Finite Group Databasebeta

← #30601061

Subgroups — #30601061

Order 15616.

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

normal subgroups only

This group has 424 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#21462704C211yesmaximal, characteristic
2#21461353C211yesmaximal, characteristic, complemented
3#21461349C211yesmaximal, characteristic, complemented
4#21461308C211yesmaximal, characteristic
5#21460686C211yesmaximal, characteristic, complemented
6#21460686C211yesmaximal, characteristic, complemented
7#21456209C211yesmaximal, characteristic
8#16840793—22no—
9#16840793—22no—
10#16840785C2211yescharacteristic
11#16840785C2211yescharacteristic
12#16840785C2211yescharacteristic
13#16840785C2211yescharacteristic
14#16840735—22no—
15#16840622—22no—
16#16840621—22no—
17#16840617—22no—
18#16840310C2211yescharacteristic
19C4⋊Q8×D61C2211yescharacteristic
20#16840120—22no—
21#16840114C411yescharacteristic
22#16840113C411yescharacteristic
23#16840108C411yescharacteristic
24#16839760—22no—
25C4×#11758189C2211yescharacteristic
26C61×#486C411yescharacteristic
27C2×#11758217—22no—
28C22×#92420—22no—
29#14519844—21no—
30#14519844—21no—
31#14519844D412yes—
32#14519844D412yes—
33#14519834—21no—
34#14519834—21no—
35#14519834—21no—
36#14519834—21no—
37C22⋊#92420—24no—
38#14519832—21no—
39#14519832—21no—
40#14519832—21no—
41#14519832—21no—
42C2×#11758224D412yes—
43C2×Q8×D61—21no—
44C2×#11758189—21no—
45#14519777C2×C411yescharacteristic
46#14519777C2×C411yescharacteristic
47#14519776—21no—
48#14519776—21no—
49#14519775—21no—
50#14519764D412yes—
51#14519748—21no—
52#14519748—21no—
53D4×Dic61—21no—
54D4×Dic61—21no—
55C4⋊C4×D61—21no—
56C4⋊C4×D61—21no—
57C42×D61C2311yescharacteristic
58#14519702—22no—
59#14519700—22no—
60#14519698—22no—
61#14519687—21no—
62C4×#92418C2×C411yescharacteristic
63C4⋊Q8×C61C2×C411yescharacteristic
64#127×C61C2×C411yescharacteristic
65#102×C61—22no—
66C4×C8×C61C2×C411yescharacteristic
67C2×Q8×C61—21no—
68C2×D4×C61—21no—
69C2×D4×C61—21no—
70C2×D4×C61C22⋊C412yes—
71C2×C22⋊D61—22no—
72C22×Dic61—22no—
73Q8×D61—82no—
74#11758224—42no—
75#11758224—42no—
76C2×C4×D61—41no—
77C2×C4×D61C2×D411yescharacteristic
78C2×C4×D61#4111yescharacteristic
79C2×C4×D61#4111yescharacteristic
80C2×Dic122—21no—
81C2×Dic122—41no—
82C2×Dic122C22⋊C412yes—
83#11758217—82no—
84C2×#92420—22no—
85C2×#92420—22no—
86C2×#92420—41no—
87C2×#92420—41no—
88C2×#92420—82no—
89C2×C8×C61—21no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61—21no—
92C42×C61C22×C411yescharacteristic
93C22⋊Dic61—22no—
94C22⋊Dic61—22no—
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61—21no—
99#11758196—41no—
100#11758196—41no—
101C4×Dic61C2×D411yescharacteristic
102C4×Dic61C2×D411yescharacteristic
103C4×Dic61C2×D411yescharacteristic
104C2×#92418—21no—
105#11758189—42no—
106C23×C61—22no—
107C22×D61#12311yescharacteristic
108Q8×C61—81no—
109D4×C61—42no—
110D4×C61—81no—
111D4×C61—81no—
112C2×C4×C61—41no—
113C2×C4×C61C2×C22⋊C411yescharacteristic
114C2×C4×C61C4×D411yescharacteristic
115C2×C4×C61C4×D411yescharacteristic
116C22⋊D61—82no—
117C2×Dic61—22no—
118C2×Dic61—42no—
119C2×Dic61—42no—
120C2×Dic61—41no—
121C2×Dic61#12011yescharacteristic
122C2×Dic61#12111yescharacteristic
123C2×Dic61#12111yescharacteristic
124C4×D61—22no—
125C4×D61—41no—
126C4×D61—41no—
127C4×D61—82no—
128Dic122—42no—
129Dic122—82no—
130Dic122—81no—
131#92420—42no—
132#92420—42no—
133#92420—81no—
134#92420—81no—
135C8×C61—41no—
136#92418—41no—
137#9419—611nomaximal, Sylow
138C22×C61—42no—
139C22×C61—42no—
140C22×C61—42no—
141C22×C61#38611yescharacteristic
142C2×D61—21no—
143C2×D61—21no—
