Finite Group Databasebeta

← #30608455

Subgroups — #30608455

Order 15616.

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

normal subgroups only

This group has 348 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#21462100C211yesmaximal, characteristic, complemented
2#21462096C211yesmaximal, characteristic, complemented
3#21460960C212yesmaximal, complemented
4#21460951C212yesmaximal, complemented
5#21456871C211yesmaximal, characteristic
6#16840741—21no—
7C2×#14519836—21no—
8#16840669—21no—
9#16840667—21no—
10#16840667C2212yes—
11#16840667C2212yes—
12#16840367C411yescharacteristic, complemented
13#16840331C2211yescharacteristic
14#16840151C411yescharacteristic, complemented
15#16840139C2211yescharacteristic
16#16840127C2211yescharacteristic
17#16840117C411yescharacteristic, complemented
18#16839978—21no—
19#16839958—21no—
20#16839909—21no—
21#16839898—21no—
22C61×#433C411yescharacteristic, complemented
23#14519856—41no—
24C2×C22⋊#6923—41no—
25#14519836—22no—
26#14519836—22no—
27#14519836—41no—
28#14519835—41no—
29C2×#11758222D411yescharacteristic
30C22×D244D411yescharacteristic
31C2×#11758190—21no—
32C2×D488—21no—
33C2×D488—21no—
34C2×D488—21no—
35#14519774C2×C411yescharacteristic, complemented
36#14519774D411yescharacteristic
37#14519774C2311yescharacteristic
38#14519769C2×C411yescharacteristic, complemented
39#14519765C2×C411yescharacteristic
40#14519765D411yescharacteristic
41#14519762—41no—
42#14519752—41no—
43#14519751—21no—
44#14519750—41no—
45#14519747—41no—
46C4×D244—21no—
47#14519702—21no—
48#14519699—21no—
49#14519699—21no—
50#14519699—21no—
51#117×C61C2×C411yescharacteristic
52C4⋊C8×C61—21no—
53C22⋊C8×C61—21no—
54#97×C61C2×C411yescharacteristic, complemented
55C4×C8×C61C2×C411yescharacteristic, complemented
56C23×D61—21no—
57C22×#6923—81no—
58C22×C4×C61C22⋊C411yescharacteristic
59C2×C22⋊D61—21no—
60C2×C22⋊D61—41no—
61#11758222—81no—
62C2×D244—21no—
63C2×D244—21no—
64C2×D244—41no—
65C2×D244—41no—
66C2×D244—41no—
67C2×D244—81no—
68C2×D244C22⋊C411yescharacteristic
69C2×D244C2×D411yescharacteristic
70C2×D244C2×D411yescharacteristic
71C2×C4×D61—21no—
72C2×C4×D61—41no—
73C2×Dic122C22⋊C411yescharacteristic
74C22⋊#6923—42no—
75C22⋊#6923—42no—
76C22⋊#6923—81no—
77C4⋊#6923—81no—
78C4×#6923—81no—
79C2×C8×C61—21no—
80C2×C8×C61—21no—
81C4⋊C4×C61—21no—
82C22⋊C4×C61—21no—
83C42×C61C22⋊C411yescharacteristic
84C42×C61C22×C411yescharacteristic
85#11758198—41no—
86#11758198—41no—
87#11758198—41no—
88#11758198—41no—
89C4⋊Dic61—21no—
90#11758196—41no—
91D488—81no—
92D488—81no—
93D488—81no—
94#11758190—81no—
95C23×C61#9911yescharacteristic
96C22×D61—21no—
97C22×D61—21no—
98C22×D61—21no—
99C22×D61—41no—
100C22×D61—41no—
101C22×D61—41no—
102C22×D61—161no—
103C2×#6923—82no—
104C2×#6923—82no—
105C2×#6923—162no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—41no—
109C2×C4×C61#9911yescharacteristic
110C2×C4×C61C2×C22⋊C411yescharacteristic
111C22⋊D61—81no—
112C22⋊D61—161no—
113C2×Dic61—21no—
114C2×Dic61—41no—
115D244—41no—
116D244—41no—
117D244—41no—
118D244—41no—
119D244—41no—
120D244—81no—
121D244—161no—
122D244—161no—
123D244—161no—
124C4×D61—41no—
125C4×D61—41no—
126C4×D61—161no—
127Dic122—41no—
128C8×C61—41no—
129C8×C61—41no—
130#13609—611nomaximal, Sylow
131C22×C61—21no—
132C22×C61—41no—
133C22×C61C2×#9911yescharacteristic
134C2×D61—41no—
135C2×D61—41no—
136C2×D61—41no—
137C2×D61—82no—
138C2×D61—81no—
139C2×D61—81no—
140C2×D61—81no—
141C2×D61—81no—
142C2×D61—81no—
143C2×D61—81no—
144C2×D61—161no—
145#6923—162no—
146#6923—162no—
147C4×C61—21no—
148C4×C61—21no—
149C4×C61—41no—
150C4×C61—41no—
151Dic61—41no—
152Dic61—81no—
153#3220—611no—
154#2128—611no—
155#2127—611no—
