Finite Group Databasebeta

← #30605600

Subgroups — #30605600

Order 15616.

306 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 78 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#21462178C211yesmaximal, characteristic, complemented
2#21461369C211yesmaximal, characteristic, complemented
3#21460835C212yesmaximal, complemented
4#21460831C212yesmaximal, complemented
5#21456387C211yesmaximal, characteristic
6#16840781—21no—
7#16840683C2212yes—
8#16840657—21no—
9C4×#11758187—21no—
10#16840625—21no—
11#16840624C2212yes—
12#16840294—21no—
13#16840163C2211yescharacteristic
14#16840145C2211yescharacteristic
15#16840115—21no—
16#16840004C411yescharacteristic
17#16839995C411yescharacteristic
18#16839990—21no—
19C4×Dic244C411yescharacteristic
20C4×#11758200—21no—
21C4×C8×D61C2211yescharacteristic
22C4×D8×C61C411yescharacteristic
23C2×#11758187—22no—
24C4⋊#92420—22no—
25#14519834—41no—
26C4×#92420—41no—
27C2×Dic244C2×C411yescharacteristic
28C2×#11758200—21no—
29C2×C8×D61C2×C411yescharacteristic
30C2×C8×D61D411yescharacteristic
31#14519770—41no—
32#14519768—21no—
33#14519764—21no—
34#14519759—41no—
35#14519757—21no—
36#14519748—21no—
37C4×Dic122—21no—
38C4×C22⋊D61—41no—
39#14519736—41no—
40C42×D61D411yescharacteristic
41#14519711C2×C411yescharacteristic
42#14519708—21no—
43#14519702—21no—
44#14519700—21no—
45#14519698—21no—
46C4×#92418D411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61C2311yescharacteristic
49C2×D8×C61C2×C411yescharacteristic
50C4×D4×C61—21no—
51#107×C61C2×C411yescharacteristic
52#102×C61—21no—
53C4×C8×C61C2×C411yescharacteristic
54C2×D4×C61—21no—
55C22×C4×C61—41no—
56C2×C22⋊D61—41no—
57C2×C4×D61C22⋊C411yescharacteristic
58C2×C4×D61D811yescharacteristic
59C2×C4×D61SD1611yescharacteristic
60C2×Dic122—21no—
61C2×#92420—42no—
62D8×C61—41no—
63C2×C8×C61C22⋊C411yescharacteristic
64C2×C8×C61C22×C411yescharacteristic
65C4⋊C4×C61—21no—
66C22⋊C4×C61—41no—
67C42×C61C22⋊C411yescharacteristic
68C22⋊Dic61—41no—
69C22⋊Dic61—41no—
70C22⋊Dic61—41no—
71#11758200—42no—
72#11758198—41no—
73C4⋊Dic61—21no—
74C4⋊Dic61—41no—
75C4⋊Dic61—41no—
76#11758196—41no—
77#11758196—41no—
78C4×Dic61—41no—
79C4×Dic61D811yescharacteristic
80C4×Dic61SD1611yescharacteristic
81C4×Dic61C2×D411yescharacteristic
82C2×#92418C22⋊C411yescharacteristic
83C2×#92418C2×D411yescharacteristic
84Dic244—41no—
85C8×D61—22no—
86C8×D61—41no—
87#11758187—42no—
88C23×C61—41no—
89C22×D61#10211yescharacteristic
90D4×C61—41no—
91D4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—82no—
94C2×C4×C61#10211yescharacteristic
95C2×C4×C61#10211yescharacteristic
96C2×C4×C61C2×C22⋊C411yescharacteristic
97C22⋊D61—82no—
98C2×Dic61—41no—
99C2×Dic61—41no—
100C2×Dic61#10211yescharacteristic
101C2×Dic61C2×D811yescharacteristic
102C2×Dic61C2×SD1611yescharacteristic
103C4×D61—22no—
104C4×D61—21no—
105C4×D61—21no—
106C4×D61—41no—
107Dic122—41no—
108Dic122—41no—
109#92420—82no—
110C8×C61—21no—
111C8×C61—21no—
112#92418—21no—
113#92418#13512yes—
114#11943—611nomaximal, Sylow
115C22×C61—81no—
116C22×C61—81no—
117C22×C61—81no—
118C22×C61C2×#10211yescharacteristic
119C2×D61—21no—
120C2×D61—21no—
121C2×D61—21no—
122C4×C61—21no—
123C4×C61—81no—
124C4×C61#35912yes—
125C4×C61#41311yescharacteristic
126C4×C61#41611yescharacteristic
127Dic61—21no—
