Finite Group Databasebeta

← #16834904

Subgroups — #16834904

Order 3712.

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

normal subgroups only

This group has 222 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#14272185C211yesmaximal, characteristic, complemented
2#14272107C211yesmaximal, characteristic, complemented
3#14272017C212yesmaximal, complemented
4#14272014C212yesmaximal
5#14271692C211yesmaximal, characteristic
6C2×C4⋊#1181—21no—
7C29×#124C411yescharacteristic, complemented
8#11745308C2211yescharacteristic
9Q8×Dic29C411yescharacteristic, complemented
10#11745300C2211yescharacteristic
11D4×Dic29C411yescharacteristic, complemented
12#11745245—21no—
13#11745243—21no—
14#11745241—21no—
15#11745239—21no—
16C42×D29C2211yescharacteristic
17#11745232C411yescharacteristic, complemented
18(C2×#1181)⋊C4—21no—
19(C2×#1181)⋊C4C2212yes—
20#11745219C2212yes—
21#11745218—21no—
22C4⋊#6599—21no—
23C22×#1181—22no—
24C2×Q8×C29C2×C411yescharacteristic
25C2×D4×C29C2×C411yescharacteristic
26C2×C22⋊D29—21no—
27C22×Dic29—21no—
28C2×C4×D29D411yescharacteristic
29C2×C4×D29D411yescharacteristic
30C2×C4×D29C2311yescharacteristic
31C2×#6599—22no—
32C4⋊#1181—42no—
33C22⋊C4×C29—21no—
34C22⋊C4×C29—21no—
35C42×C29C2×C411yescharacteristic
36C22⋊Dic29—21no—
37C22⋊Dic29—21no—
38#90781—21no—
39C4⋊Dic29—21no—
40C4⋊Dic29C2×C411yescharacteristic
41C4⋊Dic29C2×C411yescharacteristic
42#90779—21no—
43#90779—21no—
44#90779—21no—
45C4×Dic29—21no—
46C4×Dic29C2×C411yescharacteristic
47C4×Dic29D411yescharacteristic
48C4×Dic29D411yescharacteristic
49C23×C29—21no—
50C22×D29C2×D411yescharacteristic
51C2×#1181—42no—
52C2×#1181—42no—
53C2×#1181—42no—
54Q8×C29—41no—
55D4×C29—41no—
56C2×C4×C29—21no—
57C2×C4×C29C22⋊C411yescharacteristic
58C2×C4×C29C22⋊C411yescharacteristic
59C2×C4×C29C22×C411yescharacteristic
60C22⋊D29—41no—
61C22⋊D29—41no—
62C2×Dic29—21no—
63C2×Dic29—21no—
64C2×Dic29—42no—
65C2×Dic29C22⋊C411yescharacteristic
66C2×Dic29C22⋊C411yescharacteristic
67C2×Dic29C2×D411yescharacteristic
68C4×D29—21no—
69C4×D29—21no—
70C4×D29—41no—
71C4×D29—41no—
72#6599—42no—
73#1512—291nomaximal, Sylow
74C22×C29—41no—
75C22×C29—41no—
76C22×C29—41no—
77C22×C29C2×C22⋊C411yescharacteristic
78C2×D29—21no—
79C2×D29—21no—
80C2×D29AGL(1,ℤ/8)11yescharacteristic
81C2×D29#13711yescharacteristic
82#1181—82no—
83C4×C29—21no—
84C4×C29—21no—
85C4×C29—21no—
86C4×C29—41no—
87Dic29—21no—
88Dic29—21no—
89Dic29—21no—
90Dic29—41no—
91Dic29—41no—
92#529—291no—
93#432—291no—
94#382—291no—
95#328—292no—
96#327—292no—
97C2×C29—81no—
98C2×C29#41011yescharacteristic
99C2×C29#41711yescharacteristic
100C2×C29#42111yescharacteristic
101D29—21no—
102D29—21no—
103#126—581no—
104#125—291no—
105#124#118111yescharacteristic, complemented
106#123—581no—
107C22⋊Q8—291no—
108#121—291no—
109C4×Q8—291no—
110C4×D4—291no—
111C4×D4—581no—
112#117—581no—
113C2×C4⋊C4—581no—
114C2×C42—291no—
115C4⋊C8—581no—
116C22⋊C8—292no—
117#97—581no—
118#95—292no—
119#95—581no—
120C29#151211yescharacteristic, complemented, Sylow
121C2×Q8C2×#118111yescharacteristic
122C2×D4—581no—
123C2×D4C2×#118111yescharacteristic
124C22×C4—291no—
125C22×C4—291no—
126C22×C4—291no—
127C22×C4—581no—
128C22×C4—582no—
129C2×C8—582no—
130C4⋊C4—291no—
131C4⋊C4—291no—
132C4⋊C4—581no—
133C4⋊C4—581no—
134C4⋊C4—581no—
135C4⋊C4—581no—
136C4⋊C4—1162no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—581no—
140C22⋊C4—581no—
141C22⋊C4—581no—
142C42—291no—
143C42—291no—
144C42—291no—
145C42—581no—
146C42C2×#118111yescharacteristic
147C23—21no—
148C23—291no—
149Q8—41no—
150D4—41no—
151D4—1161no—
152D4—1161no—
153C2×C4—21no—
154C2×C4—291no—
155C2×C4—291no—
156C2×C4—291no—
157C2×C4—581no—
158C2×C4—581no—
159C2×C4—581no—
160C2×C4—581no—
161C2×C4—1161no—
162C2×C4—1161no—
163C2×C4—1162no—
164C2×C4—1162no—
165C2×C4—1162no—
166C2×C4—1162no—
167C2×C4C22⋊#118111yescharacteristic
168C2×C4C22⋊#118111yescharacteristic
169C2×C4C22×#118111yescharacteristic
170C8—1162no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—291no—
175C22—291no—
176C22—581no—
177C22—581no—
178C22C2×C22⋊#118111yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—41no—
183C4—581no—
184C4—581no—
185C4—581no—
186C4—1161no—
187C4—1161no—
188C4—2322no—
189C2—81no—
190C2—581no—
191C2—581no—
192C2#1427214311yescharacteristic
193C2#1427215411yescharacteristic
194C2#1427216011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#124C4
socleC22×C29C2×C22⋊C4
prime radical#11745300C22
cosocleC2×C4×D29C23
hypercenter#124#1181
hypocenterC29#1512
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #14272185C2semidirect
2. #14272107C2semidirect
3. #14272017C2semidirect
7. C29×#124C4semidirect
9. Q8×Dic29C4semidirect
11. D4×Dic29C4semidirect
17. #11745232C4semidirect
105. #124#1181semidirect
120. C29#1512semidirect

Maximal subgroups

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

subgroupindex
#142721852
#142721072
#142720172
#142720142
#142716922
#151229