Finite Group Databasebeta

← #29593803

Subgroups — #29593803

Order 15616.

366 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 69 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#21457578C211yesmaximal, characteristic
2#21448043C211yesmaximal, characteristic, complemented
3#21447961C211yesmaximal, characteristic, complemented
4#21445209C211yesmaximal, characteristic, complemented
5#21443864C211yesmaximal, characteristic, complemented
6#21443775C211yesmaximal, characteristic, complemented
7C61×#1332C211yesmaximal, characteristic, complemented
8C2×#14519800—21no—
9#16840434—21no—
10#16840167C2211yescharacteristic
11#16840139C2211yescharacteristic
12#16839999—21no—
13#16839968—21no—
14#16839962—21no—
15#16839910—22no—
16C8×D244C2211yescharacteristic
17#16839589—21no—
18C4⋊#11758185C2211yescharacteristic
19#16839566—21no—
20#16839564—22no—
21#16839509—21no—
22C4×Q16×C61C2211yescharacteristic
23C4×C16×C61C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×#11758226—22no—
26#14519800—42no—
27#14519800—42no—
28C2×#11758190—41no—
29C2×#11758201—22no—
30C2×D488—21no—
31C2×D488D412yes—
32C2×C8×D61—21no—
33#14519777—21no—
34#14519774—21no—
35#14519774—41no—
36#14519752—22no—
37#14519752—42no—
38C4×D244—41no—
39C4×D244D411yescharacteristic
40C2×#11758185—21no—
41#14519711—21no—
42#14519711—21no—
43C4⋊#92418D411yescharacteristic
44#14519702—41no—
45#14519697—22no—
46#14519689—21no—
47C2×Q16×C61D411yescharacteristic
48C4×Q8×C61—21no—
49C2×C16×C61—21no—
50#107×C61D411yescharacteristic
51C4⋊C8×C61—21no—
52#103×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—21no—
55#11758226—44no—
56#11758226—82no—
57C2×D244—22no—
58C2×D244—42no—
59C2×D244—41no—
60C2×D244—42no—
61C2×D244—41no—
62C2×D244D811yescharacteristic
63C2×C4×D61—21no—
64C2×C4×D61—42no—
65C2×Dic122—41no—
66Q16×C61—21no—
67Q16×C61SD1612yescomplemented
68C2×C8×C61—41no—
69C2×C8×C61C2×D411yescharacteristic
70C2×C8×C61C2×D411yescharacteristic
71C4⋊C4×C61—21no—
72C4⋊C4×C61—41no—
73C42×C61—41no—
74C42×C61C2×D411yescharacteristic
75#11758201—44no—
76#11758198—21no—
77#11758198—42no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80C4⋊Dic61D811yescharacteristic
81C2×#92418—21no—
82D488—42no—
83D488—41no—
84D488—41no—
85#11758190—82no—
86C8×D61—41no—
87C8×D61—41no—
88C16×C61—41no—
89#11758185—41no—
90C22×D61—21no—
91C22×D61—42no—
92Q8×C61—22no—
93Q8×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61#12011yescharacteristic
97C2×C4×C61C2×D811yescharacteristic
98C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
99C2×Dic61—21no—
100C2×Dic61—81no—
101D244—21no—
102D244—21no—
103D244—42no—
104D244—42no—
105D244—84no—
106D244—81no—
107D244—81no—
108D244—161no—
109D244—162no—
110C4×D61—41no—
111C4×D61—41no—
112C4×D61—84no—
113Dic122—81no—
114Dic122—81no—
115C8×C61—21no—
116C8×C61—81no—
117C8×C61C2×SD1611yescharacteristic
118C8×C61AGL(1,ℤ/8)11yescharacteristic
119#92418—41no—
120#12369—611nomaximal, Sylow
121C22×C61#44711yescharacteristic
122C2×D61—41no—
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—82no—
126C2×D61—82no—
127C2×D61—82no—
128C4×C61—21no—
129C4×C61—42no—
130C4×C61—81no—
131C4×C61#45011yescharacteristic
132C4×C61#45511yescharacteristic
133C4×C61#50811yescharacteristic
134C4×C61#50911yescharacteristic
135Dic61—41no—
136Dic61—161no—
137#3287—611no—
138#2240—611no—
139#2225—611no—
140#1673—611no—
141#1361—611no—
142#1332D6111yescharacteristic, complemented
143D4⋊C16—611no—
