Finite Group Databasebeta

← #16835468

Subgroups — #16835468

Order 3712.

432 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C22×D29⋊C8C211yesmaximal, characteristic, complemented
2C2×#11745219C211yesmaximal, characteristic, complemented
3C2×#11745219C212yesmaximal, complemented
4#14272029C212yesmaximal, complemented
5C2×#11745255C211yesmaximal, characteristic
6C22×D116C411yescharacteristic
7C22×C4×D29C2211yescharacteristic
8C22×C4×D29C2211yescharacteristic
9C22×#6599C2212yes—
10C22×#6599C2212yes—
11C2×D29⋊C8—22no—
12C2×D29⋊C8—24no—
13C2×C4⋊C4×C29C411yescharacteristic
14C2×#90781C411yescharacteristic
15C2×#90781C411yescharacteristic
16C2×C4×Dic29C2211yescharacteristic
17#11745255—22no—
18#11745255—22no—
19#11745219—22no—
20#11745219—24no—
21C23×D29C2×C411yescharacteristic
22C23×D29C2×C411yescharacteristic
23C22×C4×C29C2×C411yescharacteristic
24C22×C4×C29C2×C411yescharacteristic
25C22×C4×C29C2×C411yescharacteristic
26C22×Dic29C2×C411yescharacteristic
27C22×Dic29C2311yescharacteristic
28C2×D116—22no—
29C2×D116—22no—
30C2×D116C814yescomplemented
31C2×C4×D29—22no—
32C2×C4×D29—22no—
33C2×C4×D29—22no—
34C2×C4×D29—21no—
35C2×C4×D29—21no—
36C2×C4×D29—22no—
37C2×C4×D29D412yes—
38C2×C4×D29D412yes—
39C2×#6599—22no—
40C2×#6599—22no—
41C2×#6599—22no—
42C2×#6599—22no—
43C2×#6599—22no—
44C2×#6599D414yescomplemented
45D29⋊C8—28no—
46C4⋊C4×C29—22no—
47#90781—22no—
48#90781—22no—
49C4×Dic29—21no—
50C4×Dic29—21no—
51C23×C29C22×C411yescharacteristic
52C22×D29—22no—
53C22×D29—22no—
54C22×D29—21no—
55C22×D29—22no—
56C22×D29—21no—
57C22×D29—22no—
58C22×D29C22⋊C412yes—
59C22×D29C2×C812yes—
60C22×D29C2×C812yescomplemented
61C22×D29M1612yes—
62C2×C4×C29—21no—
63C2×C4×C29—22no—
64C2×C4×C29—21no—
65C2×C4×C29—21no—
66C2×C4×C29—22no—
67C2×C4×C29C22⋊C412yes—
68C2×C4×C29C2×C812yescomplemented
69C2×Dic29—21no—
70C2×Dic29—22no—
71C2×Dic29C2×D412yes—
72C2×Dic29C2×D411yescharacteristic
73C2×Dic29C2×D411yescharacteristic
74C2×Dic29#4112yes—
75D116—28no—
76C4×D29—22no—
77C4×D29—24no—
78C4×D29—22no—
79C4×D29—41no—
80C4×D29—42no—
81C4×D29—41no—
82#6599—24no—
83#6599—42no—
84#1869—291nomaximal, Sylow
85C22×C29C2×C22⋊C411yescharacteristic
86C22×C29C4×D412yes—
87C22×C29C22×C811yescharacteristic
88C22×C29C2×M1611yescharacteristic
89C22×C29#13112yes—
90C2×D29—22no—
91C2×D29—22no—
92C2×D29—24no—
93C2×D29—24no—
94C2×D29—22no—
95C2×D29—24no—
96C2×D29—41no—
97C2×D29—41no—
98C2×D29—42no—
99C2×D29C22⋊C814yescomplemented
100C4×C29—22no—
101C4×C29—22no—
102C4×C29—41no—
103Dic29—41no—
104Dic29#12011yescharacteristic
105Dic29#12112yes—
106Dic29#12311yescharacteristic
107C23×C8—291no—
108C2×C4×D4—291no—
109C2×C22⋊C8—292no—
110C2×C22⋊C8—291no—
111#336—292no—
112C2×C29#38611yescharacteristic
113C2×C29C2×C22⋊C811yescharacteristic
