Finite Group Databasebeta

← C61×#7406 #29510839

Subgroups — C61×#7406 #29510839

Order 15616.

244 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 42 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×#2017C211yesmaximal, characteristic
2C61×#1391C211yesmaximal, characteristic, complemented
3C61×#1315C211yesmaximal, characteristic, complemented
4C61×#575—21no—
5C61×#575C411yescharacteristic, complemented
6C61×#410—21no—
7C61×#408—21no—
8C61×#408C2211yescharacteristic
9C61×C22⋊C16—21no—
10C61×#338C411yescharacteristic, complemented
11C2×#41×C61—21no—
12C2×#41×C61D411yescharacteristic
13#137×C61—41no—
14#137×C61—41no—
15#137×C61—41no—
16AGL(1,ℤ/8)×C61—41no—
17AGL(1,ℤ/8)×C61—41no—
18AGL(1,ℤ/8)×C61—41no—
19#135×C61—41no—
20#135×C61—42no—
21C2×M16×C61—21no—
22C2×M16×C61C2×C411yescharacteristic
23C22×C8×C61D411yescharacteristic
24#117×C61—41no—
25C2×C16×C61—41no—
26#99×C61—22no—
27#99×C61—41no—
28C22⋊C8×C61—41no—
29C22⋊C8×C61—42no—
30#41×C61—41no—
31#41×C61—41no—
32#41×C61—41no—
33#41×C61—41no—
34#41×C61—41no—
35#41×C61—41no—
36C2×Q8×C61—21no—
37C2×Q8×C61SD1611yescharacteristic
38C2×D4×C61—21no—
39C2×D4×C61—21no—
40C2×D4×C61—41no—
41C2×D4×C61D811yescharacteristic
42C22×C4×C61—21no—
43C22×C4×C61—41no—
44C22×C4×C61C22⋊C411yescharacteristic
45Q16×C61—42no—
46Q16×C61—41no—
47SD16×C61—42no—
48SD16×C61—42no—
49SD16×C61—42no—
50D8×C61—42no—
51D8×C61—41no—
52M16×C61—41no—
53M16×C61—41no—
54M16×C61—41no—
55C2×C8×C61—22no—
56C2×C8×C61—21no—
57C2×C8×C61—21no—
58C2×C8×C61—41no—
59C4⋊C4×C61—81no—
60C22⋊C4×C61—42no—
61C42×C61—81no—
62C16×C61—81no—
63C23×C61—21no—
64C23×C61—41no—
65C23×C61#10411yescharacteristic
66Q8×C61—41no—
67Q8×C61—41no—
68Q8×C61—41no—
69D4×C61—41no—
70D4×C61—41no—
71D4×C61—41no—
72D4×C61—81no—
73D4×C61—81no—
74D4×C61—81no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61—81no—
82C2×C4×C61—81no—
83C2×C4×C61—82no—
84C2×C4×C61#9911yescharacteristic
85C2×C4×C61#10211yescharacteristic
86C8×C61—42no—
87C8×C61—41no—
88C8×C61—41no—
89#7406C6111yesmaximal, characteristic, direct product factor, Sylow
90C22×C61—21no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61—81no—
94C22×C61—82no—
95C22×C61—81no—
96C22×C61#32711yescharacteristic
97C4×C61—21no—
98C4×C61—41no—
99C4×C61—81no—
100C4×C61—162no—
101C4×C61AΣL(1,𝔽16)11yescharacteristic
102C4×C61#35311yescharacteristic
103#2017C2×C6111yescharacteristic
104#1391C2×C6111yescharacteristic, complemented
105#1315C2×C6111yescharacteristic, complemented
106C2×C61—21no—
107C2×C61—41no—
108C2×C61—81no—
109C2×C61—161no—
110C2×C61#134311yescharacteristic
111#575—21no—
112#575C4×C6111yescharacteristic, complemented
113#410—21no—
114#408—21no—
115#408C22×C6111yescharacteristic
116C22⋊C16—21no—
117#338C4×C6111yescharacteristic, complemented
118C61#740611yescharacteristic, direct product factor, Sylow
119C2×#41—21no—
120C2×#41D4×C6111yescharacteristic
121#137—41no—
122#137—41no—
123#137—41no—
124AGL(1,ℤ/8)—41no—
125AGL(1,ℤ/8)—41no—
126AGL(1,ℤ/8)—41no—
127#135—41no—
128#135—42no—
129C2×M16—21no—
130C2×M16C2×C4×C6111yescharacteristic
131C22×C8D4×C6111yescharacteristic
132#117—41no—
133C2×C16—41no—
134#99—22no—
135#99—41no—
136C22⋊C8—41no—
137C22⋊C8—42no—
138#41—41no—
139#41—41no—
140#41—41no—
141#41—41no—
142#41—41no—
143#41—41no—
144C2×Q8—21no—
145C2×Q8SD16×C6111yescharacteristic
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—41no—
149C2×D4D8×C6111yescharacteristic
150C22×C4—21no—
151C22×C4—41no—
152C22×C4C22⋊C4×C6111yescharacteristic
153Q16—41no—
154Q16—42no—
155SD16—42no—
156SD16—42no—
157SD16—42no—
158D8—41no—
159D8—42no—
160M16—41no—
161M16—41no—
162M16—41no—
163C2×C8—22no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—41no—
167C4⋊C4—81no—
168C22⋊C4—42no—
169C42—81no—
170C16—81no—
171C23—21no—
172C23—41no—
173C23#104×C6111yescharacteristic
174Q8—41no—
175Q8—41no—
176Q8—41no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—81no—
181D4—81no—
182D4—81no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4—82no—
192C2×C4#99×C6111yescharacteristic
193C2×C4#102×C6111yescharacteristic
194C8—42no—
195C8—41no—
196C8—41no—
197C22—21no—
198C22—41no—
199C22—41no—
200C22—81no—
201C22—82no—
202C22—81no—
203C22C61×#32711yescharacteristic
204C4—21no—
205C4—41no—
206C4—81no—
207C4—162no—
208C4C61×AΣL(1,𝔽16)11yescharacteristic
209C4C61×#35311yescharacteristic
210C2—21no—
211C2—41no—
212C2—81no—
213C2—161no—
214C2C61×#134311yescharacteristic
subgroupG/H
centerC4×C61#353
commutatorC2×M16C2×C4×C61
Frattini, cosocle#408C22×C61
socleC2×C61#1343
prime radicalC61×#2017C2
LCSG ▷ C2×M16 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C61 ◁ C2×C4×C61 ◁ C22×C4×C61 ◁ C61×#408 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#1391C2semidirect
3. C61×#1315C2semidirect
5. C61×#575C4semidirect
10. C61×#338C4semidirect
89. #7406C61direct (N × H)
104. #1391C2×C61semidirect
105. #1315C2×C61semidirect
112. #575C4×C61semidirect
117. #338C4×C61semidirect
118. C61#7406direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#20172
C61×#13912
C61×#13152
#740661