144C2×C61#163911yescharacteristic
145C2×C61#218611yescharacteristic
146C2×C61#219411yescharacteristic
147D61—81no—
148D61—162no—
149C2×#135—1221no—
150#550—1221no—
151#500—611no—
152#493—611no—
153#466—1221no—
154#461—1221no—
155#460—1221no—
156#449—1222no—
157C4×Q16C2×D6111yescharacteristic
158C8×D4—611no—
159#367—1221no—
160C4⋊C16—611no—
161#358—1221no—
162#357—1222no—
163C4×C16C2×D6111yescharacteristic
164#335C2×D6111yescharacteristic
165#332—1221no—
166C61#1236911yescharacteristic, complemented, Sylow
167C2×#41—1222no—
168#135—2442no—
169#135—2442no—
170C2×Q16D24411yescharacteristic
171C2×SD16—1222no—
172C2×SD16—2441no—
173C2×D8—612no—
174C2×D8—1221no—
175C22×C8—1221no—
176C4⋊Q8—1221no—
177#127—1221no—
178#127—2441no—
179#121—1222no—
180#121—2442no—
181C4×Q8—21no—
182C4×D4—611no—
183C4×D4—2441no—
184C2×C16—21no—
185C2×C16—1221no—
186#107—1221no—
187#107—1221no—
188#107D24411yescharacteristic
189C4⋊C8—21no—
190C4⋊C8—611no—
191#103—21no—
192#103—2441no—
193#102—1222no—
194C22⋊C8—1221no—
195C4×C8C22×D6111yescharacteristic
196#41—4882no—
197#41—2444no—
198C2×Q8—21no—
199C2×Q8—2441no—
200C2×D4—611no—
201C2×D4—1222no—
202C2×D4—2442no—
203C2×D4—2442no—
204C2×D4—2441no—
205C2×D4—2441no—
206C22×C4—1221no—
207C22×C4—2442no—
208Q16—21no—
209Q16#1175819012yescomplemented
210SD16—4882no—
211SD16—2444no—
212D8—2442no—
213D8—2441no—
214D8—2441no—
215C2×C8—41no—
216C2×C8—1221no—
217C2×C8—2441no—
218C2×C8—2441no—
219C2×C8C2×D24411yescharacteristic
220C2×C8D4×D6111yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—41no—
223C4⋊C4—611no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C22⋊C4—1221no—
227C22⋊C4—2442no—
228C42—41no—
229C42D4×D6111yescharacteristic
230C16—41no—
231C16—2441no—
232C23—1221no—
233C23—2442no—
234Q8—22no—
235Q8—41no—
236Q8—4881no—
237Q8—4881no—
238D4—1221no—
239D4—1221no—
240D4—9761no—
241D4—9762no—
242D4—4884no—
243D4—4881no—
244D4—4881no—
245D4—2442no—
246D4—2442no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—1221no—
250C2×C4—4884no—
251C2×C4—4881no—
252C2×C4—2441no—
253C2×C4—2441no—
254C2×C4#1451974711yescharacteristic
255C2×C4D8×D6111yescharacteristic
256C2×C4#1451980411yescharacteristic
257C8—21no—
258C8—81no—
259C8—2441no—
260C8C2×#1175819011yescharacteristic
261C8#1451980511yescharacteristic
262C22—4882no—
263C22—4882no—
264C22—4882no—
265C22—2441no—
266C22—2441no—
267C22—2441no—
268C22#1683989711yescharacteristic
269C4—21no—
270C4—42no—
271C4—81no—
272C4—9761no—
273C4—2441no—
274C4#1683991511yescharacteristic
275C4#1683994111yescharacteristic
276C4#1684019511yescharacteristic
277C4#1684019911yescharacteristic
278C2—9762no—
279C2—4881no—
280C2#2144500111yescharacteristic
281C2#2144774511yescharacteristic
282C2#2144779111yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1332C2
socleC22×C61#447
prime radical#21457578C2
hypercenter#1332D61
hypocenterC61#12369
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1332

Complements

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

NH ≅ G/Ntype
2. #21448043C2semidirect
3. #21447961C2semidirect
4. #21445209C2semidirect
5. #21443864C2semidirect
6. #21443775C2semidirect
7. C61×#1332C2semidirect
67. Q16×C61SD16semidirect
142. #1332D61semidirect
166. C61#12369semidirect
209. Q16#11758190semidirect

Maximal subgroups

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

subgroupindex
#214575782
#214480432
#214479612
#214452092
#214438642
#214437752
C61×#13322
#1236961