Finite Group Databasebeta

← #30604676

Subgroups — #30604676

Order 15616.

330 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 80 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#21462025C211yesmaximal, characteristic, complemented
2#21461376C211yesmaximal, characteristic, complemented
3#21460776C212yesmaximal, complemented
4#21460773C212yesmaximal, complemented
5#21456384C211yesmaximal, characteristic
6C2×#14519851—21no—
7#16840765—21no—
8#16840651—21no—
9#16840648C2212yes—
10#16840626—21no—
11#16840625C2212yes—
12#16840293—21no—
13#16840163C411yescharacteristic
14#16840145C411yescharacteristic
15#16840115—21no—
16#16840003C411yescharacteristic
17#16839989—21no—
18#16839856C2211yescharacteristic
19#16839853—21no—
20D8×Dic61C2211yescharacteristic
21C2×C8×Dic61C2211yescharacteristic
22C61×#466C411yescharacteristic
23C2×#11758217—41no—
24#14519851—24no—
25C2×#11758187—22no—
26#14519844—41no—
27C4⋊#92420—22no—
28C2×Dic244C2×C411yescharacteristic
29C2×#11758200—21no—
30C22×#92418D411yescharacteristic
31#14519770—41no—
32#14519768—21no—
33#14519764—21no—
34#14519758—41no—
35#14519756—21no—
36#14519742—21no—
37D4×Dic61—21no—
38D4×Dic61—41no—
39#14519733—41no—
40C2×C4×Dic61D411yescharacteristic
41#14519711C2×C411yescharacteristic
42#14519708—21no—
43#14519702—21no—
44#14519700—21no—
45#14519698—21no—
46C8×Dic61C2×C411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61C2311yescharacteristic
50C2×D8×C61C2×C411yescharacteristic
51C22×C8×C61C2×C411yescharacteristic
52#121×C61—21no—
53#107×C61C2×C411yescharacteristic
54#102×C61—21no—
55C2×D4×C61—21no—
56C2×D4×C61—41no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×Dic61—41no—
59C22×Dic61D811yescharacteristic
60C22×Dic61SD1611yescharacteristic
61C2×Dic122—21no—
62#11758217—82no—
63C2×#92420—42no—
64D8×C61—22no—
65C2×C8×C61—22no—
66C2×C8×C61C22⋊C411yescharacteristic
67C2×C8×C61C22×C411yescharacteristic
68C4⋊C4×C61—21no—
69C22⋊C4×C61—41no—
70C22⋊Dic61—41no—
71C22⋊Dic61—41no—
72C22⋊Dic61—41no—
73C22⋊Dic61—41no—
74#11758200—42no—
75C4⋊Dic61—21no—
76C4⋊Dic61—41no—
77#11758196—41no—
78#11758196—41no—
79#11758196—41no—
80C4×Dic61—41no—
81C4×Dic61C22⋊C411yescharacteristic
82C4×Dic61D811yescharacteristic
83C4×Dic61SD1611yescharacteristic
84C4×Dic61C2×D411yescharacteristic
85C2×#92418—22no—
86C2×#92418C22⋊C411yescharacteristic
87C2×#92418C2×D411yescharacteristic
88Dic244—22no—
89#11758187—24no—
90C23×C61—41no—
91C23×C61#10211yescharacteristic
92D4×C61—41no—
93D4×C61—41no—
94D4×C61—82no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—41no—
98C2×C4×C61#10211yescharacteristic
99C2×C4×C61C2×C22⋊C411yescharacteristic
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61—81no—
106C2×Dic61—81no—
107C2×Dic61#10211yescharacteristic
108C2×Dic61#10211yescharacteristic
109C2×Dic61C2×D811yescharacteristic
110C2×Dic61C2×SD1611yescharacteristic
111Dic122—41no—
112Dic122—41no—
113#92420—82no—
114C8×C61—21no—
115C8×C61#13112yes—
116#92418—21no—
117#92418#10412yes—
118#11674—611nomaximal, Sylow
119C22×C61—21no—
120C22×C61—21no—
121C22×C61—21no—
122C22×C61—81no—
123C22×C61—81no—
124C22×C61—81no—
125C22×C61C2×#10211yescharacteristic
126C4×C61—21no—
127C4×C61—81no—
128C4×C61#40811yescharacteristic
129C4×C61C2×#10411yescharacteristic
130Dic61—21no—
131Dic61—21no—
132Dic61—21no—
