Finite Group Databasebeta

← #29577533

Subgroups — #29577533

Order 15616.

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

normal subgroups only

This group has 384 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#21456201C211yesmaximal, characteristic
2#21454925C211yesmaximal, characteristic
3#21444535C212yesmaximal
4#21443692C212yesmaximal
5C61×#1537C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7#16840132—22no—
8#16840114C414yes—
9#16839893—24no—
10#16839823—22no—
11#16839819C2212yes—
12#16839770—22no—
13C4×#11758194C2211yescharacteristic
14#16839507—24no—
15C61×#533C2211yescharacteristic
16C61×#432C2212yes—
17C61×#330—22no—
18C22×Dic122—21no—
19C2×#11758194—21no—
20#14519777—22no—
21#14519777—21no—
22#14519777C2×C412yes—
23C2×C4⋊Dic61—22no—
24C4⋊#92418—24no—
25C4⋊#92418D414yes—
26#14519700—28no—
27C22⋊#92418—22no—
28#14519688—22no—
29#14519688—21no—
30#14519688—22no—
31C4×#92418—22no—
32C4×#92418C2×C412yes—
33C4⋊Q8×C61C2×C412yes—
34#125×C61D412yes—
35C22⋊Q8×C61—22no—
36C4×Q8×C61—22no—
37#117×C61D412yes—
38C2×C42×C61C2311yescharacteristic
39C4⋊C8×C61—22no—
40C22⋊C8×C61—22no—
41#97×C61—22no—
42C2×Q8×C61—22no—
43C22×C4×C61C2×D411yescharacteristic
44C22×C4×C61#4112yes—
45C22×Dic61—41no—
46C2×Dic122—22no—
47C2×Dic122—44no—
48C2×Dic122—41no—
49C2×C8×C61—42no—
50C4⋊C4×C61—22no—
51C4⋊C4×C61—24no—
52C4⋊C4×C61C22⋊C414yes—
53C22⋊C4×C61—22no—
54C42×C61—22no—
55C42×C61C22×C411yescharacteristic
56C42×C61C2×D411yescharacteristic
57C42×C61C2×D412yes—
58C4⋊Dic61—24no—
59C4⋊Dic61—42no—
60#11758194—42no—
61C2×#92418—22no—
62C2×#92418—24no—
63C23×C61#12311yescharacteristic
64Q8×C61—82no—
65C2×C4×C61—22no—
66C2×C4×C61—24no—
67C2×C4×C61—42no—
68C2×C4×C61C2×C22⋊C411yescharacteristic
69C2×C4×C61C4×D412yes—
70C2×C4×C61#12011yescharacteristic
71C2×C4×C61#12112yes—
72C2×Dic61—42no—
73C2×Dic61—82no—
74Dic122—44no—
75Dic122—82no—
76C8×C61—82no—
77#92418—42no—
78#92418—44no—
79#9422—611nomaximal, Sylow
80C22×C61—21no—
81C22×C61—22no—
82C22×C61#38611yescharacteristic
83C4×C61—21no—
84C4×C61—22no—
85C4×C61—22no—
86C4×C61—44no—
87C4×C61#45412yes—
88Dic61—82no—
89#3139—611no—
90#2987—611no—
91#1556—612no—
92#1537D6111yescharacteristic
93#1291—612no—
94C2×C61—41no—
95C2×C61#188811yescharacteristic
96C2×C61#190212yes—
97#533C2×D6111yescharacteristic
98C2×C4⋊Q8—611no—
99#491—1222no—
100#487—614no—
101#446—1224no—
102#433—1222no—
103#432—612no—
104#432C2×D6112yes—
105#419—1222no—
106C4×M16—611no—
107#332—1224no—
108#330—22no—
109C61#942211yescharacteristic, complemented, Sylow
110C22×Q8—1221no—
111C2×M16—1221no—
112C4⋊Q8—612no—
113C4⋊Q8—1222no—
114C4⋊Q8—1221no—
115C4⋊Q8C4×D6112yes—
116#125C22⋊D6112yes—
117C22⋊Q8—22no—
118C4×Q8—22no—
119#117D24412yes—
120C2×C4⋊C4—1222no—
121C2×C42C22×D6111yescharacteristic
122C4⋊C8—22no—
123C4⋊C8—614no—
124C4⋊C8—1224no—
125#103—1228no—
126C22⋊C8—22no—
127C22⋊C8—1222no—
128#97—22no—
129#97—1222no—
130#97—1222no—
131#97—1221no—
132C4×C8—612no—
133C4×C8—1222no—
134C2×Q8—22no—
135C2×Q8—1222no—
136C2×Q8—2444no—
137C2×Q8—2441no—
138C22×C4—2441no—
139C22×C4C2×D24411yescharacteristic
140C22×C4#1175822412yes—
141M16—2442no—
142C2×C8—42no—
143C2×C8—1222no—
144C2×C8—1224no—
145C4⋊C4—22no—
146C4⋊C4—24no—
147C4⋊C4—1224no—
148C4⋊C4—2442no—
149C4⋊C4#1175819814yes—
150C22⋊C4—22no—
151C42—22no—
152C42C2×C4×D6111yescharacteristic
153C42D4×D6112yes—
154C42C2×C22⋊D6111yescharacteristic
155C23#1451976111yescharacteristic
156Q8—82no—
157Q8—4882no—
158Q8—2444no—
159C2×C4—22no—
160C2×C4—24no—
161C2×C4—42no—
162C2×C4—4882no—
163C2×C4—2442no—
164C2×C4C2×#1175819811yescharacteristic
165C2×C4#1451973712yes—
166C2×C4#1451974711yescharacteristic
167C2×C4#1451974912yes—
168C8—82no—
169C8—2442no—
170C8—2444no—
171C22—21no—
172C22—22no—
173C22#1683963911yescharacteristic
174C4—21no—
175C4—22no—
176C4—22no—
177C4—44no—
178C4—4882no—
179C4#1683993712yes—
180C2—41no—
181C2#2144622011yescharacteristic
182C2#2144629012yes—
subgroupG/H
centerC22#16839639
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1537C2
socleC22×C61#386
prime radicalC23×C61#123
cosocleC2×C42×C61C23
hypercenter#1537D61
hypocenterC61#9422
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1537

Complements

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

NH ≅ G/Ntype
109. C61#9422semidirect

Maximal subgroups

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

subgroupindex
#214562012
#214549252
#214445352
#214436922
C61×#15372
#942261