Finite Group Databasebeta

← #28378938

Subgroups — #28378938

Order 13952.

306 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 70 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#20295997C211yesmaximal, characteristic
2C4×C22⋊#89137C211yesmaximal, characteristic
3#20295896C214yesmaximal, complemented
4C2×#16812657C211yesmaximal, characteristic
5C2×#13182039C2212yes—
6C2×C22⋊#89137—21no—
7C2×C4×#89137C2212yes—
8#16812756—21no—
9C22⋊#11724786—21no—
10(C2×#89137)⋊C4—21no—
11C22×C4×D109C2211yescharacteristic
12#16812657—21no—
13#16812657—21no—
14#16812657C412yescomplemented
15#16812657C2212yes—
16C2×C4⋊Dic109C411yescharacteristic, complemented
17C2×#13182006—21no—
18C2×C4×Dic109—21no—
19C2×C4⋊C4×C109C411yescharacteristic, complemented
20C22×#89137—22no—
21#13182039—24no—
22C2×#11724786—22no—
23C22⋊#89137—24no—
24C4×#89137—24no—
25C23×D109D411yescharacteristic
26C22×Dic109—21no—
27C22×Dic109D411yescharacteristic
28C2×C4×D109—24no—
29C2×C4×D109C2×C411yescharacteristic
30C2×C4×D109D411yescharacteristic
31C2×C4×D109D411yescharacteristic
32C2×C4×D109C2311yescharacteristic
33C4⋊Dic109—21no—
34C4⋊Dic109C2×C412yes—
35#13182006—22no—
36#13182006—22no—
37C4×Dic109—22no—
38C4×Dic109—22no—
39C22×C4×C109—21no—
40C22×C4×C109C2×C411yescharacteristic
41C4⋊C4×C109—21no—
42C4⋊C4×C109C2×C412yes—
43C23×C109C22⋊C411yescharacteristic
44C22×D109—22no—
45C22×D109—22no—
46C22×D109—41no—
47C22×D109C22⋊C411yescharacteristic
48C22×D109C2×D411yescharacteristic
49C2×#89137—24no—
50C2×#89137—42no—
51C2×#89137—42no—
52C2×C4×C109—22no—
53C2×C4×C109—22no—
54C2×C4×C109—42no—
55C2×C4×C109C22⋊C411yescharacteristic
56C2×C4×C109C22×C411yescharacteristic
57C2×Dic109—22no—
58C2×Dic109—22no—
59C2×Dic109—42no—
60C2×Dic109C22⋊C411yescharacteristic
61C2×Dic109C2×D411yescharacteristic
62C4×D109—22no—
63C4×D109—22no—
64C4×D109—22no—
65C4×D109#4114yes—
66#11724786—42no—
67C22×C109—21no—
68C22×C109—21no—
69C22×C109#10412yes—
70C22×C109C2×C22⋊C411yescharacteristic
71C2×D109—21no—
72C2×D109—21no—
73C2×D109—21no—
74C2×D109—21no—
75C2×D109—21no—
76C2×D109—44no—
77C2×D109#12312yes—
78#89137—44no—
79C4×C109—21no—
80C4×C109—42no—
81C4×C109#11712yes—
82Dic109—21no—
83Dic109—42no—
84Dic109#12312yes—
85C2×C109—22no—
86C2×C109#38111yescharacteristic
87C2×C109C2×#10411yescharacteristic
88C2×C109#42111yescharacteristic
89D109—22no—
90D109—41no—
91#1826—1091nomaximal, Sylow
92C109#182611yescharacteristic, complemented, Sylow
93C2×#117—1091no—
94#407—1091no—
95C4×C22⋊C4—1091no—
96#339—1094no—
97C23×C4—1091no—
98C2×M16—1092no—
99#117—1092no—
100#117—1092no—
101#117—2181no—
102#117—2181no—
103C2×C4⋊C4—1091no—
104C2×C4⋊C4#8913711yescharacteristic, complemented
105C2×C22⋊C4—2181no—
106C2×C22⋊C4—2181no—
107C2×C42—1092no—
108C2×C42—2181no—
109C22⋊C8—2181no—
110C22⋊C8—2181no—
111#95—2181no—
112C24—1091no—
113C22×C4—21no—
114C22×C4—1091no—
115C22×C4—1091no—
116C22×C4—1091no—
117C22×C4—1091no—
118C22×C4—1091no—
119C22×C4—2184no—
120C22×C4—2182no—
121C22×C4—2181no—
122C22×C4C2×#8913711yescharacteristic
123M16—2184no—
124C2×C8—2182no—
125C4⋊C4—21no—
126C4⋊C4—1092no—
127C4⋊C4—2181no—
128C4⋊C4C2×#8913712yes—
129C22⋊C4—2182no—
130C22⋊C4—2182no—
131C22⋊C4—2184no—
132C42—2182no—
133C42—2182no—
134C42—2184no—
135C23—1091no—
136C23—1091no—
137C23—4361no—
138C23—2182no—
139C23—2182no—
140C23C22⋊#8913711yescharacteristic
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—42no—
144C2×C4—1091no—
145C2×C4—1094no—
146C2×C4—1091no—
147C2×C4—4362no—
148C2×C4—4362no—
149C2×C4—4362no—
150C2×C4—2182no—
151C2×C4—2182no—
152C2×C4—2182no—
153C2×C4—2184no—
154C2×C4—2182no—
155C2×C4—2182no—
156C2×C4C22⋊#8913711yescharacteristic
157C2×C4C22×#8913711yescharacteristic
158C8—4362no—
159C22—21no—
160C22—21no—
161C22—1092no—
162C22—4364no—
163C22—2181no—
164C22—2181no—
165C22—2181no—
166C22—2181no—
167C22—2181no—
168C22#1681276312yes—
169C22C2×C22⋊#8913711yescharacteristic
170C4—21no—
171C4—42no—
172C4—1092no—
173C4—4364no—
174C4—4362no—
175C4—2181no—
176C4#1681277812yes—
177C2—22no—
178C2—4361no—
179C2—2182no—
180C2#2029596911yescharacteristic
181C2C2×#1681276311yescharacteristic
182C2#2029602511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC2×C4⋊C4×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC23×D109D4
cosocleC2×C4×D109C23
hypercenterC2×C4⋊C4#89137
hypocenterC109#1826
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #20295896C2semidirect
14. #16812657C4semidirect
16. C2×C4⋊Dic109C4semidirect
19. C2×C4⋊C4×C109C4semidirect
92. C109#1826semidirect
104. C2×C4⋊C4#89137semidirect

Maximal subgroups

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

subgroupindex
#202959972
C4×C22⋊#891372
#202958962
C2×#168126572
#1826109