Finite Group Databasebeta

← #29584104

Subgroups — #29584104

Order 15616.

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

normal subgroups only

This group has 364 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#21445972C211yesmaximal, characteristic
2#21444519C212yesmaximal
3#21444331C212yesmaximal
4#21443689C211yesmaximal, characteristic
5C61×#3249C211yesmaximal, characteristic
6#16839819C2212yes—
7C2×C4⋊#92418C2211yescharacteristic
8C2×#14519706—22no—
9#16839608C2211yescharacteristic
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—
22#14519706—44no—
23C22⋊#92418—22no—
24#14519688—22no—
25#14519684—21no—
26#14519684D412yes—
27C2×Q16×C61—22no—
28C22×C8×C61D412yes—
29C4⋊Q8×C61D412yes—
30C4⋊Q8×C61D412yes—
31#125×C61—22no—
32C22⋊Q8×C61—22no—
33C22⋊Q8×C61—22no—
34C4×Q8×C61—22no—
35C4×Q8×C61—22no—
36#117×C61—22no—
37C2×C42×C61C2311yescharacteristic
38#107×C61—22no—
39C4⋊C8×C61—22no—
40#103×C61—24no—
41C2×Q8×C61—22no—
42C2×Q8×C61—22no—
43C22×C4×C61C2×D411yescharacteristic
44C22×C4×C61C2×D411yescharacteristic
45C22×C4×C61#4111yescharacteristic
46C22×Dic61—22no—
47Q16×C61—82no—
48C2×C8×C61—22no—
49C2×C8×C61—42no—
50C4⋊C4×C61—22no—
51C4⋊C4×C61—22no—
52C4⋊C4×C61—22no—
53C4⋊C4×C61—22no—
54C4⋊C4×C61—42no—
55C4⋊C4×C61—42no—
56C22⋊C4×C61—42no—
57C42×C61—42no—
58C42×C61C2×D412yes—
59C42×C61#4112yes—
60C4×Dic61—22no—
61C4×Dic61—22no—
62C2×#92418—42no—
63C2×#92418—41no—
64C2×#92418—42no—
65C23×C61#12111yescharacteristic
66Q8×C61—42no—
67Q8×C61—42no—
68Q8×C61—82no—
69C2×C4×C61—22no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—41no—
73C2×C4×C61—42no—
74C2×C4×C61—42no—
75C2×C4×C61#12011yescharacteristic
76C2×C4×C61#12112yes—
77C2×C4×C61#12312yes—
78C2×C4×C61#12411yescharacteristic
79C2×Dic61—24no—
80C2×Dic61—42no—
81C2×Dic61—42no—
82C8×C61—42no—
83#92418—82no—
84#92418—81no—
85#10516—611nomaximal, Sylow
86C22×C61—21no—
87C22×C61—21no—
88C22×C61#39411yescharacteristic
89C22×C61#47312yes—
90C4×C61—22no—
91C4×C61—21no—
92C4×C61—22no—
93C4×C61—82no—
94C4×C61—82no—
95C4×C61#45311yescharacteristic
96C4×C61#45611yescharacteristic
97Dic61—44no—
98#3249D6111yescharacteristic
99#1843—611no—
100#1552—612no—
101#1506—612no—
102#1290—611no—
103C2×C61—22no—
104C2×C61#203911yescharacteristic
105C2×C61#204711yescharacteristic
106C2×C61#205311yescharacteristic
107#533C2×D6112yes—
108#477—22no—
109#467—22no—
110#462—22no—
111#432—612no—
112C2×C4⋊C8—611no—
113C2×C4⋊C8—1222no—
114C2×C4⋊C8C2×D6111yescharacteristic
115#376—611no—
116#332—1222no—
117#332—1222no—
118#328—1224no—
119C61#1051611yescharacteristic, complemented, Sylow
120C2×Q16—22no—
121C22×C8—1221no—
122C22×C8C22⋊D6112yes—
123C4⋊Q8C22⋊D6112yes—
124C4⋊Q8C22⋊D6112yes—
125#125—22no—
126C22⋊Q8—22no—
127C22⋊Q8—22no—
128C4×Q8—22no—
129C4×Q8—22no—
130#117—22no—
131C2×C42—1221no—
132C2×C42C22×D6111yescharacteristic
133#107—22no—
134C4⋊C8—22no—
135C4⋊C8—1222no—
136C4⋊C8—1222no—
137C4⋊C8—2444no—
138#103—24no—
139C22⋊C8—1222no—
140#97—1222no—
141#95—612no—
142#95—1221no—
143C2×Q8—22no—
144C2×Q8—22no—
145C22×C4—1222no—
146C22×C4D4×D6111yescharacteristic
147C22×C4#1175822411yescharacteristic
148C22×C4C2×C22⋊D6111yescharacteristic
149Q16—82no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—2442no—
153C2×C8—2441no—
154C2×C8—2442no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C22⋊C4—42no—
162C42—42no—
163C42—1222no—
164C42—1222no—
165C42#1175822412yes—
166C42C2×C22⋊D6112yes—
167C23#1451974811yescharacteristic
168Q8—42no—
169Q8—42no—
170Q8—82no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—1224no—
178C2×C4—2442no—
179C2×C4—2442no—
180C2×C4#1451974611yescharacteristic
181C2×C4#1451974912yes—
182C2×C4#1451975812yes—
183C2×C4#1451976411yescharacteristic
184C8—42no—
185C8—4882no—
186C8—4881no—
187C22—21no—
188C22—21no—
189C22#1683967611yescharacteristic
190C22#1684003412yes—
191C4—21no—
192C4—22no—
193C4—22no—
194C4—82no—
195C4—82no—
196C4—2444no—
197C4#1683993011yescharacteristic
198C4#1683994511yescharacteristic
199C2—22no—
200C2#2144704011yescharacteristic
201C2#2144708411yescharacteristic
202C2#2144712211yescharacteristic
subgroupG/H
centerC22#16839676
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3249C2
socleC22×C61#394
prime radicalC23×C61#121
hypercenter#3249D61
hypocenterC61#10516
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
119. C61#10516semidirect

Maximal subgroups

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

subgroupindex
#214459722
#214445192
#214443312
#214436892
C61×#32492
#1051661