Finite Group Databasebeta

← C61×#19743 #29523176

Subgroups — C61×#19743 #29523176

Order 15616.

814 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 230 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×#3207C213yesmaximal, complemented
2C61×#3205C213yesmaximal, complemented
3C61×#1721C213yesmaximal, complemented
4C61×#1717C213yesmaximal, complemented
5C61×#1712C211yesmaximal, characteristic, complemented
6C61×#1711C211yesmaximal, characteristic, complemented
7C61×#1454C211yesmaximal, characteristic, complemented
8C61×#532C2213yes—
9C2×#127×C61C2211yescharacteristic
10C61×#493C2213yes—
11C61×#493C2213yes—
12C61×#493C2213yescomplemented
13C61×#492C2213yescomplemented
14C61×#487C2213yescomplemented
15C61×#486C2213yes—
16C61×#486C2213yes—
17C61×#486C2213yescomplemented
18C61×#463—26no—
19C61×#459—26no—
20C61×#449—26no—
21C61×#447—26no—
22C61×#431C2213yes—
23C61×#322C2213yescomplemented
24C82×C61C2211yescharacteristic, complemented
25C2×#41×C61—23no—
26C22×D4×C61—23no—
27C2×SD16×C61—26no—
28C2×D8×C61—26no—
29C2×D8×C61—26no—
30C2×D8×C61—26no—
31C4⋊Q8×C61C2313yes—
32#127×C61—23no—
33#127×C61C2311yescharacteristic
34#127×C61C2311yescharacteristic
35#127×C61C2313yes—
36#124×C61—23no—
37#121×C61—23no—
38#121×C61—23no—
39C4×D4×C61—23no—
40C4×D4×C61—23no—
41C2×C42×C61C2311yescharacteristic
42C4⋊C8×C61D416yes—
43#103×C61—26no—
44#102×C61—26no—
45#102×C61—26no—
46#102×C61—26no—
47C22⋊C8×C61D416yes—
48C4×C8×C61C2313yes—
49C4×C8×C61C2313yes—
50C24×C61—41no—
51#41×C61—86no—
52C2×Q8×C61—23no—
53C2×D4×C61—23no—
54C2×D4×C61—23no—
55C2×D4×C61—23no—
56C2×D4×C61—23no—
57C2×D4×C61—23no—
58C2×D4×C61—43no—
59C2×D4×C61—43no—
60C2×D4×C61—86no—
61C22×C4×C61—43no—
62C22×C4×C61C2×D413yes—
63SD16×C61—86no—
64D8×C61—86no—
65D8×C61—86no—
66D8×C61—86no—
67C2×C8×C61C2×D416yes—
68C2×C8×C61C2×D416yes—
69C4⋊C4×C61—23no—
70C4⋊C4×C61—23no—
71C22⋊C4×C61—43no—
72C22⋊C4×C61—43no—
73C42×C61C2×D413yes—
74C42×C61C2411yescharacteristic
75C23×C61—43no—
76C23×C61—41no—
77C23×C61—41no—
78C23×C61—86no—
79C23×C61#12711yescharacteristic
80Q8×C61—46no—
81D4×C61—46no—
82D4×C61—46no—
83D4×C61—46no—
84D4×C61—46no—
85D4×C61—46no—
86D4×C61—86no—
87D4×C61—86no—
88C2×C4×C61—26no—
89C2×C4×C61—43no—
90C2×C4×C61—86no—
91C2×C4×C61#12713yes—
92C2×C4×C61C22×D413yes—
93C8×C61—26no—
94C8×C61—26no—
95#19743C6111yesmaximal, characteristic, direct product factor, Sylow
96C22×C61—23no—
97C22×C61—83no—
98C22×C61—83no—
99C22×C61—83no—
100C22×C61—83no—
101C22×C61—83no—
102C22×C61—164no—
103C22×C61C2×#12711yescharacteristic
104C4×C61—23no—
105C4×C61—83no—
106C4×C61#57616yes—
107#3207C2×C6113yescomplemented
108#3205C2×C6113yescomplemented
109#1721C2×C6113yescomplemented
110#1717C2×C6113yescomplemented
111#1712C2×C6111yescharacteristic, complemented
112#1711C2×C6111yescharacteristic, complemented
113#1454C2×C6111yescharacteristic, complemented
114C2×C61—41no—
115C2×C61—163no—
116C2×C61—161no—
117C2×C61—161no—
118C2×C61#315513yes—
