Finite Group Databasebeta

← #21425261

Subgroups — #21425261

Order 7552.

466 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 67 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, complemented
2#16837257C212yesmaximal
3#16837257C211yesmaximal, characteristic
4#16837168C212yesmaximal, complemented
5C59×#342C211yesmaximal, characteristic, complemented
6C24×D59C2211yescharacteristic
7#14273706—22no—
8#14273704—24no—
9C2×C22⋊Dic59C2211yescharacteristic
10C2×C22⋊Dic59C2212yes—
11C2×(C2×D59)⋊C4—22no—
12C2×(C2×D59)⋊C4—24no—
13C2×C22⋊C4×C59C2212yes—
14C2×C22⋊C4×C59C2211yescharacteristic
15C24×C59C2311yescharacteristic
16C23×D59—21no—
17C23×D59—22no—
18C23×D59—22no—
19C23×D59—21no—
20C23×D59—44no—
21C23×D59Q812yescomplemented
22C22×C4×C59—22no—
23C22×C4×C59D412yes—
24C22×Dic59—21no—
25C22×Dic59D414yes—
26C2×Dic118—22no—
27C22⋊C4×C59—22no—
28C22⋊C4×C59—22no—
29C22⋊C4×C59—22no—
30C22⋊Dic59—22no—
31C22⋊Dic59—22no—
32C22⋊Dic59—22no—
33(C2×D59)⋊C4—48no—
34(C2×D59)⋊C4—44no—
35C4⋊Dic59—22no—
36Dic59⋊C4—24no—
37C23×C59—42no—
38C23×C59C2×D411yescharacteristic
39C23×C59C2×D412yes—
40C23×C59C2×Q811yescharacteristic
41C23×C59#4112yes—
42C23×C59#4111yescharacteristic
43C22×D59—24no—
44C22×D59—28no—
45C22×D59—24no—
46C22×D59—22no—
47C22×D59—44no—
48C22×D59—48no—
49C22×D59—44no—
50C22×D59—42no—
51C22×D59—44no—
52C22×D59—41no—
53C22×D59—42no—
54C22×D59—41no—
55C2×C4×C59—22no—
56C2×C4×C59—42no—
57C2×C4×C59—44no—
58C2×C4×C59—42no—
59C2×Dic59—24no—
60C2×Dic59—44no—
61C2×Dic59—42no—
62C2×Dic59—41no—
63Dic118—82no—
64C22×C59—22no—
65C22×C59—24no—
66C22×C59—41no—
67C22×C59—42no—
68C22×C59—41no—
69C22×C59#12011yescharacteristic
70C22×C59C22⋊Q812yes—
71C22×C59C22⋊Q811yescharacteristic
72C22×C59#12412yes—
73C22×C59#12411yescharacteristic
74C2×D59—28no—
75C2×D59—24no—
76C2×D59—44no—
77C2×D59—48no—
78C2×D59—44no—
79C2×D59—42no—
80C2×D59—42no—
81C2×D59—44no—
82C4×C59—42no—
83C4×C59—82no—
84Dic59—44no—
85Dic59—81no—
86#2029—591nomaximal, Sylow
87C2×C59—21no—
88C2×C59—22no—
89C2×C59—22no—
90C2×C59—21no—
91C2×C59#39311yescharacteristic
92C2×C59B(4,𝔽2)12yes—
93D59—44no—
94#543—591no—
95#379—592no—
96#379—591no—
97#342—592no—
98#342D5911yescharacteristic, complemented
99C59#202911yescharacteristic, complemented, Sylow
100C25—591no—
101C22⋊Q8—1184no—
102C22⋊Q8—1182no—
103C2×C22⋊C4—592no—
104C2×C22⋊C4—591no—
105C2×C22⋊C4—1184no—
106C2×C22⋊C4—1182no—
107C2×C22⋊C4C2×D5912yes—
108C2×C22⋊C4C2×D5911yescharacteristic
109C24—592no—
110C24—1181no—
111C24—1182no—
112C24—1182no—
113C24—1181no—
114C24—2364no—
115C24C22×D5911yescharacteristic
116C2×Q8—1182no—
117C22×C4—22no—
118C22×C4—594no—
119C22×C4—1181no—
120C22×C4D23612yes—
121C4⋊C4—1184no—
122C4⋊C4—1182no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—1182no—
127C22⋊C4—1182no—
128C22⋊C4—1182no—
129C22⋊C4—2364no—
130C22⋊C4—2368no—
131C23—42no—
132C23—1184no—
133C23—1188no—
134C23—1184no—
135C23—1182no—
136C23—2362no—
137C23—2364no—
138C23—2364no—
139C23—2368no—
140C23—2364no—
141C23—2361no—
142C23—2362no—
143C23—2361no—
144C23C2×D23611yescharacteristic
145C23#1174568512yes—
146C23D4×D5912yes—
147C23#1174568711yescharacteristic
148C23Q8×D5911yescharacteristic
149Q8—4722no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—42no—
154C2×C4—1184no—
155C2×C4—2362no—
156C2×C4—2361no—
157C2×C4—2364no—
158C22—22no—
159C22—24no—
160C22—42no—
161C22—41no—
162C22—41no—
163C22—1188no—
164C22—1184no—
165C22—2368no—
166C22—2364no—
167C22—2364no—
168C22—2362no—
169C22—2362no—
170C22—2364no—
171C22#1427369711yescharacteristic
172C22#1427370512yes—
173C22#1427370711yescharacteristic
174C22#1427371312yes—
175C22#1427371511yescharacteristic
176C4—42no—
177C4—82no—
178C4—4721no—
179C4—2364no—
180C2—22no—
181C2—21no—
182C2—22no—
183C2—21no—
184C2—2364no—
185C2#1683731511yescharacteristic
186C2#1683759012yes—
subgroupG/H
centerC22#14273697
commutatorC24×C59C23
FrattiniC24C22×D59
FittingC59×#342C2
socleC22×C59#120
hypercenter#342D59
hypocenterC59#2029
LCSG ▷ C24×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #16838028C2semidirect
4. #16837168C2semidirect
5. C59×#342C2semidirect
21. C23×D59Q8semidirect
98. #342D59semidirect
99. C59#2029semidirect