Finite Group Databasebeta

← #28374832

Subgroups — #28374832

Order 13952.

476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 125 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#20295831C212yesmaximal, complemented
2#20295828C212yesmaximal, complemented
3#20295403C211yesmaximal, characteristic, complemented
4#20295297C212yesmaximal, complemented
5#20295296C212yesmaximal, complemented
6#20295195C214yesmaximal, complemented
7#20295144C211yesmaximal, characteristic, complemented
8#443×C109C211yesmaximal, characteristic, complemented
9#16812745C2214yescomplemented
10#16812727—24no—
11#16812727C2214yescomplemented
12#16812726—24no—
13#16812724C2214yescomplemented
14#16812722—22no—
15#16812721—22no—
16#16812721C2211yescharacteristic
17C2×D872—22no—
18C2×D872C2212yescomplemented
19C2×D872C2212yescomplemented
20D8×D109—22no—
21#16812705C2212yescomplemented
22#16812696C2212yescomplemented
23#16812635C2211yescharacteristic, complemented
24#16812627C2212yescomplemented
25#16812615C2214yescomplemented
26#135×C109C2211yescharacteristic
27#131×C109C2212yescomplemented
28#108×C109C2211yescharacteristic, complemented
29#104×C109C2212yescomplemented
30C4×C8×C109C2211yescharacteristic, complemented
31#13182030—24no—
32#13182029—24no—
33#13182029C2312yes—
34C2×D436—24no—
35C2×D436—42no—
36C2×D436C2314yes—
37D4×D109—24no—
38D4×D109—44no—
39Dic436D411yescharacteristic, complemented
40#13182018—24no—
41#13182018D412yescomplemented
42#13182016—24no—
43D872—24no—
44D872—22no—
45D872—22no—
46D872—22no—
47D872—22no—
48D872D411yescharacteristic, complemented
49#13182014—24no—
50#13182013C2312yes—
51#13182012—22no—
52C8×D109—22no—
53#41×C109C2312yes—
54Q16×C109D411yescharacteristic, complemented
55SD16×C109D412yescomplemented
56D8×C109D411yescharacteristic, complemented
57M16×C109—22no—
58M16×C109C2312yes—
59C2×C8×C109—22no—
60C2×C8×C109C2311yescharacteristic
61C2×C8×C109C2311yescharacteristic
62C42×C109C2311yescharacteristic
63C22×D109—24no—
64C22×D109—44no—
65Q8×C109C2×D412yes—
66D4×C109—22no—
67D4×C109C2×D412yes—
68C2×C4×C109—21no—
69C2×C4×C109—22no—
70C2×C4×C109C2411yescharacteristic
71C22⋊D109—22no—
72C22⋊D109—44no—
73D436—24no—
74D436—24no—
75D436—44no—
76D436—84no—
77D436C2×D412yes—
78C4×D109—22no—
79C4×D109—44no—
80Dic218C2×D412yes—
81C8×C109—22no—
82C8×C109C2×D411yescharacteristic
83C8×C109C2×D411yescharacteristic
84C8×C109C2×D411yescharacteristic
85C8×C109C2×D411yescharacteristic
86#11724784—22no—
87C22×C109—22no—
88C22×C109H(5,𝔽2)11yescharacteristic
89C2×D109—22no—
90C2×D109—44no—
91C2×D109—84no—
92C2×D109—164no—
93C4×C109—22no—
94C4×C109—22no—
95C4×C109C22×D411yescharacteristic
96C4×C109C22×D411yescharacteristic
97Dic109—22no—
98C2×C109—21no—
99C2×C109—42no—
100C2×C109D4211yescharacteristic
101D109—42no—
102D109—84no—
103#3292—1091nomaximal, Sylow
104C109#329211yescharacteristic, complemented, Sylow
105#576—1092no—
106#576—1092no—
107#493—1091no—
108#472—1092no—
109#472—1092no—
110#453—1094no—
111#443—1091no—
112#443D10911yescharacteristic, complemented
113H(5,𝔽2)—1094no—
114AGL(1,ℤ/8)—1094no—
115AGL(1,ℤ/8)—1094no—
116AGL(1,ℤ/8)—2184no—
117AGL(1,ℤ/8)—2184no—
