Finite Group Databasebeta

← #30601072

Subgroups — #30601072

Order 15616.

422 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 74 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#21462364C211yesmaximal, characteristic
2#21461353C211yesmaximal, characteristic
3#21461243C211yesmaximal, characteristic
4#21461242C211yesmaximal, characteristic
5#21460679C211yesmaximal, characteristic
6#21460679C211yesmaximal, characteristic
7#21456196C211yesmaximal, characteristic
8#16840785C2211yescharacteristic
9#16840785C2211yescharacteristic
10(C2×#6923)⋊Q8—22no—
11#16840711—22no—
12#16840711—22no—
13#16840707C2211yescharacteristic
14#16840707C2211yescharacteristic
15#16840622—22no—
16#16840616—22no—
17#16840615—22no—
18#16840317C2211yescharacteristic
19C4⋊Q8×D61C2211yescharacteristic
20#16840129—22no—
21#16840114C411yescharacteristic, complemented
22#16840113C411yescharacteristic, complemented
23#16840112C411yescharacteristic, complemented
24#16839769—22no—
25C4×#11758189C2211yescharacteristic
26C61×#487C411yescharacteristic, complemented
27C2×C4⋊#6923—22no—
28C2×C4×#6923—22no—
29#14519844—21no—
30#14519844—21no—
31#14519834—21no—
32#14519834—21no—
33#14519832—21no—
34#14519832—21no—
35(C2×#6923)⋊C4—24no—
36(C2×#6923)⋊C4—21no—
37(C2×#6923)⋊C4—21no—
38(C2×#6923)⋊C4—21no—
39(C2×#6923)⋊C4—21no—
40(C2×#6923)⋊C4D412yes—
41(C2×#6923)⋊C4D412yes—
42C2×Q8×D61D412yes—
43C2×#11758189—21no—
44#14519777C2×C411yescharacteristic
45#14519777C2×C411yescharacteristic
46#14519776—21no—
47#14519776—21no—
48#14519775D412yes—
49#14519768—21no—
50#14519757—21no—
51#14519753—21no—
52Q8×Dic61—21no—
53#14519742—21no—
54#14519735—21no—
55C4⋊C4×D61—21no—
56C4⋊C4×D61—21no—
57C42×D61C2311yescharacteristic
58#14519702—22no—
59#14519701—22no—
60#14519700—22no—
61#14519687—21no—
62C4×#92418C2×C411yescharacteristic
63C4⋊Q8×C61C2×C411yescharacteristic
64C4⋊Q8×C61C2×C411yescharacteristic
65#103×C61—22no—
66C4×C8×C61C2×C411yescharacteristic
67C22×#6923—22no—
68C22×#6923—22no—
69C2×Q8×C61—21no—
70C2×Q8×C61C22⋊C412yes—
71Q8×D61—42no—
72Q8×D61—42no—
73C2×C4×D61—22no—
74C2×C4×D61C2×D411yescharacteristic
75C2×C4×D61C2×D411yescharacteristic
76C2×C4×D61C2×D411yescharacteristic
77C2×Dic122—22no—
78C2×Dic122—21no—
79C2×Dic122C22⋊C412yes—
80C2×#92420—41no—
81C2×#92420—41no—
82C4⋊#6923—82no—
83C4×#6923—82no—
84C2×C8×C61—21no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61—21no—
89C42×C61C22×C411yescharacteristic
90#11758198—41no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61—41no—
96#11758196—22no—
97#11758196—22no—
98#11758196—41no—
99C4×Dic61—41no—
100C4×Dic61C2×D411yescharacteristic
101C4×Dic61#4111yescharacteristic
102C4×Dic61#4111yescharacteristic
103C2×#92418—21no—
104#11758189—42no—
105C22×D61#12011yescharacteristic
106C2×#6923—42no—
107C2×#6923—42no—
108C2×#6923—42no—
109C2×#6923—42no—
110C2×#6923—42no—
111C2×#6923—42no—
112Q8×C61—42no—
113Q8×C61—81no—
114C2×C4×C61—22no—
115C2×C4×C61—41no—
116C2×C4×C61C2×C22⋊C411yescharacteristic
117C2×C4×C61C4×D411yescharacteristic
118C2×C4×C61C4×D411yescharacteristic
119C2×Dic61—22no—
120C2×Dic61—41no—
121C2×Dic61#12111yescharacteristic
122C2×Dic61#12111yescharacteristic
123C2×Dic61#12311yescharacteristic
124C4×D61—22no—
125C4×D61—41no—
126C4×D61—41no—
127C4×D61—42no—
128C4×D61—42no—
129Dic122—42no—
130Dic122—82no—
131Dic122—81no—
132#92420—81no—
133#92420—81no—
134C8×C61—41no—
135#92418—41no—
136#9426—611nomaximal, Sylow
137C22×C61#38611yescharacteristic
138C2×D61—21no—
139C2×D61—21no—
140C2×D61#45512yes—
141#6923—82no—
142#6923—82no—
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—42no—
