Finite Group Databasebeta

← #30601049

Subgroups — #30601049

Order 15616.

380 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 72 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#21462733C211yesmaximal, characteristic
2#21461311C211yesmaximal, characteristic
3#21461243C211yesmaximal, characteristic
4#21461243C211yesmaximal, characteristic
5#21460686C211yesmaximal, characteristic
6#21460679C211yesmaximal, characteristic
7#21456563C211yesmaximal, characteristic
8#16840814—22no—
9#16840813—22no—
10#16840787—22no—
11#16840785C2211yescharacteristic
12#16840785C2211yescharacteristic
13#16840785C2211yescharacteristic
14#16840707C2211yescharacteristic
15#16840619—22no—
16#16840616—22no—
17#16840616—22no—
18#16840317C2211yescharacteristic
19#16840317C2211yescharacteristic
20#16840158C411yescharacteristic, complemented
21#16840141C411yescharacteristic, complemented
22#16840113C411yescharacteristic, complemented
23#16840019—22no—
24#16839866—22no—
25C4×#11758189C2211yescharacteristic
26C61×#487C411yescharacteristic, complemented
27#14519844—22no—
28#14519844—21no—
29#14519844—21no—
30#14519844—21no—
31C4⋊#92420—22no—
32#14519834—21no—
33#14519834—21no—
34#14519834D412yes—
35#14519832—22no—
36#14519832—21no—
37#14519832—21no—
38#14519832D412yes—
39C4×#92420—22no—
40(C2×#6923)⋊C4—21no—
41(C2×#6923)⋊C4—21no—
42(C2×#6923)⋊C4—21no—
43C2×#11758202—22no—
44C2×#11758189—21no—
45#14519777C2×C411yescharacteristic
46#14519777C2×C411yescharacteristic
47#14519768—21no—
48#14519768—21no—
49#14519757—21no—
50#14519757—21no—
51#14519753—21no—
52#14519753D412yes—
53Q8×Dic61—21no—
54Q8×Dic61D412yes—
55#14519742—21no—
56#14519742—21no—
57#14519735—21no—
58#14519735—21no—
59C42×D61C2311yescharacteristic
60#14519708—22no—
61#14519702—22no—
62#14519687—21no—
63C4×#92418C2×C411yescharacteristic
64C4⋊Q8×C61C2×C411yescharacteristic
65C4⋊Q8×C61C2×C411yescharacteristic
66#103×C61—22no—
67C4×C8×C61C2×C411yescharacteristic
68C22×#6923—41no—
69C2×Q8×C61—21no—
70C2×Q8×C61C22⋊C412yes—
71C2×C4×D61C2×D411yescharacteristic
72C2×C4×D61C2×D411yescharacteristic
73C2×C4×D61#4111yescharacteristic
74C2×Dic122—21no—
75C2×Dic122—21no—
76C2×#92420—22no—
77C2×#92420—22no—
78C2×#92420—41no—
79C2×C8×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61—21no—
84C42×C61C22×C411yescharacteristic
85#11758202—44no—
86#11758198—22no—
87#11758198—41no—
88C4⋊Dic61—21no—
89C4⋊Dic61—22no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—41no—
93C4⋊Dic61C22⋊C412yes—
94#11758196—22no—
95#11758196—41no—
96C4×Dic61—22no—
97C4×Dic61—41no—
98C4×Dic61C2×D411yescharacteristic
99C4×Dic61C2×D411yescharacteristic
100C4×Dic61#4111yescharacteristic
101C2×#92418—21no—
102#11758189—42no—
103C22×D61#12111yescharacteristic
104C2×#6923—81no—
105C2×#6923—81no—
106C2×#6923—81no—
107Q8×C61—42no—
108Q8×C61—81no—
109C2×C4×C61—22no—
110C2×C4×C61—41no—
111C2×C4×C61C2×C22⋊C411yescharacteristic
112C2×C4×C61C4×D411yescharacteristic
113C2×C4×C61C4×D411yescharacteristic
114C2×Dic61—22no—
115C2×Dic61—41no—
116C2×Dic61#12011yescharacteristic
117C2×Dic61#12111yescharacteristic
118C2×Dic61#12311yescharacteristic
119C4×D61—41no—
120C4×D61—41no—
121C4×D61—41no—
122Dic122—42no—
123Dic122—81no—
124#92420—42no—
125#92420—42no—
126#92420—81no—
127C8×C61—41no—
128#92418—22no—
129#9416—611nomaximal, Sylow
130C22×C61#38611yescharacteristic
131C2×D61—21no—
132C2×D61—21no—
133C2×D61—21no—
134#6923—161no—
