Finite Group Databasebeta

← #30601925

Subgroups — #30601925

Order 15616.

462 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 86 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#21461475C211yesmaximal, characteristic, complemented
2#21461380C211yesmaximal, characteristic, complemented
3#21461289C212yesmaximal, complemented
4#21461208C212yesmaximal, complemented
5#21456396C211yesmaximal, characteristic
6#16840784C2212yes—
7#16840721C2211yescharacteristic
8C2×#14519831—21no—
9C2×C8×#6923—21no—
10#16840698C2211yescharacteristic
11#16840625—21no—
12#16840623—21no—
13#16840617—24no—
14#16840613—24no—
15#16840310C2212yes—
16#16840167C411yescharacteristic, complemented
17#16840108C412yescomplemented
18#16839995—21no—
19#16839995—21no—
20D8×Dic61—21no—
21D8×Dic61—21no—
22C4×C8×D61C2211yescharacteristic
23C61×#493C411yescharacteristic, complemented
24C2×D61⋊C8—21no—
25C2×C4×#6923—21no—
26C4⋊#92420—22no—
27#14519834—22no—
28#14519832—22no—
29#14519832—21no—
30#14519832D412yes—
31#14519831—24no—
32C8×#6923—24no—
33(C2×#6923)⋊C4—21no—
34(C2×#6923)⋊C4D412yes—
35C2×#11758224—22no—
36C2×C8×D61D411yescharacteristic
37C2×C8×D61D411yescharacteristic
38#14519777C2×C412yes—
39#14519764—22no—
40#14519748—22no—
41#14519748—22no—
42D4×Dic61—22no—
43D4×Dic61—22no—
44C42×D61C2311yescharacteristic
45#14519711—21no—
46#14519711—21no—
47#14519698—22no—
48#14519698—22no—
49C4×#92418C2×C411yescharacteristic
50C8×Dic61D411yescharacteristic
51C8×Dic61D411yescharacteristic
52C2×D8×C61—21no—
53C2×D8×C61—21no—
54#127×C61C2×C412yes—
55C4×C8×C61C2×C411yescharacteristic
56C22×#6923—22no—
57C2×D4×C61—22no—
58C2×D4×C61—22no—
59C2×D4×C61—22no—
60C2×C22⋊D61—42no—
61C22×Dic61—42no—
62#11758224—84no—
63C2×C4×D61C2×D411yescharacteristic
64C2×C4×D61C2×D411yescharacteristic
65C2×C4×D61#4111yescharacteristic
66C2×Dic122—22no—
67C2×#92420—22no—
68C2×#92420—42no—
69C4×#6923—22no—
70C4×#6923—22no—
71D61⋊C8—22no—
72D61⋊C8—22no—
73D8×C61—42no—
74D8×C61—42no—
75C2×C8×C61C22⋊C411yescharacteristic
76C2×C8×C61C22⋊C411yescharacteristic
77C42×C61C22×C411yescharacteristic
78C22⋊Dic61—42no—
79C22⋊Dic61—42no—
80C4⋊Dic61—22no—
81C4⋊Dic61—22no—
82C4×Dic61C2×D411yescharacteristic
83C4×Dic61C2×D411yescharacteristic
84C4×Dic61#4111yescharacteristic
85C2×#92418C22⋊C411yescharacteristic
86C2×#92418C22⋊C411yescharacteristic
87C8×D61—22no—
88C8×D61—22no—
89C23×C61—42no—
90C22×D61#12111yescharacteristic
91C2×#6923—24no—
92C2×#6923—42no—
93C2×#6923—42no—
94D4×C61—42no—
95D4×C61—42no—
96D4×C61—82no—
97D4×C61—82no—
98C2×C4×C61C2×C22⋊C411yescharacteristic
99C2×C4×C61C4×D411yescharacteristic
100C2×C4×C61C4×D411yescharacteristic
101C22⋊D61—84no—
102C2×Dic61—42no—
103C2×Dic61—84no—
104C2×Dic61#12111yescharacteristic
105C2×Dic61#12411yescharacteristic
106C2×Dic61#12711yescharacteristic
107C4×D61—22no—
108C4×D61—21no—
109C4×D61—21no—
110C4×D61—41no—
111Dic122—82no—
112#92420—24no—
113#92420—82no—
114C8×C61#10412yes—
115C8×C61#10412yes—
116#92418—21no—
117#92418—21no—
118#9762—611nomaximal, Sylow
119C22×C61—82no—
120C22×C61—82no—
121C22×C61—82no—
122C22×C61#39011yescharacteristic
123C2×D61—21no—
124C2×D61—21no—
125C2×D61#47212yes—
126#6923—44no—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61C2×#10411yescharacteristic
130C4×C61C2×#10411yescharacteristic
131Dic61—21no—
132Dic61—21no—