147C4×C61—81no—
148Dic61—21no—
149Dic61—21no—
150Dic61—21no—
151Dic61—42no—
152Dic61—81no—
153#3139—611no—
154#2381—611no—
155#1558—611no—
156#1515—611no—
157#1515—611no—
158#1288—611no—
159#1288—611no—
160C2×C61#188511yescharacteristic
161C2×C61#190511yescharacteristic
162C2×C61#190511yescharacteristic
163D61—22no—
164#533—611no—
165C2×C4⋊Q8—611no—
166#491—1222no—
167#487—611no—
168#487—611no—
169#487—611no—
170#487#692311yescharacteristic, complemented
171#432—611no—
172#432—611no—
173#419—1222no—
174C4×M16—611no—
175#391—1222no—
176#387—1222no—
177#387—1222no—
178#383—611no—
179#383—611no—
180#333—1222no—
181#328—1222no—
182#328—1222no—
183C61#942611yescharacteristic, complemented, Sylow
184C22×Q8—612no—
185C2×M16—1221no—
186C4⋊Q8—612no—
187C4⋊Q8—611no—
188C4⋊Q8—611no—
189C4⋊Q8—1221no—
190C4⋊Q8—1221no—
191C4⋊Q8C2×#692311yescharacteristic
192C4⋊Q8C2×#692311yescharacteristic
193#125—1221no—
194C22⋊Q8—1221no—
195C22⋊Q8—1221no—
196C4×Q8—1221no—
197C4×Q8—1221no—
198#117—1221no—
199C2×C4⋊C4—1221no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—1222no—
202C2×C42—611no—
203C2×C42—1222no—
204C4⋊C8—1221no—
205C4⋊C8—1221no—
206#103—22no—
207#103—1222no—
208#103—1222no—
209#103—1222no—
210C22⋊C8—1221no—
211C22⋊C8—1221no—
212#97—1221no—
213#97—1221no—
214#97—1221no—
215C4×C8—611no—
216C4×C8C2×#692311yescharacteristic
217#95—612no—
218#95—612no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222#95—1221no—
223#95—1224no—
224C2×Q8—21no—
225C2×Q8—612no—
226C2×Q8—1222no—
227C2×Q8—1221no—
228C2×Q8—2442no—
229C2×Q8—2442no—
230C2×Q8C22⋊#692312yes—
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—611no—
234C22×C4—1222no—
235C22×C4—1222no—
236C22×C4—1222no—
237M16—2442no—
238C2×C8—21no—
239C2×C8—1221no—
240C2×C8—2441no—
241C2×C8—2441no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—1222no—
247C4⋊C4—1222no—
248C4⋊C4—1221no—
249C4⋊C4—1221no—
250C4⋊C4—1221no—
251C4⋊C4—1221no—
252C4⋊C4—4882no—
253C4⋊C4—2441no—
254C4⋊C4—2441no—
255C22⋊C4—2441no—
256C42—611no—
257C42—611no—
258C42—611no—
259C42—4882no—
260C42—2441no—
261C42C22×#692311yescharacteristic
262C23—611no—
263Q8—42no—
264Q8—81no—
265Q8—4881no—
266Q8—4882no—
267Q8—2442no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—611no—
271C2×C4—611no—
272C2×C4—611no—
273C2×C4—1222no—
274C2×C4—1222no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2442no—
278C2×C4—2442no—
279C2×C4—2442no—
280C2×C4—2442no—
281C2×C4—2442no—
282C2×C4—2442no—
283C2×C4—2442no—
284C2×C4—2442no—
285C2×C4—2441no—
286C2×C4C2×C22⋊#692311yescharacteristic
287C2×C4D4×#692311yescharacteristic
288C2×C4D4×#692311yescharacteristic
289C8—41no—
290C8—4881no—
291C8—4881no—
292C8—2441no—
293C22—612no—
294C22—1221no—
295C22—1221no—
296C22#1684071011yescharacteristic
297C4—21no—
298C4—21no—
299C4—21no—
300C4—42no—
301C4—81no—
302C4—1221no—
303C4—1221no—
304C4—1221no—
305C4—4882no—
306C4—4882no—
307C4—4881no—
308C4—2442no—
309C2—1222no—
310C2#2146182411yescharacteristic
311C2#2146185411yescharacteristic
312C2#2146185511yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#487C4
socleC22×C61#386
prime radicalC22×D61#120
cosocleC42×D61C23
hypercenter#487#6923
hypocenterC61#9426
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
21. #16840114C4semidirect
22. #16840113C4semidirect
23. #16840112C4semidirect
26. C61×#487C4semidirect
170. #487#6923semidirect
183. C61#9426semidirect

Maximal subgroups

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

subgroupindex
#214623642
#214613532
#214612432
#214612422
#214606792
#214561962
#942661