Finite Group Databasebeta

← #34055488

Subgroups — #34055488

Order 19072.

514 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#18011885C211yesmaximal, characteristic, complemented
2#23749943C212yesmaximal, complemented
3#23749941C212yesmaximal, complemented
4#23749876C214yesmaximal, complemented
5#23749759C212yesmaximal, complemented
6#23749758C212yesmaximal, complemented
7#23749589C211yesmaximal, characteristic, complemented
8C2×#121×C149C211yesmaximal, characteristic, complemented
9C22×D596C2211yescharacteristic, complemented
10C22×C22⋊D149—21no—
11C2×#14558721C2214yescomplemented
12C2×#14558720C2212yescomplemented
13#18011885—21no—
14#18011885—21no—
15#18011885C2212yes—
16#18011885C2212yescomplemented
17C2×C4⋊Dic149C2211yescharacteristic, complemented
18C2×#14558713—21no—
19#18011842C2214yescomplemented
20#18011832C2214yescomplemented
21#18011831C2214yescomplemented
22C22⋊#11924746C2212yescomplemented
23C22⋊#11924746C2212yescomplemented
24C22×D4×C149—21no—
25C22×D4×C149C2211yescharacteristic, complemented
26C23×C4×C149C2211yescharacteristic
27#121×C149—21no—
28#121×C149—21no—
29#121×C149C2212yes—
30#121×C149C2212yescomplemented
31C2×C4⋊C4×C149C2211yescharacteristic, complemented
32C2×C22⋊C4×C149—21no—
33C23×D149—21no—
34C2×D596—21no—
35C2×D596—42no—
36C2×D596C2312yes—
37C2×C22⋊D149—22no—
38C2×C22⋊D149—22no—
39C2×C22⋊D149—44no—
40C22×Dic149—21no—
41#14558721—44no—
42#14558720—42no—
43C2×#11924746C2314yes—
44C4⋊Dic149—21no—
45C4⋊Dic149C2312yes—
46#14558713—22no—
47#14558713—22no—
48C24×C149—21no—
49C24×C149D411yescharacteristic
50C2×D4×C149—22no—
51C2×D4×C149—22no—
52C2×D4×C149—21no—
53C2×D4×C149—42no—
54C2×D4×C149—44no—
55C2×D4×C149C2312yes—
56C22×C4×C149—21no—
57C22×C4×C149—42no—
58C22×C4×C149D411yescharacteristic
59C22×C4×C149D411yescharacteristic
60C22×C4×C149D411yescharacteristic
61C22×C4×C149C2311yescharacteristic
62C22×C4×C149C2311yescharacteristic
63C22×C4×C149C2311yescharacteristic
64C4⋊C4×C149—21no—
65C4⋊C4×C149C2312yes—
66C22⋊C4×C149—22no—
67C22⋊C4×C149—22no—
68C22×D149—22no—
69C22×D149—42no—
70C22×D149—42no—
71C22×D149—42no—
72D596—24no—
73D596—42no—
74C22⋊D149—44no—
75C22⋊D149—44no—
76C2×Dic149—22no—
77C2×Dic149—42no—
78#11924746—24no—
79C23×C149—22no—
80C23×C149—22no—
81C23×C149—22no—
82C23×C149—41no—
83C23×C149—42no—
84C23×C149—42no—
85C23×C149—42no—
86C23×C149C2×D411yescharacteristic
87C23×C149C2×D411yescharacteristic
88C23×C149C2×D411yescharacteristic
89D4×C149—24no—
90D4×C149—42no—
91D4×C149—44no—
92D4×C149—44no—
93C2×C4×C149—22no—
94C2×C4×C149—22no—
95C2×C4×C149—22no—
96C2×C4×C149—22no—
97C2×C4×C149—41no—
98C2×C4×C149—41no—
99C2×C4×C149—41no—
100C2×C4×C149—42no—
101C2×C4×C149C2×D411yescharacteristic
102C2×C4×C149C2×D411yescharacteristic
103C2×C4×C149C2×D411yescharacteristic
104C2×C4×C149C2411yescharacteristic
105C22×C149—21no—
106C22×C149—21no—
107C22×C149—21no—
108C22×C149—21no—
109C22×C149—21no—
110C22×C149—21no—
111C22×C149—21no—
112C22×C149—44no—
113C22×C149—42no—
114C22×C149—42no—
115C22×C149—42no—
116C22×C149—84no—
117C22×C149AGL(1,ℤ/8)12yes—
118C22×C149AGL(1,ℤ/8)12yes—
119C22×C149C22×D411yescharacteristic
120C2×D149—42no—
121C2×D149—42no—
122C2×D149—42no—
123C2×D149—84no—
124C4×C149—21no—
125C4×C149—21no—
126C4×C149—21no—
127C4×C149—42no—
128C4×C149H(5,𝔽2)12yes—
129Dic149—42no—
130C2×C149—22no—
131C2×C149—22no—
132C2×C149—41no—
133C2×C149—82no—
134C2×C149#53411yescharacteristic
135C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
136C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
137D149—82no—
138C149#319211yescharacteristic, complemented, Sylow
139#3192—1491nomaximal, Sylow
