Finite Group Databasebeta

← C61×#12311 #29515744

Subgroups — C61×#12311 #29515744

Order 15616.

366 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 78 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×#3293C211yesmaximal, characteristic, complemented
2C61×#2213C212yesmaximal, complemented
3C61×#1709C211yesmaximal, characteristic, complemented
4C61×#1358C211yesmaximal, characteristic, complemented
5C61×#1335C212yesmaximal, complemented
6C61×#578—22no—
7C61×#509—22no—
8C61×#494C2211yescharacteristic
9C61×#493C2211yescharacteristic
10C61×#486—22no—
11C61×#473—22no—
12C61×#456—22no—
13C61×#443C2212yes—
14C61×#364C2212yes—
15C61×#361—22no—
16C82×C61C2211yescharacteristic
172−1+4×C61—22no—
18#137×C61—24no—
19#137×C61—44no—
20#135×C61—42no—
21#135×C61D412yes—
22C2×Q16×C61—22no—
23C2×Q16×C61—42no—
24C2×D8×C61—22no—
25#131×C61—22no—
26C4⋊Q8×C61D412yes—
27#127×C61—21no—
28SD32×C61—42no—
29D16×C61—42no—
30M32×C61—22no—
31#108×C61D412yes—
32#104×C61—22no—
33#102×C61—44no—
34#101×C61—22no—
35C4×C8×C61—21no—
36C4×C8×C61C2311yescharacteristic
37#41×C61—22no—
38#41×C61—44no—
39#41×C61—82no—
40C2×Q8×C61—22no—
41C2×Q8×C61—44no—
42C2×D4×C61—42no—
43C2×D4×C61—41no—
44Q16×C61—44no—
45Q16×C61—42no—
46Q16×C61—42no—
47Q16×C61D812yes—
48SD16×C61—22no—
49SD16×C61—44no—
50D8×C61—42no—
51D8×C61—42no—
52D8×C61D812yes—
53M16×C61—22no—
54M16×C61—42no—
55C2×C8×C61—22no—
56C2×C8×C61—42no—
57C2×C8×C61C2×D412yes—
58C4⋊C4×C61—42no—
59C42×C61C2×D411yescharacteristic
60C16×C61—42no—
61C23×C61—81no—
62Q8×C61—22no—
63Q8×C61—44no—
64Q8×C61—82no—
65D4×C61—22no—
66D4×C61—42no—
67D4×C61—84no—
68D4×C61—82no—
69D4×C61—82no—
70C2×C4×C61—21no—
71C2×C4×C61—42no—
72C2×C4×C61—42no—
73C2×C4×C61—84no—
74C2×C4×C61#12011yescharacteristic
75C8×C61—42no—
76C8×C61—42no—
77C8×C61C2×D812yes—
78C8×C61AGL(1,ℤ/8)12yes—
79#12311C6111yesmaximal, characteristic, direct product factor, Sylow
80C22×C61—42no—
81C22×C61—162no—
82C22×C61—161no—
83C22×C61#45311yescharacteristic
84C4×C61—22no—
85C4×C61—42no—
86C4×C61—82no—
87C4×C61#44712yes—
88#3293C2×C6111yescharacteristic, complemented
89#2213C2×C6112yescomplemented
90#1709C2×C6111yescharacteristic, complemented
91#1358C2×C6111yescharacteristic, complemented
92#1335C2×C6112yescomplemented
93C2×C61—21no—
94C2×C61—82no—
95C2×C61—321no—
96C2×C61#161911yescharacteristic
97#578—22no—
98#509—22no—
99#494C22×C6111yescharacteristic
100#493C22×C6111yescharacteristic
101#486—22no—
102#473—22no—
103#456—22no—
104#443C22×C6112yes—
105#364C22×C6112yes—
106#361—22no—
107C82C22×C6111yescharacteristic
108C61#1231111yescharacteristic, direct product factor, Sylow
1092−1+4—22no—
110#137—24no—
111#137—44no—
112#135—42no—
113#135D4×C6112yes—
114C2×Q16—22no—
115C2×Q16—42no—
116C2×D8—22no—
117#131—22no—
118C4⋊Q8D4×C6112yes—
119#127—21no—
120SD32—42no—
121D16—42no—
122M32—22no—
123#108D4×C6112yes—
124#104—22no—
125#102—44no—
126#101—22no—
127C4×C8—21no—
128C4×C8C23×C6111yescharacteristic
129#41—22no—
130#41—44no—
131#41—82no—
132C2×Q8—22no—
133C2×Q8—44no—
134C2×D4—42no—
135C2×D4—41no—
136Q16—44no—
137Q16—42no—
138Q16—42no—
139Q16D8×C6112yes—
140SD16—22no—
141SD16—44no—
142D8—42no—
143D8—42no—
144D8D8×C6112yes—
145M16—22no—
146M16—42no—
147C2×C8—22no—
148C2×C8—42no—
149C2×C8C2×D4×C6112yes—
150C4⋊C4—42no—
151C42C2×D4×C6111yescharacteristic
152C16—42no—
153C23—81no—
154Q8—22no—
155Q8—44no—
156Q8—82no—
157D4—22no—
158D4—42no—
159D4—84no—
160D4—82no—
161D4—82no—
162C2×C4—21no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—84no—
166C2×C4#120×C6111yescharacteristic
167C8—42no—
168C8—42no—
169C8C2×D8×C6112yes—
170C8AGL(1,ℤ/8)×C6112yes—
171C22—42no—
172C22—162no—
173C22—161no—
174C22C61×#45311yescharacteristic
175C4—22no—
176C4—42no—
177C4—82no—
178C4C61×#44712yes—
179C2—21no—
180C2—82no—
181C2—321no—
182C2C61×#161911yescharacteristic
subgroupG/H
center, socleC2×C61#1619
commutator, Frattini, cosocleC4×C8C23×C61
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C61 ◁ C2×C4×C61 ◁ C4×C8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3293C2semidirect
2. C61×#2213C2semidirect
3. C61×#1709C2semidirect
4. C61×#1358C2semidirect
5. C61×#1335C2semidirect
79. #12311C61direct (N × H)
88. #3293C2×C61semidirect
89. #2213C2×C61semidirect
90. #1709C2×C61semidirect
91. #1358C2×C61semidirect
92. #1335C2×C61semidirect
108. C61#12311direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#32932
C61×#22132
C61×#17092
C61×#13582
C61×#13352
#1231161