Finite Group Databasebeta

← #30594022

Subgroups — #30594022

Order 15616.

354 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 44 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#21460739C212yesmaximal, complemented
2#21445730C211yesmaximal, characteristic
3C22⋊#11758187—22no—
4C22×#11758222C411yescharacteristic
5C2×C22⋊#92418C2211yescharacteristic
6C2×#14519689—22no—
7C2×C22⋊C8×C61C411yescharacteristic
8C2×#11758187—42no—
9C2×#11758222—44no—
10C2×#11758222—41no—
11C2×#11758222—41no—
12C22×Dic122C811yescharacteristic
13C22×D244C811yescharacteristic
14C22×C22⋊D61—21no—
15C22×C4×D61—21no—
16C22×#92418D412yes—
17C22⋊#92418—41no—
18#14519689—44no—
19C23×C4×C61C2×C411yescharacteristic
20C22×C8×C61—21no—
21C22⋊C8×C61—41no—
22C24×C61M1611yescharacteristic
23C23×D61—21no—
24C22×C4×C61—21no—
25C22×C4×C61—21no—
26C22×C4×C61—42no—
27C22×C4×C61C22⋊C411yescharacteristic
28C22×C4×C61C2×C811yescharacteristic
29C2×C22⋊D61—42no—
30C2×C22⋊D61—42no—
31C2×C22⋊D61—42no—
32C22×Dic61—21no—
33#11758222—44no—
34#11758222—44no—
35#11758222—44no—
36#11758222—44no—
37C2×D244—41no—
38C2×D244—42no—
39C2×C4×D61—24no—
40C2×C4×D61—42no—
41C2×C4×D61—41no—
42C2×C4×D61—41no—
43C2×Dic122—41no—
44C2×Dic122—42no—
45C2×C8×C61—42no—
46C2×C8×C61—41no—
47C2×#92418—22no—
48C2×#92418—42no—
49#11758187—82no—
50C23×C61—21no—
51C23×C61—22no—
52C23×C61—41no—
53C23×C61—41no—
54C23×C61C22⋊C811yescharacteristic
55C22×D61—22no—
56C22×D61—41no—
57C22×D61—42no—
58C22×D61—41no—
59C22×D61—42no—
60C2×C4×C61—22no—
61C2×C4×C61—21no—
62C2×C4×C61—42no—
63C2×C4×C61—42no—
64C2×C4×C61—41no—
65C2×C4×C61#9911yescharacteristic
66C2×C4×C61#10011yescharacteristic
67C22⋊D61—48no—
68C2×Dic61—22no—
69C2×Dic61—41no—
70C2×Dic61—41no—
71D244—42no—
72D244—42no—
73C4×D61—44no—
74C4×D61—44no—
75Dic122—42no—
76Dic122—42no—
77C8×C61—81no—
78#92418—42no—
79#7058—611nomaximal, Sylow
80C22×C61—21no—
81C22×C61—21no—
82C22×C61—41no—
83C22×C61—41no—
84C22×C61—41no—
85C22×C61—82no—
86C22×C61#32311yescharacteristic
87C22×C61#35012yes—
88C2×D61—44no—
89C2×D61—42no—
90C2×D61—82no—
91C2×D61—81no—
92C2×D61—81no—
93C4×C61—21no—
94C4×C61—41no—
95C4×C61AΣL(1,𝔽16)12yes—
96Dic61—42no—
97#1780—611no—
98#1314—612no—
99C2×C61—22no—
100C2×C61—81no—
101C2×C61#131511yescharacteristic
102C2×C61#131611yescharacteristic
103C2×C61#132111yescharacteristic
104D61—82no—
105C22×#41—611no—
106C2×C22⋊C8—611no—
107C2×C22⋊C8—1222no—
108C2×C22⋊C8#692311yescharacteristic
109C22⋊C16—1222no—
110C61#705811yescharacteristic, complemented, Sylow
111C2×#41—2441no—
112C2×#41—2441no—
113C2×#41—2444no—
114C22×Q8—611no—
115C22×D4—611no—
116C22×D4—1221no—
117C23×C4—1221no—
118C23×C4C2×#692311yescharacteristic
119C22×C8—21no—
120C22×C8—612no—
121C2×C16—2442no—
122C22⋊C8—41no—
123C22⋊C8—2444no—
124C22⋊C8—2441no—
125C24—1221no—
126C24#1175821311yescharacteristic
127#41—2444no—
128#41—2444no—
129#41—2444no—
130#41—2444no—
131C2×Q8—2441no—
132C2×Q8—2442no—
133C2×D4—2441no—
134C2×D4—2442no—
135C2×D4—2442no—
136C2×D4—2442no—
137C2×D4—2442no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—42no—
141C22×C4—1224no—
142C22×C4—1221no—
143C22×C4—2442no—
144C22×C4—2441no—
145C22×C4—2441no—
146C22×C4D61⋊C811yescharacteristic
147C22×C4C22⋊#692311yescharacteristic
148C2×C8—42no—
149C2×C8—41no—
150C2×C8—1222no—
151C2×C8—2442no—
152C16—4882no—
153C23—21no—
154C23—22no—
155C23—41no—
156C23—41no—
157C23—1222no—
158C23—2441no—
159C23—2442no—
160C23—2441no—
161C23—2442no—
162C23#1451983411yescharacteristic
163Q8—2442no—
164Q8—2442no—
165D4—2442no—
166D4—2442no—
167D4—2448no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—1222no—
174C2×C4—2444no—
175C2×C4—2441no—
176C2×C4—2441no—
177C2×C4—2444no—
178C2×C4#1451983611yescharacteristic
179C2×C4#1451983711yescharacteristic
180C8—81no—
181C8—2442no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22—82no—
188C22—4882no—
189C22—4881no—
190C22—4881no—
191C22—2444no—
192C22—2442no—
193C22#1684060611yescharacteristic
194C22#1684066112yes—
195C4—21no—
196C4—41no—
197C4—2442no—
198C4#1684066312yes—
199C2—22no—
200C2—81no—
201C2—4882no—
202C2#2146074211yescharacteristic
203C2#2146074411yescharacteristic
204C2#2146075411yescharacteristic
subgroupG/H
centerC2×C4#14519836
commutatorC22×C4×C61C2×C8
FrattiniC23×C4C2×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61#323
prime radicalC22×#11758222C4
cosocleC2×C22⋊#92418C22
hypercenterC2×C22⋊C8#6923
hypocenterC61#7058
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #21460739C2semidirect
110. C61#7058semidirect

Maximal subgroups

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

subgroupindex
#214607392
#214457302
#705861