Finite Group Databasebeta

← #29593658

Subgroups — #29593658

Order 15616.

314 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 61 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#21458423C211yesmaximal, characteristic, complemented
2#21447851C211yesmaximal, characteristic, complemented
3#21445295C211yesmaximal, characteristic, complemented
4#21443871C211yesmaximal, characteristic, complemented
5#21443787C211yesmaximal, characteristic, complemented
6#21443778C211yesmaximal, characteristic, complemented
7C61×#2244C211yesmaximal, characteristic, complemented
8#16840465—21no—
9C2×#14519718—21no—
10#16840089—21no—
11#16840077—21no—
12#16840059—21no—
13#16840016—21no—
14#16839954—21no—
15C4×D488C2211yescharacteristic
16#16839841C2211yescharacteristic
17#16839801—21no—
18C4⋊#11758185C2211yescharacteristic
19#16839563—21no—
20#16839513C2211yescharacteristic
21#16839506—21no—
22C61×#499C2211yescharacteristic
23C61×#493C2211yescharacteristic
24C61×#357—21no—
25C61×#357—21no—
26C61×#346C2211yescharacteristic
27C2×D488D411yescharacteristic
28C2×#11758199—41no—
29C2×#11758189—21no—
30#14519772—41no—
31#14519762—41no—
32#14519752—21no—
33#14519752—21no—
34#14519752—41no—
35C4×D244—21no—
36C4×D244D411yescharacteristic
37#14519739—41no—
38#14519735—21no—
39C4⋊C4×D61—21no—
40#14519718—42no—
41C2×#11758185—21no—
42#14519711D411yescharacteristic
43#14519710—21no—
44#14519708—21no—
45C4⋊#92418—21no—
46C4⋊#92418D411yescharacteristic
47#14519699—21no—
48#14519698—41no—
49#14519697—21no—
50#14519697—21no—
51#14519689—21no—
52C2×D8×C61—21no—
53C2×D8×C61—21no—
54#127×C61—21no—
55#125×C61—21no—
56C2×C16×C61—21no—
57#107×C61D411yescharacteristic
58#107×C61D411yescharacteristic
59#106×C61—21no—
60C4×C8×C61C2311yescharacteristic
61C2×D4×C61—41no—
62C2×D4×C61—41no—
63C2×D4×C61—41no—
64C2×D244—21no—
65C2×D244—41no—
66C2×D244—41no—
67C2×D244D811yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61—41no—
70C2×C4×D61—41no—
71D8×C61—42no—
72D8×C61—41no—
73D8×C61—41no—
74C2×C8×C61C2×D411yescharacteristic
75C2×C8×C61C2×D411yescharacteristic
76C4⋊C4×C61—21no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C42×C61C2×D411yescharacteristic
81#11758199—82no—
82#11758198—21no—
83#11758198—41no—
84#11758198—41no—
85#11758198—41no—
86#11758198—41no—
87C4⋊Dic61—21no—
88C4⋊Dic61D811yescharacteristic
89#11758196—41no—
90C4×Dic61—41no—
91C2×#92418—21no—
92C2×#92418—41no—
93D488—21no—
94D488—21no—
95#11758189—41no—
96#11758189—41no—
97C16×C61—41no—
98#11758185—41no—
99C23×C61—81no—
100C22×D61—21no—
101C22×D61—41no—
102D4×C61—81no—
103D4×C61—81no—
104D4×C61—81no—
105D4×C61—81no—
106D4×C61—161no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61#12011yescharacteristic
110C2×C4×C61C2×D811yescharacteristic
111C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
112C2×Dic61—21no—
113C2×Dic61—41no—
114D244—41no—
115D244—41no—
116D244—41no—
117D244—82no—
118D244—161no—
119C4×D61—41no—
120C4×D61—41no—
121C4×D61—161no—
122C4×D61—161no—
123C8×C61—21no—
124C8×C61#13511yescharacteristic
125C8×C61AGL(1,ℤ/8)11yescharacteristic
126#92418—41no—
127#92418—81no—
128#12348—611nomaximal, Sylow
129C22×C61—161no—
130C22×C61—161no—
131C22×C61—161no—
132C22×C61#44711yescharacteristic
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—41no—
136C2×D61—81no—
137C2×D61—81no—
138C2×D61—81no—
139C4×C61—21no—
140C4×C61—21no—
141C4×C61—81no—
142C4×C61—81no—
143C4×C61#44911yescharacteristic
144C4×C61#45411yescharacteristic
145Dic61—41no—
146Dic61—81no—
147#3355—611no—
148#2244D6111yescharacteristic, complemented
