Finite Group Databasebeta

← #30605018

Subgroups — #30605018

Order 15616.

316 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 62 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#21462194C211yesmaximal, characteristic, complemented
2#21461540C211yesmaximal, characteristic, complemented
3#21460793C212yesmaximal, complemented
4#21460789C212yesmaximal, complemented
5#21456466C211yesmaximal, characteristic
6#16840725—21no—
7#16840684—21no—
8#16840659C2212yes—
9#16840654—21no—
10#16840631C2211yescharacteristic
11#16840630C2211yescharacteristic
12#16840629—21no—
13#16840366—21no—
14#16840164C411yescharacteristic, complemented
15#16840126—21no—
16#16840012C2212yes—
17#16839995—21no—
18#16839874C412yescomplemented
19D8×Dic61—21no—
20#16839716C2211yescharacteristic
21C61×#493C411yescharacteristic, complemented
22D61⋊M16—21no—
23#14519856—21no—
24#14519851—22no—
25#14519831—22no—
26C8×#6923—22no—
27C2×#11758189C2311yescharacteristic
28C2×C8×D61D411yescharacteristic
29#14519769—21no—
30#14519758—42no—
31#14519749—42no—
32#14519748—22no—
33D4×Dic61—22no—
34#14519734D411yescharacteristic
35#14519711—21no—
36#14519709C2×C412yes—
37#14519698—22no—
38#14519698—22no—
39#14519688D411yescharacteristic
40#14519687C2×C411yescharacteristic
41C8×Dic61D411yescharacteristic
42C2×D8×C61—21no—
43C2×D8×C61C2×C412yes—
44#127×C61—21no—
45C4×C8×C61C2×C411yescharacteristic
46C2×D4×C61—22no—
47C2×D4×C61—42no—
48C2×C22⋊D61—42no—
49C22×Dic61—42no—
50C2×C4×D61C2×D411yescharacteristic
51C22⋊#6923—41no—
52#11758217—41no—
53C4⋊#6923—41no—
54C4×#6923—22no—
55#11758213—41no—
56D61⋊C8—22no—
57D8×C61—42no—
58D8×C61—41no—
59D8×C61—41no—
60C2×C8×C61C22⋊C411yescharacteristic
61C2×C8×C61C22×C411yescharacteristic
62C42×C61C22⋊C411yescharacteristic
63C22⋊Dic61—42no—
64C22⋊Dic61—42no—
65#11758198—21no—
66C4⋊Dic61—22no—
67#11758196—21no—
68#11758196—42no—
69C4×Dic61C22⋊C411yescharacteristic
70C2×#92418C22⋊C411yescharacteristic
71C2×#92418C2×D411yescharacteristic
72#11758189—41no—
73C8×D61—21no—
74C8×D61—21no—
75#11758187—42no—
76C23×C61—42no—
77C22×D61AGL(1,ℤ/8)11yescharacteristic
78C2×#6923—42no—
79D4×C61—42no—
80D4×C61—42no—
81D4×C61—162no—
82C2×C4×C61—21no—
83C2×C4×C61C2×C22⋊C411yescharacteristic
84C22⋊D61—162no—
85C2×Dic61—21no—
86C2×Dic61—42no—
87C2×Dic61—162no—
88C2×Dic61AGL(1,ℤ/8)11yescharacteristic
89C4×D61—21no—
90C4×D61—21no—
91#92420—42no—
92C8×C61—21no—
93C8×C61#10411yescharacteristic
94C8×C61#10411yescharacteristic
95#92418—21no—
96#92418—21no—
97#11770—611nomaximal, Sylow
98C22×C61—82no—
99C22×C61—82no—
100C22×C61—82no—
101C22×C61#41811yescharacteristic
102C2×D61—21no—
103C2×D61—41no—
104#6923—82no—
105C4×C61—41no—
106C4×C61#41011yescharacteristic
107C4×C61C2×#10411yescharacteristic
108Dic61—21no—
109Dic61—41no—
110Dic61—82no—
