Finite Group Databasebeta

← #29594228

Subgroups — #29594228

Order 15616.

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

normal subgroups only

This group has 252 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#21448074C211yesmaximal, characteristic, complemented
2#21447638C211yesmaximal, characteristic, complemented
3#21445185C211yesmaximal, characteristic, complemented
4#21445171C211yesmaximal, characteristic
5#21443892C211yesmaximal, characteristic, complemented
6#21443869C211yesmaximal, characteristic, complemented
7C61×#1361C211yesmaximal, characteristic, complemented
8C2×#14519721—21no—
9C2×#14519721—21no—
10C2×C16×D61—21no—
11#16840142C2211yescharacteristic
12#16840043—21no—
13#16839954—21no—
14C8×D244C2211yescharacteristic
15#16839541—21no—
16C4×#11758185C2211yescharacteristic
17#16839515C2211yescharacteristic
18#16839507—21no—
19#16839506—21no—
20C61×#493C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×Dic244—21no—
24C2×Dic244—21no—
25C2×#11758199—41no—
26C2×C8×D61—21no—
27#14519777—21no—
28C4×D244D411yescharacteristic
29#14519721—42no—
30#14519721—42no—
31C2×#11758185D411yescharacteristic
32C2×#11758185D411yescharacteristic
33C16×D61—42no—
34#14519711—41no—
35C4⋊#92418—21no—
36C4⋊#92418D411yescharacteristic
37#14519699—41no—
38#14519698—41no—
39#14519689—21no—
40C2×D8×C61—21no—
41C2×D8×C61—21no—
42#127×C61—21no—
43C2×C16×C61—21no—
44C4⋊C8×C61—21no—
45C4×C8×C61C2311yescharacteristic
46C2×D4×C61—41no—
47C2×D4×C61—41no—
48C2×D4×C61—41no—
49C2×D244D811yescharacteristic
50C2×C4×D61—21no—
51C2×Dic122—41no—
52D8×C61—41no—
53D8×C61—41no—
54D8×C61—81no—
55C2×C8×C61—41no—
56C2×C8×C61C2×D411yescharacteristic
57C2×C8×C61#4111yescharacteristic
58C42×C61C2×D411yescharacteristic
59#11758199—82no—
60#11758198—21no—
61C4⋊Dic61—41no—
62C4⋊Dic61—41no—
63C4⋊Dic61D811yescharacteristic
64C2×#92418—21no—
65C2×#92418—41no—
66Dic244—41no—
67Dic244—41no—
68Dic244—81no—
69C8×D61—41no—
70C8×D61—41no—
71C16×C61—41no—
72#11758185—21no—
73#11758185D812yescomplemented
74C23×C61—81no—
75C22×D61—21no—
76D4×C61—81no—
77D4×C61—81no—
78D4×C61—81no—
79D4×C61—81no—
80D4×C61—161no—
81C2×C4×C61#12111yescharacteristic
82C2×C4×C61C2×D811yescharacteristic
83C2×C4×C61#13511yescharacteristic
84C2×Dic61—21no—
85C2×Dic61—81no—
86D244—21no—
87D244SD3212yescomplemented
88C4×D61—41no—
89C4×D61—41no—
90Dic122—81no—
91Dic122—81no—
92C8×C61—21no—
93C8×C61—81no—
94C8×C61C2×D811yescharacteristic
95C8×C61AGL(1,ℤ/8)11yescharacteristic
96#92418—41no—
97#92418—81no—
98#12432—611nomaximal, Sylow
99C22×C61—161no—
100C22×C61—161no—
101C22×C61—161no—
102C22×C61#46611yescharacteristic
103C2×D61—22no—
104C2×D61—41no—
105C2×D61—41no—
106C4×C61—21no—
107C4×C61#45911yescharacteristic
108C4×C61#47211yescharacteristic
109C4×C61C2×SD3211yescharacteristic
110C4×C61#50811yescharacteristic
111Dic61—41no—
112Dic61—161no—
113#2248—611no—
114D4×C16—611no—
115#1669—611no—
116#1667—611no—
117#1372—611no—
118#1362—611no—
