Finite Group Databasebeta

← #29593746

Subgroups — #29593746

Order 15616.

308 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 63 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#21458780C211yesmaximal, characteristic, complemented
2#21448062C211yesmaximal, characteristic, complemented
3#21447855C211yesmaximal, characteristic
4#21445304C211yesmaximal, characteristic, complemented
5#21443800C211yesmaximal, characteristic, complemented
6#21443785C211yesmaximal, characteristic, complemented
7C61×#1363C211yesmaximal, characteristic, complemented
8#16840468—21no—
9C2×D976—21no—
10#16840169—21no—
11#16840139C2211yescharacteristic
12#16840065—21no—
13#16840059—21no—
14#16840041—21no—
15#16839963—21no—
16#16839892C2211yescharacteristic
17#16839873—21no—
18C4×D488C2211yescharacteristic
19#16839564—21no—
20#16839562—21no—
21#16839562—21no—
22#16839538C2211yescharacteristic
23#16839505—21no—
24C61×#499C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#334C2211yescharacteristic
27C2×#11758190—41no—
28C2×D488—21no—
29C2×D488—21no—
30C2×D488D411yescharacteristic
31#14519776—21no—
32#14519774—21no—
33#14519768—21no—
34#14519757—41no—
35#14519755—41no—
36#14519755—41no—
37C4×Dic122D411yescharacteristic
38C4×D244—21no—
39#14519739—21no—
40#14519739—21no—
41C4⋊C4×D61—41no—
42D976—42no—
43C2×#11758185—21no—
44#14519711D411yescharacteristic
45#14519710—21no—
46#14519708—21no—
47C4⋊#92418D411yescharacteristic
48#14519706—21no—
49#14519699—21no—
50#14519699—41no—
51#14519697—21no—
52#14519697—21no—
53#14519687—21no—
54#125×C61—21no—
55C2×C16×C61—21no—
56#107×C61D411yescharacteristic
57#107×C61D411yescharacteristic
58#106×C61—21no—
59C4⋊C8×C61—21no—
60C4×C8×C61C2311yescharacteristic
61C2×D244—21no—
62C2×D244—41no—
63C2×D244—41no—
64C2×D244—41no—
65C2×C4×D61—41no—
66C2×C4×D61—41no—
67C2×C4×D61—41no—
68C2×Dic122—41no—
69C2×Dic122D811yescharacteristic
70C2×C8×C61—41no—
71C2×C8×C61C2×D411yescharacteristic
72C2×C8×C61C2×D411yescharacteristic
73C4⋊C4×C61—21no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C42×C61C2×D411yescharacteristic
78#11758198—41no—
79#11758198—41no—
80#11758198—41no—
81C4⋊Dic61—21no—
82C4⋊Dic61—41no—
83C4⋊Dic61D811yescharacteristic
84#11758196—21no—
85#11758196—41no—
86#11758196—41no—
87C4×Dic61—21no—
88C2×#92418—21no—
89D488—21no—
90D488—42no—
91D488—41no—
92D488—41no—
93D488SD1612yescomplemented
94#11758190—82no—
95C16×C61—41no—
96#11758185—41no—
97C22×D61—41no—
98C22×D61—81no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61#12011yescharacteristic
102C2×C4×C61C2×D811yescharacteristic
103C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—41no—
107D244—22no—
108D244—41no—
109D244—81no—
110D244—81no—
111D244—81no—
112D244—81no—
113D244—161no—
114C4×D61—82no—
115C4×D61—161no—
116C4×D61—161no—
117Dic122—41no—
118Dic122—161no—
119C8×C61—21no—
120C8×C61—81no—
121C8×C61C2×SD1611yescharacteristic
122C8×C61#13711yescharacteristic
123#92418—41no—
124#12360—611nomaximal, Sylow
125C22×C61#44711yescharacteristic
126C2×D61—42no—
127C2×D61—81no—
128C2×D61—81no—
129C2×D61—161no—
130C2×D61—161no—
131C2×D61—161no—
132C4×C61—21no—
133C4×C61—21no—
134C4×C61—81no—
135C4×C61—81no—
136C4×C61#44811yescharacteristic
137C4×C61#45411yescharacteristic
138Dic61—41no—
139Dic61—41no—
140Dic61—81no—
141#3389—611no—
142#2244—611no—
143#2206—611no—
144#1688—611no—
145#1363D6111yescharacteristic, complemented