128Dic61—21no—
129Dic61—21no—
130Dic61—81no—
131Dic61—81no—
132#3168—611no—
133#2162—611no—
134#1564—611no—
135#1363—612no—
136#1360—612no—
137C2×C61—161no—
138C2×C61#154011yescharacteristic
139C2×C61C2×#35911yescharacteristic
140C2×C61#214511yescharacteristic
141D61—41no—
142#529—1221no—
143#499—611no—
144#495—611no—
145#488—1221no—
146#467—611no—
147#466—611no—
148#465—1221no—
149C4×Q16—611no—
150C4×SD16—1221no—
151C4×D8#692311yescharacteristic
152#431—1221no—
153C2×C4×C8—611no—
154C4⋊C16—612no—
155C22⋊C16—1221no—
156C4×C16—1221no—
157#335—1221no—
158#334—612no—
159C61#1194311yescharacteristic, complemented, Sylow
160C2×Q16—611no—
161C2×SD16—1221no—
162C2×D8C2×#692311yescharacteristic
163C22×C8—611no—
164C22×C8—611no—
165#126—2441no—
166#125—1221no—
167#124—1221no—
168#123—2441no—
169C22⋊Q8—1221no—
170#121—1221no—
171C4×Q8—1221no—
172C4×D4—21no—
173C4×D4—2441no—
174#117—2441no—
175C2×C42—611no—
176C2×C16—1222no—
177#107—611no—
178#107C2×#692311yescharacteristic
179#106—1221no—
180C4⋊C8—1222no—
181#103—1221no—
182#103—1221no—
183#102—21no—
184#102—1221no—
185C22⋊C8—2441no—
186C4×C8—611no—
187C4×C8—611no—
188C4×C8—611no—
189C4×C8—2441no—
190C4×C8C2×#692311yescharacteristic
191C2×Q8—1221no—
192C2×D4—21no—
193C2×D4—2441no—
194C22×C4—41no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—611no—
198Q16—2441no—
199SD16—2442no—
200D8—41no—
201C2×C8—611no—
202C2×C8—611no—
203C2×C8—1222no—
204C2×C8—2441no—
205C2×C8—2442no—
206C2×C8C22⋊#692311yescharacteristic
207C2×C8C22×#692311yescharacteristic
208C4⋊C4—21no—
209C4⋊C4—1221no—
210C4⋊C4—2441no—
211C4⋊C4—2441no—
212C4⋊C4—2441no—
213C4⋊C4—2441no—
214C22⋊C4—41no—
215C22⋊C4—2441no—
216C22⋊C4—2441no—
217C22⋊C4—2441no—
218C22⋊C4—2441no—
219C42—611no—
220C42—611no—
221C42—611no—
222C42—2441no—
223C42C22⋊#692311yescharacteristic
224C16—2442no—
225C23—41no—
226C23—611no—
227Q8—2441no—
228Q8—2441no—
229D4—41no—
230D4—41no—
231D4—4882no—
232C2×C4—41no—
233C2×C4—82no—
234C2×C4—611no—
235C2×C4—611no—
236C2×C4—611no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—1222no—
240C2×C4—2441no—
241C2×C4—2441no—
242C2×C4—2441no—
243C2×C4#1451983911yescharacteristic
244C2×C4#1451983911yescharacteristic
245C2×C4C2×C22⋊#692311yescharacteristic
246C8—21no—
247C8—21no—
248C8—612no—
249C8—1221no—
250C8—4882no—
251C22—81no—
252C22—81no—
253C22—81no—
254C22—1221no—
255C22—1221no—
256C22—1221no—
257C22C2×#1451983911yescharacteristic
258C4—21no—
259C4—81no—
260C4—1221no—
261C4—1221no—
262C4—1221no—
263C4—4881no—
264C4—4881no—
265C4#1684067612yes—
266C4#1684074811yescharacteristic
267C4#1684075211yescharacteristic
268C2—161no—
269C2—2441no—
270C2#2146131611yescharacteristic
271C2C2×#1684067611yescharacteristic
272C2#2146213911yescharacteristic
subgroupG/H
centerC2×C4#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC4×D8×C61C4
socleC22×C61C2×#102
prime radical#16839995C4
cosocleC8×Dic61C23
hypercenterC4×D8#6923
hypocenterC61#11943
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #21462178C2semidirect
2. #21461369C2semidirect
3. #21460835C2semidirect
4. #21460831C2semidirect
159. C61#11943semidirect

Maximal subgroups

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

subgroupindex
#214621782
#214613692
#214608352
#214608312
#214563872
#1194361