Finite Group Databasebeta

← #29593815

Subgroups — #29593815

Order 15616.

356 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 67 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#21457539C211yesmaximal, characteristic
2#21448046C211yesmaximal, characteristic, complemented
3#21447957C211yesmaximal, characteristic, complemented
4#21445209C211yesmaximal, characteristic, complemented
5#21443779C211yesmaximal, characteristic, complemented
6#21443773C211yesmaximal, characteristic, complemented
7C61×#1362C211yesmaximal, characteristic, complemented
8C2×#14519800—21no—
9#16840415—21no—
10#16840167C2211yescharacteristic
11#16840000—21no—
12#16839968—21no—
13#16839964—21no—
14#16839923—22no—
15C4×D488C2211yescharacteristic
16C8×D244C2211yescharacteristic
17#16839588—21no—
18#16839566—22no—
19#16839564—21no—
20C4×#11758185C2211yescharacteristic
21#16839509—21no—
22C61×#494C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×#11758226—22no—
26#14519800—42no—
27#14519800—42no—
28C2×#11758190—41no—
29C2×#11758201—22no—
30C2×D488D411yescharacteristic
31C2×C8×D61—21no—
32#14519777—21no—
33#14519762—42no—
34#14519753—22no—
35#14519752—41no—
36C4×D244—21no—
37C4×D244D411yescharacteristic
38C4⋊C4×D61—41no—
39C2×#11758185—21no—
40#14519711—21no—
41#14519711—21no—
42#14519711D411yescharacteristic
43C4⋊#92418D411yescharacteristic
44#14519702—41no—
45#14519701—22no—
46#14519699—21no—
47#14519689—21no—
48C2×Q16×C61—21no—
49C2×Q16×C61D412yes—
50C4⋊Q8×C61—21no—
51C2×C16×C61—21no—
52C4⋊C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—22no—
55#11758226—44no—
56#11758226—82no—
57C2×D244—21no—
58C2×D244—42no—
59C2×D244D811yescharacteristic
60C2×C4×D61—21no—
61C2×C4×D61—42no—
62C2×C4×D61—41no—
63C2×Dic122—41no—
64Q16×C61—42no—
65Q16×C61—41no—
66Q16×C61—41no—
67C2×C8×C61—41no—
68C2×C8×C61C2×D411yescharacteristic
69C2×C8×C61C2×D411yescharacteristic
70C4⋊C4×C61—41no—
71C4⋊C4×C61—41no—
72C42×C61C2×D411yescharacteristic
73#11758201—44no—
74#11758198—21no—
75#11758198—42no—
76#11758198—41no—
77C4⋊Dic61—21no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80C4⋊Dic61D811yescharacteristic
81#11758196—42no—
82C2×#92418—21no—
83D488—21no—
84D488SD1612yescomplemented
85#11758190—82no—
86C8×D61—41no—
87C8×D61—41no—
88C16×C61—41no—
89#11758185—41no—
90C22×D61—21no—
91C22×D61—41no—
92Q8×C61—42no—
93Q8×C61—42no—
94C2×C4×C61—42no—
95C2×C4×C61#12011yescharacteristic
96C2×C4×C61C2×D811yescharacteristic
97C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
98C2×Dic61—21no—
99C2×Dic61—41no—
100C2×Dic61—81no—
101D244—22no—
102D244—21no—
103D244—21no—
104D244—41no—
105D244—84no—
106C4×D61—41no—
107C4×D61—41no—
108C4×D61—84no—
109C4×D61—81no—
110C4×D61—81no—
111Dic122—81no—
112Dic122—81no—
113C8×C61—21no—
114C8×C61—81no—
115C8×C61C2×SD1611yescharacteristic
116C8×C61AGL(1,ℤ/8)11yescharacteristic
117#92418—41no—
118#12371—611nomaximal, Sylow
119C22×C61#44711yescharacteristic
120C2×D61—41no—
121C2×D61—42no—
122C2×D61—41no—
123C2×D61—41no—
124C2×D61—81no—
125C2×D61—81no—
126C4×C61—21no—
127C4×C61—82no—
128C4×C61#45011yescharacteristic
129C4×C61#45511yescharacteristic
130C4×C61#50811yescharacteristic
131C4×C61#50911yescharacteristic
132Dic61—41no—
133Dic61—81no—
134Dic61—161no—
135#3283—611no—
136#2241—611no—
137#2224—611no—
138#1673—611no—