144C2×D61—21no—
145C4×C61—21no—
146C4×C61—21no—
147C4×C61—21no—
148C4×C61—81no—
149Dic61—21no—
150Dic61—21no—
151Dic61—42no—
152Dic61—81no—
153Dic61#45512yes—
154#3141—611no—
155#2980—611no—
156#1558—611no—
157#1556—611no—
158#1536—611no—
159#1291—611no—
160#1291—611no—
161C2×C61—82no—
162C2×C61#188511yescharacteristic
163C2×C61#190211yescharacteristic
164C2×C61#190311yescharacteristic
165D61—41no—
166#532—611no—
167C2×C4⋊Q8—611no—
168#489—1222no—
169#487—611no—
170#487—611no—
171#486—611no—
172#486#692311yescharacteristic
173#435—1222no—
174#435—1222no—
175#432—611no—
176#432—611no—
177#432—611no—
178#432—611no—
179#417—1222no—
180#408—1222no—
181C4×M16—611no—
182#333—1222no—
183#332—1222no—
184#329—1222no—
185C61#941911yescharacteristic, complemented, Sylow
186C2×#41—612no—
187C22×Q8—1221no—
188C2×M16—1221no—
189C2×M16—1222no—
190C22×C8—1222no—
191C4⋊Q8—611no—
192C4⋊Q8—611no—
193C4⋊Q8—1221no—
194C4⋊Q8—1221no—
195C4⋊Q8—1221no—
196C4⋊Q8C2×#692311yescharacteristic
197#127C2×#692311yescharacteristic
198#124—612no—
199#121—1221no—
200#121—1221no—
201C4×D4—1221no—
202C4×D4—1221no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4—1221no—
205C2×C42—611no—
206C4⋊C8—612no—
207C4⋊C8—612no—
208C4⋊C8—1221no—
209C4⋊C8—1221no—
210#103—1222no—
211#103—1222no—
212#102—22no—
213#102—1222no—
214C22⋊C8—1221no—
215C22⋊C8—1221no—
216C22⋊C8—1224no—
217C22⋊C8—1221no—
218C22⋊C8—1221no—
219#97—1221no—
220#97—1221no—
221#97—1221no—
222#97—1221no—
223#97—1221no—
224C4×C8—611no—
225C4×C8C2×#692311yescharacteristic
226#41—2442no—
227#41—2442no—
228C2×Q8—21no—
229C2×Q8—612no—
230C2×Q8—1221no—
231C2×Q8—4882no—
232C2×Q8—2441no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—1222no—
236C2×D4C22⋊#692312yes—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—1222no—
241C22×C4—2441no—
242M16—4882no—
243M16—2442no—
244C2×C8—21no—
245C2×C8—1222no—
246C2×C8—1222no—
247C2×C8—1221no—
248C2×C8—4882no—
249C2×C8—2441no—
250C2×C8—2441no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—1221no—
254C4⋊C4—1221no—
255C4⋊C4—1221no—
256C4⋊C4—1221no—
257C4⋊C4—2441no—
258C4⋊C4—2441no—
259C22⋊C4—1222no—
260C22⋊C4—1222no—
261C42—611no—
262C42—611no—
263C42—611no—
264C42C22×#692311yescharacteristic
265C23—22no—
266C23—611no—
267Q8—81no—
268Q8—4881no—
269Q8—4882no—
270Q8—2442no—
271D4—42no—
272D4—81no—
273D4—81no—
274D4—4882no—
275C2×C4—41no—
276C2×C4—611no—
277C2×C4—611no—
278C2×C4—611no—
279C2×C4—1222no—
280C2×C4—1222no—
281C2×C4—4882no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2442no—
285C2×C4—2442no—
286C2×C4—2441no—
287C2×C4C2×C22⋊#692311yescharacteristic
288C2×C4D4×#692311yescharacteristic
289C2×C4D4×#692311yescharacteristic
290C8—41no—
291C8—4881no—
292C8—4881no—
293C8—2441no—
294C8—2442no—
295C8—2442no—
296C22—42no—
297C22—42no—
298C22—42no—
299C22—1221no—
300C22—1221no—
301C22—1221no—
302C22#1684071011yescharacteristic
303C4—21no—
304C4—21no—
305C4—21no—
306C4—81no—
307C4—612no—
308C4—1221no—
309C4—1221no—
310C4—4881no—
311C4—2442no—
312C2—82no—
313C2—2441no—
314C2#2146182411yescharacteristic
315C2#2146184811yescharacteristic
316C2#2146185011yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#486C4
socleC22×C61#386
prime radical#16840310C22
cosocleC42×D61C23
hypercenter#486#6923
hypocenterC61#9419
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #21461353C2semidirect
3. #21461349C2semidirect
5. #21460686C2semidirect
6. #21460686C2semidirect
185. C61#9419semidirect

Maximal subgroups

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

subgroupindex
#214627042
#214613532
#214613492
#214613082
#214606862
#214562092
#941961