Finite Group Databasebeta

← #16835541

Subgroups — #16835541

Order 3712.

380 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 66 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#14272230C211yesmaximal, characteristic, complemented
2D29⋊#99C211yesmaximal, characteristic, complemented
3C2×#11745227C212yesmaximal, complemented
4#14272040C212yesmaximal, complemented
5#14271723C211yesmaximal, characteristic
6C22×C22⋊D29C2211yescharacteristic
7C2×D4×D29C2211yescharacteristic
8C2×C22⋊#1181—21no—
9C2×C22⋊#1181C2212yes—
10C2×C22⋊#1181C2212yes—
11D4×#1181—24no—
12#11745345—21no—
13C29×#120C411yescharacteristic, complemented
14#11745315C411yescharacteristic, complemented
15#11745300—21no—
16#11745299—21no—
17#11745297C411yescharacteristic, complemented
18#11745248C411yescharacteristic, complemented
19#11745246—21no—
20#11745245—21no—
21C22⋊C4×D29C2211yescharacteristic
22#11745227—21no—
23#11745227—24no—
24#11745215—21no—
25C24×C29C2×C411yescharacteristic, complemented
26C23×D29D411yescharacteristic
27C23×D29C2311yescharacteristic
28C22×#1181—22no—
29C22×#1181—22no—
30C22×#1181—22no—
31C2×D4×C29—21no—
32C2×D4×C29C2×C411yescharacteristic
33C2×C22⋊D29—21no—
34C2×C22⋊D29—21no—
35C2×C22⋊D29—22no—
36C2×C22⋊D29—22no—
37C2×C22⋊D29—21no—
38C2×C22⋊D29C2×C411yescharacteristic
39C2×C22⋊D29D411yescharacteristic
40C22×Dic29C2×C411yescharacteristic, complemented
41D4×D29—22no—
42D4×D29—22no—
43C2×D116D411yescharacteristic
44C2×C4×D29—21no—
45C2×C4×D29D411yescharacteristic
46C22⋊#1181—22no—
47C22⋊#1181—22no—
48C22⋊#1181—22no—
49C22⋊#1181—22no—
50C22⋊#1181D414yescomplemented
51C4⋊#1181—22no—
52C4×#1181—22no—
53C22⋊C4×C29—21no—
54C22⋊C4×C29C2×C411yescharacteristic, complemented
55C22⋊Dic29—21no—
56C22⋊Dic29—21no—
57C22⋊Dic29C2×C411yescharacteristic, complemented
58#90781—21no—
59#90781—21no—
60C4⋊Dic29—21no—
61#90779—21no—
62C23×C29—21no—
63C23×C29—22no—
64C23×C29—81no—
65C23×C29C22⋊C411yescharacteristic
66C23×C29C22×C411yescharacteristic
67C22×D29—21no—
68C22×D29—21no—
69C22×D29—81no—
70C22×D29—81no—
71C22×D29C22⋊C411yescharacteristic
72C22×D29C2×D412yes—
73C22×D29C2×D411yescharacteristic
74C22×D29C2×D411yescharacteristic
75C22×D29#4112yes—
76C2×#1181—24no—
77C2×#1181—42no—
78C2×#1181—82no—
79C2×#1181—82no—
80C2×#1181—82no—
81D4×C29—22no—
82D4×C29—81no—
83C2×C4×C29—21no—
84C2×C4×C29C22⋊C411yescharacteristic
85C22⋊D29—22no—
86C22⋊D29—22no—
87C22⋊D29—41no—
88C22⋊D29—42no—
89C22⋊D29—41no—
90C22⋊D29—81no—
91C2×Dic29—21no—
92C2×Dic29—21no—
93C2×Dic29—22no—
94C2×Dic29C22⋊C411yescharacteristic
95D116—22no—
96C4×D29—21no—
97C4×D29—21no—
98C4×D29—81no—
99#1913—291nomaximal, Sylow
100C22×C29—21no—
101C22×C29—41no—
102C22×C29—41no—
103C22×C29—41no—
104C22×C29—41no—
105C22×C29—41no—
106C22×C29—82no—
107C22×C29C2×C22⋊C411yescharacteristic
108C22×C29C4×D412yes—
109C2×D29—21no—
110C2×D29—41no—
111C2×D29—42no—
112C2×D29—42no—
113C2×D29—41no—
114C2×D29—42no—
115C2×D29—41no—
116C2×D29—81no—
117C2×D29#12011yescharacteristic
118C2×D29#12112yes—
119C2×D29#12311yescharacteristic
120#1181—44no—
121#1181—82no—
122C4×C29—21no—
123C4×C29—41no—
124Dic29—21no—
125Dic29—41no—
126Dic29—41no—
127#534—291no—
128#518—291no—
129C2×#99—292no—
130C2×#99—291no—
131#342—292no—
132C2×C29—21no—
133C2×C29—22no—
