Finite Group Databasebeta

← #34053540

Subgroups — #34053540

Order 19072.

528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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×D8×D149C211yesmaximal, characteristic
2#23750097C212yesmaximal, complemented
3#23749738C211yesmaximal, characteristic, complemented
4#23749737C211yesmaximal, characteristic, complemented
5#23749736C211yesmaximal, characteristic, complemented
6C4×#14558721C212yesmaximal, complemented
7#23749705C212yesmaximal, complemented
8#23749660C211yesmaximal, characteristic, complemented
9#23749628C212yesmaximal, complemented
10#23749582C211yesmaximal, characteristic, complemented
11#442×C149C211yesmaximal, characteristic, complemented
12C2×D4×D149C2212yes—
13C2×D1192C2211yescharacteristic
14C2×#14558721C2212yes—
15D8×D149C418yescomplemented
16C2×#14558719C2211yescharacteristic
17C2×C8×D149C2211yescharacteristic
18C4×D596C2212yescomplemented
19D4×Dic149C2212yescomplemented
20#18011873C2212yescomplemented
21C4×C22⋊D149—22no—
22#18011871—22no—
23#18011869C2212yes—
24#18011868C2211yescharacteristic
25C2×#14558713—22no—
26C22⋊C4×D149—22no—
27#18011844C2212yescomplemented
28#18011843C2211yescharacteristic, complemented
29#18011833C2212yescomplemented
30#18011832C2212yescomplemented
31#18011831C2212yescomplemented
32#18011821C2211yescharacteristic, complemented
33C4×#11924746C2211yescharacteristic, complemented
34C8×Dic149C2211yescharacteristic, complemented
35C2×D8×C149C2211yescharacteristic
36C4×D4×C149C2212yescomplemented
37#106×C149C2211yescharacteristic, complemented
38#102×C149C2212yescomplemented
39#97×C149C2211yescharacteristic, complemented
40C23×D149—22no—
41C2×D596C2312yes—
42C2×C22⋊D149—22no—
43D4×D149—24no—
44D4×D149C2×C418yescomplemented
45C22×Dic149—22no—
46C2×C4×D149—22no—
47C2×C4×D149—22no—
48C2×C4×D149C2311yescharacteristic
49D1192C2×C414yescomplemented
50#14558721C2×C418yescomplemented
51#14558719—22no—
52C2×#11924746C2311yescharacteristic
53C2×#11924746C2311yescharacteristic
54C8×D149C2×C414yescomplemented
55C4⋊Dic149C2312yes—
56#14558715D412yes—
57C22⋊Dic149—22no—
58#14558713—22no—
59#14558713—22no—
60#14558713—22no—
61#14558713D412yes—
62C4×Dic149—22no—
63C4×Dic149C2311yescharacteristic
64C2×D4×C149C2312yes—
65C22×C4×C149—22no—
66D8×C149C2×C414yescomplemented
67C2×C8×C149C2311yescharacteristic
68C2×C8×C149C2311yescharacteristic
69C4⋊C4×C149C2312yes—
70C22⋊C4×C149—22no—
71C42×C149C2311yescharacteristic
72C22×D149—22no—
73C22×D149—28no—
74C22×D149—82no—
75C22×D149—82no—
76C22×D149C2×D411yescharacteristic
77D596—22no—
78D596C22×C414yes—
79C22⋊D149—28no—
80C2×Dic149—22no—
81C2×Dic149—82no—
82C2×Dic149C2×D412yes—
83C2×Dic149C2×D411yescharacteristic
84C4×D149—82no—
85C4×D149—82no—
86C4×D149C22×C412yes—
87C4×D149#4112yes—
88#11924746—21no—
89#11924746C22×C412yes—
90C23×C149—22no—
91D4×C149—22no—
92D4×C149C22×C414yes—
93C2×C4×C149—22no—
94C2×C4×C149—82no—
95C2×C4×C149C2×D412yes—
96C2×C4×C149C2411yescharacteristic
97C8×C149—21no—
98C8×C149C22×C412yes—
99C22×C149—24no—
100C22×C149—42no—
101C22×C149—42no—
102C22×C149C22×D411yescharacteristic
103C2×D149—22no—
104C2×D149—24no—
105C2×D149—42no—
106C2×D149—42no—
107C2×D149—88no—
108C2×D149C4×D412yes—
109C4×C149—22no—
110C4×C149—42no—
111C4×C149C23×C411yescharacteristic
112C4×C149C2×#4111yescharacteristic
113Dic149—22no—
114Dic149—42no—
115Dic149C4×D412yes—
116C2×C149—44no—
117C2×C149C2×C4×D411yescharacteristic
118C2×C149#57612yes—
119D149—22no—
120D149—44no—
121C149#294811yescharacteristic, complemented, Sylow
122#2948—1491nomaximal, Sylow
123C22×D8—1491no—
124#518—1492no—
125#442—1491no—
126#442—1491no—
127#442—1491no—
