Finite Group Databasebeta

← #29600829

Subgroups — #29600829

Order 15616.

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

normal subgroups only

This group has 200 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#21448131C211yesmaximal, characteristic
2#21448081C211yesmaximal, characteristic, complemented
3#21447700C211yesmaximal, characteristic, complemented
4#21444016C211yesmaximal, characteristic, complemented
5#21444012C211yesmaximal, characteristic, complemented
6#21444010C211yesmaximal, characteristic, complemented
7C61×#2264C211yesmaximal, characteristic, complemented
8C2×#14519720—21no—
9C2×D976C2211yescharacteristic
10#16840147—21no—
11#16839879—21no—
12#16839599—21no—
13#16839597—21no—
14#16839596C2211yescharacteristic
15#16839592C2211yescharacteristic
16#16839569—21no—
17C16×Dic61C2211yescharacteristic
18C61×#508C2211yescharacteristic
19C2×Q32×C61C2211yescharacteristic
20C61×Q64—21no—
21C61×SD64—21no—
22C61×M64C2211yescharacteristic
23C2×#11758201—41no—
24C2×D488—21no—
25#14519784—41no—
26#14519766—41no—
27#14519720—42no—
28D976—21no—
29D976—21no—
30C2×#11758185D411yescharacteristic
31#14519713—21no—
32#14519704—41no—
33C8×Dic61D411yescharacteristic
34#14519683—21no—
35#135×C61—21no—
36C2×Q16×C61—21no—
37Q32×C61—21no—
38Q32×C61—21no—
39Q32×C61D411yescharacteristic
40SD32×C61—21no—
41D16×C61D411yescharacteristic
42C2×C16×C61C2311yescharacteristic
43C32×C61—21no—
44#41×C61—41no—
45C2×Q8×C61—41no—
46C2×D244—41no—
47Q16×C61—21no—
48Q16×C61—41no—
49Q16×C61—41no—
50SD16×C61—41no—
51D8×C61—21no—
52C2×C8×C61C2×D411yescharacteristic
53#11758201—81no—
54#11758201—81no—
55#11758198—82no—
56C4×Dic61D811yescharacteristic
57#11758194—41no—
58#11758194—81no—
59C2×#92418—81no—
60C2×#92418D811yescharacteristic
61D488—41no—
62D488—41no—
63C16×C61C2×D411yescharacteristic
64C16×C61#4111yescharacteristic
65#11758185—21no—
66C22×D61—81no—
67Q8×C61—41no—
68Q8×C61—81no—
69Q8×C61—81no—
70D4×C61—41no—
71D4×C61—81no—
72C2×C4×C61—81no—
73C2×C4×C61—81no—
74C2×C4×C61C2×D811yescharacteristic
75C2×Dic61—21no—
76D244—81no—
77D244—81no—
78C8×C61#12111yescharacteristic
79C8×C61AGL(1,ℤ/8)11yescharacteristic
80#92418—81no—
81#92418D1611yescharacteristic
82#92418D1611yescharacteristic
83#13691—611nomaximal, Sylow
84C22×C61—81no—
85C22×C61#50911yescharacteristic
86C2×D61—162no—
87C2×D61—161no—
88C4×C61—81no—
89C4×C61—161no—
90C4×C61#45911yescharacteristic
91C4×C61C2×D1611yescharacteristic
92Dic61—41no—
93#2264D6111yescharacteristic, complemented
94#2263—611no—
95#2249—611no—
96#2178—611no—
97#1422—611no—
98#1420—611no—
99#1419—611no—
100C2×C61—21no—
101C2×C61—161no—
102C2×C61#220611yescharacteristic
103D61—321no—
104#508C2×D6111yescharacteristic
105C2×Q32C2×D6111yescharacteristic
106C2×SD32—1221no—
107C2×D16—611no—
108#495—1221no—
109#443—1221no—
110Q64—21no—
111SD64—21no—
112SD64—1221no—
113D32—1221no—
114M64—611no—
115M64C2×D6111yescharacteristic
116#368—611no—
117#359—1221no—
118C4×C16—611no—
119C61#1369111yescharacteristic, complemented, Sylow
120#135—21no—
121C2×Q16—21no—
122C2×SD16—2441no—
123C2×D8—1221no—
124#131—2441no—
125#124—2441no—
126Q32—21no—
127Q32—21no—
128Q32C22⋊D6111yescharacteristic
129SD32—21no—
130SD32—2442no—
131D16—1221no—
132D16—1221no—
133D16C22⋊D6111yescharacteristic
134C2×C16—611no—
135C2×C16C22×D6111yescharacteristic
136#108—1221no—
137#104—2441no—
138C4×C8—611no—
139C32—21no—
140C32—1221no—
141#41—41no—
142C2×Q8—41no—
143C2×D4—2441no—
144Q16—21no—
145Q16—41no—
146Q16—41no—
147SD16—41no—
148SD16—4881no—
149SD16—4881no—
150D8—21no—
151D8—2441no—
152D8—2441no—
153M16—4881no—
154M16—2441no—
155C2×C8—611no—
156C2×C8—4881no—
157C2×C8D4×D6111yescharacteristic
158C22⋊C4—4882no—
159C42—611no—
160C16—1221no—
161C16#1175822411yescharacteristic
162C16C2×C22⋊D6111yescharacteristic
163C23—4881no—
164Q8—41no—
165Q8—81no—
166Q8—81no—
167D4—41no—
168D4—81no—
169D4—4881no—
170D4—4881no—
171C2×C4—81no—
172C2×C4—81no—
173C2×C4—1221no—
174C2×C4D8×D6111yescharacteristic
175C8—611no—
176C8—611no—
177C8—4881no—
178C8#1451974911yescharacteristic
179C8#1451980111yescharacteristic
180C22—81no—
181C22—9762no—
182C22—9761no—
183C22#1684019611yescharacteristic
184C4—81no—
185C4—161no—
186C4—2441no—
187C4#1683995511yescharacteristic
188C4D16×D6111yescharacteristic
189C2—21no—
190C2—161no—
191C2—19521no—
192C2#2144785211yescharacteristic
subgroupG/H
centerC2#21447852
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#2264C2
socleC2×C61#2206
prime radical#21448131C2
hypercenter#2264D61
hypocenterC61#13691
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2264

Complements

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

NH ≅ G/Ntype
2. #21448081C2semidirect
3. #21447700C2semidirect
4. #21444016C2semidirect
5. #21444012C2semidirect
6. #21444010C2semidirect
7. C61×#2264C2semidirect
93. #2264D61semidirect
119. C61#13691semidirect

Maximal subgroups

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

subgroupindex
#214481312
#214480812
#214477002
#214440162
#214440122
#214440102
C61×#22642
#1369161