111#3176—611no—
112#2166—611no—
113#1747—611no—
114#1341—612no—
115#1339—612no—
116C2×C61—21no—
117C2×C61—162no—
118C2×C61#150511yescharacteristic
119D61—41no—
120#540—1221no—
121#499—611no—
122#493#692311yescharacteristic, complemented
123#490—1221no—
124#469—612no—
125#466—1221no—
126#442—612no—
127C4×D8—1221no—
128#405—611no—
129#405—1221no—
130#364—1221no—
131#349—612no—
132#347—1221no—
133#338—611no—
134H(3,ℤ/4)—611no—
135H(3,ℤ/4)—1221no—
136C61#1177011yescharacteristic, complemented, Sylow
137C2×D8—21no—
138C2×D8C2×#692312yes—
139C2×M16—611no—
140C2×M16—1221no—
141C22×C8—611no—
142#127—21no—
143#125—1221no—
144#123—2442no—
145#121—1222no—
146#121—2442no—
147C4×D4—1222no—
148#117—611no—
149#117—1221no—
150M32—1222no—
151#107—1221no—
152#106—612no—
153#102—1222no—
154#102—1222no—
155#97—611no—
156#97—611no—
157#97—1222no—
158C4×C8—611no—
159C4×C8—1222no—
160C4×C8C2×#692311yescharacteristic
161C2×D4—22no—
162C2×D4—42no—
163C2×D4—2442no—
164C22×C4—611no—
165C22×C4—2442no—
166D8—42no—
167D8—41no—
168D8—41no—
169M16—2441no—
170M16—2441no—
171M16—2441no—
172C2×C8—611no—
173C2×C8—611no—
174C2×C8—1221no—
175C2×C8—1221no—
176C2×C8—1222no—
177C2×C8C22⋊#692311yescharacteristic
178C2×C8C22×#692311yescharacteristic
179C4⋊C4—1221no—
180C4⋊C4—1222no—
181C4⋊C4—2442no—
182C4⋊C4—2441no—
183C22⋊C4—1221no—
184C22⋊C4—2442no—
185C22⋊C4—2442no—
186C22⋊C4—2441no—
187C42—611no—
188C42—1222no—
189C42C22⋊#692311yescharacteristic
190C16—2442no—
191C23—42no—
192C23—611no—
193D4—42no—
194D4—42no—
195D4—162no—
196D4—9762no—
197C2×C4—21no—
198C2×C4—611no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—9762no—
203C2×C4—2442no—
204C2×C4—2442no—
205C2×C4C2×C22⋊#692311yescharacteristic
206C8—21no—
207C8—1221no—
208C8—1221no—
209C8—2442no—
210C8#1451984111yescharacteristic
211C8#1451984111yescharacteristic
212C22—82no—
213C22—82no—
214C22—82no—
215C22—1221no—
216C22—2441no—
217C22#1684075411yescharacteristic
218C4—41no—
219C4—1221no—
220C4—4882no—
221C4—4882no—
222C4—2441no—
223C4#1684074211yescharacteristic
224C4C2×#1451984111yescharacteristic
225C2—21no—
226C2—162no—
227C2—2441no—
228C2#2146120811yescharacteristic
subgroupG/H
centerC2#21461208
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#493C4
socleC2×C61#1505
prime radical#21456466C2
cosocleC2×#11758189C23
hypercenter#493#6923
hypocenterC61#11770
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #21462194C2semidirect
2. #21461540C2semidirect
3. #21460793C2semidirect
4. #21460789C2semidirect
14. #16840164C4semidirect
18. #16839874C4semidirect
21. C61×#493C4semidirect
122. #493#6923semidirect
136. C61#11770semidirect

Maximal subgroups

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

subgroupindex
#214621942
#214615402
#214607932
#214607892
#214564662
#1177061