Finite Group Databasebeta

← #21431219

Subgroups — #21431219

Order 7552.

416 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 129 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#16837343C212yesmaximal, complemented
2#16837338C211yesmaximal, characteristic
3#16837321C212yesmaximal, complemented
4#16837299C212yesmaximal, complemented
5#16837290C212yesmaximal
6#16837284C212yesmaximal, complemented
7#16837274C211yesmaximal, characteristic
8#16837260C212yesmaximal
9C59×#393C211yesmaximal, characteristic
10C23×Dic59C2211yescharacteristic
11C2×C4⋊Dic59C2211yescharacteristic
12C2×Dic59⋊C4C2212yes—
13C2×Dic59⋊C4C2212yes—
14C2×Dic59⋊C4C2212yes—
15C2×Dic59⋊C4C2212yes—
16C2×Dic59⋊C4C2212yes—
17C2×C22⋊Dic59C2212yes—
18C2×C22⋊Dic59C2211yescharacteristic
19C2×C4×Dic59C2212yes—
20C59⋊#95C2212yes—
21C59⋊#95C2212yes—
22C59⋊#95C2212yes—
23C59⋊#95C2212yes—
24C59⋊#95C2212yes—
25C59⋊#95C2211yescharacteristic
26C22×Q8×C59C2211yescharacteristic
27C2×C22⋊C4×C59C2212yes—
28C2×C22⋊C4×C59C2211yescharacteristic
29#95×C59C2211yescharacteristic
30#95×C59C2212yes—
31C24×C59C2311yescharacteristic
32C2×Q8×C59—42no—
33C2×Q8×C59—41no—
34C22×C4×C59C2312yes—
35C22×C4×C59C2311yescharacteristic
36C22×C4×C59C2311yescharacteristic
37C22×C4×C59C2312yes—
38C22×Dic59—24no—
39C22×Dic59—41no—
40C22×Dic59C2312yes—
41C22×Dic59C2312yes—
42C22×Dic59C2312yes—
43C22×Dic59C2312yes—
44C22⋊C4×C59—42no—
45C22⋊C4×C59—41no—
46C22⋊Dic59—42no—
47C22⋊Dic59Q814yescomplemented
48C4⋊Dic59—41no—
49Dic59⋊C4—24no—
50Dic59⋊C4—24no—
51Dic59⋊C4—42no—
52Dic59⋊C4—42no—
53Dic59⋊C4—42no—
54C4×Dic59—42no—
55C23×C59—22no—
56C23×C59—22no—
57C23×C59—21no—
58C23×C59—21no—
59C23×C59C2×Q812yes—
60C23×C59C2411yescharacteristic
61Q8×C59—44no—
62C2×C4×C59—22no—
63C2×C4×C59—22no—
64C2×C4×C59—22no—
65C2×C4×C59—22no—
66C2×C4×C59—22no—
67C2×C4×C59—22no—
68C2×C4×C59—21no—
69C2×C4×C59—22no—
70C2×C4×C59—21no—
71C2×C4×C59—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—22no—
82C2×Dic59—44no—
83C2×Dic59C2×Q814yes—
84C2×Dic59#4114yes—
85C22×C59—22no—
86C22×C59—24no—
87C22×C59—42no—
88C22×C59—41no—
89C22×C59—41no—
90C22×C59C22×Q811yescharacteristic
91C22×C59C2×#4112yes—
92C22×C59H(5,𝔽2)12yes—
93C22×C59H(5,𝔽2)11yescharacteristic
94C22×C592−1+411yescharacteristic
95C4×C59—42no—
96C4×C59—41no—
97C4×C59—41no—
98C4×C59—42no—
99Dic59—24no—
100Dic59—24no—
101Dic59—42no—
102Dic59—42no—
103#2742—591nomaximal, Sylow
104C2×C59—42no—
105C2×C59#54212yes—
106C2×C59#54411yescharacteristic
107C2×C59#55111yescharacteristic
108C2×C59#55412yes—
109C2×C59#56011yescharacteristic
110#400—592no—
111#399—591no—
112#395—592no—
113#393D5911yescharacteristic
114#389—592no—
115#388—592no—
116#387—592no—
117#385—591no—
118#380—592no—
119C59#274211yescharacteristic, complemented, Sylow
120C22×Q8C2×D5911yescharacteristic
121C23×C4—591no—
122C2×C4⋊C4—592no—
123C2×C4⋊C4—592no—
124C2×C4⋊C4—592no—
125C2×C4⋊C4—592no—
126C2×C4⋊C4—592no—
127C2×C4⋊C4—591no—
128C2×C22⋊C4—591no—
129C2×C22⋊C4—592no—
130C2×C22⋊C4C2×D5912yes—
131C2×C22⋊C4C2×D5911yescharacteristic
132C2×C42—592no—
133#95—592no—
134#95—592no—
135#95—592no—
136#95—592no—
137#95—592no—
138#95—591no—
139#95C2×D5911yescharacteristic
140#95C2×D5912yes—
141C24C22×D5911yescharacteristic
142C2×Q8—42no—
143C2×Q8—41no—
144C22×C4—592no—
145C22×C4—592no—
146C22×C4—592no—
147C22×C4—592no—
148C22×C4—1184no—
149C22×C4—2361no—
150C22×C4C22×D5912yes—
151C22×C4C22×D5912yes—
152C22×C4C22×D5911yescharacteristic
153C22×C4C22×D5911yescharacteristic
154C4⋊C4—1184no—
155C4⋊C4—1184no—
156C4⋊C4—2362no—
157C4⋊C4—2362no—
158C4⋊C4—2362no—
159C4⋊C4—2361no—
160C22⋊C4—42no—
161C22⋊C4—41no—
162C22⋊C4—594no—
163C22⋊C4—2362no—
164C42—2362no—
165C23—22no—
166C23—22no—
167C23—21no—
168C23—21no—
169C23Q8×D5912yes—
170C23C23×D5911yescharacteristic
171Q8—44no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—594no—
183C2×C4—594no—
184C2×C4—1182no—
185C2×C4—1182no—
186C2×C4—1182no—
187C2×C4—1182no—
188C2×C4—1182no—
189C2×C4—1182no—
190C2×C4—1182no—
191C2×C4—1182no—
192C2×C4—1182no—
193C2×C4—1182no—
194C2×C4—2364no—
195C22—22no—
196C22—24no—
197C22—42no—
198C22—41no—
199C22—41no—
200C22C2×Q8×D5911yescharacteristic
201C22#41×D5912yes—
202C22#1427377212yes—
203C22#1427377211yescharacteristic
204C22#1427377411yescharacteristic
205C4—42no—
206C4—41no—
207C4—42no—
208C4—41no—
209C4—1184no—
210C4—1184no—
211C4—2362no—
212C4—2362no—
213C2—42no—
214C2#1683801612yes—
215C2#1683803111yescharacteristic
216C2#1683808211yescharacteristic
217C2#1683810612yes—
218C2#1683814111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#393C2
hypercenter#393D59
hypocenterC59#2742
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. #16837343C2semidirect
3. #16837321C2semidirect
4. #16837299C2semidirect
6. #16837284C2semidirect
47. C22⋊Dic59Q8semidirect
119. C59#2742semidirect