133Dic61—21no—
134Dic61—82no—
135#3169—611no—
136#1726—611no—
137#1568—611no—
138#1530—612no—
139#1505—612no—
140C2×C61—162no—
141C2×C61#196211yescharacteristic
142C2×C61#197611yescharacteristic
143C2×C61#197811yescharacteristic
144D61—22no—
145#532—612no—
146#500—611no—
147#493#692311yescharacteristic, complemented
148#486—612no—
149#466—1221no—
150#466—1221no—
151C4×D8—1221no—
152C4×D8—1221no—
153#432—612no—
154C2×#97—611no—
155C2×#97—1221no—
156C2×C4×C8—611no—
157C2×C4×C8—1221no—
158#376—611no—
159#335—1221no—
160#334—1221no—
161#329—1224no—
162#327—1224no—
163C61#976211yescharacteristic, complemented, Sylow
164C2×#41—1222no—
165C2×D8—21no—
166C2×D8—21no—
167C22×C8—611no—
168C22×C8—611no—
169C22×C8—1221no—
170C4⋊Q8—612no—
171#127C2×#692312yes—
172#124—1222no—
173#121—1222no—
174#121—1222no—
175C4×D4—1222no—
176C4×D4—1222no—
177C2×C42—611no—
178C2×C42—1221no—
179#107—1221no—
180#107—1221no—
181C4⋊C8—1222no—
182#102—1222no—
183#102—1222no—
184C22⋊C8—1222no—
185#97—612no—
186#97—1221no—
187#97—1222no—
188#97—1224no—
189C4×C8—611no—
190C4×C8—611no—
191C4×C8—611no—
192C4×C8—1224no—
193C4×C8C2×#692311yescharacteristic
194#95—612no—
195#95—1221no—
196#41—4884no—
197C2×Q8—1222no—
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—22no—
201C2×D4—2442no—
202C22×C4—611no—
203C22×C4—611no—
204C22×C4—611no—
205C22×C4—1222no—
206C22×C4—2442no—
207D8—42no—
208D8—42no—
209C2×C8—611no—
210C2×C8—611no—
211C2×C8—1222no—
212C2×C8—1222no—
213C2×C8—1222no—
214C2×C8—1222no—
215C2×C8—1222no—
216C2×C8—2442no—
217C2×C8C22⋊#692311yescharacteristic
218C2×C8C22⋊#692311yescharacteristic
219C4⋊C4—1222no—
220C4⋊C4—1222no—
221C22⋊C4—2442no—
222C22⋊C4—2442no—
223C42—611no—
224C42—611no—
225C42—611no—
226C42—1222no—
227C42—1222no—
228C42C22×#692311yescharacteristic
229C23—42no—
230C23—611no—
231Q8—4882no—
232D4—42no—
233D4—42no—
234D4—82no—
235D4—82no—
236D4—4884no—
237C2×C4—611no—
238C2×C4—611no—
239C2×C4—611no—
240C2×C4—1222no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—1224no—
244C2×C4—4884no—
245C2×C4—2441no—
246C2×C4—2442no—
247C2×C4—2442no—
248C2×C4—2442no—
249C2×C4C2×C22⋊#692311yescharacteristic
250C2×C4D4×#692311yescharacteristic
251C2×C4D4×#692311yescharacteristic
252C8—1224no—
253C8—1221no—
254C8—1221no—
255C8—4882no—
256C8#1451984112yes—
257C8#1451984112yes—
258C22—82no—
259C22—82no—
260C22—82no—
261C22—612no—
262C22—1221no—
263C22—1221no—
264C22#1684071411yescharacteristic
265C4—21no—
266C4—21no—
267C4—1221no—
268C4—1221no—
269C4—1221no—
270C4—4882no—
271C4—2444no—
272C4C2×#1451984111yescharacteristic
273C4C2×#1451984111yescharacteristic
274C2—162no—
275C2—1222no—
276C2#2146195311yescharacteristic
277C2#2146197611yescharacteristic
278C2#2146198011yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#493C4
socleC22×C61#390
prime radical#21456396C2
cosocleC42×D61C23
hypercenter#493#6923
hypocenterC61#9762
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #21461475C2semidirect
2. #21461380C2semidirect
3. #21461289C2semidirect
4. #21461208C2semidirect
16. #16840167C4semidirect
17. #16840108C4semidirect
23. C61×#493C4semidirect
147. #493#6923semidirect
163. C61#9762semidirect

Maximal subgroups

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

subgroupindex
#214614752
#214613802
#214612892
#214612082
#214563962
#976261