Finite Group Databasebeta

← C61×#10389 #29513822

Subgroups — C61×#10389 #29513822

Order 15616.

406 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2608C211yesmaximal, characteristic
2C61×#1826C212yesmaximal
3C61×#1820C211yesmaximal, characteristic
4C61×#1306C211yesmaximal, characteristic
5C61×#1284C212yesmaximal
6C2×#117×C61C2211yescharacteristic
7C61×#407C2212yes—
8C61×#396—22no—
9C61×#389—22no—
10C61×#387—22no—
11C61×#381C2211yescharacteristic
12C61×#381C2211yescharacteristic
13C4×C22⋊C4×C61C2212yes—
14C61×#342—22no—
15C61×#339—22no—
16C61×#339—22no—
17C23×C4×C61C2311yescharacteristic
18C2×M16×C61—22no—
19#117×C61—22no—
20#117×C61—22no—
21C2×C4⋊C4×C61—22no—
22C2×C4⋊C4×C61—22no—
23C2×C4⋊C4×C61—22no—
24C2×C4⋊C4×C61Q812yes—
25C2×C22⋊C4×C61—21no—
26C2×C22⋊C4×C61—22no—
27C2×C22⋊C4×C61—21no—
28C2×C22⋊C4×C61D412yes—
29C2×C42×C61—21no—
30C2×C42×C61D412yes—
31C2×C42×C61D412yes—
32C22⋊C8×C61—22no—
33C22⋊C8×C61—22no—
34#95×C61—22no—
35#95×C61—22no—
36#95×C61—22no—
37#95×C61—22no—
38C24×C61C2×D411yescharacteristic
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61—22no—
42C22×C4×C61—22no—
43C22×C4×C61—42no—
44C22×C4×C61—41no—
45C22×C4×C61C2×D412yes—
46C22×C4×C61C2×Q811yescharacteristic
47C22×C4×C61#4112yes—
48C22×C4×C61#4111yescharacteristic
49M16×C61—42no—
50M16×C61—42no—
51C2×C8×C61—42no—
52C4⋊C4×C61—24no—
53C4⋊C4×C61—44no—
54C4⋊C4×C61—44no—
55C4⋊C4×C61—82no—
56C22⋊C4×C61—44no—
57C22⋊C4×C61—41no—
58C22⋊C4×C61—41no—
59C22⋊C4×C61—42no—
60C22⋊C4×C61—42no—
61C42×C61—42no—
62C42×C61—42no—
63C42×C61—42no—
64C23×C61—22no—
65C23×C61—42no—
66C23×C61#12011yescharacteristic
67C23×C61C22⋊Q811yescharacteristic
68C23×C61#12411yescharacteristic
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—24no—
72C2×C4×C61—41no—
73C2×C4×C61—41no—
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—42no—
82C2×C4×C61—42no—
83C2×C4×C61—42no—
84C2×C4×C61—82no—
85C2×C4×C61—81no—
86C2×C4×C61—82no—
87C2×C4×C61C22⋊Q812yes—
88C2×C4×C61#12412yes—
89C8×C61—82no—
90#10389C6111yesmaximal, characteristic, direct product factor, Sylow
91C22×C61—22no—
92C22×C61—21no—
93C22×C61—21no—
94C22×C61—22no—
95C22×C61—22no—
96C22×C61—82no—
97C22×C61#39311yescharacteristic
98C22×C61#45812yes—
99C4×C61—22no—
100C4×C61—22no—
101C4×C61—44no—
102C4×C61—82no—
103C4×C61—82no—
104C4×C61—82no—
105C4×C61—161no—
106#2608C2×C6111yescharacteristic
107#1826C2×C6112yes—
108#1820C2×C6111yescharacteristic
109#1306C2×C6111yescharacteristic
110#1284C2×C6112yes—
111C2×C61—22no—
112C2×C61—41no—
113C2×C61—41no—
114C2×C61#203011yescharacteristic
115C2×C61#203112yes—
116C2×#117C22×C6111yescharacteristic
117#407C22×C6112yes—
118#396—22no—
119#389—22no—
120#387—22no—
121#381C22×C6111yescharacteristic
122#381C22×C6111yescharacteristic
123C4×C22⋊C4C22×C6112yes—
124#342—22no—
125#339—22no—
126#339—22no—
127C61#1038911yescharacteristic, direct product factor, Sylow
128C23×C4C23×C6111yescharacteristic
129C2×M16—22no—
130#117—22no—
131#117—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4Q8×C6112yes—
136C2×C22⋊C4—21no—
137C2×C22⋊C4—22no—
138C2×C22⋊C4—21no—
139C2×C22⋊C4D4×C6112yes—
140C2×C42—21no—
141C2×C42D4×C6112yes—
142C2×C42D4×C6112yes—
143C22⋊C8—22no—
144C22⋊C8—22no—
145#95—22no—
146#95—22no—
147#95—22no—
148#95—22no—
149C24C2×D4×C6111yescharacteristic
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—42no—
155C22×C4—41no—
156C22×C4C2×D4×C6112yes—
157C22×C4C2×Q8×C6111yescharacteristic
158C22×C4#41×C6112yes—
159C22×C4#41×C6111yescharacteristic
160M16—42no—
161M16—42no—
162C2×C8—42no—
163C4⋊C4—24no—
164C4⋊C4—44no—
165C4⋊C4—44no—
166C4⋊C4—82no—
167C22⋊C4—44no—
168C22⋊C4—41no—
169C22⋊C4—41no—
170C22⋊C4—42no—
171C22⋊C4—42no—
172C42—42no—
173C42—42no—
174C42—42no—
175C23—22no—
176C23—42no—
177C23#120×C6111yescharacteristic
178C23C22⋊Q8×C6111yescharacteristic
179C23#124×C6111yescharacteristic
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—82no—
196C2×C4—81no—
197C2×C4—82no—
198C2×C4C22⋊Q8×C6112yes—
199C2×C4#124×C6112yes—
200C8—82no—
201C22—22no—
202C22—21no—
203C22—21no—
204C22—22no—
205C22—22no—
206C22—82no—
207C22C61×#39311yescharacteristic
208C22C61×#45812yes—
209C4—22no—
210C4—22no—
211C4—44no—
212C4—82no—
213C4—82no—
214C4—82no—
215C4—161no—
216C2—22no—
217C2—41no—
218C2—41no—
219C2C61×#203011yescharacteristic
220C2C61×#203112yes—
subgroupG/H
center, socleC22×C61#393
commutator, Frattini, cosocleC23×C4C23×C61
prime radicalC24×C61C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
90. #10389C61direct (N × H)
127. C61#10389direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#26082
C61×#18262
C61×#18202
C61×#13062
C61×#12842
#1038961