Finite Group Databasebeta

← #21431615

Subgroups — #21431615

Order 7552.

392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837344C212yesmaximal, complemented
2#16837344C212yesmaximal, complemented
3#16837338C211yesmaximal, characteristic
4#16837297C212yesmaximal, complemented
5#16837295C212yesmaximal
6#16837287C212yesmaximal, complemented
7#16837274C212yesmaximal
8#16837263C211yesmaximal, characteristic
9C59×#397C211yesmaximal, characteristic
10C23×Dic59C2211yescharacteristic
11C2×C4⋊Dic59C2212yes—
12C2×C4⋊Dic59C2211yescharacteristic
13C2×Dic59⋊C4C2212yes—
14C2×Dic59⋊C4C2212yes—
15C2×Dic59⋊C4C2212yes—
16C2×C22⋊Dic59C2212yes—
17C2×C22⋊Dic59C2211yescharacteristic
18C2×C4×Dic59C2212yes—
19C59⋊#95C2212yes—
20C59⋊#95C2212yes—
21C59⋊#95C2212yes—
22C59⋊#95C2212yes—
23C59⋊#95C2211yescharacteristic
24C59⋊#95C2212yes—
25C59⋊#95C2212yes—
26C2×C4⋊C4×C59C2211yescharacteristic
27C2×C22⋊C4×C59C2212yes—
28C2×C22⋊C4×C59C2211yescharacteristic
29#95×C59C2212yes—
30#95×C59C2211yescharacteristic
31C24×C59C2311yescharacteristic
32C22×C4×C59C2312yes—
33C22×C4×C59C2311yescharacteristic
34C22×C4×C59C2311yescharacteristic
35C22×C4×C59C2312yes—
36C22×Dic59—22no—
37C22×Dic59—41no—
38C22×Dic59—41no—
39C22×Dic59C2312yes—
40C22×Dic59C2312yes—
41C22×Dic59C2312yes—
42C22×Dic59C2312yes—
43C4⋊C4×C59—41no—
44C22⋊C4×C59—24no—
45C22⋊C4×C59—41no—
46C22⋊Dic59—24no—
47C22⋊Dic59—41no—
48C4⋊Dic59—24no—
49C4⋊Dic59—41no—
50Dic59⋊C4—24no—
51Dic59⋊C4—42no—
52Dic59⋊C4—42no—
53C4×Dic59—42no—
54C23×C59—22no—
55C23×C59—21no—
56C23×C59—21no—
57C23×C59—22no—
58C23×C59#4112yes—
59C23×C59C2411yescharacteristic
60C2×C4×C59—22no—
61C2×C4×C59—22no—
62C2×C4×C59—22no—
63C2×C4×C59—22no—
64C2×C4×C59—22no—
65C2×C4×C59—22no—
66C2×C4×C59—21no—
67C2×C4×C59—21no—
68C2×C4×C59—22no—
69C2×C4×C59—22no—
70C2×Dic59—22no—
71C2×Dic59—22no—
72C2×Dic59—22no—
73C2×Dic59—22no—
74C2×Dic59—22no—
75C2×Dic59—22no—
76C2×Dic59—22no—
77C2×Dic59—22no—
78C2×Dic59—22no—
79C2×Dic59—22no—
80C2×Dic59—22no—
81C2×Dic59—44no—
82C2×Dic59#4114yes—
83C22×C59—22no—
84C22×C59—24no—
85C22×C59—42no—
86C22×C59—41no—
87C22×C59—41no—
88C22×C59C2×#4112yes—
89C22×C59C2×#4111yescharacteristic
90C22×C59H(5,𝔽2)11yescharacteristic
91C22×C59H(5,𝔽2)11yescharacteristic
92C22×C592−1+412yes—
93C4×C59—42no—
94C4×C59—42no—
95C4×C59—41no—
96C4×C59—41no—
97Dic59—24no—
98Dic59—42no—
99Dic59—42no—
100Dic59—42no—
101#2771—591nomaximal, Sylow
102C2×C59—42no—
103C2×C59#53811yescharacteristic
104C2×C59#53912yes—
105C2×C59#55212yes—
106C2×C59#55911yescharacteristic
107C2×C59#56311yescharacteristic
108#400—592no—
109#400—592no—
110#399—591no—
111#397D5911yescharacteristic
112#389—592no—
113#388—592no—
114#387—592no—
115#385—592no—
116#381—591no—
117C59#277111yescharacteristic, complemented, Sylow
118C23×C4—591no—
119C2×C4⋊C4—592no—
120C2×C4⋊C4—592no—
121C2×C4⋊C4—592no—
122C2×C4⋊C4—592no—
123C2×C4⋊C4—591no—
124C2×C4⋊C4C2×D5911yescharacteristic
125C2×C22⋊C4—592no—
126C2×C22⋊C4—591no—
127C2×C22⋊C4C2×D5912yes—
128C2×C22⋊C4C2×D5911yescharacteristic
129C2×C42—592no—
130#95—592no—
131#95—592no—
132#95—592no—
133#95—592no—
134#95—591no—
135#95—592no—
136#95—592no—
137#95C2×D5912yes—
138#95C2×D5911yescharacteristic
139C24C22×D5911yescharacteristic
140C22×C4—592no—
141C22×C4—592no—
142C22×C4—592no—
143C22×C4—592no—
144C22×C4—1182no—
145C22×C4—2361no—
146C22×C4—2361no—
147C22×C4C22×D5912yes—
148C22×C4C22×D5911yescharacteristic
149C22×C4C22×D5911yescharacteristic
150C22×C4C22×D5912yes—
151C4⋊C4—41no—
152C4⋊C4—1184no—
153C4⋊C4—1184no—
154C4⋊C4—2362no—
155C4⋊C4—2362no—
156C4⋊C4—2361no—
157C22⋊C4—24no—
158C22⋊C4—41no—
159C22⋊C4—1184no—
160C22⋊C4—2361no—
161C42—2362no—
162C23—22no—
163C23—21no—
164C23—21no—
165C23—22no—
166C23#1174568712yes—
167C23C23×D5911yescharacteristic
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—594no—
179C2×C4—1182no—
180C2×C4—1182no—
181C2×C4—1182no—
182C2×C4—1182no—
183C2×C4—1182no—
184C2×C4—1182no—
185C2×C4—1182no—
186C2×C4—1182no—
187C2×C4—1182no—
188C2×C4—1182no—
189C2×C4—1182no—
190C2×C4—2364no—
191C22—22no—
192C22—24no—
193C22—41no—
194C22—42no—
195C22—41no—
196C22#41×D5912yes—
197C22C2×#1174568711yescharacteristic
198C22#1427377211yescharacteristic
199C22#1427377311yescharacteristic
200C22#1427377412yes—
201C4—41no—
202C4—42no—
203C4—42no—
204C4—41no—
205C4—1184no—
206C4—2362no—
207C4—2362no—
208C4—2362no—
209C2—42no—
210C2#1683798911yescharacteristic
211C2#1683799312yes—
212C2#1683808912yes—
213C2#1683813611yescharacteristic
214C2#1683815211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#397C2
hypercenter#397D59
hypocenterC59#2771
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #16837344C2semidirect
2. #16837344C2semidirect
4. #16837297C2semidirect
6. #16837287C2semidirect
117. C59#2771semidirect