Finite Group Databasebeta

← #21423178

Subgroups — #21423178

Order 7552.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#16838117C211yesmaximal, characteristic, complemented
2#16837774C211yesmaximal, characteristic, complemented
3#16837594C211yesmaximal, characteristic, complemented
4#16837150C211yesmaximal, characteristic, complemented
5D4⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
6#16837129C211yesmaximal, characteristic, complemented
7C59×#459C211yesmaximal, characteristic, complemented
8C2×#11745670—22no—
9C2×#11745669—21no—
10#14273727C2211yescharacteristic
11#14273713—22no—
12#14273701—21no—
13#14273698—21no—
14C4×D236C2211yescharacteristic
15#14273686—21no—
16#14273685—21no—
17C4⋊(C59⋊C8)C2211yescharacteristic
18#14273648—21no—
19C4×C59⋊C8C2211yescharacteristic
20C2×D8×C59—21no—
21#127×C59C2211yescharacteristic
22C4×D4×C59C2211yescharacteristic
23C4⋊C8×C59C2211yescharacteristic
24#102×C59—21no—
25C2×D4×C59—21no—
26C2×D4×C59—21no—
27C2×D4×C59—21no—
28C2×D4×C59D411yescharacteristic
29C22×C4×C59—21no—
30C2×C22⋊D59—22no—
31C2×D236D411yescharacteristic
32C2×C4×D59—21no—
33C2×Dic118D412yes—
34D8×C59—42no—
35C2×C8×C59—21no—
36C4⋊C4×C59D411yescharacteristic
37C22⋊C4×C59—21no—
38C42×C59C2311yescharacteristic
39C22⋊Dic59—22no—
40#11745670—44no—
41#11745669—42no—
42(C2×D59)⋊C4—22no—
43(C2×D59)⋊C4—21no—
44C4⋊Dic59—21no—
45C4⋊Dic59—21no—
46C4⋊Dic59D411yescharacteristic
47C4×Dic59—22no—
48C2×C59⋊C8—21no—
49C2×C59⋊C8—21no—
50C23×C59—21no—
51C23×C59—41no—
52C22×D59—21no—
53D4×C59—21no—
54D4×C59—21no—
55D4×C59—42no—
56D4×C59—41no—
57D4×C59—41no—
58D4×C59—41no—
59D4×C59—41no—
60C2×C4×C59—21no—
61C2×C4×C59—41no—
62C2×C4×C59—41no—
63C2×C4×C59C2×D411yescharacteristic
64C2×C4×C59C2×D411yescharacteristic
65C2×C4×C59C2×D411yescharacteristic
66C22⋊D59—82no—
67C2×Dic59—21no—
68C2×Dic59—22no—
69D236—21no—
70D236—21no—
71C4×D59—41no—
72C4×D59—41no—
73Dic118—42no—
74C8×C59—41no—
75C59⋊C8—22no—
76C59⋊C8—41no—
77C22×C59—41no—
78C22×C59—41no—
79C22×C59—41no—
80C22×C59—81no—
81C22×C59—81no—
82C22×C59—81no—
83C22×C59#12011yescharacteristic
84C2×D59—41no—
85C2×D59—41no—
86C2×D59—41no—
87C4×C59—21no—
88C4×C59—41no—
89C4×C59#13511yescharacteristic
90C4×C59#13511yescharacteristic
91C4×C59AGL(1,ℤ/8)11yescharacteristic
92C4×C59AGL(1,ℤ/8)11yescharacteristic
93Dic59—41no—
94Dic59—42no—
95#1624—591nomaximal, Sylow
96C2×C59—81no—
97C2×C59—161no—
98C2×C59#44911yescharacteristic
99C2×C59#44911yescharacteristic
100C2×C59#45311yescharacteristic
101D59—81no—
102#555—591no—
103#492—591no—
104#459—591no—
105#459D5911yescharacteristic, complemented
106#333—591no—
107D4⋊C8—591no—
108D4⋊C8—591no—
109C59#162411yescharacteristic, complemented, Sylow
110C2×SD16—1182no—
111C2×D8—21no—
112C2×D8—1181no—
113C4⋊Q8—591no—
114#127C2×D5911yescharacteristic
115#124—1182no—
116#121—1181no—
117#121—1181no—
118C4×D4—591no—
119C4×D4C2×D5911yescharacteristic
120#117—1181no—
121#117—1181no—
122C4⋊C8—591no—
123C4⋊C8C2×D5911yescharacteristic
124#102—21no—
125#102—1181no—
126C4×C8—591no—
127C2×Q8—592no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—591no—
132C2×D4—1182no—
133C2×D4C22⋊D5911yescharacteristic
134C22×C4—21no—
135C22×C4—1181no—
136SD16—2364no—
137D8—42no—
138D8—2362no—
139C2×C8—21no—
140C2×C8—1181no—
141C2×C8—1181no—
142C4⋊C4—591no—
143C4⋊C4—1181no—
144C4⋊C4—1181no—
145C4⋊C4C22⋊D5911yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—1182no—
148C22⋊C4—1182no—
149C22⋊C4—1181no—
150C42—1182no—
151C42C22×D5911yescharacteristic
152C23—21no—
153C23—41no—
154C23—1181no—
155Q8—2362no—
156D4—21no—
157D4—21no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—1181no—
164D4—1181no—
165D4—4722no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—1181no—
170C2×C4—1182no—
171C2×C4—2361no—
172C2×C4—2361no—
173C2×C4D4×D5911yescharacteristic
174C2×C4D4×D5911yescharacteristic
175C2×C4C2×C22⋊D5911yescharacteristic
176C8—41no—
177C8—1182no—
178C8—2361no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—2361no—
186C22—2361no—
187C22—2361no—
188C22#1427369511yescharacteristic
189C4—21no—
190C4—41no—
191C4—2361no—
192C4—2362no—
193C4#1427374611yescharacteristic
194C4#1427374711yescharacteristic
195C4#1427375111yescharacteristic
196C4#1427375311yescharacteristic
197C2—81no—
198C2—161no—
199C2—4721no—
200C2#1683754411yescharacteristic
201C2#1683754511yescharacteristic
202C2#1683756811yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#459C2
socleC22×C59#120
hypercenter#459D59
hypocenterC59#1624
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #16838117C2semidirect
2. #16837774C2semidirect
3. #16837594C2semidirect
4. #16837150C2semidirect
5. D4⋊(C59⋊C8)C2semidirect
6. #16837129C2semidirect
7. C59×#459C2semidirect
105. #459D59semidirect
109. C59#1624semidirect