Finite Group Databasebeta

← #21425228

Subgroups — #21425228

Order 7552.

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

normal subgroups only

This group has 430 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#16837964C211yesmaximal, characteristic
2C2×#14273711C212yesmaximal, complemented
3C2×#14273641C212yesmaximal, complemented
4#16837263C211yesmaximal, characteristic, complemented
5C59×#342C211yesmaximal, characteristic, complemented
6C22×C22⋊D59C2212yes—
7C23×Dic59C2211yescharacteristic
8#14273711—22no—
9#14273711—24no—
10#14273711—24no—
11#14273701—22no—
12#14273697—22no—
13C2×C4⋊Dic59—22no—
14C2×C22⋊Dic59C2211yescharacteristic
15C2×(C2×D59)⋊C4—22no—
16#14273641—24no—
17C59⋊#95—22no—
18C2×C22⋊C4×C59C2211yescharacteristic
19C2×C22⋊C4×C59C2212yes—
20C24×C59C2311yescharacteristic
21C23×D59D412yes—
22C22×C4×C59—22no—
23C22×C4×C59D412yes—
24C2×C22⋊D59—22no—
25C2×C22⋊D59—22no—
26C2×C22⋊D59—22no—
27C2×C22⋊D59—22no—
28C2×C22⋊D59—22no—
29C2×C22⋊D59—22no—
30C22×Dic59—21no—
31C22×Dic59—22no—
32C22×Dic59—22no—
33C22×Dic59—21no—
34C22×Dic59—21no—
35C22×Dic59D412yes—
36C22×Dic59D412yescomplemented
37C2×D236—22no—
38C22⋊C4×C59—22no—
39C22⋊C4×C59—22no—
40C22⋊C4×C59D414yescomplemented
41C22⋊Dic59—22no—
42(C2×D59)⋊C4—28no—
43(C2×D59)⋊C4—24no—
44C4⋊Dic59—28no—
45C4⋊Dic59—22no—
46C23×C59—42no—
47C23×C59C2×D411yescharacteristic
48C23×C59C2×D412yes—
49C23×C59C2×D412yes—
50C23×C59C2×D411yescharacteristic
51C23×C59#4111yescharacteristic
52C22×D59—22no—
53C22×D59—22no—
54C22×D59—22no—
55C22×D59—44no—
56C2×C4×C59—24no—
57C2×C4×C59—22no—
58C2×C4×C59—44no—
59C2×C4×C59—42no—
60C22⋊D59—42no—
61C22⋊D59—42no—
62C22⋊D59—42no—
63C22⋊D59—42no—
64C2×Dic59—22no—
65C2×Dic59—24no—
66C2×Dic59—22no—
67C2×Dic59—22no—
68C2×Dic59—22no—
69C2×Dic59—41no—
70C2×Dic59—42no—
71C2×Dic59—41no—
72C2×Dic59—42no—
73C2×Dic59—41no—
74D236—82no—
75C22×C59—22no—
76C22×C59—24no—
77C22×C59—42no—
78C22×C59—41no—
79C22×C59—41no—
80C22×C59#12012yes—
81C22×C59#12011yescharacteristic
82C22×C59#12111yescharacteristic
83C22×C59#12112yes—
84C22×C59#12711yescharacteristic
85C2×D59—44no—
86C2×D59—42no—
87C2×D59—44no—
88C2×D59—82no—
89C4×C59—44no—
90C4×C59—42no—
91Dic59—42no—
92Dic59—42no—
93Dic59—81no—
94#2022—591nomaximal, Sylow
95C2×C59—21no—
96C2×C59—22no—
97C2×C59—22no—
98C2×C59—21no—
99C2×C59#39211yescharacteristic
100C2×C59#45812yes—
101D59—82no—
102#534—591no—
103C2×#123—592no—
104C2×#99—592no—
105#381—591no—
106#342D5911yescharacteristic, complemented
107C59#202211yescharacteristic, complemented, Sylow
108C22×D4—592no—
109C23×C4—591no—
110#123—1184no—
111#123—1182no—
112#123—1184no—
113#121—1182no—
114#120—1182no—
115C2×C4⋊C4—1182no—
116C2×C22⋊C4—591no—
117C2×C22⋊C4—1182no—
118C2×C22⋊C4C2×D5911yescharacteristic
119C2×C22⋊C4C2×D5912yes—
120#99—1184no—
121#95—1182no—
122C24—592no—
123C24C22×D5911yescharacteristic
124C2×D4—1182no—
125C2×D4—1182no—
126C2×D4—1182no—
127C2×D4—1182no—
128C2×D4—1182no—
129C2×D4—1182no—
130C2×D4—1182no—
131C22×C4—22no—
132C22×C4—592no—
133C22×C4—592no—
134C22×C4—1181no—
135C22×C4—1182no—
136C22×C4—1182no—
137C22×C4—1181no—
138C22×C4—1181no—
139C22×C4D23612yes—
140C4⋊C4—1188no—
141C4⋊C4—1182no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—1188no—
145C22⋊C4—1184no—
146C22⋊C4—1182no—
147C22⋊C4D23614yescomplemented
148C23—42no—
149C23—1182no—
150C23—1182no—
151C23—1182no—
152C23—2364no—
153C23C2×D23611yescharacteristic
154C23C2×D23612yes—
155C23D4×D5912yes—
156C23D4×D5911yescharacteristic
157C23#1174568911yescharacteristic
158D4—4722no—
159D4—2362no—
160D4—2362no—
161D4—2362no—
162D4—2362no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—44no—
166C2×C4—42no—
167C2×C4—1184no—
168C2×C4—1182no—
169C2×C4—1182no—
170C2×C4—1182no—
171C2×C4—1182no—
172C2×C4—2362no—
173C2×C4—2361no—
174C2×C4—2361no—
175C2×C4—2362no—
176C2×C4—2361no—
177C22—22no—
178C22—24no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—4722no—
183C22—2364no—
184C22—2362no—
185C22—2364no—
186C22#1427369712yes—
187C22#1427369711yescharacteristic
188C22#1427370211yescharacteristic
189C22#1427370212yes—
190C22#1427372411yescharacteristic
191C4—44no—
192C4—42no—
193C4—4721no—
194C4—2362no—
195C4—2362no—
196C2—22no—
197C2—21no—
198C2—22no—
199C2—21no—
200C2—4722no—
201C2#1683731211yescharacteristic
202C2#1683759312yes—
subgroupG/H
centerC22#14273697
commutatorC24×C59C23
FrattiniC24C22×D59
FittingC59×#342C2
socleC22×C59#120
hypercenter#342D59
hypocenterC59#2022
LCSG ▷ C24×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#14273711C2semidirect
3. C2×#14273641C2semidirect
4. #16837263C2semidirect
5. C59×#342C2semidirect
36. C22×Dic59D4semidirect
40. C22⋊C4×C59D4semidirect
106. #342D59semidirect
107. C59#2022semidirect
147. C22⋊C4D236semidirect