Finite Group Databasebeta

← C61×#10428 #29513861

Subgroups — C61×#10428 #29513861

Order 15616.

386 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2822C211yesmaximal, characteristic
2C61×#1992C212yesmaximal
3C61×#1836C211yesmaximal, characteristic
4C2×C61×#330C212yesmaximal
5C61×#1295C211yesmaximal, characteristic
6C2×#125×C61C2212yes—
7C2×#97×C61C2212yes—
8C2×#97×C61C2211yescharacteristic
9C61×#400—22no—
10C61×#398—22no—
11C61×#398—22no—
12C61×#384C2211yescharacteristic
13C61×#382C2211yescharacteristic
14C61×#340—22no—
15C61×#340—22no—
16C61×#340—22no—
17C61×#330—24no—
18C22×C8×C61—22no—
19C22×C8×C61—21no—
20#125×C61—22no—
21#125×C61—22no—
22#125×C61—22no—
23#125×C61—22no—
24C2×C4⋊C4×C61—22no—
25C2×C4⋊C4×C61—22no—
26C2×C4⋊C4×C61—22no—
27C2×C4⋊C4×C61—21no—
28C2×C4⋊C4×C61—22no—
29C2×C4⋊C4×C61D412yes—
30C2×C4⋊C4×C61D412yes—
31C2×C4⋊C4×C61D412yes—
32C2×C42×C61C2311yescharacteristic
33#97×C61—22no—
34#97×C61—21no—
35#97×C61—22no—
36#97×C61D412yes—
37#95×C61—24no—
38#95×C61—22no—
39#95×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61—22no—
42C22×C4×C61—22no—
43C22×C4×C61—41no—
44C22×C4×C61C2×D412yes—
45C22×C4×C61C2×D411yescharacteristic
46C2×C8×C61—24no—
47C2×C8×C61—22no—
48C2×C8×C61—42no—
49C2×C8×C61—41no—
50C2×C8×C61—41no—
51C2×C8×C61—42no—
52C4⋊C4×C61—22no—
53C4⋊C4×C61—22no—
54C4⋊C4×C61—22no—
55C4⋊C4×C61—22no—
56C4⋊C4×C61—42no—
57C4⋊C4×C61—44no—
58C4⋊C4×C61—42no—
59C4⋊C4×C61—42no—
60C4⋊C4×C61—42no—
61C4⋊C4×C61—42no—
62C4⋊C4×C61—42no—
63C4⋊C4×C61—82no—
64C42×C61C2×D411yescharacteristic
65C42×C61#4111yescharacteristic
66C42×C61#4112yes—
67C23×C61#12011yescharacteristic
68C2×C4×C61—22no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—22no—
72C2×C4×C61—42no—
73C2×C4×C61—42no—
74C2×C4×C61—42no—
75C2×C4×C61—42no—
76C2×C4×C61—42no—
77C2×C4×C61—42no—
78C2×C4×C61—42no—
79C2×C4×C61—42no—
80C2×C4×C61—42no—
81C2×C4×C61—81no—
82C2×C4×C61—82no—
83C2×C4×C61#12112yes—
84C2×C4×C61#12111yescharacteristic
85C2×C4×C61#12312yes—
86C2×C4×C61#12411yescharacteristic
87C8×C61—44no—
88C8×C61—42no—
89#10428C6111yesmaximal, characteristic, direct product factor, Sylow
90C22×C61#39411yescharacteristic
91C22×C61#45411yescharacteristic
92C22×C61#45412yes—
93C22×C61#45511yescharacteristic
94C22×C61#45612yes—
95C4×C61—22no—
96C4×C61—22no—
97C4×C61—21no—
98C4×C61—21no—
99C4×C61—82no—
100C4×C61—82no—
101C4×C61—82no—
102C4×C61—161no—
103#2822C2×C6111yescharacteristic
104#1992C2×C6112yes—
105#1836C2×C6111yescharacteristic
106C2×#330C2×C6112yes—
107#1295C2×C6111yescharacteristic
108C2×C61#165811yescharacteristic
109C2×C61#166311yescharacteristic
110C2×C61#166412yes—
111C2×C61#203812yes—
112C2×C61#204011yescharacteristic
113C2×#125C22×C6112yes—
114C2×#97C22×C6112yes—
115C2×#97C22×C6111yescharacteristic
116#400—22no—
117#398—22no—
118#398—22no—
119#384C22×C6111yescharacteristic
120#382C22×C6111yescharacteristic
121#340—22no—
122#340—22no—
123#340—22no—
124#330—24no—
125C61#1042811yescharacteristic, direct product factor, Sylow
126C22×C8—22no—
127C22×C8—21no—
128#125—22no—
129#125—22no—
130#125—22no—
131#125—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4D4×C6112yes—
138C2×C4⋊C4D4×C6112yes—
139C2×C4⋊C4D4×C6112yes—
140C2×C42C23×C6111yescharacteristic
141#97—22no—
142#97—21no—
143#97—22no—
144#97D4×C6112yes—
145#95—24no—
146#95—22no—
147#95—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—41no—
152C22×C4C2×D4×C6112yes—
153C22×C4C2×D4×C6111yescharacteristic
154C2×C8—24no—
155C2×C8—22no—
156C2×C8—42no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—42no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—42no—
165C4⋊C4—44no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—42no—
170C4⋊C4—42no—
171C4⋊C4—82no—
172C42C2×D4×C6111yescharacteristic
173C42#41×C6111yescharacteristic
174C42#41×C6112yes—
175C23#120×C6111yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—82no—
190C2×C4—81no—
191C2×C4#121×C6112yes—
192C2×C4#121×C6111yescharacteristic
193C2×C4#123×C6112yes—
194C2×C4#124×C6111yescharacteristic
195C8—44no—
196C8—42no—
197C22C61×#39411yescharacteristic
198C22C61×#45412yes—
199C22C61×#45411yescharacteristic
200C22C61×#45511yescharacteristic
201C22C61×#45612yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—82no—
208C4—82no—
209C4—161no—
210C2C61×#165811yescharacteristic
211C2C61×#166311yescharacteristic
212C2C61×#166412yes—
213C2C61×#203812yes—
214C2C61×#204011yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C61#120
commutator, Frattini, cosocleC2×C42C23×C61
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
89. #10428C61direct (N × H)
125. C61#10428direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#28222
C61×#19922
C61×#18362
C2×C61×#3302
C61×#12952
#1042861