Finite Group Databasebeta

← #34055487

Subgroups — #34055487

Order 19072.

514 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 113 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#121×D149C212yesmaximal, complemented
2#23749945C212yesmaximal, complemented
3#23749942C212yesmaximal, complemented
4#23749878C211yesmaximal, characteristic, complemented
5#23749876C212yesmaximal, complemented
6#23749760C212yesmaximal, complemented
7#23749757C212yesmaximal, complemented
8#23749588C211yesmaximal, characteristic, complemented
9#469×C149C211yesmaximal, characteristic, complemented
10C2×D4×D149—22no—
11C2×D4×D149C2212yescomplemented
12C22×C4×D149C2211yescharacteristic
13C2×D1192C2211yescharacteristic, complemented
14C2×#14558721C2212yescomplemented
15C2×#14558720C2211yescharacteristic, complemented
16#18011886C2212yes—
17#18011885C2212yescomplemented
18#18011884—22no—
19#18011883—22no—
20#18011882C2212yes—
21C4⋊C4×D149C2212yescomplemented
22C22⋊C4×D149—22no—
23#18011843C2211yescharacteristic, complemented
24#18011842C2212yescomplemented
25#18011833C2212yescomplemented
26#18011832C2212yescomplemented
27#18011831C2212yescomplemented
28#18011823C2212yescomplemented
29#18011823C2212yescomplemented
30C2×D8×C149C2211yescharacteristic, complemented
31C2×M16×C149C2211yescharacteristic, complemented
32#121×C149C2212yescomplemented
33#106×C149C2211yescharacteristic, complemented
34#102×C149C2212yescomplemented
35C23×D149—22no—
36C23×D149D411yescharacteristic
37C2×D596—22no—
38C2×D596C2312yes—
39C2×C22⋊D149—22no—
40C2×C22⋊D149—22no—
41C2×C22⋊D149—22no—
42D4×D149—42no—
43D4×D149—42no—
44D4×D149—48no—
45C22×Dic149D411yescharacteristic
46C2×C4×D149—22no—
47C2×C4×D149—41no—
48C2×C4×D149—41no—
49C2×C4×D149D412yes—
50C2×C4×D149C2312yes—
51D1192—41no—
52#14558721—42no—
53#14558720—41no—
54C2×#11924746C2312yes—
55C4⋊Dic149C2312yes—
56#14558715—22no—
57C22⋊Dic149—22no—
58#14558713—22no—
59#14558713—22no—
60C2×D4×C149—22no—
61C2×D4×C149C2312yes—
62C22×C4×C149C2311yescharacteristic
63D8×C149—41no—
64M16×C149—41no—
65C2×C8×C149C2311yescharacteristic
66C2×C8×C149C2311yescharacteristic
67C4⋊C4×C149C2312yes—
68C22⋊C4×C149—22no—
69C22×D149—24no—
70C22×D149—22no—
71C22×D149—41no—
72C22×D149—44no—
73C22×D149—44no—
74C22×D149—44no—
75C22×D149C2×D412yes—
76D596—22no—
77D596—22no—
78D596—44no—
79C22⋊D149—44no—
80C22⋊D149—44no—
81C22⋊D149—44no—
82C2×Dic149—22no—
83C2×Dic149—41no—
84C2×Dic149C2×D412yes—
85C4×D149—22no—
86C4×D149—22no—
87C4×D149—42no—
88C4×D149—44no—
89#11924746—22no—
90C23×C149—22no—
91C23×C149C2×D411yescharacteristic
92D4×C149—22no—
93D4×C149—22no—
94D4×C149—44no—
95C2×C4×C149—21no—
96C2×C4×C149—21no—
97C2×C4×C149—22no—
98C2×C4×C149C2×D411yescharacteristic
99C2×C4×C149C2411yescharacteristic
100C8×C149—21no—
101C8×C149—21no—
102C22×C149—21no—
103C22×C149—22no—
104C22×C149—42no—
105C22×C149—42no—
106C22×C149—42no—
107C22×C149C22×D411yescharacteristic
108C2×D149—22no—
109C2×D149—22no—
110C2×D149—44no—
111C2×D149—42no—
112C2×D149—42no—
113C2×D149—42no—
114C2×D149—88no—
115C2×D149AGL(1,ℤ/8)14yes—
116C4×C149—21no—
117C4×C149—42no—
118C4×C149H(5,𝔽2)11yescharacteristic
119C4×C149H(5,𝔽2)11yescharacteristic
120Dic149—22no—
121Dic149—42no—
122C2×C149—41no—
123C2×C149—82no—
124C2×C149#53411yescharacteristic
125C2×C149C2×AGL(1,ℤ/8)12yes—
126D149—24no—
127D149—82no—
128C149#319211yescharacteristic, complemented, Sylow
129#3192—1491nomaximal, Sylow
130C2×#121—1492no—
131#481—1492no—
132#481—1492no—
133#469—1491no—
134#469—1492no—
