Finite Group Databasebeta

← #28379209

Subgroups — #28379209

Order 13952.

260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C4×#13182039C211yesmaximal, characteristic
2C4×C4⋊#89137C211yesmaximal, characteristic
3#20295896C212yesmaximal
4#20295896C212yesmaximal
5#20295582C211yesmaximal, characteristic
6C2×#13182039C2212yes—
7C2×C4⋊#89137—21no—
8C2×C4×#89137C2212yes—
9#16812754—21no—
10C4×#11724786—21no—
11(C2×#89137)⋊C4—21no—
12#16812698C411yescharacteristic, complemented
13#16812698C411yescharacteristic, complemented
14#16812691C411yescharacteristic, complemented
15#16812677—21no—
16#16812677—21no—
17#16812664—21no—
18#16812664—21no—
19#16812657C2211yescharacteristic
20#16812657C2211yescharacteristic
21C42×D109C2211yescharacteristic
22#125×C109C411yescharacteristic, complemented
23C22×#89137—22no—
24#13182039—22no—
25#13182039Q814yescomplemented
26C2×#11724786—22no—
27C4⋊#89137—24no—
28C4×#89137—24no—
29C2×Dic218—21no—
30C2×Dic218—21no—
31C2×C4×D109D411yescharacteristic
32C2×C4×D109D411yescharacteristic
33C2×C4×D109C2311yescharacteristic
34C4⋊Dic109C2×C411yescharacteristic
35C4⋊Dic109C2×C411yescharacteristic
36#13182008—21no—
37#13182008—21no—
38#13182008—21no—
39#13182008—21no—
40#13182006—21no—
41#13182006—21no—
42C4×Dic109—21no—
43C4×Dic109—21no—
44C4×Dic109C2×C411yescharacteristic
45C4×Dic109D411yescharacteristic
46C4×Dic109D411yescharacteristic
47C4⋊C4×C109—21no—
48C4⋊C4×C109—21no—
49C4⋊C4×C109C2×C411yescharacteristic
50C4⋊C4×C109C2×C411yescharacteristic
51C42×C109C2×C411yescharacteristic
52C22×D109C2×D411yescharacteristic
53C2×#89137—24no—
54C2×#89137—42no—
55C2×#89137—42no—
56C2×C4×C109—21no—
57C2×C4×C109—21no—
58C2×C4×C109C22⋊C411yescharacteristic
59C2×C4×C109C22⋊C411yescharacteristic
60C2×C4×C109C22×C411yescharacteristic
61C2×Dic109—21no—
62C2×Dic109—21no—
63C2×Dic109C22⋊C411yescharacteristic
64C2×Dic109C22⋊C411yescharacteristic
65C2×Dic109C2×D411yescharacteristic
66C4×D109—22no—
67C4×D109—41no—
68C4×D109C2×Q812yes—
69C4×D109#4112yes—
70Dic218—42no—
71Dic218—42no—
72#11724786—24no—
73C22×C109C2×C22⋊C411yescharacteristic
74C2×D109—21no—
75C2×D109—21no—
76C2×D109#12411yescharacteristic
77C2×D109C4⋊Q811yescharacteristic
78#89137—44no—
79C4×C109—21no—
80C4×C109—21no—
81C4×C109—41no—
82C4×C109—41no—
83C4×C109C4×Q812yes—
84Dic109—21no—
85Dic109—41no—
86Dic109—41no—
87Dic109#10412yes—
88Dic109C22⋊Q812yes—
89C2×C109#39111yescharacteristic
90C2×C109C2×#10411yescharacteristic
91C2×C109#42111yescharacteristic
92D109—21no—
93D109—21no—
94#1986—1091nomaximal, Sylow
95C109#198611yescharacteristic, complemented, Sylow
96#533—1091no—
97C4×M16—1091no—
98C4×C4⋊C4—1091no—
99#339—1092no—
100#339—1092no—
101C2×M16—1092no—
102C4⋊Q8—1091no—
103C4⋊Q8—1091no—
104#125—1091no—
105#125#8913711yescharacteristic, complemented
106C22⋊Q8—2181no—
107C22⋊Q8—2181no—
108C4×Q8—2181no—
109C4×Q8—2181no—
110#117—1091no—
111#117—1091no—
112C2×C4⋊C4—2181no—
113C2×C42—1091no—
114C2×C42—1092no—
115#97—2181no—
116C4×C8—2181no—
117#95—2181no—
118C2×Q8—2181no—
119C2×Q8—2181no—
120C22×C4—1091no—
121C22×C4—1091no—
122C22×C4—1091no—
123C22×C4—2182no—
124M16—1094no—
125M16—2182no—
126C2×C8—2182no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—1091no—
130C4⋊C4—1091no—
131C4⋊C4—2181no—
132C4⋊C4—2181no—
133C4⋊C4—2184no—
134C4⋊C4—2181no—
135C4⋊C4—2181no—
136C4⋊C4C2×#8913711yescharacteristic
137C4⋊C4C2×#8913711yescharacteristic
138C22⋊C4—2181no—
139C22⋊C4—2181no—
140C42—1091no—
141C42—1091no—
142C42—1091no—
143C42—2181no—
144C42—2181no—
145C42—2184no—
146C42C2×#8913711yescharacteristic
147C23—1091no—
148Q8—4362no—
149Q8—4362no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—1091no—
153C2×C4—1091no—
154C2×C4—1092no—
155C2×C4—1092no—
156C2×C4—1091no—
157C2×C4—4361no—
158C2×C4—4362no—
159C2×C4—4362no—
160C2×C4—2182no—
161C2×C4—2184no—
162C2×C4—2181no—
163C2×C4—2181no—
164C2×C4C22⋊#8913711yescharacteristic
165C2×C4C22⋊#8913711yescharacteristic
166C2×C4C22×#8913711yescharacteristic
167C8—2184no—
168C22—1091no—
169C22—1091no—
170C22—2181no—
171C22—2181no—
172C22C2×C22⋊#8913711yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—1092no—
178C4—1092no—
179C4—4364no—
180C4—4361no—
181C4—4361no—
182C4—2181no—
183C4Q8×#8913712yes—
184C2—2181no—
185C2—2181no—
186C2(C2×#89137)⋊Q811yescharacteristic
187C2D109⋊#10411yescharacteristic
188C2#2029602311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#125×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC22×D109C2×D4
cosocleC2×C4×D109C23
hypercenter#125#89137
hypocenterC109#1986
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
12. #16812698C4semidirect
13. #16812698C4semidirect
14. #16812691C4semidirect
22. #125×C109C4semidirect
25. #13182039Q8semidirect
95. C109#1986semidirect
105. #125#89137semidirect

Maximal subgroups

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

subgroupindex
C4×#131820392
C4×C4⋊#891372
#202958962
#202955822
#1986109