118#135—1091no—
119#135—2182no—
120#135—2182no—
121#135C2×D10911yescharacteristic
122C2×D8—1092no—
123C2×D8—1092no—
124C2×D8—2182no—
125C2×D8—2182no—
126#131—1092no—
127#131C2×D10912yescomplemented
128#127—1092no—
129#108—1091no—
130#108C2×D10911yescharacteristic, complemented
131#104—1092no—
132#104C2×D10912yescomplemented
133#100—1094no—
134C4×C8C2×D10911yescharacteristic, complemented
135#41—1092no—
136#41—2184no—
137#41—2184no—
138#41C22×D10912yes—
139C2×D4—1094no—
140C2×D4—4362no—
141C2×D4—4364no—
142C2×D4—2184no—
143C2×D4—2184no—
144Q16—1091no—
145Q16D43611yescharacteristic, complemented
146SD16—1092no—
147SD16—2184no—
148SD16—2184no—
149SD16D43612yescomplemented
150D8—1091no—
151D8—2184no—
152D8—2184no—
153D8—2182no—
154D8—2182no—
155D8—2182no—
156D8—2182no—
157D8D43611yescharacteristic, complemented
158M16—22no—
159M16—1092no—
160M16—2182no—
161M16C22×D10912yes—
162C2×C8—22no—
163C2×C8—2182no—
164C2×C8C22×D10911yescharacteristic
165C2×C8C22×D10911yescharacteristic
166C42C22×D10911yescharacteristic
167C23—4364no—
168C23—2184no—
169Q8—1092no—
170Q8C2×D43612yes—
171D4—22no—
172D4—8724no—
173D4—1092no—
174D4—4364no—
175D4—4364no—
176D4—2182no—
177D4—2184no—
178D4—2184no—
179D4C2×D43612yes—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—4364no—
183C2×C4—2182no—
184C2×C4C23×D10911yescharacteristic
185C8—22no—
186C8—2182no—
187C8D4×D10911yescharacteristic
188C8D4×D10911yescharacteristic
189C8C2×D43611yescharacteristic
190C8C2×D43611yescharacteristic
191C22—22no—
192C22—8724no—
193C22—4364no—
194C22—17444no—
195C22—2182no—
196C22#1681274511yescharacteristic
197C4—22no—
198C4—22no—
199C4—2182no—
200C4C2×D4×D10911yescharacteristic
201C4C22×D43611yescharacteristic
202C2—21no—
203C2—42no—
204C2—8724no—
205C2—4362no—
206C2D4×D43611yescharacteristic
subgroupG/H
centerC2D4×D436
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#443×C109C2
socleC2×C109D42
hypercenter#443D109
hypocenterC109#3292
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #20295831C2semidirect
2. #20295828C2semidirect
3. #20295403C2semidirect
4. #20295297C2semidirect
5. #20295296C2semidirect
6. #20295195C2semidirect
7. #20295144C2semidirect
8. #443×C109C2semidirect
9. #16812745C22semidirect
11. #16812727C22semidirect
13. #16812724C22semidirect
18. C2×D872C22semidirect
19. C2×D872C22semidirect
21. #16812705C22semidirect
22. #16812696C22semidirect
23. #16812635C22semidirect
24. #16812627C22semidirect
25. #16812615C22semidirect
27. #131×C109C22semidirect
28. #108×C109C22semidirect
29. #104×C109C22semidirect
30. C4×C8×C109C22semidirect
39. Dic436D4semidirect
41. #13182018D4semidirect
48. D872D4semidirect
54. Q16×C109D4semidirect
55. SD16×C109D4semidirect
56. D8×C109D4semidirect
104. C109#3292semidirect
112. #443D109semidirect
127. #131C2×D109semidirect
130. #108C2×D109semidirect
132. #104C2×D109semidirect
134. C4×C8C2×D109semidirect
145. Q16D436semidirect
149. SD16D436semidirect
157. D8D436semidirect

Maximal subgroups

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

subgroupindex
#202958312
#202958282
#202954032
#202952972
#202952962
#202951952
#202951442
#443×C1092
#3292109