Finite Group Databasebeta

← #29584107

Subgroups — #29584107

Order 15616.

364 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 79 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#21457164C211yesmaximal, characteristic
2#21444517C212yesmaximal
3#21444330C212yesmaximal
4#21443689C211yesmaximal, characteristic
5C61×#1843C211yesmaximal, characteristic
6#16840319C2212yes—
7#16840058—22no—
8#16840003—22no—
9#16839973—22no—
10#16839819C2212yes—
11#16839509—22no—
12#16839507—22no—
13#16839498—24no—
14C2×C4⋊C8×C61—22no—
15C2×C4⋊C8×C61C2211yescharacteristic
16C2×C4⋊C8×C61C2211yescharacteristic
17C61×#376C2211yescharacteristic
18C2×Dic244—22no—
19#14519777D412yes—
20#14519777D412yes—
21#14519769—22no—
22#14519756—22no—
23#14519756—22no—
24C4×Dic122—22no—
25C4×Dic122—22no—
26#14519736—22no—
27#14519711—22no—
28C4⋊#92418—22no—
29#14519702—24no—
30C22⋊#92418—22no—
31#14519688—22no—
32C22×C8×C61—21no—
33C22×C8×C61D412yes—
34C2×C42×C61—21no—
35C2×C42×C61C2311yescharacteristic
36C4⋊C8×C61—22no—
37C4⋊C8×C61—22no—
38C4⋊C8×C61—44no—
39#95×C61—21no—
40#95×C61D412yes—
41C22×C4×C61—22no—
42C22×C4×C61C2×D411yescharacteristic
43C22×C4×C61C2×D411yescharacteristic
44C22×C4×C61#4111yescharacteristic
45C2×Dic122—22no—
46C2×Dic122—22no—
47C2×C8×C61—22no—
48C2×C8×C61—42no—
49C2×C8×C61—42no—
50C2×C8×C61—41no—
51C42×C61—22no—
52C42×C61—22no—
53C42×C61C2×D412yes—
54C42×C61#4112yes—
55C22⋊Dic61—42no—
56C4⋊Dic61—22no—
57C4⋊Dic61—22no—
58C4⋊Dic61—22no—
59C4⋊Dic61—22no—
60#11758196—42no—
61#11758196—42no—
62C4×Dic61—42no—
63C2×#92418—42no—
64Dic244—82no—
65C23×C61#12111yescharacteristic
66C2×C4×C61—22no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—24no—
70C2×C4×C61—41no—
71C2×C4×C61—42no—
72C2×C4×C61—42no—
73C2×C4×C61#12011yescharacteristic
74C2×C4×C61#12112yes—
75C2×C4×C61#12312yes—
76C2×C4×C61#12411yescharacteristic
77C2×Dic61—42no—
78C2×Dic61—42no—
79Dic122—42no—
80Dic122—42no—
81Dic122—82no—
82C8×C61—42no—
83C8×C61—81no—
84#92418—82no—
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—44no—
94C4×C61#45311yescharacteristic
95C4×C61#45611yescharacteristic
96Dic61—82no—
97Dic61—82no—
98#3249—611no—
99#1843D6111yescharacteristic
100#1552—612no—
101#1506—612no—
102#1290—611no—
103C2×C61—22no—
104C2×C61#203911yescharacteristic
105C2×C61#204711yescharacteristic
106C2×C61#205311yescharacteristic
107#533—612no—
108#477—1222no—
109#467—1222no—
110#462—1222no—
111#432—612no—
112C2×C4⋊C8—22no—
113C2×C4⋊C8C2×D6111yescharacteristic
114C2×C4⋊C8C2×D6111yescharacteristic
115#376C2×D6111yescharacteristic
116#332—1222no—
117#332—1222no—
118#328—1224no—
119C61#1051611yescharacteristic, complemented, Sylow
120C2×Q16—1222no—
121C22×C8—21no—
122C22×C8C22⋊D6112yes—
123C4⋊Q8—612no—
124C4⋊Q8—612no—
125#125—1222no—
126C22⋊Q8—1222no—
127C22⋊Q8—1222no—
128C4×Q8—1222no—
129C4×Q8—1222no—
130#117—1222no—
131C2×C42—21no—
132C2×C42C22×D6111yescharacteristic
133#107—1222no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—44no—
137C4⋊C8—1222no—
138#103—1224no—
139C22⋊C8—1222no—
140#97—1222no—
141#95—21no—
142#95D24412yes—
143C2×Q8—1222no—
144C2×Q8—1222no—
145C22×C4—22no—
146C22×C4C2×D24411yescharacteristic
147C22×C4#1175822211yescharacteristic
148C22×C4C2×C22⋊D6111yescharacteristic
149Q16—4882no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—42no—
153C2×C8—41no—
154C2×C8—2442no—
155C4⋊C4—1222no—
156C4⋊C4—1222no—
157C4⋊C4—1222no—
158C4⋊C4—1222no—
159C4⋊C4—2442no—
160C4⋊C4—2442no—
161C22⋊C4—2442no—
162C42—22no—
163C42—22no—
164C42—2442no—
165C42D4×D6112yes—
166C42#1175822612yes—
167C23#1451975111yescharacteristic
168Q8—4882no—
169Q8—2442no—
170Q8—2442no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—2442no—
179C2×C4—2442no—
180C2×C4#1451974511yescharacteristic
181C2×C4#1451975212yes—
182C2×C4#1451976212yes—
183C2×C4#1451976611yescharacteristic
184C8—42no—
185C8—81no—
186C8—4882no—
187C22—21no—
188C22—21no—
189C22#1683967911yescharacteristic
190C22#1684003712yes—
191C4—21no—
192C4—22no—
193C4—22no—
194C4—44no—
195C4—4882no—
196C4—4882no—
197C4#1683992911yescharacteristic
198C4#1683994411yescharacteristic
199C2—22no—
200C2#2144704311yescharacteristic
201C2#2144708711yescharacteristic
202C2#2144712511yescharacteristic
subgroupG/H
centerC22#16839679
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1843C2
socleC22×C61#394
prime radicalC23×C61#121
hypercenter#1843D61
hypocenterC61#10516
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1843

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
#214571642
#214445172
#214443302
#214436892
C61×#18432
#1051661