Finite Group Databasebeta

← #29593538

Subgroups — #29593538

Order 15616.

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

normal subgroups only

This group has 322 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#21458824C211yesmaximal, characteristic, complemented
2#21448075C211yesmaximal, characteristic
3#21447859C211yesmaximal, characteristic
4#21445180C211yesmaximal, characteristic
5#21443867C211yesmaximal, characteristic, complemented
6#21443799C211yesmaximal, characteristic, complemented
7C61×#1332C211yesmaximal, characteristic, complemented
8#16840490—21no—
9C2×#14519722—22no—
10C2×#14519720—21no—
11#16840142C2211yescharacteristic
12#16840140—21no—
13#16840139C2211yescharacteristic
14#16839972—21no—
15#16839971—22no—
16#16839963—21no—
17C8×Dic122C2211yescharacteristic
18#16839856—21no—
19C4⋊#11758185C2211yescharacteristic
20#16839562—21no—
21#16839505—21no—
22C4×Q16×C61C2211yescharacteristic
23C4×C16×C61C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×Dic244—21no—
26C2×Dic244D412yes—
27C2×#11758202—22no—
28C2×#11758190—41no—
29C2×D488—21no—
30C2×D488—21no—
31#14519777—21no—
32#14519775—22no—
33#14519774—21no—
34#14519769—41no—
35#14519767—42no—
36C4×Dic122—41no—
37C4×Dic122D411yescharacteristic
38#14519742—22no—
39#14519722—44no—
40#14519720—42no—
41C2×#11758185—21no—
42C4⋊#92418D411yescharacteristic
43#14519706—21no—
44#14519700—22no—
45#14519699—41no—
46C8×Dic61—21no—
47C2×Q16×C61D411yescharacteristic
48C4×Q8×C61—21no—
49C2×C16×C61—21no—
50#107×C61D411yescharacteristic
51C4⋊C8×C61—21no—
52#103×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—21no—
55C2×D244—41no—
56C2×D244—41no—
57C2×D244—41no—
58C2×Dic122—22no—
59C2×Dic122D811yescharacteristic
60Q16×C61—21no—
61Q16×C61—21no—
62C2×C8×C61—41no—
63C2×C8×C61C2×D411yescharacteristic
64C2×C8×C61C2×D411yescharacteristic
65C4⋊C4×C61—21no—
66C4⋊C4×C61—41no—
67C42×C61—41no—
68C42×C61C2×D411yescharacteristic
69#11758202—82no—
70C4⋊Dic61—41no—
71C4⋊Dic61—41no—
72C4⋊Dic61D811yescharacteristic
73#11758196—21no—
74#11758196—42no—
75#11758196—42no—
76#11758196—42no—
77C4×Dic61—21no—
78C4×Dic61—42no—
79C2×#92418—21no—
80Dic244—42no—
81Dic244—41no—
82Dic244—41no—
83D488—42no—
84D488—41no—
85D488—41no—
86#11758190—82no—
87C16×C61—22no—
88#11758185—41no—
89C22×D61—81no—
90Q8×C61—41no—
91Q8×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61#12011yescharacteristic
95C2×C4×C61C2×D811yescharacteristic
96C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—42no—
100D244—81no—
101D244—81no—
102D244—81no—
103D244—81no—
104D244—161no—
105Dic122—21no—
106Dic122—42no—
107Dic122—42no—
108Dic122SD3212yescomplemented
109C8×C61—21no—
110C8×C61—81no—
111C8×C61#13511yescharacteristic
112C8×C61AGL(1,ℤ/8)11yescharacteristic
113#92418—41no—
114#12330—611nomaximal, Sylow
115C22×C61#44711yescharacteristic
116C2×D61—161no—
117C2×D61—161no—
118C2×D61—161no—
119C4×C61—21no—
120C4×C61—81no—
121C4×C61—81no—
122C4×C61#44911yescharacteristic
123C4×C61#45311yescharacteristic
124C4×C61C2×SD3211yescharacteristic
125C4×C61#51011yescharacteristic
126Dic61—22no—
127Dic61—41no—
128Dic61—82no—
129#3395—611no—
130#2248—611no—
131#2207—611no—
132#1668—611no—
133#1362—611no—
134Q8⋊C16—611no—
