Finite Group Databasebeta

← #29593747

Subgroups — #29593747

Order 15616.

308 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 65 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#21458779C211yesmaximal, characteristic, complemented
2#21448061C211yesmaximal, characteristic, complemented
3#21447855C211yesmaximal, characteristic
4#21445303C211yesmaximal, characteristic, complemented
5#21443870C211yesmaximal, characteristic, complemented
6#21443787C211yesmaximal, characteristic, complemented
7C61×#1338C211yesmaximal, characteristic, complemented
8#16840472—21no—
9C2×D976—21no—
10#16840171—21no—
11#16840164C2211yescharacteristic
12#16840139C2211yescharacteristic
13#16840063—21no—
14#16840063—21no—
15#16840043—21no—
16#16839962—21no—
17#16839875—21no—
18C4×D488C2211yescharacteristic
19#16839564—21no—
20#16839564—21no—
21#16839564—21no—
22#16839513C2211yescharacteristic
23#16839505—21no—
24C61×#446C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#346C2211yescharacteristic
27C2×#11758201—41no—
28C2×D488—21no—
29C2×D488—21no—
30C2×D488D411yescharacteristic
31#14519777—21no—
32#14519774—21no—
33#14519769—21no—
34#14519769—21no—
35#14519755—41no—
36#14519755—41no—
37#14519753—41no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C4⋊C4×D61—41no—
42D976—42no—
43#14519711—21no—
44#14519711D411yescharacteristic
45#14519711D411yescharacteristic
46#14519711D411yescharacteristic
47#14519709—21no—
48#14519709—21no—
49C4⋊#92418—21no—
50#14519699—21no—
51#14519699—21no—
52#14519699—21no—
53#14519697—41no—
54C4×Q8×C61D411yescharacteristic
55C2×C16×C61—21no—
56C2×C16×C61—21no—
57C4⋊C8×C61—21no—
58C4⋊C8×C61D411yescharacteristic
59#97×C61—21no—
60C4×C8×C61C2311yescharacteristic
61C2×Q8×C61D811yescharacteristic
62C2×D244—21no—
63C2×D244—41no—
64C2×D244—41no—
65C2×D244—41no—
66C2×C4×D61—41no—
67C2×C4×D61—41no—
68C2×C4×D61—41no—
69C2×Dic122—41no—
70C2×C8×C61—21no—
71C2×C8×C61C2×D411yescharacteristic
72C2×C8×C61C2×D411yescharacteristic
73C4⋊C4×C61—21no—
74C4⋊C4×C61D811yescharacteristic
75C42×C61—21no—
76C42×C61C2×D411yescharacteristic
77#11758201—82no—
78#11758198—41no—
79#11758198—41no—
80#11758198—41no—
81C4⋊Dic61—21no—
82C4⋊Dic61—21no—
83C4⋊Dic61—21no—
84C4⋊Dic61—41no—
85#11758196—41no—
86#11758196—41no—
87#11758196—41no—
88#11758196—41no—
89C2×#92418—41no—
90D488—21no—
91D488—42no—
92D488—41no—
93D488—41no—
94D488SD1612yescomplemented
95C16×C61—41no—
96C16×C61—41no—
97C22×D61—41no—
98C22×D61—81no—
99Q8×C61—41no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61#12011yescharacteristic
103C2×C4×C61C2×D811yescharacteristic
104C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108D244—22no—
109D244—41no—
110D244—81no—
111D244—81no—
112D244—81no—
113D244—81no—
114D244—161no—
115C4×D61—82no—
116C4×D61—161no—
117C4×D61—161no—
118Dic122—161no—
119C8×C61—21no—
120C8×C61—41no—
121C8×C61C2×SD1611yescharacteristic
122C8×C61#13711yescharacteristic
123#92418—81no—
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—41no—
135C4×C61—41no—
136C4×C61#44811yescharacteristic
137C4×C61#45411yescharacteristic
138Dic61—81no—
139Dic61—81no—
140Dic61—81no—
141#3389—611no—
