Finite Group Databasebeta

← #29593625

Subgroups — #29593625

Order 15616.

318 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 65 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#21458243C211yesmaximal, characteristic, complemented
2#21448042C211yesmaximal, characteristic, complemented
3#21445171C211yesmaximal, characteristic, complemented
4#21443876C211yesmaximal, characteristic, complemented
5#21443780C211yesmaximal, characteristic, complemented
6#21443773C211yesmaximal, characteristic, complemented
7C61×#2206C211yesmaximal, characteristic, complemented
8#16840477—21no—
9#16840167C2211yescharacteristic
10#16840084—22no—
11#16840052—21no—
12#16839995—21no—
13#16839954—21no—
14C8×D244C2211yescharacteristic
15#16839799—21no—
16#16839563—22no—
17C4×#11758185C2211yescharacteristic
18#16839515C2211yescharacteristic
19#16839506—21no—
20C2×D16×C61—21no—
21C61×#493C2211yescharacteristic
22C4×D8×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#357—21no—
25C2×#11758199—41no—
26C2×C8×D61—21no—
27#14519777—21no—
28#14519763—42no—
29#14519751—41no—
30#14519748—22no—
31C4×D244D411yescharacteristic
32#14519736—41no—
33#14519735—22no—
34C2×#11758185—21no—
35#14519711—21no—
36#14519711D412yes—
37#14519708—22no—
38C4⋊#92418—21no—
39C4⋊#92418D411yescharacteristic
40#14519698—22no—
41#14519698—41no—
42#14519689—21no—
43C2×D8×C61—21no—
44C2×D8×C61—21no—
45C2×D8×C61D411yescharacteristic
46#127×C61—21no—
47C4×D4×C61—21no—
48D16×C61—42no—
49C2×C16×C61—21no—
50#107×C61D411yescharacteristic
51#102×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×D4×C61—21no—
54C2×D4×C61—41no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C22×C4×C61—41no—
58C2×C22⋊D61—42no—
59C2×D244D811yescharacteristic
60C2×C4×D61—21no—
61C2×Dic122—41no—
62D8×C61—21no—
63D8×C61—21no—
64D8×C61—42no—
65D8×C61—41no—
66D8×C61—41no—
67C2×C8×C61C2×D411yescharacteristic
68C2×C8×C61C2×D411yescharacteristic
69C4⋊C4×C61—21no—
70C22⋊C4×C61—41no—
71C42×C61C2×D411yescharacteristic
72C22⋊Dic61—42no—
73#11758199—82no—
74#11758198—21no—
75#11758198—42no—
76C4⋊Dic61—22no—
77C4⋊Dic61—41no—
78C4⋊Dic61D811yescharacteristic
79C4×Dic61—42no—
80C2×#92418—21no—
81C2×#92418—41no—
82C8×D61—41no—
83C8×D61—41no—
84C16×C61—41no—
85#11758185—41no—
86C23×C61—41no—
87C23×C61—81no—
88C22×D61—21no—
89D4×C61—41no—
90D4×C61—41no—
91D4×C61—81no—
92D4×C61—81no—
93D4×C61—81no—
94D4×C61—81no—
95D4×C61—161no—
96C2×C4×C61—41no—
97C2×C4×C61—81no—
98C2×C4×C61—81no—
99C2×C4×C61#12011yescharacteristic
100C2×C4×C61C2×D811yescharacteristic
101C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
102C22⋊D61—162no—
103C2×Dic61—21no—
104C2×Dic61—42no—
105D244—21no—
106D244—21no—
107C4×D61—41no—
108C4×D61—41no—
109Dic122—161no—
110C8×C61—21no—
111C8×C61#13511yescharacteristic
112C8×C61AGL(1,ℤ/8)11yescharacteristic
113#92418—41no—
114#92418—81no—
115#12343—611nomaximal, Sylow
116C22×C61—81no—
117C22×C61—81no—
118C22×C61—81no—
119C22×C61—161no—
120C22×C61—161no—
121C22×C61—161no—
122C22×C61#44711yescharacteristic
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—41no—
126C4×C61—21no—
127C4×C61—81no—
128C4×C61#44911yescharacteristic
129C4×C61#45411yescharacteristic
130C4×C61#50811yescharacteristic
131C4×C61#50911yescharacteristic
132Dic61—41no—
133Dic61—82no—
134#3341—611no—
135#2240—611no—
