Finite Group Databasebeta

← #28362322

Subgroups — #28362322

Order 13952.

262 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 45 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#20295768C211yesmaximal, characteristic, complemented
2#20295416C211yesmaximal, characteristic, complemented
3#20295415C212yesmaximal, complemented
4#20294765C212yesmaximal, complemented
5#329×C109C211yesmaximal, characteristic, complemented
6C2×#13182018—22no—
7C2×#13182016—21no—
8C2×D872—22no—
9C2×#13182014—21no—
10#16812696C2211yescharacteristic, complemented
11#16812688—21no—
12#16812687C2212yes—
13#16812685—22no—
14#16812669—22no—
15#16812667—21no—
16#16812610C2211yescharacteristic, complemented
17#124×C109C2211yescharacteristic
18#97×C109C2212yescomplemented
19C23×D109—21no—
20C2×Dic218D412yes—
21C2×D436—21no—
22C2×D436—22no—
23C2×D436—21no—
24C2×D436D412yes—
25C2×C22⋊D109—22no—
26#13182018—44no—
27#13182016—42no—
28D872—44no—
29#13182014—42no—
30C2×#11724784—21no—
31C22⋊Dic109—21no—
32#13182006—22no—
33#13182006—22no—
34#13182006—22no—
35C4×Dic109—21no—
36C2×Q8×C109D411yescharacteristic
37C2×D4×C109D411yescharacteristic
38C2×C8×C109—22no—
39C22⋊C4×C109—22no—
40C42×C109C2311yescharacteristic
41C23×C109—21no—
42C22×D109—22no—
43C22×D109—41no—
44C22×D109—82no—
45C22×D109—81no—
46Q8×C109—41no—
47D4×C109—41no—
48C2×C4×C109—21no—
49C2×C4×C109C2×D412yes—
50C2×C4×C109C2×D411yescharacteristic
51C22⋊D109—82no—
52C2×Dic109—22no—
53D436—42no—
54D436—41no—
55D436—42no—
56D436—41no—
57D436—42no—
58D436—81no—
59Dic218—42no—
60C8×C109—24no—
61#11724784—22no—
62C22×C109—42no—
63C22×C109—41no—
64C22×C109#12011yescharacteristic
65C2×D109—42no—
66C2×D109—42no—
67C2×D109—42no—
68C2×D109—84no—
69C2×D109—82no—
70C2×D109—81no—
71C4×C109—21no—
72C4×C109—22no—
73C4×C109—41no—
74Dic109—42no—
75C2×C109—81no—
76C2×C109#45312yes—
77C2×C109#45311yescharacteristic
78D109—82no—
79D109—161no—
80#1655—1091nomaximal, Sylow
81C109#165511yescharacteristic, complemented, Sylow
82H(3,𝔽4)—1091no—
83#496—1091no—
84#496—1092no—
85#329—1092no—
86#329D10911yescharacteristic, complemented
87C2×SD16—2182no—
88C2×SD16—2181no—
89C2×D8—2182no—
90C2×D8—2181no—
91#127—1091no—
92#124—1092no—
93#124—2182no—
94#124—2181no—
95#124C2×D10911yescharacteristic
96#120—2182no—
97#120—2181no—
98#97—1091no—
99#97C2×D10912yescomplemented
100C24—2181no—
101C2×Q8—1092no—
102C2×Q8D43611yescharacteristic
103C2×D4—1092no—
104C2×D4—2181no—
105C2×D4—2182no—
106C2×D4—2182no—
107C2×D4—2181no—
108C2×D4D43611yescharacteristic
109SD16—4364no—
110SD16—4362no—
111D8—4364no—
112D8—4362no—
113C2×C8—22no—
114C2×C8—2181no—
115C22⋊C4—22no—
116C22⋊C4—2182no—
117C22⋊C4—2181no—
118C22⋊C4—2182no—
119C22⋊C4—2182no—
120C42—2181no—
121C42C22×D10911yescharacteristic
122C23—21no—
123C23—8722no—
124C23—8721no—
125C23—4361no—
126C23—2182no—
127Q8—41no—
128Q8—4362no—
129D4—41no—
130D4—8721no—
131D4—8722no—
132D4—4362no—
133D4—4361no—
134D4—4362no—
135D4—4361no—
136D4—4362no—
137C2×C4—21no—
138C2×C4—2182no—
139C2×C4D4×D10912yes—
140C2×C4C2×D43611yescharacteristic
141C8—24no—
142C8—2182no—
143C22—42no—
144C22—41no—
145C22—8724no—
146C22—8722no—
147C22—8721no—
148C22—4362no—
149C22—4362no—
150C22—4362no—
151C22#1681266911yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—4362no—
156C2—81no—
157C2—8722no—
158C2—17441no—
159C2#2029519512yes—
160C2#2029519611yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#329×C109C2
socleC22×C109#120
hypercenter#329D109
hypocenterC109#1655
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
1. #20295768C2semidirect
2. #20295416C2semidirect
3. #20295415C2semidirect
4. #20294765C2semidirect
5. #329×C109C2semidirect
10. #16812696C22semidirect
16. #16812610C22semidirect
18. #97×C109C22semidirect
81. C109#1655semidirect
86. #329D109semidirect
99. #97C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202957682
#202954162
#202954152
#202947652
#329×C1092
#1655109