Finite Group Databasebeta

← #29594223

Subgroups — #29594223

Order 15616.

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

normal subgroups only

This group has 236 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#21448071C211yesmaximal, characteristic, complemented
2#21447638C211yesmaximal, characteristic
3#21445185C211yesmaximal, characteristic
4#21445181C211yesmaximal, characteristic
5#21443890C211yesmaximal, characteristic, complemented
6#21443869C211yesmaximal, characteristic, complemented
7C61×#1362C211yesmaximal, characteristic, complemented
8C2×#14519723—21no—
9C2×#14519723—21no—
10C2×C16×D61—21no—
11#16840142C2211yescharacteristic
12#16840043—21no—
13#16840039—21no—
14C8×D244C2211yescharacteristic
15#16839541—21no—
16C4×#11758185C2211yescharacteristic
17#16839515C2211yescharacteristic
18#16839508—21no—
19#16839507—21no—
20C61×#494C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×Dic244—21no—
24C2×Dic244—21no—
25C2×C8×D61—21no—
26#14519777—21no—
27C4×D244D411yescharacteristic
28#14519723—42no—
29#14519723—42no—
30C2×#11758185D411yescharacteristic
31C2×#11758185D411yescharacteristic
32C16×D61—42no—
33#14519711—41no—
34#14519710—41no—
35C4⋊#92418—21no—
36C4⋊#92418D411yescharacteristic
37#14519699—41no—
38#14519697—41no—
39#14519689—21no—
40C2×Q16×C61—21no—
41C2×Q16×C61—21no—
42C4⋊Q8×C61—21no—
43C2×C16×C61—21no—
44C4⋊C8×C61—21no—
45C4×C8×C61C2311yescharacteristic
46C2×Q8×C61—41no—
47C2×D244D811yescharacteristic
48C2×C4×D61—21no—
49C2×Dic122—41no—
50Q16×C61—41no—
51Q16×C61—41no—
52Q16×C61—81no—
53C2×C8×C61—41no—
54C2×C8×C61C2×D411yescharacteristic
55C2×C8×C61#4111yescharacteristic
56C4⋊C4×C61—41no—
57C4⋊C4×C61—41no—
58C42×C61C2×D411yescharacteristic
59#11758198—21no—
60C4⋊Dic61—41no—
61C4⋊Dic61—41no—
62C4⋊Dic61D811yescharacteristic
63C2×#92418—21no—
64C2×#92418—41no—
65Dic244—41no—
66Dic244—41no—
67Dic244—81no—
68C8×D61—41no—
69C8×D61—41no—
70C16×C61—41no—
71#11758185—21no—
72#11758185D812yes—
73C22×D61—21no—
74Q8×C61—81no—
75Q8×C61—81no—
76C2×C4×C61—81no—
77C2×C4×C61#12111yescharacteristic
78C2×C4×C61C2×D811yescharacteristic
79C2×C4×C61#13511yescharacteristic
80C2×Dic61—21no—
81C2×Dic61—81no—
82D244—21no—
83D244Q3212yescomplemented
84C4×D61—41no—
85C4×D61—41no—
86Dic122—81no—
87Dic122—81no—
88C8×C61—21no—
89C8×C61—81no—
90C8×C61C2×D811yescharacteristic
91C8×C61AGL(1,ℤ/8)11yescharacteristic
92#92418—41no—
93#92418—81no—
94#12431—611nomaximal, Sylow
95C22×C61#46611yescharacteristic
96C2×D61—22no—
97C2×D61—41no—
98C2×D61—41no—
99C4×C61—21no—
100C4×C61—161no—
101C4×C61#45911yescharacteristic
102C4×C61#47211yescharacteristic
103C4×C61C2×Q3211yescharacteristic
104C4×C61#50811yescharacteristic
105Dic61—41no—
106Dic61—161no—
107#2247—611no—
108D4×C16—611no—
109#1669—611no—
110#1669—611no—
111#1371—611no—