119#532C22×C6113yes—
120C2×#127C22×C6111yescharacteristic
121#493C22×C6113yes—
122#493C22×C6113yes—
123#493C22×C6113yescomplemented
124#492C22×C6113yescomplemented
125#487C22×C6113yescomplemented
126#486C22×C6113yes—
127#486C22×C6113yes—
128#486C22×C6113yescomplemented
129#463—26no—
130#459—26no—
131#449—26no—
132#447—26no—
133#431C22×C6113yes—
134#322C22×C6113yescomplemented
135C82C22×C6111yescharacteristic, complemented
136C61#1974311yescharacteristic, direct product factor, Sylow
137C2×#41—23no—
138C22×D4—23no—
139C2×SD16—26no—
140C2×D8—26no—
141C2×D8—26no—
142C2×D8—26no—
143C4⋊Q8C23×C6113yes—
144#127—23no—
145#127C23×C6111yescharacteristic
146#127C23×C6111yescharacteristic
147#127C23×C6113yes—
148#124—23no—
149#121—23no—
150#121—23no—
151C4×D4—23no—
152C4×D4—23no—
153C2×C42C23×C6111yescharacteristic
154C4⋊C8D4×C6116yes—
155#103—26no—
156#102—26no—
157#102—26no—
158#102—26no—
159C22⋊C8D4×C6116yes—
160C4×C8C23×C6113yes—
161C4×C8C23×C6113yes—
162C24—41no—
163#41—86no—
164C2×Q8—23no—
165C2×D4—23no—
166C2×D4—23no—
167C2×D4—23no—
168C2×D4—23no—
169C2×D4—23no—
170C2×D4—43no—
171C2×D4—43no—
172C2×D4—86no—
173C22×C4—43no—
174C22×C4C2×D4×C6113yes—
175SD16—86no—
176D8—86no—
177D8—86no—
178D8—86no—
179C2×C8C2×D4×C6116yes—
180C2×C8C2×D4×C6116yes—
181C4⋊C4—23no—
182C4⋊C4—23no—
183C22⋊C4—43no—
184C22⋊C4—43no—
185C42C2×D4×C6113yes—
186C42C24×C6111yescharacteristic
187C23—43no—
188C23—41no—
189C23—41no—
190C23—86no—
191C23#127×C6111yescharacteristic
192Q8—46no—
193D4—46no—
194D4—46no—
195D4—46no—
196D4—46no—
197D4—46no—
198D4—86no—
199D4—86no—
200C2×C4—26no—
201C2×C4—43no—
202C2×C4—86no—
203C2×C4#127×C6113yes—
204C2×C4C22×D4×C6113yes—
205C8—26no—
206C8—26no—
207C22—23no—
208C22—83no—
209C22—83no—
210C22—83no—
211C22—83no—
212C22—83no—
213C22—164no—
214C22C2×#127×C6111yescharacteristic
215C4—23no—
216C4—83no—
217C4C61×#57616yes—
218C2—41no—
219C2—161no—
220C2—161no—
221C2—163no—
222C2C61×#315513yes—
subgroupG/H
center, socleC22×C61C2×#127
commutator, Frattini, cosocleC42C24×C61
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3207C2semidirect
2. C61×#3205C2semidirect
3. C61×#1721C2semidirect
4. C61×#1717C2semidirect
5. C61×#1712C2semidirect
6. C61×#1711C2semidirect
7. C61×#1454C2semidirect
12. C61×#493C22semidirect
13. C61×#492C22semidirect
14. C61×#487C22semidirect
17. C61×#486C22semidirect
23. C61×#322C22semidirect
24. C82×C61C22semidirect
95. #19743C61direct (N × H)
107. #3207C2×C61semidirect
108. #3205C2×C61semidirect
109. #1721C2×C61semidirect
110. #1717C2×C61semidirect
111. #1712C2×C61semidirect
112. #1711C2×C61semidirect
113. #1454C2×C61semidirect
123. #493C22×C61semidirect
124. #492C22×C61semidirect
125. #487C22×C61semidirect
128. #486C22×C61semidirect
134. #322C22×C61semidirect
135. C82C22×C61semidirect
136. C61#19743direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#32072
C61×#32052
C61×#17212
C61×#17172
C61×#17122
C61×#17112
C61×#14542
#1974361