135C4×C61—21no—
136C4×C61—21no—
137C4×C61—21no—
138C4×C61—42no—
139C4×C61—81no—
140Dic61—21no—
141Dic61—21no—
142Dic61—21no—
143Dic61—42no—
144Dic61—81no—
145#3185—611no—
146#2987—611no—
147#1537—611no—
148#1515—611no—
149#1515—611no—
150#1291—611no—
151#1288—611no—
152C2×C61#188411yescharacteristic
153C2×C61#190211yescharacteristic
154C2×C61#190511yescharacteristic
155D61—41no—
156#533—611no—
157#533—611no—
158#498—611no—
159#494—611no—
160#487—611no—
161#487#692311yescharacteristic, complemented
162#470—1222no—
163#446—1222no—
164#446—1222no—
165#441—1222no—
166#433—1222no—
167#432—611no—
168#432—611no—
169#432—611no—
170C4×M16—611no—
171#383—611no—
172#330—1222no—
173#328—1222no—
174#328—1222no—
175C61#941611yescharacteristic, complemented, Sylow
176C2×Q16—1222no—
177C2×M16—1221no—
178C4⋊Q8—611no—
179C4⋊Q8—611no—
180C4⋊Q8C2×#692311yescharacteristic
181C4⋊Q8C2×#692311yescharacteristic
182#125—1221no—
183#125—1221no—
184C22⋊Q8—612no—
185C22⋊Q8—1221no—
186C22⋊Q8—1221no—
187C22⋊Q8—1221no—
188C4×Q8—612no—
189C4×Q8—1221no—
190C4×Q8—1221no—
191C4×Q8—1221no—
192#117—1221no—
193#117—1221no—
194C2×C42—611no—
195#106—1222no—
196C4⋊C8—1221no—
197C4⋊C8—1221no—
198C4⋊C8—1221no—
199C4⋊C8—1222no—
200C4⋊C8—1222no—
201#103—22no—
202#103—1222no—
203C22⋊C8—612no—
204C22⋊C8—1221no—
205C22⋊C8—1221no—
206#97—612no—
207#97—1221no—
208#97—1221no—
209#97—1221no—
210#97—1222no—
211C4×C8—611no—
212C4×C8—1222no—
213C4×C8C2×#692311yescharacteristic
214#95—1221no—
215#95—1221no—
216#95—1221no—
217C2×Q8—21no—
218C2×Q8—1221no—
219C2×Q8—1221no—
220C2×Q8C22⋊#692312yes—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—611no—
224C22×C4—2441no—
225Q16—2444no—
226M16—2442no—
227C2×C8—21no—
228C2×C8—1221no—
229C2×C8—1222no—
230C2×C8—1222no—
231C2×C8—2441no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—612no—
237C4⋊C4—1222no—
238C4⋊C4—1222no—
239C4⋊C4—1221no—
240C4⋊C4—1221no—
241C4⋊C4—1221no—
242C4⋊C4—2441no—
243C4⋊C4—2441no—
244C22⋊C4—1222no—
245C22⋊C4—2441no—
246C42—611no—
247C42—611no—
248C42—611no—
249C42—1222no—
250C42—2441no—
251C42C22×#692311yescharacteristic
252C23—611no—
253Q8—42no—
254Q8—81no—
255Q8—4881no—
256Q8—2442no—
257C2×C4—22no—
258C2×C4—41no—
259C2×C4—611no—
260C2×C4—611no—
261C2×C4—611no—
262C2×C4—1222no—
263C2×C4—4881no—
264C2×C4—4881no—
265C2×C4—4881no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4C2×C22⋊#692311yescharacteristic
271C2×C4D4×#692311yescharacteristic
272C2×C4D4×#692311yescharacteristic
273C8—41no—
274C8—1222no—
275C8—4881no—
276C8—2442no—
277C8—2442no—
278C22—1221no—
279C22—1221no—
280C22—1221no—
281C22#1684071011yescharacteristic
282C4—21no—
283C4—21no—
284C4—21no—
285C4—42no—
286C4—81no—
287C4—1221no—
288C4—1221no—
289C4—1221no—
290C4—9761no—
291C4—4881no—
292C4—2442no—
293C2—2441no—
294C2#2146182011yescharacteristic
295C2#2146184911yescharacteristic
296C2#2146185511yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#487C4
socleC22×C61#386
prime radicalC22×D61#121
cosocleC42×D61C23
hypercenter#487#6923
hypocenterC61#9416
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
20. #16840158C4semidirect
21. #16840141C4semidirect
22. #16840113C4semidirect
26. C61×#487C4semidirect
161. #487#6923semidirect
175. C61#9416semidirect

Maximal subgroups

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

subgroupindex
#214627332
#214613112
#214612432
#214606862
#214606792
#214565632
#941661