Finite Group Databasebeta

← #29600397

Subgroups — #29600397

Order 15616.

344 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 67 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#21456869C211yesmaximal, characteristic
2#21447511C211yesmaximal, characteristic, complemented
3#21443993C212yesmaximal, complemented
4#21443975C212yesmaximal, complemented
5C61×#2127C211yesmaximal, characteristic, complemented
6#16840367C411yescharacteristic, complemented
7#16840152C2211yescharacteristic
8#16840138C411yescharacteristic, complemented
9#16840126C411yescharacteristic, complemented
10#16840116C2211yescharacteristic
11#16839974—21no—
12#16839954—21no—
13#16839907—21no—
14#16839896—21no—
15#16839823C411yescharacteristic, complemented
16#16839746—21no—
17#16839559—21no—
18#16839559C2212yes—
19C61×#535C2211yescharacteristic
20C2×#99×C61—21no—
21C61×#354C2212yes—
22C61×#353—21no—
23C2×#11758201—21no—
24C2×#11758199—21no—
25C2×#11758199—21no—
26C2×#11758199—21no—
27C2×#11758194—41no—
28#14519774C2×C411yescharacteristic, complemented
29#14519769C2×C411yescharacteristic, complemented
30#14519762—41no—
31#14519751—21no—
32#14519750—41no—
33C4×D244—21no—
34C4⋊#92418—21no—
35#14519701—21no—
36#14519698—21no—
37#14519698—21no—
38#14519698—21no—
39#14519696—22no—
40#14519694—41no—
41C22⋊#92418—21no—
42#14519688C2×C411yescharacteristic, complemented
43C4×#92418C2×C411yescharacteristic, complemented
44C2×#41×C61D411yescharacteristic
45C22×D4×C61D411yescharacteristic
46#127×C61C2×C411yescharacteristic
47#127×C61D411yescharacteristic
48#124×C61D411yescharacteristic
49#124×C61C2311yescharacteristic
50#121×C61—41no—
51#120×C61—41no—
52#117×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61—41no—
54#99×C61—22no—
55#99×C61—41no—
56C24×C61—21no—
57#41×C61—81no—
58C2×Q8×C61C2×D411yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61—41no—
62C2×D4×C61—41no—
63C2×D4×C61—81no—
64C2×D4×C61C22⋊C411yescharacteristic
65C2×D4×C61C22⋊C411yescharacteristic
66C2×D4×C61C2×D411yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61—81no—
69C22×C4×C61C22⋊C411yescharacteristic
70C2×C22⋊D61—41no—
71C2×D244—21no—
72C2×D244—41no—
73C2×C4×D61—41no—
74C4⋊C4×C61—21no—
75C22⋊C4×C61—21no—
76C22⋊C4×C61—41no—
77C22⋊C4×C61—41no—
78C22⋊C4×C61—42no—
79C22⋊C4×C61—81no—
80C42×C61C22⋊C411yescharacteristic
81C42×C61C22×C411yescharacteristic
82#11758201—81no—
83#11758199—81no—
84#11758199—81no—
85#11758199—81no—
86#11758198—41no—
87#11758198—41no—
88C4⋊Dic61—21no—
89#11758196—41no—
90#11758194—42no—
91#11758194—81no—
92C2×#92418—21no—
93C2×#92418—21no—
94C2×#92418—81no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—41no—
99C23×C61—41no—
100C23×C61—161no—
101C23×C61#9911yescharacteristic
102C22×D61—41no—
103Q8×C61—41no—
104D4×C61—41no—
105D4×C61—41no—
106D4×C61—41no—
107D4×C61—81no—
108D4×C61—81no—
109D4×C61—161no—
110D4×C61—161no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—82no—
118C2×C4×C61—162no—
119C2×C4×C61#9911yescharacteristic
120C2×C4×C61C2×C22⋊C411yescharacteristic
121C22⋊D61—161no—
122C2×Dic61—41no—
123D244—41no—
124D244—41no—
125D244—161no—
126C4×D61—161no—
127#92418—41no—
128#92418—41no—
129#92418—82no—
130#13605—611nomaximal, Sylow
131C22×C61—21no—
132C22×C61—41no—
133C22×C61—41no—
134C22×C61—41no—
135C22×C61—41no—
136C22×C61—81no—
137C22×C61—81no—
138C22×C61—81no—
139C22×C61—82no—
140C22×C61—161no—
141C22×C61C2×#9911yescharacteristic
142C2×D61—81no—
143C2×D61—81no—
144C2×D61—81no—
145C4×C61—21no—
146C4×C61—21no—
147C4×C61—41no—
148C4×C61—41no—
149C4×C61—41no—
150C4×C61—162no—
151Dic61—81no—
152#3220—611no—
153#2134—611no—
154#2127D6111yescharacteristic, complemented
155#1414—612no—
156#1406—612no—
