Finite Group Databasebeta

← #28363473

Subgroups — #28363473

Order 13952.

442 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 97 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#20295537C211yesmaximal, characteristic
2C22×C4×Dic109C211yesmaximal, characteristic, complemented
3C2×#16812625C212yesmaximal, complemented
4#20294787C212yesmaximal, complemented
5#407×C109C211yesmaximal, characteristic, complemented
6C2×#13182029C2211yescharacteristic
7C23×Dic109—21no—
8#16812682—21no—
9#16812678C412yescomplemented
10#16812673C412yescomplemented
11#16812668—21no—
12C4×C22⋊D109—22no—
13#16812658C2211yescharacteristic
14C2×C4×Dic109—24no—
15C2×C4×Dic109—21no—
16C2×C4×Dic109C2212yes—
17#16812625—24no—
18C23×C4×C109C2211yescharacteristic
19C2×M16×C109C2212yes—
20C22⋊C8×C109—22no—
21#13182029—22no—
22#13182029—22no—
23C2×Dic218C2×C411yescharacteristic, complemented
24C2×D436C2×C411yescharacteristic, complemented
25C2×C22⋊D109—22no—
26C2×C22⋊D109—21no—
27C22×Dic109—24no—
28C22×Dic109—28no—
29C22×Dic109—22no—
30C2×C4×D109—21no—
31C4⋊Dic109C2×C412yescomplemented
32#13182008—22no—
33C22⋊Dic109—22no—
34C22⋊Dic109—21no—
35#13182006—22no—
36C4×Dic109—24no—
37C4×Dic109—22no—
38C4×Dic109—21no—
39C4×Dic109D414yescomplemented
40C24×C109D411yescharacteristic
41C22×C4×C109—22no—
42C22×C4×C109—22no—
43C22×C4×C109C2×C412yes—
44C22×C4×C109D411yescharacteristic
45C22×C4×C109D412yes—
46C22×C4×C109C2311yescharacteristic
47M16×C109—22no—
48M16×C109—22no—
49C2×C8×C109—22no—
50C23×C109—24no—
51C23×C109—21no—
52C23×C109—21no—
53C23×C109C22⋊C412yes—
54C23×C109C2×D411yescharacteristic
55C22×D109—21no—
56C2×C4×C109—21no—
57C2×C4×C109—21no—
58C2×C4×C109—24no—
59C2×C4×C109—24no—
60C2×C4×C109C22⋊C412yes—
61C2×C4×C109C22×C411yescharacteristic
62C2×C4×C109C2×D412yes—
63C2×C4×C109C2×D411yescharacteristic
64C2×C4×C109#4112yes—
65C22⋊D109—44no—
66C22⋊D109—41no—
67C22⋊D109—41no—
68C2×Dic109—216no—
69C2×Dic109—28no—
70C2×Dic109—24no—
71C2×Dic109—22no—
72C2×Dic109—21no—
73D436—22no—
74C4×D109—42no—
75Dic218—22no—
76C8×C109—42no—
77C22×C109—24no—
78C22×C109—24no—
79C22×C109—22no—
80C22×C109—22no—
81C22×C109—22no—
82C22×C109#10414yescomplemented
83C22×C109C2×C22⋊C411yescharacteristic
84C22×C109#12011yescharacteristic
85C22×C109#12311yescharacteristic
86C2×D109—41no—
87C2×D109—42no—
88C4×C109—22no—
89C4×C109C4×D412yes—
90C4×C109#12112yes—
91Dic109—28no—
92Dic109—41no—
93Dic109—42no—
94C2×C109—21no—
95C2×C109—24no—
96C2×C109—21no—
97C2×C109#38611yescharacteristic
98C2×C109C2×#10412yes—
99D109—81no—
100#1896—1091nomaximal, Sylow
101C109#189611yescharacteristic, complemented, Sylow
102#525—1091no—
103C22×C42—1091no—
104C2×#104—1092no—
105#407D10911yescharacteristic, complemented
106#339—1092no—
107C2×#41—1091no—
108C23×C4—2181no—
109C23×C4C2×D10911yescharacteristic
110C2×M16C2×D10912yes—
111#123—2181no—
112C22⋊Q8—1092no—
113#121—1092no—
114#120—2181no—
115C4×D4—2182no—
116#117—1091no—
117C2×C42—1092no—
118C2×C42—2184no—
119C2×C42—2181no—
120#104—2184no—
121C22⋊C8—22no—
122C24D43611yescharacteristic
123#41—2182no—
124#41—2182no—
125C2×Q8—1091no—
126C2×D4—1091no—
127C2×D4—2182no—
128C2×D4—2181no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—2181no—
132C22×C4—2184no—
133C22×C4—2188no—
134C22×C4—2182no—
135C22×C4C4×D10912yes—
136C22×C4D43611yescharacteristic
137C22×C4C22⋊D10912yes—
138C22×C4C22×D10911yescharacteristic
139M16—22no—
140M16—22no—
141C2×C8—22no—
142C4⋊C4—1092no—
143C4⋊C4—2182no—
144C22⋊C4—2182no—
145C22⋊C4—2181no—
146C22⋊C4—2182no—
147C42—1094no—
148C42—2184no—
149C42—2182no—
150C42—2181no—
151C23—24no—
152C23—21no—
153C23—21no—
154C23—2181no—
155C23#1318200612yes—
156C23C2×D43611yescharacteristic
157Q8—2182no—
158D4—4364no—
159D4—4361no—
160D4—4361no—
161D4—2182no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—4362no—
167C2×C4—2182no—
168C2×C4—2181no—
169C2×C4—21816no—
170C2×C4—2188no—
171C2×C4—2184no—
172C2×C4#1318200612yes—
173C2×C4C2×C4×D10911yescharacteristic
174C2×C4D4×D10912yes—
175C2×C4C2×C22⋊D10911yescharacteristic
176C2×C4#1318202812yes—
177C8—42no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—4362no—
184C22—4361no—
185C22#1681262514yescomplemented
186C22C2×#1318200611yescharacteristic
187C22#1681266911yescharacteristic
188C22#1681268311yescharacteristic
189C4—22no—
190C4—4362no—
191C4—4361no—
192C4—2188no—
193C4#1681265912yes—
194C4#1681267112yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—8721no—
199C2#2029490311yescharacteristic
200C2C2×#1681262512yes—
subgroupG/H
centerC2×C4C2×C22⋊D109
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
Fitting#407×C109C2
socleC22×C109C2×C22⋊C4
prime radical#20295537C2
cosocleC22×C4×C109C23
hypercenter#407D109
hypocenterC109#1896
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic109C2semidirect
3. C2×#16812625C2semidirect
4. #20294787C2semidirect
5. #407×C109C2semidirect
9. #16812678C4semidirect
10. #16812673C4semidirect
23. C2×Dic218C2×C4semidirect
24. C2×D436C2×C4semidirect
31. C4⋊Dic109C2×C4semidirect
39. C4×Dic109D4semidirect
82. C22×C109#104semidirect
101. C109#1896semidirect
105. #407D109semidirect
185. C22#16812625semidirect

Maximal subgroups

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

subgroupindex
#202955372
C22×C4×Dic1092
C2×#168126252
#202947872
#407×C1092
#1896109