Finite Group Databasebeta

← #29594256

Subgroups — #29594256

Order 15616.

214 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 59 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#21447900C211yesmaximal, characteristic
3#21447656C211yesmaximal, characteristic
4#21443894C211yesmaximal, characteristic, complemented
5#21443858C211yesmaximal, characteristic, complemented
6#21443857C211yesmaximal, characteristic, complemented
7C61×#2214C211yesmaximal, characteristic
8#16840202—21no—
9C2×#14519723—21no—
10C2×#14519723—21no—
11#16840179—21no—
12#16840142C2211yescharacteristic
13#16839583C2211yescharacteristic
14#16839583C2211yescharacteristic
15#16839577—21no—
16#16839546—21no—
17C4×#11758185C2211yescharacteristic
18C61×#510—21no—
19C61×#494C2211yescharacteristic
20C61×#443C2211yescharacteristic
21C61×#364C2211yescharacteristic
22C61×#362—21no—
23C2×Dic244—21no—
24C2×Dic244—21no—
25#14519777—21no—
26#14519723—42no—
27#14519723—41no—
28#14519723—41no—
29#14519723—41no—
30#14519721—41no—
31#14519717—21no—
32#14519717—21no—
33#14519717—41no—
34C2×#11758185—41no—
35C2×#11758185D411yescharacteristic
36C2×#11758185D411yescharacteristic
37#135×C61D411yescharacteristic
38C2×Q16×C61—21no—
39C2×Q16×C61—21no—
40#131×C61—21no—
41C4⋊Q8×C61—21no—
42Q32×C61—41no—
43SD32×C61—41no—
44M32×C61—21no—
45#108×C61D411yescharacteristic
46#104×C61—21no—
47C4×C8×C61C2311yescharacteristic
48#41×C61—21no—
49C2×Q8×C61—41no—
50C2×Dic122—41no—
51Q16×C61—41no—
52Q16×C61—41no—
53Q16×C61—41no—
54Q16×C61—41no—
55Q16×C61D811yescharacteristic
56SD16×C61—21no—
57D8×C61D811yescharacteristic
58M16×C61—21no—
59M16×C61—41no—
60C2×C8×C61—41no—
61C2×C8×C61C2×D411yescharacteristic
62C2×C8×C61C2×D411yescharacteristic
63C4⋊C4×C61—81no—
64C42×C61#4111yescharacteristic
65C4⋊Dic61—81no—
66Dic244—41no—
67Dic244—41no—
68Dic244—41no—
69Dic244—41no—
70C16×C61—41no—
71#11758185—21no—
72#11758185—41no—
73#11758185—41no—
74#11758185D811yescharacteristic
75#11758185D811yescharacteristic
76Q8×C61—21no—
77Q8×C61—81no—
78Q8×C61—81no—
79D4×C61—21no—
80D4×C61—41no—
81C2×C4×C61—21no—
82C2×C4×C61—41no—
83C2×C4×C61—81no—
84C2×C4×C61#12111yescharacteristic
85C2×Dic61—81no—
86Dic122—81no—
87Dic122—81no—
88C8×C61—41no—
89C8×C61C2×D811yescharacteristic
90C8×C61C2×D811yescharacteristic
91C8×C61#13511yescharacteristic
92C8×C61AGL(1,ℤ/8)11yescharacteristic
93#12437—611nomaximal, Sylow
94C22×C61—41no—
95C22×C61#47211yescharacteristic
96C4×C61—22no—
97C4×C61—41no—
98C4×C61—161no—
99C4×C61#45911yescharacteristic
100C4×C61#46611yescharacteristic
101Dic61—161no—
102#2247—611no—
103#2214—611no—
104#2214D6111yescharacteristic
105#2170—611no—
106#1373—611no—
107#1358—611no—
108#1358—611no—
109C2×C61—21no—
110C2×C61—81no—
111C2×C61#166711yescharacteristic
112#510—21no—
113#510—1221no—
114C2×Q32—1221no—
115C2×Q32—1221no—
116#504—1221no—
117#494—611no—
118#494C2×D6111yescharacteristic
119#443C2×D6111yescharacteristic
120#364—611no—
121#364—611no—
122#364C2×D6111yescharacteristic
123#362—21no—
124#362—1221no—
125#350—1221no—
126C4×C16—611no—
127C61#1243711yescharacteristic, complemented, Sylow
128#135C22⋊D6111yescharacteristic
129C2×Q16—21no—
130C2×Q16—21no—
131C2×Q16—1221no—
132C2×Q16—1221no—
133#131—21no—
134C4⋊Q8—21no—
135C4⋊Q8—1221no—
136Q32—41no—
137Q32—2441no—
138Q32—2441no—
139Q32—2442no—
140Q32—2441no—
141SD32—41no—
142SD32—2441no—
143M32—21no—
144M32—1221no—
145M32—1221no—
146M32—2441no—
147C2×C16—611no—
148C2×C16—611no—
149C2×C16—2441no—
150#108C22⋊D6111yescharacteristic
151#104—21no—
152C4×C8C22×D6111yescharacteristic
153#41—21no—
154C2×Q8—41no—
155C2×Q8—2441no—
156Q16—41no—
157Q16—41no—
158Q16—41no—
159Q16—41no—
160Q16—2441no—
161Q16—2441no—
162Q16—2441no—
163Q16—2441no—
164Q16#1175819911yescharacteristic
165SD16—21no—
166D8#1175819911yescharacteristic
167M16—21no—
168M16—41no—
169C2×C8—41no—
170C2×C8D4×D6111yescharacteristic
171C2×C8C2×C22⋊D6111yescharacteristic
172C4⋊C4—81no—
173C4⋊C4—4881no—
174C42#1175822411yescharacteristic
175C16—41no—
176C16—611no—
177C16—611no—
178C16—1221no—
179C16—2441no—
180C16—2441no—
181Q8—21no—
182Q8—81no—
183Q8—81no—
184Q8—4881no—
185Q8—4881no—
186D4—21no—
187D4—41no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—81no—
191C2×C4—4881no—
192C2×C4#1451974911yescharacteristic
193C8—41no—
194C8D8×D6111yescharacteristic
195C8C2×#1175819911yescharacteristic
196C8#1451979711yescharacteristic
197C8#1451980111yescharacteristic
198C22—41no—
199C22#1684003011yescharacteristic
200C4—22no—
201C4—41no—
202C4—161no—
203C4—9761no—
204C4#1683995511yescharacteristic
205C4#1683999611yescharacteristic
206C2—21no—
207C2—81no—
208C2#2144517211yescharacteristic
subgroupG/H
centerC2#21445172
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2214C2
socleC2×C61#1667
prime radical#135×C61D4
hypercenter#2214D61
hypocenterC61#12437
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2214

Complements

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

NH ≅ G/Ntype
1. #21448071C2semidirect
4. #21443894C2semidirect
5. #21443858C2semidirect
6. #21443857C2semidirect
127. C61#12437semidirect

Maximal subgroups

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

subgroupindex
#214480712
#214479002
#214476562
#214438942
#214438582
#214438572
C61×#22142
#1243761