Finite Group Databasebeta

← #28362168

Subgroups — #28362168

Order 13952.

214 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 57 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#20295733C211yesmaximal, characteristic
2#20295406C211yesmaximal, characteristic, complemented
3#20295322C211yesmaximal, characteristic, complemented
4#20295316C211yesmaximal, characteristic
5#20294774C211yesmaximal, characteristic, complemented
6#20294758C211yesmaximal, characteristic, complemented
7D4⋊C8×C109C211yesmaximal, characteristic
8C2×Dic436—22no—
9#16812699C2211yescharacteristic
10#16812699C2211yescharacteristic
11#16812690—21no—
12#16812678—21no—
13#16812676—22no—
14C4×Dic218C2211yescharacteristic
15D4×Dic109—21no—
16C2×C4⋊Dic109—21no—
17#16812633—21no—
18#16812630—21no—
19C4⋊#11724784C2211yescharacteristic
20#16812624—21no—
21#16812620—21no—
22C4×D4×C109C2211yescharacteristic
23C4⋊C8×C109C2211yescharacteristic
24C4×C8×C109C2211yescharacteristic
25C2×Dic218—21no—
26C2×Dic218D411yescharacteristic
27C2×Dic218D412yes—
28C22×Dic109—22no—
29Dic436—44no—
30C2×#11724784—21no—
31C4⋊Dic109—22no—
32C4⋊Dic109—21no—
33C4⋊Dic109—21no—
34C4⋊Dic109—21no—
35C4⋊Dic109—21no—
36C4⋊Dic109D411yescharacteristic
37#13182008—22no—
38#13182008—21no—
39C22⋊Dic109—22no—
40C4×Dic109—21no—
41C2×D4×C109D411yescharacteristic
42C22×C4×C109—21no—
43C2×C8×C109—21no—
44C2×C8×C109—21no—
45C4⋊C4×C109D411yescharacteristic
46C22⋊C4×C109—21no—
47C42×C109C2311yescharacteristic
48C23×C109—21no—
49D4×C109—21no—
50D4×C109Q1612yescomplemented
51C2×C4×C109—21no—
52C2×C4×C109—41no—
53C2×C4×C109—41no—
54C2×C4×C109C2×D411yescharacteristic
55C2×C4×C109C2×D411yescharacteristic
56C2×C4×C109C2×D411yescharacteristic
57C2×Dic109—21no—
58C2×Dic109—21no—
59C2×Dic109—22no—
60C2×Dic109—41no—
61C2×Dic109—82no—
62Dic218—21no—
63Dic218—21no—
64Dic218—42no—
65Dic218—42no—
66C8×C109—22no—
67C8×C109—41no—
68#11724784—41no—
69C22×C109—22no—
70C22×C109—41no—
71C22×C109—41no—
72C22×C109#12011yescharacteristic
73C4×C109—21no—
74C4×C109—41no—
75C4×C109C2×Q1611yescharacteristic
76C4×C109#13511yescharacteristic
77C4×C109#13711yescharacteristic
78C4×C109#13711yescharacteristic
79Dic109—41no—
80Dic109—42no—
81Dic109—41no—
82Dic109—81no—
83C2×C109—42no—
84C2×C109#45111yescharacteristic
85C2×C109#45211yescharacteristic
86C2×C109#45311yescharacteristic
87#1632—1091nomaximal, Sylow
88C109#163211yescharacteristic, complemented, Sylow
89#554—1091no—
90#494—1091no—
91#477—1091no—
92#476—1091no—
93#333—1091no—
94Q8⋊C8—1091no—
95D4⋊C8D10911yescharacteristic
96C2×Q16—2182no—
97C4⋊Q8—1091no—
98C4⋊Q8—1091no—
99#125—2181no—
100C22⋊Q8—2182no—
101C22⋊Q8—2181no—
102C4×Q8—1091no—
103C4×D4—2181no—
104C4×D4C2×D10911yescharacteristic
105C2×C4⋊C4—2181no—
106#107—2181no—
107#106—2181no—
108C4⋊C8—1091no—
109C4⋊C8C2×D10911yescharacteristic
110#103—2181no—
111#102—2181no—
112C4×C8C2×D10911yescharacteristic
113C2×Q8—1092no—
114C2×Q8—1091no—
115C2×Q8—2181no—
116C2×D4D43611yescharacteristic
117C22×C4—21no—
118C22×C4—2182no—
119Q16—4364no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—2181no—
123C4⋊C4—1091no—
124C4⋊C4—2182no—
125C4⋊C4—2182no—
126C4⋊C4—2181no—
127C4⋊C4—2181no—
128C4⋊C4—2181no—
129C4⋊C4—2181no—
130C4⋊C4—2181no—
131C4⋊C4D43611yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—2182no—
134C42—2181no—
135C42C22×D10911yescharacteristic
136C23—21no—
137Q8—4362no—
138Q8—4362no—
139Q8—2181no—
140Q8—2181no—
141D4—21no—
142D4Dic43612yescomplemented
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—8722no—
147C2×C4—4361no—
148C2×C4—2181no—
149C2×C4—2181no—
150C2×C4—2182no—
151C2×C4D4×D10911yescharacteristic
152C2×C4D4×D10911yescharacteristic
153C2×C4C2×D43611yescharacteristic
154C8—22no—
155C8—41no—
156C8—4361no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#1681266911yescharacteristic
161C4—21no—
162C4—41no—
163C4—8721no—
164C4—4361no—
165C4—4361no—
166C4—4362no—
167C4C2×Dic43611yescharacteristic
168C4#1681271811yescharacteristic
169C4#1681272811yescharacteristic
170C4#1681273211yescharacteristic
171C2—42no—
172C2#2029518411yescharacteristic
173C2#2029518911yescharacteristic
174C2#2029519511yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
FittingD4⋊C8×C109C2
socleC22×C109#120
prime radicalC2×D4×C109D4
hypercenterD4⋊C8D109
hypocenterC109#1632
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20295406C2semidirect
3. #20295322C2semidirect
5. #20294774C2semidirect
6. #20294758C2semidirect
50. D4×C109Q16semidirect
88. C109#1632semidirect
142. D4Dic436semidirect

Maximal subgroups

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

subgroupindex
#202957332
#202954062
#202953222
#202953162
#202947742
#202947582
D4⋊C8×C1092
#1632109