157C2×C61—21no—
158C2×C61—41no—
159C2×C61—81no—
160C2×C61—81no—
161C2×C61—81no—
162C2×C61#212711yescharacteristic
163D61—161no—
164#540—611no—
165#535C2×D6111yescharacteristic
166#496—611no—
167#493—611no—
168#490—611no—
169#488—611no—
170#463—1221no—
171#459—1221no—
172#449—1221no—
173#447—1221no—
174#433—611no—
175#413—1221no—
176C2×#99—21no—
177#355—612no—
178#355—1221no—
179#354C2×D6112yes—
180#353—21no—
181C61#1360511yescharacteristic, complemented, Sylow
182C2×#41D24411yescharacteristic
183C22×D4C22⋊D6111yescharacteristic
184C2×SD16—1221no—
185C2×D8—1221no—
186C2×D8—1221no—
187C2×D8—1221no—
188C2×M16—2441no—
189#127—611no—
190#127C4×D6111yescharacteristic
191#127C22⋊D6111yescharacteristic
192#125—611no—
193#124D24411yescharacteristic
194#124C22×D6111yescharacteristic
195#123—2441no—
196#121—41no—
197#121—1221no—
198#121—2441no—
199#120—41no—
200C4×D4—1221no—
201#117C4×D6111yescharacteristic
202C2×C22⋊C4—41no—
203C4⋊C8—1221no—
204#103—1221no—
205#102—1221no—
206#102—1221no—
207#102—1221no—
208#101—1222no—
209#100—2441no—
210#99—22no—
211#99—41no—
212C22⋊C8—1221no—
213#97—611no—
214C4×C8—611no—
215C24—21no—
216#41—81no—
217C2×Q8C2×D24411yescharacteristic
218C2×D4—21no—
219C2×D4—21no—
220C2×D4—41no—
221C2×D4—41no—
222C2×D4—81no—
223C2×D4—1221no—
224C2×D4—2441no—
225C2×D4—2441no—
226C2×D4#1175819811yescharacteristic
227C2×D4#1175819811yescharacteristic
228C2×D4C2×C22⋊D6111yescharacteristic
229C22×C4—21no—
230C22×C4—81no—
231C22×C4—2441no—
232C22×C4#1175819811yescharacteristic
233SD16—4881no—
234D8—4881no—
235D8—4881no—
236D8—4881no—
237M16—4881no—
238M16—2442no—
239C2×C8—1221no—
240C2×C8—1221no—
241C2×C8—4881no—
242C4⋊C4—21no—
243C4⋊C4—1221no—
244C4⋊C4—2441no—
245C22⋊C4—21no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—42no—
249C22⋊C4—81no—
250C22⋊C4—2441no—
251C22⋊C4—2441no—
252C42#1175819811yescharacteristic
253C42C2×C4×D6111yescharacteristic
254C23—21no—
255C23—21no—
256C23—21no—
257C23—41no—
258C23—41no—
259C23—161no—
260C23—2441no—
261C23#1451969111yescharacteristic
262Q8—41no—
263D4—41no—
264D4—41no—
265D4—41no—
266D4—81no—
267D4—81no—
268D4—161no—
269D4—161no—
270D4—9761no—
271D4—9761no—
272D4—2441no—
273D4—2441no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—82no—
281C2×C4—162no—
282C2×C4—9761no—
283C2×C4—2441no—
284C2×C4#1451969111yescharacteristic
285C2×C4C2×#1175819811yescharacteristic
286C8—4882no—
287C8—2441no—
288C8—2441no—
289C22—21no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—81no—
295C22—81no—
296C22—81no—
297C22—82no—
298C22—161no—
299C22—4881no—
300C22—4881no—
301C22—4881no—
302C22C2×#1451969111yescharacteristic
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—162no—
309C4—4881no—
310C2—21no—
311C2—41no—
312C2—81no—
313C2—81no—
314C2—81no—
315C2—9761no—
316C2#2144748611yescharacteristic
subgroupG/H
centerC2#21447486
commutatorC42×C61C22×C4
Frattini#124C22×D61
FittingC61×#2127C2
socleC2×C61#2127
prime radical#21456869C2
cosocle#124×C61C23
hypercenter#2127D61
hypocenterC61#13605
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C22×C4 ◁ #535 ◁ #2127

Complements

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

NH ≅ G/Ntype
2. #21447511C2semidirect
3. #21443993C2semidirect
4. #21443975C2semidirect
5. C61×#2127C2semidirect
6. #16840367C4semidirect
8. #16840138C4semidirect
9. #16840126C4semidirect
15. #16839823C4semidirect
28. #14519774C2×C4semidirect
29. #14519769C2×C4semidirect
42. #14519688C2×C4semidirect
43. C4×#92418C2×C4semidirect
154. #2127D61semidirect
181. C61#13605semidirect

Maximal subgroups

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

subgroupindex
#214568692
#214475112
#214439932
#214439752
C61×#21272
#1360561