133Dic61—81no—
134Dic61—81no—
135Dic61#50911yescharacteristic
136Dic61#51011yescharacteristic
137#3168—611no—
138C4×M32—611no—
139#1567—611no—
140#1332—612no—
141#1331—612no—
142C2×C61—41no—
143C2×C61—161no—
144C2×C61#149211yescharacteristic
145C2×C61#213911yescharacteristic
146C2×C61#214311yescharacteristic
147#529—1221no—
148C2×M32—1221no—
149#499—611no—
150#495—611no—
151#488—1221no—
152#467—611no—
153#466#692311yescharacteristic
154#465—1221no—
155C4×Q16—611no—
156C4×SD16—1221no—
157C4×D8—611no—
158#423—1221no—
159C2×C4×C8—611no—
160#346—1221no—
161C4×C16—612no—
162#335—612no—
163#335—1221no—
164C61#1167411yescharacteristic, complemented, Sylow
165C2×Q16—611no—
166C2×SD16—1221no—
167C2×D8C2×#692311yescharacteristic
168C2×M16—2441no—
169C22×C8—611no—
170C22×C8C2×#692311yescharacteristic
171#126—2441no—
172#125—1221no—
173#124—1221no—
174#123—2441no—
175C22⋊Q8—1221no—
176#121—21no—
177C4×Q8—1221no—
178C4×D4—1221no—
179C4×D4—2441no—
180#117—2441no—
181C2×C42—611no—
182M32—1224no—
183C2×C16—1222no—
184#107—611no—
185#107C2×#692311yescharacteristic
186#106—1221no—
187C4⋊C8—1222no—
188C4⋊C8—2441no—
189#103—1221no—
190#103—1221no—
191#102—21no—
192#102—1221no—
193C4×C8—611no—
194C4×C8—611no—
195C4×C8—611no—
196C4×C8—611no—
197C2×Q8—1221no—
198C2×D4—21no—
199C2×D4—41no—
200C22×C4—611no—
201C22×C4—611no—
202C22×C4—2441no—
203C22×C4C22⋊#692311yescharacteristic
204Q16—1222no—
205SD16—2442no—
206D8—22no—
207M16—4882no—
208C2×C8—22no—
209C2×C8—611no—
210C2×C8—611no—
211C2×C8—1222no—
212C2×C8—2442no—
213C2×C8C22⋊#692311yescharacteristic
214C2×C8C22×#692311yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—1221no—
217C4⋊C4—2441no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C22⋊C4—41no—
222C22⋊C4—2441no—
223C22⋊C4—2441no—
224C22⋊C4—2441no—
225C22⋊C4—2441no—
226C42—611no—
227C42—611no—
228C42—611no—
229C42—611no—
230C42—2441no—
231C16—1224no—
232C23—41no—
233C23#1451983911yescharacteristic
234Q8—2441no—
235Q8—2441no—
236D4—41no—
237D4—41no—
238D4—82no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—611no—
245C2×C4—611no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—4881no—
249C2×C4—4881no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4#1451983911yescharacteristic
254C2×C4C2×C22⋊#692311yescharacteristic
255C8—21no—
256C8—612no—
257C8—1221no—
258C8—4882no—
259C8#1451986412yes—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—81no—
264C22—81no—
265C22—81no—
266C22C2×#1451983911yescharacteristic
267C4—21no—
268C4—81no—
269C4—611no—
270C4—611no—
271C4—1221no—
272C4—1221no—
273C4—1221no—
274C4—4881no—
275C4—4881no—
276C4#1684073511yescharacteristic
277C4D61⋊#10411yescharacteristic
278C2—41no—
279C2—161no—
280C2#2146116411yescharacteristic
281C2#2146212711yescharacteristic
282C2#2146213411yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
Fitting, prime radicalC61×#466C4
socleC22×C61C2×#102
cosocleC8×Dic61C23
hypercenter#466#6923
hypocenterC61#11674
LCSG ▷ C2×C8×C61 ▷ 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. #21462025C2semidirect
2. #21461376C2semidirect
3. #21460776C2semidirect
4. #21460773C2semidirect
164. C61#11674semidirect

Maximal subgroups

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

subgroupindex
#214620252
#214613762
#214607762
#214607732
#214563842
#1167461