Finite Group Databasebeta

← C61×#7319 #29510752

Subgroups — C61×#7319 #29510752

Order 15616.

456 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C61×#1785C212yesmaximal
2C61×#1782C211yesmaximal, characteristic
3C22×#41×C61C2211yescharacteristic
4C2×#101×C61—22no—
5C2×#100×C61—22no—
6C2×#99×C61—22no—
7C61×#407C414yescomplemented
8C61×#381C412yes—
9C2×#41×C61—42no—
10C2×#41×C61—44no—
11C22×Q8×C61D411yescharacteristic
12C22×D4×C61D412yes—
13C22×D4×C61Q811yescharacteristic
14C23×C4×C61C2×C412yes—
15C23×C4×C61C2×C411yescharacteristic
16C2×M16×C61—24no—
17C2×C22⋊C4×C61—22no—
18#101×C61—44no—
19#100×C61—44no—
20#99×C61—44no—
21C22⋊C8×C61—44no—
22#95×C61—42no—
23C24×C61C22⋊C411yescharacteristic
24C24×C61C4⋊C412yes—
25#41×C61—416no—
26C2×Q8×C61—24no—
27C2×Q8×C61—41no—
28C2×D4×C61—24no—
29C2×D4×C61—24no—
30C2×D4×C61—42no—
31C2×D4×C61—41no—
32C2×D4×C61—42no—
33C22×C4×C61—22no—
34C22×C4×C61—24no—
35C22×C4×C61—42no—
36C22×C4×C61—42no—
37C22×C4×C61—42no—
38C22×C4×C61—42no—
39C22×C4×C61C4211yescharacteristic
40C22×C4×C61C22⋊C412yes—
41C22×C4×C61C4⋊C411yescharacteristic
42M16×C61—44no—
43M16×C61—44no—
44C2×C8×C61—44no—
45C22⋊C4×C61—44no—
46C23×C61—22no—
47C23×C61—22no—
48C23×C61—22no—
49C23×C61—22no—
50C23×C61—81no—
51C23×C61—82no—
52C23×C61#9511yescharacteristic
53C23×C61#9912yes—
54Q8×C61—44no—
55D4×C61—48no—
56D4×C61—44no—
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61—21no—
60C2×C4×C61—22no—
61C2×C4×C61—21no—
62C2×C4×C61—22no—
63C2×C4×C61—48no—
64C2×C4×C61—44no—
65C2×C4×C61—82no—
66C2×C4×C61—84no—
67C2×C4×C61#9914yes—
68C8×C61—84no—
69#7319C6111yesmaximal, characteristic, direct product factor, Sylow
70C22×C61—22no—
71C22×C61—41no—
72C22×C61—42no—
73C22×C61—44no—
74C22×C61—42no—
75C22×C61—82no—
76C22×C61—82no—
77C22×C61—82no—
78C22×C61#34211yescharacteristic
79C22×C61#34212yes—
80C4×C61—24no—
81C4×C61—41no—
82C4×C61—41no—
83C4×C61—162no—
84#1785C2×C6112yes—
85#1782C2×C6111yescharacteristic
86C2×C61—21no—
87C2×C61—22no—
88C2×C61—42no—
89C2×C61—82no—
90C2×C61#130411yescharacteristic
91C22×#41C22×C6111yescharacteristic
92C2×#101—22no—
93C2×#100—22no—
94C2×#99—22no—
95#407C4×C6114yescomplemented
96#381C4×C6112yes—
97C61#731911yescharacteristic, direct product factor, Sylow
98C2×#41—42no—
99C2×#41—44no—
100C22×Q8D4×C6111yescharacteristic
101C22×D4D4×C6112yes—
102C22×D4Q8×C6111yescharacteristic
103C23×C4C2×C4×C6112yes—
104C23×C4C2×C4×C6111yescharacteristic
105C2×M16—24no—
106C2×C22⋊C4—22no—
107#101—44no—
108#100—44no—
109#99—44no—
110C22⋊C8—44no—
111#95—42no—
112C24C22⋊C4×C6111yescharacteristic
113C24C4⋊C4×C6112yes—
114#41—416no—
115C2×Q8—24no—
116C2×Q8—41no—
117C2×D4—24no—
118C2×D4—24no—
119C2×D4—42no—
120C2×D4—41no—
121C2×D4—42no—
122C22×C4—22no—
123C22×C4—24no—
124C22×C4—42no—
125C22×C4—42no—
126C22×C4—42no—
127C22×C4—42no—
128C22×C4C42×C6111yescharacteristic
129C22×C4C22⋊C4×C6112yes—
130C22×C4C4⋊C4×C6111yescharacteristic
131M16—44no—
132M16—44no—
133C2×C8—44no—
134C22⋊C4—44no—
135C23—22no—
136C23—22no—
137C23—22no—
138C23—22no—
139C23—81no—
140C23—82no—
141C23#95×C6111yescharacteristic
142C23#99×C6112yes—
143Q8—44no—
144D4—48no—
145D4—44no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—22no—
152C2×C4—48no—
153C2×C4—44no—
154C2×C4—82no—
155C2×C4—84no—
156C2×C4#99×C6114yes—
157C8—84no—
158C22—22no—
159C22—41no—
160C22—42no—
161C22—44no—
162C22—42no—
163C22—82no—
164C22—82no—
165C22—82no—
166C22C61×#34211yescharacteristic
167C22C61×#34212yes—
168C4—24no—
169C4—41no—
170C4—41no—
171C4—162no—
172C2—21no—
173C2—22no—
174C2—42no—
175C2—82no—
176C2C61×#130411yescharacteristic
subgroupG/H
center, socleC2×C61#1304
commutatorC22×C4C42×C61
Frattini, cosocleC22×#41C22×C61
prime radicalC22×#41×C61C22
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C61 ◁ C23×C61 ◁ C22×#41×C61 ◁ G

Complements

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

NH ≅ G/Ntype
7. C61×#407C4semidirect
69. #7319C61direct (N × H)
95. #407C4×C61semidirect
97. C61#7319direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#17852
C61×#17822
#731961