140C2×#121—1491no—
141C2×#121D14911yescharacteristic, complemented
142#481—1492no—
143#481—1492no—
144#469—1494no—
145#447—1492no—
146#447—1492no—
147#407—1491no—
148C22×D4—21no—
149C22×D4—2981no—
150C22×D4—1491no—
151C22×D4C2×D14911yescharacteristic, complemented
152C23×C4C2×D14911yescharacteristic
153C2×D8—1494no—
154C2×M16—1492no—
155#121—21no—
156#121—21no—
157#121—2981no—
158#121—2981no—
159#121—1492no—
160#121—1492no—
161#121C2×D14912yes—
162#121C2×D14912yescomplemented
163C2×C4⋊C4—1491no—
164C2×C4⋊C4C2×D14911yescharacteristic, complemented
165C2×C22⋊C4—21no—
166C2×C22⋊C4—2981no—
167#106—1494no—
168#102—1494no—
169#102—1494no—
170C22⋊C8—1492no—
171C22⋊C8—1492no—
172C24—21no—
173C24—2981no—
174C24C22⋊D14911yescharacteristic
175C2×D4—22no—
176C2×D4—22no—
177C2×D4—21no—
178C2×D4—42no—
179C2×D4—44no—
180C2×D4—2982no—
181C2×D4—2982no—
182C2×D4—2981no—
183C2×D4—5962no—
184C2×D4—5964no—
185C2×D4—1492no—
186C2×D4C22×D14912yes—
187C22×C4—21no—
188C22×C4—42no—
189C22×C4—2981no—
190C22×C4C22⋊D14911yescharacteristic
191C22×C4C22⋊D14911yescharacteristic
192C22×C4C22⋊D14911yescharacteristic
193C22×C4C22×D14911yescharacteristic
194C22×C4C22×D14911yescharacteristic
195C22×C4C22×D14911yescharacteristic
196D8—5964no—
197M16—5962no—
198C2×C8—1494no—
199C4⋊C4—21no—
200C4⋊C4—2981no—
201C4⋊C4—1492no—
202C4⋊C4C22×D14912yes—
203C22⋊C4—22no—
204C22⋊C4—22no—
205C22⋊C4—2982no—
206C22⋊C4—2982no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23—41no—
211C23—42no—
212C23—42no—
213C23—42no—
214C23—2982no—
215C23—5962no—
216C23—5962no—
217C23—5962no—
218C23C2×C22⋊D14911yescharacteristic
219C23C2×C22⋊D14911yescharacteristic
220C23C2×C22⋊D14911yescharacteristic
221D4—24no—
222D4—42no—
223D4—44no—
224D4—44no—
225D4—2984no—
226D4—5962no—
227D4—5964no—
228D4—5964no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—2982no—
238C2×C4—5962no—
239C2×C4C2×C22⋊D14911yescharacteristic
240C2×C4C2×C22⋊D14911yescharacteristic
241C2×C4C2×C22⋊D14911yescharacteristic
242C2×C4C23×D14911yescharacteristic
243C8—2984no—
244C22—21no—
245C22—21no—
246C22—21no—
247C22—21no—
248C22—21no—
249C22—21no—
250C22—21no—
251C22—44no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—84no—
256C22—5962no—
257C22—5962no—
258C22—5962no—
259C22—11924no—
260C22#1801193612yes—
261C22#1801193712yes—
262C22C22×C22⋊D14911yescharacteristic
263C4—21no—
264C4—21no—
265C4—21no—
266C4—42no—
267C4—5962no—
268C4#1801195612yes—
269C2—22no—
270C2—22no—
271C2—41no—
272C2—82no—
273C2—11922no—
274C2#2375018411yescharacteristic
275C2C2×#1801193611yescharacteristic
276C2C2×#1801193711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#121×C149C2
socleC22×C149C22×D4
hypercenterC2×#121D149
hypocenterC149#3192
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#18011885C2semidirect
2. #23749943C2semidirect
3. #23749941C2semidirect
4. #23749876C2semidirect
5. #23749759C2semidirect
6. #23749758C2semidirect
7. #23749589C2semidirect
8. C2×#121×C149C2semidirect
9. C22×D596C22semidirect
11. C2×#14558721C22semidirect
12. C2×#14558720C22semidirect
16. #18011885C22semidirect
17. C2×C4⋊Dic149C22semidirect
19. #18011842C22semidirect
20. #18011832C22semidirect
21. #18011831C22semidirect
22. C22⋊#11924746C22semidirect
23. C22⋊#11924746C22semidirect
25. C22×D4×C149C22semidirect
30. #121×C149C22semidirect
31. C2×C4⋊C4×C149C22semidirect
138. C149#3192semidirect
141. C2×#121D149semidirect
151. C22×D4C2×D149semidirect
162. #121C2×D149semidirect
164. C2×C4⋊C4C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118852
#237499432
#237499412
#237498762
#237497592
#237497582
#237495892
C2×#121×C1492
#3192149