Finite Group Databasebeta

← #30606038

Subgroups — #30606038

Order 15616.

220 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 60 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#21461466C211yesmaximal, characteristic, complemented
2#21461417C211yesmaximal, characteristic
3#21460844C211yesmaximal, characteristic, complemented
4#21460779C211yesmaximal, characteristic, complemented
5#21460778C211yesmaximal, characteristic
6#21460738C211yesmaximal, characteristic, complemented
7#21447686C211yesmaximal, characteristic
8#16840813—21no—
9#16840790—21no—
10#16840651C2211yescharacteristic
11#16840623C2211yescharacteristic
12#16840623C2211yescharacteristic
13Q8⋊#92420—21no—
14#16840610—21no—
15#16840603C2211yescharacteristic
16C2×#14519720C411yescharacteristic
17Q16×Dic61C2211yescharacteristic
18#16839844C2211yescharacteristic
19#16839587C411yescharacteristic
20#16839564C411yescharacteristic
21#16839537C2211yescharacteristic
22C61×#358C411yescharacteristic
23C2×D61⋊C8—41no—
24C2×#11758187—21no—
25#14519844—41no—
26C4⋊#92420—21no—
27C4⋊#92420—21no—
28#14519834—41no—
29#14519832—41no—
30C4×#92420D411yescharacteristic
31C4×#92420D411yescharacteristic
32C2×D488C2×C411yescharacteristic
33Q8×Dic61—21no—
34#14519739—21no—
35#14519720—22no—
36C2×#11758185C2×C411yescharacteristic
37#14519711C2×C411yescharacteristic
38#14519701—21no—
39#14519697—21no—
40C8×Dic61C2311yescharacteristic
41C2×Q16×C61C2×C411yescharacteristic
42C2×C16×C61C2×C411yescharacteristic
43#107×C61C2×C411yescharacteristic
44C2×Q8×C61—21no—
45C2×D244—21no—
46C2×C4×D61—41no—
47C2×#92420—21no—
48C2×#92420—21no—
49C2×#92420—41no—
50C2×#92420—41no—
51D61⋊C8—82no—
52Q16×C61—21no—
53Q16×C61—21no—
54C2×C8×C61C22×C411yescharacteristic
55C4⋊C4×C61—21no—
56#11758198—41no—
57C4⋊Dic61—21no—
58C4⋊Dic61—41no—
59C4×Dic61—41no—
60C4×Dic61C2×D411yescharacteristic
61C2×#92418#4111yescharacteristic
62D488—21no—
63D488M1612yes—
64#11758187—22no—
65C16×C61—21no—
66#11758185—21no—
67C22×D61—41no—
68Q8×C61—41no—
69Q8×C61—41no—
70C2×C4×C61—41no—
71C2×C4×C61—41no—
72C2×C4×C61C4×D411yescharacteristic
73C2×Dic61—41no—
74C2×Dic61AGL(1,ℤ/8)11yescharacteristic
75C2×Dic61AGL(1,ℤ/8)11yescharacteristic
76D244—22no—
77D244—41no—
78C4×D61—81no—
79C4×D61—81no—
80#92420—41no—
81#92420—41no—
82#92420—81no—
83#92420—81no—
84C8×C61C2×M1611yescharacteristic
85C8×C61#13111yescharacteristic
86#92418—21no—
87#12077—611nomaximal, Sylow
88C22×C61#44211yescharacteristic
89C2×D61—42no—
90C2×D61—81no—
91C2×D61—81no—
92C4×C61—81no—
93C4×C61—81no—
94C4×C61#43511yescharacteristic
95C4×C61#44311yescharacteristic
96Dic61—21no—
97Dic61—21no—
98Dic61—81no—
99#2175—611no—
100#1593—611no—
101#1580—611no—
102#1368—611no—
103#1334—611no—
104#1333—611no—
105#1313—611no—
106C2×C61#158611yescharacteristic
107C2×C61#218011yescharacteristic
108C2×C61AGL(1,ℤ/16)11yescharacteristic
109D61—82no—
110C2×SD32—611no—
111#446—1221no—
112C4×Q16—611no—
113C4×D8—611no—
114C8×D4—1221no—
115#366—611no—
116#358#692311yescharacteristic
117#357—611no—
118#346—611no—
119#346—611no—
120#334—611no—
121#334—611no—
122Q8⋊C8—1221no—
123D4⋊C8—1221no—
124#322—611no—
125C61#1207711yescharacteristic, complemented, Sylow
126C2×Q16C2×#692311yescharacteristic
127C2×D8—611no—
128C22×C8—2441no—
129C4×Q8—1221no—
130C4×D4—1221no—
131SD32—1222no—
132C2×C16—611no—
133C2×C16—1221no—
134C2×C16C2×#692311yescharacteristic
135#107—611no—
136#107C2×#692311yescharacteristic
137C4⋊C8—1221no—
138C4⋊C8—1221no—
139C4⋊C8—2441no—
140#103—1221no—
141#102—1221no—
142C22⋊C8—2441no—
143#97—2441no—
144C4×C8—611no—
145C4×C8—611no—
146C4×C8—611no—
147C2×Q8—21no—
148C2×D4—1221no—
149C22×C4—2441no—
150Q16—21no—
151Q16—21no—
152D8—612no—
153D8—1221no—
154C2×C8—611no—
155C2×C8—1221no—
156C2×C8—1221no—
157C2×C8—4882no—
158C2×C8—2441no—
159C2×C8—2441no—
160C2×C8C22×#692311yescharacteristic
161C4⋊C4—21no—
162C4⋊C4—1221no—
163C4⋊C4—2441no—
164C22⋊C4—2441no—
165C42—611no—
166C42—2441no—
167C16—21no—
168C16—1222no—
169C16—1221no—
170C23—2441no—
171Q8—41no—
172Q8—41no—
173D4—1222no—
174D4—2441no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—611no—
178C2×C4—611no—
179C2×C4—4881no—
180C2×C4—4881no—
181C2×C4—2441no—
182C2×C4D4×#692311yescharacteristic
183C8—1221no—
184C8—4881no—
185C8—4881no—
186C8—2441no—
187C8—2441no—
188C8D61⋊M1611yescharacteristic
189C8#1451986411yescharacteristic
190C22—4881no—
191C22—4881no—
192C22—2442no—
193C22#1684080311yescharacteristic
194C4—81no—
195C4—81no—
196C4—1221no—
197C4—1221no—
198C4—4881no—
199C4#1684079411yescharacteristic
200C4#1684080511yescharacteristic
201C2—4882no—
202C2#2146144111yescharacteristic
203C2#2146222711yescharacteristic
204C2#2146223011yescharacteristic
subgroupG/H
centerC22#16840803
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#358C4
socleC22×C61#442
prime radicalC2×D488C2×C4
cosocleC8×Dic61C23
hypercenter#358#6923
hypocenterC61#12077
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
1. #21461466C2semidirect
3. #21460844C2semidirect
4. #21460779C2semidirect
6. #21460738C2semidirect
125. C61#12077semidirect

Maximal subgroups

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

subgroupindex
#214614662
#214614172
#214608442
#214607792
#214607782
#214607382
#214476862
#1207761