Finite Group Databasebeta

← #21435294

Subgroups — #21435294

Order 7552.

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

normal subgroups only

This group has 366 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#16837952C211yesmaximal, characteristic
2#16837812C212yesmaximal, complemented
3#16837768C212yesmaximal, complemented
4#16837726C214yesmaximal, complemented
5#16837689C212yesmaximal, complemented
6#16837679C212yesmaximal, complemented
7#16837459C211yesmaximal, characteristic, complemented
8C59×#533C211yesmaximal, characteristic, complemented
9C2×#11745685—21no—
10#14273727C2211yescharacteristic
11#14273724C2211yescharacteristic
12#14273715—21no—
13#14273701—21no—
14#14273701C2212yes—
15C4×D236—21no—
16C4×D236C2212yes—
17#14273660C2214yes—
18#14273658C2214yes—
19C4⋊(C59⋊C8)C2212yes—
20#14273647C2214yes—
21#14273647C2214yes—
22C22⋊(C59⋊C8)C2212yes—
23#14273638C2212yes—
24C4⋊Q8×C59C2211yescharacteristic
25C4⋊Q8×C59C2211yescharacteristic
26#125×C59C2212yes—
27C22⋊Q8×C59—21no—
28C22⋊Q8×C59—21no—
29C4×Q8×C59—21no—
30C4×Q8×C59—21no—
31#117×C59C2212yes—
32C2×C42×C59C2211yescharacteristic
33C2×Q8×C59—21no—
34C2×Q8×C59—21no—
35C22×C4×C59D411yescharacteristic
36C22×C4×C59D411yescharacteristic
37C22×C4×C59C2311yescharacteristic
38C2×C22⋊D59—22no—
39#11745685—44no—
40C2×D236—21no—
41C2×D236—21no—
42C2×D236C2312yes—
43C2×C4×D59—22no—
44C2×Dic118—21no—
45C4⋊C4×C59—22no—
46C4⋊C4×C59—22no—
47C4⋊C4×C59—21no—
48C4⋊C4×C59—21no—
49C4⋊C4×C59C2312yes—
50C4⋊C4×C59C2312yes—
51C22⋊C4×C59—22no—
52C42×C59—22no—
53C42×C59D411yescharacteristic
54C42×C59D411yescharacteristic
55C42×C59C2311yescharacteristic
56C42×C59C2311yescharacteristic
57(C2×D59)⋊C4—22no—
58(C2×D59)⋊C4—22no—
59C4⋊Dic59—21no—
60C4⋊Dic59C2312yes—
61C2×C59⋊C8C2314yes—
62C23×C59C2×D411yescharacteristic
63C22×D59—22no—
64Q8×C59—42no—
65Q8×C59—42no—
66C2×C4×C59—22no—
67C2×C4×C59—22no—
68C2×C4×C59—22no—
69C2×C4×C59—22no—
70C2×C4×C59—41no—
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59C2×D411yescharacteristic
73C2×C4×C59C2×D411yescharacteristic
74C2×C4×C59C2×D411yescharacteristic
75C2×C4×C59C2×D411yescharacteristic
76C2×C4×C59C2411yescharacteristic
77C22⋊D59—44no—
78C2×Dic59—22no—
79D236—24no—
80D236—42no—
81D236—42no—
82C4×D59—44no—
83Dic118—42no—
84C59⋊C8—24no—
85C22×C59—21no—
86C22×C59—21no—
87C22×C59—21no—
88C22×C59C22×D411yescharacteristic
89C2×D59—42no—
90C2×D59—42no—
91C2×D59—42no—
92C4×C59—21no—
93C4×C59—21no—
94C4×C59—21no—
95C4×C59—21no—
96C4×C59—42no—
97C4×C59—42no—
98C4×C59AGL(1,ℤ/8)12yes—
99C4×C592−1+412yes—
100Dic59—42no—
101#3235—591nomaximal, Sylow
102C2×C59—41no—
103C2×C59#53611yescharacteristic
104C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
105C2×C59#57511yescharacteristic
106D59—82no—
107#533D5911yescharacteristic, complemented
108#532—591no—
109#501—592no—
110#490—592no—
111#482—594no—
112#476—592no—
113#474—592no—
114#432—591no—
115C59#323511yescharacteristic, complemented, Sylow
116C2×#41—1181no—
117C4⋊Q8—591no—
118C4⋊Q8C2×D5911yescharacteristic
119C4⋊Q8C2×D5911yescharacteristic
120#127—591no—
121#125C2×D5912yes—
122#124—1181no—
123C22⋊Q8—21no—
124C22⋊Q8—21no—
125#121—592no—
126#121—1181no—
127C4×Q8—21no—
128C4×Q8—21no—
129C4×D4—592no—
130C4×D4—1181no—
131#117C2×D5912yes—
132C2×C42C2×D5911yescharacteristic
133#107—594no—
134#106—594no—
135C4⋊C8—592no—
136#102—594no—
137#102—594no—
138C22⋊C8—592no—
139#97—592no—
140#41—2364no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—1181no—
144C2×D4—592no—
145C2×D4—1182no—
146C2×D4—1181no—
147C2×D4—1181no—
148C22×C4—1182no—
149C22×C4C22⋊D5911yescharacteristic
150C22×C4C22⋊D5911yescharacteristic
151C22×C4C22×D5911yescharacteristic
152C2×C8—594no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—592no—
158C4⋊C4—1181no—
159C4⋊C4C22×D5912yes—
160C4⋊C4C22×D5912yes—
161C22⋊C4—22no—
162C22⋊C4—1182no—
163C22⋊C4—1182no—
164C42—22no—
165C42C22⋊D5911yescharacteristic
166C42C22⋊D5911yescharacteristic
167C42C22×D5911yescharacteristic
168C42C22×D5911yescharacteristic
169C23—1182no—
170C23C2×C22⋊D5911yescharacteristic
171Q8—42no—
172Q8—42no—
173Q8—2362no—
174D4—1184no—
175D4—2362no—
176D4—2362no—
177D4—2364no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—1182no—
184C2×C4—2364no—
185C2×C4C2×C22⋊D5911yescharacteristic
186C2×C4C2×C22⋊D5911yescharacteristic
187C2×C4C2×C22⋊D5911yescharacteristic
188C2×C4C2×C22⋊D5911yescharacteristic
189C2×C4C2×C22⋊D5911yescharacteristic
190C2×C4C23×D5911yescharacteristic
191C8—1184no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—2362no—
196C22—2362no—
197C22—2362no—
198C22C22×C22⋊D5911yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—42no—
204C4—42no—
205C4—2362no—
206C4#1427375212yes—
207C4#1427377512yes—
208C2—41no—
209C2—4722no—
210C2#1683797611yescharacteristic
211C2C2×#1427375211yescharacteristic
212C2#1683820011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#533C2
socleC22×C59C22×D4
hypercenter#533D59
hypocenterC59#3235
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #16837812C2semidirect
3. #16837768C2semidirect
4. #16837726C2semidirect
5. #16837689C2semidirect
6. #16837679C2semidirect
7. #16837459C2semidirect
8. C59×#533C2semidirect
107. #533D59semidirect
115. C59#3235semidirect