Finite Group Databasebeta

← #21425722

Subgroups — #21425722

Order 7552.

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

normal subgroups only

This group has 220 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#131×D59C211yesmaximal, characteristic
2C2×#14273666C211yesmaximal, characteristic, complemented
3M32×D59C211yesmaximal, characteristic, complemented
4#16837187C211yesmaximal, characteristic, complemented
5#16837186C211yesmaximal, characteristic, complemented
6#16837185C211yesmaximal, characteristic, complemented
7C59×#350C211yesmaximal, characteristic, complemented
8#41×D59C411yescharacteristic
9#14273735—21no—
10#14273735C411yescharacteristic
11#14273734C411yescharacteristic
12#14273733—21no—
13#14273733C2211yescharacteristic
14M16×D59—21no—
15M16×D59C411yescharacteristic
16C2×C8×D59—21no—
17C2×C8×D59C2211yescharacteristic
18#14273667C2211yescharacteristic, complemented
19#14273666—21no—
20#14273666—21no—
21#14273666—21no—
22C2×C59⋊C16C2211yescharacteristic, complemented
23C16×D59—21no—
24#131×C59C2211yescharacteristic
25M32×C59C2211yescharacteristic, complemented
26C2×C16×C59C2211yescharacteristic, complemented
27#41×C59C2×C411yescharacteristic
28#11745689C811yescharacteristic
29Q8×D59C811yescharacteristic
30#11745687—21no—
31#11745687C811yescharacteristic
32D4×D59—21no—
33D4×D59C811yescharacteristic
34#11745685—21no—
35#11745685C2×C411yescharacteristic
36C2×C4×D59—21no—
37C2×C4×D59C2×C411yescharacteristic
38M16×C59—21no—
39M16×C59C2×C411yescharacteristic
40C2×C8×C59—21no—
41C2×C8×C59C2311yescharacteristic
42#11745664—21no—
43#11745664C2×C411yescharacteristic
44C2×C59⋊C8—21no—
45C2×C59⋊C8C2×C411yescharacteristic
46#11745659—21no—
47#11745659—21no—
48#11745659—21no—
49C8×D59—21no—
50C8×D59—21no—
51C8×D59—21no—
52C8×D59D411yescharacteristic
53C8×D59D411yescharacteristic
54C8×D59D411yescharacteristic
55C8×D59D411yescharacteristic
56C16×C59—21no—
57C16×C59—21no—
58C59⋊C16—21no—
59C59⋊C16—21no—
60C22×D59—21no—
61C22×D59M1611yescharacteristic
62Q8×C59C2×C811yescharacteristic
63D4×C59—21no—
64D4×C59C2×C811yescharacteristic
65C2×C4×C59—21no—
66C2×C4×C59C22×C411yescharacteristic
67C22⋊D59—21no—
68C22⋊D59—21no—
69C22⋊D59—21no—
70C2×Dic59—21no—
71C2×Dic59M1611yescharacteristic
72D236—21no—
73D236C2×C811yescharacteristic
74C4×D59—21no—
75C4×D59—21no—
76C4×D59—21no—
77C4×D59C22⋊C411yescharacteristic
78C4×D59C22⋊C411yescharacteristic
79C4×D59C2×C811yescharacteristic
80C4×D59C2×C811yescharacteristic
81Dic118—21no—
82Dic118C2×C811yescharacteristic
83C8×C59—21no—
84C8×C59C2×D411yescharacteristic
85C8×C59C2×D411yescharacteristic
86C59⋊C8—21no—
87C59⋊C8C22⋊C411yescharacteristic
88C59⋊C8C22⋊C411yescharacteristic
89C22×C59—21no—
90C22×C59C2×M1611yescharacteristic
91C2×D59—21no—
92C2×D59—41no—
93C2×D59—42no—
94C2×D59C22⋊C811yescharacteristic
95C2×D59C22⋊C811yescharacteristic
96C4×C59—21no—
97C4×C59C2×C22⋊C411yescharacteristic