156#1412—612no—
157#1408—612no—
158C2×C61—21no—
159C2×C61—41no—
160C2×C61#212711yescharacteristic
161D61—81no—
162D61—81no—
163D61—81no—
164D61—161no—
165#540—611no—
166#535—611no—
167#496—611no—
168#493—611no—
169#490—611no—
170#488—611no—
171#463—1221no—
172#459—1221no—
173#449—1221no—
174#447—1221no—
175#433#692311yescharacteristic, complemented
176#410—1221no—
177C2×#99—1221no—
178#354—1221no—
179#353—612no—
180#353—612no—
181#353—1221no—
182C61#1360911yescharacteristic, complemented, Sylow
183C2×#41—611no—
184C22×D4—611no—
185C2×SD16—1221no—
186C2×D8—1221no—
187C2×D8—1221no—
188C2×D8—1221no—
189#127—611no—
190#127—611no—
191#127—611no—
192#125—611no—
193#124—611no—
194#124—611no—
195#123—2441no—
196#121—1221no—
197#121—2441no—
198#121—2441no—
199#120—2441no—
200C4×D4—1221no—
201#117—2441no—
202#117C2×#692311yescharacteristic
203C2×C22⋊C4—2441no—
204C4⋊C8—21no—
205#103—1221no—
206#102—1221no—
207#102—1221no—
208#102—1221no—
209#99—1222no—
210#99—1222no—
211#99—2441no—
212#99—2441no—
213C22⋊C8—21no—
214#97C2×#692311yescharacteristic, complemented
215C4×C8C2×#692311yescharacteristic, complemented
216C24—1221no—
217#41—4881no—
218C2×Q8—611no—
219C2×D4—611no—
220C2×D4—611no—
221C2×D4—611no—
222C2×D4—1221no—
223C2×D4—1221no—
224C2×D4—1221no—
225C2×D4—4881no—
226C2×D4—2441no—
227C2×D4—2441no—
228C2×D4—2441no—
229C2×D4—2441no—
230C22×C4—1221no—
231C22×C4—4881no—
232C22×C4—2441no—
233C22×C4C22⋊#692311yescharacteristic
234SD16—4881no—
235D8—4881no—
236D8—4881no—
237D8—4881no—
238C2×C8—21no—
239C2×C8—21no—
240C4⋊C4—21no—
241C4⋊C4—1221no—
242C4⋊C4—4881no—
243C4⋊C4—2441no—
244C22⋊C4—21no—
245C22⋊C4—4881no—
246C22⋊C4—2441no—
247C22⋊C4—2441no—
248C22⋊C4—2441no—
249C22⋊C4—2442no—
250C22⋊C4—2442no—
251C22⋊C4—2441no—
252C42—4881no—
253C42C22⋊#692311yescharacteristic
254C42C22×#692311yescharacteristic
255C23—1221no—
256C23—1221no—
257C23—1221no—
258C23—9761no—
259C23—2441no—
260C23—2441no—
261C23—2441no—
262C23#1451983611yescharacteristic
263Q8—2441no—
264D4—9761no—
265D4—9761no—
266D4—9761no—
267D4—9761no—
268D4—4881no—
269D4—4881no—
270D4—2441no—
271D4—2441no—
272D4—2441no—
273D4—2441no—
274D4—2441no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—1221no—
279C2×C4—9761no—
280C2×C4—9762no—
281C2×C4—4882no—
282C2×C4—4882no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4#1451983611yescharacteristic
287C2×C4C2×C22⋊#692311yescharacteristic
288C8—41no—
289C8—41no—
290C22—21no—
291C22—41no—
292C22—9761no—
293C22—4881no—
294C22—4881no—
295C22—4881no—
296C22—4881no—
297C22—4881no—
298C22—4882no—
299C22—4881no—
300C22—2441no—
301C22—2441no—
302C22—2441no—
303C22C2×#1451983611yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—9762no—
309C4—9762no—
310C4—4881no—
311C4—2441no—
312C2—21no—
313C2—41no—
314C2—9761no—
315C2—4881no—
316C2—4881no—
317C2—4881no—
318C2#2146209611yescharacteristic
subgroupG/H
centerC2#21462096
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#433C4
socleC2×C61#2127
prime radical#21456871C2
cosocle#14519774C23
hypercenter#433#6923
hypocenterC61#13609
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C22×C4 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #21462100C2semidirect
2. #21462096C2semidirect
3. #21460960C2semidirect
4. #21460951C2semidirect
12. #16840367C4semidirect
14. #16840151C4semidirect
17. #16840117C4semidirect
22. C61×#433C4semidirect
35. #14519774C2×C4semidirect
38. #14519769C2×C4semidirect
54. #97×C61C2×C4semidirect
55. C4×C8×C61C2×C4semidirect
175. #433#6923semidirect
182. C61#13609semidirect
214. #97C2×#6923semidirect
215. C4×C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214621002
#214620962
#214609602
#214609512
#214568712
#1360961