128#442D14911yescharacteristic, complemented
129C4×D8—1492no—
130C4×D8—1492no—
131#427—1491no—
132#418—1492no—
133#405—1491no—
134C22×D4—1492no—
135C2×D8—1492no—
136C2×D8—1498no—
137C2×D8—1491no—
138C2×D8C2×D14911yescharacteristic
139C2×M16—1491no—
140C22×C8—1491no—
141C4×D4—2982no—
142C4×D4—2982no—
143C4×D4—1492no—
144C4×D4—1492no—
145C4×D4—1492no—
146C4×D4C2×D14912yescomplemented
147#117—1492no—
148#117—1491no—
149C2×C22⋊C4—2982no—
150C2×C22⋊C4—2982no—
151#107—1492no—
152#106—1491no—
153#106C2×D14911yescharacteristic, complemented
154#102—1492no—
155#102—1492no—
156#102—1492no—
157#102C2×D14912yescomplemented
158#97—1491no—
159#97C2×D14911yescharacteristic, complemented
160C4×C8—1491no—
161C4×C8—1491no—
162C24—2982no—
163C2×D4—2984no—
164C2×D4—2982no—
165C2×D4—1498no—
166C2×D4—1492no—
167C2×D4C22×D14912yes—
168C22×C4—22no—
169C22×C4—2982no—
170C22×C4—2982no—
171C22×C4—2982no—
172C22×C4—1491no—
173D8—1498no—
174D8—1494no—
175D8C4×D14914yescomplemented
176M16—2982no—
177C2×C8—1491no—
178C2×C8—1491no—
179C2×C8—1494no—
180C2×C8C22×D14911yescharacteristic
181C2×C8C22×D14911yescharacteristic
182C4⋊C4—1492no—
183C4⋊C4—1492no—
184C4⋊C4C22×D14912yes—
185C22⋊C4—22no—
186C22⋊C4—2982no—
187C22⋊C4—2982no—
188C22⋊C4—2982no—
189C22⋊C4—2982no—
190C22⋊C4—1492no—
191C42—2982no—
192C42—1491no—
193C42C22×D14911yescharacteristic
194C23—22no—
195C23—2988no—
196C23—2982no—
197C23—1491no—
198C23—11922no—
199C23—11922no—
200D4—22no—
201D4—2988no—
202D4—2982no—
203D4—1494no—
204D4C2×C4×D14914yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—2982no—
208C2×C4—1492no—
209C2×C4—1491no—
210C2×C4—1492no—
211C2×C4—1492no—
212C2×C4—11922no—
213C2×C4—11922no—
214C2×C4—11922no—
215C2×C4D4×D14912yes—
216C2×C4C23×D14911yescharacteristic
217C8—21no—
218C8—2981no—
219C8—1492no—
220C8C2×C4×D14912yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—2982no—
225C22—2984no—
226C22—5962no—
227C22—5962no—
228C22—1492no—
229C22—11928no—
230C22C2×D4×D14911yescharacteristic
231C4—22no—
232C4—42no—
233C4—2982no—
234C4—5962no—
235C4—1492no—
236C4C22×C4×D14911yescharacteristic
237C4#41×D14911yescharacteristic
238C2—44no—
239C2—2982no—
240C2—5964no—
241C2C4×D4×D14911yescharacteristic
242C2#2375042912yes—
subgroupG/H
centerC22C2×D4×D149
commutatorC4×C149C23×C4
FrattiniC2×C4C23×D149
Fitting#442×C149C2
socleC22×C149C22×D4
prime radicalC2×D8×D149C2
cosocleC2×C4×C149C24
hypercenter#442D149
hypocenterC149#2948
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #23750097C2semidirect
3. #23749738C2semidirect
4. #23749737C2semidirect
5. #23749736C2semidirect
6. C4×#14558721C2semidirect
7. #23749705C2semidirect
8. #23749660C2semidirect
9. #23749628C2semidirect
10. #23749582C2semidirect
11. #442×C149C2semidirect
15. D8×D149C4semidirect
18. C4×D596C22semidirect
19. D4×Dic149C22semidirect
20. #18011873C22semidirect
27. #18011844C22semidirect
28. #18011843C22semidirect
29. #18011833C22semidirect
30. #18011832C22semidirect
31. #18011831C22semidirect
32. #18011821C22semidirect
33. C4×#11924746C22semidirect
34. C8×Dic149C22semidirect
36. C4×D4×C149C22semidirect
37. #106×C149C22semidirect
38. #102×C149C22semidirect
39. #97×C149C22semidirect
44. D4×D149C2×C4semidirect
49. D1192C2×C4semidirect
50. #14558721C2×C4semidirect
54. C8×D149C2×C4semidirect
66. D8×C149C2×C4semidirect
121. C149#2948semidirect
128. #442D149semidirect
146. C4×D4C2×D149semidirect
153. #106C2×D149semidirect
157. #102C2×D149semidirect
159. #97C2×D149semidirect
175. D8C4×D149semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1492
#237500972
#237497382
#237497372
#237497362
C4×#145587212
#237497052
#237496602
#237496282
#237495822
#442×C1492
#2948149