Finite Group Databasebeta

← #34056934

Subgroups — #34056934

Order 19072.

460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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#23750340C211yesmaximal, characteristic, complemented
2D4×D596C211yesmaximal, characteristic, complemented
3#23749972C211yesmaximal, characteristic, complemented
4#23749950C212yesmaximal, complemented
5#23749916C211yesmaximal, characteristic, complemented
6#23749878C212yesmaximal, complemented
7#23749821C211yesmaximal, characteristic, complemented
8#23749761C212yesmaximal, complemented
9C4×D1192C211yesmaximal, characteristic, complemented
10#23749631C212yesmaximal, complemented
11#436×C149C211yesmaximal, characteristic, complemented
12C22×D596C2212yes—
13C2×D4×D149—21no—
14C2×D1192C2211yescharacteristic
15C2×D1192C2212yescomplemented
16#18011911C2211yescharacteristic, complemented
17#18011908C2211yescharacteristic
18#18011897—22no—
19#18011886—21no—
20#18011885C2212yes—
21#18011885C2212yescomplemented
22#18011882—21no—
23#18011881—22no—
24C4×D596C2211yescharacteristic
25C4×D596C2211yescharacteristic, complemented
26#18011870C2212yescomplemented
27#18011869—21no—
28#18011845C2211yescharacteristic, complemented
29#18011843C2212yescomplemented
30#18011833C2212yes—
31#18011833C2211yescharacteristic
32#18011833C2212yescomplemented
33#18011833C2212yescomplemented
34#18011833C2211yescharacteristic, complemented
35#18011833C2212yescomplemented
36C2×M16×C149C2212yescomplemented
37C4×D4×C149C2211yescharacteristic
38C4⋊C8×C149C2211yescharacteristic, complemented
39C22⋊C8×C149C2212yescomplemented
40C4×C8×C149C2211yescharacteristic, complemented
41C23×D149—22no—
42C2×Dic298—21no—
43C2×D596—24no—
44C2×D596—21no—
45C2×D596—22no—
46C2×D596—21no—
47C2×D596—42no—
48C2×D596C2312yes—
49C2×D596C2311yescharacteristic
50C2×D596C2311yescharacteristic
51C2×C22⋊D149—22no—
52C2×C22⋊D149—22no—
53D4×D149—44no—
54C2×C4×D149—21no—
55C2×C4×D149—21no—
56D1192—22no—
57D1192—42no—
58C4⋊Dic149—21no—
59C4⋊Dic149C2312yes—
60C4⋊Dic149C2311yescharacteristic
61C4⋊Dic149C2311yescharacteristic
62C22⋊Dic149—22no—
63#14558713—22no—
64#14558713—21no—
65#14558713—21no—
66#14558713—22no—
67C4×Dic149—22no—
68C2×D4×C149D411yescharacteristic
69C22×C4×C149C2312yes—
70M16×C149—42no—
71C2×C8×C149C2311yescharacteristic
72C2×C8×C149C2312yes—
73C2×C8×C149C2311yescharacteristic
74C4⋊C4×C149D411yescharacteristic
75C22⋊C4×C149D412yes—
76C42×C149C2311yescharacteristic
77C22×D149—21no—
78C22×D149—21no—
79C22×D149—22no—
80C22×D149—44no—
81C22×D149—44no—
82C22×D149—82no—
83Dic298—81no—
84D596—21no—
85D596—22no—
86D596—21no—
87D596—21no—
88D596—22no—
89D596—44no—
90D596—42no—
91D596—81no—
92D596#4112yes—
93C22⋊D149—44no—
94C22⋊D149—82no—
95C2×Dic149—21no—
96C2×Dic149—21no—
97C2×Dic149—22no—
98C4×D149—42no—
99C4×D149—42no—
100C23×C149C2×D412yes—
101D4×C149—22no—
102C2×C4×C149—22no—
103C2×C4×C149—22no—
104C2×C4×C149C2×D411yescharacteristic
105C2×C4×C149C2×D412yes—
106C2×C4×C149C2×D411yescharacteristic
107C2×C4×C149C2411yescharacteristic
108C8×C149—21no—
109C8×C149—22no—
110C8×C149—21no—
111C22×C149—22no—
112C22×C149—22no—
113C22×C149—22no—
114C22×C149C22×D411yescharacteristic
115C2×D149—22no—
116C2×D149—41no—
117C2×D149—41no—
118C2×D149—42no—
119C2×D149—41no—
120C2×D149—41no—
121C2×D149—42no—
122C2×D149—41no—
123C2×D149—42no—
124C2×D149—88no—
125C4×C149—22no—
126C4×C149—21no—
127C4×C149AGL(1,ℤ/8)12yes—
128C4×C149C2×#4111yescharacteristic
129C4×C149H(5,𝔽2)11yescharacteristic
130Dic149—41no—
131Dic149—41no—
132Dic149—42no—
133C2×C149—42no—
134C2×C149#54611yescharacteristic
135C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
136C2×C149#57611yescharacteristic
137D149—42no—
138D149—81no—
139D149—82no—
140C149#332511yescharacteristic, complemented, Sylow
141#3325—1491nomaximal, Sylow
142#555—1491no—
