Finite Group Databasebeta

← #30605601

Subgroups — #30605601

Order 15616.

306 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 76 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#21462177C211yesmaximal, characteristic, complemented
2#21461368C211yesmaximal, characteristic, complemented
3#21460836C212yesmaximal, complemented
4#21460831C212yesmaximal, complemented
5#21456384C211yesmaximal, characteristic
6#16840778—21no—
7#16840683C2212yes—
8C22⋊#11758187—21no—
9#16840648—21no—
10#16840626—21no—
11#16840624C2212yes—
12#16840293—21no—
13#16840163C2211yescharacteristic
14#16840145C2211yescharacteristic
15#16840115—21no—
16#16840003C411yescharacteristic
17#16839989—21no—
18#16839856C411yescharacteristic
19#16839853—21no—
20D8×Dic61C411yescharacteristic
21C2×C8×Dic61C2211yescharacteristic
22C61×#466C411yescharacteristic
23C2×#11758187—22no—
24C4⋊#92420—22no—
25C22⋊#92420—41no—
26C4×#92420—41no—
27C2×Dic244C2×C411yescharacteristic
28C2×#11758200—21no—
29C22×#92418D411yescharacteristic
30#14519770—41no—
31#14519768—21no—
32#14519764—21no—
33#14519758—41no—
34#14519756—21no—
35#14519742—21no—
36D4×Dic61—21no—
37D4×Dic61—41no—
38#14519733—41no—
39C2×C4×Dic61D411yescharacteristic
40#14519711C2×C411yescharacteristic
41#14519708—21no—
42#14519702—21no—
43#14519700—21no—
44#14519698—21no—
45C8×Dic61C2×C411yescharacteristic
46C8×Dic61D411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61C2311yescharacteristic
49C2×D8×C61C2×C411yescharacteristic
50C22×C8×C61C2×C411yescharacteristic
51#121×C61—21no—
52#107×C61C2×C411yescharacteristic
53#102×C61—21no—
54C2×D4×C61—21no—
55C2×D4×C61—41no—
56C22×C4×C61C22⋊C411yescharacteristic
57C22×Dic61—41no—
58C22×Dic61D811yescharacteristic
59C22×Dic61SD1611yescharacteristic
60C2×Dic122—21no—
61C2×#92420—42no—
62D8×C61—41no—
63C2×C8×C61—41no—
64C2×C8×C61C22⋊C411yescharacteristic
65C2×C8×C61C22×C411yescharacteristic
66C4⋊C4×C61—21no—
67C22⋊C4×C61—41no—
68C22⋊Dic61—41no—
69C22⋊Dic61—41no—
70C22⋊Dic61—41no—
71C22⋊Dic61—41no—
72#11758200—42no—
73C4⋊Dic61—21no—
74C4⋊Dic61—41no—
75#11758196—41no—
76#11758196—41no—
77#11758196—41no—
78C4×Dic61—41no—
79C4×Dic61C22⋊C411yescharacteristic
80C4×Dic61D811yescharacteristic
81C4×Dic61SD1611yescharacteristic
82C4×Dic61C2×D411yescharacteristic
83C2×#92418—22no—
84C2×#92418C22⋊C411yescharacteristic
85C2×#92418C2×D411yescharacteristic
86Dic244—41no—
87#11758187—42no—
88C23×C61—41no—
89C23×C61#10211yescharacteristic
90D4×C61—41no—
91D4×C61—41no—
92D4×C61—82no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—41no—
96C2×C4×C61#10211yescharacteristic
97C2×C4×C61C2×C22⋊C411yescharacteristic
98C2×Dic61—22no—
99C2×Dic61—41no—
100C2×Dic61—41no—
101C2×Dic61—41no—
102C2×Dic61—82no—
103C2×Dic61#10211yescharacteristic
104C2×Dic61#10211yescharacteristic
105C2×Dic61C2×D811yescharacteristic
106C2×Dic61C2×SD1611yescharacteristic
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—21no—
116C22×C61—21no—
117C22×C61—21no—
118C22×C61—81no—
119C22×C61—81no—
120C22×C61—81no—
121C22×C61C2×#10211yescharacteristic
122C4×C61—21no—
123C4×C61—81no—
124C4×C61#41311yescharacteristic
125C4×C61#41611yescharacteristic
126Dic61—21no—
127Dic61—21no—
128Dic61—21no—
129Dic61—81no—
130Dic61—81no—
131Dic61#35912yes—
132#3168—611no—
133#2162—611no—
134#1564—611no—
135#1363—612no—
136#1360—612no—
137C2×C61—41no—
138C2×C61—161no—
139C2×C61#154011yescharacteristic
140C2×C61C2×#35911yescharacteristic
141C2×C61#214511yescharacteristic
142#529—1221no—
143#499—611no—
144#495—611no—
145#488—1221no—
146#467—611no—
147#466#692311yescharacteristic
148#465—1221no—
149C4×Q16—611no—
150C4×SD16—1221no—
151C4×D8—611no—
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×C8C2×#692311yescharacteristic
165#126—2441no—
166#125—1221no—
167#124—1221no—
168#123—2441no—
169C22⋊Q8—1221no—
170#121—21no—
171C4×Q8—1221no—
172C4×D4—1221no—
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—611no—
190C4×C8—2441no—
191C2×Q8—1221no—
192C2×D4—21no—
193C2×D4—41no—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—2441no—
197C22×C4C22⋊#692311yescharacteristic
198Q16—2441no—
199SD16—2442no—
200D8—41no—
201C2×C8—41no—
202C2×C8—611no—
203C2×C8—611no—
204C2×C8—1222no—
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—611no—
223C42—2441no—
224C16—2442no—
225C23—41no—
226C23#1451983911yescharacteristic
227Q8—2441no—
228Q8—2441no—
229D4—41no—
230D4—41no—
231D4—82no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—611no—
236C2×C4—611no—
237C2×C4—611no—
238C2×C4—611no—
239C2×C4—1222no—
240C2×C4—4882no—
241C2×C4—2441no—
242C2×C4—2441no—
243C2×C4—2441no—
244C2×C4#1451983911yescharacteristic
245C2×C4C2×C22⋊#692311yescharacteristic
246C8—21no—
247C8—21no—
248C8—612no—
249C8—1221no—
250C8—4882no—
251C22—21no—
252C22—21no—
253C22—21no—
254C22—81no—
255C22—81no—
256C22—81no—
257C22C2×#1451983911yescharacteristic
258C4—21no—
259C4—81no—
260C4—612no—
261C4—1221no—
262C4—1221no—
263C4—1221no—
264C4—4881no—
265C4—4881no—
266C4#1684074911yescharacteristic
267C4#1684075211yescharacteristic
268C2—41no—
269C2—161no—
270C2#2146131711yescharacteristic
271C2D61⋊#35911yescharacteristic
272C2#2146214011yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
Fitting, prime radicalC61×#466C4
socleC22×C61C2×#102
cosocleC8×Dic61C23
hypercenter#466#6923
hypocenterC61#11943
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #21462177C2semidirect
2. #21461368C2semidirect
3. #21460836C2semidirect
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
#214621772
#214613682
#214608362
#214608312
#214563842
#1194361