Finite Group Databasebeta

← #29593665

Subgroups — #29593665

Order 15616.

302 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 61 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#21458392C211yesmaximal, characteristic, complemented
2#21447856C211yesmaximal, characteristic, complemented
3#21445295C211yesmaximal, characteristic
4#21443871C211yesmaximal, characteristic, complemented
5#21443790C211yesmaximal, characteristic, complemented
6#21443778C211yesmaximal, characteristic, complemented
7C61×#2244C211yesmaximal, characteristic, complemented
8#16840450—21no—
9C2×#14519721—21no—
10#16840105—21no—
11#16840099—21no—
12#16840066—21no—
13#16840021—21no—
14#16839954—21no—
15C4×Dic244C2211yescharacteristic
16#16839841C2211yescharacteristic
17#16839801—21no—
18C4⋊#11758185C2211yescharacteristic
19#16839563—21no—
20#16839513C2211yescharacteristic
21#16839506—21no—
22C61×#499C2211yescharacteristic
23C61×#493C2211yescharacteristic
24C61×#357—21no—
25C61×#357—21no—
26C61×#346C2211yescharacteristic
27C2×Dic244D411yescharacteristic
28C2×#11758199—41no—
29C2×#11758189—21no—
30#14519772—41no—
31#14519768—41no—
32#14519762—41no—
33#14519757—21no—
34#14519757—21no—
35C4×Dic122—21no—
36C4×D244D411yescharacteristic
37#14519735—21no—
38#14519735—41no—
39C4⋊C4×D61—21no—
40#14519721—42no—
41C2×#11758185—21no—
42#14519711D411yescharacteristic
43#14519710—21no—
44#14519708—21no—
45C4⋊#92418—21no—
46C4⋊#92418D411yescharacteristic
47#14519702—21no—
48#14519700—21no—
49#14519700—21no—
50#14519698—41no—
51#14519689—21no—
52C2×D8×C61—21no—
53C2×D8×C61—21no—
54#127×C61—21no—
55#125×C61—21no—
56C2×C16×C61—21no—
57#107×C61D411yescharacteristic
58#107×C61D411yescharacteristic
59#106×C61—21no—
60C4×C8×C61C2311yescharacteristic
61C2×D4×C61—41no—
62C2×D4×C61—41no—
63C2×D4×C61—41no—
64C2×D244D811yescharacteristic
65C2×C4×D61—21no—
66C2×C4×D61—41no—
67C2×Dic122—21no—
68D8×C61—42no—
69D8×C61—41no—
70D8×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#11758199—82no—
79#11758198—21no—
80#11758198—41no—
81#11758198—41no—
82#11758198—41no—
83C4⋊Dic61—21no—
84C4⋊Dic61—41no—
85C4⋊Dic61—41no—
86C4⋊Dic61D811yescharacteristic
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—41no—
90C4×Dic61—41no—
91C2×#92418—21no—
92C2×#92418—41no—
93Dic244—21no—
94Dic244—21no—
95#11758189—41no—
96#11758189—41no—
97C16×C61—41no—
98#11758185—41no—
99C23×C61—81no—
100C22×D61—21no—
101D4×C61—81no—
102D4×C61—81no—
103D4×C61—81no—
104D4×C61—81no—
105D4×C61—161no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61#12011yescharacteristic
109C2×C4×C61C2×D811yescharacteristic
110C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
111C2×Dic61—21no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114D244—41no—
115C4×D61—41no—
116C4×D61—41no—
117C4×D61—82no—
118Dic122—41no—
119Dic122—41no—
120C8×C61—21no—
121C8×C61#13511yescharacteristic
122C8×C61AGL(1,ℤ/8)11yescharacteristic
123#92418—41no—
124#92418—81no—
125#12349—611nomaximal, Sylow
126C22×C61—161no—
127C22×C61—161no—
128C22×C61—161no—
129C22×C61#44711yescharacteristic
130C2×D61—41no—
131C2×D61—41no—
132C2×D61—41no—
133C4×C61—21no—
134C4×C61—21no—
135C4×C61—81no—
136C4×C61—81no—
137C4×C61#44911yescharacteristic
138C4×C61#45411yescharacteristic
139Dic61—41no—
140Dic61—81no—
141Dic61—81no—
142#3352—611no—
143#2244D6111yescharacteristic, complemented
144#2207—611no—
145#1687—611no—
146#1363—611no—
