Finite Group Databasebeta

← #29575327

Subgroups — #29575327

Order 15616.

404 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 103 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#21456329C211yesmaximal, characteristic
2#21454921C211yesmaximal, characteristic
3#21444241C212yesmaximal
4#21443657C212yesmaximal
5C61×#1526C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7#16840165C412yes—
8#16840161—22no—
9#16840158C412yes—
10#16839893—22no—
11Q8×#92418—22no—
12#16839823—22no—
13#16839815C2212yes—
14#16839798—22no—
15C2×C4×#92418C2211yescharacteristic
16#16839494—22no—
17#16839494—22no—
18C61×#533C2211yescharacteristic
19C4×M16×C61C2212yes—
20C61×#330—22no—
21C22×#92418—21no—
22#14519777C2×C412yes—
23#14519769—21no—
24#14519756—22no—
25C4×Dic122—22no—
26#14519736—21no—
27#14519710—24no—
28#14519708—24no—
29C4⋊#92418—24no—
30C4⋊#92418D412yes—
31C4⋊#92418D412yes—
32C22⋊#92418—22no—
33#14519688—22no—
34C4×#92418—22no—
35C4×#92418—21no—
36C4×#92418—22no—
37C4×#92418C2×C411yescharacteristic
38C4×#92418C2×C411yescharacteristic
39C2×M16×C61—22no—
40C4⋊Q8×C61C2×C412yes—
41#125×C61D412yes—
42C22⋊Q8×C61—22no—
43C4×Q8×C61—22no—
44#117×C61D412yes—
45C2×C42×C61C2311yescharacteristic
46#97×C61—22no—
47C4×C8×C61—22no—
48C2×Q8×C61—22no—
49C22×C4×C61C2×D411yescharacteristic
50C22×C4×C61#4112yes—
51C2×Dic122—22no—
52M16×C61—24no—
53M16×C61—42no—
54C2×C8×C61—42no—
55C4⋊C4×C61—22no—
56C4⋊C4×C61—24no—
57C4⋊C4×C61C22⋊C414yes—
58C22⋊C4×C61—22no—
59C42×C61—22no—
60C42×C61C22×C411yescharacteristic
61C42×C61C2×D411yescharacteristic
62C42×C61C2×D412yes—
63C22⋊Dic61—41no—
64C4⋊Dic61—22no—
65C4⋊Dic61—22no—
66#11758196—42no—
67C4×Dic61—41no—
68C2×#92418—24no—
69C2×#92418—21no—
70C2×#92418—21no—
71C2×#92418—22no—
72C2×#92418—22no—
73C23×C61#12311yescharacteristic
74Q8×C61—42no—
75Q8×C61—42no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—24no—
80C2×C4×C61C2×C22⋊C411yescharacteristic
81C2×C4×C61C4×D412yes—
82C2×C4×C61#12011yescharacteristic
83C2×C4×C61#12112yes—
84C2×Dic61—42no—
85Dic122—42no—
86Dic122—42no—
87C8×C61—44no—
88#92418—22no—
89#92418—22no—
90#92418—42no—
91#92418—42no—
92#9068—611nomaximal, Sylow
93C22×C61—22no—
94C22×C61—21no—
95C22×C61#38611yescharacteristic
96C4×C61—22no—
97C4×C61—21no—
98C4×C61—44no—
99C4×C61#44312yes—
100C4×C61#44412yes—
101C4×C61#45612yes—
102Dic61—82no—
103#3160—611no—
104#2986—611no—
105#1526D6111yescharacteristic
106#1485—612no—
107#1278—612no—
108C2×C61—41no—
109C2×C61#187612yes—
110C2×C61#188611yescharacteristic
111#533—611no—
112#533C2×D6111yescharacteristic
113#500—612no—
114#499—1222no—
115#498—612no—
116#446—1222no—
117C8×Q8—1222no—
118#433—1222no—
119#431—612no—
120#427—1222no—
121C4×M16C2×D6112yes—
122C2×C4×C8—611no—
123#330—22no—
124Q8⋊C8—1222no—
125Q8⋊C8—1222no—
126C61#906811yescharacteristic, complemented, Sylow
127C2×M16—22no—
128C22×C8—1221no—
129C4⋊Q8—612no—
130C4⋊Q8C4×D6112yes—
131#125—1221no—
132#125C22⋊D6112yes—
133C22⋊Q8—22no—
134C22⋊Q8—1222no—
135C4×Q8—22no—
136C4×Q8—1222no—
137#117—1221no—
138#117D24412yes—
139C2×C42C22×D6111yescharacteristic
140#107—1224no—
141#106—1224no—
142C4⋊C8—612no—
143C4⋊C8—612no—
144C4⋊C8—1224no—
145C22⋊C8—1222no—
146#97—22no—
147#97—1222no—
148C4×C8—22no—
149C4×C8—611no—
150C4×C8—611no—
151C4×C8—1222no—
152C4×C8—1222no—
153C4×C8—1221no—
154C2×Q8—22no—
155C2×Q8—1222no—
156C22×C4C2×D24411yescharacteristic
157C22×C4#1175822412yes—
158M16—24no—
159M16—42no—
160C2×C8—42no—
161C2×C8—1224no—
162C2×C8—1221no—
163C2×C8—1221no—
164C2×C8—1222no—
165C2×C8—1222no—
166C4⋊C4—22no—
167C4⋊C4—24no—
168C4⋊C4—1222no—
169C4⋊C4—1222no—
170C4⋊C4—2442no—
171C4⋊C4#1175819814yes—
172C22⋊C4—22no—
173C22⋊C4—2441no—
174C42—22no—
175C42—2441no—
176C42C2×C4×D6111yescharacteristic
177C42D4×D6112yes—
178C42C2×C22⋊D6111yescharacteristic
179C23#1451976111yescharacteristic
180Q8—42no—
181Q8—42no—
182Q8—2442no—
183Q8—2442no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—2442no—
189C2×C4C2×#1175819811yescharacteristic
190C2×C4#1451973712yes—
191C2×C4#1451974711yescharacteristic
192C2×C4#1451974912yes—
193C8—44no—
194C8—1222no—
195C8—1222no—
196C8—2442no—
197C8—2442no—
198C22—22no—
199C22—21no—
200C22#1683963911yescharacteristic
201C4—22no—
202C4—21no—
203C4—44no—
204C4—4882no—
205C4#1683987612yes—
206C4#1683988112yes—
207C4#1683994712yes—
208C2—41no—
209C2#2144614412yes—
210C2#2144621011yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1526C2
socleC22×C61#386
prime radicalC23×C61#123
cosocleC2×C42×C61C23
hypercenter#1526D61
hypocenterC61#9068
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1526

Complements

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

NH ≅ G/Ntype
126. C61#9068semidirect

Maximal subgroups

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

subgroupindex
#214563292
#214549212
#214442412
#214436572
C61×#15262
#906861