134C2×C29—41no—
135C2×C29—81no—
136C2×C29#38611yescharacteristic
137D29—21no—
138D29—22no—
139D29—21no—
140D29—41no—
141C22×D4—291no—
142C22×D4—291no—
143#123—291no—
144#123—291no—
145#123—581no—
146#121—581no—
147#121—581no—
148#120—291no—
149#120—581no—
150#120#118111yescharacteristic, complemented
151C4×D4—584no—
152#117—581no—
153C2×C22⋊C4—292no—
154C2×C22⋊C4—291no—
155C2×C22⋊C4—292no—
156C2×C22⋊C4—581no—
157#99—584no—
158#99—581no—
159#99—581no—
160C29#191311yescharacteristic, complemented, Sylow
161C24—291no—
162C24—291no—
163C24C2×#118111yescharacteristic, complemented
164C2×D4—21no—
165C2×D4—291no—
166C2×D4—291no—
167C2×D4—291no—
168C2×D4—582no—
169C2×D4—582no—
170C2×D4—582no—
171C2×D4—581no—
172C2×D4—581no—
173C2×D4—582no—
174C2×D4—581no—
175C2×D4C2×#118111yescharacteristic
176C22×C4—291no—
177C22×C4—291no—
178C22×C4—581no—
179C22×C4—582no—
180C22×C4—582no—
181C22×C4—582no—
182C4⋊C4—581no—
183C4⋊C4—582no—
184C4⋊C4—581no—
185C22⋊C4—21no—
186C22⋊C4—294no—
187C22⋊C4—291no—
188C22⋊C4—581no—
189C22⋊C4—581no—
190C22⋊C4—581no—
191C22⋊C4—582no—
192C22⋊C4—582no—
193C22⋊C4—581no—
194C22⋊C4—582no—
195C22⋊C4—582no—
196C22⋊C4C2×#118111yescharacteristic, complemented
197C42—582no—
198C23—21no—
199C23—22no—
200C23—81no—
201C23—292no—
202C23—292no—
203C23—291no—
204C23—291no—
205C23—291no—
206C23—581no—
207C23—581no—
208C23—2321no—
209C23—2321no—
210C23C22⋊#118111yescharacteristic
211C23C22×#118111yescharacteristic
212D4—22no—
213D4—81no—
214D4—582no—
215D4—582no—
216D4—582no—
217D4—1161no—
218D4—1161no—
219D4—1162no—
220D4—2321no—
221C2×C4—21no—
222C2×C4—291no—
223C2×C4—581no—
224C2×C4—581no—
225C2×C4—584no—
226C2×C4—582no—
227C2×C4—581no—
228C2×C4—581no—
229C2×C4—1162no—
230C2×C4—2321no—
231C2×C4—2322no—
232C2×C4—2322no—
233C2×C4—2322no—
234C2×C4C22⋊#118111yescharacteristic
235C22—21no—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—82no—
242C22—291no—
243C22—291no—
244C22—292no—
245C22—581no—
246C22—1161no—
247C22—1162no—
248C22—1162no—
249C22—1161no—
250C22—1161no—
251C22—1162no—
252C22—2321no—
253C22D4×#118112yes—
254C22C2×C22⋊#118111yescharacteristic
255C4—21no—
256C4—41no—
257C4—581no—
258C4—1161no—
259C4—1164no—
260C4—1161no—
261C4—2322no—
262C2—21no—
263C2—22no—
264C2—41no—
265C2—81no—
266C2—581no—
267C2—582no—
268C2—581no—
269C2—1161no—
270C2#1427211111yescharacteristic
subgroupG/H
centerC2#14272111
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC29×#120C4
socleC2×C29#386
prime radical#14271723C2
cosocleC23×D29C23
hypercenter#120#1181
hypocenterC29#1913
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C23 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #14272230C2semidirect
2. D29⋊#99C2semidirect
3. C2×#11745227C2semidirect
4. #14272040C2semidirect
13. C29×#120C4semidirect
14. #11745315C4semidirect
17. #11745297C4semidirect
18. #11745248C4semidirect
25. C24×C29C2×C4semidirect
40. C22×Dic29C2×C4semidirect
50. C22⋊#1181D4semidirect
54. C22⋊C4×C29C2×C4semidirect
57. C22⋊Dic29C2×C4semidirect
150. #120#1181semidirect
160. C29#1913semidirect
163. C24C2×#1181semidirect
196. C22⋊C4C2×#1181semidirect

Maximal subgroups

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

subgroupindex
#142722302
D29⋊#992
C2×#117452272
#142720402
#142717232
#191329