Finite Group Databasebeta

← #28378316

Subgroups — #28378316

Order 13952.

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

normal subgroups only

This group has 214 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, complemented
2#20296042C211yesmaximal, characteristic, complemented
3#20295871C212yesmaximal, complemented
4#20295870C212yesmaximal
5C2×#16812694C211yesmaximal, characteristic
6#16812766—21no—
7C4⋊#11724786—21no—
8C22⋊#11724786C2212yes—
9C22⋊#11724786C2212yes—
10#16812754—21no—
11C4×#11724786—21no—
12#16812694—21no—
13#16812694—21no—
14#16812694—21no—
15#16812694—21no—
16C2×C4⋊Dic109C2211yescharacteristic
17C2×#13182008C411yescharacteristic
18C2×#13182006C411yescharacteristic
19C2×#13182006C411yescharacteristic
20C2×#13182006C2211yescharacteristic
21C2×C4×Dic109C2211yescharacteristic
22C2×C4⋊C4×C109C411yescharacteristic
23C2×#11724786—22no—
24C2×#11724786—22no—
25C23×D109C2×C411yescharacteristic
26C22×Dic109C2×C411yescharacteristic
27C22×Dic109C2×C411yescharacteristic
28C22×Dic109C2311yescharacteristic
29C4⋊Dic109—21no—
30C4⋊Dic109—21no—
31#13182008—21no—
32#13182008—21no—
33#13182006—21no—
34#13182006—21no—
35#13182006—21no—
36#13182006—21no—
37#13182006—21no—
38#13182006—21no—
39C4×Dic109D411yescharacteristic
40C4×Dic109D411yescharacteristic
41C4×Dic109D411yescharacteristic
42C4×Dic109D411yescharacteristic
43C22×C4×C109C2×C411yescharacteristic
44C22×C4×C109C2×C411yescharacteristic
45C22×C4×C109C2×C411yescharacteristic
46C4⋊C4×C109—21no—
47C4⋊C4×C109—21no—
48C23×C109C22×C411yescharacteristic
49C22×D109—21no—
50C22×D109—22no—
51C22×D109—41no—
52C22×D109—41no—
53C2×C4×C109—22no—
54C2×C4×C109—21no—
55C2×C4×C109—21no—
56C2×C4×C109—22no—
57C2×C4×C109—41no—
58C2×C4×C109C22⋊C411yescharacteristic
59C2×C4×C109C22⋊C411yescharacteristic
60C2×Dic109—21no—
61C2×Dic109—41no—
62C2×Dic109—41no—
63C2×Dic109—41no—
64C2×Dic109C22⋊C411yescharacteristic
65C2×Dic109C22⋊C411yescharacteristic
66C2×Dic109C2×D411yescharacteristic
67C2×Dic109C2×D411yescharacteristic
68#11724786—42no—
69#11724786—42no—
70C22×C109—21no—
71C22×C109—21no—
72C22×C109C2×C22⋊C411yescharacteristic
73C22×C109#13112yes—
74C2×D109—41no—
75C2×D109—41no—
76C2×D109—41no—
77C2×D109—82no—
78C4×C109—21no—
79C4×C109—21no—
80C4×C109—41no—
81C4×C109—41no—
82Dic109—21no—
83Dic109—21no—
84Dic109—21no—
85Dic109—21no—
86Dic109—41no—
87C2×C109—22no—
88C2×C109#40811yescharacteristic
89C2×C109#41011yescharacteristic
90C2×C109#41311yescharacteristic
91D109—81no—
92#1473—1091nomaximal, Sylow
93C109#147311yescharacteristic, complemented, Sylow
94C2×#126—1091no—
95#432—1091no—
96#431—1091no—
97#324—1092no—
98#323—1092no—
99#126—2181no—
100#126—2181no—
101#126—2181no—
102#126—2181no—
103C2×C4⋊C4—1091no—
104C2×C4⋊C4—1091no—
105C2×C4⋊C4#8913711yescharacteristic
106C2×C22⋊C4—1091no—
107C2×C22⋊C4—1091no—
108C2×C22⋊C4—1091no—
109C2×C42—1091no—
110C4⋊C8—2181no—
111C4⋊C8—2181no—
112C22⋊C8—1092no—
113C22⋊C8—1092no—
114#97—2181no—
115C4×C8—2181no—
116C24—1091no—
117C22×C4—1091no—
118C22×C4—1091no—
119C22×C4—1091no—
120C22×C4C2×#8913711yescharacteristic
121C22×C4C2×#8913711yescharacteristic
122C22×C4C2×#8913711yescharacteristic
123C2×C8—2182no—
124C2×C8—2182no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—2181no—
128C4⋊C4—2181no—
129C4⋊C4—2181no—
130C4⋊C4—2181no—
131C22⋊C4—2181no—
132C22⋊C4—2181no—
133C22⋊C4—2181no—
134C22⋊C4—2181no—
135C22⋊C4—2181no—
136C22⋊C4—2181no—
137C42—1091no—
138C42—1091no—
139C42—1091no—
140C42—1091no—
141C23—4361no—
142C23—4361no—
143C23—2182no—
144C23—2181no—
145C23C22×#8913711yescharacteristic
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—1091no—
152C2×C4—1091no—
153C2×C4—1091no—
154C2×C4—1091no—
155C2×C4—4361no—
156C2×C4—4361no—
157C2×C4—4361no—
158C2×C4—2181no—
159C2×C4C22⋊#8913711yescharacteristic
160C2×C4C22⋊#8913711yescharacteristic
161C8—4362no—
162C8—4362no—
163C22—21no—
164C22—21no—
165C22—8722no—
166C22—4361no—
167C22—4361no—
168C22—4361no—
169C22C2×C22⋊#8913711yescharacteristic
170C22#1681278612yes—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—41no—
175C4—4361no—
176C4—2181no—
177C4—2181no—
178C4—2181no—
179C4—2181no—
180C2—22no—
181C2—8721no—
182C2#2029599911yescharacteristic
183C2#2029600711yescharacteristic
184C2#2029601211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC23×C109C22×C4
FrattiniC23C22×#89137
FittingC2×C4⋊C4×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC23×D109C2×C4
cosocleC22×Dic109C23
hypercenterC2×C4⋊C4#89137
hypocenterC109#1473
LCSG ▷ C23×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
1. #20296046C2semidirect
2. #20296042C2semidirect
3. #20295871C2semidirect
93. C109#1473semidirect

Maximal subgroups

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

subgroupindex
#202960462
#202960422
#202958712
#202958702
C2×#168126942
#1473109