Finite Group Databasebeta

← #16835397

Subgroups — #16835397

Order 3712.

300 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 74 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
1D29⋊(C22⋊C8)C211yesmaximal, characteristic
2#14272105C211yesmaximal, characteristic
3#14272036C212yesmaximal, complemented
4#14272036C212yesmaximal, complemented
5#117×D29C211yesmaximal, characteristic
6C22×C4×D29C2211yescharacteristic
7C2×C22⋊#1181—21no—
8C2×C4⋊#1181C2212yes—
9C2×D29⋊C8C2212yes—
10C29×#117C411yescharacteristic, complemented
11#11745288C411yescharacteristic, complemented
12#11745254C411yescharacteristic, complemented
13#11745254C411yescharacteristic, complemented
14C4⋊C4×D29C2211yescharacteristic
15C4⋊C4×D29C2211yescharacteristic
16C22⋊C4×D29—21no—
17#11745239—21no—
18#11745234—21no—
19C42×D29—21no—
20C22⋊#6599—21no—
21(C2×#1181)⋊C4—21no—
22#11745219—21no—
23C23×D29D411yescharacteristic
24C22×#1181—22no—
25C22×C4×C29C2×C411yescharacteristic
26C22×Dic29D411yescharacteristic
27C2×C4×D29—24no—
28C2×C4×D29—21no—
29C2×C4×D29—21no—
30C2×C4×D29C2×C411yescharacteristic
31C2×C4×D29D411yescharacteristic
32C2×C4×D29D411yescharacteristic
33C2×C4×D29C2311yescharacteristic
34C22⋊#1181—42no—
35C2×#6599—22no—
36C4⋊#1181—24no—
37D29⋊C8—24no—
38C4⋊C4×C29C2×C411yescharacteristic
39C4⋊C4×C29C2×C411yescharacteristic
40C22⋊C4×C29—21no—
41C42×C29—21no—
42C22⋊Dic29—21no—
43#90781—21no—
44#90781—21no—
45C4⋊Dic29C2×C411yescharacteristic
46C4⋊Dic29C2×C411yescharacteristic
47#90779—21no—
48#90779—21no—
49C4×Dic29—21no—
50C4×Dic29—21no—
51C4×Dic29—21no—
52C23×C29C22⋊C411yescharacteristic
53C22×D29—22no—
54C22×D29—22no—
55C22×D29—21no—
56C22×D29—21no—
57C22×D29C22⋊C411yescharacteristic
58C22×D29C2×D411yescharacteristic
59C2×#1181—42no—
60C2×#1181—42no—
61C2×#1181—42no—
62C2×C4×C29—22no—
63C2×C4×C29—21no—
64C2×C4×C29—21no—
65C2×C4×C29C22⋊C411yescharacteristic
66C2×C4×C29C22×C411yescharacteristic
67C2×Dic29—22no—
68C2×Dic29—21no—
69C2×Dic29—21no—
70C2×Dic29C22⋊C411yescharacteristic
71C2×Dic29C2×D411yescharacteristic
72C4×D29—22no—
73C4×D29—22no—
74C4×D29—22no—
75C4×D29—42no—
76C4×D29—41no—
77C4×D29—41no—
78C4×D29#4114yes—
79#6599—42no—
80#1825—291nomaximal, Sylow
81C22×C29—21no—
82C22×C29—21no—
83C22×C29—21no—
84C22×C29C2×C22⋊C411yescharacteristic
85C2×D29—21no—
86C2×D29—21no—
87C2×D29—21no—
88C2×D29—42no—
89C2×D29—42no—
90C2×D29#12312yes—
91C2×D29#13512yes—
92C2×D29AGL(1,ℤ/8)11yescharacteristic
93C2×D29#13711yescharacteristic
94#1181—82no—
95C4×C29—21no—
96C4×C29—41no—
97C4×C29—41no—
98C4×C29#11712yes—
99Dic29—21no—
100Dic29—41no—
101Dic29—41no—
102Dic29#12312yes—
103C2×#117—291no—
104C2×C22⋊C8—291no—
105#380—291no—
106#340—292no—
107#340—292no—
108C2×C29—41no—
109C2×C29#38111yescharacteristic
110C2×C29#41611yescharacteristic
111C2×C29#41711yescharacteristic
112D29—41no—
113D29#48212yes—
114D29#48512yes—
115C23×C4—291no—
116C22×C8—292no—
117#117—291no—
118#117—291no—
119#117—291no—
120#117—581no—
121#117—581no—
122#117#118111yescharacteristic, complemented
123C2×C4⋊C4—291no—
124C2×C4⋊C4—291no—
125C2×C4⋊C4—292no—
126C2×C22⋊C4—581no—
127C2×C22⋊C4—581no—
128C2×C42—581no—
129C22⋊C8—581no—
130C22⋊C8—581no—
131#95—581no—
132C29#182511yescharacteristic, complemented, Sylow
133C24—291no—
134C22×C4—291no—
135C22×C4—291no—
136C22×C4—291no—
137C22×C4—291no—
138C22×C4—291no—
139C22×C4—584no—
140C22×C4—581no—
141C22×C4—581no—
142C22×C4—582no—
143C22×C4C2×#118111yescharacteristic
144C2×C8—582no—
145C2×C8—584no—
146C4⋊C4—291no—
147C4⋊C4—291no—
148C4⋊C4—581no—
149C4⋊C4—581no—
150C4⋊C4—584no—
151C4⋊C4C2×#118111yescharacteristic
152C4⋊C4C2×#118111yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—581no—
155C22⋊C4—581no—
156C22⋊C4—581no—
157C22⋊C4—1162no—
158C42—21no—
159C42—581no—
160C42—581no—
161C42—581no—
162C23—291no—
163C23—291no—
164C23—581no—
165C23—582no—
166C23—582no—
167C23—581no—
168C23C22⋊#118111yescharacteristic
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—291no—
173C2×C4—294no—
174C2×C4—291no—
175C2×C4—582no—
176C2×C4—582no—
177C2×C4—582no—
178C2×C4—582no—
179C2×C4—581no—
180C2×C4—581no—
181C2×C4—1162no—
182C2×C4—1161no—
183C2×C4—1161no—
184C2×C4—1162no—
185C2×C4—1162no—
186C2×C4—1162no—
187C2×C4C22⋊#118111yescharacteristic
188C2×C4C22×#118111yescharacteristic
189C8—1162no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—292no—
194C22—292no—
195C22—291no—
196C22—291no—
197C22—581no—
198C22—581no—
199C22—581no—
200C22—1162no—
201C22—1162no—
202C22C2×C22⋊#118111yescharacteristic
203C4—21no—
204C4—41no—
205C4—41no—
206C4—292no—
207C4—581no—
208C4—1161no—
209C4—1161no—
210C4—2322no—
211C4#1174534512yes—
212C2—41no—
213C2—292no—
214C2—292no—
215C2—1161no—
216C2#1427210611yescharacteristic
217C2#1427215311yescharacteristic
218C2#1427215411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#117C4
socleC22×C29C2×C22⋊C4
prime radicalC23×D29D4
cosocleC2×C4×D29C23
hypercenter#117#1181
hypocenterC29#1825
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #14272036C2semidirect
4. #14272036C2semidirect
10. C29×#117C4semidirect
11. #11745288C4semidirect
12. #11745254C4semidirect
13. #11745254C4semidirect
122. #117#1181semidirect
132. C29#1825semidirect

Maximal subgroups

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

subgroupindex
D29⋊(C22⋊C8)2
#142721052
#142720362
#117×D292
#182529