136#2206D6111yescharacteristic, complemented
137#1667—611no—
138#1365—611no—
139#1331—611no—
140D4⋊C16—611no—
141C2×C61—161no—
142C2×C61—321no—
143C2×C61#162511yescharacteristic
144C2×C61#218611yescharacteristic
145C2×C61#219211yescharacteristic
146D61—81no—
147#555—1221no—
148C2×D16—21no—
149#500—611no—
150#493C2×D6111yescharacteristic
151#482—1222no—
152#476—1221no—
153#466—1221no—
154#459—1221no—
155C4×D8C2×D6111yescharacteristic
156C8×D4—611no—
157#427—1221no—
158C4⋊C16C2×D6111yescharacteristic
159#357—21no—
160#357—1222no—
161C4×C16—611no—
162#335—611no—
163#331—1221no—
164C61#1234311yescharacteristic, complemented, Sylow
165C2×D8—21no—
166C2×D8—21no—
167C2×D8—2441no—
168C2×D8C22⋊D6111yescharacteristic
169C22×C8—1221no—
170C4⋊Q8—1221no—
171#127—21no—
172#124—2442no—
173#121—1222no—
174#121—2441no—
175C4×D4—21no—
176C4×D4—611no—
177#117—1222no—
178#117—2441no—
179D16—42no—
180C2×C16—21no—
181C2×C16—1221no—
182#107—612no—
183#107—1221no—
184#107C22⋊D6111yescharacteristic
185#106—1222no—
186C4⋊C8—611no—
187C4⋊C8—1221no—
188#102—21no—
189#102—1222no—
190#102—2441no—
191C22⋊C8—1221no—
192C4×C8C22×D6111yescharacteristic
193C2×Q8—2441no—
194C2×D4—21no—
195C2×D4—41no—
196C2×D4—41no—
197C2×D4—41no—
198C2×D4—611no—
199C2×D4—2442no—
200C22×C4—41no—
201C22×C4—1221no—
202D8—21no—
203D8—21no—
204D8—42no—
205D8—41no—
206D8—41no—
207D8—4882no—
208C2×C8—1221no—
209C2×C8—2441no—
210C2×C8—2441no—
211C2×C8—2441no—
212C2×C8D4×D6111yescharacteristic
213C2×C8C2×C22⋊D6111yescharacteristic
214C4⋊C4—21no—
215C4⋊C4—611no—
216C4⋊C4—1222no—
217C4⋊C4—2441no—
218C22⋊C4—41no—
219C22⋊C4—1221no—
220C22⋊C4—2442no—
221C22⋊C4—2442no—
222C42—2442no—
223C42D4×D6111yescharacteristic
224C16—41no—
225C16—2441no—
226C23—41no—
227C23—81no—
228C23—1221no—
229Q8—9761no—
230D4—41no—
231D4—41no—
232D4—81no—
233D4—81no—
234D4—81no—
235D4—81no—
236D4—161no—
237D4—1221no—
238D4—1221no—
239D4—9762no—
240C2×C4—41no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—1221no—
244C2×C4—2442no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4#1451974511yescharacteristic
248C2×C4D8×D6111yescharacteristic
249C2×C4#1451980111yescharacteristic
250C8—21no—
251C8—4881no—
252C8—2441no—
253C8#1451979711yescharacteristic
254C8#1451980311yescharacteristic
255C22—81no—
256C22—81no—
257C22—81no—
258C22—161no—
259C22—161no—
260C22—161no—
261C22—2441no—
262C22—2441no—
263C22—2441no—
264C22#1683989411yescharacteristic
265C4—21no—
266C4—81no—
267C4—4882no—
268C4—2441no—
269C4#1683990511yescharacteristic
270C4#1683993311yescharacteristic
271C4#1684019111yescharacteristic
272C4#1684019611yescharacteristic
273C2—161no—
274C2—321no—
275C2—4881no—
276C2#2144490711yescharacteristic
277C2#2144773911yescharacteristic
278C2#2144777311yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2206C2
socleC22×C61#447
hypercenter#2206D61
hypocenterC61#12343
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. #21458243C2semidirect
2. #21448042C2semidirect
3. #21445171C2semidirect
4. #21443876C2semidirect
5. #21443780C2semidirect
6. #21443773C2semidirect
7. C61×#2206C2semidirect
136. #2206D61semidirect
164. C61#12343semidirect

Maximal subgroups

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

subgroupindex
#214582432
#214480422
#214451712
#214438762
#214437802
#214437732
C61×#22062
#1234361