Finite Group Databasebeta

← C61×#11515 #29514948

Subgroups — C61×#11515 #29514948

Order 15616.

418 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2317C211yesmaximal, characteristic
2C61×#1464C212yesmaximal
3C61×#1324C214yesmaximal, complemented
4C2×#117×C61C411yescharacteristic
5C2×#117×C61C2211yescharacteristic
6C22×C4⋊C4×C61C411yescharacteristic
7C61×#432—22no—
8C61×#389—22no—
9C61×#385—22no—
10C61×#384C412yes—
11C61×#382C2212yes—
12C61×#324C2214yes—
13C61×#323—22no—
14C23×C4×C61—21no—
15C23×C4×C61C2×C411yescharacteristic
16#117×C61—24no—
17#117×C61—42no—
18C2×C4⋊C4×C61—21no—
19C2×C4⋊C4×C61—21no—
20C2×C4⋊C4×C61—24no—
21C2×C4⋊C4×C61—42no—
22C2×C4⋊C4×C61C2×C412yes—
23C2×C4⋊C4×C61C2×C411yescharacteristic
24C2×C4⋊C4×C61C2311yescharacteristic
25C2×C22⋊C4×C61—21no—
26C2×C22⋊C4×C61D412yes—
27C2×C42×C61C2×C412yes—
28C2×C42×C61D412yes—
29C4⋊C8×C61—42no—
30C22⋊C8×C61—24no—
31#97×C61—42no—
32#95×C61—24no—
33C24×C61C22⋊C411yescharacteristic
34C22×C4×C61—22no—
35C22×C4×C61—22no—
36C22×C4×C61—22no—
37C22×C4×C61—22no—
38C22×C4×C61—22no—
39C22×C4×C61—42no—
40C22×C4×C61—82no—
41C22×C4×C61C22⋊C412yes—
42C22×C4×C61C22⋊C411yescharacteristic
43C22×C4×C61C22×C411yescharacteristic
44C22×C4×C61C2×D412yes—
45C2×C8×C61—44no—
46C4⋊C4×C61—24no—
47C4⋊C4×C61—41no—
48C4⋊C4×C61—41no—
49C4⋊C4×C61—42no—
50C4⋊C4×C61—42no—
51C4⋊C4×C61—84no—
52C22⋊C4×C61—24no—
53C22⋊C4×C61—42no—
54C42×C61—22no—
55C42×C61—22no—
56C42×C61—22no—
57C42×C61M1614yes—
58C23×C61—21no—
59C23×C61—21no—
60C23×C61—41no—
61C23×C61—41no—
62C23×C61#10112yes—
63C23×C61C2×C22⋊C411yescharacteristic
64C2×C4×C61—28no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—24no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—42no—
73C2×C4×C61—42no—
74C2×C4×C61—42no—
75C2×C4×C61—42no—
76C2×C4×C61—44no—
77C2×C4×C61—42no—
78C2×C4×C61—84no—
79C2×C4×C61#9912yes—
80C2×C4×C61C2×M1612yes—
81C8×C61—84no—
82#11515C6111yesmaximal, characteristic, direct product factor, Sylow
83C22×C61—21no—
84C22×C61—21no—
85C22×C61—22no—
86C22×C61—42no—
87C22×C61—42no—
88C22×C61—41no—
89C22×C61—41no—
90C22×C61#40711yescharacteristic
91C22×C61C2×#9911yescharacteristic
92C22×C61C2×#10111yescharacteristic
93C4×C61—22no—
94C4×C61—22no—
95C4×C61—44no—
96C4×C61—42no—
97C4×C61—42no—
98C4×C61—82no—
99#2317C2×C6111yescharacteristic
100#1464C2×C6112yes—
101#1324C2×C6114yescomplemented
102C2×C61—21no—
103C2×C61—21no—
104C2×C61—42no—
105C2×C61#146311yescharacteristic
106C2×C61#212911yescharacteristic
107C2×C61#213411yescharacteristic
108C2×#117C4×C6111yescharacteristic
109C2×#117C22×C6111yescharacteristic
110C22×C4⋊C4C4×C6111yescharacteristic
111#432—22no—
112#389—22no—
113#385—22no—
114#384C4×C6112yes—
115#382C22×C6112yes—
116#324C22×C6114yes—
117#323—22no—
118C61#1151511yescharacteristic, direct product factor, Sylow
119C23×C4—21no—
120C23×C4C2×C4×C6111yescharacteristic
121#117—24no—
122#117—42no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—24no—
126C2×C4⋊C4—42no—
127C2×C4⋊C4C2×C4×C6112yes—
128C2×C4⋊C4C2×C4×C6111yescharacteristic
129C2×C4⋊C4C23×C6111yescharacteristic
130C2×C22⋊C4—21no—
131C2×C22⋊C4D4×C6112yes—
132C2×C42C2×C4×C6112yes—
133C2×C42D4×C6112yes—
134C4⋊C8—42no—
135C22⋊C8—24no—
136#97—42no—
137#95—24no—
138C24C22⋊C4×C6111yescharacteristic
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—42no—
145C22×C4—82no—
146C22×C4C22⋊C4×C6111yescharacteristic
147C22×C4C22⋊C4×C6112yes—
148C22×C4C22×C4×C6111yescharacteristic
149C22×C4C2×D4×C6112yes—
150C2×C8—44no—
151C4⋊C4—24no—
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C4⋊C4—84no—
157C22⋊C4—24no—
158C22⋊C4—42no—
159C42—22no—
160C42—22no—
161C42—22no—
162C42M16×C6114yes—
163C23—21no—
164C23—21no—
165C23—41no—
166C23—41no—
167C23#101×C6112yes—
168C23C2×C22⋊C4×C6111yescharacteristic
169C2×C4—28no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—44no—
182C2×C4—42no—
183C2×C4—84no—
184C2×C4#99×C6112yes—
185C2×C4C2×M16×C6112yes—
186C8—84no—
187C22—21no—
188C22—21no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22C61×#40711yescharacteristic
195C22C2×#99×C6111yescharacteristic
196C22C2×#101×C6111yescharacteristic
197C4—22no—
198C4—22no—
199C4—44no—
200C4—42no—
201C4—42no—
202C4—82no—
203C2—21no—
204C2—21no—
205C2—42no—
206C2C61×#146311yescharacteristic
207C2C61×#212911yescharacteristic
208C2C61×#213411yescharacteristic
subgroupG/H
center, socleC22×C61C2×#99
commutatorC22×C4C22×C4×C61
Frattini, cosocleC2×C4⋊C4C23×C61
prime radicalC24×C61C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C2×#117×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C61×#1324C2semidirect
82. #11515C61direct (N × H)
101. #1324C2×C61semidirect
118. C61#11515direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#23172
C61×#14642
C61×#13242
#1151561