Finite Group Databasebeta

← #30608428

Subgroups — #30608428

Order 15616.

344 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 56 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#21462120C211yesmaximal, characteristic, complemented
2#21462096C211yesmaximal, characteristic, complemented
3#21460964C212yesmaximal, complemented
4#21460946C212yesmaximal, complemented
5#21456863C211yesmaximal, characteristic
6#16840748—21no—
7C2×#14519836—21no—
8#16840671—21no—
9#16840671C2212yes—
10#16840669C2212yes—
11#16840667—21no—
12#16840331C2211yescharacteristic
13#16840149C2211yescharacteristic
14#16840138C411yescharacteristic, complemented
15#16840128C411yescharacteristic, complemented
16#16840119C2211yescharacteristic
17#16839977—21no—
18#16839957—21no—
19#16839905—21no—
20#16839895—21no—
21#16839823C411yescharacteristic, complemented
22C61×#540C411yescharacteristic, complemented
23D61⋊M16—41no—
24C2×C22⋊#6923—41no—
25#14519838—22no—
26#14519837—41no—
27#14519836—22no—
28#14519836—41no—
29C2×#11758222D411yescharacteristic
30C22×D244D411yescharacteristic
31C2×#11758200—21no—
32C2×#11758199—21no—
33C2×#11758199—21no—
34C2×#11758199—21no—
35#14519774C2×C411yescharacteristic
36#14519774D411yescharacteristic
37#14519765D411yescharacteristic
38#14519765C2311yescharacteristic
39#14519752—41no—
40#14519747—41no—
41C4⋊#92418—21no—
42#14519700—21no—
43#14519697—21no—
44#14519697—21no—
45#14519697—21no—
46C22⋊#92418—21no—
47#14519688C2×C411yescharacteristic, complemented
48C4×#92418C2×C411yescharacteristic, complemented
49#127×C61C2×C411yescharacteristic, complemented
50#125×C61C2×C411yescharacteristic, complemented
51#123×C61—41no—
52#121×C61—21no—
53#121×C61—41no—
54C4×D4×C61—21no—
55#117×C61C2×C411yescharacteristic
56C23×D61—21no—
57C22×#6923—81no—
58C2×D4×C61—21no—
59C2×D4×C61—41no—
60C2×D4×C61—41no—
61C22×C4×C61—41no—
62C22×C4×C61C22⋊C411yescharacteristic
63C2×C22⋊D61—21no—
64#11758222—81no—
65C2×D244—21no—
66C2×D244—41no—
67C2×D244—41no—
68C2×D244—81no—
69C2×D244C22⋊C411yescharacteristic
70C2×D244C22⋊C411yescharacteristic
71C2×D244C2×D411yescharacteristic
72C2×C4×D61—21no—
73C2×Dic122C2×D411yescharacteristic
74C22⋊#6923—42no—
75C22⋊#6923—81no—
76#11758217—42no—
77#11758213—81no—
78D61⋊C8—81no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—41no—
82C22⋊C4×C61—21no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C42×C61C22⋊C411yescharacteristic
86C42×C61C22×C411yescharacteristic
87#11758200—81no—
88#11758199—81no—
89#11758199—81no—
90#11758199—81no—
91#11758198—41no—
92#11758198—41no—
93C2×#92418—21no—
94C2×#92418—21no—
95C23×C61—41no—
96C23×C61#9911yescharacteristic
97C22×D61—21no—
98C22×D61—21no—
99C22×D61—21no—
100C22×D61—41no—
101C22×D61—41no—
102C22×D61—161no—
103C2×#6923—82no—
104C2×#6923—162no—
105D4×C61—41no—
106D4×C61—41no—
107D4×C61—161no—
108D4×C61—161no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—161no—
114C2×C4×C61#9911yescharacteristic
115C2×C4×C61C2×C22⋊C411yescharacteristic
116C22⋊D61—81no—
117C2×Dic61—21no—
118D244—41no—
119D244—41no—
120D244—41no—
121D244—81no—
122D244—161no—
123D244—161no—
124C4×D61—41no—
125C4×D61—41no—
126Dic122—41no—
127#92420—82no—
128#92418—41no—
129#92418—41no—
130#13605—611nomaximal, Sylow
131C22×C61—21no—
132C22×C61—41no—
133C22×C61—81no—
134C22×C61—81no—
135C22×C61—81no—
136C22×C61C2×#9911yescharacteristic
137C2×D61—41no—
138C2×D61—41no—
139C2×D61—41no—
140C2×D61—82no—
141C2×D61—81no—
142C2×D61—81no—
143C2×D61—81no—
144C2×D61—161no—
145#6923—162no—
146C4×C61—21no—
147C4×C61—21no—
148C4×C61—41no—
149C4×C61—41no—
150C4×C61—81no—
151Dic61—41no—
152#3220—611no—
153#2134—611no—
154#2127—611no—
155#1414—612no—
156#1406—612no—
