Finite Group Databasebeta

← C59×#1511 #21419829

Subgroups — C59×#1511 #21419829

Order 7552.

274 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 92 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×C22⋊Q8×C59C211yesmaximal, characteristic
2C59×#407C211yesmaximal, characteristic
3C59×#381C211yesmaximal, characteristic
4C59×#328C214yesmaximal, complemented
5C22×Q8×C59C411yescharacteristic, complemented
6C23×C4×C59C2211yescharacteristic
7C2×M16×C59—21no—
8C22⋊Q8×C59—21no—
9C22⋊Q8×C59—21no—
10C22⋊Q8×C59C412yescomplemented
11C22⋊Q8×C59C2212yes—
12C2×C4⋊C4×C59—21no—
13C2×C4⋊C4×C59C411yescharacteristic, complemented
14C2×C22⋊C4×C59—21no—
15C2×C22⋊C4×C59—21no—
16C22⋊C8×C59—21no—
17C22⋊C8×C59C2212yes—
18#95×C59—21no—
19#95×C59C2212yes—
20C24×C59D411yescharacteristic
21C2×Q8×C59—21no—
22C2×Q8×C59—42no—
23C2×Q8×C59C2×C412yes—
24C22×C4×C59—21no—
25C22×C4×C59—21no—
26C22×C4×C59—22no—
27C22×C4×C59—42no—
28C22×C4×C59C2×C411yescharacteristic
29C22×C4×C59C2×C411yescharacteristic
30C22×C4×C59D411yescharacteristic
31C22×C4×C59D411yescharacteristic
32C22×C4×C59D411yescharacteristic
33C22×C4×C59C2311yescharacteristic
34M16×C59—42no—
35C2×C8×C59—22no—
36C4⋊C4×C59—22no—
37C4⋊C4×C59—21no—
38C4⋊C4×C59—22no—
39C4⋊C4×C59C2×C412yes—
40C22⋊C4×C59—22no—
41C22⋊C4×C59—22no—
42C22⋊C4×C59—42no—
43C23×C59—22no—
44C23×C59—22no—
45C23×C59—41no—
46C23×C59C22⋊C411yescharacteristic
47C23×C59C22⋊C411yescharacteristic
48C23×C59C2×D411yescharacteristic
49Q8×C59—42no—
50Q8×C59—42no—
51C2×C4×C59—22no—
52C2×C4×C59—22no—
53C2×C4×C59—22no—
54C2×C4×C59—22no—
55C2×C4×C59—41no—
56C2×C4×C59—41no—
57C2×C4×C59—41no—
58C2×C4×C59—41no—
59C2×C4×C59—42no—
60C2×C4×C59—42no—
61C2×C4×C59—42no—
62C2×C4×C59—42no—
63C2×C4×C59—42no—
64C2×C4×C59C22⋊C411yescharacteristic
65C2×C4×C59C22⋊C411yescharacteristic
66C2×C4×C59C22×C411yescharacteristic
67C2×C4×C59C2×D411yescharacteristic
68C8×C59—42no—
69C22×C59—21no—
70C22×C59—21no—
71C22×C59—21no—
72C22×C59—21no—
73C22×C59—21no—
74C22×C59—21no—
75C22×C59—21no—
76C22×C59—44no—
77C22×C59#9912yes—
78C22×C59C2×C22⋊C411yescharacteristic
79C22×C59#13712yes—
80C4×C59—21no—
81C4×C59—21no—
82C4×C59—21no—
83C4×C59—21no—
84C4×C59—42no—
85C4×C59—42no—
86C4×C59—82no—
87#1511C5911yesmaximal, characteristic, direct product factor, Sylow
88C2×C59—22no—
89C2×C59—22no—
90C2×C59—41no—
91C2×C59C2×#9911yescharacteristic
92C2×C59#41911yescharacteristic
93C2×C59#42111yescharacteristic
94C2×C22⋊Q8C2×C5911yescharacteristic
95#407C2×C5911yescharacteristic
96#381C2×C5911yescharacteristic
97#328C2×C5914yescomplemented
98C59#151111yescharacteristic, direct product factor, Sylow
99C22×Q8C4×C5911yescharacteristic, complemented
100C23×C4C22×C5911yescharacteristic
101C2×M16—21no—
102C22⋊Q8—21no—
103C22⋊Q8—21no—
104C22⋊Q8C4×C5912yescomplemented
105C22⋊Q8C22×C5912yes—
106C2×C4⋊C4—21no—
107C2×C4⋊C4C4×C5911yescharacteristic, complemented
108C2×C22⋊C4—21no—
109C2×C22⋊C4—21no—
110C22⋊C8—21no—
111C22⋊C8C22×C5912yes—
112#95—21no—
113#95C22×C5912yes—
114C24D4×C5911yescharacteristic
115C2×Q8—21no—
116C2×Q8—42no—
117C2×Q8C2×C4×C5912yes—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—22no—
121C22×C4—42no—
122C22×C4C2×C4×C5911yescharacteristic
123C22×C4C2×C4×C5911yescharacteristic
124C22×C4D4×C5911yescharacteristic
125C22×C4D4×C5911yescharacteristic
126C22×C4D4×C5911yescharacteristic
127C22×C4C23×C5911yescharacteristic
128M16—42no—
129C2×C8—22no—
130C4⋊C4—22no—
131C4⋊C4—21no—
132C4⋊C4—22no—
133C4⋊C4C2×C4×C5912yes—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—42no—
137C23—22no—
138C23—22no—
139C23—41no—
140C23C22⋊C4×C5911yescharacteristic
141C23C22⋊C4×C5911yescharacteristic
142C23C2×D4×C5911yescharacteristic
143Q8—42no—
144Q8—42no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4C22⋊C4×C5911yescharacteristic
159C2×C4C22⋊C4×C5911yescharacteristic
160C2×C4C22×C4×C5911yescharacteristic
161C2×C4C2×D4×C5911yescharacteristic
162C8—42no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—44no—
171C22#99×C5912yes—
172C22C2×C22⋊C4×C5911yescharacteristic
173C22#137×C5912yes—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—42no—
179C4—42no—
180C4—82no—
181C2—22no—
182C2—22no—
183C2—41no—
184C2C2×#99×C5911yescharacteristic
185C2C59×#41911yescharacteristic
186C2C59×#42111yescharacteristic
subgroupG/H
center, socleC22×C59C2×C22⋊C4
commutatorC2×C4C22×C4×C59
Frattini, cosocleC22×C4C23×C59
prime radicalC24×C59D4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
4. C59×#328C2semidirect
5. C22×Q8×C59C4semidirect
10. C22⋊Q8×C59C4semidirect
13. C2×C4⋊C4×C59C4semidirect
87. #1511C59direct (N × H)
97. #328C2×C59semidirect
98. C59#1511direct (N × H)
99. C22×Q8C4×C59semidirect
104. C22⋊Q8C4×C59semidirect
107. C2×C4⋊C4C4×C59semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×C592
C59×#4072
C59×#3812
C59×#3282
#151159