Finite Group Databasebeta

← #29593539

Subgroups — #29593539

Order 15616.

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

normal subgroups only

This group has 328 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#21458809C211yesmaximal, characteristic, complemented
2#21447851C211yesmaximal, characteristic
3#21445176C211yesmaximal, characteristic, complemented
4#21443868C211yesmaximal, characteristic, complemented
5#21443799C211yesmaximal, characteristic, complemented
6#21443781C211yesmaximal, characteristic, complemented
7C61×#2248C211yesmaximal, characteristic, complemented
8#16840486—21no—
9C2×#14519718—21no—
10#16840147—21no—
11#16839986—22no—
12#16839964—21no—
13#16839959—21no—
14C8×Dic122C2211yescharacteristic
15Q16×Dic61—21no—
16C4×D488C2211yescharacteristic
17C4⋊#11758185C2211yescharacteristic
18#16839563—21no—
19#16839515C2211yescharacteristic
20#16839506—21no—
21C2×SD32×C61—22no—
22C61×#494C2211yescharacteristic
23C61×#493C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×#11758200—41no—
26C2×#11758201—22no—
27C2×D488D411yescharacteristic
28#14519772—42no—
29#14519766—22no—
30#14519757—41no—
31Q8×Dic61—22no—
32C4×Dic122D411yescharacteristic
33C4×D244—21no—
34#14519735—41no—
35#14519718—42no—
36C2×#11758185—21no—
37#14519711D411yescharacteristic
38C4⋊#92418—21no—
39C4⋊#92418D411yescharacteristic
40#14519706—21no—
41#14519701—22no—
42#14519699—21no—
43#14519698—41no—
44C8×Dic61—21no—
45C2×Q16×C61—21no—
46C2×Q16×C61D412yes—
47C2×D8×C61—21no—
48C2×D8×C61—21no—
49C4⋊Q8×C61—21no—
50#127×C61—21no—
51SD32×C61—44no—
52C2×C16×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—22no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C2×D4×C61—41no—
58C2×D244—21no—
59C2×C4×D61—41no—
60C2×Dic122D811yescharacteristic
61Q16×C61—42no—
62Q16×C61—41no—
63Q16×C61—41no—
64D8×C61—42no—
65D8×C61—41no—
66D8×C61—41no—
67C2×C8×C61C2×D411yescharacteristic
68C2×C8×C61C2×D411yescharacteristic
69C4⋊C4×C61—41no—
70C4⋊C4×C61—41no—
71C42×C61C2×D411yescharacteristic
72#11758201—82no—
73#11758200—82no—
74#11758198—42no—
75#11758198—42no—
76#11758198—41no—
77C4⋊Dic61—21no—
78C4⋊Dic61—42no—
79C4⋊Dic61D811yescharacteristic
80#11758196—21no—
81C4×Dic61—21no—
82C4×Dic61—42no—
83C2×#92418—21no—
84C2×#92418—41no—
85D488—21no—
86D488—21no—
87C16×C61—22no—
88#11758185—41no—
89C23×C61—81no—
90C22×D61—41no—
91Q8×C61—42no—
92Q8×C61—42no—
93D4×C61—81no—
94D4×C61—81no—
95D4×C61—81no—
96D4×C61—81no—
97D4×C61—161no—
98C2×C4×C61—42no—
99C2×C4×C61#12011yescharacteristic
100C2×C4×C61C2×D811yescharacteristic
101C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—41no—
105D244—41no—
106D244—41no—
107C4×D61—81no—
108C4×D61—81no—
109Dic122—21no—
110Dic122—21no—
111C8×C61—21no—
112C8×C61#13511yescharacteristic
113C8×C61AGL(1,ℤ/8)11yescharacteristic
114#92418—41no—
115#92418—81no—
116#12331—611nomaximal, Sylow
117C22×C61—161no—
118C22×C61—161no—
119C22×C61—161no—
120C22×C61#44711yescharacteristic
121C2×D61—81no—
122C2×D61—81no—
123C2×D61—81no—
124C4×C61—21no—
125C4×C61—82no—
126C4×C61#44911yescharacteristic
127C4×C61#45311yescharacteristic
128C4×C61#50811yescharacteristic
129C4×C61#50911yescharacteristic
130Dic61—41no—
131Dic61—41no—
132Dic61—81no—
133#3393—611no—
134#2248D6111yescharacteristic, complemented