143D42—1491no—
144#486—1491no—
145#482—1492no—
146#476—1491no—
147#469—1492no—
148#459—1491no—
149#447—1492no—
150C4×D8—1491no—
151#436D14911yescharacteristic, complemented
152#418—1492no—
153C22×D4—2981no—
154C22×D4—1492no—
155C2×D8—1491no—
156C2×D8—1492no—
157C2×M16C2×D14912yescomplemented
158C4⋊Q8—1491no—
159#127—1491no—
160#124—2982no—
161#121—2981no—
162#121—2981no—
163#121—1492no—
164#121—1492no—
165#120—2982no—
166C4×D4—1491no—
167C4×D4—1491no—
168C4×D4C2×D14911yescharacteristic
169#117—2981no—
170#117—1492no—
171#107—1491no—
172#106—1492no—
173C4⋊C8C2×D14911yescharacteristic, complemented
174#102—1491no—
175#102—1492no—
176#102—1492no—
177#102—1492no—
178#102—1491no—
179#102—1492no—
180C22⋊C8C2×D14912yescomplemented
181C4×C8C2×D14911yescharacteristic, complemented
182C24—2982no—
183C2×Q8—2981no—
184C2×D4—2984no—
185C2×D4—2982no—
186C2×D4—2982no—
187C2×D4—2982no—
188C2×D4—2981no—
189C2×D4—2981no—
190C2×D4—5962no—
191C2×D4—5964no—
192C2×D4—1492no—
193C2×D4—1491no—
194C2×D4—1491no—
195C2×D4D59611yescharacteristic
196C22×C4—2981no—
197C22×C4—2981no—
198C22×C4C22×D14912yes—
199D8—2982no—
200D8—5962no—
201M16—42no—
202C2×C8C22×D14911yescharacteristic
203C2×C8C22×D14911yescharacteristic
204C2×C8C22×D14912yes—
205C4⋊C4—2981no—
206C4⋊C4—1492no—
207C4⋊C4—1491no—
208C4⋊C4—1491no—
209C4⋊C4D59611yescharacteristic
210C22⋊C4—2982no—
211C22⋊C4—2982no—
212C22⋊C4—2981no—
213C22⋊C4—2981no—
214C22⋊C4—2982no—
215C22⋊C4D59612yes—
216C42—2982no—
217C42C22×D14911yescharacteristic
218C23—2981no—
219C23—2981no—
220C23—2982no—
221C23—5964no—
222C23—5964no—
223C23—11922no—
224C23C2×D59612yes—
225Q8—11921no—
226D4—22no—
227D4—2981no—
228D4—2982no—
229D4—2981no—
230D4—2981no—
231D4—2982no—
232D4—5964no—
233D4—5964no—
234D4—5962no—
235D4—1492no—
236D4—11921no—
237D4—11922no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—2981no—
241C2×C4—2982no—
242C2×C4—2981no—
243C2×C4—5962no—
244C2×C4—5962no—
245C2×C4C2×D59612yes—
246C2×C4C2×D59611yescharacteristic
247C2×C4C2×D59611yescharacteristic
248C2×C4C23×D14911yescharacteristic
249C8—21no—
250C8—21no—
251C8—22no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—2982no—
256C22—5961no—
257C22—5961no—
258C22—5961no—
259C22—5962no—
260C22—5961no—
261C22—5962no—
262C22—5962no—
263C22—5961no—
264C22—11928no—
265C22C22×D59611yescharacteristic
266C4—21no—
267C4—22no—
268C4—5961no—
269C4—5961no—
270C4—5962no—
271C4#1801193912yes—
272C4#41×D14911yescharacteristic
273C4#1801195611yescharacteristic
274C2—42no—
275C2—5962no—
276C2—11922no—
277C2—11921no—
278C2#2375027011yescharacteristic
279C2C2×#1801193911yescharacteristic
280C2#2375043011yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#436×C149C2
socleC22×C149C22×D4
hypercenter#436D149
hypocenterC149#3325
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #23750340C2semidirect
2. D4×D596C2semidirect
3. #23749972C2semidirect
4. #23749950C2semidirect
5. #23749916C2semidirect
6. #23749878C2semidirect
7. #23749821C2semidirect
8. #23749761C2semidirect
9. C4×D1192C2semidirect
10. #23749631C2semidirect
11. #436×C149C2semidirect
15. C2×D1192C22semidirect
16. #18011911C22semidirect
21. #18011885C22semidirect
25. C4×D596C22semidirect
26. #18011870C22semidirect
28. #18011845C22semidirect
29. #18011843C22semidirect
32. #18011833C22semidirect
33. #18011833C22semidirect
34. #18011833C22semidirect
35. #18011833C22semidirect
36. C2×M16×C149C22semidirect
38. C4⋊C8×C149C22semidirect
39. C22⋊C8×C149C22semidirect
40. C4×C8×C149C22semidirect
140. C149#3325semidirect
151. #436D149semidirect
157. C2×M16C2×D149semidirect
173. C4⋊C8C2×D149semidirect
180. C22⋊C8C2×D149semidirect
181. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237503402
D4×D5962
#237499722
#237499502
#237499162
#237498782
#237498212
#237497612
C4×D11922
#237496312
#436×C1492
#3325149