Finite Group Databasebeta

← C59×#2092 #21420410

Subgroups — C59×#2092 #21420410

Order 7552.

274 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C2×#107×C59C211yesmaximal, characteristic, complemented
2C2×#106×C59C211yesmaximal, characteristic, complemented
3C2×#102×C59C211yesmaximal, characteristic
4C2×#102×C59C211yesmaximal, characteristic
5C59×#390C211yesmaximal, characteristic
6C59×#382C211yesmaximal, characteristic, complemented
7C59×#336C211yesmaximal, characteristic, complemented
8C22×D4×C59C2211yescharacteristic
9C22×C8×C59C2211yescharacteristic
10C22×C8×C59C2211yescharacteristic
11C2×C4⋊C4×C59C2211yescharacteristic
12C2×C4⋊C4×C59C2211yescharacteristic
13C2×C4⋊C4×C59C2211yescharacteristic
14C2×C22⋊C4×C59—22no—
15C2×C42×C59C2211yescharacteristic
16#107×C59—22no—
17#106×C59—22no—
18#102×C59—22no—
19#102×C59—22no—
20#95×C59—22no—
21C24×C59—21no—
22C2×D4×C59—21no—
23C2×D4×C59—21no—
24C2×D4×C59—21no—
25C2×D4×C59—21no—
26C2×D4×C59—21no—
27C2×D4×C59Q812yes—
28C22×C4×C59—21no—
29C22×C4×C59—21no—
30C22×C4×C59—21no—
31C22×C4×C59D412yes—
32C22×C4×C59C2311yescharacteristic
33C2×C8×C59—21no—
34C2×C8×C59—21no—
35C2×C8×C59—21no—
36C2×C8×C59—21no—
37C2×C8×C59D412yes—
38C2×C8×C59D412yes—
39C4⋊C4×C59—21no—
40C4⋊C4×C59—21no—
41C4⋊C4×C59—21no—
42C4⋊C4×C59—21no—
43C4⋊C4×C59—21no—
44C4⋊C4×C59—21no—
45C22⋊C4×C59—44no—
46C42×C59—21no—
47C42×C59—21no—
48C23×C59—22no—
49C23×C59—41no—
50C23×C59—41no—
51C23×C59—42no—
52C23×C59—42no—
53C23×C59C2×D411yescharacteristic
54D4×C59—22no—
55D4×C59—22no—
56D4×C59—41no—
57D4×C59—41no—
58C2×C4×C59—22no—
59C2×C4×C59—22no—
60C2×C4×C59—22no—
61C2×C4×C59—41no—
62C2×C4×C59—41no—
63C2×C4×C59—41no—
64C2×C4×C59—42no—
65C2×C4×C59—42no—
66C2×C4×C59—42no—
67C2×C4×C59C2×D411yescharacteristic
68C2×C4×C59C2×D411yescharacteristic
69C2×C4×C59C2×Q811yescharacteristic
70C2×C4×C59#4111yescharacteristic
71C2×C4×C59#4111yescharacteristic
72C2×C4×C59#4111yescharacteristic
73C8×C59—22no—
74C8×C59—22no—
75C22×C59—42no—
76C22×C59—44no—
77C22×C59—82no—
78C22×C59—81no—
79C22×C59—81no—
80C22×C59C22⋊Q811yescharacteristic
81C22×C59#12311yescharacteristic
82C22×C59#12711yescharacteristic
83C22×C59#13512yes—
84C22×C59AGL(1,ℤ/8)12yes—
85C4×C59—42no—
86C4×C59—81no—
87C4×C59—81no—
88C4×C59—81no—
89C4×C59C22⋊Q811yescharacteristic
90C4×C59C22⋊Q811yescharacteristic
91C4×C59#12311yescharacteristic
92C4×C59#12311yescharacteristic
93#2092C5911yesmaximal, characteristic, direct product factor, Sylow
94C2×C59—82no—
95C2×C59#39911yescharacteristic
96C2×C59#47812yes—
97C2×C59#48212yes—
98C2×C59#49511yescharacteristic
99C2×C59#49611yescharacteristic
100C2×#107C2×C5911yescharacteristic, complemented
101C2×#106C2×C5911yescharacteristic, complemented
102C2×#102C2×C5911yescharacteristic
103C2×#102C2×C5911yescharacteristic
104#390C2×C5911yescharacteristic
105#382C2×C5911yescharacteristic, complemented
106#336C2×C5911yescharacteristic, complemented
107C59#209211yescharacteristic, direct product factor, Sylow
108C22×D4C22×C5911yescharacteristic
109C22×C8C22×C5911yescharacteristic
110C22×C8C22×C5911yescharacteristic
111C2×C4⋊C4C22×C5911yescharacteristic
112C2×C4⋊C4C22×C5911yescharacteristic
113C2×C4⋊C4C22×C5911yescharacteristic
114C2×C22⋊C4—22no—
115C2×C42C22×C5911yescharacteristic
116#107—22no—
117#106—22no—
118#102—22no—
119#102—22no—
120#95—22no—
121C24—21no—
122C2×D4—21no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4Q8×C5912yes—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4D4×C5912yes—
132C22×C4C23×C5911yescharacteristic
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8D4×C5912yes—
138C2×C8D4×C5912yes—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C22⋊C4—44no—
146C42—21no—
147C42—21no—
148C23—22no—
149C23—41no—
150C23—41no—
151C23—42no—
152C23—42no—
153C23C2×D4×C5911yescharacteristic
154D4—22no—
155D4—22no—
156D4—41no—
157D4—41no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4C2×D4×C5911yescharacteristic
168C2×C4C2×D4×C5911yescharacteristic
169C2×C4C2×Q8×C5911yescharacteristic
170C2×C4#41×C5911yescharacteristic
171C2×C4#41×C5911yescharacteristic
172C2×C4#41×C5911yescharacteristic
173C8—22no—
174C8—22no—
175C22—42no—
176C22—44no—
177C22—82no—
178C22—81no—
179C22—81no—
180C22C22⋊Q8×C5911yescharacteristic
181C22#123×C5911yescharacteristic
182C22#127×C5911yescharacteristic
183C22#135×C5912yes—
184C22AGL(1,ℤ/8)×C5912yes—
185C4—42no—
186C4—81no—
187C4—81no—
188C4—81no—
189C4C22⋊Q8×C5911yescharacteristic
190C4C22⋊Q8×C5911yescharacteristic
191C4#123×C5911yescharacteristic
192C4#123×C5911yescharacteristic
193C2—82no—
194C2C59×#39911yescharacteristic
195C2C59×#47812yes—
196C2C59×#48212yes—
197C2C59×#49511yescharacteristic
198C2C59×#49611yescharacteristic
subgroupG/H
center, socleC23×C59C2×D4
commutator, Frattini, cosocleC22×C4C23×C59
prime radicalC22×D4×C59C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#107×C59C2semidirect
2. C2×#106×C59C2semidirect
6. C59×#382C2semidirect
7. C59×#336C2semidirect
93. #2092C59direct (N × H)
100. C2×#107C2×C59semidirect
101. C2×#106C2×C59semidirect
105. #382C2×C59semidirect
106. #336C2×C59semidirect
107. C59#2092direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#107×C592
C2×#106×C592
C2×#102×C592
C59×#3902
C59×#3822
C59×#3362
#209259