Finite Group Databasebeta

← #29594290

Subgroups — #29594290

Order 15616.

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

normal subgroups only

This group has 212 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#21448071C211yesmaximal, characteristic
2#21447728C211yesmaximal, characteristic
3#21445189C211yesmaximal, characteristic
4#21443892C211yesmaximal, characteristic
5#21443868C211yesmaximal, characteristic
6#21443867C211yesmaximal, characteristic
7C61×#1670C211yesmaximal, characteristic
8C2×#14519723—21no—
9C2×#14519723—21no—
10#16840142C2211yescharacteristic
11#16840047—21no—
12C4⋊#11758185—21no—
13C4⋊#11758185C2211yescharacteristic
14#16839538—21no—
15C4×#11758185C2211yescharacteristic
16#16839515C2211yescharacteristic
17#16839509—21no—
18C61×#494C2211yescharacteristic
19C61×#475—21no—
20C8×Q8×C61C2211yescharacteristic
21C61×#335C2211yescharacteristic
22C61×#332—21no—
23C2×Dic244—21no—
24C2×Dic244—21no—
25#14519777—21no—
26#14519723—42no—
27#14519723—42no—
28C2×#11758185—21no—
29C2×#11758185D411yescharacteristic
30C2×#11758185D411yescharacteristic
31#14519708—41no—
32C4⋊#92418—21no—
33#14519701—41no—
34C2×Q16×C61—21no—
35C2×Q16×C61—21no—
36C4⋊Q8×C61—21no—
37C4×Q8×C61D411yescharacteristic
38#106×C61—41no—
39C4⋊C8×C61—21no—
40C4⋊C8×C61—21no—
41C4⋊C8×C61D411yescharacteristic
42#103×C61—41no—
43C4×C8×C61—21no—
44C4×C8×C61C2311yescharacteristic
45C2×Q8×C61—41no—
46C2×Q8×C61D811yescharacteristic
47C2×Dic122—41no—
48Q16×C61—41no—
49Q16×C61—41no—
50Q16×C61—81no—
51C2×C8×C61—21no—
52C2×C8×C61—41no—
53C2×C8×C61C2×D411yescharacteristic
54C2×C8×C61#4111yescharacteristic
55C4⋊C4×C61—21no—
56C4⋊C4×C61—41no—
57C4⋊C4×C61—41no—
58C4⋊C4×C61D811yescharacteristic
59C42×C61—21no—
60C42×C61C2×D411yescharacteristic
61C4⋊Dic61—41no—
62C4⋊Dic61—41no—
63C2×#92418—41no—
64Dic244—41no—
65Dic244—41no—
66Dic244—81no—
67#11758185—21no—
68#11758185—41no—
69#11758185SD1612yes—
70Q8×C61—21no—
71Q8×C61—21no—
72Q8×C61—81no—
73Q8×C61—81no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—81no—
77C2×C4×C61#12111yescharacteristic
78C2×C4×C61C2×D811yescharacteristic
79C2×C4×C61#13511yescharacteristic
80C2×Dic61—81no—
81Dic122—81no—
82Dic122—81no—
83C8×C61—21no—
84C8×C61—41no—
85C8×C61—81no—
86C8×C61C2×SD1611yescharacteristic
87C8×C61AGL(1,ℤ/8)11yescharacteristic
88#92418—81no—
89#12443—611nomaximal, Sylow
90C22×C61#46611yescharacteristic
91C4×C61—21no—
92C4×C61—41no—
93C4×C61—41no—
94C4×C61—161no—
95C4×C61#46011yescharacteristic
96C4×C61#47211yescharacteristic
97C4×C61#51011yescharacteristic
98C4×C61#51011yescharacteristic
99Dic61—161no—
100#2247—611no—
101#2183—611no—
102#1670—611no—
103#1670D6111yescharacteristic
104#1372—611no—
105#1362—611no—
106#1362—611no—
107C2×C61#166811yescharacteristic
108C2×C61#221911yescharacteristic
109C2×C61#222211yescharacteristic
110C2×Q32—1221no—
111C2×Q32—1221no—
112#494—611no—
113#494C2×D6111yescharacteristic
114#475—21no—
115#475—1221no—
116C8×Q8C2×D6111yescharacteristic
117C4⋊C16—611no—
118C4⋊C16—1221no—
119#346—1221no—
120C4×C16—611no—
121#335—611no—
122#335C2×D6111yescharacteristic
123#332—21no—
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×Q8C22⋊D6111yescharacteristic
133Q32—2442no—
134Q32—2442no—
135C2×C16—611no—
136C2×C16—611no—
137C2×C16—1221no—
138#106—41no—
139#106—2441no—
140C4⋊C8—21no—
141C4⋊C8—21no—
142C4⋊C8—1221no—
143C4⋊C8C22⋊D6111yescharacteristic
144#103—41no—
145#103—2441no—
146C4×C8—21no—
147C4×C8C22×D6111yescharacteristic
148C2×Q8—41no—
149C2×Q8—2441no—
150C2×Q8#1175819911yescharacteristic
151Q16—41no—
152Q16—41no—
153Q16—81no—
154Q16—4881no—
155Q16—2441no—
156Q16—2441no—
157C2×C8—21no—
158C2×C8—41no—
159C2×C8—2441no—
160C2×C8D4×D6111yescharacteristic
161C2×C8#1175822411yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—41no—
164C4⋊C4—41no—
165C4⋊C4—2441no—
166C4⋊C4—2441no—
167C4⋊C4#1175819911yescharacteristic
168C42—21no—
169C42C2×C22⋊D6111yescharacteristic
170C16—612no—
171C16—1221no—
172C16—2441no—
173Q8—21no—
174Q8—21no—
175Q8—81no—
176Q8—81no—
177Q8—4881no—
178Q8—4881no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—81no—
182C2×C4—4881no—
183C2×C4#1451974911yescharacteristic
184C2×C4C2×#1175819911yescharacteristic
185C2×C4#1451979711yescharacteristic
186C8—21no—
187C8—41no—
188C8—81no—
189C8—4881no—
190C8SD16×D6111yescharacteristic
191C8#1451980411yescharacteristic
192C22#1683999611yescharacteristic
193C4—21no—
194C4—41no—
195C4—41no—
196C4—161no—
197C4—9761no—
198C4#1683996011yescharacteristic
199C4#1684003011yescharacteristic
200C4#1684020211yescharacteristic
201C4#1684020311yescharacteristic
202C2#2144517711yescharacteristic
203C2#2144792511yescharacteristic
204C2#2144794211yescharacteristic
subgroupG/H
centerC22#16839996
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1670C2
socle, prime radicalC22×C61#466
hypercenter#1670D61
hypocenterC61#12443
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1670

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
#214477282
#214451892
#214438922
#214438682
#214438672
C61×#16702
#1244361