Finite Group Databasebeta

← #28378474

Subgroups — #28378474

Order 13952.

218 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 56 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#20296044C211yesmaximal, characteristic, complemented
2#20295971C211yesmaximal, characteristic, complemented
3#20295879C212yesmaximal, complemented
4#20295877C212yesmaximal
5#20295558C211yesmaximal, characteristic
6#16812766—21no—
7#16812756C2212yes—
8C4×#11724786—21no—
9(C2×#89137)⋊C4—21no—
10(C2×#89137)⋊C4—21no—
11(C2×#89137)⋊C4C2212yes—
12#16812692—21no—
13#16812690C411yescharacteristic, complemented
14#16812686C411yescharacteristic, complemented
15#16812681—21no—
16#16812679C2211yescharacteristic
17#16812670C2211yescharacteristic
18C4×Dic218C411yescharacteristic, complemented
19C4×C22⋊D109—21no—
20#16812658—21no—
21C42×D109C2211yescharacteristic
22C4×D4×C109C411yescharacteristic, complemented
23C22×#89137—22no—
24C2×#11724786—22no—
25C2×Dic218C2×C411yescharacteristic
26C2×C22⋊D109—21no—
27C2×C4×D109D411yescharacteristic
28C2×C4×D109D411yescharacteristic
29C2×C4×D109C2311yescharacteristic
30C4⋊Dic109—21no—
31C4⋊Dic109—21no—
32C4⋊Dic109C2×C411yescharacteristic
33#13182008—21no—
34#13182008—21no—
35C22⋊Dic109—21no—
36C22⋊Dic109—21no—
37C22⋊Dic109—21no—
38#13182006—21no—
39C4×Dic109—21no—
40C4×Dic109C2×C411yescharacteristic
41C4×Dic109D411yescharacteristic
42C4×Dic109D411yescharacteristic
43C2×D4×C109C2×C411yescharacteristic
44C22×C4×C109—21no—
45C4⋊C4×C109C2×C411yescharacteristic
46C22⋊C4×C109—21no—
47C42×C109C2×C411yescharacteristic
48C23×C109—21no—
49C22×D109C2×D411yescharacteristic
50C2×#89137—42no—
51C2×#89137—42no—
52C2×#89137—42no—
53D4×C109—41no—
54C2×C4×C109—21no—
55C2×C4×C109—42no—
56C2×C4×C109C22⋊C411yescharacteristic
57C2×C4×C109C22⋊C411yescharacteristic
58C2×C4×C109C22×C411yescharacteristic
59C22⋊D109—42no—
60C2×Dic109—21no—
61C2×Dic109—21no—
62C2×Dic109C22⋊C411yescharacteristic
63C2×Dic109C22⋊C411yescharacteristic
64C2×Dic109C2×D411yescharacteristic
65C4×D109—22no—
66C4×D109—41no—
67C4×D109—41no—
68Dic218—41no—
69#11724786—42no—
70C22×C109—41no—
71C22×C109—41no—
72C22×C109—41no—
73C22×C109C2×C22⋊C411yescharacteristic
74C2×D109—21no—
75C2×D109—21no—
76C2×D109#13512yes—
77#89137—82no—
78C4×C109—21no—
79C4×C109—21no—
80C4×C109—21no—
81C4×C109—41no—
82Dic109—21no—
83Dic109—21no—
84Dic109—21no—
85Dic109—41no—
86Dic109—41no—
87C2×C109—81no—
88C2×C109#41011yescharacteristic
89C2×C109#41611yescharacteristic
90C2×C109#42111yescharacteristic
91D109—22no—
92#1521—1091nomaximal, Sylow
93C109#152111yescharacteristic, complemented, Sylow
94#529—1091no—
95#431—1091no—
96#383—1091no—
97#328—1092no—
98#327—1092no—
99#126—2181no—
100#125—1091no—
101#124—1091no—
102#123—2181no—
103C22⋊Q8—1091no—
104#121—1091no—
105C4×Q8—1091no—
106C4×D4—2181no—
107C4×D4#8913711yescharacteristic, complemented
108#117—2181no—
109C2×C42—1091no—
110C4⋊C8—2181no—
111C22⋊C8—1092no—
112C4×C8—2181no—
113#95—1092no—
114#95—2181no—
115#95—2181no—
116C2×Q8—1091no—
117C2×D4—2181no—
118C2×D4C2×#8913711yescharacteristic
119C22×C4—21no—
120C22×C4—1091no—
121C22×C4—1091no—
122C22×C4—1091no—
123C22×C4—2182no—
124C2×C8—2182no—
125C4⋊C4—1091no—
126C4⋊C4—2181no—
127C4⋊C4—2181no—
128C4⋊C4—2181no—
129C4⋊C4—2181no—
130C4⋊C4C2×#8913711yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—2181no—
133C22⋊C4—2181no—
134C22⋊C4—2181no—
135C22⋊C4—2181no—
136C42—1091no—
137C42—1091no—
138C42—1091no—
139C42—2181no—
140C42C2×#8913711yescharacteristic
141C23—21no—
142C23—1091no—
143Q8—4361no—
144D4—41no—
145D4—4362no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—1091no—
149C2×C4—1091no—
150C2×C4—1091no—
151C2×C4—4361no—
152C2×C4—4361no—
153C2×C4—4362no—
154C2×C4—4362no—
155C2×C4—4362no—
156C2×C4—2182no—
157C2×C4—2181no—
158C2×C4—2181no—
159C2×C4C22⋊#8913711yescharacteristic
160C2×C4C22⋊#8913711yescharacteristic
161C2×C4C22×#8913711yescharacteristic
162C8—4362no—
163C22—41no—
164C22—41no—
165C22—41no—
166C22—1092no—
167C22—2181no—
168C22—2181no—
169C22C2×C22⋊#8913711yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—8722no—
175C4—4361no—
176C4—4361no—
177C4—2181no—
178C4—2181no—
179C4—2181no—
180C2—81no—
181C2—2182no—
182C2#2029600511yescharacteristic
183C2#2029601611yescharacteristic
184C2#2029602411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC4×D4×C109C4
socleC22×C109C2×C22⋊C4
prime radical#16812670C22
cosocleC2×C4×D109C23
hypercenterC4×D4#89137
hypocenterC109#1521
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #20296044C2semidirect
2. #20295971C2semidirect
3. #20295879C2semidirect
13. #16812690C4semidirect
14. #16812686C4semidirect
18. C4×Dic218C4semidirect
22. C4×D4×C109C4semidirect
93. C109#1521semidirect
107. C4×D4#89137semidirect

Maximal subgroups

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

subgroupindex
#202960442
#202959712
#202958792
#202958772
#202955582
#1521109