Finite Group Databasebeta

← #29575329

Subgroups — #29575329

Order 15616.

404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 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#21444414C211yesmaximal, characteristic
3#21444239C212yesmaximal
4#21443655C212yesmaximal
5C61×#2986C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7#16840165C412yes—
8#16840161—22no—
9#16840158C412yes—
10#16839798—22no—
11C4×#11758194C2212yes—
12C2×C4×#92418C2211yescharacteristic
13#16839504—22no—
14#16839492—22no—
15#16839492—22no—
16C61×#533C2211yescharacteristic
17C61×#446—22no—
18C8×Q8×C61—22no—
19C61×#433—22no—
20C61×#431C2212yes—
21C2×#11758194—22no—
22C22×#92418—21no—
23#14519777C2×C412yes—
24#14519769—21no—
25#14519756—22no—
26C4×Dic122—22no—
27#14519736—21no—
28#14519710—24no—
29#14519708—24no—
30#14519688—22no—
31C4×#92418—21no—
32C4×#92418—22no—
33C4×#92418C2×C411yescharacteristic
34C4×#92418C2×C411yescharacteristic
35C4⋊Q8×C61C2×C412yes—
36#125×C61D412yes—
37C22⋊Q8×C61—22no—
38C4×Q8×C61—22no—
39#117×C61D412yes—
40C2×C42×C61C2311yescharacteristic
41C4⋊C8×C61—24no—
42C4⋊C8×C61D412yes—
43C4⋊C8×C61D412yes—
44C22⋊C8×C61—22no—
45#97×C61—22no—
46C4×C8×C61—22no—
47C4×C8×C61—22no—
48C2×Q8×C61—22no—
49C22×C4×C61C2×D411yescharacteristic
50C22×C4×C61#4112yes—
51C2×Dic122—22no—
52C2×C8×C61—22no—
53C2×C8×C61—22no—
54C4⋊C4×C61—22no—
55C4⋊C4×C61—24no—
56C4⋊C4×C61C22⋊C414yes—
57C22⋊C4×C61—22no—
58C42×C61—22no—
59C42×C61C22×C411yescharacteristic
60C42×C61C2×D411yescharacteristic
61C42×C61C2×D412yes—
62C22⋊Dic61—41no—
63C4⋊Dic61—22no—
64C4⋊Dic61—22no—
65#11758196—42no—
66C4×Dic61—41no—
67#11758194—24no—
68#11758194—42no—
69C2×#92418—24no—
70C2×#92418—21no—
71C2×#92418—21no—
72C2×#92418—42no—
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—42no—
88C8×C61—42no—
89#92418—22no—
90#92418—22no—
91#92418—44no—
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#2986D6111yescharacteristic
105#1526—611no—
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—22no—
117C8×Q8—22no—
118#433—22no—
119#431C2×D6112yes—
120#427—1222no—
121C4×M16—612no—
122C2×C4×C8—611no—
123#330—1222no—
124Q8⋊C8—1222no—
125Q8⋊C8—1222no—
126C61#906811yescharacteristic, complemented, Sylow
127C2×M16—1222no—
128C22×C8—1221no—
129C4⋊Q8—612no—
130C4⋊Q8C4×D6112yes—
131#125—1221no—
132#125D24412yes—
133C22⋊Q8—22no—
134C22⋊Q8—1222no—
135C4×Q8—22no—
136C4×Q8—1222no—
137#117—1221no—
138#117C22⋊D6112yes—
139C2×C42C22×D6111yescharacteristic
140#107—1224no—
141#106—1224no—
142C4⋊C8—24no—
143C4⋊C8C22⋊D6112yes—
144C4⋊C8C22⋊D6112yes—
145C22⋊C8—22no—
146#97—22no—
147#97—1222no—
148C4×C8—22no—
149C4×C8—22no—
150C4×C8—611no—
151C4×C8—611no—
152C4×C8—1221no—
153C4×C8—1222no—
154C2×Q8—22no—
155C2×Q8—1222no—
156C22×C4#1175822212yes—
157C22×C4C2×C22⋊D6111yescharacteristic
158M16—1224no—
159M16—2442no—
160C2×C8—22no—
161C2×C8—22no—
162C2×C8—1224no—
163C2×C8—1221no—
164C2×C8—1221no—
165C2×C8—2442no—
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
177C42C2×D24411yescharacteristic
178C42C2×C22⋊D6112yes—
179C23#1451976011yescharacteristic
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×C4C4×C22⋊D6112yes—
191C2×C4#1451974611yescharacteristic
192C2×C4#1451975112yes—
193C8—42no—
194C8—42no—
195C8—1222no—
196C8—1222no—
197C8—2444no—
198C22—22no—
199C22—21no—
200C22#1683964111yescharacteristic
201C4—22no—
202C4—21no—
203C4—44no—
204C4—4882no—
205C4#1683987712yes—
206C4#1683988212yes—
207C4#1683994512yes—
208C2—41no—
209C2#2144614612yes—
210C2#2144621211yescharacteristic
subgroupG/H
centerC2×C4#14519746
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2986C2
socleC22×C61#386
prime radicalC23×C61#123
cosocleC2×C42×C61C23
hypercenter#2986D61
hypocenterC61#9068
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2986

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
#214444142
#214442392
#214436552
C61×#29862
#906861