Finite Group Databasebeta

← C61×#8733 #29512166

Subgroups — C61×#8733 #29512166

Order 15616.

404 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2298C211yesmaximal, characteristic
2C61×#1458C212yesmaximal
3C61×#1276C212yesmaximal, complemented
4C61×#1274C212yesmaximal, complemented
5C2×#117×C61C2211yescharacteristic
6C61×#431C2214yes—
7C61×#388—22no—
8C61×#387—22no—
9C4×C4⋊C4×C61C412yes—
10C4×C22⋊C4×C61C412yes—
11C61×#376C2211yescharacteristic
12C43×C61C2211yescharacteristic
13C61×#324—22no—
14C61×#323—22no—
15C23×C4×C61C2×C411yescharacteristic
16#117×C61—22no—
17#117×C61—22no—
18C2×C4⋊C4×C61—22no—
19C2×C4⋊C4×C61D412yes—
20C2×C22⋊C4×C61—22no—
21C2×C22⋊C4×C61D412yes—
22C2×C42×C61—22no—
23C2×C42×C61C2×C412yes—
24C2×C42×C61C2×C412yes—
25C2×C42×C61C2×C411yescharacteristic
26C2×C42×C61C2311yescharacteristic
27C4⋊C8×C61—24no—
28C22⋊C8×C61—24no—
29C4×C8×C61—24no—
30#95×C61—22no—
31#95×C61—22no—
32#95×C61—22no—
33C24×C61C22⋊C411yescharacteristic
34C22×C4×C61—22no—
35C22×C4×C61—21no—
36C22×C4×C61—21no—
37C22×C4×C61—24no—
38C22×C4×C61—22no—
39C22×C4×C61C22⋊C411yescharacteristic
40C22×C4×C61C22⋊C412yes—
41C22×C4×C61C22×C411yescharacteristic
42C22×C4×C61C2×D412yes—
43C2×C8×C61—44no—
44C4⋊C4×C61—24no—
45C4⋊C4×C61—44no—
46C22⋊C4×C61—24no—
47C22⋊C4×C61—44no—
48C42×C61—21no—
49C42×C61—21no—
50C42×C61—24no—
51C42×C61—24no—
52C42×C61—44no—
53C42×C61#4112yes—
54C42×C61#4112yes—
55C23×C61—21no—
56C23×C61—22no—
57C23×C61—42no—
58C23×C61C2×C22⋊C411yescharacteristic
59C2×C4×C61—24no—
60C2×C4×C61—22no—
61C2×C4×C61—21no—
62C2×C4×C61—22no—
63C2×C4×C61—42no—
64C2×C4×C61—42no—
65C2×C4×C61—42no—
66C2×C4×C61—42no—
67C2×C4×C61—42no—
68C2×C4×C61—42no—
69C2×C4×C61—42no—
70C2×C4×C61—42no—
71C2×C4×C61—42no—
72C2×C4×C61#11711yescharacteristic
73C2×C4×C61#11711yescharacteristic
74C2×C4×C61#12314yes—
75C2×C4×C61#13114yes—
76C8×C61—84no—
77#8733C6111yesmaximal, characteristic, direct product factor, Sylow
78C22×C61—22no—
79C22×C61—41no—
80C22×C61—42no—
81C22×C61—82no—
82C22×C61#38111yescharacteristic
83C22×C61#40812yes—
84C4×C61—24no—
85C4×C61—44no—
86C4×C61—41no—
87C4×C61—42no—
88C4×C61—82no—
89C4×C61#43312yes—
90C4×C61#43312yes—
91#2298C2×C6111yescharacteristic
92#1458C2×C6112yes—
93#1276C2×C6112yescomplemented
94#1274C2×C6112yescomplemented
95C2×C61—22no—
96C2×C61—81no—
97C2×C61#181811yescharacteristic
98C2×C61#182712yes—
99C2×#117C22×C6111yescharacteristic
100#431C22×C6114yes—
101#388—22no—
102#387—22no—
103C4×C4⋊C4C4×C6112yes—
104C4×C22⋊C4C4×C6112yes—
105#376C22×C6111yescharacteristic
106C43C22×C6111yescharacteristic
107#324—22no—
108#323—22no—
109C61#873311yescharacteristic, direct product factor, Sylow
110C23×C4C2×C4×C6111yescharacteristic
111#117—22no—
112#117—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4D4×C6112yes—
115C2×C22⋊C4—22no—
116C2×C22⋊C4D4×C6112yes—
117C2×C42—22no—
118C2×C42C2×C4×C6112yes—
119C2×C42C2×C4×C6112yes—
120C2×C42C2×C4×C6111yescharacteristic
121C2×C42C23×C6111yescharacteristic
122C4⋊C8—24no—
123C22⋊C8—24no—
124C4×C8—24no—
125#95—22no—
126#95—22no—
127#95—22no—
128C24C22⋊C4×C6111yescharacteristic
129C22×C4—22no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—24no—
133C22×C4—22no—
134C22×C4C22⋊C4×C6111yescharacteristic
135C22×C4C22⋊C4×C6112yes—
136C22×C4C22×C4×C6111yescharacteristic
137C22×C4C2×D4×C6112yes—
138C2×C8—44no—
139C4⋊C4—24no—
140C4⋊C4—44no—
141C22⋊C4—24no—
142C22⋊C4—44no—
143C42—21no—
144C42—21no—
145C42—24no—
146C42—24no—
147C42—44no—
148C42#41×C6112yes—
149C42#41×C6112yes—
150C23—21no—
151C23—22no—
152C23—42no—
153C23C2×C22⋊C4×C6111yescharacteristic
154C2×C4—24no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4#117×C6111yescharacteristic
168C2×C4#117×C6111yescharacteristic
169C2×C4#123×C6114yes—
170C2×C4#131×C6114yes—
171C8—84no—
172C22—22no—
173C22—41no—
174C22—42no—
175C22—82no—
176C22C61×#38111yescharacteristic
177C22C61×#40812yes—
178C4—24no—
179C4—44no—
180C4—41no—
181C4—42no—
182C4—82no—
183C4C61×#43312yes—
184C4C61×#43312yes—
185C2—22no—
186C2—81no—
187C2C61×#181811yescharacteristic
188C2C61×#182712yes—
subgroupG/H
centerC2×C4×C61#117
commutatorC22×C4C22×C4×C61
Frattini, cosocleC2×C42C23×C61
socleC22×C61#381
prime radicalC24×C61C22⋊C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C61×#376 ◁ G

Complements

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

NH ≅ G/Ntype
3. C61×#1276C2semidirect
4. C61×#1274C2semidirect
77. #8733C61direct (N × H)
93. #1276C2×C61semidirect
94. #1274C2×C61semidirect
109. C61#8733direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#22982
C61×#14582
C61×#12762
C61×#12742
#873361