157C2×C61—21no—
158C2×C61—41no—
159C2×C61—161no—
160C2×C61#212711yescharacteristic
161D61—81no—
162D61—81no—
163D61—81no—
164#540#692311yescharacteristic, complemented
165#535—611no—
166#496—611no—
167#493—611no—
168#490—611no—
169#488—611no—
170#463—1221no—
171#459—1221no—
172#449—1221no—
173#447—1221no—
174#433—611no—
175#413—1221no—
176C2×#99—1221no—
177#355—612no—
178#355—1221no—
179#354—612no—
180#353—1221no—
181C61#1360511yescharacteristic, complemented, Sylow
182C2×#41—611no—
183C22×D4—611no—
184C2×SD16—1221no—
185C2×D8—1221no—
186C2×D8—1221no—
187C2×D8—1221no—
188C2×M16—2441no—
189#127—611no—
190#127—611no—
191#127C2×#692311yescharacteristic, complemented
192#125C2×#692311yescharacteristic, complemented
193#124—611no—
194#124—611no—
195#123—41no—
196#121—21no—
197#121—41no—
198#121—2441no—
199#120—2441no—
200C4×D4—21no—
201#117C2×#692311yescharacteristic
202C2×C22⋊C4—2441no—
203C4⋊C8—1221no—
204#103—1221no—
205#102—1221no—
206#102—1221no—
207#102—1221no—
208#101—1222no—
209#100—2441no—
210#99—1222no—
211#99—2441no—
212C22⋊C8—1221no—
213#97—611no—
214C4×C8—611no—
215C24—1221no—
216#41—4881no—
217C2×Q8—611no—
218C2×D4—21no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—611no—
222C2×D4—611no—
223C2×D4—611no—
224C2×D4—1221no—
225C2×D4—1221no—
226C2×D4—4881no—
227C2×D4—2441no—
228C2×D4—2441no—
229C22×C4—41no—
230C22×C4—1221no—
231C22×C4—4881no—
232C22×C4C22⋊#692311yescharacteristic
233SD16—4881no—
234D8—4881no—
235D8—4881no—
236D8—4881no—
237M16—4881no—
238M16—2442no—
239C2×C8—1221no—
240C2×C8—1221no—
241C2×C8—4881no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—41no—
245C22⋊C4—21no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—4881no—
249C22⋊C4—2441no—
250C22⋊C4—2441no—
251C22⋊C4—2442no—
252C42C22⋊#692311yescharacteristic
253C42C22×#692311yescharacteristic
254C23—41no—
255C23—1221no—
256C23—1221no—
257C23—1221no—
258C23—9761no—
259C23—2441no—
260C23—2441no—
261C23#1451983511yescharacteristic
262Q8—2441no—
263D4—41no—
264D4—41no—
265D4—161no—
266D4—161no—
267D4—9761no—
268D4—9761no—
269D4—4881no—
270D4—4881no—
271D4—2441no—
272D4—2441no—
273D4—2441no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—161no—
279C2×C4—1221no—
280C2×C4—9762no—
281C2×C4—4882no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4#1451983511yescharacteristic
285C2×C4C2×C22⋊#692311yescharacteristic
286C8—4882no—
287C8—2441no—
288C8—2441no—
289C22—21no—
290C22—41no—
291C22—81no—
292C22—81no—
293C22—81no—
294C22—9761no—
295C22—4881no—
296C22—4881no—
297C22—4881no—
298C22—4882no—
299C22—2441no—
300C22—2441no—
301C22—2441no—
302C22C2×#1451983511yescharacteristic
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—81no—
308C4—9762no—
309C4—2441no—
310C2—21no—
311C2—41no—
312C2—161no—
313C2—4881no—
314C2—4881no—
315C2—4881no—
316C2#2146209411yescharacteristic
subgroupG/H
centerC2#21462094
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#540C4
socleC2×C61#2127
prime radical#21456863C2
cosocle#14519765C23
hypercenter#540#6923
hypocenterC61#13605
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C22×C4 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #21462120C2semidirect
2. #21462096C2semidirect
3. #21460964C2semidirect
4. #21460946C2semidirect
14. #16840138C4semidirect
15. #16840128C4semidirect
21. #16839823C4semidirect
22. C61×#540C4semidirect
47. #14519688C2×C4semidirect
48. C4×#92418C2×C4semidirect
49. #127×C61C2×C4semidirect
50. #125×C61C2×C4semidirect
164. #540#6923semidirect
181. C61#13605semidirect
191. #127C2×#6923semidirect
192. #125C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214621202
#214620962
#214609642
#214609462
#214568632
#1360561