146#1338—611no—
147#1333—611no—
148C2×C61#162711yescharacteristic
149C2×C61#219011yescharacteristic
150C2×C61#219211yescharacteristic
151D61—82no—
152D61—321no—
153#554—1221no—
154C2×D16—1221no—
155#501—1221no—
156#499C2×D6111yescharacteristic
157#493—611no—
158#478—1221no—
159#478—1221no—
160#474—1221no—
161#460—1221no—
162#446—611no—
163#442—1221no—
164C4×D8—611no—
165C4⋊C16C2×D6111yescharacteristic
166#357—1221no—
167#357—1221no—
168#357—1221no—
169#346—611no—
170#334C2×D6111yescharacteristic
171#331—1221no—
172C61#1236011yescharacteristic, complemented, Sylow
173C2×SD16—2441no—
174C2×D8—611no—
175C2×D8—1221no—
176C2×D8—1221no—
177C4⋊Q8—1221no—
178#127—1221no—
179#125—21no—
180#125—1221no—
181C22⋊Q8—2441no—
182C22⋊Q8—2441no—
183C22⋊Q8—2441no—
184C4×Q8—611no—
185C4×D4—1221no—
186C4×D4—1221no—
187C4×D4—1221no—
188C2×C4⋊C4—2441no—
189D16—2442no—
190C2×C16—21no—
191C2×C16—1221no—
192#107—611no—
193#107—1221no—
194#107D24411yescharacteristic
195#107D24411yescharacteristic
196#106—21no—
197#106—1221no—
198C4⋊C8—21no—
199C4⋊C8—611no—
200C4⋊C8—1221no—
201#102—1221no—
202#102—1221no—
203#102—1221no—
204#102—2441no—
205#97—1221no—
206C4×C8C22×D6111yescharacteristic
207C2×Q8—611no—
208C2×Q8—2441no—
209C2×D4—1221no—
210C2×D4—2441no—
211C2×D4—2441no—
212C2×D4—2441no—
213C22×C4—2441no—
214C22×C4—2441no—
215C22×C4—2441no—
216SD16—4882no—
217D8—612no—
218D8—1221no—
219D8—2442no—
220D8—2441no—
221D8—2441no—
222C2×C8—41no—
223C2×C8—1221no—
224C2×C8C2×D24411yescharacteristic
225C2×C8D4×D6111yescharacteristic
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—611no—
231C4⋊C4—1221no—
232C4⋊C4—1221no—
233C4⋊C4—2441no—
234C4⋊C4—2441no—
235C4⋊C4—2441no—
236C22⋊C4—2441no—
237C22⋊C4—2441no—
238C22⋊C4—2441no—
239C42—1221no—
240C42D4×D6111yescharacteristic
241C16—41no—
242C16—2441no—
243C23—4881no—
244C23—2441no—
245Q8—9761no—
246Q8—2441no—
247D4—1222no—
248D4—9761no—
249D4—4881no—
250D4—4881no—
251D4—4881no—
252D4—4881no—
253D4—2441no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—9761no—
259C2×C4—9761no—
260C2×C4—4882no—
261C2×C4—2441no—
262C2×C4#1451974711yescharacteristic
263C2×C4D8×D6111yescharacteristic
264C2×C4#1451980411yescharacteristic
265C8—21no—
266C8—81no—
267C8—2441no—
268C8SD16×D6111yescharacteristic
269C8#1451980911yescharacteristic
270C22—9761no—
271C22—9761no—
272C22—9761no—
273C22—4881no—
274C22—4881no—
275C22—2442no—
276C22#1683989711yescharacteristic
277C4—21no—
278C4—21no—
279C4—81no—
280C4—81no—
281C4—4881no—
282C4—2441no—
283C4—2441no—
284C4#1683990211yescharacteristic
285C4#1683993711yescharacteristic
286C2—19521no—
287C2—4882no—
288C2#2144492311yescharacteristic
289C2#2144776611yescharacteristic
290C2#2144777711yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1363C2
socleC22×C61#447
prime radical#21447855C2
hypercenter#1363D61
hypocenterC61#12360
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1363

Complements

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

NH ≅ G/Ntype
1. #21458780C2semidirect
2. #21448062C2semidirect
4. #21445304C2semidirect
5. #21443800C2semidirect
6. #21443785C2semidirect
7. C61×#1363C2semidirect
93. D488SD16semidirect
145. #1363D61semidirect
172. C61#12360semidirect

Maximal subgroups

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

subgroupindex
#214587802
#214480622
#214478552
#214453042
#214438002
#214437852
C61×#13632
#1236061