Finite Group Databasebeta

← #28373484

Subgroups — #28373484

Order 13952.

656 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 173 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×#16812727C214yesmaximal, complemented
2#20295576C211yesmaximal, characteristic, complemented
3C2×#16812696C211yesmaximal, characteristic, complemented
4#20295415C214yesmaximal, complemented
5#20295403C212yesmaximal, complemented
6#20295399C212yesmaximal, complemented
7C4×M16×C109C211yesmaximal, characteristic, complemented
8C2×#13182029C2212yes—
9C22×D436—22no—
10C22×D436C2212yes—
11#16812727—216no—
12C2×#13182018C2218yescomplemented
13C2×D872C2218yescomplemented
14#16812699C2211yescharacteristic, complemented
15#16812696—22no—
16#16812696C2212yes—
17#16812696C2212yes—
18#16812696C2211yescharacteristic, complemented
19#16812687C2212yescomplemented
20#16812673—22no—
21C4×D436—22no—
22C2×M16×C109C2212yes—
23C2×C42×C109C2211yescharacteristic
24#97×C109C2212yescomplemented
25C4×C8×C109C2212yescomplemented
26C23×D109—22no—
27#13182029—28no—
28C2×Dic218C2312yes—
29C2×D436—28no—
30C2×D436—22no—
31C2×D436—22no—
32C2×D436—24no—
33C2×D436—24no—
34C2×D436—48no—
35C2×D436C2312yes—
36C2×D436C2314yes—
37C2×C22⋊D109—22no—
38C2×C4×D109—22no—
39#13182018—216no—
40D872—216no—
41C4⋊Dic109—22no—
42#13182006—24no—
43C22×C4×C109D412yes—
44C22×C4×C109C2311yescharacteristic
45M16×C109D418yescomplemented
46C2×C8×C109C2314yes—
47C42×C109D412yes—
48C42×C109C2311yescharacteristic
49C42×C109C2311yescharacteristic
50C23×C109C2×D411yescharacteristic
51C22×D109—22no—
52C22×D109—24no—
53C22×D109—48no—
54C22×D109—44no—
55C2×C4×C109—24no—
56C2×C4×C109C2×D412yes—
57C2×C4×C109C2×D411yescharacteristic
58C2×C4×C109C2×D414yes—
59C2×C4×C109C2×D412yes—
60C2×C4×C109C2411yescharacteristic
61C22⋊D109—44no—
62C2×Dic109—22no—
63D436—24no—
64D436—28no—
65D436—48no—
66D436—44no—
67D436—44no—
68D436—48no—
69C4×D109—44no—
70Dic218—24no—
71C8×C109C2×D418yescomplemented
72C22×C109—22no—
73C22×C109#12712yes—
74C22×C109C22×D411yescharacteristic
75C2×D109—42no—
76C2×D109—44no—
77C2×D109—48no—
78C2×D109—44no—
79C2×D109—88no—
80C4×C109—22no—
81C4×C109#12712yes—
82C4×C109AGL(1,ℤ/8)14yescomplemented
83C4×C109C22×D412yes—
84Dic109—42no—
85C2×C109—22no—
86C2×C109C2×#12711yescharacteristic
87C2×C109C2×AGL(1,ℤ/8)12yes—
88D109—82no—
89D109—84no—
90#3151—1091nomaximal, Sylow
91C109#315111yescharacteristic, complemented, Sylow
92C2×AGL(1,ℤ/8)—1094no—
93#532—1091no—
94C2×#127—1091no—
95#496—1094no—
96#493—1092no—
97#492—1092no—
98C4×M16D10911yescharacteristic, complemented
99C2×#41—1092no—
100C22×D4—1092no—
101C22×D4—2182no—
102AGL(1,ℤ/8)—21816no—
103C2×SD16—1098no—
104C2×D8—1098no—
105C2×M16C2×D10912yes—
106C4⋊Q8—1091no—
107#127—1092no—
108#127—1092no—
109#127—1091no—
110#127—2182no—
111#124—1092no—
112#121—2182no—
113C4×D4—2182no—
114C2×C42C2×D10911yescharacteristic
115#97C2×D10912yescomplemented
116C4×C8C2×D10912yescomplemented
117C24—2182no—
118#41—2188no—
119C2×Q8—1092no—
120C2×D4—1092no—
121C2×D4—1094no—
122C2×D4—4368no—
123C2×D4—2182no—
124C2×D4—2182no—
125C2×D4—2184no—
126C2×D4—2184no—
127C2×D4—2182no—
128C2×D4—2188no—
129C22×C4—2182no—
130C22×C4D43612yes—
131C22×C4C22×D10911yescharacteristic
132SD16—21816no—
133D8—21816no—
134M16D43618yescomplemented
135C2×C8C22×D10914yes—
136C4⋊C4—2182no—
137C22⋊C4—2184no—
138C42D43612yes—
139C42C22×D10911yescharacteristic
140C42C22×D10911yescharacteristic
141C23—4368no—
142C23—4364no—
143C23—2182no—
144C23—2184no—
145C23C2×D43611yescharacteristic
146Q8—2184no—
147D4—4368no—
148D4—4364no—
149D4—4364no—
150D4—4368no—
151D4—4364no—
152D4—2184no—
153D4—2188no—
154C2×C4—24no—
155C2×C4—4364no—
156C2×C4—2182no—
157C2×C4C2×D43612yes—
158C2×C4C2×D43611yescharacteristic
159C2×C4C2×D43614yes—
160C2×C4C2×D43612yes—
161C2×C4C23×D10911yescharacteristic
162C8C2×D43618yescomplemented
163C22—22no—
164C22—8728no—
165C22—4368no—
166C22—4364no—
167C22—4362no—
168C22—4364no—
169C22#1681269612yes—
170C22C22×D43611yescharacteristic
171C4—22no—
172C4—4362no—
173C4#1681269612yes—
174C4#1681272714yescomplemented
175C4C22×D43612yes—
176C2—22no—
177C2—8724no—
178C2—8722no—
179C2C2×#1681269611yescharacteristic
180C2C2×#1681272712yes—
subgroupG/H
centerC22C22×D436
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC4×M16×C109C2
socleC22×C109C22×D4
hypercenterC4×M16D109
hypocenterC109#3151
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#16812727C2semidirect
2. #20295576C2semidirect
3. C2×#16812696C2semidirect
4. #20295415C2semidirect
5. #20295403C2semidirect
6. #20295399C2semidirect
7. C4×M16×C109C2semidirect
12. C2×#13182018C22semidirect
13. C2×D872C22semidirect
14. #16812699C22semidirect
18. #16812696C22semidirect
19. #16812687C22semidirect
24. #97×C109C22semidirect
25. C4×C8×C109C22semidirect
45. M16×C109D4semidirect
71. C8×C109C2×D4semidirect
82. C4×C109AGL(1,ℤ/8)semidirect
91. C109#3151semidirect
98. C4×M16D109semidirect
115. #97C2×D109semidirect
116. C4×C8C2×D109semidirect
134. M16D436semidirect
162. C8C2×D436semidirect
174. C4#16812727semidirect

Maximal subgroups

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

subgroupindex
C2×#168127272
#202955762
C2×#168126962
#202954152
#202954032
#202953992
C4×M16×C1092
#3151109