Finite Group Databasebeta

← #28362364

Subgroups — #28362364

Order 13952.

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

normal subgroups only

This group has 184 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#20295780C211yesmaximal, characteristic
2#20295394C211yesmaximal, characteristic, complemented
3#20295388C211yesmaximal, characteristic
4#20294768C211yesmaximal, characteristic, complemented
5#20294767C211yesmaximal, characteristic, complemented
6#20294765C211yesmaximal, characteristic
7#501×C109C211yesmaximal, characteristic, complemented
8#16812698—21no—
9#16812694—21no—
10#16812694—21no—
11#16812691C2211yescharacteristic
12#16812687C2211yescharacteristic
13#16812684—21no—
14#16812679—21no—
15#16812677—21no—
16#16812623—21no—
17#16812623—21no—
18#16812622—21no—
19#16812619—21no—
20#16812610C2211yescharacteristic
21#16812610C2211yescharacteristic
22C4⋊Q8×C109C2211yescharacteristic
23#125×C109C2211yescharacteristic
24#107×C109—21no—
25#106×C109—21no—
26#97×C109C2211yescharacteristic
27C2×Dic218—21no—
28C2×Dic218D411yescharacteristic
29C2×D436D411yescharacteristic
30C2×C4×D109—21no—
31C2×#11724784—21no—
32C2×#11724784—21no—
33C4⋊Dic109—21no—
34C4⋊Dic109D411yescharacteristic
35C4⋊Dic109D411yescharacteristic
36#13182008—21no—
37#13182008—21no—
38#13182008—21no—
39#13182006—21no—
40#13182006—21no—
41#13182006—21no—
42#13182006—21no—
43#13182006—21no—
44C4×Dic109—21no—
45C2×Q8×C109—21no—
46C2×C8×C109—21no—
47C4⋊C4×C109—21no—
48C4⋊C4×C109—21no—
49C4⋊C4×C109—21no—
50C4⋊C4×C109—21no—
51C4⋊C4×C109D411yescharacteristic
52C4⋊C4×C109D411yescharacteristic
53C42×C109C2311yescharacteristic
54C22×D109—21no—
55Q8×C109—42no—
56C2×C4×C109—21no—
57C2×C4×C109—21no—
58C2×C4×C109—41no—
59C2×C4×C109C2×D411yescharacteristic
60C2×C4×C109C2×D411yescharacteristic
61C2×C4×C109C2×D411yescharacteristic
62C2×Dic109—21no—
63C2×Dic109—21no—
64C2×Dic109—21no—
65D436—41no—
66C4×D109—81no—
67Dic218—41no—
68Dic218—81no—
69C8×C109—22no—
70#11724784—41no—
71#11724784—41no—
72C22×C109#12011yescharacteristic
73C2×D109—41no—
74C2×D109—41no—
75C2×D109—41no—
76C4×C109—21no—
77C4×C109—21no—
78C4×C109—21no—
79C4×C109—41no—
80C4×C109—41no—
81C4×C109—81no—
82Dic109—41no—
83Dic109—41no—
84Dic109—41no—
85C2×C109#45411yescharacteristic
86C2×C109#45511yescharacteristic
87C2×C109#45611yescharacteristic
88D109—81no—
89#1664—1091nomaximal, Sylow
90C109#166411yescharacteristic, complemented, Sylow
91#563—1091no—
92#501D10911yescharacteristic, complemented
93#491—1091no—
94#489—1091no—
95#330—1091no—
96#330—1091no—
97#329—1091no—
98C4⋊Q8—2181no—
99C4⋊Q8C2×D10911yescharacteristic
100#126—2181no—
101#126—2181no—
102#125—1091no—
103#125C2×D10911yescharacteristic
104#124—1091no—
105#123—2181no—
106C22⋊Q8—2181no—
107C22⋊Q8—2181no—
108#107—21no—
109#106—21no—
110#103—2181no—
111#103—2181no—
112#103—2181no—
113#102—2181no—
114#97—1091no—
115#97—1091no—
116#97C2×D10911yescharacteristic
117C2×Q8—21no—
118C2×Q8—1091no—
119C2×Q8—2181no—
120C2×D4—1091no—
121C22×C4—2181no—
122C2×C8—21no—
123C2×C8—2181no—
124C2×C8—2181no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—1091no—
130C4⋊C4—1091no—
131C4⋊C4—2181no—
132C4⋊C4—2181no—
133C4⋊C4—2181no—
134C4⋊C4—2181no—
135C4⋊C4C22⋊D10911yescharacteristic
136C4⋊C4C22⋊D10911yescharacteristic
137C22⋊C4—2181no—
138C22⋊C4—2181no—
139C22⋊C4—2181no—
140C22⋊C4—2181no—
141C22⋊C4—2181no—
142C42—2181no—
143C42C22×D10911yescharacteristic
144C23—2181no—
145Q8—42no—
146Q8—8721no—
147Q8—4361no—
148D4—4361no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—8721no—
153C2×C4—2181no—
154C2×C4—2181no—
155C2×C4—2181no—
156C2×C4D4×D10911yescharacteristic
157C2×C4D4×D10911yescharacteristic
158C2×C4C2×C22⋊D10911yescharacteristic
159C8—22no—
160C8—4361no—
161C8—4361no—
162C22—4361no—
163C22—4361no—
164C22—4361no—
165C22#1681266711yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—4361no—
173C4—4361no—
174C4—4361no—
175C2—8721no—
176C2#2029519711yescharacteristic
177C2#2029520211yescharacteristic
178C2#2029520811yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#501×C109C2
socleC22×C109#120
prime radicalC2×D436D4
hypercenter#501D109
hypocenterC109#1664
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #20295394C2semidirect
4. #20294768C2semidirect
5. #20294767C2semidirect
7. #501×C109C2semidirect
90. C109#1664semidirect
92. #501D109semidirect

Maximal subgroups

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

subgroupindex
#202957802
#202953942
#202953882
#202947682
#202947672
#202947652
#501×C1092
#1664109