Finite Group Databasebeta

← #28378568

Subgroups — #28378568

Order 13952.

202 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 58 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#20296046C211yesmaximal, characteristic
2#20296029C211yesmaximal, characteristic
3#20295886C212yesmaximal, complemented
4#20295885C212yesmaximal, complemented
5#20295578C211yesmaximal, characteristic
6C2×#13182038—21no—
7#16812766C2212yes—
8#16812766C2212yes—
9C4⋊#11724786—21no—
10C22⋊#11724786—21no—
11#16812754—21no—
12#16812698C2211yescharacteristic
13#16812697C2211yescharacteristic
14#16812689—21no—
15#16812678C411yescharacteristic
16#16812676—21no—
17Q8×Dic109C411yescharacteristic
18#16812664—21no—
19#16812664C411yescharacteristic
20#16812655—21no—
21C2×C4×Dic109C2211yescharacteristic
22C22⋊Q8×C109C411yescharacteristic
23#13182038—42no—
24C2×#11724786—22no—
25C2×#11724786—22no—
26C2×Dic218—21no—
27C2×Dic218C2×C411yescharacteristic
28C22×Dic109D411yescharacteristic
29C22×Dic109D411yescharacteristic
30C4⋊Dic109—21no—
31C4⋊Dic109C2×C411yescharacteristic
32#13182008—21no—
33#13182008—21no—
34#13182008—21no—
35#13182008—21no—
36#13182008—21no—
37C22⋊Dic109—21no—
38C4×Dic109—21no—
39C4×Dic109—21no—
40C4×Dic109C2×C411yescharacteristic
41C4×Dic109D411yescharacteristic
42C4×Dic109D411yescharacteristic
43C4×Dic109C2311yescharacteristic
44C2×Q8×C109C2×C411yescharacteristic
45C22×C4×C109C2×C411yescharacteristic
46C4⋊C4×C109—21no—
47C4⋊C4×C109C2×C411yescharacteristic
48C22⋊C4×C109—21no—
49C23×C109C22⋊C411yescharacteristic
50Q8×C109—41no—
51C2×C4×C109—21no—
52C2×C4×C109—21no—
53C2×C4×C109—41no—
54C2×C4×C109C22⋊C411yescharacteristic
55C2×C4×C109C22×C411yescharacteristic
56C2×Dic109—21no—
57C2×Dic109—21no—
58C2×Dic109—22no—
59C2×Dic109—21no—
60C2×Dic109—21no—
61C2×Dic109C22⋊C411yescharacteristic
62C2×Dic109C22⋊C411yescharacteristic
63C2×Dic109C2×D411yescharacteristic
64C2×Dic109C2×D411yescharacteristic
65Dic218—41no—
66Dic218—41no—
67Dic218—41no—
68#11724786—42no—
69#11724786—42no—
70C22×C109—21no—
71C22×C109—21no—
72C22×C109—21no—
73C22×C109C2×C22⋊C411yescharacteristic
74C4×C109—21no—
75C4×C109—21no—
76C4×C109—41no—
77C4×C109—41no—
78Dic109—21no—
79Dic109—21no—
80Dic109—41no—
81Dic109—41no—
82Dic109AGL(1,ℤ/8)11yescharacteristic
83Dic109#13711yescharacteristic
84Dic109#13712yes—
85C2×C109—41no—
86C2×C109#41311yescharacteristic
87C2×C109#41711yescharacteristic
88C2×C109#41911yescharacteristic
89#1559—1091nomaximal, Sylow
90C109#155911yescharacteristic, complemented, Sylow
91#533—1091no—
92#432—1091no—
93#423—1091no—
94#333—1092no—
95#332—1092no—
96C2×M16—2181no—
97C4⋊Q8—1091no—
98C4⋊Q8—1091no—
99#125—2181no—
100C22⋊Q8—1091no—
101C22⋊Q8—2181no—
102C22⋊Q8#8913711yescharacteristic
103C4×Q8—1091no—
104C4×Q8—1091no—
105C4×Q8—2181no—
106#117—2181no—
107C2×C42—1091no—
108C4⋊C8—1092no—
109C4⋊C8—1092no—
110C4⋊C8—2181no—
111C22⋊C8—2181no—
112#97—2181no—
113C2×Q8—1091no—
114C2×Q8—2181no—
115C2×Q8C2×#8913711yescharacteristic
116C22×C4—1091no—
117C22×C4—1091no—
118C22×C4C2×#8913711yescharacteristic
119M16—4362no—
120C2×C8—2182no—
121C2×C8—2182no—
122C4⋊C4—21no—
123C4⋊C4—1091no—
124C4⋊C4—2181no—
125C4⋊C4—2181no—
126C4⋊C4—2181no—
127C4⋊C4—2181no—
128C4⋊C4—2181no—
129C4⋊C4—2181no—
130C4⋊C4C2×#8913711yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—2181no—
133C42—1091no—
134C42—1091no—
135C42—1091no—
136C42—1091no—
137C42—2181no—
138C42—2181no—
139C23C22⋊#8913711yescharacteristic
140Q8—41no—
141Q8—4361no—
142Q8—4361no—
143Q8—4361no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—1091no—
148C2×C4—1091no—
149C2×C4—1091no—
150C2×C4—1091no—
151C2×C4—2181no—
152C2×C4—2181no—
153C2×C4—2182no—
154C2×C4—2181no—
155C2×C4—2181no—
156C2×C4C22⋊#8913711yescharacteristic
157C2×C4C22×#8913711yescharacteristic
158C8—4362no—
159C8—4362no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22C2×C22⋊#8913711yescharacteristic
164C4—21no—
165C4—21no—
166C4—41no—
167C4—41no—
168C4—1091no—
169C4—1091no—
170C4—1092no—
171C4—4361no—
172C4—4361no—
173C4—2181no—
174C4—2181no—
175C2—41no—
176C2#2029601311yescharacteristic
177C2#2029601711yescharacteristic
178C2#2029601911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC22⋊Q8×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC23×C109C22⋊C4
cosocleC4×Dic109C23
hypercenterC22⋊Q8#89137
hypocenterC109#1559
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #20295886C2semidirect
4. #20295885C2semidirect
90. C109#1559semidirect

Maximal subgroups

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

subgroupindex
#202960462
#202960292
#202958862
#202958852
#202955782
#1559109