Finite Group Databasebeta

← #29600891

Subgroups — #29600891

Order 15616.

184 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C2×#16839599C211yesmaximal, characteristic, complemented
2#21448114C211yesmaximal, characteristic, complemented
3#21447941C211yesmaximal, characteristic, complemented
4#21447940C211yesmaximal, characteristic
5#21444022C211yesmaximal, characteristic, complemented
6#21444010C211yesmaximal, characteristic, complemented
7C61×#1420C211yesmaximal, characteristic, complemented
8C2×D976C2211yescharacteristic
9#16840178C2211yescharacteristic
10#16840034—21no—
11#16840033—21no—
12#16839599—21no—
13#16839599—21no—
14#16839595—21no—
15C2×#14519683C2211yescharacteristic
16C32×D61—21no—
17#16839592C2211yescharacteristic
18#16839578—21no—
19#16839574—21no—
20C2×Q32×C61C2211yescharacteristic
21C61×M64C2211yescharacteristic
22C61×#368C2211yescharacteristic
23#14519808—41no—
24#14519805—41no—
25C2×D488—21no—
26#14519783D411yescharacteristic
27D976—21no—
28D976—21no—
29#14519717D411yescharacteristic
30#14519716—21no—
31C16×D61—21no—
32#14519713—21no—
33#14519696—41no—
34#14519693—41no—
35#14519683D411yescharacteristic
36#14519683D411yescharacteristic
37C2×Q16×C61—21no—
38Q32×C61—21no—
39Q32×C61—21no—
40C2×C16×C61C2311yescharacteristic
41#108×C61—21no—
42C32×C61—21no—
43C2×Q8×C61—41no—
44#11758222D811yescharacteristic
45C2×D244—41no—
46Q16×C61—41no—
47Q16×C61—41no—
48M16×C61—41no—
49C2×C8×C61C2×D411yescharacteristic
50#11758202—81no—
51#11758201—81no—
52#11758194—41no—
53#11758194D811yescharacteristic
54D488—41no—
55D488—41no—
56D488—81no—
57#11758190—81no—
58#11758189—21no—
59C8×D61—21no—
60C16×C61C2×D411yescharacteristic
61C16×C61#4111yescharacteristic
62#11758185—21no—
63C22×D61—81no—
64Q8×C61—81no—
65Q8×C61—81no—
66C2×C4×C61—81no—
67C2×C4×C61C2×D811yescharacteristic
68C22⋊D61—21no—
69D244—81no—
70D244—81no—
71D244D1611yescharacteristic
72C4×D61—21no—
73Dic122D1611yescharacteristic
74C8×C61—81no—
75C8×C61#12111yescharacteristic
76C8×C61#13511yescharacteristic
77#92418—21no—
78#92418—81no—
79#13702—611nomaximal, Sylow
80C22×C61#50811yescharacteristic
81C2×D61—21no—
82C2×D61—161no—
83C2×D61—321no—
84C4×C61—161no—
85C4×C61#46611yescharacteristic
86C4×C61C2×D1611yescharacteristic
87Dic61—21no—
88C2×SD64—611no—
89#2258—611no—
90#2222—611no—
91#2221—611no—
92#1425—611no—
93#1420D6111yescharacteristic, complemented
94#1419—611no—
95C2×C61—21no—
96C2×C61#221511yescharacteristic
97D61—41no—
98D61—321no—
99C2×Q32C2×D6111yescharacteristic
100C2×D16—611no—
101#504—611no—
102#473—1221no—
103#472—1221no—
104SD64—1221no—
105SD64—1221no—
106M64—1221no—
107M64C2×D6111yescharacteristic
108C2×C32—611no—
109C2×C32—1221no—
110#368—611no—
111#368C2×D6111yescharacteristic
112#362—1221no—
113#361—1221no—
114C61#1370211yescharacteristic, complemented, Sylow
115#137—2441no—
116AGL(1,ℤ/8)—2441no—
117C2×Q16—21no—
118C2×D8—1221no—
119#131—611no—
120Q32—21no—
121Q32—21no—
122D16—1221no—
123D16—1221no—
124M32—611no—
125M32—1221no—
126C2×C16—1221no—
127C2×C16C22×D6111yescharacteristic
128#108—21no—
129#108—1221no—
130#101—2441no—
131#100—2441no—
132C32—21no—
133C32—611no—
134C32—611no—
135#41—611no—
136C2×Q8—41no—
137C2×D4—2441no—
138Q16—41no—
139Q16—41no—
140Q16—4881no—
141SD16—4881no—
142SD16—4881no—
143D8—4881no—
144D8—2441no—
145D8—2441no—
146M16—41no—
147M16—611no—
148M16—1221no—
149M16—2441no—
150C2×C8—1221no—
151C2×C8D4×D6111yescharacteristic
152C16—1221no—
153C16#1175822211yescharacteristic
154C16D4×D6111yescharacteristic
155C23—4881no—
156Q8—81no—
157Q8—81no—
158Q8—611no—
159D4—611no—
160D4—1221no—
161D4—4881no—
162D4—4881no—
163C2×C4—81no—
164C2×C4—1221no—
165C2×C4D8×D6111yescharacteristic
166C8—81no—
167C8—1221no—
168C8—4881no—
169C8#1451975011yescharacteristic
170C8#1451979811yescharacteristic
171C22—1221no—
172C22—19521no—
173C22—9761no—
174C22#1684019311yescharacteristic
175C4—161no—
176C4—1221no—
177C4#1683999711yescharacteristic
178C4D16×D6111yescharacteristic
179C2—21no—
180C2—19521no—
181C2—2441no—
182C2#2144790411yescharacteristic
subgroupG/H
centerC2#21447904
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#1420C2
socleC2×C61#2215
prime radical#21447940C2
hypercenter#1420D61
hypocenterC61#13702
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1420

Complements

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

NH ≅ G/Ntype
1. C2×#16839599C2semidirect
2. #21448114C2semidirect
3. #21447941C2semidirect
5. #21444022C2semidirect
6. #21444010C2semidirect
7. C61×#1420C2semidirect
93. #1420D61semidirect
114. C61#13702semidirect

Maximal subgroups

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

subgroupindex
C2×#168395992
#214481142
#214479412
#214479402
#214440222
#214440102
C61×#14202
#1370261