Finite Group Databasebeta

← C59×#1595 #21419913

Subgroups — C59×#1595 #21419913

Order 7552.

368 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C59×#534C211yesmaximal, characteristic, complemented
2C59×#447C212yesmaximal, complemented
3C59×#392C211yesmaximal, characteristic, complemented
4C59×#327C212yesmaximal, complemented
5C59×#323C211yesmaximal, characteristic, complemented
6C22×D4×C59—21no—
7C22×D4×C59—21no—
8C22×D4×C59C2211yescharacteristic, complemented
9C2×D8×C59—22no—
10#123×C59—22no—
11#121×C59—21no—
12#121×C59C2212yes—
13#120×C59—22no—
14C2×C22⋊C4×C59—21no—
15C2×C22⋊C4×C59C2211yescharacteristic
16#102×C59—22no—
17C22⋊C8×C59C2212yescomplemented
18#95×C59C2211yescharacteristic, complemented
19C24×C59—21no—
20C24×C59—21no—
21C24×C59D411yescharacteristic
22C2×D4×C59—22no—
23C2×D4×C59—22no—
24C2×D4×C59—21no—
25C2×D4×C59—22no—
26C2×D4×C59—42no—
27C2×D4×C59—42no—
28C2×D4×C59—42no—
29C2×D4×C59—42no—
30C2×D4×C59—42no—
31C2×D4×C59—42no—
32C2×D4×C59D412yescomplemented
33C22×C4×C59—21no—
34C22×C4×C59—21no—
35C22×C4×C59D411yescharacteristic
36C22×C4×C59C2311yescharacteristic
37D8×C59—44no—
38C2×C8×C59—22no—
39C4⋊C4×C59—21no—
40C4⋊C4×C59D412yescomplemented
41C22⋊C4×C59—22no—
42C22⋊C4×C59—22no—
43C22⋊C4×C59—22no—
44C22⋊C4×C59—42no—
45C23×C59—21no—
46C23×C59—21no—
47C23×C59—22no—
48C23×C59—22no—
49C23×C59—41no—
50C23×C59—41no—
51C23×C59—41no—
52C23×C59—41no—
53C23×C59—41no—
54C23×C59—42no—
55C23×C59—41no—
56C23×C59—41no—
57C23×C59—41no—
58C23×C59—81no—
59C23×C59—81no—
60C23×C59D812yescomplemented
61C23×C59C2×D411yescharacteristic
62D4×C59—24no—
63D4×C59—42no—
64D4×C59—42no—
65D4×C59—44no—
66D4×C59—48no—
67D4×C59—42no—
68D4×C59—42no—
69D4×C59—81no—
70C2×C4×C59—22no—
71C2×C4×C59—21no—
72C2×C4×C59—22no—
73C2×C4×C59—41no—
74C2×C4×C59—41no—
75C2×C4×C59—42no—
76C2×C4×C59—41no—
77C2×C4×C59—41no—
78C2×C4×C59C2×D412yes—
79C8×C59—42no—
80C22×C59—21no—
81C22×C59—21no—
82C22×C59—22no—
83C22×C59—42no—
84C22×C59—42no—
85C22×C59—42no—
86C22×C59—41no—
87C22×C59—41no—
88C22×C59—42no—
89C22×C59—42no—
90C22×C59—42no—
91C22×C59—42no—
92C22×C59—81no—
93C22×C59—81no—
94C22×C59—81no—
95C22×C59—84no—
96C22×C59—81no—
97C22×C59—81no—
98C22×C59#12011yescharacteristic
99C22×C59C2×D811yescharacteristic
100C22×C59AGL(1,ℤ/8)11yescharacteristic
101C4×C59—22no—
102C4×C59—42no—
103C4×C59—42no—
104C4×C59—41no—
105#1595C5911yesmaximal, characteristic, direct product factor, Sylow
106C2×C59—21no—
107C2×C59—21no—
108C2×C59—42no—
109C2×C59—82no—
110C2×C59—82no—
111C2×C59#44711yescharacteristic
112C2×C59#45311yescharacteristic
113C2×C59B(4,𝔽2)11yescharacteristic
114#534C2×C5911yescharacteristic, complemented
115#447C2×C5912yescomplemented
116#392C2×C5911yescharacteristic, complemented
117#327C2×C5912yescomplemented
118#323C2×C5911yescharacteristic, complemented
