Finite Group Databasebeta

← #29593878

Subgroups — #29593878

Order 15616.

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

normal subgroups only

This group has 344 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#21458792C211yesmaximal, characteristic
2#21448042C211yesmaximal, characteristic, complemented
3#21447957C211yesmaximal, characteristic, complemented
4#21445214C211yesmaximal, characteristic, complemented
5#21443797C211yesmaximal, characteristic, complemented
6#21443779C211yesmaximal, characteristic, complemented
7C61×#1361C211yesmaximal, characteristic, complemented
8#16840432—21no—
9#16840167C2211yescharacteristic
10#16840137—21no—
11#16839973—21no—
12#16839955—22no—
13#16839954—21no—
14C8×Dic122C2211yescharacteristic
15C4×D488C2211yescharacteristic
16D8×Dic61—21no—
17#16839588—21no—
18#16839564—21no—
19#16839563—22no—
20C4×#11758185C2211yescharacteristic
21#16839509—21no—
22C61×#493C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×#11758224—41no—
26C2×Dic244—41no—
27C2×D488D411yescharacteristic
28C2×#11758199—22no—
29#14519777—21no—
30#14519773—22no—
31#14519749—42no—
32#14519748—41no—
33C4×Dic122D411yescharacteristic
34C4×D244—21no—
35D4×Dic61—22no—
36C2×#11758185—21no—
37#14519711—21no—
38#14519711—21no—
39#14519711D411yescharacteristic
40C4⋊#92418D411yescharacteristic
41#14519706—21no—
42#14519702—41no—
43#14519699—21no—
44#14519698—22no—
45C8×Dic61—21no—
46C2×D8×C61—21no—
47C2×D8×C61D412yes—
48#127×C61—21no—
49C2×C16×C61—21no—
50C4⋊C8×C61—21no—
51C4×C8×C61C2311yescharacteristic
52C2×D4×C61—22no—
53C2×D4×C61—41no—
54C2×D4×C61—41no—
55C2×C22⋊D61—42no—
56C2×C22⋊D61—42no—
57C22×Dic61—42no—
58#11758224—82no—
59#11758224—82no—
60C2×D244—21no—
61C2×C4×D61—41no—
62C2×Dic122—41no—
63C2×Dic122D811yescharacteristic
64D8×C61—42no—
65D8×C61—41no—
66D8×C61—41no—
67C2×C8×C61—41no—
68C2×C8×C61C2×D411yescharacteristic
69C2×C8×C61C2×D411yescharacteristic
70C42×C61C2×D411yescharacteristic
71C22⋊Dic61—42no—
72#11758199—82no—
73#11758198—41no—
74C4⋊Dic61—21no—
75C4⋊Dic61—41no—
76C4⋊Dic61—41no—
77C4⋊Dic61D811yescharacteristic
78#11758196—21no—
79C4×Dic61—21no—
80C2×#92418—21no—
81Dic244—82no—
82D488—21no—
83D488—21no—
84C16×C61—41no—
85#11758185—41no—
86C23×C61—42no—
87C22×D61—41no—
88D4×C61—42no—
89D4×C61—42no—
90D4×C61—81no—
91D4×C61—81no—
92D4×C61—161no—
93C2×C4×C61#12011yescharacteristic
94C2×C4×C61C2×D811yescharacteristic
95C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
96C22⋊D61—84no—
97C22⋊D61—162no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—41no—
101C2×Dic61—84no—
102C2×Dic61—81no—
103D244—41no—
104D244—41no—
105C4×D61—81no—
106C4×D61—81no—
107Dic122—21no—
108Dic122—81no—
109Dic122—81no—
110Dic122D1612yes—
111C8×C61—21no—
112C8×C61—81no—
113C8×C61#13511yescharacteristic
114C8×C61#13711yescharacteristic
115#92418—41no—
116#12380—611nomaximal, Sylow
117C22×C61—82no—
118C22×C61—82no—
119C22×C61—82no—
120C22×C61#44711yescharacteristic
121C2×D61—81no—
122C2×D61—81no—
123C2×D61—81no—
124C4×C61—21no—
125C4×C61#45211yescharacteristic
126C4×C61#45511yescharacteristic
127C4×C61C2×D1611yescharacteristic
128C4×C61#50911yescharacteristic
129Dic61—22no—
130Dic61—41no—
131Dic61—81no—
132Dic61—161no—
133#3391—611no—
134#2240—611no—
