Finite Group Databasebeta

← #30604679

Subgroups — #30604679

Order 15616.

330 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 82 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#21462026C211yesmaximal, characteristic, complemented
2#21461377C211yesmaximal, characteristic, complemented
3#21460776C212yesmaximal, complemented
4#21460774C212yesmaximal, complemented
5#21456391C211yesmaximal, characteristic
6C2×#14519852—21no—
7#16840766—21no—
8#16840650—21no—
9#16840648C2212yes—
10#16840625—21no—
11#16840625C2212yes—
12#16840297—21no—
13#16840146C411yescharacteristic
14#16840119—21no—
15#16840004C411yescharacteristic
16#16839999C411yescharacteristic
17#16839992—21no—
18#16839856C2211yescharacteristic
19#16839849—21no—
20#16839844C2211yescharacteristic
21C4×C8×D61C2211yescharacteristic
22C61×#499C411yescharacteristic
23C2×#11758213—41no—
24#14519852—24no—
25C2×#11758187—22no—
26C4⋊#92420—22no—
27C4⋊#92420—41no—
28C2×Dic244C2×C411yescharacteristic
29C2×#11758190—21no—
30C2×D488C2×C411yescharacteristic
31C2×C8×D61C2×C411yescharacteristic
32C2×C8×D61D411yescharacteristic
33#14519772—41no—
34#14519765—21no—
35#14519762—41no—
36#14519757—21no—
37#14519752—21no—
38#14519742—21no—
39#14519739—21no—
40#14519739—41no—
41#14519735—41no—
42C42×D61D411yescharacteristic
43#14519700—21no—
44#14519700—21no—
45#14519697—21no—
46#14519697—21no—
47C4×#92418D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61C2311yescharacteristic
50#125×C61—21no—
51#107×C61C2×C411yescharacteristic
52#107×C61C2×C411yescharacteristic
53#106×C61—21no—
54C4×C8×C61C2×C411yescharacteristic
55C2×D244—21no—
56C2×D244—41no—
57C2×C4×D61—41no—
58C2×C4×D61C22⋊C411yescharacteristic
59C2×C4×D61D811yescharacteristic
60C2×C4×D61SD1611yescharacteristic
61C2×Dic122—21no—
62C2×#92420—42no—
63#11758213—82no—
64C2×C8×C61C22⋊C411yescharacteristic
65C2×C8×C61C22×C411yescharacteristic
66C4⋊C4×C61—21no—
67C4⋊C4×C61—21no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61—41no—
70C42×C61C22⋊C411yescharacteristic
71#11758198—41no—
72#11758198—41no—
73#11758198—41no—
74#11758198—41no—
75#11758198—41no—
76C4⋊Dic61—41no—
77#11758196—41no—
78C4×Dic61—41no—
79C4×Dic61D811yescharacteristic
80C4×Dic61SD1611yescharacteristic
81C4×Dic61C2×D411yescharacteristic
82C2×#92418C22⋊C411yescharacteristic
83C2×#92418C2×D411yescharacteristic
84Dic244—22no—
85D488—22no—
86#11758190—42no—
87C8×D61—22no—
88C8×D61—22no—
89#11758187—24no—
90C22×D61—41no—
91C22×D61#10211yescharacteristic
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61#10211yescharacteristic
95C2×C4×C61#10211yescharacteristic
96C2×C4×C61C2×C22⋊C411yescharacteristic
97C2×Dic61—41no—
98C2×Dic61#10211yescharacteristic
99C2×Dic61C2×D811yescharacteristic
100C2×Dic61C2×SD1611yescharacteristic
101D244—41no—
102D244—41no—
103D244—82no—
104C4×D61—21no—
105C4×D61—21no—
106C4×D61—21no—
107C4×D61—21no—
108C4×D61—41no—
109C4×D61—81no—
110C4×D61—81no—
111Dic122—41no—
112Dic122—41no—
113#92420—82no—
114C8×C61#10412yes—
115C8×C61#13112yes—
116#92418—21no—
117#92418—21no—
118#11674—611nomaximal, Sylow
119C22×C61C2×#10211yescharacteristic
120C2×D61—21no—
121C2×D61—21no—
122C2×D61—21no—
123C2×D61—81no—
124C2×D61—81no—
