Finite Group Databasebeta

← #30600730

Subgroups — #30600730

Order 15616.

382 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 76 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#21462727C211yesmaximal, characteristic
2#21461213C211yesmaximal, characteristic
3#21461213C211yesmaximal, characteristic
4#21461183C211yesmaximal, characteristic
5#21460676C211yesmaximal, characteristic
6#21460642C211yesmaximal, characteristic
7#21456975C211yesmaximal, characteristic
8#16840813—22no—
9#16840812—21no—
10#16840811—21no—
11#16840787—22no—
12#16840784C2211yescharacteristic
13#16840784C2211yescharacteristic
14#16840780C2211yescharacteristic
15#16840698C2211yescharacteristic
16#16840616—22no—
17#16840616—22no—
18#16840612—21no—
19#16840612—21no—
20#16840317C2211yescharacteristic
21#16840317C2211yescharacteristic
22#16840167C411yescharacteristic, complemented
23#16840158C411yescharacteristic, complemented
24#16840112C411yescharacteristic, complemented
25#16840102—22no—
26#16840071—22no—
27#16839813C2211yescharacteristic
28C61×#487C411yescharacteristic, complemented
29C2×C4×#6923—21no—
30#14519844—22no—
31#14519844—21no—
32C4⋊#92420—22no—
33C4⋊#92420—21no—
34C4⋊#92420—21no—
35#14519834—21no—
36#14519834—21no—
37#14519834D412yes—
38#14519832—22no—
39#14519832—21no—
40#14519832—21no—
41C4×#92420—22no—
42C4×#92420D411yescharacteristic
43C4×#92420D411yescharacteristic
44(C2×#6923)⋊C4—21no—
45(C2×#6923)⋊C4—21no—
46#14519777C2×C411yescharacteristic
47#14519777C2×C411yescharacteristic
48#14519768—21no—
49#14519768—21no—
50#14519757—21no—
51#14519757—21no—
52#14519753—21no—
53#14519753D412yes—
54Q8×Dic61—21no—
55Q8×Dic61D412yes—
56#14519742—21no—
57#14519742—21no—
58#14519735—21no—
59#14519735—21no—
60C42×D61C2311yescharacteristic
61#14519711—22no—
62#14519708—22no—
63#14519706—21no—
64#14519701—22no—
65#14519689—21no—
66C4×#92418C2×C411yescharacteristic
67C4⋊Q8×C61C2×C411yescharacteristic
68C4⋊Q8×C61C2×C411yescharacteristic
69#103×C61—22no—
70C4×C8×C61C2×C411yescharacteristic
71C22×#6923—41no—
72C2×Q8×C61—21no—
73C2×Q8×C61C22⋊C412yes—
74C2×C4×D61C2×D411yescharacteristic
75C2×C4×D61C2×D411yescharacteristic
76C2×C4×D61#4111yescharacteristic
77C2×Dic122—21no—
78C2×Dic122—21no—
79C2×#92420—21no—
80C2×#92420—22no—
81C2×#92420—21no—
82C2×#92420—41no—
83C4×#6923—22no—
84C4×#6923—41no—
85C2×C8×C61—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—21no—
90C42×C61C22×C411yescharacteristic
91#11758198—22no—
92#11758198—41no—
93C4⋊Dic61—21no—
94C4⋊Dic61—22no—
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61—41no—
98C4⋊Dic61C22⋊C412yes—
99#11758196—22no—
100#11758196—41no—
101C4×Dic61—22no—
102C4×Dic61—41no—
103C4×Dic61C2×D411yescharacteristic
104C4×Dic61C2×D411yescharacteristic
105C4×Dic61#4111yescharacteristic
106C2×#92418—21no—
107C22×D61#12111yescharacteristic
108C2×#6923—42no—
109C2×#6923—81no—
110C2×#6923—81no—
111Q8×C61—42no—
112Q8×C61—81no—
113C2×C4×C61—22no—
114C2×C4×C61—41no—
115C2×C4×C61C2×C22⋊C411yescharacteristic
116C2×C4×C61C4×D411yescharacteristic
117C2×C4×C61C4×D411yescharacteristic
118C2×Dic61—22no—
119C2×Dic61—41no—
120C2×Dic61#12011yescharacteristic
121C2×Dic61#12111yescharacteristic
122C2×Dic61#12311yescharacteristic
123C4×D61—21no—
124C4×D61—21no—
125C4×D61—41no—
126C4×D61—41no—
127Dic122—41no—
128Dic122—41no—
129Dic122—41no—
130Dic122—41no—
131#92420—41no—
132#92420—42no—
133#92420—41no—
134#92420—81no—
135C8×C61—41no—
136#92418—41no—
137#9280—611nomaximal, Sylow
138C22×C61#38611yescharacteristic
139C2×D61—21no—
140C2×D61—21no—
141C2×D61—21no—
142#6923—82no—
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—42no—
