Finite Group Databasebeta

← #28361609

Subgroups — #28361609

Order 13952.

218 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 77 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#20295079C211yesmaximal, characteristic, complemented
2#20294894C211yesmaximal, characteristic, complemented
3#20294763C212yesmaximal, complemented
4#20294760C212yesmaximal
5#529×C109C211yesmaximal, characteristic
6C4⋊#11724784—21no—
7C22⋊#11724784C2212yes—
8C4×#11724784—21no—
9#16812606—21no—
10#16812606—21no—
11#16812606C2212yes—
12#126×C109—21no—
13#125×C109C411yescharacteristic, complemented
14#124×C109C411yescharacteristic, complemented
15#123×C109—21no—
16C22⋊Q8×C109C2211yescharacteristic
17#121×C109C2211yescharacteristic
18C4×Q8×C109C411yescharacteristic, complemented
19C4×D4×C109—21no—
20C4×D4×C109C411yescharacteristic, complemented
21#117×C109—21no—
22C2×C42×C109C2211yescharacteristic
23C22×Dic109—22no—
24C2×#11724784—22no—
25C2×Q8×C109C2×C411yescharacteristic
26C2×D4×C109—21no—
27C2×D4×C109C2×C411yescharacteristic
28C22×C4×C109—21no—
29C22×C4×C109D411yescharacteristic
30C22×C4×C109D411yescharacteristic
31C22×C4×C109C2311yescharacteristic
32C4⋊C4×C109—21no—
33C4⋊C4×C109—21no—
34C4⋊C4×C109—21no—
35C4⋊C4×C109—21no—
36C4⋊C4×C109C2×C411yescharacteristic
37C4⋊C4×C109C2×C411yescharacteristic
38C22⋊C4×C109—21no—
39C22⋊C4×C109—21no—
40C22⋊C4×C109—21no—
41C22⋊C4×C109—21no—
42C22⋊C4×C109—21no—
43C42×C109—21no—
44C42×C109C2×C411yescharacteristic
45C42×C109C2×C411yescharacteristic
46C42×C109D411yescharacteristic
47C42×C109D411yescharacteristic
48C23×C109—21no—
49C23×C109C2×D411yescharacteristic
50Q8×C109—41no—
51D4×C109—41no—
52D4×C109—42no—
53C2×C4×C109—22no—
54C2×C4×C109—21no—
55C2×C4×C109—21no—
56C2×C4×C109—21no—
57C2×C4×C109—41no—
58C2×C4×C109—41no—
59C2×C4×C109—42no—
60C2×C4×C109C22⋊C411yescharacteristic
61C2×C4×C109C22⋊C411yescharacteristic
62C2×C4×C109C22⋊C411yescharacteristic
63C2×C4×C109C22⋊C411yescharacteristic
64C2×C4×C109C22×C411yescharacteristic
65C2×C4×C109C2×D411yescharacteristic
66C2×Dic109—42no—
67C2×Dic109—42no—
68C2×Dic109—42no—
69#11724784—42no—
70C22×C109—21no—
71C22×C109—21no—
72C22×C109—41no—
73C22×C109—41no—
74C22×C109—41no—
75C22×C109C2×C22⋊C411yescharacteristic
76C22×C109#13512yes—
77C4×C109—21no—
78C4×C109—21no—
79C4×C109—21no—
80C4×C109—21no—
81C4×C109—21no—
82C4×C109—21no—
83C4×C109—41no—
84C4×C109—41no—
85C4×C109—41no—
86Dic109—82no—
87C2×C109—22no—
88C2×C109—81no—
89C2×C109#41011yescharacteristic
90C2×C109#41611yescharacteristic
91C2×C109#42111yescharacteristic
92#1521—1091nomaximal, Sylow
93C109#152111yescharacteristic, complemented, Sylow
94#529D10911yescharacteristic
95#431—1091no—
96#383—1091no—
97#328—1092no—
98#327—1092no—
99#126—21no—
100#125Dic10911yescharacteristic, complemented
101#124Dic10911yescharacteristic, complemented
102#123—21no—
103C22⋊Q8C2×D10911yescharacteristic
104#121C2×D10911yescharacteristic
105C4×Q8Dic10911yescharacteristic, complemented
106C4×D4—21no—
107C4×D4Dic10911yescharacteristic, complemented
108#117—21no—
109C2×C42C2×D10911yescharacteristic
110C4⋊C8—2181no—
111C22⋊C8—1092no—
112C4×C8—2181no—
113#95—1092no—
114#95—2181no—
115#95—2181no—
116C2×Q8C2×Dic10911yescharacteristic
117C2×D4—21no—
118C2×D4C2×Dic10911yescharacteristic
119C22×C4—21no—
120C22×C4—2182no—
121C22×C4C22⋊D10911yescharacteristic
122C22×C4C22⋊D10911yescharacteristic
123C22×C4C22×D10911yescharacteristic
124C2×C8—2182no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4C2×Dic10911yescharacteristic
130C4⋊C4C2×Dic10911yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—21no—
133C22⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—21no—
136C42—21no—
137C42C2×Dic10911yescharacteristic
138C42C2×Dic10911yescharacteristic
139C42C22⋊D10911yescharacteristic
140C42C22⋊D10911yescharacteristic
141C23—21no—
142C23C2×C22⋊D10911yescharacteristic
143Q8—41no—
144D4—41no—
145D4—42no—
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—4362no—
154C2×C4—4362no—
155C2×C4—4362no—
156C2×C4C22⋊Dic10911yescharacteristic
157C2×C4C22⋊Dic10911yescharacteristic
158C2×C4C22⋊Dic10911yescharacteristic
159C2×C4C22⋊Dic10911yescharacteristic
160C2×C4C22×Dic10911yescharacteristic
161C2×C4C2×C22⋊D10911yescharacteristic
162C8—4362no—
163C22—21no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22C2×C22⋊Dic10911yescharacteristic
169C22#1681271912yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—41no—
179C4—8722no—
180C2—22no—
181C2—81no—
182C2#2029500011yescharacteristic
183C2#2029502211yescharacteristic
184C2#2029504311yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic109
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
Fitting#529×C109C2
socleC22×C109C2×C22⋊C4
prime radical#121×C109C22
cosocleC22×C4×C109C23
hypercenter#529D109
hypocenterC109#1521
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #20295079C2semidirect
2. #20294894C2semidirect
3. #20294763C2semidirect
13. #125×C109C4semidirect
14. #124×C109C4semidirect
18. C4×Q8×C109C4semidirect
20. C4×D4×C109C4semidirect
93. C109#1521semidirect
100. #125Dic109semidirect
101. #124Dic109semidirect
105. C4×Q8Dic109semidirect
107. C4×D4Dic109semidirect

Maximal subgroups

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

subgroupindex
#202950792
#202948942
#202947632
#202947602
#529×C1092
#1521109