139#1362D6111yescharacteristic, complemented
140#1331—611no—
141D4⋊C16—611no—
142C2×C61#163911yescharacteristic
143C2×C61#218611yescharacteristic
144C2×C61#219511yescharacteristic
145D61—81no—
146D61—82no—
147C2×#135—1221no—
148#547—1221no—
149#500—611no—
150#494C2×D6111yescharacteristic
151#467—1221no—
152#461—1221no—
153#461—1221no—
154#452—1222no—
155C4×D8—611no—
156C8×D4—611no—
157#366—1221no—
158C4⋊C16C2×D6111yescharacteristic
159#358—1222no—
160#357—1221no—
161C4×C16—611no—
162#335C2×D6111yescharacteristic
163#332—1221no—
164C61#1237111yescharacteristic, complemented, Sylow
165C2×#41—1222no—
166#135—2442no—
167#135—2442no—
168C2×Q16—21no—
169C2×Q16D24412yes—
170C2×SD16—1222no—
171C2×SD16—2441no—
172C2×D8—611no—
173C22×C8—1221no—
174C4⋊Q8—21no—
175C4⋊Q8—1221no—
176#123—2442no—
177C22⋊Q8—1222no—
178#121—2441no—
179C4×D4—611no—
180C4×D4—1221no—
181C2×C4⋊C4—2441no—
182C2×C16—21no—
183C2×C16—1221no—
184#107—611no—
185#107—1221no—
186#107—1221no—
187C4⋊C8—21no—
188C4⋊C8—611no—
189#103—1222no—
190#103—2441no—
191#102—1221no—
192C22⋊C8—1221no—
193C4×C8C22×D6111yescharacteristic
194#41—4882no—
195#41—2444no—
196C2×Q8—22no—
197C2×Q8—2441no—
198C2×D4—611no—
199C2×D4—1221no—
200C2×D4—2442no—
201C22×C4—1221no—
202C22×C4—2442no—
203C22×C4—2441no—
204Q16—42no—
205Q16—41no—
206Q16—41no—
207SD16—4882no—
208SD16—2444no—
209D8—612no—
210D8—1221no—
211C2×C8—41no—
212C2×C8—1221no—
213C2×C8—2441no—
214C2×C8—2441no—
215C2×C8C2×D24411yescharacteristic
216C2×C8D4×D6111yescharacteristic
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—611no—
220C4⋊C4—1221no—
221C4⋊C4—2442no—
222C4⋊C4—2441no—
223C4⋊C4—2441no—
224C22⋊C4—1221no—
225C22⋊C4—2442no—
226C22⋊C4—2441no—
227C42D4×D6111yescharacteristic
228C16—41no—
229C16—2441no—
230C23—1221no—
231C23—2441no—
232Q8—42no—
233Q8—42no—
234Q8—4881no—
235Q8—4881no—
236D4—1221no—
237D4—1221no—
238D4—1222no—
239D4—4884no—
240D4—2441no—
241C2×C4—42no—
242C2×C4—1221no—
243C2×C4—4884no—
244C2×C4—4881no—
245C2×C4—4881no—
246C2×C4—4881no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4#1451974711yescharacteristic
251C2×C4D8×D6111yescharacteristic
252C2×C4#1451980411yescharacteristic
253C8—21no—
254C8—81no—
255C8—2441no—
256C8SD16×D6111yescharacteristic
257C8#1451980111yescharacteristic
258C22—4881no—
259C22—4881no—
260C22—2441no—
261C22—2441no—
262C22—2442no—
263C22—2441no—
264C22#1683989711yescharacteristic
265C4—21no—
266C4—82no—
267C4—9761no—
268C4—4881no—
269C4—2441no—
270C4#1683991411yescharacteristic
271C4#1683994211yescharacteristic
272C4#1684019511yescharacteristic
273C4#1684019911yescharacteristic
274C2—4882no—
275C2—4881no—
276C2#2144499911yescharacteristic
277C2#2144774511yescharacteristic
278C2#2144780011yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1362C2
socleC22×C61#447
prime radical#21457539C2
hypercenter#1362D61
hypocenterC61#12371
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
2. #21448046C2semidirect
3. #21447957C2semidirect
4. #21445209C2semidirect
5. #21443779C2semidirect
6. #21443773C2semidirect
7. C61×#1362C2semidirect
84. D488SD16semidirect
139. #1362D61semidirect
164. C61#12371semidirect

Maximal subgroups

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

subgroupindex
#214575392
#214480462
#214479572
#214452092
#214437792
#214437732
C61×#13622
#1237161