Finite Group Databasebeta

← #29600974

Subgroups — #29600974

Order 15616.

170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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#21447923C211yesmaximal, characteristic
2#21447612C211yesmaximal, characteristic, complemented
3#21444024C211yesmaximal, characteristic, complemented
4#21444010C211yesmaximal, characteristic, complemented
5#21444008C211yesmaximal, characteristic, complemented
6#21443958C211yesmaximal, characteristic, complemented
7C61×#1426C211yesmaximal, characteristic, complemented
8C2×D976C2211yescharacteristic
9C2×#14519716C2211yescharacteristic
10#16839999—21no—
11#108×D61—21no—
12#16839596C2211yescharacteristic
13#16839592C2211yescharacteristic
14#16839591—21no—
15#16839562—21no—
16C61×M64C2211yescharacteristic
17C61×#368C2211yescharacteristic
18C61×#367C2211yescharacteristic
19C2×D488—21no—
20M16×D61—41no—
21C2×C8×D61D411yescharacteristic
22#14519752—41no—
23D976—21no—
24D976—21no—
25#14519716—21no—
26#14519716—21no—
27C2×#11758185D411yescharacteristic
28#14519713—21no—
29#14519712—41no—
30#14519697—41no—
31#14519683—21no—
32C2×C16×C61C2311yescharacteristic
33#108×C61—21no—
34#107×C61—21no—
35C32×C61—21no—
36C2×D244—41no—
37C2×D244—81no—
38C2×C4×D61D811yescharacteristic
39M16×C61—41no—
40C2×C8×C61C2×D411yescharacteristic
41C4⋊C4×C61—41no—
42#11758198—81no—
43#11758194—41no—
44C2×#92418D811yescharacteristic
45D488—41no—
46D488—41no—
47#11758189—81no—
48C8×D61—21no—
49C8×D61—21no—
50C8×D61—81no—
51C16×C61#4111yescharacteristic
52C16×C61#4111yescharacteristic
53#11758185—21no—
54C22×D61—81no—
55C22×D61SD3211yescharacteristic
56C2×C4×C61—81no—
57C2×C4×C61C2×D811yescharacteristic
58C2×Dic61SD3211yescharacteristic
59D244—81no—
60D244—81no—
61D244—162no—
62C4×D61—21no—
63C4×D61—21no—
64C8×C61—81no—
65C8×C61#12311yescharacteristic
66C8×C61#13711yescharacteristic
67#92418—21no—
68#92418—81no—
69#13717—611nomaximal, Sylow
70C22×C61C2×SD3211yescharacteristic
71C2×D61—21no—
72C2×D61—41no—
73C2×D61—161no—
74C2×D61—161no—
75C2×D61—161no—
76C4×C61—161no—
77C4×C61#48011yescharacteristic
78C4×C61#50911yescharacteristic
79Dic61—21no—
80#2218—611no—
81#2161—611no—
82#1426—611no—
83#1426D6111yescharacteristic, complemented
84#1419—611no—
85#1419—611no—
86#1400—611no—
87C2×C61—21no—
88C2×C61#223311yescharacteristic
89D61—41no—
90D61—321no—
91C2×D16—611no—
92C2×M32—611no—
93#466—1221no—
94C2×#108—1221no—
95M64—611no—
96M64C2×D6111yescharacteristic
97#368—611no—
98#368—1221no—
99#368C2×D6111yescharacteristic
100#367C2×D6111yescharacteristic
101#357—1221no—
102C61#1371711yescharacteristic, complemented, Sylow
103C2×D8—1221no—
104C2×M16—2441no—
105C22×C8—611no—
106#121—2441no—
107D16—1221no—
108D16—1221no—
109M32—1221no—
110M32—1221no—
111C2×C16—611no—
112C2×C16C22×D6111yescharacteristic
113#108—21no—
114#108—1221no—
115#108—2441no—
116#107—21no—
117#102—2441no—
118C32—21no—
119C32—1221no—
120C2×D4—4881no—
121C2×D4—2441no—
122C22×C4—611no—
123D8—2441no—
124D8—2441no—
125M16—41no—
126M16—4881no—
127M16—2441no—
128C2×C8—611no—
129C2×C8—1221no—
130C2×C8—1221no—
131C2×C8—4881no—
132C2×C8D4×D6111yescharacteristic
133C4⋊C4—41no—
134C22⋊C4—4881no—
135C16—1221no—
136C16#1175822211yescharacteristic
137C16#1175822611yescharacteristic
138C23—611no—
139C23—4881no—
140D4—9762no—
141D4—4881no—
142D4—4881no—
143C2×C4—81no—
144C2×C4—611no—
145C2×C4—1221no—
146C2×C4—1221no—
147C2×C4D8×D6111yescharacteristic
148C8—81no—
149C8—1221no—
150C8—4881no—
151C8#1451976211yescharacteristic
152C8#1451980911yescharacteristic
153C22—1221no—
154C22—9761no—
155C22—9761no—
156C22—9761no—
157C22—2441no—
158C22SD32×D6111yescharacteristic
159C4—161no—
160C4—1221no—
161C4#1684007711yescharacteristic
162C4#1684019911yescharacteristic
163C2—21no—
164C2—19521no—
165C2—2441no—
166C2#2144800611yescharacteristic
subgroupG/H
centerC2#21448006
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#1426C2
socleC2×C61#2233
prime radical#21447923C2
hypercenter#1426D61
hypocenterC61#13717
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1426

Complements

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

NH ≅ G/Ntype
2. #21447612C2semidirect
3. #21444024C2semidirect
4. #21444010C2semidirect
5. #21444008C2semidirect
6. #21443958C2semidirect
7. C61×#1426C2semidirect
83. #1426D61semidirect
102. C61#13717semidirect

Maximal subgroups

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

subgroupindex
#214479232
#214476122
#214440242
#214440102
#214440082
#214439582
C61×#14262
#1371761