147#1334—611no—
148#1330—611no—
149C2×C61—321no—
150C2×C61#162511yescharacteristic
151C2×C61#219011yescharacteristic
152C2×C61#219311yescharacteristic
153D61—81no—
154#552—1221no—
155C2×SD32—1221no—
156#499C2×D6111yescharacteristic
157#493C2×D6111yescharacteristic
158#485—1221no—
159#484—1221no—
160#479—1221no—
161#470—1221no—
162#459—1221no—
163C4×Q16—611no—
164#436—611no—
165#428—1221no—
166C4⋊C16—611no—
167#357—21no—
168#357—21no—
169#357—1221no—
170#346C2×D6111yescharacteristic
171#334—611no—
172#331—1221no—
173C61#1234911yescharacteristic, complemented, Sylow
174C2×Q16—611no—
175C2×D8—21no—
176C2×D8—21no—
177C2×D8—2441no—
178C2×M16—1221no—
179#127—21no—
180#126—2441no—
181#125—21no—
182#125—2441no—
183#123—2441no—
184C22⋊Q8—1221no—
185C22⋊Q8—1221no—
186C4×Q8—1221no—
187C4×D4—611no—
188#117—1221no—
189#117—2441no—
190C2×C4⋊C4—1221no—
191SD32—2442no—
192C2×C16—21no—
193C2×C16—1221no—
194#107—611no—
195#107—1221no—
196#107C22⋊D6111yescharacteristic
197#107C22⋊D6111yescharacteristic
198#106—21no—
199#106—1221no—
200C4⋊C8—611no—
201C4⋊C8—1221no—
202#103—1221no—
203#103—1221no—
204#103—1221no—
205#102—2441no—
206C22⋊C8—1221no—
207C4×C8C22×D6111yescharacteristic
208C2×Q8—1221no—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4—41no—
212C2×D4—611no—
213C22×C4—1221no—
214C22×C4—2441no—
215Q16—1221no—
216Q16—1221no—
217D8—42no—
218D8—41no—
219D8—41no—
220D8—4882no—
221M16—2441no—
222M16—2441no—
223C2×C8—1221no—
224C2×C8—2441no—
225C2×C8D4×D6111yescharacteristic
226C2×C8C2×C22⋊D6111yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—611no—
232C4⋊C4—1221no—
233C4⋊C4—2441no—
234C4⋊C4—2441no—
235C4⋊C4—2441no—
236C4⋊C4—2441no—
237C22⋊C4—1221no—
238C22⋊C4—2441no—
239C22⋊C4—2441no—
240C22⋊C4—2441no—
241C42—2441no—
242C42—2441no—
243C42D4×D6111yescharacteristic
244C16—41no—
245C16—2441no—
246C23—81no—
247C23—1221no—
248Q8—2441no—
249Q8—2441no—
250D4—81no—
251D4—81no—
252D4—81no—
253D4—81no—
254D4—161no—
255D4—2441no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—1221no—
259C2×C4—4882no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4—2441no—
263C2×C4—2441no—
264C2×C4#1451974511yescharacteristic
265C2×C4D8×D6111yescharacteristic
266C2×C4#1451980111yescharacteristic
267C8—21no—
268C8—4881no—
269C8—2441no—
270C8#1451979811yescharacteristic
271C8#1451980411yescharacteristic
272C22—161no—
273C22—161no—
274C22—161no—
275C22—2441no—
276C22—2441no—
277C22—2441no—
278C22#1683989411yescharacteristic
279C4—21no—
280C4—21no—
281C4—81no—
282C4—81no—
283C4—4881no—
284C4—4881no—
285C4—2441no—
286C4#1683990611yescharacteristic
287C4#1683993411yescharacteristic
288C2—321no—
289C2—4881no—
290C2#2144490511yescharacteristic
291C2#2144776311yescharacteristic
292C2#2144778011yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2244C2
socleC22×C61#447
prime radical#21445295C2
hypercenter#2244D61
hypocenterC61#12349
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2244

Complements

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

NH ≅ G/Ntype
1. #21458392C2semidirect
2. #21447856C2semidirect
4. #21443871C2semidirect
5. #21443790C2semidirect
6. #21443778C2semidirect
7. C61×#2244C2semidirect
143. #2244D61semidirect
173. C61#12349semidirect

Maximal subgroups

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

subgroupindex
#214583922
#214478562
#214452952
#214438712
#214437902
#214437782
C61×#22442
#1234961