Finite Group Databasebeta

← #16818034

Subgroups — #16818034

Order 3712.

286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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#14271676C211yesmaximal, characteristic
2#14271125C211yesmaximal, characteristic, complemented
3#14271022C211yesmaximal, characteristic, complemented
4#14270900C211yesmaximal, characteristic, complemented
5#14270898C211yesmaximal, characteristic, complemented
6#14270896C211yesmaximal, characteristic, complemented
7C29×#328C211yesmaximal, characteristic, complemented
8C2×#90809C411yescharacteristic, complemented
9C22×C4×D29C2211yescharacteristic
10C29×C22⋊Q8C2211yescharacteristic
11#11745308C411yescharacteristic, complemented
12#11745292C2211yescharacteristic
13C2×#90781—21no—
14C2×#90779—21no—
15C2×#90772—21no—
16#11745257C411yescharacteristic, complemented
17#11745256—21no—
18#11745255—21no—
19#11745254C411yescharacteristic, complemented
20#11745244—21no—
21#11745243—21no—
22C29×C22⋊C8C2211yescharacteristic
23C29×#95C2211yescharacteristic
24#11745179C2211yescharacteristic
25C22⋊#6597C2211yescharacteristic
26#11745168—21no—
27C23×D29D411yescharacteristic
28C2×Q8×C29C2×C411yescharacteristic
29C22×C4×C29—21no—
30C22×C4×C29C2311yescharacteristic
31C2×C22⋊D29—21no—
32C22×Dic29—21no—
33C22×Dic29D411yescharacteristic
34#90809—42no—
35C2×D116—21no—
36C2×D116—21no—
37C2×D116C2×C411yescharacteristic
38C2×C4×D29—21no—
39C2×C4×D29—42no—
40C2×C4×D29C2×C411yescharacteristic
41C2×C4×D29C2×C411yescharacteristic
42C2×C4×D29D411yescharacteristic
43C2×C4×D29D411yescharacteristic
44C2×C8×C29—21no—
45C4⋊C4×C29—21no—
46C4⋊C4×C29C2×C411yescharacteristic
47C22⋊C4×C29—21no—
48#90781—21no—
49#90781—21no—
50#90781—21no—
51#90781—21no—
52#90781—42no—
53C4⋊Dic29C2×C411yescharacteristic
54#90779—21no—
55#90779—42no—
56C4×Dic29—21no—
57C2×#6597—21no—
58#90772—42no—
59C23×C29C2×D411yescharacteristic
60C22×D29—21no—
61C22×D29—21no—
62C22×D29—21no—
63C22×D29—41no—
64C22×D29—41no—
65C22×D29C22⋊C411yescharacteristic
66C22×D29C22⋊C411yescharacteristic
67Q8×C29—41no—
68C2×C4×C29—21no—
69C2×C4×C29—21no—
70C2×C4×C29—41no—
71C2×C4×C29—41no—
72C2×C4×C29—41no—
73C2×C4×C29—41no—
74C2×C4×C29C22×C411yescharacteristic
75C2×C4×C29C2×D411yescharacteristic
76C22⋊D29—41no—
77C22⋊D29—41no—
78C2×Dic29—22no—
79C2×Dic29—21no—
80C2×Dic29—41no—
81C2×Dic29—41no—
82C2×Dic29—41no—
83C2×Dic29C22⋊C411yescharacteristic
84C2×Dic29C22⋊C411yescharacteristic
85D116—41no—
86D116—42no—
87D116—42no—
88C4×D29—22no—
89C4×D29—22no—
90C4×D29—41no—
91C4×D29—41no—
92C4×D29—42no—
93C8×C29—41no—
94#6597—41no—
95#1513—291nomaximal, Sylow
96C22×C29—21no—
97C22×C29—21no—
98C22×C29C2×C22⋊C411yescharacteristic
99C22×C29AGL(1,ℤ/8)11yescharacteristic
100C22×C29#13711yescharacteristic
101C2×D29—21no—
102C2×D29—21no—
103C2×D29—21no—
104C2×D29—21no—
105C2×D29—21no—
106C2×D29—21no—
107C2×D29—42no—
108C2×D29—42no—
109C2×D29—41no—
110C2×D29—41no—
111C2×D29—41no—
112C4×C29—21no—
113C4×C29—21no—
114C4×C29—41no—
115C4×C29—41no—
116C4×C29—81no—
117Dic29—21no—
118Dic29—41no—
119Dic29—81no—
120Dic29#9912yes—
121#525—291no—
122#407—291no—
123#380—291no—
124#328—291no—