98C4×C59C22×C811yescharacteristic
99Dic59—21no—
100Dic59C22⋊C811yescharacteristic
101Dic59C22⋊C811yescharacteristic
102#2117—591nomaximal, Sylow
103C2×C59—21no—
104C2×C59—41no—
105C2×C59C2×C22⋊C811yescharacteristic
106D59—21no—
107D59—21no—
108D59—41no—
109C2×#131—591no—
110C2×M32—591no—
111C2×M32—591no—
112#350—591no—
113#350—591no—
114#350—591no—
115#350D5911yescharacteristic, complemented
116C59#211711yescharacteristic, complemented, Sylow
117C2×#41—591no—
118#131—591no—
119#131—591no—
120#131—591no—
121#131—1181no—
122#131—1181no—
123#131C2×D5911yescharacteristic
124C2×M16—591no—
125C2×M16—1181no—
126C22×C8—591no—
127C22×C8—1181no—
128M32—591no—
129M32—1181no—
130M32—1181no—
131M32—1181no—
132M32C2×D5911yescharacteristic, complemented
133C2×C16—591no—
134C2×C16—1181no—
135C2×C16C2×D5911yescharacteristic, complemented
136#41—591no—
137#41—591no—
138#41—591no—
139#41—1181no—
140#41—1181no—
141#41C4×D5911yescharacteristic
142C2×Q8—591no—
143C2×D4—591no—
144C2×D4—1181no—
145C22×C4—591no—
146C22×C4—1181no—
147M16—21no—
148M16—591no—
149M16—1181no—
150M16—1181no—
151M16—1181no—
152M16—1181no—
153M16C4×D5911yescharacteristic
154C2×C8—21no—
155C2×C8—591no—
156C2×C8—591no—
157C2×C8—591no—
158C2×C8—591no—
159C2×C8—591no—
160C2×C8—1181no—
161C2×C8—1181no—
162C2×C8—1181no—
163C2×C8—1181no—
164C2×C8C22×D5911yescharacteristic
165C16—21no—
166C16—21no—
167C16—1181no—
168C16—1181no—
169C23—591no—
170C23—1181no—
171Q8—591no—
172Q8—1181no—
173Q8C8×D5911yescharacteristic
174D4—21no—
175D4—591no—
176D4—1181no—
177D4—1181no—
178D4—1181no—
179D4—1181no—
180D4C8×D5911yescharacteristic
181C2×C4—21no—
182C2×C4—591no—
183C2×C4—591no—
184C2×C4—591no—
185C2×C4—591no—
186C2×C4—591no—
187C2×C4—1181no—
188C2×C4—1181no—
189C2×C4—1181no—
190C2×C4—1181no—
191C2×C4C2×C4×D5911yescharacteristic
192C8—21no—
193C8—591no—
194C8—591no—
195C8—1181no—
196C8D4×D5911yescharacteristic
197C8D4×D5911yescharacteristic
198C22—21no—
199C22—591no—
200C22—591no—
201C22—1181no—
202C22—2361no—
203C22—2362no—
204C22M16×D5911yescharacteristic
205C4—21no—
206C4—591no—
207C4—591no—
208C4—1181no—
209C4C22⋊C4×D5911yescharacteristic
210C4C2×C8×D5911yescharacteristic
211C2—21no—
212C2—41no—
213C2—1181no—
214C2—1181no—
215C2—2361no—
216C2C22⋊C8×D5911yescharacteristic
subgroupG/H
centerC8D4×D59
commutatorC4×C59C22×C8
FrattiniC2×C8C22×D59
FittingC59×#350C2
socleC2×C59C2×C22⋊C8
hypercenter#350D59
hypocenterC59#2117
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C8 ◁ C2×C8 ◁ #350

Complements

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

NH ≅ G/Ntype
2. C2×#14273666C2semidirect
3. M32×D59C2semidirect
4. #16837187C2semidirect
5. #16837186C2semidirect
6. #16837185C2semidirect
7. C59×#350C2semidirect
18. #14273667C22semidirect
22. C2×C59⋊C16C22semidirect
25. M32×C59C22semidirect
26. C2×C16×C59C22semidirect
115. #350D59semidirect
116. C59#2117semidirect
132. M32C2×D59semidirect
135. C2×C16C2×D59semidirect