Finite Group Databasebeta

← #30605253

Subgroups — #30605253

Order 15616.

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

normal subgroups only

This group has 324 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, complemented
2#21461749C211yesmaximal, characteristic, complemented
3#21460793C212yesmaximal, complemented
4#21460789C212yesmaximal, complemented
5#21456555C211yesmaximal, characteristic
6#16840685—21no—
7#16840659C2212yes—
8#16840655—21no—
9#16840644—21no—
10#16840633—21no—
11#16840631C2211yescharacteristic
12#16840630C2211yescharacteristic
13#16840310—21no—
14#16840160C411yescharacteristic, complemented
15#16840108—21no—
16#16840012—21no—
17#16840012C2212yes—
18#16839874—21no—
19#16839874C412yescomplemented
20C4×#11758189C2211yescharacteristic
21C61×#493C411yescharacteristic, complemented
22D61⋊M16—21no—
23#14519856—21no—
24#14519851—22no—
25C2×#11758224—41no—
26C2×#11758189D411yescharacteristic
27C2×#11758189C2311yescharacteristic
28#14519777—21no—
29#14519764—41no—
30#14519748—22no—
31#14519748—41no—
32D4×Dic61—22no—
33D4×Dic61—41no—
34C42×D61D411yescharacteristic
35#14519709—21no—
36#14519709C2×C412yes—
37#14519698—22no—
38#14519698—22no—
39#14519687C2×C411yescharacteristic
40#14519687D411yescharacteristic
41C4×#92418D411yescharacteristic
42C2×D8×C61—21no—
43C2×D8×C61C2×C412yes—
44#127×C61—21no—
45C4×C8×C61C2×C411yescharacteristic
46C2×D4×C61—22no—
47C2×D4×C61—41no—
48C2×D4×C61—41no—
49C2×C22⋊D61—42no—
50C22×Dic61—42no—
51#11758224—84no—
52C2×C4×D61—21no—
53C2×C4×D61C2×D411yescharacteristic
54C2×Dic122—41no—
55C22⋊#6923—41no—
56#11758217—41no—
57C4⋊#6923—41no—
58C4×#6923—41no—
59#11758213—41no—
60D61⋊C8—41no—
61D8×C61—42no—
62D8×C61—42no—
63C2×C8×C61C22⋊C411yescharacteristic
64C2×C8×C61C22×C411yescharacteristic
65C42×C61C22⋊C411yescharacteristic
66C22⋊Dic61—42no—
67C22⋊Dic61—42no—
68C4⋊Dic61—22no—
69C4⋊Dic61—41no—
70C4×Dic61—21no—
71C4×Dic61C22⋊C411yescharacteristic
72C2×#92418C22⋊C411yescharacteristic
73C2×#92418C2×D411yescharacteristic
74#11758189—41no—
75#11758189—41no—
76#11758187—42no—
77C23×C61—42no—
78C22×D61AGL(1,ℤ/8)11yescharacteristic
79C2×#6923—81no—
80D4×C61—42no—
81D4×C61—42no—
82D4×C61—82no—
83D4×C61—82no—
84C2×C4×C61—21no—
85C2×C4×C61C2×C22⋊C411yescharacteristic
86C22⋊D61—84no—
87C2×Dic61—21no—
88C2×Dic61—42no—
89C2×Dic61—84no—
90C2×Dic61AGL(1,ℤ/8)11yescharacteristic
91C4×D61—21no—
92C4×D61—21no—
93C4×D61—42no—
94Dic122—82no—
95#92420—81no—
96C8×C61—21no—
97C8×C61—21no—
98#92418—21no—
99#92418—21no—
100#11837—611nomaximal, Sylow
101C22×C61—82no—
102C22×C61—82no—
103C22×C61—82no—
104C22×C61#41811yescharacteristic
105C2×D61—21no—
106C2×D61—41no—
107#6923—161no—
108C4×C61—22no—
109C4×C61#41011yescharacteristic
110C4×C61#42111yescharacteristic
111Dic61—21no—
112Dic61—41no—
113Dic61—82no—
