Finite Group Databasebeta

← #30605256

Subgroups — #30605256

Order 15616.

280 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 58 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#21462191C211yesmaximal, characteristic
2#21461749C211yesmaximal, characteristic
3#21460795C212yesmaximal
4#21460791C212yesmaximal
5#21456562C211yesmaximal, characteristic
6#16840685—21no—
7#16840659C2212yes—
8#16840655—21no—
9#16840644—21no—
10#16840633—21no—
11#16840631C2211yescharacteristic
12#16840630C2211yescharacteristic
13#16840317—21no—
14#16840160C411yescharacteristic, complemented
15#16840112—21no—
16#16840017—21no—
17#16840017C2212yes—
18#16839869—21no—
19#16839869C412yescomplemented
20C4×#11758189C2211yescharacteristic
21C61×#494C411yescharacteristic, complemented
22D61⋊M16—21no—
23#14519856—21no—
24#14519851—22no—
25C2×#11758189D411yescharacteristic
26C2×#11758189C2311yescharacteristic
27#14519777—21no—
28#14519768—41no—
29#14519757—41no—
30#14519753—22no—
31Q8×Dic61—22no—
32#14519742—41no—
33#14519735—41no—
34C42×D61D411yescharacteristic
35#14519709—21no—
36#14519709C2×C412yes—
37#14519701—22no—
38#14519701—22no—
39#14519687C2×C411yescharacteristic
40#14519687D411yescharacteristic
41C4×#92418D411yescharacteristic
42C2×Q16×C61—21no—
43C2×Q16×C61C2×C412yes—
44C4⋊Q8×C61—21no—
45C4×C8×C61C2×C411yescharacteristic
46C2×Q8×C61—22no—
47C2×C4×D61—21no—
48C2×C4×D61C2×D411yescharacteristic
49C2×Dic122—41no—
50C22⋊#6923—41no—
51#11758217—41no—
52C4⋊#6923—41no—
53C4×#6923—41no—
54#11758213—41no—
55D61⋊C8—41no—
56Q16×C61—42no—
57Q16×C61—42no—
58C2×C8×C61C22⋊C411yescharacteristic
59C2×C8×C61C22×C411yescharacteristic
60C4⋊C4×C61—41no—
61C4⋊C4×C61—41no—
62C42×C61C22⋊C411yescharacteristic
63#11758198—42no—
64C4⋊Dic61—22no—
65C4⋊Dic61—42no—
66C4⋊Dic61—41no—
67#11758196—42no—
68C4×Dic61—21no—
69C4×Dic61—42no—
70C4×Dic61C22⋊C411yescharacteristic
71C2×#92418C22⋊C411yescharacteristic
72C2×#92418C2×D411yescharacteristic
73#11758189—41no—
74#11758189—41no—
75#11758187—42no—
76C22×D61AGL(1,ℤ/8)11yescharacteristic
77C2×#6923—81no—
78Q8×C61—42no—
79Q8×C61—42no—
80C2×C4×C61—21no—
81C2×C4×C61—42no—
82C2×C4×C61C2×C22⋊C411yescharacteristic
83C2×Dic61—21no—
84C2×Dic61—42no—
85C2×Dic61AGL(1,ℤ/8)11yescharacteristic
86C4×D61—21no—
87C4×D61—21no—
88C4×D61—42no—
89Dic122—82no—
90#92420—81no—
91C8×C61—21no—
92C8×C61—21no—
93#92418—21no—
94#92418—21no—
95#11838—611nomaximal, Sylow
96C22×C61#41811yescharacteristic
97C2×D61—21no—
98C2×D61—41no—
99#6923—161no—
100C4×C61—22no—
101C4×C61—82no—
102C4×C61#41011yescharacteristic
103C4×C61#42111yescharacteristic
104Dic61—21no—
105Dic61—41no—
106Dic61—82no—
107#3185—611no—
108#2165—611no—
109#1841—611no—
110#1342—612no—
111#1340—612no—
112C2×C61—21no—
113C2×C61#151411yescharacteristic
114D61—41no—
115#533—1221no—
116#498—611no—
117#494#692311yescharacteristic, complemented
118#487—1221no—
119#470—612no—
120#470—1221no—
121#441—612no—
122#441—1221no—
123C4×M16—611no—
124#364—1221no—
125#349—612no—
126#347—1221no—
127#344—1221no—
128#339—1221no—
129#338—611no—
130H(3,ℤ/4)—611no—
131C61#1183811yescharacteristic, complemented, Sylow
132C2×Q16—21no—
133C2×Q16C2×#692312yes—
134C2×M16—611no—
135C2×M16—611no—
136C2×M16—1221no—
137C4⋊Q8—21no—
138C4⋊Q8—1221no—
139#125—2441no—
140C22⋊Q8—1222no—
141C22⋊Q8—2441no—
142C4×Q8—1222no—
143C4×Q8—2441no—
144#117—1221no—
145#117—2441no—
146C2×C42—611no—
147M32—1222no—
148#106—612no—
149#106—1221no—
150#103—1222no—
151#103—1222no—
152#97—611no—
153#97—611no—
154C4×C8—611no—
155C4×C8C2×#692311yescharacteristic
156C2×Q8—22no—
157C2×Q8—2441no—
158C22×C4—611no—
159C22×C4—1221no—
160Q16—42no—
161Q16—42no—
162M16—2441no—
163M16—2441no—
164M16—2441no—
165M16—2441no—
166C2×C8—611no—
167C2×C8—611no—
168C2×C8—2441no—
169C2×C8C22⋊#692311yescharacteristic
170C2×C8C22×#692311yescharacteristic
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—1222no—
174C4⋊C4—2441no—
175C4⋊C4—2442no—
176C4⋊C4—2442no—
177C4⋊C4—2441no—
178C22⋊C4—2442no—
179C22⋊C4—2441no—
180C42—611no—
181C42—1221no—
182C42—2442no—
183C42—2441no—
184C42C22⋊#692311yescharacteristic
185C16—2442no—
186C23—611no—
187Q8—42no—
188Q8—42no—
189Q8—4882no—
190C2×C4—21no—
191C2×C4—42no—
192C2×C4—611no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—4881no—
197C2×C4—2442no—
198C2×C4—2442no—
199C2×C4C2×C22⋊#692311yescharacteristic
200C8—21no—
201C8—21no—
202C8—1221no—
203C8—1221no—
204C8—4881no—
205C22—1221no—
206C22—2441no—
207C22#1684075411yescharacteristic
208C4—22no—
209C4—82no—
210C4—1221no—
211C4—9761no—
212C4—4882no—
213C4—2441no—
214C4#1684074211yescharacteristic
215C4#1684076011yescharacteristic
216C2—21no—
217C2—2441no—
218C2#2146123911yescharacteristic
subgroupG/H
centerC2#21461239
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#494C4
socleC2×C61#1514
prime radicalC22×D61AGL(1,ℤ/8)
cosocleC2×#11758189C23
hypercenter#494#6923
hypocenterC61#11838
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #494

Complements

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

NH ≅ G/Ntype
14. #16840160C4semidirect
19. #16839869C4semidirect
21. C61×#494C4semidirect
117. #494#6923semidirect
131. C61#11838semidirect

Maximal subgroups

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

subgroupindex
#214621912
#214617492
#214607952
#214607912
#214565622
#1183861