Finite Group Databasebeta

← #29584109

Subgroups — #29584109

Order 15616.

344 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 81 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#21445938C211yesmaximal, characteristic
2#21444519C212yesmaximal
3#21444331C212yesmaximal
4#21443689C211yesmaximal, characteristic
5C61×#3249C211yesmaximal, characteristic
6#16839819C2212yes—
7C2×C4⋊#92418C2211yescharacteristic
8#16839608C2211yescharacteristic
9#16839516—22no—
10#16839508—22no—
11#16839508—22no—
12#16839499—24no—
13C61×#533C2212yes—
14C61×#477—22no—
15C61×#467—22no—
16C61×#462—22no—
17C2×C4⋊C8×C61C2211yescharacteristic
18C22×#92418—21no—
19C2×C4×Dic61—21no—
20C4⋊#92418—22no—
21C4⋊#92418—22no—
22C22⋊#92418—22no—
23#14519688—22no—
24#14519684—21no—
25#14519684D412yes—
26C2×Q16×C61—22no—
27C22×C8×C61D412yes—
28C4⋊Q8×C61D412yes—
29C4⋊Q8×C61D412yes—
30#125×C61—22no—
31C22⋊Q8×C61—22no—
32C22⋊Q8×C61—22no—
33C4×Q8×C61—22no—
34C4×Q8×C61—22no—
35#117×C61—22no—
36C2×C42×C61C2311yescharacteristic
37#107×C61—22no—
38C4⋊C8×C61—22no—
39#103×C61—24no—
40C2×Q8×C61—22no—
41C2×Q8×C61—22no—
42C22×C4×C61C2×D411yescharacteristic
43C22×C4×C61C2×D411yescharacteristic
44C22×C4×C61#4111yescharacteristic
45C22×Dic61—22no—
46Q16×C61—82no—
47C2×C8×C61—22no—
48C2×C8×C61—42no—
49C4⋊C4×C61—22no—
50C4⋊C4×C61—22no—
51C4⋊C4×C61—22no—
52C4⋊C4×C61—22no—
53C4⋊C4×C61—42no—
54C4⋊C4×C61—42no—
55C22⋊C4×C61—42no—
56C42×C61—42no—
57C42×C61C2×D412yes—
58C42×C61#4112yes—
59C4×Dic61—41no—
60C4×Dic61—41no—
61C2×#92418—42no—
62C2×#92418—41no—
63C2×#92418—42no—
64C23×C61#12111yescharacteristic
65Q8×C61—42no—
66Q8×C61—42no—
67Q8×C61—82no—
68C2×C4×C61—22no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—41no—
72C2×C4×C61—42no—
73C2×C4×C61—42no—
74C2×C4×C61#12011yescharacteristic
75C2×C4×C61#12112yes—
76C2×C4×C61#12312yes—
77C2×C4×C61#12411yescharacteristic
78C2×Dic61—42no—
79C2×Dic61—42no—
80C2×Dic61—42no—
81C8×C61—42no—
82#92418—82no—
83#92418—81no—
84#10517—611nomaximal, Sylow
85C22×C61—21no—
86C22×C61—21no—
87C22×C61#39411yescharacteristic
88C22×C61#47312yes—
89C4×C61—22no—
90C4×C61—21no—
91C4×C61—22no—
92C4×C61—82no—
93C4×C61—82no—
94C4×C61#45411yescharacteristic
95C4×C61#45511yescharacteristic
96Dic61—82no—
97#3249D6111yescharacteristic
98#1832—611no—
99#1552—612no—
100#1506—612no—
101#1290—611no—
102C2×C61—22no—
103C2×C61#204011yescharacteristic
104C2×C61#204711yescharacteristic
105C2×C61#205311yescharacteristic
106#533C2×D6112yes—
107#477—22no—
108#467—22no—
109#462—22no—
110#432—612no—
111C2×C4⋊C8—611no—
112C2×C4⋊C8C2×D6111yescharacteristic
113#376—611no—
114#336—1222no—
115#332—1222no—
116#332—1222no—
117#328—1224no—
118C61#1051711yescharacteristic, complemented, Sylow
119C2×Q16—22no—
120C22×C8—1221no—
121C22×C8C22⋊D6112yes—
122C4⋊Q8C22⋊D6112yes—
123C4⋊Q8C22⋊D6112yes—
124#125—22no—
125C22⋊Q8—22no—
126C22⋊Q8—22no—
127C4×Q8—22no—
128C4×Q8—22no—
129#117—22no—
130C2×C42—1221no—
131C2×C42C22×D6111yescharacteristic
132#107—22no—
133C4⋊C8—22no—
134C4⋊C8—1222no—
135C4⋊C8—1222no—
136#103—24no—
137C22⋊C8—1222no—
138#97—1222no—
139#95—612no—
140#95—1221no—
141C2×Q8—22no—
142C2×Q8—22no—
143C22×C4—1222no—
144C22×C4D4×D6111yescharacteristic
145C22×C4#1175822411yescharacteristic
146C22×C4C2×C22⋊D6111yescharacteristic
147Q16—82no—
148C2×C8—22no—
149C2×C8—42no—
150C2×C8—2442no—
151C2×C8—2441no—
152C2×C8—2442no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C22⋊C4—42no—
160C42—42no—
161C42—2441no—
162C42—2441no—
163C42#1175822412yes—
164C42C2×C22⋊D6112yes—
165C23#1451974811yescharacteristic
166Q8—42no—
167Q8—42no—
168Q8—82no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—2442no—
176C2×C4—2442no—
177C2×C4—2442no—
178C2×C4#1451974611yescharacteristic
179C2×C4#1451974912yes—
180C2×C4#1451975812yes—
181C2×C4#1451976411yescharacteristic
182C8—42no—
183C8—4882no—
184C8—4881no—
185C22—21no—
186C22—21no—
187C22#1683967611yescharacteristic
188C22#1684003412yes—
189C4—21no—
190C4—22no—
191C4—22no—
192C4—82no—
193C4—82no—
194C4—4882no—
195C4#1683993511yescharacteristic
196C4#1683994011yescharacteristic
197C2—22no—
198C2#2144704511yescharacteristic
199C2#2144708411yescharacteristic
200C2#2144712211yescharacteristic
subgroupG/H
centerC22#16839676
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3249C2
socleC22×C61#394
prime radicalC23×C61#121
hypercenter#3249D61
hypocenterC61#10517
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
118. C61#10517semidirect

Maximal subgroups

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

subgroupindex
#214459382
#214445192
#214443312
#214436892
C61×#32492
#1051761