Finite Group Databasebeta

← #21423091

Subgroups — #21423091

Order 7552.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#16837999C211yesmaximal, characteristic
2#16837732C211yesmaximal, characteristic, complemented
3#16837715C211yesmaximal, characteristic
4#16837138C211yesmaximal, characteristic, complemented
5#16837135C211yesmaximal, characteristic
6#16837128C211yesmaximal, characteristic, complemented
7C59×#398C211yesmaximal, characteristic, complemented
8#14273722—21no—
9#14273717—21no—
10#14273712—21no—
11#14273710—21no—
12#14273706C2211yescharacteristic
13#14273705—21no—
14#14273701C2211yescharacteristic
15C4×C22⋊D59—21no—
16#14273660—21no—
17#14273658—21no—
18#14273650—21no—
19#14273647—21no—
20C22⋊(C59⋊C8)C2211yescharacteristic
21C22⋊(C59⋊C8)C2211yescharacteristic
22C2×C4⋊C4×C59—21no—
23C2×C4⋊C4×C59C2211yescharacteristic
24C2×C4⋊C4×C59C2211yescharacteristic
25#95×C59—21no—
26#95×C59C2211yescharacteristic
27C22×C4×C59—21no—
28C22×C4×C59—21no—
29C22×C4×C59D411yescharacteristic
30C22×C4×C59D411yescharacteristic
31C22×C4×C59C2311yescharacteristic
32C2×C22⋊D59—21no—
33C2×D236D411yescharacteristic
34C2×C4×D59—21no—
35C2×Dic118D411yescharacteristic
36C4⋊C4×C59—21no—
37C4⋊C4×C59—21no—
38C4⋊C4×C59—21no—
39C4⋊C4×C59—21no—
40C4⋊C4×C59—42no—
41C22⋊Dic59—21no—
42(C2×D59)⋊C4—21no—
43(C2×D59)⋊C4—21no—
44(C2×D59)⋊C4—21no—
45(C2×D59)⋊C4—21no—
46C4⋊Dic59D411yescharacteristic
47C4⋊Dic59D411yescharacteristic
48Dic59⋊C4—21no—
49Dic59⋊C4—21no—
50Dic59⋊C4—21no—
51Dic59⋊C4—21no—
52C4×Dic59—21no—
53C2×C59⋊C8—21no—
54C2×C59⋊C8—21no—
55C23×C59C2×D411yescharacteristic
56C22×D59—21no—
57C2×C4×C59—22no—
58C2×C4×C59—21no—
59C2×C4×C59—21no—
60C2×C4×C59—21no—
61C2×C4×C59—21no—
62C2×C4×C59—41no—
63C2×C4×C59—41no—
64C2×C4×C59—41no—
65C2×C4×C59—41no—
66C2×C4×C59—41no—
67C2×C4×C59—41no—
68C2×C4×C59—41no—
69C2×C4×C59C2×D411yescharacteristic
70C2×C4×C59C2×D411yescharacteristic
71C22⋊D59—41no—
72C22⋊D59—41no—
73C2×Dic59—21no—
74C2×Dic59—21no—
75C2×Dic59—21no—
76D236—41no—
77C4×D59—81no—
78Dic118—41no—
79C59⋊C8—41no—
80C59⋊C8—41no—
81C22×C59—21no—
82C22×C59—21no—
83C22×C59#12011yescharacteristic
84C22×C59#13511yescharacteristic
85C22×C59AGL(1,ℤ/8)11yescharacteristic
86C2×D59—41no—
87C2×D59—41no—
88C2×D59—41no—
89C4×C59—21no—
90C4×C59—21no—
91C4×C59—42no—
92C4×C59—41no—
93C4×C59—41no—
94C4×C59—81no—
95Dic59—41no—
96Dic59—41no—
97Dic59—41no—
98#1609—591nomaximal, Sylow
99C2×C59—21no—
100C2×C59—21no—
101C2×C59#44911yescharacteristic
102C2×C59#45611yescharacteristic
103C2×C59#45811yescharacteristic
104D59—81no—
105#539—591no—
106#483—591no—
107#480—591no—
108#398D5911yescharacteristic, complemented
109#328—591no—
110#327—591no—
111#324—591no—
112C59#160911yescharacteristic, complemented, Sylow
113#126—1181no—
114#125—1181no—
115#123—1181no—
116#123—1181no—
117C22⋊Q8—591no—
118C22⋊Q8—1181no—
119#121—591no—
120C4×D4—1181no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4C2×D5911yescharacteristic
123C2×C4⋊C4C2×D5911yescharacteristic
124#107—1181no—
125#106—1181no—
126#103—1181no—
127#102—1181no—
128C22⋊C8—591no—
129C22⋊C8—591no—
130#95—21no—
131#95C2×D5911yescharacteristic
132C2×Q8—591no—
133C2×D4—591no—
134C2×D4—1181no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—1181no—
138C22×C4C22⋊D5911yescharacteristic
139C22×C4C22⋊D5911yescharacteristic
140C22×C4C22×D5911yescharacteristic
141C2×C8—1181no—
142C2×C8—1181no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—42no—
148C4⋊C4—591no—
149C4⋊C4—591no—
150C4⋊C4—1181no—
151C4⋊C4—1181no—
152C4⋊C4—1181no—
153C4⋊C4—1181no—
154C22⋊C4—1181no—
155C22⋊C4—1181no—
156C22⋊C4—1181no—
157C22⋊C4—1181no—
158C22⋊C4—1181no—
159C42—1181no—
160C23—1181no—
161C23C2×C22⋊D5911yescharacteristic
162Q8—2361no—
163D4—2361no—
164D4—2361no—
165D4—2361no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—1181no—
179C2×C4—1181no—
180C2×C4—1181no—
181C2×C4—4721no—
182C2×C4D4×D5911yescharacteristic
183C2×C4D4×D5911yescharacteristic
184C8—2361no—
185C8—2361no—
186C22—21no—
187C22—21no—
188C22—2361no—
189C22—2361no—
190C22—2361no—
191C22#1427369511yescharacteristic
192C22#1427374711yescharacteristic
193C22#1427375311yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4—81no—
200C4—2361no—
201C4—2361no—
202C4—2361no—
203C2—21no—
204C2—21no—
205C2—4721no—
206C2#1683754511yescharacteristic
207C2#1683758411yescharacteristic
208C2#1683759111yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#398C2
socleC22×C59#120
hypercenter#398D59
hypocenterC59#1609
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
2. #16837732C2semidirect
4. #16837138C2semidirect
6. #16837128C2semidirect
7. C59×#398C2semidirect
108. #398D59semidirect
112. C59#1609semidirect