119#1361D6111yescharacteristic, complemented
120C2×C61—321no—
121C2×C61#166711yescharacteristic
122C2×C61#221711yescharacteristic
123C2×C61#222311yescharacteristic
124D61—42no—
125C2×SD32—1221no—
126C2×SD32—1221no—
127C22×C16—1221no—
128#494—611no—
129#493C2×D6111yescharacteristic
130#474—1221no—
131#459—1221no—
132C8×D4—611no—
133C4⋊C16C2×D6111yescharacteristic
134C22⋊C16—1221no—
135C4×C16—611no—
136#335—611no—
137#335C2×D6111yescharacteristic
138#332—1221no—
139#331—1221no—
140C61#1243211yescharacteristic, complemented, Sylow
141C2×Q16—1221no—
142C2×Q16—1221no—
143C2×D8—21no—
144C2×D8—21no—
145C2×D8—2441no—
146C22×C8—1221no—
147C4⋊Q8—1221no—
148#127—21no—
149C4×D4—611no—
150SD32—2442no—
151SD32—2442no—
152C2×C16—21no—
153C2×C16—611no—
154C2×C16—611no—
155C2×C16—2442no—
156#107—2441no—
157C4⋊C8—21no—
158C4⋊C8—611no—
159C4⋊C8—1221no—
160#102—2441no—
161#102—2441no—
162C22⋊C8—1221no—
163C4×C8C22×D6111yescharacteristic
164C2×Q8—2441no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4—41no—
168C2×D4—611no—
169C22×C4—1221no—
170Q16—4881no—
171Q16—2441no—
172Q16—2441no—
173D8—41no—
174D8—41no—
175D8—81no—
176D8—4882no—
177C2×C8—41no—
178C2×C8—1221no—
179C2×C8—2441no—
180C2×C8—2441no—
181C2×C8—2441no—
182C2×C8#1175822211yescharacteristic
183C2×C8D4×D6111yescharacteristic
184C4⋊C4—611no—
185C4⋊C4—2441no—
186C4⋊C4—2441no—
187C22⋊C4—1221no—
188C42D4×D6111yescharacteristic
189C16—41no—
190C16—612no—
191C16—1221no—
192C23—81no—
193C23—1221no—
194Q8—4881no—
195Q8—4881no—
196D4—81no—
197D4—81no—
198D4—81no—
199D4—81no—
200D4—161no—
201D4—612no—
202D4—1221no—
203C2×C4—1221no—
204C2×C4—4881no—
205C2×C4—2441no—
206C2×C4—2441no—
207C2×C4#1451975011yescharacteristic
208C2×C4D8×D6111yescharacteristic
209C2×C4#1451979811yescharacteristic
210C8—21no—
211C8—81no—
212C8—4881no—
213C8—2441no—
214C8D8×D6111yescharacteristic
215C8#1451980411yescharacteristic
216C22—161no—
217C22—161no—
218C22—161no—
219C22—1222no—
220C22—2441no—
221C22—2441no—
222C22#1683999711yescharacteristic
223C4—21no—
224C4—9761no—
225C4—2441no—
226C4#1683995611yescharacteristic
227C4#1684003111yescharacteristic
228C4SD32×D6111yescharacteristic
229C4#1684019111yescharacteristic
230C2—321no—
231C2—2442no—
232C2#2144517311yescharacteristic
233C2#2144791411yescharacteristic
234C2#2144794811yescharacteristic
subgroupG/H
centerC22#16839997
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1361C2
socleC22×C61#466
prime radical#21445171C2
hypercenter#1361D61
hypocenterC61#12432
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
1. #21448074C2semidirect
2. #21447638C2semidirect
3. #21445185C2semidirect
5. #21443892C2semidirect
6. #21443869C2semidirect
7. C61×#1361C2semidirect
73. #11758185D8semidirect
87. D244SD32semidirect
119. #1361D61semidirect
140. C61#12432semidirect

Maximal subgroups

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

subgroupindex
#214480742
#214476382
#214451852
#214451712
#214438922
#214438692
C61×#13612
#1243261