Finite Group Databasebeta

← #29594291

Subgroups — #29594291

Order 15616.

212 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 63 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
2#21447724C211yesmaximal, characteristic
3#21445190C211yesmaximal, characteristic
4#21445186C211yesmaximal, characteristic
5#21443892C211yesmaximal, characteristic
6#21443869C211yesmaximal, characteristic
7C61×#1362C211yesmaximal, characteristic
8C2×#14519723—21no—
9C2×#14519723—21no—
10#16840142C2211yescharacteristic
11#16840048—21no—
12#16840044—21no—
13C8×Dic122C2211yescharacteristic
14#16839580—21no—
15#16839537—21no—
16C4×#11758185C2211yescharacteristic
17#16839515C2211yescharacteristic
18#16839508—21no—
19#16839507—21no—
20C61×#494C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×Dic244—21no—
24C2×Dic244—21no—
25#14519777—21no—
26C4×Dic122D411yescharacteristic
27#14519723—42no—
28#14519723—42no—
29C2×#11758185D411yescharacteristic
30C2×#11758185D411yescharacteristic
31#14519709—41no—
32#14519708—41no—
33C4⋊#92418—21no—
34C4⋊#92418D411yescharacteristic
35#14519706—21no—
36#14519702—41no—
37#14519700—41no—
38C8×Dic61—21no—
39C2×Q16×C61—21no—
40C2×Q16×C61—21no—
41C4⋊Q8×C61—21no—
42C2×C16×C61—21no—
43C4⋊C8×C61—21no—
44C4×C8×C61C2311yescharacteristic
45C2×Q8×C61—41no—
46C2×Dic122—41no—
47C2×Dic122D811yescharacteristic
48Q16×C61—41no—
49Q16×C61—41no—
50Q16×C61—81no—
51C2×C8×C61—41no—
52C2×C8×C61C2×D411yescharacteristic
53C2×C8×C61#4111yescharacteristic
54C4⋊C4×C61—41no—
55C4⋊C4×C61—41no—
56C42×C61C2×D411yescharacteristic
57C4⋊Dic61—41no—
58C4⋊Dic61—41no—
59C4⋊Dic61D811yescharacteristic
60#11758196—21no—
61C4×Dic61—21no—
62C2×#92418—21no—
63C2×#92418—41no—
64Dic244—41no—
65Dic244—41no—
66Dic244—81no—
67C16×C61—41no—
68#11758185—21no—
69#11758185SD1612yes—
70Q8×C61—81no—
71Q8×C61—81no—
72C2×C4×C61—81no—
73C2×C4×C61#12111yescharacteristic
74C2×C4×C61C2×D811yescharacteristic
75C2×C4×C61#13511yescharacteristic
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—81no—
79Dic122—21no—
80Dic122—21no—
81Dic122—81no—
82Dic122—81no—
83C8×C61—21no—
84C8×C61—81no—
85C8×C61C2×SD1611yescharacteristic
86C8×C61AGL(1,ℤ/8)11yescharacteristic
87#92418—41no—
88#92418—81no—
89#12443—611nomaximal, Sylow
90C22×C61#46611yescharacteristic
91C4×C61—21no—
92C4×C61—161no—
93C4×C61#46011yescharacteristic
94C4×C61#47211yescharacteristic
95C4×C61#51011yescharacteristic
96C4×C61#51011yescharacteristic
97Dic61—41no—
98Dic61—41no—
99Dic61—161no—
100#2247—611no—
101#2183—611no—
102#1670—611no—
103#1670—611no—
104#1372—611no—
105#1362—611no—
106#1362D6111yescharacteristic
107C2×C61#166811yescharacteristic
108C2×C61#221911yescharacteristic
109C2×C61#222211yescharacteristic
110C2×Q32—1221no—
111C2×Q32—1221no—
112#494—611no—
113#494C2×D6111yescharacteristic
114#475—1221no—
115#475—1221no—
116C8×Q8—611no—
117C4⋊C16—1221no—
118C4⋊C16C2×D6111yescharacteristic
119#346—1221no—
120C4×C16—611no—
121#335—611no—
122#335C2×D6111yescharacteristic
123#332—1221no—
124#332—1221no—
125C61#1244311yescharacteristic, complemented, Sylow
126C2×Q16—21no—
127C2×Q16—21no—
128C2×Q16—1221no—
129C2×Q16—1221no—
130C4⋊Q8—21no—
131C4⋊Q8—1221no—
132C4×Q8—611no—
133Q32—2442no—
134Q32—2442no—
135C2×C16—21no—
136C2×C16—611no—
137C2×C16—611no—
138#106—2441no—
139#106—2441no—
140C4⋊C8—21no—
141C4⋊C8—611no—
142C4⋊C8—1221no—
143C4⋊C8—1221no—
144#103—2441no—
145#103—2441no—
146C4×C8—1221no—
147C4×C8C22×D6111yescharacteristic
148C2×Q8—41no—
149C2×Q8—611no—
150C2×Q8—2441no—
151Q16—41no—
152Q16—41no—
153Q16—81no—
154Q16—4881no—
155Q16—2441no—
156Q16—2441no—
157C2×C8—41no—
158C2×C8—1221no—
159C2×C8—2441no—
160C2×C8#1175822211yescharacteristic
161C2×C8D4×D6111yescharacteristic
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—611no—
165C4⋊C4—1221no—
166C4⋊C4—2441no—
167C4⋊C4—2441no—
168C42—1221no—
169C42D4×D6111yescharacteristic
170C16—41no—
171C16—612no—
172C16—1221no—
173Q8—81no—
174Q8—81no—
175Q8—1221no—
176Q8—1221no—
177Q8—4881no—
178Q8—4881no—
179C2×C4—81no—
180C2×C4—1221no—
181C2×C4—1221no—
182C2×C4—4881no—
183C2×C4#1451975011yescharacteristic
184C2×C4D8×D6111yescharacteristic
185C2×C4#1451979811yescharacteristic
186C8—21no—
187C8—81no—
188C8—4881no—
189C8—2441no—
190C8SD16×D6111yescharacteristic
191C8#1451980111yescharacteristic
192C22#1683999711yescharacteristic
193C4—21no—
194C4—161no—
195C4—9761no—
196C4—2441no—
197C4—2441no—
198C4#1683996111yescharacteristic
199C4#1684003111yescharacteristic
200C4#1684020111yescharacteristic
201C4#1684020411yescharacteristic
202C2#2144517811yescharacteristic
203C2#2144792611yescharacteristic
204C2#2144794311yescharacteristic
subgroupG/H
centerC22#16839997
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1362C2
socle, prime radicalC22×C61#466
hypercenter#1362D61
hypocenterC61#12443
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
125. C61#12443semidirect

Maximal subgroups

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

subgroupindex
#214480712
#214477242
#214451902
#214451862
#214438922
#214438692
C61×#13622
#1244361