112#1362—611no—
113#1362D6111yescharacteristic, complemented
114C2×C61#166711yescharacteristic
115C2×C61#221611yescharacteristic
116C2×C61#222211yescharacteristic
117D61—42no—
118C2×Q32—1221no—
119C2×Q32—1221no—
120C22×C16—1221no—
121#494—611no—
122#494C2×D6111yescharacteristic
123#474—1221no—
124#474—1221no—
125C8×D4—611no—
126C4⋊C16C2×D6111yescharacteristic
127C22⋊C16—1221no—
128C4×C16—611no—
129#335—611no—
130#335C2×D6111yescharacteristic
131#332—1221no—
132#332—1221no—
133C61#1243111yescharacteristic, complemented, Sylow
134C2×Q16—21no—
135C2×Q16—21no—
136C2×Q16—1221no—
137C2×Q16—1221no—
138C22×C8—1221no—
139C4⋊Q8—21no—
140C4⋊Q8—1221no—
141C4×D4—611no—
142Q32—2442no—
143Q32—2442no—
144C2×C16—21no—
145C2×C16—611no—
146C2×C16—611no—
147C2×C16—2442no—
148#107—2441no—
149#107—2441no—
150C4⋊C8—21no—
151C4⋊C8—611no—
152C4⋊C8—1221no—
153#102—2441no—
154#102—2441no—
155C22⋊C8—1221no—
156C4×C8C22×D6111yescharacteristic
157C2×Q8—41no—
158C2×Q8—2441no—
159C2×D4—611no—
160C22×C4—1221no—
161Q16—41no—
162Q16—41no—
163Q16—81no—
164Q16—4881no—
165Q16—2441no—
166Q16—2441no—
167C2×C8—41no—
168C2×C8—1221no—
169C2×C8—2441no—
170C2×C8—2441no—
171C2×C8—2441no—
172C2×C8#1175822211yescharacteristic
173C2×C8D4×D6111yescharacteristic
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—611no—
177C4⋊C4—2441no—
178C4⋊C4—2441no—
179C22⋊C4—1221no—
180C42D4×D6111yescharacteristic
181C16—41no—
182C16—612no—
183C16—1221no—
184C23—1221no—
185Q8—81no—
186Q8—81no—
187Q8—4881no—
188Q8—4881no—
189D4—612no—
190D4—1221no—
191C2×C4—81no—
192C2×C4—1221no—
193C2×C4—4881no—
194C2×C4—2441no—
195C2×C4—2441no—
196C2×C4#1451975011yescharacteristic
197C2×C4D8×D6111yescharacteristic
198C2×C4#1451979811yescharacteristic
199C8—21no—
200C8—81no—
201C8—4881no—
202C8—2441no—
203C8D8×D6111yescharacteristic
204C8#1451980411yescharacteristic
205C22—1222no—
206C22—2441no—
207C22—2441no—
208C22#1683999711yescharacteristic
209C4—21no—
210C4—161no—
211C4—9761no—
212C4—2441no—
213C4#1683995611yescharacteristic
214C4#1684003111yescharacteristic
215C4Q32×D6111yescharacteristic
216C4#1684019311yescharacteristic
217C2—2442no—
218C2#2144517311yescharacteristic
219C2#2144790911yescharacteristic
220C2#2144794311yescharacteristic
subgroupG/H
centerC22#16839997
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1362C2
socleC22×C61#466
prime radicalC2×D244D8
hypercenter#1362D61
hypocenterC61#12431
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
1. #21448071C2semidirect
5. #21443890C2semidirect
6. #21443869C2semidirect
7. C61×#1362C2semidirect
83. D244Q32semidirect
113. #1362D61semidirect
133. C61#12431semidirect

Maximal subgroups

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

subgroupindex
#214480712
#214476382
#214451852
#214451812
#214438902
#214438692
C61×#13622
#1243161