Finite Group Databasebeta

← #29577553

Subgroups — #29577553

Order 15616.

422 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 95 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#21456199C211yesmaximal, characteristic
2#21449000C211yesmaximal, characteristic
3#21444371C212yesmaximal
4#21443685C212yesmaximal
5C61×#1558C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7#16840130—22no—
8#16840112C414yescomplemented
9#16839771—22no—
10C4×#11758194C2211yescharacteristic
11#16839669—22no—
12#16839648—24no—
13#16839630C2212yes—
14#16839500—24no—
15C2×C4⋊Q8×C61C2211yescharacteristic
16C61×#432C2212yes—
17C61×#333—22no—
18C2×#11758194—21no—
19#14519777C2×C412yes—
20#14519769—21no—
21#14519756—22no—
22C4×Dic122—22no—
23#14519736—21no—
24C2×C4⋊Dic61—22no—
25C2×C4×Dic61—22no—
26#14519701—28no—
27#14519688—21no—
28C4×#92418C2×C412yes—
29#14519684—24no—
30#14519684—22no—
31#14519684—22no—
32#14519684D414yes—
33C22×Q8×C61D412yes—
34C4⋊Q8×C61—22no—
35C4⋊Q8×C61C2×C412yes—
36C4⋊Q8×C61D412yes—
37C2×C4⋊C4×C61—22no—
38C2×C42×C61C2311yescharacteristic
39C4⋊C8×C61—22no—
40C22⋊C8×C61—22no—
41#97×C61—22no—
42C2×Q8×C61—22no—
43C2×Q8×C61—42no—
44C2×Q8×C61—42no—
45C2×Q8×C61C22⋊C414yes—
46C22×C4×C61—22no—
47C22×C4×C61C2×D411yescharacteristic
48C22×C4×C61C2×D412yes—
49C22×Dic61—24no—
50C2×Dic122—22no—
51C2×C8×C61—42no—
52C4⋊C4×C61—24no—
53C4⋊C4×C61—24no—
54C42×C61C22×C411yescharacteristic
55C42×C61C2×D411yescharacteristic
56C42×C61#4112yes—
57C22⋊Dic61—41no—
58C4⋊Dic61—22no—
59C4⋊Dic61—22no—
60C4⋊Dic61—82no—
61#11758196—42no—
62C4×Dic61—41no—
63C4×Dic61—82no—
64#11758194—42no—
65C2×#92418—22no—
66C23×C61#12011yescharacteristic
67Q8×C61—44no—
68Q8×C61—82no—
69C2×C4×C61—22no—
70C2×C4×C61—24no—
71C2×C4×C61—42no—
72C2×C4×C61—42no—
73C2×C4×C61—42no—
74C2×C4×C61C2×C22⋊C411yescharacteristic
75C2×C4×C61C4×D412yes—
76C2×C4×C61#12112yes—
77C2×C4×C61#12311yescharacteristic
78C2×Dic61—48no—
79C2×Dic61—42no—
80C2×Dic61—44no—
81Dic122—82no—
82C8×C61—82no—
83#92418—42no—
84#9426—611nomaximal, Sylow
85C22×C61—22no—
86C22×C61#38611yescharacteristic
87C22×C61#45512yes—
88C4×C61—21no—
89C4×C61—21no—
90C4×C61—22no—
91C4×C61—22no—
92C4×C61—44no—
93Dic61—84no—
94Dic61—82no—
95#3139—611no—
96#2381—611no—
97#1558D6111yescharacteristic
98#1515—612no—
99#1288—612no—
100C2×C61—22no—
101C2×C61#188511yescharacteristic
102C2×C61#190512yes—
103#533—611no—
104C2×C4⋊Q8C2×D6111yescharacteristic
105#491—1222no—
106#487—614no—
107#432C2×D6112yes—
108#419—1222no—
109C4×M16—611no—
110#391—1222no—
111#387—1224no—
112#383—612no—
113#333—22no—
114#328—1224no—
115C61#942611yescharacteristic, complemented, Sylow
116C22×Q8D24412yes—
117C2×M16—1221no—
118C4⋊Q8—22no—
119C4⋊Q8—612no—
120C4⋊Q8C4×D6112yes—
121C4⋊Q8C22⋊D6112yes—
122#125—1221no—
123C22⋊Q8—1222no—
124C4×Q8—1222no—
125#117—1221no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—1222no—
128C2×C42—1222no—
129C2×C42C22×D6111yescharacteristic
130C4⋊C8—22no—
131#103—1228no—
132C22⋊C8—22no—
133#97—22no—
134#97—1221no—
135C4×C8—612no—
136#95—614no—
137#95—1224no—
138#95—1222no—
139#95—1222no—
140C2×Q8—22no—
141C2×Q8—42no—
142C2×Q8—42no—
143C2×Q8—1222no—
144C2×Q8#1175819814yes—
145C22×C4—22no—
146C22×C4—1224no—
147C22×C4C2×D24411yescharacteristic
148C22×C4D4×D6112yes—
149M16—2442no—
150C2×C8—42no—
151C2×C8—1222no—
152C4⋊C4—24no—
153C4⋊C4—24no—
154C4⋊C4—1222no—
155C4⋊C4—1222no—
156C4⋊C4—4882no—
157C4⋊C4—2442no—
158C22⋊C4—2441no—
159C42—4882no—
160C42—2441no—
161C42C2×C4×D6111yescharacteristic
162C42#1175822412yes—
163C42C2×C22⋊D6111yescharacteristic
164C23#1451974711yescharacteristic
165Q8—44no—
166Q8—82no—
167Q8—4882no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—2448no—
174C2×C4—2444no—
175C2×C4—2442no—
176C2×C4C2×#1175819811yescharacteristic
177C2×C4#1451973712yes—
178C2×C4#1451974912yes—
179C2×C4#1451976111yescharacteristic
180C8—82no—
181C8—2442no—
182C22—22no—
183C22#1683963911yescharacteristic
184C22#1683994212yes—
185C4—21no—
186C4—21no—
187C4—22no—
188C4—22no—
189C4—44no—
190C4—4884no—
191C4—4882no—
192C2—22no—
193C2#2144620511yescharacteristic
194C2#2144631112yes—
subgroupG/H
centerC22#16839639
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1558C2
socleC22×C61#386
prime radicalC23×C61#120
cosocleC2×C42×C61C23
hypercenter#1558D61
hypocenterC61#9426
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1558

Complements

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

NH ≅ G/Ntype
8. #16840112C4semidirect
115. C61#9426semidirect

Maximal subgroups

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

subgroupindex
#214561992
#214490002
#214443712
#214436852
C61×#15582
#942661