Finite Group Databasebeta

← #29600885

Subgroups — #29600885

Order 15616.

184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 53 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#21448112C211yesmaximal, characteristic, complemented
2#21447941C211yesmaximal, characteristic, complemented
3#21447936C211yesmaximal, characteristic
4#21444023C211yesmaximal, characteristic, complemented
5#21444012C211yesmaximal, characteristic, complemented
6#21444009C211yesmaximal, characteristic, complemented
7C2×C61×SD64C211yesmaximal, characteristic, complemented
8#16840178C2211yescharacteristic
9#16840034—21no—
10#16840029—21no—
11#16839596C2211yescharacteristic
12#16839595—21no—
13C32×D61—21no—
14#16839592C2211yescharacteristic
15#16839592C2211yescharacteristic
16#16839578—21no—
17#16839575—21no—
18C2×Q32×C61C2211yescharacteristic
19C2×D16×C61C2211yescharacteristic
20C61×SD64—21no—
21C61×SD64—21no—
22C2×C32×C61C2211yescharacteristic
23#14519808—41no—
24#14519803—41no—
25#14519783D411yescharacteristic
26#14519717D411yescharacteristic
27#14519716—21no—
28C16×D61—21no—
29#14519713—21no—
30#14519713—21no—
31#14519696—41no—
32#14519694—41no—
33#14519683—21no—
34C2×Q16×C61—21no—
35C2×D8×C61—21no—
36Q32×C61—21no—
37Q32×C61—21no—
38D16×C61—21no—
39D16×C61—21no—
40C2×C16×C61C2311yescharacteristic
41C32×C61D411yescharacteristic
42C32×C61D411yescharacteristic
43C2×Q8×C61—41no—
44C2×D4×C61—41no—
45#11758222D811yescharacteristic
46Q16×C61—41no—
47Q16×C61—41no—
48D8×C61—41no—
49D8×C61—41no—
50C2×C8×C61C2×D411yescharacteristic
51#11758202—81no—
52#11758201—81no—
53#11758200—81no—
54#11758199—81no—
55#11758194—41no—
56#11758194—41no—
57#11758194D811yescharacteristic
58#11758189—21no—
59C8×D61—21no—
60C16×C61C2×D411yescharacteristic
61C16×C61#4111yescharacteristic
62#11758185—21no—
63C23×C61—81no—
64Q8×C61—81no—
65Q8×C61—81no—
66D4×C61—81no—
67D4×C61—81no—
68C2×C4×C61—81no—
69C2×C4×C61C2×D811yescharacteristic
70C22⋊D61—21no—
71D244D1611yescharacteristic
72C4×D61—21no—
73Dic122D1611yescharacteristic
74C8×C61#12111yescharacteristic
75C8×C61#13511yescharacteristic
76#92418—21no—
77#92418—81no—
78#92418—81no—
79#13702—611nomaximal, Sylow
80C22×C61—161no—
81C22×C61—321no—
82C22×C61#50811yescharacteristic
83C2×D61—21no—
84C4×C61—161no—
85C4×C61#46611yescharacteristic
86C4×C61C2×D1611yescharacteristic
87Dic61—21no—
88C2×SD64D6111yescharacteristic, complemented
89#2258—611no—
90#2222—611no—
91#2221—611no—
92#1425—611no—
93#1420—611no—
94#1419—611no—
95C2×C61—21no—
96C2×C61—321no—
97C2×C61#221511yescharacteristic
98D61—41no—
99C2×Q32C2×D6111yescharacteristic
100C2×D16C2×D6111yescharacteristic
101#504—611no—
102#473—1221no—
103#472—1221no—
104SD64—21no—
105SD64—21no—
106M64—611no—
107M64—1221no—
108C2×C32—1221no—
109C2×C32C2×D6111yescharacteristic
110#368—611no—
111#368—611no—
112#362—1221no—
113#361—1221no—
114C61#1370211yescharacteristic, complemented, Sylow
115#137—2441no—
116AGL(1,ℤ/8)—2441no—
117C2×Q16—21no—
118C2×D8—21no—
119#131—611no—
120Q32—21no—
121Q32—21no—
122D16—21no—
123D16—21no—
124M32—611no—
125M32—1221no—
126C2×C16—1221no—
127C2×C16C22×D6111yescharacteristic
128#108—1221no—
129#108—1221no—
130#101—2441no—
131#100—2441no—
132C32—1221no—
133C32C22⋊D6111yescharacteristic
134C32C22⋊D6111yescharacteristic
135#41—611no—
136C2×Q8—41no—
137C2×D4—41no—
138Q16—41no—
139Q16—41no—
140Q16—4881no—
141SD16—4881no—
142SD16—4881no—
143D8—41no—
144D8—41no—
145D8—4881no—
146M16—611no—
147M16—1221no—
148M16—2441no—
149M16—2441no—
150C2×C8—1221no—
151C2×C8D4×D6111yescharacteristic
152C16—1221no—
153C16#1175822411yescharacteristic
154C16C2×C22⋊D6111yescharacteristic
155C23—81no—
156Q8—81no—
157Q8—81no—
158Q8—611no—
159D4—81no—
160D4—81no—
161D4—611no—
162D4—1221no—
163C2×C4—81no—
164C2×C4—1221no—
165C2×C4D8×D6111yescharacteristic
166C8—1221no—
167C8—4881no—
168C8—4881no—
169C8#1451974811yescharacteristic
170C8#1451979611yescharacteristic
171C22—161no—
172C22—321no—
173C22—1221no—
174C22#1684019111yescharacteristic
175C4—161no—
176C4—1221no—
177C4#1683999511yescharacteristic
178C4D16×D6111yescharacteristic
179C2—21no—
180C2—321no—
181C2—2441no—
182C2#2144790211yescharacteristic
subgroupG/H
centerC2#21447902
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC2×C61×SD64C2
socleC2×C61#2215
prime radical#21447936C2
hypercenterC2×SD64D61
hypocenterC61#13702
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×SD64

Complements

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

NH ≅ G/Ntype
1. #21448112C2semidirect
2. #21447941C2semidirect
4. #21444023C2semidirect
5. #21444012C2semidirect
6. #21444009C2semidirect
7. C2×C61×SD64C2semidirect
88. C2×SD64D61semidirect
114. C61#13702semidirect

Maximal subgroups

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

subgroupindex
#214481122
#214479412
#214479362
#214440232
#214440122
#214440092
C2×C61×SD642
#1370261