149#2206—611no—
150#1687—611no—
151#1363—611no—
152#1333—611no—
153#1330—611no—
154C2×C61—321no—
155C2×C61#162511yescharacteristic
156C2×C61#219011yescharacteristic
157C2×C61#219211yescharacteristic
158D61—81no—
159D61—161no—
160#553—1221no—
161C2×D16—1221no—
162#499C2×D6111yescharacteristic
163#493C2×D6111yescharacteristic
164#482—1221no—
165#480—1221no—
166#478—1221no—
167#469—1221no—
168#459—1221no—
169C4×D8—611no—
170#436—611no—
171#428—1221no—
172C4⋊C16—611no—
173#357—21no—
174#357—21no—
175#357—1221no—
176#346C2×D6111yescharacteristic
177#334—611no—
178#331—1221no—
179C61#1234811yescharacteristic, complemented, Sylow
180C2×D8—21no—
181C2×D8—21no—
182C2×D8—611no—
183C2×D8—2441no—
184C2×M16—1221no—
185#127—21no—
186#126—2441no—
187#125—21no—
188#123—2441no—
189#121—1221no—
190#121—1221no—
191#121—2441no—
192C4×D4—611no—
193C4×D4—1221no—
194C4×D4—2441no—
195#117—1221no—
196C2×C4⋊C4—1221no—
197D16—2442no—
198C2×C16—21no—
199C2×C16—1221no—
200#107—611no—
201#107—1221no—
202#107C22⋊D6111yescharacteristic
203#107C22⋊D6111yescharacteristic
204#106—21no—
205#106—1221no—
206C4⋊C8—611no—
207C4⋊C8—1221no—
208#102—1221no—
209#102—1221no—
210#102—1221no—
211#102—2441no—
212C22⋊C8—1221no—
213C4×C8C22×D6111yescharacteristic
214C2×D4—41no—
215C2×D4—41no—
216C2×D4—41no—
217C2×D4—611no—
218C2×D4—1221no—
219C2×D4—2441no—
220C2×D4—2441no—
221C22×C4—1221no—
222C22×C4—2441no—
223C22×C4—2441no—
224D8—42no—
225D8—41no—
226D8—41no—
227D8—1221no—
228D8—1221no—
229D8—4882no—
230M16—2441no—
231M16—2441no—
232C2×C8—1221no—
233C2×C8—2441no—
234C2×C8D4×D6111yescharacteristic
235C2×C8C2×C22⋊D6111yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—611no—
241C4⋊C4—1221no—
242C4⋊C4—2441no—
243C22⋊C4—1221no—
244C22⋊C4—2441no—
245C22⋊C4—2441no—
246C22⋊C4—2441no—
247C22⋊C4—2441no—
248C42—2441no—
249C42D4×D6111yescharacteristic
250C16—41no—
251C16—2441no—
252C23—81no—
253C23—1221no—
254C23—2441no—
255D4—81no—
256D4—81no—
257D4—81no—
258D4—81no—
259D4—161no—
260D4—9761no—
261D4—4882no—
262D4—2441no—
263D4—2441no—
264D4—2441no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—1221no—
268C2×C4—9761no—
269C2×C4—9761no—
270C2×C4—2441no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4#1451974511yescharacteristic
274C2×C4D8×D6111yescharacteristic
275C2×C4#1451980111yescharacteristic
276C8—21no—
277C8—4881no—
278C8—2441no—
279C8#1451979811yescharacteristic
280C8#1451980411yescharacteristic
281C22—161no—
282C22—161no—
283C22—161no—
284C22—4881no—
285C22—4881no—
286C22—4881no—
287C22—2441no—
288C22—2441no—
289C22—2441no—
290C22#1683989411yescharacteristic
291C4—21no—
292C4—21no—
293C4—81no—
294C4—81no—
295C4—4881no—
296C4—2441no—
297C4#1683990611yescharacteristic
298C4#1683993411yescharacteristic
299C2—321no—
300C2—9761no—
301C2—4881no—
302C2#2144490511yescharacteristic
303C2#2144776311yescharacteristic
304C2#2144777311yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2244C2
socleC22×C61#447
hypercenter#2244D61
hypocenterC61#12348
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2244

Complements

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

NH ≅ G/Ntype
1. #21458423C2semidirect
2. #21447851C2semidirect
3. #21445295C2semidirect
4. #21443871C2semidirect
5. #21443787C2semidirect
6. #21443778C2semidirect
7. C61×#2244C2semidirect
148. #2244D61semidirect
179. C61#12348semidirect

Maximal subgroups

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

subgroupindex
#214584232
#214478512
#214452952
#214438712
#214437872
#214437782
C61×#22442
#1234861