125C2×D61—81no—
126C4×C61—21no—
127C4×C61—21no—
128C4×C61—81no—
129C4×C61—81no—
130C4×C61#40811yescharacteristic
131C4×C61C2×#10411yescharacteristic
132Dic61—21no—
133Dic61—21no—
134Dic61—81no—
135Dic61#50911yescharacteristic
136Dic61#51011yescharacteristic
137#3168—611no—
138C4×M32—611no—
139#1567—611no—
140#1332—612no—
141#1331—612no—
142C2×C61#149211yescharacteristic
143C2×C61#213911yescharacteristic
144C2×C61#214311yescharacteristic
145D61—41no—
146D61—161no—
147#529—1221no—
148C2×M32—1221no—
149#499#692311yescharacteristic
150#495—611no—
151#488—1221no—
152#467—611no—
153#466—611no—
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×D8—611no—
168C2×M16—2441no—
169C22×C8—611no—
170C22×C8—611no—
171#126—2441no—
172#125—21no—
173#124—1221no—
174#123—2441no—
175C22⋊Q8—1221no—
176#121—1221no—
177C4×Q8—1221no—
178C4×D4—1221no—
179C4×D4—2441no—
180#117—2441no—
181C2×C42—611no—
182M32—1224no—
183C2×C16—1222no—
184#107C2×#692311yescharacteristic
185#107C2×#692311yescharacteristic
186#106—21no—
187C4⋊C8—1222no—
188C4⋊C8—2441no—
189#103—1221no—
190#103—1221no—
191#102—1221no—
192#102—1221no—
193C4×C8—611no—
194C4×C8—611no—
195C4×C8—611no—
196C4×C8C2×#692311yescharacteristic
197C2×Q8—1221no—
198C2×D4—1221no—
199C2×D4—2441no—
200C22×C4—611no—
201C22×C4—611no—
202C22×C4—611no—
203C22×C4—2441no—
204Q16—1222no—
205SD16—2442no—
206D8—1222no—
207M16—4882no—
208C2×C8—611no—
209C2×C8—611no—
210C2×C8—1222no—
211C2×C8—1222no—
212C2×C8—2442no—
213C2×C8C22⋊#692311yescharacteristic
214C2×C8C22×#692311yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C22⋊C4—2441no—
222C22⋊C4—2441no—
223C22⋊C4—2441no—
224C22⋊C4—2441no—
225C22⋊C4—2441no—
226C42—611no—
227C42—611no—
228C42—611no—
229C42—2441no—
230C42C22⋊#692311yescharacteristic
231C16—1224no—
232C23—611no—
233C23—2441no—
234Q8—2441no—
235Q8—2441no—
236D4—4882no—
237D4—2441no—
238D4—2441no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—611no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—4881no—
249C2×C4—4881no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4#1451983911yescharacteristic
253C2×C4#1451983911yescharacteristic
254C2×C4C2×C22⋊#692311yescharacteristic
255C8—1221no—
256C8—1221no—
257C8—4882no—
258C8#1451984212yes—
259C8#1451986512yes—
260C22—1221no—
261C22—1221no—
262C22—1221no—
263C22—4881no—
264C22—4881no—
265C22—4881no—
266C22C2×#1451983911yescharacteristic
267C4—21no—
268C4—21no—
269C4—81no—
270C4—81no—
271C4—611no—
272C4—611no—
273C4—1221no—
274C4—1221no—
275C4—4881no—
276C4#1684073711yescharacteristic
277C4C2×#1451984211yescharacteristic
278C2—9761no—
279C2—2441no—
280C2#2146116611yescharacteristic
281C2#2146212711yescharacteristic
282C2#2146213311yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#499C4
socleC22×C61C2×#102
prime radical#16839999C4
cosocleC8×Dic61C23
hypercenter#499#6923
hypocenterC61#11674
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #21462026C2semidirect
2. #21461377C2semidirect
3. #21460776C2semidirect
4. #21460774C2semidirect
164. C61#11674semidirect

Maximal subgroups

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

subgroupindex
#214620262
#214613772
#214607762
#214607742
#214563912
#1167461