Finite Group Databasebeta

← #29567393

Subgroups — #29567393

Order 15616.

204 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 43 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#21446638C211yesmaximal, characteristic
2#21443763C211yesmaximal, characteristic
3C61×#1324C211yesmaximal, characteristic
4C2×#14519777C411yescharacteristic
5C2×#14519700—21no—
6C2×#14519700—21no—
7C2×#14519688C411yescharacteristic
8#16839488—21no—
9C61×#382C2211yescharacteristic
10C61×#324—21no—
11C22×Dic122—21no—
12C22×#92418—21no—
13#14519777—21no—
14#14519777—41no—
15#14519777C812yescomplemented
16C2×C4⋊Dic61—41no—
17#14519700—42no—
18#14519700—42no—
19C22⋊#92418—41no—
20#14519688—41no—
21C2×C4⋊C4×C61D411yescharacteristic
22C2×C4⋊C4×C61D411yescharacteristic
23C2×C42×C61C2×C411yescharacteristic
24C22⋊C8×C61—41no—
25#95×C61—41no—
26C22×C4×C61—21no—
27C22×C4×C61—21no—
28C22×C4×C61—21no—
29C22×C4×C61C22⋊C411yescharacteristic
30C22×Dic61—41no—
31C2×Dic122—22no—
32C2×Dic122—41no—
33C2×Dic122—41no—
34C2×Dic122—41no—
35C2×Dic122—41no—
36C2×Dic122—41no—
37C2×C8×C61—81no—
38C4⋊C4×C61—41no—
39C4⋊C4×C61—41no—
40C42×C61—21no—
41C42×C61C2×C811yescharacteristic
42C42×C61M1611yescharacteristic
43C4⋊Dic61—42no—
44C4⋊Dic61—42no—
45C2×#92418—22no—
46C2×#92418—41no—
47C2×#92418—41no—
48C2×#92418—81no—
49C23×C61#9911yescharacteristic
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61—41no—
58C2×C4×C61—81no—
59C2×C4×C61—81no—
60C2×C4×C61C22⋊C811yescharacteristic
61C2×C4×C61#10011yescharacteristic
62C2×Dic61—42no—
63C2×Dic61—81no—
64C2×Dic61—81no—
65Dic122—42no—
66Dic122—42no—
67Dic122—81no—
68Dic122—81no—
69C8×C61—161no—
70#92418—42no—
71#92418—161no—
72#7353—611nomaximal, Sylow
73C22×C61—21no—
74C22×C61—21no—
75C22×C61#32311yescharacteristic
76C22×C61#35311yescharacteristic
77C22×C61#35511yescharacteristic
78C4×C61—21no—
79C4×C61—21no—
80C4×C61—41no—
81C4×C61—41no—
82C4×C61—81no—
83C4×C61—81no—
84Dic61—82no—
85#1960—611no—
86#1324—611no—
87#1324D6111yescharacteristic
88C2×C61—21no—
89C2×C61—21no—
90C2×C61#131811yescharacteristic
91C2×C61#140711yescharacteristic
92C2×C61#140711yescharacteristic
93C2×C4⋊Q8—611no—
94C2×#103—1221no—
95C2×#103—1221no—
96C2×#97—611no—
97#382C2×D6111yescharacteristic
98#324—21no—
99#324—1221no—
100C61#735311yescharacteristic, complemented, Sylow
101C22×Q8—1221no—
102C22×C8—1221no—
103C4⋊Q8—612no—
104C4⋊Q8—1221no—
105C4⋊Q8—2441no—
106C2×C4⋊C4—2441no—
107C2×C4⋊C4D24411yescharacteristic
108C2×C4⋊C4C22⋊D6111yescharacteristic
109C2×C42C4×D6111yescharacteristic
110#103—2442no—
111#103—2442no—
112C22⋊C8—41no—
113C22⋊C8—2441no—
114#97—2441no—
115#95—41no—
116C2×Q8—1222no—
117C2×Q8—2441no—
118C2×Q8—2441no—
119C2×Q8—2441no—
120C2×Q8—2441no—
121C2×Q8—2441no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—2441no—
126C22×C4#1175819811yescharacteristic
127C2×C8—81no—
128C2×C8—1222no—
129C2×C8—4881no—
130C2×C8—2441no—
131C2×C8—2441no—
132C4⋊C4—41no—
133C4⋊C4—41no—
134C4⋊C4—2442no—
135C4⋊C4—2442no—
136C42—21no—
137C42C8×D6111yescharacteristic
138C42#1175818911yescharacteristic
139C23#1451969111yescharacteristic
140Q8—4881no—
141Q8—4881no—
142Q8—2442no—
143Q8—2442no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—81no—
153C2×C4—81no—
154C2×C4—4881no—
155C2×C4—4881no—
156C2×C4—2442no—
157C2×C4#1451968911yescharacteristic
158C2×C4#1451969311yescharacteristic
159C8—161no—
160C8—9761no—
161C8—2442no—
162C22—21no—
163C22—21no—
164C22#1683948511yescharacteristic
165C22#1683955411yescharacteristic
166C22#1683955811yescharacteristic
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—81no—
173C4—4882no—
174C2—21no—
175C2—21no—
176C2#2144375011yescharacteristic
177C2#2144397811yescharacteristic
178C2#2144398011yescharacteristic
subgroupG/H
centerC22#16839554
commutatorC42×C61C2×C8
Frattini#382C2×D61
FittingC61×#1324C2
socleC22×C61#353
prime radicalC23×C61#99
cosocleC61×#382C22
hypercenter#1324D61
hypocenterC61#7353
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #382 ◁ #1324

Complements

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

NH ≅ G/Ntype
15. #14519777C8semidirect
100. C61#7353semidirect

Maximal subgroups

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

subgroupindex
#214466382
#214437632
C61×#13242
#735361