146C4×C61—81no—
147C4×C61#44311yescharacteristic
148C4×C61#44411yescharacteristic
149Dic61—21no—
150Dic61—21no—
151Dic61—21no—
152Dic61—42no—
153Dic61—81no—
154#3231—611no—
155#2985—611no—
156#1506—611no—
157#1506—611no—
158#1497—611no—
159#1287—611no—
160#1274—611no—
161C2×C61#187611yescharacteristic
162C2×C61#190511yescharacteristic
163C2×C61#190911yescharacteristic
164D61—41no—
165#533—611no—
166#533—611no—
167#500—611no—
168#498—611no—
169#487—611no—
170#487#692311yescharacteristic, complemented
171#485—1222no—
172#479—1222no—
173#446—1221no—
174#446—1222no—
175C8×Q8—1221no—
176#433—1222no—
177#432—611no—
178#432—611no—
179#431—611no—
180#431—611no—
181#376—611no—
182#328—1222no—
183#328—1222no—
184Q8⋊C8—1221no—
185Q8⋊C8—1221no—
186C61#928011yescharacteristic, complemented, Sylow
187C4⋊Q8—611no—
188C4⋊Q8—611no—
189C4⋊Q8C2×#692311yescharacteristic
190C4⋊Q8C2×#692311yescharacteristic
191#125—1221no—
192#125—1221no—
193C22⋊Q8—612no—
194C22⋊Q8—1221no—
195C22⋊Q8—1221no—
196C22⋊Q8—1221no—
197C4×Q8—612no—
198C4×Q8—1221no—
199C4×Q8—1221no—
200C4×Q8—1221no—
201#117—1221no—
202#117—1221no—
203C2×C42—611no—
204C2×C42—1221no—
205#107—1222no—
206#106—1222no—
207C4⋊C8—1221no—
208C4⋊C8—1221no—
209C4⋊C8—1221no—
210C4⋊C8—1221no—
211C4⋊C8—1222no—
212C4⋊C8—1222no—
213#103—22no—
214#103—1222no—
215C22⋊C8—612no—
216C22⋊C8—1221no—
217C22⋊C8—1221no—
218C22⋊C8—1221no—
219#97—1221no—
220#97—1221no—
221#97—1222no—
222C4×C8—611no—
223C4×C8—611no—
224C4×C8—611no—
225C4×C8—1222no—
226C4×C8C2×#692311yescharacteristic
227#95—1221no—
228#95—1221no—
229C2×Q8—21no—
230C2×Q8—1221no—
231C2×Q8—1221no—
232C2×Q8C22⋊#692312yes—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—2441no—
237C2×C8—21no—
238C2×C8—1221no—
239C2×C8—1221no—
240C2×C8—1222no—
241C2×C8—1221no—
242C2×C8—2441no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—612no—
248C4⋊C4—1222no—
249C4⋊C4—1222no—
250C4⋊C4—1221no—
251C4⋊C4—1221no—
252C4⋊C4—1221no—
253C4⋊C4—2441no—
254C4⋊C4—2441no—
255C22⋊C4—1222no—
256C22⋊C4—2441no—
257C42—611no—
258C42—611no—
259C42—611no—
260C42—1222no—
261C42—1222no—
262C42—2441no—
263C42—2441no—
264C42C22×#692311yescharacteristic
265C23—611no—
266Q8—42no—
267Q8—81no—
268Q8—2441no—
269Q8—2441no—
270Q8—2441no—
271Q8—2441no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—611no—
275C2×C4—611no—
276C2×C4—611no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—1222no—
280C2×C4—4881no—
281C2×C4—4881no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2442no—
285C2×C4—2441no—
286C2×C4C2×C22⋊#692311yescharacteristic
287C2×C4D4×#692311yescharacteristic
288C2×C4D4×#692311yescharacteristic
289C8—41no—
290C8—4881no—
291C8—2441no—
292C8—2441no—
293C8—2441no—
294C8—2442no—
295C22—1221no—
296C22—1221no—
297C22—1221no—
298C22#1684071011yescharacteristic
299C4—21no—
300C4—21no—
301C4—42no—
302C4—81no—
303C4—1221no—
304C4—1221no—
305C4—1221no—
306C4—4882no—
307C4—4881no—
308C4—2442no—
309C4#1684080611yescharacteristic
310C4#1684080811yescharacteristic
311C2—2441no—
312C2#2146180911yescharacteristic
313C2#2146185511yescharacteristic
314C2#2146186011yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#487C4
socleC22×C61#386
prime radicalC22×D61#121
cosocleC42×D61C23
hypercenter#487#6923
hypocenterC61#9280
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
22. #16840167C4semidirect
23. #16840158C4semidirect
24. #16840112C4semidirect
28. C61×#487C4semidirect
170. #487#6923semidirect
186. C61#9280semidirect

Maximal subgroups

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

subgroupindex
#214627272
#214612132
#214611832
#214606762
#214606422
#214569752
#928061