Finite Group Databasebeta

← #29584517

Subgroups — #29584517

Order 15616.

382 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 97 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
1#21445988C212yesmaximal
2#21445952C211yesmaximal, characteristic
3#21443700C212yesmaximal
4#21443700C211yesmaximal, characteristic
5C61×#2845C211yesmaximal, characteristic
6C2×#14519710—22no—
7C2×#14519708—22no—
8C2×#14519688C2211yescharacteristic
9C2×#14519688C2212yes—
10#16839632C2211yescharacteristic
11#16839524—22no—
12C61×#398—22no—
13C61×#398—22no—
14C61×#398—22no—
15C61×#382C2211yescharacteristic
16C61×#382C2212yes—
17C22×#92418—22no—
18C22×#92418—21no—
19C2×C4⋊Dic61—21no—
20C2×C4⋊Dic61—22no—
21#14519710—44no—
22#14519708—44no—
23#14519688—22no—
24#14519688—21no—
25#14519688Q814yes—
26#14519688Q812yes—
27C2×C4⋊C4×C61—22no—
28C2×C4⋊C4×C61—22no—
29C2×C4⋊C4×C61—22no—
30C2×C4⋊C4×C61D412yes—
31C2×C4⋊C4×C61D412yes—
32C2×C4⋊C4×C61D412yes—
33C2×C42×C61C2311yescharacteristic
34#95×C61—22no—
35#95×C61—22no—
36#95×C61—22no—
37#95×C61—22no—
38C22×C4×C61—22no—
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61C2×D412yes—
42C22×C4×C61C2×D411yescharacteristic
43C22×Dic61—41no—
44C4⋊C4×C61—42no—
45C4⋊C4×C61—42no—
46C4⋊C4×C61—42no—
47C4⋊C4×C61—82no—
48C4⋊C4×C61—82no—
49C4⋊C4×C61—82no—
50C42×C61C2×Q812yes—
51C42×C61C2×Q811yescharacteristic
52C42×C61#4111yescharacteristic
53C4⋊Dic61—42no—
54C4⋊Dic61—42no—
55C4⋊Dic61—42no—
56C2×#92418—24no—
57C2×#92418—24no—
58C2×#92418—24no—
59C2×#92418—22no—
60C2×#92418—41no—
61C2×#92418—41no—
62C23×C61#12011yescharacteristic
63C2×C4×C61—22no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61—22no—
67C2×C4×C61—42no—
68C2×C4×C61—42no—
69C2×C4×C61—42no—
70C2×C4×C61—42no—
71C2×C4×C61—42no—
72C2×C4×C61—42no—
73C2×C4×C61—42no—
74C2×C4×C61—42no—
75C2×C4×C61—42no—
76C2×C4×C61C22⋊Q812yes—
77C2×C4×C61C22⋊Q811yescharacteristic
78C2×C4×C61C4⋊Q812yes—
79C2×C4×C61C4⋊Q811yescharacteristic
80C2×Dic61—82no—
81C2×Dic61—81no—
82#92418—28no—
83#92418—42no—
84#10585—611nomaximal, Sylow
85C22×C61#39511yescharacteristic
86C22×C61#45312yes—
87C22×C61#45411yescharacteristic
88C22×C61#45511yescharacteristic
89C22×C61#45612yes—
90C4×C61—22no—
91C4×C61—22no—
92C4×C61—21no—
93C4×C61—21no—
94C4×C61—82no—
95C4×C61—82no—
96C4×C61—82no—
97Dic61—161no—
98#2845D6111yescharacteristic
99#1847—612no—
100#1836—611no—
101#1295—611no—
102#1295—612no—
103C2×C61#165611yescharacteristic
104C2×C61#166112yes—
105C2×C61#166311yescharacteristic
106C2×C61#206012yes—
107C2×C61#206111yescharacteristic
108C2×#107—1222no—
109C2×#106—1222no—
110C2×#97—611no—
111C2×#97—612no—
112#398—22no—
113#398—22no—
114#398—22no—
115#384—611no—
116#382C2×D6111yescharacteristic
117#382C2×D6112yes—
118#340—1222no—
119C61#1058511yescharacteristic, complemented, Sylow
120C22×C8—1222no—
121C22×C8—1221no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—1221no—
126C2×C4⋊C4—1222no—
127C2×C4⋊C4C22⋊D6112yes—
128C2×C4⋊C4C22⋊D6112yes—
129C2×C4⋊C4C22⋊D6112yes—
130C2×C42C22×D6111yescharacteristic
131#107—2444no—
132#106—2444no—
133#97—614no—
134#97—612no—
135#97—1222no—
136#97—1221no—
137#95—22no—
138#95—22no—
139#95—22no—
140#95—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—2441no—
145C22×C4C2×C22⋊D6111yescharacteristic
146C22×C4C2×C22⋊D6112yes—
147C2×C8—1224no—
148C2×C8—1224no—
149C2×C8—1224no—
150C2×C8—1222no—
151C2×C8—2441no—
152C2×C8—2441no—
153C4⋊C4—42no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C4⋊C4—82no—
157C4⋊C4—82no—
158C4⋊C4—82no—
159C4⋊C4—2442no—
160C4⋊C4—2442no—
161C4⋊C4—2442no—
162C42Q8×D6112yes—
163C42Q8×D6111yescharacteristic
164C42#1175822611yescharacteristic
165C23#1451974611yescharacteristic
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—4882no—
180C2×C4—4881no—
181C2×C4#1451975312yes—
182C2×C4#1451975311yescharacteristic
183C2×C4#1451977512yes—
184C2×C4#1451977511yescharacteristic
185C8—1228no—
186C8—2442no—
187C22#1683968111yescharacteristic
188C22#1683993012yes—
189C22#1683993511yescharacteristic
190C22#1683994011yescharacteristic
191C22#1683994512yes—
192C4—22no—
193C4—22no—
194C4—21no—
195C4—21no—
196C4—82no—
197C4—82no—
198C4—82no—
199C4—9761no—
200C2#2144511211yescharacteristic
201C2#2144513612yes—
202C2#2144514711yescharacteristic
203C2#2144716112yes—
204C2#2144716611yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2845C2
socle, prime radicalC23×C61#120
hypercenter#2845D61
hypocenterC61#10585
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2845

Complements

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

NH ≅ G/Ntype
119. C61#10585semidirect

Maximal subgroups

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

subgroupindex
#214459882
#214459522
#214437002
C61×#28452
#1058561