Finite Group Databasebeta

← C59×#1891 #21420209

Subgroups — C59×#1891 #21420209

Order 7552.

342 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 108 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×#568C211yesmaximal, characteristic, complemented
2C59×#525C211yesmaximal, characteristic
3C59×#413C211yesmaximal, characteristic, complemented
4C59×#407C212yesmaximal, complemented
5C59×#344C212yesmaximal, complemented
6C2×#41×C59C2211yescharacteristic
7C23×C4×C59C2211yescharacteristic
8#131×C59—24no—
9C2×M16×C59—22no—
10C2×M16×C59C2212yes—
11C2×M16×C59C2212yes—
12#123×C59C412yes—
13C22⋊Q8×C59—21no—
14#121×C59—21no—
15#120×C59C412yes—
16C4×D4×C59—22no—
17#117×C59C2211yescharacteristic
18#101×C59—21no—
19#100×C59—21no—
20C22⋊C8×C59—24no—
21C24×C59C2×C411yescharacteristic
22#41×C59—22no—
23#41×C59—22no—
24C2×Q8×C59D411yescharacteristic
25C2×D4×C59—22no—
26C2×D4×C59C2×C412yes—
27C2×D4×C59D411yescharacteristic
28C22×C4×C59—22no—
29C22×C4×C59—21no—
30C22×C4×C59—21no—
31C22×C4×C59—22no—
32C22×C4×C59C2×C411yescharacteristic
33C22×C4×C59D412yes—
34C22×C4×C59C2311yescharacteristic
35M16×C59—24no—
36M16×C59—22no—
37M16×C59—22no—
38M16×C59—22no—
39M16×C59—22no—
40C2×C8×C59—24no—
41C2×C8×C59—22no—
42C2×C8×C59D414yescomplemented
43C4⋊C4×C59—22no—
44C4⋊C4×C59—21no—
45C22⋊C4×C59—22no—
46C22⋊C4×C59—22no—
47C22⋊C4×C59C2×C412yes—
48C42×C59—21no—
49C23×C59—21no—
50C23×C59—22no—
51C23×C59—42no—
52C23×C59C22⋊C412yes—
53C23×C59C22×C411yescharacteristic
54Q8×C59—22no—
55D4×C59—24no—
56D4×C59—22no—
57D4×C59—44no—
58C2×C4×C59—22no—
59C2×C4×C59—22no—
60C2×C4×C59—22no—
61C2×C4×C59—21no—
62C2×C4×C59—22no—
63C2×C4×C59—41no—
64C2×C4×C59—42no—
65C2×C4×C59—41no—
66C2×C4×C59C22⋊C412yes—
67C2×C4×C59C2×D412yes—
68C2×C4×C59C2×D411yescharacteristic
69C2×C4×C59C2×D411yescharacteristic
70C2×C4×C59#4112yes—
71C8×C59—24no—
72C8×C59—42no—
73C22×C59—22no—
74C22×C59—24no—
75C22×C59—22no—
76C22×C59—41no—
77C22×C59—42no—
78C22×C59—41no—
79C22×C59—42no—
80C22×C59—41no—
81C22×C59C2×C22⋊C411yescharacteristic
82C22×C59C4×D412yes—
83C4×C59—22no—
84C4×C59—42no—
85C4×C59—41no—
86C4×C59#12011yescharacteristic
87C4×C59#12112yes—
88C4×C59#12311yescharacteristic
89#1891C5911yesmaximal, characteristic, direct product factor, Sylow
90C2×C59—21no—
91C2×C59—22no—
92C2×C59—42no—
93C2×C59—42no—
94C2×C59#38611yescharacteristic
95#568C2×C5911yescharacteristic, complemented
96#525C2×C5911yescharacteristic
97#413C2×C5911yescharacteristic, complemented
98#407C2×C5912yescomplemented
99#344C2×C5912yescomplemented
100C59#189111yescharacteristic, direct product factor, Sylow
101C2×#41C22×C5911yescharacteristic
102C23×C4C22×C5911yescharacteristic
103#131—24no—
104C2×M16—22no—
105C2×M16C22×C5912yes—
106C2×M16C22×C5912yes—
107#123C4×C5912yes—
108C22⋊Q8—21no—
109#121—21no—
110#120C4×C5912yes—
111C4×D4—22no—
112#117C22×C5911yescharacteristic
113#101—21no—
114#100—21no—
115C22⋊C8—24no—
116C24C2×C4×C5911yescharacteristic
117#41—22no—
118#41—22no—
119C2×Q8D4×C5911yescharacteristic
120C2×D4—22no—
121C2×D4C2×C4×C5912yes—
122C2×D4D4×C5911yescharacteristic
123C22×C4—22no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—22no—
127C22×C4C2×C4×C5911yescharacteristic
128C22×C4D4×C5912yes—
129C22×C4C23×C5911yescharacteristic
130M16—24no—
131M16—22no—
132M16—22no—
133M16—22no—
134M16—22no—
135C2×C8—24no—
136C2×C8—22no—
137C2×C8D4×C5914yescomplemented
138C4⋊C4—22no—
139C4⋊C4—21no—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4C2×C4×C5912yes—
143C42—21no—
144C23—21no—
145C23—22no—
146C23—42no—
147C23C22⋊C4×C5912yes—
148C23C22×C4×C5911yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—44no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4C22⋊C4×C5912yes—
162C2×C4C2×D4×C5912yes—
163C2×C4C2×D4×C5911yescharacteristic
164C2×C4C2×D4×C5911yescharacteristic
165C2×C4#41×C5912yes—
166C8—24no—
167C8—42no—
168C22—22no—
169C22—24no—
170C22—22no—
171C22—41no—
172C22—42no—
173C22—41no—
174C22—42no—
175C22—41no—
176C22C2×C22⋊C4×C5911yescharacteristic
177C22C4×D4×C5912yes—
178C4—22no—
179C4—42no—
180C4—41no—
181C4#120×C5911yescharacteristic
182C4#121×C5912yes—
183C4#123×C5911yescharacteristic
184C2—21no—
185C2—22no—
186C2—42no—
187C2—42no—
188C2C59×#38611yescharacteristic
subgroupG/H
centerC4×C59#120
commutatorC23C22×C4×C59
Frattini, cosocleC22×C4C23×C59
socleC2×C59#386
prime radicalC59×#525C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C4×C59 ◁ C22×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#568C2semidirect
3. C59×#413C2semidirect
4. C59×#407C2semidirect
5. C59×#344C2semidirect
42. C2×C8×C59D4semidirect
89. #1891C59direct (N × H)
95. #568C2×C59semidirect
97. #413C2×C59semidirect
98. #407C2×C59semidirect
99. #344C2×C59semidirect
100. C59#1891direct (N × H)
137. C2×C8D4×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#5682
C59×#5252
C59×#4132
C59×#4072
C59×#3442
#189159