119C59#159511yescharacteristic, direct product factor, Sylow
120C22×D4—21no—
121C22×D4—21no—
122C22×D4C22×C5911yescharacteristic, complemented
123C2×D8—22no—
124#123—22no—
125#121—21no—
126#121C22×C5912yes—
127#120—22no—
128C2×C22⋊C4—21no—
129C2×C22⋊C4C22×C5911yescharacteristic
130#102—22no—
131C22⋊C8C22×C5912yescomplemented
132#95C22×C5911yescharacteristic, complemented
133C24—21no—
134C24—21no—
135C24D4×C5911yescharacteristic
136C2×D4—22no—
137C2×D4—22no—
138C2×D4—21no—
139C2×D4—22no—
140C2×D4—42no—
141C2×D4—42no—
142C2×D4—42no—
143C2×D4—42no—
144C2×D4—42no—
145C2×D4—42no—
146C2×D4D4×C5912yescomplemented
147C22×C4—21no—
148C22×C4—21no—
149C22×C4D4×C5911yescharacteristic
150C22×C4C23×C5911yescharacteristic
151D8—44no—
152C2×C8—22no—
153C4⋊C4—21no—
154C4⋊C4D4×C5912yescomplemented
155C22⋊C4—22no—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—42no—
159C23—21no—
160C23—21no—
161C23—22no—
162C23—22no—
163C23—41no—
164C23—41no—
165C23—41no—
166C23—41no—
167C23—41no—
168C23—42no—
169C23—41no—
170C23—41no—
171C23—41no—
172C23—81no—
173C23—81no—
174C23D8×C5912yescomplemented
175C23C2×D4×C5911yescharacteristic
176D4—24no—
177D4—42no—
178D4—42no—
179D4—44no—
180D4—48no—
181D4—42no—
182D4—42no—
183D4—81no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—42no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4C2×D4×C5912yes—
193C8—42no—
194C22—21no—
195C22—21no—
196C22—22no—
197C22—42no—
198C22—42no—
199C22—42no—
200C22—41no—
201C22—41no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—81no—
207C22—81no—
208C22—81no—
209C22—84no—
210C22—81no—
211C22—81no—
212C22#120×C5911yescharacteristic
213C22C2×D8×C5911yescharacteristic
214C22AGL(1,ℤ/8)×C5911yescharacteristic
215C4—22no—
216C4—42no—
217C4—42no—
218C4—41no—
219C2—21no—
220C2—21no—
221C2—42no—
222C2—82no—
223C2—82no—
224C2C59×#44711yescharacteristic
225C2C59×#45311yescharacteristic
226C2C59×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C59#120
commutator, Frattini, cosocleC22×C4C23×C59
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C22×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#534C2semidirect
2. C59×#447C2semidirect
3. C59×#392C2semidirect
4. C59×#327C2semidirect
5. C59×#323C2semidirect
8. C22×D4×C59C22semidirect
17. C22⋊C8×C59C22semidirect
18. #95×C59C22semidirect
32. C2×D4×C59D4semidirect
40. C4⋊C4×C59D4semidirect
60. C23×C59D8semidirect
105. #1595C59direct (N × H)
114. #534C2×C59semidirect
115. #447C2×C59semidirect
116. #392C2×C59semidirect
117. #327C2×C59semidirect
118. #323C2×C59semidirect
119. C59#1595direct (N × H)
122. C22×D4C22×C59semidirect
131. C22⋊C8C22×C59semidirect
132. #95C22×C59semidirect
146. C2×D4D4×C59semidirect
154. C4⋊C4D4×C59semidirect
174. C23D8×C59semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C59×#5342
C59×#4472
C59×#3922
C59×#3272
C59×#3232
#159559