Finite Group Databasebeta

← #30605254

Subgroups — #30605254

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#21460794C212yesmaximal, complemented
4#21460790C212yesmaximal, complemented
5#21456558C211yesmaximal, characteristic
6#16840685—21no—
7#16840659C2212yes—
8#16840655—21no—
9#16840644—21no—
10#16840633—21no—
11#16840631C2211yescharacteristic
12#16840630C2211yescharacteristic
13#16840313—21no—
14#16840139C411yescharacteristic, complemented
15#16840110—21no—
16#16840016—21no—
17#16840016C2212yes—
18#16839873—21no—
19#16839873C412yescomplemented
20C4×#11758189C2211yescharacteristic
21C61×#498C411yescharacteristic, complemented
22D61⋊M16—21no—
23#14519856—21no—
24#14519851—22no—
25C2×#11758226—41no—
26C2×D488—21no—
27C2×D488C2×C412yes—
28C2×#11758189D411yescharacteristic
29C2×#11758189C2311yescharacteristic
30#14519774—21no—
31#14519766—41no—
32#14519752—22no—
33#14519752—41no—
34#14519739—22no—
35#14519739—41no—
36C42×D61D411yescharacteristic
37#14519697—22no—
38#14519697—22no—
39#14519687C2×C411yescharacteristic
40#14519687D411yescharacteristic
41C4×#92418D411yescharacteristic
42C4⋊Q8×C61—21no—
43#106×C61—21no—
44#106×C61C2×C412yes—
45C4×C8×C61C2×C411yescharacteristic
46C2×Q8×C61—41no—
47#11758226—84no—
48C2×D244—22no—
49C2×D244—41no—
50C2×D244—41no—
51C2×D244—42no—
52C2×C4×D61—21no—
53C2×C4×D61—42no—
54C2×C4×D61C2×D411yescharacteristic
55C22⋊#6923—41no—
56#11758217—41no—
57C4⋊#6923—41no—
58C4×#6923—41no—
59#11758213—41no—
60D61⋊C8—41no—
61C2×C8×C61C22⋊C411yescharacteristic
62C2×C8×C61C22×C411yescharacteristic
63C4⋊C4×C61—22no—
64C4⋊C4×C61—41no—
65C42×C61C22⋊C411yescharacteristic
66#11758198—42no—
67#11758198—42no—
68C4×Dic61—21no—
69C4×Dic61C22⋊C411yescharacteristic
70C2×#92418C22⋊C411yescharacteristic
71C2×#92418C2×D411yescharacteristic
72D488—42no—
73D488—42no—
74#11758189—41no—
75#11758189—41no—
76#11758187—42no—
77C22×D61—42no—
78C22×D61AGL(1,ℤ/8)11yescharacteristic
79C2×#6923—81no—
80Q8×C61—82no—
81C2×C4×C61—21no—
82C2×C4×C61—42no—
83C2×C4×C61C2×C22⋊C411yescharacteristic
84C2×Dic61—21no—
85C2×Dic61AGL(1,ℤ/8)11yescharacteristic
86D244—42no—
87D244—42no—
88D244—82no—
89D244—82no—
90D244—84no—
91C4×D61—21no—
92C4×D61—21no—
93C4×D61—42no—
94C4×D61—84no—
95#92420—81no—
96C8×C61—21no—
97C8×C61—21no—
98#92418—21no—
99#92418—21no—
100#11837—611nomaximal, Sylow
101C22×C61#41811yescharacteristic
102C2×D61—21no—
103C2×D61—41no—
104C2×D61—82no—
105C2×D61—82no—
106C2×D61—82no—
107#6923—161no—
108C4×C61—22no—
109C4×C61—82no—
110C4×C61#41011yescharacteristic
111C4×C61#42111yescharacteristic
112Dic61—21no—
113Dic61—41no—
114#3184—611no—
115#2165—611no—
116#1841—611no—
117#1341—612no—
118#1339—612no—
119C2×C61—21no—
120C2×C61#151411yescharacteristic
121D61—41no—
122D61—162no—
123#532—1221no—
124#498#692311yescharacteristic, complemented
125#493—611no—
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—612no—
142C2×D8—1221no—
143C2×M16—611no—
144C2×M16—611no—
145C2×M16—1221no—
146C4⋊Q8—21no—
147#127—1221no—
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—21no—
157#106C2×#692312yes—
158#102—1222no—
159#102—1222no—
160#97—611no—
161#97—611no—
162C4×C8—611no—
163C4×C8C2×#692311yescharacteristic
164#41—4884no—
165C2×Q8—41no—
166C2×D4—1222no—
167C2×D4—2441no—
168C2×D4—2441no—
169C2×D4—2442no—
170C22×C4—611no—
171C22×C4—1221no—
172C22×C4—2442no—
173D8—2442no—
174D8—2442no—
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—22no—
185C4⋊C4—41no—
186C4⋊C4—2441no—
187C22⋊C4—2442no—
188C22⋊C4—2442no—
189C22⋊C4—2441no—
190C42—611no—
191C42—1221no—
192C42—2441no—
193C42C22⋊#692311yescharacteristic
194C16—2442no—
195C23—611no—
196C23—2442no—
197Q8—82no—
198D4—4882no—
199D4—4882no—
200D4—4884no—
201D4—2442no—
202D4—2442no—
203C2×C4—21no—
204C2×C4—42no—
205C2×C4—611no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—1221no—
209C2×C4—4884no—
210C2×C4—4881no—
211C2×C4—2442no—
212C2×C4C2×C22⋊#692311yescharacteristic
213C8—21no—
214C8—21no—
215C8—1221no—
216C8—1221no—
217C8—4881no—
218C22—1221no—
219C22—4882no—
220C22—4882no—
221C22—4882no—
222C22—2441no—
223C22#1684075411yescharacteristic
224C4—22no—
225C4—82no—
226C4—1221no—
227C4—9761no—
228C4—2441no—
229C4#1684074311yescharacteristic
230C4#1684076111yescharacteristic
231C2—21no—
232C2—9762no—
233C2—2441no—
234C2#2146124011yescharacteristic
subgroupG/H
centerC2#21461240
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#498C4
socleC2×C61#1514
prime radical#21456558C2
cosocleC2×#11758189C23
hypercenter#498#6923
hypocenterC61#11837
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #498

Complements

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

NH ≅ G/Ntype
1. #21462191C2semidirect
2. #21461749C2semidirect
3. #21460794C2semidirect
4. #21460790C2semidirect
14. #16840139C4semidirect
19. #16839873C4semidirect
21. C61×#498C4semidirect
124. #498#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
#214607942
#214607902
#214565582
#1183761