135#2224—611no—
136#1674—611no—
137#1361D6111yescharacteristic, complemented
138Q8⋊C16—611no—
139#1331—611no—
140C2×C61—162no—
141C2×C61#164111yescharacteristic
142C2×C61#218411yescharacteristic
143C2×C61#219411yescharacteristic
144D61—161no—
145#550—1221no—
146#500—611no—
147#493—1221no—
148#493C2×D6111yescharacteristic
149#462—1221no—
150#459—1221no—
151#459—1222no—
152C8×Q8—611no—
153C4×D8—611no—
154C4×D8—1221no—
155#366—1221no—
156C4⋊C16C2×D6111yescharacteristic
157#357—1221no—
158#357—1222no—
159C4×C16—611no—
160#335C2×D6111yescharacteristic
161#332—1221no—
162C61#1238011yescharacteristic, complemented, Sylow
163C2×#41—2441no—
164C2×Q16—2441no—
165C2×D8—21no—
166C2×D8—611no—
167C2×D8—1222no—
168C2×D8D24412yes—
169C4⋊Q8—1221no—
170#127—21no—
171#127—1222no—
172#121—2441no—
173#121—2442no—
174C4×Q8—611no—
175C4×D4—1222no—
176C4×D4—1221no—
177C2×C16—21no—
178C2×C16—1221no—
179#107—611no—
180#107—1221no—
181#107—1221no—
182C4⋊C8—21no—
183C4⋊C8—611no—
184C4⋊C8—1221no—
185#103—2441no—
186#102—1222no—
187#102—1221no—
188C4×C8—1221no—
189C4×C8C22×D6111yescharacteristic
190#41—4882no—
191#41—4882no—
192C2×Q8—611no—
193C2×Q8—2441no—
194C2×D4—22no—
195C2×D4—41no—
196C2×D4—41no—
197C2×D4—1221no—
198C2×D4—2442no—
199C2×D4—2442no—
200C22×C4—2442no—
201C22×C4—2441no—
202Q16—4882no—
203D8—42no—
204D8—41no—
205D8—41no—
206D8—1221no—
207D8—1221no—
208D8—4882no—
209C2×C8—41no—
210C2×C8—1221no—
211C2×C8C2×D24411yescharacteristic
212C2×C8D4×D6111yescharacteristic
213C4⋊C4—611no—
214C4⋊C4—1221no—
215C4⋊C4—1221no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C22⋊C4—2442no—
219C22⋊C4—2441no—
220C42—1221no—
221C42D4×D6111yescharacteristic
222C16—41no—
223C16—2441no—
224C23—42no—
225C23—2441no—
226Q8—612no—
227Q8—1221no—
228Q8—4881no—
229Q8—4881no—
230D4—42no—
231D4—42no—
232D4—81no—
233D4—81no—
234D4—161no—
235D4—9762no—
236D4—4884no—
237D4—2441no—
238D4—2441no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—4884no—
242C2×C4—4881no—
243C2×C4—4881no—
244C2×C4—4881no—
245C2×C4—2441no—
246C2×C4#1451974711yescharacteristic
247C2×C4D8×D6111yescharacteristic
248C2×C4#1451980411yescharacteristic
249C8—21no—
250C8—81no—
251C8—2441no—
252C8#1451979611yescharacteristic
253C8#1451980611yescharacteristic
254C22—82no—
255C22—82no—
256C22—82no—
257C22—4881no—
258C22—4881no—
259C22—4881no—
260C22#1683989711yescharacteristic
261C4—21no—
262C4—1222no—
263C4—9761no—
264C4—4881no—
265C4—2441no—
266C4#1683992511yescharacteristic
267C4#1683994211yescharacteristic
268C4D16×D6111yescharacteristic
269C4#1684019911yescharacteristic
270C2—162no—
271C2—9761no—
272C2#2144501311yescharacteristic
273C2#2144773211yescharacteristic
274C2#2144779311yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1361C2
socleC22×C61#447
prime radical#21458792C2
hypercenter#1361D61
hypocenterC61#12380
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
2. #21448042C2semidirect
3. #21447957C2semidirect
4. #21445214C2semidirect
5. #21443797C2semidirect
6. #21443779C2semidirect
7. C61×#1361C2semidirect
137. #1361D61semidirect
162. C61#12380semidirect

Maximal subgroups

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

subgroupindex
#214587922
#214480422
#214479572
#214452142
#214437972
#214437792
C61×#13612
#1238061