125#328D2911yescharacteristic, complemented
126#327—291no—
127#327—291no—
128C2×C29—21no—
129C2×C29—21no—
130C2×C29C2×#9911yescharacteristic
131C2×C29#41711yescharacteristic
132C2×C29#42111yescharacteristic
133D29—41no—
134D29—41no—
135D29—81no—
136C2×#41—291no—
137C23×C4—291no—
138C2×M16—581no—
139#123—581no—
140C22⋊Q8—291no—
141C22⋊Q8C2×D2911yescharacteristic
142#121—291no—
143#121—291no—
144#120—581no—
145C4×D4—581no—
146C4×D4—581no—
147#117—291no—
148C2×C4⋊C4—581no—
149C2×C22⋊C4—581no—
150C22⋊C8—291no—
151C22⋊C8—581no—
152C22⋊C8C2×D2911yescharacteristic
153#95—291no—
154#95C2×D2911yescharacteristic
155C29#151311yescharacteristic, complemented, Sylow
156C24—291no—
157#41—1162no—
158C2×Q8C4×D2911yescharacteristic
159C2×D4—291no—
160C2×D4—581no—
161C2×D4—581no—
162C2×D4—581no—
163C22×C4—21no—
164C22×C4—291no—
165C22×C4—291no—
166C22×C4—291no—
167C22×C4—291no—
168C22×C4—291no—
169C22×C4—581no—
170C22×C4—581no—
171C22×C4—1162no—
172C22×C4C22×D2911yescharacteristic
173M16—1162no—
174C2×C8—21no—
175C2×C8—581no—
176C4⋊C4—21no—
177C4⋊C4—291no—
178C4⋊C4—581no—
179C4⋊C4—1162no—
180C4⋊C4C4×D2911yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—581no—
183C22⋊C4—581no—
184C22⋊C4—581no—
185C22⋊C4—581no—
186C22⋊C4—1162no—
187C42—581no—
188C23—291no—
189C23—291no—
190C23—581no—
191C23—581no—
192C23—581no—
193C23—1161no—
194C23—1161no—
195C23D4×D2911yescharacteristic
196Q8—41no—
197D4—1161no—
198D4—1162no—
199D4—1162no—
200D4—1161no—
201D4—1161no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—291no—
209C2×C4—291no—
210C2×C4—582no—
211C2×C4—582no—
212C2×C4—582no—
213C2×C4—581no—
214C2×C4—1161no—
215C2×C4—1161no—
216C2×C4—1162no—
217C2×C4—1161no—
218C2×C4—1161no—
219C2×C4—1161no—
220C2×C4C2×C4×D2911yescharacteristic
221C2×C4D4×D2911yescharacteristic
222C8—41no—
223C8—1161no—
224C22—21no—
225C22—21no—
226C22—581no—
227C22—581no—
228C22—581no—
229C22—581no—
230C22—581no—
231C22—581no—
232C22—1162no—
233C22—1162no—
234C22—1161no—
235C22—1161no—
236C22—1161no—
237C22C22⋊C4×D2911yescharacteristic
238C22#1174527611yescharacteristic
239C22#1174528011yescharacteristic
240C4—21no—
241C4—21no—
242C4—41no—
243C4—41no—
244C4—81no—
245C4—292no—
246C4—581no—
247C4—1161no—
248C4—2321no—
249C2—21no—
250C2—21no—
251C2—1161no—
252C2—1161no—
253C2—2321no—
254C2#99×D2911yescharacteristic
255C2#1427116311yescharacteristic
256C2#1427117811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D29
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#328C2
socleC22×C29C2×C22⋊C4
prime radical#14271676C2
cosocleC22×C4×C29C23
hypercenter#328D29
hypocenterC29#1513
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #14271125C2semidirect
3. #14271022C2semidirect
4. #14270900C2semidirect
5. #14270898C2semidirect
6. #14270896C2semidirect
7. C29×#328C2semidirect
8. C2×#90809C4semidirect
11. #11745308C4semidirect
16. #11745257C4semidirect
19. #11745254C4semidirect
125. #328D29semidirect
155. C29#1513semidirect

Maximal subgroups

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

subgroupindex
#142716762
#142711252
#142710222
#142709002
#142708982
#142708962
C29×#3282
#151329