4⋊Dic83—41no—
39C4⋊Dic83—41no—
40C4⋊Dic83—42no—
41Dic83⋊C4—42no—
42Dic83⋊C4—42no—
43Dic83⋊C4—42no—
44C4×Dic83Q814yescomplemented
45C22×C4×C83C2312yes—
46C22×C4×C83C2312yes—
47C22×C4×C83C2311yescharacteristic
48C22×C4×C83C2311yescharacteristic
49C22×C4×C83C2311yescharacteristic
50C4⋊C4×C83—41no—
51C4⋊C4×C83—41no—
52C23×C83C2411yescharacteristic
53C2×C4×C83—21no—
54C2×C4×C83—21no—
55C2×C4×C83—21no—
56C2×C4×C83—21no—
57C2×C4×C83—22no—
58C2×C4×C83—22no—
59C2×C4×C83—22no—
60C2×C4×C83—22no—
61C2×C4×C83—22no—
62C2×C4×C83—22no—
63C2×C4×C83—22no—
64C2×C4×C83—22no—
65C2×C4×C83C2×Q812yes—
66C2×Dic83—22no—
67C2×Dic83—22no—
68C2×Dic83—22no—
69C2×Dic83—22no—
70C2×Dic83—22no—
71C2×Dic83—22no—
72C2×Dic83—22no—
73C2×Dic83—22no—
74C2×Dic83—22no—
75C2×Dic83—22no—
76C2×Dic83—22no—
77C2×Dic83C2×Q814yes—
78Dic166—48no—
79C22×C83C22×Q811yescharacteristic
80C22×C83H(5,𝔽2)11yescharacteristic
81C22×C83H(5,𝔽2)12yes—
82C22×C832−1+411yescharacteristic
83C22×C832−1+412yes—
84C4×C83—22no—
85C4×C83—42no—
86C4×C83—42no—
87C4×C83—41no—
88C4×C83—41no—
89Dic83—24no—
90Dic83—42no—
91Dic83—42no—
92Dic83—42no—
93C2×C83#54411yescharacteristic
94C2×C83#54412yes—
95C2×C83H(3,𝔽4)11yescharacteristic
96C2×C83#56312yes—
97C2×C83#56311yescharacteristic
98#2844—831nomaximal, Sylow
99C83#284411yescharacteristic, complemented, Sylow
100#400—831no—
101#400—832no—
102#400—832no—
103#400D8311yescharacteristic
104#395—832no—
105#395—832no—
106#395—832no—
107#382—831no—
108#382—832no—
109C22×Q8—832no—
110C2×C4⋊C4—832no—
111C2×C4⋊C4—831no—
112C2×C4⋊C4—832no—
113C2×C4⋊C4—832no—
114C2×C4⋊C4—831no—
115C2×C4⋊C4—832no—
116C2×C4⋊C4C2×D8311yescharacteristic
117C2×C4⋊C4C2×D8311yescharacteristic
118C2×C42—831no—
119#95—832no—
120#95—832no—
121#95—832no—
122#95—832no—
123#95—832no—
124#95—832no—
125#95—832no—
126#95—831no—
127#95C2×D8312yes—
128#95C2×D8312yes—
129#95C2×D8311yescharacteristic
130C2×Q8—3322no—
131C2×Q8—3322no—
132C2×Q8—3322no—
133C22×C4—832no—
134C22×C4—832no—
135C22×C4—832no—
136C22×C4—832no—
137C22×C4C22×D8311yescharacteristic
138C22×C4C22×D8311yescharacteristic
139C22×C4C22×D8312yes—
140C22×C4C22×D8312yes—
141C22×C4C22×D8311yescharacteristic
142C4⋊C4—41no—
143C4⋊C4—41no—
144C4⋊C4—3322no—
145C4⋊C4—3322no—
146C4⋊C4—3322no—
147C4⋊C4—3321no—
148C4⋊C4—3321no—
149C4⋊C4—3322no—
150C42—834no—
151C23C23×D8311yescharacteristic
152Q8—3328no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—834no—
166C2×C4—1662no—
167C2×C4—1662no—
168C2×C4—1662no—
169C2×C4—1662no—
170C2×C4—1662no—
171C2×C4—1662no—
172C2×C4—1662no—
173C2×C4—1662no—
174C2×C4—1662no—
175C2×C4—1662no—
176C2×C4—1662no—
177C2×C4Q8×D8312yes—
178C22C2×Q8×D8311yescharacteristic
179C22#1458183711yescharacteristic
180C22#1458183812yes—
181C22#1458183911yescharacteristic
182C22#1458183912yes—
183C4—22no—
184C4—42no—
185C4—42no—
186C4—41no—
187C4—41no—
188C4—3322no—
189C4—3322no—
190C4—3322no—
191C4—1664no—
192C2#1912833011yescharacteristic
193C2#1912833112yes—
194C2#1912844311yescharacteristic
195C2#1912845312yes—
196C2#1912845411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#400×C83C2
hypercenter#400D83
hypocenterC83#2844
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
44. C4×Dic83Q8semidirect
99. C83#2844semidirect

Maximal subgroups

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

subgroupindex
#191276422
#191276412
#191276402
#191276222
#191276212
#191275662
#191275652
#400×C832
#284483