114#3184—611no—
115#2165—611no—
116#1841—611no—
117#1341—612no—
118#1339—612no—
119C2×C61—21no—
120C2×C61—162no—
121C2×C61#151411yescharacteristic
122D61—41no—
123#532—1221no—
124#498—611no—
125#493#692311yescharacteristic, complemented
126#486—1221no—
127#469—612no—
128#469—1221no—
129#442—612no—
130#442—1221no—
131C4×M16—611no—
132#364—1221no—
133#349—612no—
134#347—1221no—
135#344—1221no—
136#339—1221no—
137#338—611no—
138H(3,ℤ/4)—611no—
139C61#1183711yescharacteristic, complemented, Sylow
140C2×#41—2441no—
141C2×D8—21no—
142C2×D8C2×#692312yes—
143C2×M16—611no—
144C2×M16—611no—
145C2×M16—1221no—
146C4⋊Q8—1221no—
147#127—21no—
148#124—2441no—
149#121—1222no—
150#121—2441no—
151C4×D4—1222no—
152C4×D4—2441no—
153#117—1221no—
154C2×C42—611no—
155M32—1222no—
156#106—612no—
157#106—1221no—
158#102—1222no—
159#102—1222no—
160#97—611no—
161#97—611no—
162C4×C8—611no—
163C4×C8C2×#692311yescharacteristic
164#41—4884no—
165C2×Q8—2441no—
166C2×D4—22no—
167C2×D4—41no—
168C2×D4—41no—
169C2×D4—2442no—
170C22×C4—611no—
171C22×C4—1221no—
172C22×C4—2442no—
173D8—42no—
174D8—42no—
175M16—2441no—
176M16—2441no—
177M16—2441no—
178M16—2441no—
179C2×C8—611no—
180C2×C8—611no—
181C2×C8—2441no—
182C2×C8C22⋊#692311yescharacteristic
183C2×C8C22×#692311yescharacteristic
184C4⋊C4—1222no—
185C4⋊C4—2441no—
186C4⋊C4—2441no—
187C22⋊C4—2442no—
188C22⋊C4—2442no—
189C22⋊C4—2441no—
190C42—611no—
191C42—1221no—
192C42—2441no—
193C42C22⋊#692311yescharacteristic
194C16—2442no—
195C23—42no—
196C23—611no—
197Q8—4882no—
198D4—42no—
199D4—42no—
200D4—82no—
201D4—82no—
202D4—4884no—
203C2×C4—21no—
204C2×C4—611no—
205C2×C4—1221no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—4881no—
209C2×C4—4884no—
210C2×C4—2442no—
211C2×C4—2442no—
212C2×C4C2×C22⋊#692311yescharacteristic
213C8—21no—
214C8—21no—
215C8—1221no—
216C8—1221no—
217C8—4881no—
218C22—82no—
219C22—82no—
220C22—82no—
221C22—1221no—
222C22—2441no—
223C22#1684075411yescharacteristic
224C4—22no—
225C4—1221no—
226C4—9761no—
227C4—4882no—
228C4—2441no—
229C4#1684074211yescharacteristic
230C4#1684076011yescharacteristic
231C2—21no—
232C2—162no—
233C2—2441no—
234C2#2146123911yescharacteristic
subgroupG/H
centerC2#21461239
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#493C4
socleC2×C61#1514
prime radical#21456555C2
cosocleC2×#11758189C23
hypercenter#493#6923
hypocenterC61#11837
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. #21462191C2semidirect
2. #21461749C2semidirect
3. #21460793C2semidirect
4. #21460789C2semidirect
14. #16840160C4semidirect
19. #16839874C4semidirect
21. C61×#493C4semidirect
125. #493#6923semidirect
139. C61#11837semidirect

Maximal subgroups

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

subgroupindex
#214621912
#214617492
#214607932
#214607892
#214565552
#1183761