Finite Group Databasebeta

← #21425450

Subgroups — #21425450

Order 7552.

314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 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#16838028C211yesmaximal, characteristic
2#16837277C212yesmaximal
3#16837274C211yesmaximal, characteristic
4#16837168C212yesmaximal
5C59×#342C211yesmaximal, characteristic
6C23×Dic59C2211yescharacteristic
7#14273706—21no—
8#14273706—21no—
9#14273704—22no—
10#14273704—22no—
11C2×C4⋊Dic59—22no—
12C2×Dic59⋊C4—21no—
13C2×C22⋊Dic59C2212yes—
14C2×C22⋊Dic59C2211yescharacteristic
15C59⋊#95—21no—
16C59⋊#95—22no—
17C2×C22⋊C4×C59C2211yescharacteristic
18C2×C22⋊C4×C59C2212yes—
19C24×C59C2311yescharacteristic
20C22×C4×C59—22no—
21C22×C4×C59D411yescharacteristic
22C22×C4×C59D411yescharacteristic
23C22×Dic59—21no—
24C22×Dic59—21no—
25C22×Dic59—22no—
26C22×Dic59—42no—
27C22×Dic59D412yes—
28C22×Dic59D412yes—
29C2×Dic118—21no—
30C2×Dic118—21no—
31C22⋊C4×C59—22no—
32C22⋊C4×C59—22no—
33C22⋊C4×C59Q814yescomplemented
34C22⋊Dic59—22no—
35C22⋊Dic59—22no—
36C22⋊Dic59—21no—
37C22⋊Dic59Q812yescomplemented
38C4⋊Dic59—21no—
39C4⋊Dic59—21no—
40C4⋊Dic59—44no—
41Dic59⋊C4—22no—
42Dic59⋊C4—22no—
43Dic59⋊C4—42no—
44C23×C59—41no—
45C23×C59—41no—
46C23×C59C2×D411yescharacteristic
47C23×C59C2×D412yes—
48C23×C59C2×Q812yes—
49C23×C59C2×Q811yescharacteristic
50C23×C59#4111yescharacteristic
51C2×C4×C59—21no—
52C2×C4×C59—21no—
53C2×C4×C59—24no—
54C2×C4×C59—42no—
55C2×C4×C59—42no—
56C2×C4×C59—41no—
57C2×C4×C59—41no—
58C2×Dic59—22no—
59C2×Dic59—24no—
60C2×Dic59—22no—
61C2×Dic59—22no—
62C2×Dic59—22no—
63C2×Dic59—41no—
64C2×Dic59—41no—
65C2×Dic59—41no—
66C2×Dic59—42no—
67C2×Dic59—41no—
68C2×Dic59—42no—
69C2×Dic59—42no—
70Dic118—81no—
71Dic118—81no—
72C22×C59—21no—
73C22×C59—22no—
74C22×C59—21no—
75C22×C59—22no—
76C22×C59—42no—
77C22×C59—41no—
78C22×C59—41no—
79C22×C59#12011yescharacteristic
80C22×C59C22⋊Q812yes—
81C22×C59C22⋊Q811yescharacteristic
82C22×C59C4⋊Q812yes—
83C22×C59C4⋊Q811yescharacteristic
84C4×C59—44no—
85C4×C59—41no—
86C4×C59—41no—
87Dic59—42no—
88Dic59—42no—
89Dic59—42no—
90Dic59—42no—
91#2062—591nomaximal, Sylow
92C2×C59—21no—
93C2×C59—22no—
94C2×C59—22no—
95C2×C59—21no—
96C2×C59#39511yescharacteristic
97C2×C59B(4,𝔽2)11yescharacteristic
98C2×C59#45811yescharacteristic
99#543—591no—
100#385—591no—
101#385—592no—
102#342—592no—
103#342D5911yescharacteristic
104C59#206211yescharacteristic, complemented, Sylow
105C23×C4—591no—
106C22⋊Q8—1182no—
107C22⋊Q8—1182no—
108C22⋊Q8—1181no—
109C22⋊Q8—1181no—
110C2×C4⋊C4—1182no—
111C2×C4⋊C4—1181no—
112C2×C22⋊C4—591no—
113C2×C22⋊C4—592no—
114C2×C22⋊C4C2×D5911yescharacteristic
115C2×C22⋊C4C2×D5912yes—
116#95—1182no—
117#95—1181no—
118C24C22×D5911yescharacteristic
119C2×Q8—1181no—
120C2×Q8—1181no—
121C22×C4—22no—
122C22×C4—592no—
123C22×C4—592no—
124C22×C4—1181no—
125C22×C4—1181no—
126C22×C4—1182no—
127C22×C4—2362no—
128C22×C4D23611yescharacteristic
129C22×C4D23611yescharacteristic
130C4⋊C4—1182no—
131C4⋊C4—1182no—
132C4⋊C4—1181no—
133C4⋊C4—1181no—
134C4⋊C4—2362no—
135C4⋊C4—2364no—
136C22⋊C4—22no—
137C22⋊C4—22no—
138C22⋊C4—592no—
139C22⋊C4—1182no—
140C22⋊C4—1182no—
141C22⋊C4—1181no—
142C22⋊C4Dic11814yescomplemented
143C23—41no—
144C23—41no—
145C23C2×Dic11812yes—
146C23C2×D23611yescharacteristic
147C23D4×D5912yes—
148C23#1174568711yescharacteristic
149C23Q8×D5911yescharacteristic
150Q8—4721no—
151Q8—4721no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—24no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—1182no—
160C2×C4—1184no—
161C2×C4—1182no—
162C2×C4—1182no—
163C2×C4—1182no—
164C2×C4—2361no—
165C2×C4—2361no—
166C2×C4—2361no—
167C2×C4—2362no—
168C2×C4—2361no—
169C2×C4—2362no—
170C2×C4—2362no—
171C22—21no—
172C22—22no—
173C22—21no—
174C22—22no—
175C22—42no—
176C22—41no—
177C22—41no—
178C22#1427369711yescharacteristic
179C22#1427370412yes—
180C22#1427370711yescharacteristic
181C22#1427372612yes—
182C22#1427372711yescharacteristic
183C4—44no—
184C4—41no—
185C4—41no—
186C4—2362no—
187C4—2362no—
188C4—2362no—
189C4—2362no—
190C2—22no—
191C2—21no—
192C2—22no—
193C2—21no—
194C2#1683732311yescharacteristic
195C2#1683759011yescharacteristic
196C2#1683759311yescharacteristic
subgroupG/H
centerC22#14273697
commutatorC24×C59C23
FrattiniC24C22×D59
FittingC59×#342C2
socleC22×C59#120
hypercenter#342D59
hypocenterC59#2062
LCSG ▷ C24×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
33. C22⋊C4×C59Q8semidirect
37. C22⋊Dic59Q8semidirect
104. C59#2062semidirect
142. C22⋊C4Dic118semidirect