135#469D14911yescharacteristic, complemented
136#447—1492no—
137#447—1492no—
138#407—1491no—
139C22×D4—2982no—
140C22×D4—1492no—
141C23×C4—1491no—
142C2×D8—1492no—
143C2×D8—1491no—
144C2×D8C2×D14911yescharacteristic, complemented
145C2×M16—1491no—
146C2×M16C2×D14911yescharacteristic, complemented
147#121—2982no—
148#121—2982no—
149#121—1492no—
150#121—1492no—
151#121—1492no—
152#121C2×D14912yescomplemented
153C2×C4⋊C4—1492no—
154C2×C22⋊C4—2982no—
155#106—1491no—
156#106—1492no—
157#106C2×D14911yescharacteristic, complemented
158#102—1492no—
159#102—1492no—
160#102—1492no—
161#102C2×D14912yescomplemented
162C22⋊C8—1492no—
163C22⋊C8—1492no—
164C24—2982no—
165C24—1491no—
166C2×D4—22no—
167C2×D4—2982no—
168C2×D4—2982no—
169C2×D4—2982no—
170C2×D4—2982no—
171C2×D4—5962no—
172C2×D4—5962no—
173C2×D4—5968no—
174C2×D4—1492no—
175C2×D4C22×D14912yes—
176C22×C4—2982no—
177C22×C4—5961no—
178C22×C4—5961no—
179C22×C4—1492no—
180C22×C4—1491no—
181C22×C4—1492no—
182C22×C4C22×D14911yescharacteristic
183D8—41no—
184D8—5961no—
185D8—5962no—
186M16—41no—
187M16—5961no—
188C2×C8—1492no—
189C2×C8C22×D14911yescharacteristic
190C2×C8C22×D14911yescharacteristic
191C4⋊C4—2982no—
192C4⋊C4—1492no—
193C4⋊C4C22×D14912yes—
194C22⋊C4—22no—
195C22⋊C4—2982no—
196C22⋊C4—2982no—
197C22⋊C4—2982no—
198C23—22no—
199C23—2984no—
200C23—2982no—
201C23—5961no—
202C23—5964no—
203C23—5964no—
204C23—5964no—
205C23—1492no—
206C23D4×D14911yescharacteristic
207D4—22no—
208D4—22no—
209D4—44no—
210D4—2982no—
211D4—2982no—
212D4—5964no—
213D4—5964no—
214D4—5964no—
215D4—5964no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—2982no—
220C2×C4—2982no—
221C2×C4—2982no—
222C2×C4—5962no—
223C2×C4—5964no—
224C2×C4—5961no—
225C2×C4—1492no—
226C2×C4D4×D14911yescharacteristic
227C2×C4C23×D14911yescharacteristic
228C8—21no—
229C8—21no—
230C8—2982no—
231C22—22no—
232C22—21no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—2982no—
237C22—2982no—
238C22—5964no—
239C22—5962no—
240C22—5962no—
241C22—5962no—
242C22—1494no—
243C22—11928no—
244C22C2×D4×D14911yescharacteristic
245C4—21no—
246C4—42no—
247C4—2982no—
248C4—5962no—
249C4#1801195611yescharacteristic
250C4#1801195711yescharacteristic
251C2—41no—
252C2—82no—
253C2—2984no—
254C2—11922no—
255C2#2375018311yescharacteristic
256C2AGL(1,ℤ/8)×D14912yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#469×C149C2
socleC22×C149C22×D4
hypercenter#469D149
hypocenterC149#3192
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #121×D149C2semidirect
2. #23749945C2semidirect
3. #23749942C2semidirect
4. #23749878C2semidirect
5. #23749876C2semidirect
6. #23749760C2semidirect
7. #23749757C2semidirect
8. #23749588C2semidirect
9. #469×C149C2semidirect
11. C2×D4×D149C22semidirect
13. C2×D1192C22semidirect
14. C2×#14558721C22semidirect
15. C2×#14558720C22semidirect
17. #18011885C22semidirect
21. C4⋊C4×D149C22semidirect
23. #18011843C22semidirect
24. #18011842C22semidirect
25. #18011833C22semidirect
26. #18011832C22semidirect
27. #18011831C22semidirect
28. #18011823C22semidirect
29. #18011823C22semidirect
30. C2×D8×C149C22semidirect
31. C2×M16×C149C22semidirect
32. #121×C149C22semidirect
33. #106×C149C22semidirect
34. #102×C149C22semidirect
128. C149#3192semidirect
135. #469D149semidirect
144. C2×D8C2×D149semidirect
146. C2×M16C2×D149semidirect
152. #121C2×D149semidirect
157. #106C2×D149semidirect
161. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#121×D1492
#237499452
#237499422
#237498782
#237498762
#237497602
#237497572
#237495882
#469×C1492
#3192149