135#2206—611no—
136#1668—611no—
137#1362—611no—
138Q8⋊C16—611no—
139#1331—611no—
140C2×C61—321no—
141C2×C61#162111yescharacteristic
142C2×C61#218611yescharacteristic
143C2×C61#219311yescharacteristic
144D61—161no—
145#556—1221no—
146C2×SD32—22no—
147C2×D16—1221no—
148#495—1221no—
149#494C2×D6111yescharacteristic
150#493C2×D6111yescharacteristic
151#464—1222no—
152#461—1221no—
153#460—1221no—
154C8×Q8—611no—
155C4×Q16—1221no—
156C4×D8—611no—
157C4⋊C16—611no—
158#357—1221no—
159C4×C16C2×D6111yescharacteristic
160#335—611no—
161#331—1221no—
162C61#1233111yescharacteristic, complemented, Sylow
163C2×Q16—21no—
164C2×Q16C22⋊D6112yes—
165C2×SD16—1222no—
166C2×SD16—2441no—
167C2×D8—21no—
168C2×D8—21no—
169C2×D8—611no—
170C4⋊Q8—21no—
171#127—21no—
172#126—2442no—
173#124—1222no—
174C22⋊Q8—2441no—
175C4×Q8—611no—
176C4×Q8—1222no—
177C4×D4—1221no—
178#117—2441no—
179SD32—44no—
180D16—2442no—
181C2×C16—21no—
182C2×C16—1221no—
183#107—611no—
184C4⋊C8—611no—
185C4⋊C8—1221no—
186C4⋊C8—1221no—
187#103—1222no—
188#102—1221no—
189#102—2441no—
190C4×C8—1221no—
191C4×C8C22×D6111yescharacteristic
192C2×Q8—22no—
193C2×Q8—611no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4—41no—
197C2×D4—1221no—
198C22×C4—2441no—
199Q16—42no—
200Q16—41no—
201Q16—41no—
202SD16—4882no—
203SD16—4882no—
204D8—42no—
205D8—41no—
206D8—41no—
207D8—1221no—
208D8—1221no—
209C2×C8—1221no—
210C2×C8—2441no—
211C2×C8D4×D6111yescharacteristic
212C2×C8C2×C22⋊D6111yescharacteristic
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—611no—
216C4⋊C4—1221no—
217C4⋊C4—1221no—
218C4⋊C4—2442no—
219C22⋊C4—2442no—
220C22⋊C4—2442no—
221C22⋊C4—2441no—
222C42—1221no—
223C42—2442no—
224C42D4×D6111yescharacteristic
225C16—22no—
226C16—2441no—
227C23—81no—
228C23—2441no—
229Q8—42no—
230Q8—42no—
231Q8—1221no—
232Q8—1221no—
233D4—81no—
234D4—81no—
235D4—81no—
236D4—81no—
237D4—161no—
238D4—2441no—
239D4—2441no—
240C2×C4—42no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—4881no—
244C2×C4—4881no—
245C2×C4—2441no—
246C2×C4#1451974511yescharacteristic
247C2×C4D8×D6111yescharacteristic
248C2×C4#1451980111yescharacteristic
249C8—21no—
250C8—4881no—
251C8—2441no—
252C8#1451979611yescharacteristic
253C8#1451980111yescharacteristic
254C22—161no—
255C22—161no—
256C22—161no—
257C22—4881no—
258C22—4881no—
259C22—4881no—
260C22#1683989411yescharacteristic
261C4—21no—
262C4—82no—
263C4—4881no—
264C4—2441no—
265C4—2441no—
266C4#1683990411yescharacteristic
267C4#1683992911yescharacteristic
268C4#1684019311yescharacteristic
269C4#1684019911yescharacteristic
270C2—321no—
271C2—9761no—
272C2#2144488111yescharacteristic
273C2#2144774111yescharacteristic
274C2#2144778211yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2248C2
socleC22×C61#447
prime radical#21447851C2
hypercenter#2248D61
hypocenterC61#12331
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
1. #21458809C2semidirect
3. #21445176C2semidirect
4. #21443868C2semidirect
5. #21443799C2semidirect
6. #21443781C2semidirect
7. C61×#2248C2semidirect
134. #2248D61semidirect
162. C61#12331semidirect

Maximal subgroups

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

subgroupindex
#214588092
#214478512
#214451762
#214438682
#214437992
#214437812
C61×#22482
#1233161