114C2×C29#40811yescharacteristic
115C2×C29C8×D412yes—
116C2×C29#43512yes—
117D29—24no—
118D29—42no—
119C22×D4—291no—
120C23×C4—291no—
121C23×C4—291no—
122C22×C8—292no—
123C22×C8—292no—
124C22×C8—584no—
125C22×C8—582no—
126C4×D4—582no—
127C4×D4—582no—
128C2×C4⋊C4#118111yescharacteristic
129C2×C22⋊C4—291no—
130C2×C22⋊C4—291no—
131C2×C42—291no—
132C22⋊C8—584no—
133C22⋊C8—582no—
134C29#186911yescharacteristic, complemented, Sylow
135C24—291no—
136C24—291no—
137C2×D4—294no—
138C2×D4—582no—
139C2×D4—582no—
140C22×C4—291no—
141C22×C4—292no—
142C22×C4—292no—
143C22×C4—291no—
144C22×C4—582no—
145C22×C4—582no—
146C22×C4—582no—
147C22×C4—581no—
148C22×C4—581no—
149C22×C4—582no—
150C22×C4C2×#118111yescharacteristic
151C22×C4C2×#118111yescharacteristic
152C22×C4C2×#118111yescharacteristic
153C2×C8—294no—
154C2×C8—582no—
155C2×C8—582no—
156C2×C8—588no—
157C2×C8—582no—
158C2×C8—582no—
159C2×C8—582no—
160C4⋊C4—22no—
161C22⋊C4—582no—
162C22⋊C4—582no—
163C42—581no—
164C42—581no—
165C23—292no—
166C23—292no—
167C23—292no—
168C23—292no—
169C23—582no—
170C23—582no—
171C23—581no—
172C23—582no—
173C23—582no—
174C23—581no—
175C23C22×#118111yescharacteristic
176D4—588no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—292no—
183C2×C4—292no—
184C2×C4—291no—
185C2×C4—291no—
186C2×C4—582no—
187C2×C4—584no—
188C2×C4—582no—
189C2×C4—582no—
190C2×C4—581no—
191C2×C4—1161no—
192C2×C4—1162no—
193C2×C4—1161no—
194C2×C4D29⋊C812yescomplemented
195C2×C4C22⋊#118112yes—
196C8—584no—
197C8—1162no—
198C22—294no—
199C22—582no—
200C22—582no—
201C22—584no—
202C22—584no—
203C22—582no—
204C22—584no—
205C22—1161no—
206C22—1161no—
207C22—1162no—
208C22C2×D29⋊C811yescharacteristic
209C22D29⋊M1611yescharacteristic
210C22D4×#118112yes—
211C22#1174534812yes—
212C22C2×C22⋊#118111yescharacteristic
213C4—22no—
214C4—22no—
215C4—41no—
216C4—291no—
217C4—292no—
218C4—291no—
219C4—1161no—
220C2—584no—
221C2—1162no—
222C2#1427211111yescharacteristic
223C2D29⋊(C22⋊C8)11yescharacteristic
224C2#1427213811yescharacteristic
225C2#1427219112yes—
226C2#1427219312yes—
subgroupG/H
center, FrattiniC23C22×#1181
commutatorC22×C29C22×C8
FittingC2×C4⋊C4×C29C4
socleC23×C29C22×C4
prime radicalC22×D116C4
cosocleC22×Dic29C23
hypercenterC2×C4⋊C4#1181
hypocenterC29#1869
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D29⋊C8C2semidirect
2. C2×#11745219C2semidirect
3. C2×#11745219C2semidirect
4. #14272029C2semidirect
30. C2×D116C8semidirect
44. C2×#6599D4semidirect
60. C22×D29C2×C8semidirect
68. C2×C4×C29C2×C8semidirect
99. C2×D29C22⋊C8semidirect
134. C29#1869semidirect
194. C2×C4D29⋊C8semidirect

Maximal subgroups

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

subgroupindex
C22×D29⋊C82
C2×#117452192
#142720292
C2×#117452552
#186929