Finite Group Databasebeta

← #28362367

Subgroups — #28362367

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#20295435C211yesmaximal, characteristic, complemented
3#20295396C211yesmaximal, characteristic, complemented
4#20295386C211yesmaximal, characteristic
5#20294767C211yesmaximal, characteristic, complemented
6#20294765C211yesmaximal, characteristic
7#330×C109C211yesmaximal, characteristic, complemented
8#16812699C2211yescharacteristic
9#16812698—21no—
10#16812694—21no—
11#16812694—21no—
12#16812691C2211yescharacteristic
13#16812687C2211yescharacteristic
14#16812684—21no—
15#16812679—21no—
16#16812677—21no—
17#16812633—21no—
18#16812631—21no—
19#16812624—21no—
20#16812622—21no—
21#16812622—21no—
22#16812621—21no—
23#16812610C2211yescharacteristic
24#125×C109C2211yescharacteristic
25#97×C109C2211yescharacteristic
26#97×C109C2211yescharacteristic
27C2×Dic218—21no—
28C2×Dic218—21no—
29C2×Dic218D411yescharacteristic
30C2×D436D411yescharacteristic
31C2×C4×D109—21no—
32C2×#11724784—21no—
33C4⋊Dic109—21no—
34C4⋊Dic109—21no—
35C4⋊Dic109—21no—
36C4⋊Dic109D411yescharacteristic
37C4⋊Dic109D411yescharacteristic
38#13182008—21no—
39#13182008—21no—
40#13182008—21no—
41#13182006—21no—
42#13182006—21no—
43#13182006—21no—
44#13182006—21no—
45#13182006—21no—
46C4×Dic109—21no—
47C2×C8×C109—21no—
48C2×C8×C109—21no—
49C4⋊C4×C109—21no—
50C4⋊C4×C109—21no—
51C4⋊C4×C109D411yescharacteristic
52C4⋊C4×C109D411yescharacteristic
53C42×C109C2311yescharacteristic
54C22×D109—21no—
55C2×C4×C109—21no—
56C2×C4×C109—21no—
57C2×C4×C109C2×D411yescharacteristic
58C2×C4×C109C2×D411yescharacteristic
59C2×C4×C109C2×D411yescharacteristic
60C2×Dic109—21no—
61C2×Dic109—21no—
62C2×Dic109—21no—
63C2×Dic109—41no—
64D436—41no—
65C4×D109—81no—
66Dic218—41no—
67Dic218—42no—
68Dic218—81no—
69C8×C109—22no—
70C8×C109—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—
81Dic109—41no—
82Dic109—41no—
83Dic109—41no—
84Dic109—81no—
85C2×C109#45411yescharacteristic
86C2×C109#45511yescharacteristic
87C2×C109#45611yescharacteristic
88D109—81no—
89#1664—1091nomaximal, Sylow
90C109#166411yescharacteristic, complemented, Sylow
91#563—1091no—
92#501—1091no—
93#491—1091no—
94#489—1091no—
95#330—1091no—
96#330D10911yescharacteristic, complemented
97#329—1091no—
98C4⋊Q8—1091no—
99C4⋊Q8—2181no—
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—2181no—
109#106—2181no—
110#103—2181no—
111#103—2181no—
112#103—2181no—
113#102—2181no—
114#97—1091no—
115#97C2×D10911yescharacteristic
116#97C2×D10911yescharacteristic
117C2×Q8—1091no—
118C2×Q8—2181no—
119C2×Q8—2181no—
120C2×D4—1091no—
121C22×C4—2181no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—2181no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—1091no—
128C4⋊C4—1091no—
129C4⋊C4—2181no—
130C4⋊C4—2181no—
131C4⋊C4—2181no—
132C4⋊C4—2181no—
133C4⋊C4—2181no—
134C4⋊C4—2181no—
135C4⋊C4D43611yescharacteristic
136C4⋊C4D43611yescharacteristic
137C22⋊C4—2181no—
138C22⋊C4—2181no—
139C22⋊C4—2181no—
140C22⋊C4—2181no—
141C22⋊C4—2181no—
142C42—2181no—
143C42C22×D10911yescharacteristic
144C23—2181no—
145Q8—8721no—
146Q8—4362no—
147Q8—4361no—
148D4—4361no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—8721no—
152C2×C4—4361no—
153C2×C4—2181no—
154C2×C4—2181no—
155C2×C4—2181no—
156C2×C4D4×D10911yescharacteristic
157C2×C4D4×D10911yescharacteristic
158C2×C4C2×D43611yescharacteristic
159C8—22no—
160C8—41no—
161C8—4361no—
162C22—4361no—
163C22—4361no—
164C22—4361no—
165C22#1681266911yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—8721no—
172C4—4361no—
173C4—4361no—
174C4—4361no—
175C2—8721no—
176C2#2029520111yescharacteristic
177C2#2029520511yescharacteristic
178C2#2029521011yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#330×C109C2
socleC22×C109#120
prime radicalC2×D436D4
hypercenter#330D109
hypocenterC109#1664
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #20295435C2semidirect
3. #20295396C2semidirect
5. #20294767C2semidirect
7. #330×C109C2semidirect
90. C109#1664semidirect
96. #330D109semidirect

Maximal subgroups

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

subgroupindex
#202957802
#202954352
#202953962
#202953862
#202947672
#202947652
#330×C1092
#1664109