Finite Group Databasebeta

← C59×#1609 #21419927

Subgroups — C59×#1609 #21419927

Order 7552.

216 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 64 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×#539C211yesmaximal, characteristic
2C59×#483C211yesmaximal, characteristic, complemented
3C59×#480C211yesmaximal, characteristic
4C59×#398C211yesmaximal, characteristic, complemented
5C59×#328C211yesmaximal, characteristic, complemented
6C59×#327C211yesmaximal, characteristic
7C59×#324C211yesmaximal, characteristic, complemented
8#126×C59—21no—
9#125×C59—21no—
10#123×C59—21no—
11#123×C59—21no—
12C22⋊Q8×C59—21no—
13C22⋊Q8×C59C2211yescharacteristic
14#121×C59C2211yescharacteristic
15C4×D4×C59—21no—
16C2×C4⋊C4×C59—21no—
17C2×C4⋊C4×C59C2211yescharacteristic
18C2×C4⋊C4×C59C2211yescharacteristic
19#107×C59—21no—
20#106×C59—21no—
21#103×C59—21no—
22#102×C59—21no—
23C22⋊C8×C59C2211yescharacteristic
24C22⋊C8×C59C2211yescharacteristic
25#95×C59—21no—
26#95×C59C2211yescharacteristic
27C2×Q8×C59D411yescharacteristic
28C2×D4×C59—21no—
29C2×D4×C59D411yescharacteristic
30C22×C4×C59—21no—
31C22×C4×C59—21no—
32C22×C4×C59—21no—
33C22×C4×C59D411yescharacteristic
34C22×C4×C59D411yescharacteristic
35C22×C4×C59C2311yescharacteristic
36C2×C8×C59—21no—
37C2×C8×C59—21no—
38C4⋊C4×C59—21no—
39C4⋊C4×C59—21no—
40C4⋊C4×C59—21no—
41C4⋊C4×C59—21no—
42C4⋊C4×C59—21no—
43C4⋊C4×C59—21no—
44C4⋊C4×C59—21no—
45C4⋊C4×C59—21no—
46C4⋊C4×C59—42no—
47C4⋊C4×C59D411yescharacteristic
48C4⋊C4×C59D411yescharacteristic
49C22⋊C4×C59—21no—
50C22⋊C4×C59—21no—
51C22⋊C4×C59—21no—
52C22⋊C4×C59—21no—
53C22⋊C4×C59—21no—
54C42×C59—21no—
55C23×C59—21no—
56C23×C59C2×D411yescharacteristic
57Q8×C59—41no—
58D4×C59—41no—
59D4×C59—41no—
60D4×C59—41no—
61C2×C4×C59—22no—
62C2×C4×C59—21no—
63C2×C4×C59—21no—
64C2×C4×C59—21no—
65C2×C4×C59—21no—
66C2×C4×C59—21no—
67C2×C4×C59—21no—
68C2×C4×C59—21no—
69C2×C4×C59—41no—
70C2×C4×C59—41no—
71C2×C4×C59—41no—
72C2×C4×C59—41no—
73C2×C4×C59—41no—
74C2×C4×C59—41no—
75C2×C4×C59—41no—
76C2×C4×C59—81no—
77C2×C4×C59C2×D411yescharacteristic
78C2×C4×C59C2×D411yescharacteristic
79C8×C59—41no—
80C8×C59—41no—
81C22×C59—21no—
82C22×C59—21no—
83C22×C59—41no—
84C22×C59—41no—
85C22×C59—41no—
86C22×C59#12011yescharacteristic
87C22×C59#13511yescharacteristic
88C22×C59AGL(1,ℤ/8)11yescharacteristic
89C4×C59—21no—
90C4×C59—21no—
91C4×C59—42no—
92C4×C59—41no—
93C4×C59—41no—
94C4×C59—41no—
95C4×C59—41no—
96C4×C59—41no—
97C4×C59—81no—
98#1609C5911yesmaximal, characteristic, direct product factor, Sylow
99C2×C59—21no—
100C2×C59—21no—
101C2×C59—81no—
102C2×C59#44911yescharacteristic
103C2×C59#45611yescharacteristic
104C2×C59#45811yescharacteristic
105#539C2×C5911yescharacteristic
106#483C2×C5911yescharacteristic, complemented
107#480C2×C5911yescharacteristic
108#398C2×C5911yescharacteristic, complemented
109#328C2×C5911yescharacteristic, complemented
110#327C2×C5911yescharacteristic
111#324C2×C5911yescharacteristic, complemented
112C59#160911yescharacteristic, direct product factor, Sylow
113#126—21no—
114#125—21no—
115#123—21no—
116#123—21no—
117C22⋊Q8—21no—
118C22⋊Q8C22×C5911yescharacteristic
119#121C22×C5911yescharacteristic
120C4×D4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4C22×C5911yescharacteristic
123C2×C4⋊C4C22×C5911yescharacteristic
124#107—21no—
125#106—21no—
126#103—21no—
127#102—21no—
128C22⋊C8C22×C5911yescharacteristic
129C22⋊C8C22×C5911yescharacteristic
130#95—21no—
131#95C22×C5911yescharacteristic
132C2×Q8D4×C5911yescharacteristic
133C2×D4—21no—
134C2×D4D4×C5911yescharacteristic
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4D4×C5911yescharacteristic
139C22×C4D4×C5911yescharacteristic
140C22×C4C23×C5911yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—42no—
152C4⋊C4D4×C5911yescharacteristic
153C4⋊C4D4×C5911yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—21no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C42—21no—
160C23—21no—
161C23C2×D4×C5911yescharacteristic
162Q8—41no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—81no—
182C2×C4C2×D4×C5911yescharacteristic
183C2×C4C2×D4×C5911yescharacteristic
184C8—41no—
185C8—41no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#120×C5911yescharacteristic
192C22#135×C5911yescharacteristic
193C22AGL(1,ℤ/8)×C5911yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4—41no—
200C4—41no—
201C4—41no—
202C4—81no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2C59×#44911yescharacteristic
207C2C59×#45611yescharacteristic
208C2C59×#45811yescharacteristic
subgroupG/H
center, socleC22×C59#120
commutator, Frattini, cosocleC22×C4C23×C59
prime radical#121×C59C22
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
2. C59×#483C2semidirect
4. C59×#398C2semidirect
5. C59×#328C2semidirect
7. C59×#324C2semidirect
98. #1609C59direct (N × H)
106. #483C2×C59semidirect
108. #398C2×C59semidirect
109. #328C2×C59semidirect
111. #324C2×C59semidirect
112. C59#1609direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#5392
C59×#4832
C59×#4802
C59×#3982
C59×#3282
C59×#3272
C59×#3242
#160959