142#2244—611no—
143#2206—611no—
144#1688—611no—
145#1363—611no—
146#1338D6111yescharacteristic, complemented
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#499—611no—
157#493—611no—
158#478—1221no—
159#478—1221no—
160#474—1221no—
161#460—1221no—
162#446C2×D6111yescharacteristic
163#442—1221no—
164C4×D8—611no—
165C4⋊C16C2×D6111yescharacteristic
166#357—1221no—
167#357—1221no—
168#357—1221no—
169#346C2×D6111yescharacteristic
170#334—611no—
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—1221no—
180#125—1221no—
181C22⋊Q8—2441no—
182C22⋊Q8—2441no—
183C22⋊Q8—2441no—
184C4×Q8D24411yescharacteristic
185C4×D4—1221no—
186C4×D4—1221no—
187C4×D4—1221no—
188C2×C4⋊C4—2441no—
189D16—2442no—
190C2×C16—21no—
191C2×C16—21no—
192#107—611no—
193#107—611no—
194#107—611no—
195#107—1221no—
196#106—1221no—
197#106—1221no—
198C4⋊C8—21no—
199C4⋊C8—1221no—
200C4⋊C8D24411yescharacteristic
201#102—1221no—
202#102—1221no—
203#102—1221no—
204#102—2441no—
205#97—21no—
206C4×C8C22×D6111yescharacteristic
207C2×Q8—2441no—
208C2×Q8D48811yescharacteristic
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—21no—
223C2×C8—2441no—
224C2×C8D4×D6111yescharacteristic
225C2×C8D4×D6111yescharacteristic
226C4⋊C4—21no—
227C4⋊C4—1221no—
228C4⋊C4—1221no—
229C4⋊C4—1221no—
230C4⋊C4—2441no—
231C4⋊C4—2441no—
232C4⋊C4—2441no—
233C4⋊C4—2441no—
234C4⋊C4—2441no—
235C4⋊C4D48811yescharacteristic
236C22⋊C4—2441no—
237C22⋊C4—2441no—
238C22⋊C4—2441no—
239C42—21no—
240C42C2×D24411yescharacteristic
241C16—41no—
242C16—41no—
243C23—4881no—
244C23—2441no—
245Q8—41no—
246Q8—9761no—
247D4—1222no—
248D4—9761no—
249D4—4881no—
250D4—4881no—
251D4—4881no—
252D4—4881no—
253D4—2441no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—9761no—
257C2×C4—9761no—
258C2×C4—4882no—
259C2×C4—2441no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4#1451974711yescharacteristic
263C2×C4C2×D48811yescharacteristic
264C2×C4#1451980511yescharacteristic
265C8—21no—
266C8—41no—
267C8—4881no—
268C8SD16×D6111yescharacteristic
269C8#1451980911yescharacteristic
270C22—9761no—
271C22—9761no—
272C22—9761no—
273C22—4881no—
274C22—4881no—
275C22—2442no—
276C22#1683989811yescharacteristic
277C4—21no—
278C4—21no—
279C4—41no—
280C4—41no—
281C4—4881no—
282C4—4881no—
283C4—4881no—
284C4#1683990211yescharacteristic
285C4#1683993611yescharacteristic
286C2—19521no—
287C2—4882no—
288C2#2144492411yescharacteristic
289C2#2144776711yescharacteristic
290C2#2144777811yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1338C2
socleC22×C61#447
prime radical#21447855C2
hypercenter#1338D61
hypocenterC61#12360
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #446 ◁ #1338

Complements

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

NH ≅ G/Ntype
1. #21458779C2semidirect
2. #21448061C2semidirect
4. #21445303C2semidirect
5. #21443870C2semidirect
6. #21443787C2semidirect
7. C61×#1338C2semidirect
94. D488SD16semidirect
146. #1338D61semidirect
172. C61#12360semidirect

Maximal subgroups

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

subgroupindex
#214587792
#214480612
#214478552
#214453032
#214438702
#214437872
C61×#13382
#1236061