135#1332D6111yescharacteristic, complemented
136C2×C61#162111yescharacteristic
137C2×C61#218511yescharacteristic
138C2×C61#219311yescharacteristic
139D61—321no—
140#557—1221no—
141C2×SD32—1222no—
142C2×SD32—1221no—
143#494—611no—
144#494—1221no—
145#493—611no—
146#462—1222no—
147#462—1221no—
148#460—1221no—
149C8×Q8—611no—
150C4×Q16—1221no—
151C4×Q16C2×D6111yescharacteristic
152C4⋊C16—611no—
153#357—1221no—
154C4×C16C2×D6111yescharacteristic
155#335C2×D6111yescharacteristic
156#331—1221no—
157C61#1233011yescharacteristic, complemented, Sylow
158C2×Q16—612no—
159C2×Q16—1222no—
160C2×Q16—1221no—
161C2×Q16D24411yescharacteristic
162C2×SD16—2441no—
163C2×D8—1221no—
164C2×D8—1221no—
165C4⋊Q8—1222no—
166C4⋊Q8—1221no—
167#127—1221no—
168#125—2441no—
169#125—2442no—
170C4×Q8—21no—
171C4×Q8—611no—
172C4×Q8—1222no—
173C4×Q8—2441no—
174SD32—2444no—
175SD32—2442no—
176C2×C16—21no—
177C2×C16—1221no—
178#107D24411yescharacteristic
179C4⋊C8—21no—
180C4⋊C8—611no—
181C4⋊C8—1221no—
182#103—21no—
183#103—1222no—
184#102—2441no—
185C4×C8—1221no—
186C4×C8C22×D6111yescharacteristic
187C2×Q8—21no—
188C2×Q8—611no—
189C2×Q8—1222no—
190C2×D4—2441no—
191C2×D4—2441no—
192C2×D4—2441no—
193Q16—21no—
194Q16—21no—
195Q16—4882no—
196Q16—2442no—
197Q16—2441no—
198Q16—2441no—
199SD16—4882no—
200D8—2442no—
201D8—2441no—
202D8—2441no—
203C2×C8—41no—
204C2×C8—1221no—
205C2×C8C2×D24411yescharacteristic
206C2×C8D4×D6111yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—41no—
209C4⋊C4—611no—
210C4⋊C4—1221no—
211C4⋊C4—2442no—
212C4⋊C4—2442no—
213C4⋊C4—2442no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C42—41no—
217C42—1221no—
218C42—2442no—
219C42D4×D6111yescharacteristic
220C16—22no—
221C16—2441no—
222C23—4881no—
223Q8—41no—
224Q8—41no—
225Q8—612no—
226Q8—1221no—
227Q8—2442no—
228Q8—2442no—
229D4—9761no—
230D4—4881no—
231D4—4881no—
232D4—4881no—
233D4—4881no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—1221no—
237C2×C4—1221no—
238C2×C4—2442no—
239C2×C4#1451974711yescharacteristic
240C2×C4D8×D6111yescharacteristic
241C2×C4#1451980411yescharacteristic
242C8—21no—
243C8—81no—
244C8—2441no—
245C8#1451979911yescharacteristic
246C8#1451980511yescharacteristic
247C22—9761no—
248C22—9761no—
249C22—9761no—
250C22#1683989711yescharacteristic
251C4—21no—
252C4—81no—
253C4—81no—
254C4—1222no—
255C4—4882no—
256C4—2441no—
257C4#1683990911yescharacteristic
258C4#1683993111yescharacteristic
259C4SD32×D6111yescharacteristic
260C4#1684020411yescharacteristic
261C2—19521no—
262C2#2144488711yescharacteristic
263C2#2144773711yescharacteristic
264C2#2144778411yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1332C2
socleC22×C61#447
prime radical#16840139C22
hypercenter#1332D61
hypocenterC61#12330
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1332

Complements

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

NH ≅ G/Ntype
1. #21458824C2semidirect
5. #21443867C2semidirect
6. #21443799C2semidirect
7. C61×#1332C2semidirect
108. Dic122SD32semidirect
135. #1332D61semidirect
157. C61#12330semidirect

Maximal subgroups

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

subgroupindex
#214588242
#214480752
#214478592
#214451802
#214438672
#214437992
C61×#13322
#1233061