Finite Group Databasebeta

← #29584113

Subgroups — #29584113

Order 15616.

344 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 77 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#21445938C211yesmaximal, characteristic
3#21444520C212yesmaximal
4#21444332C212yesmaximal
5C61×#1290C211yesmaximal, characteristic
6#16840319C2212yes—
7#16840058—22no—
8#16840003—22no—
9#16839973—22no—
10C2×C4⋊#92418C2211yescharacteristic
11#16839608C2211yescharacteristic
12#16839516—22no—
13#16839509—22no—
14#16839507—22no—
15#16839500—24no—
16C61×#432C2212yes—
17C2×C4⋊C8×C61C2211yescharacteristic
18C2×Dic244—22no—
19C22×#92418—21no—
20#14519777D412yes—
21#14519777D412yes—
22#14519769—22no—
23#14519756—22no—
24#14519756—22no—
25C4×Dic122—22no—
26C4×Dic122—22no—
27#14519736—22no—
28C2×C4×Dic61—21no—
29#14519711—22no—
30C4⋊#92418—22no—
31#14519702—24no—
32#14519684—21no—
33#14519684D412yes—
34C22×C8×C61D412yes—
35C2×C42×C61C2311yescharacteristic
36C4⋊C8×C61—22no—
37C4⋊C8×C61—22no—
38C22⋊C8×C61—22no—
39#97×C61—22no—
40C22×C4×C61C2×D411yescharacteristic
41C22×C4×C61C2×D411yescharacteristic
42C22×C4×C61#4111yescharacteristic
43C22×Dic61—22no—
44C2×Dic122—22no—
45C2×Dic122—22no—
46C2×C8×C61—22no—
47C2×C8×C61—42no—
48C2×C8×C61—42no—
49C42×C61C2×D412yes—
50C42×C61#4112yes—
51C22⋊Dic61—42no—
52C4⋊Dic61—22no—
53C4⋊Dic61—22no—
54C4⋊Dic61—22no—
55C4⋊Dic61—22no—
56#11758196—42no—
57#11758196—42no—
58C4×Dic61—41no—
59C4×Dic61—41no—
60C4×Dic61—42no—
61C2×#92418—42no—
62C2×#92418—41no—
63Dic244—82no—
64C23×C61#12111yescharacteristic
65C2×C4×C61—22no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—41no—
69C2×C4×C61#12011yescharacteristic
70C2×C4×C61#12112yes—
71C2×C4×C61#12312yes—
72C2×C4×C61#12411yescharacteristic
73C2×Dic61—42no—
74C2×Dic61—42no—
75C2×Dic61—42no—
76C2×Dic61—42no—
77C2×Dic61—42no—
78Dic122—42no—
79Dic122—42no—
80Dic122—82no—
81C8×C61—42no—
82C8×C61—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#45411yescharacteristic
93C4×C61#45511yescharacteristic
94Dic61—82no—
95Dic61—82no—
96Dic61—82no—
97#3249—611no—
98#1832—611no—
99#1552—612no—
100#1506—612no—
101#1290D6111yescharacteristic
102C2×C61—22no—
103C2×C61#204011yescharacteristic
104C2×C61#204711yescharacteristic
105C2×C61#205311yescharacteristic
106#533—612no—
107#477—1222no—
108#467—1222no—
109#462—1222no—
110#432C2×D6112yes—
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—1222no—
120C22×C8—1221no—
121C22×C8D24412yes—
122C4⋊Q8—612no—
123C4⋊Q8—612no—
124#125—1222no—
125C22⋊Q8—1222no—
126C22⋊Q8—1222no—
127C4×Q8—1222no—
128C4×Q8—1222no—
129#117—1222no—
130C2×C42—1221no—
131C2×C42C22×D6111yescharacteristic
132#107—1222no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135C4⋊C8—1222no—
136#103—1224no—
137C22⋊C8—22no—
138#97—22no—
139#95—612no—
140#95—1221no—
141C2×Q8—1222no—
142C2×Q8—1222no—
143C22×C4—1222no—
144C22×C4C2×D24411yescharacteristic
145C22×C4D4×D6111yescharacteristic
146C22×C4#1175822611yescharacteristic
147Q16—4882no—
148C2×C8—22no—
149C2×C8—42no—
150C2×C8—42no—
151C2×C8—2442no—
152C2×C8—2441no—
153C4⋊C4—1222no—
154C4⋊C4—1222no—
155C4⋊C4—1222no—
156C4⋊C4—1222no—
157C4⋊C4—2442no—
158C4⋊C4—2442no—
159C22⋊C4—2442no—
160C42—2441no—
161C42—2441no—
162C42—2442no—
163C42#1175822212yes—
164C42D4×D6112yes—
165C23#1451975211yescharacteristic
166Q8—4882no—
167Q8—2442no—
168Q8—2442no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—2442no—
174C2×C4—2442no—
175C2×C4—2442no—
176C2×C4—2442no—
177C2×C4—2442no—
178C2×C4#1451974711yescharacteristic
179C2×C4#1451975012yes—
180C2×C4#1451976212yes—
181C2×C4#1451976511yescharacteristic
182C8—42no—
183C8—82no—
184C8—4881no—
185C22—21no—
186C22—21no—
187C22#1683968011yescharacteristic
188C22#1684003812yes—
189C4—21no—
190C4—22no—
191C4—22no—
192C4—4882no—
193C4—4882no—
194C4—4882no—
195C4#1683993711yescharacteristic
196C4#1683994211yescharacteristic
197C2—22no—
198C2#2144704911yescharacteristic
199C2#2144708811yescharacteristic
200C2#2144712611yescharacteristic
subgroupG/H
centerC22#16839680
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1290C2
socleC22×C61#394
prime radicalC23×C61#121
hypercenter#1290D61
hypocenterC61#10517
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

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
#214571642
#214459382
#214445202
#214443322
C61×#12902
#1051761