Finite Group Databasebeta

← #29593667

Subgroups — #29593667

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#21458395C211yesmaximal, characteristic, complemented
2#21448060C211yesmaximal, characteristic, complemented
3#21445295C211yesmaximal, characteristic
4#21443870C211yesmaximal, characteristic, complemented
5#21443789C211yesmaximal, characteristic, complemented
6#21443776C211yesmaximal, characteristic, complemented
7C61×#2207C211yesmaximal, characteristic, complemented
8#16840453—21no—
9#16840164C2211yescharacteristic
10#16840102—21no—
11#16840096—21no—
12#16840069—21no—
13#16840017—21no—
14#16839954—21no—
15#16839841C2211yescharacteristic
16#16839803—21no—
17#16839563—21no—
18#16839563—21no—
19#16839538C2211yescharacteristic
20#16839513C2211yescharacteristic
21#16839506—21no—
22C2×SD32×C61—21no—
23C61×#493C2211yescharacteristic
24C4×Q16×C61C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#357—21no—
27C2×#11758199—41no—
28C2×#11758189—21no—
29#14519771—41no—
30#14519769—21no—
31#14519767—41no—
32#14519762—41no—
33#14519753—21no—
34#14519753—21no—
35C4×D244D411yescharacteristic
36#14519735—21no—
37#14519734—41no—
38C4⋊C4×D61—21no—
39C2×#11758185—21no—
40#14519711D411yescharacteristic
41#14519711D411yescharacteristic
42#14519710—21no—
43#14519709—21no—
44#14519708—21no—
45C4⋊#92418—21no—
46C4⋊#92418D411yescharacteristic
47#14519701—21no—
48#14519701—21no—
49#14519698—41no—
50#14519689—21no—
51C2×Q16×C61D411yescharacteristic
52C2×D8×C61—21no—
53C2×D8×C61—21no—
54#127×C61—21no—
55C4×Q8×C61—21no—
56SD32×C61—42no—
57C2×C16×C61—21no—
58#107×C61D411yescharacteristic
59#103×C61—21no—
60C4×C8×C61C2311yescharacteristic
61C2×Q8×C61—21no—
62C2×D4×C61—41no—
63C2×D4×C61—41no—
64C2×D4×C61—41no—
65C2×D244D811yescharacteristic
66C2×C4×D61—21no—
67C2×C4×D61—41no—
68Q16×C61—21no—
69Q16×C61—21no—
70D8×C61—42no—
71D8×C61—41no—
72D8×C61—41no—
73C2×C8×C61C2×D411yescharacteristic
74C2×C8×C61C2×D411yescharacteristic
75C4⋊C4×C61—21no—
76C4⋊C4×C61—41no—
77C42×C61—41no—
78C42×C61C2×D411yescharacteristic
79#11758199—82no—
80#11758198—21no—
81#11758198—41no—
82#11758198—41no—
83#11758198—41no—
84C4⋊Dic61—21no—
85C4⋊Dic61—21no—
86C4⋊Dic61D811yescharacteristic
87#11758196—41no—
88#11758196—41no—
89#11758196—41no—
90#11758196—41no—
91#11758196—41no—
92C4×Dic61—41no—
93C2×#92418—21no—
94C2×#92418—41no—
95#11758189—41no—
96#11758189—41no—
97C16×C61—41no—
98#11758185—41no—
99C23×C61—81no—
100C22×D61—21no—
101Q8×C61—41no—
102Q8×C61—41no—
103D4×C61—81no—
104D4×C61—81no—
105D4×C61—81no—
106D4×C61—81no—
107D4×C61—161no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61#12011yescharacteristic
111C2×C4×C61C2×D811yescharacteristic
112C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
113C2×Dic61—21no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116D244—41no—
117C4×D61—41no—
118C4×D61—41no—
119C4×D61—82no—
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#2244—611no—
144#2207D6111yescharacteristic, complemented
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—21no—
156#499—611no—
157#493C2×D6111yescharacteristic
158#485—1221no—
159#484—1221no—
160#479—1221no—
161#470—1221no—
162#459—1221no—
163C4×Q16C2×D6111yescharacteristic
164#436—611no—
165#428—1221no—
166C4⋊C16C2×D6111yescharacteristic
167#357—21no—
168#357—1221no—
169#357—1221no—
170#346—611no—
171#334—611no—
172#331—1221no—
173C61#1234911yescharacteristic, complemented, Sylow
174C2×Q16C22⋊D6111yescharacteristic
175C2×D8—21no—
176C2×D8—21no—
177C2×D8—2441no—
178C2×M16—1221no—
179#127—21no—
180#126—2441no—
181#125—1221no—
182#125—2441no—
183#123—2441no—
184C22⋊Q8—1221no—
185C22⋊Q8—1221no—
186C4×Q8—21no—
187C4×D4—611no—
188#117—1221no—
189#117—2441no—
190C2×C4⋊C4—1221no—
191SD32—42no—
192C2×C16—21no—
193C2×C16—1221no—
194#107—611no—
195#107—611no—
196#107—1221no—
197#107C22⋊D6111yescharacteristic
198#106—1221no—
199#106—1221no—
200C4⋊C8—611no—
201C4⋊C8—1221no—
202#103—21no—
203#103—1221no—
204#103—1221no—
205#102—2441no—
206C22⋊C8—1221no—
207C4×C8C22×D6111yescharacteristic
208C2×Q8—21no—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4—41no—
212C2×D4—611no—
213C22×C4—1221no—
214C22×C4—2441no—
215Q16—21no—
216Q16—21no—
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—41no—
229C4⋊C4—611no—
230C4⋊C4—1221no—
231C4⋊C4—1221no—
232C4⋊C4—2441no—
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—41no—
242C42—2441no—
243C42D4×D6111yescharacteristic
244C16—41no—
245C16—2441no—
246C23—81no—
247C23—1221no—
248Q8—41no—
249Q8—41no—
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#1451979711yescharacteristic
271C8#1451980311yescharacteristic
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#1683990511yescharacteristic
287C4#1683993311yescharacteristic
288C2—321no—
289C2—4881no—
290C2#2144490711yescharacteristic
291C2#2144776311yescharacteristic
292C2#2144778211yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2207C2
socleC22×C61#447
prime radical#21445295C2
hypercenter#2207D61
hypocenterC61#12349
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
1. #21458395C2semidirect
2. #21448060C2semidirect
4. #21443870C2semidirect
5. #21443789C2semidirect
6. #21443776C2semidirect
7. C61×#2207C2semidirect
144. #2207D61semidirect
173. C61#12349semidirect

Maximal subgroups

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

subgroupindex
#214583952
#214480602
#214452952
#214438702
#214437892
#214437762
C61×#22072
#1234961