Finite Group Databasebeta

← #34056515

Subgroups — #34056515

Order 19072.

462 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 141 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#23750332C211yesmaximal, characteristic, complemented
2#23749971C211yesmaximal, characteristic, complemented
3#23749941C212yesmaximal, complemented
4#23749915C211yesmaximal, characteristic, complemented
5#23749852C212yesmaximal, complemented
6#23749822C211yesmaximal, characteristic, complemented
7#23749776C212yesmaximal, complemented
8C4×#14558724C211yesmaximal, characteristic, complemented
9D4×#11924746C211yesmaximal, characteristic, complemented
10C2×#18011832C212yesmaximal, complemented
11D42×C149C211yesmaximal, characteristic
12C2×#14558724C2211yescharacteristic
13C2×#14558724C2212yescomplemented
14C22×#11924746C2212yescomplemented
15#18011911C2211yescharacteristic, complemented
16#18011902—21no—
17#18011890C2212yescomplemented
18#18011888—22no—
19C4×Dic298C2211yescharacteristic, complemented
20D4×Dic149—21no—
21C2×C4⋊Dic149C2212yescomplemented
22#18011842C2212yescomplemented
23#18011842C2211yescharacteristic, complemented
24C4⋊#11924746C2211yescharacteristic, complemented
25#18011834C2211yescharacteristic, complemented
26#18011832C2212yes—
27#18011832C2211yescharacteristic
28#18011832C2212yescomplemented
29#18011832C2212yescomplemented
30#18011832C2212yescomplemented
31C22⋊#11924746C2212yescomplemented
32C4×#11924746C2211yescharacteristic, complemented
33C22×D4×C149—21no—
34C22×D4×C149C2212yes—
35#127×C149C2211yescharacteristic
36#121×C149—21no—
37#121×C149C2212yes—
38#120×C149—22no—
39C4×D4×C149C2211yescharacteristic
40C4×D4×C149C2211yescharacteristic
41C2×Dic298—21no—
42C2×Dic298C2311yescharacteristic
43C22×Dic149—22no—
44#14558724—22no—
45#14558724—42no—
46C2×#11924746—42no—
47C2×#11924746C2311yescharacteristic
48C2×#11924746C2312yes—
49C2×#11924746C2311yescharacteristic
50C4⋊Dic149—21no—
51C4⋊Dic149—22no—
52C4⋊Dic149C2312yes—
53C4⋊Dic149C2311yescharacteristic
54#14558715—21no—
55#14558715—22no—
56C22⋊Dic149—22no—
57C4×Dic149—21no—
58C24×C149—22no—
59C2×D4×C149—24no—
60C2×D4×C149—22no—
61C2×D4×C149—22no—
62C2×D4×C149—21no—
63C2×D4×C149—21no—
64C2×D4×C149—42no—
65C2×D4×C149—44no—
66C2×D4×C149D411yescharacteristic
67C2×D4×C149C2312yes—
68C2×D4×C149C2311yescharacteristic
69C22×C4×C149—21no—
70C22×C4×C149C2312yes—
71C4⋊C4×C149D411yescharacteristic
72C4⋊C4×C149C2311yescharacteristic
73C22⋊C4×C149—21no—
74C22⋊C4×C149—22no—
75C22⋊C4×C149D412yes—
76C42×C149C2311yescharacteristic
77Dic298—21no—
78Dic298—21no—
79Dic298—81no—
80C2×Dic149—21no—
81C2×Dic149—22no—
82C2×Dic149—21no—
83C2×Dic149—82no—
84#11924746—21no—
85#11924746—22no—
86#11924746—21no—
87C23×C149—21no—
88C23×C149—22no—
89C23×C149—44no—
90C23×C149—44no—
91C23×C149—82no—
92C23×C149C2×D412yes—
93D4×C149—22no—
94D4×C149—21no—
95D4×C149—22no—
96D4×C149—44no—
97D4×C149—44no—
98D4×C149—42no—
99D4×C149—81no—
100D4×C149SD1614yescomplemented
101D4×C149#4112yes—
102C2×C4×C149—22no—
103C2×C4×C149—22no—
104C2×C4×C149—21no—
105C2×C4×C149—42no—
106C2×C4×C149C2×D411yescharacteristic
107C2×C4×C149C2×D412yes—
108C2×C4×C149C2×D411yescharacteristic
109C2×C4×C149C2411yescharacteristic
110C22×C149—22no—
111C22×C149—22no—
112C22×C149—22no—
113C22×C149—41no—
114C22×C149—41no—
115C22×C149—42no—
116C22×C149—42no—
117C22×C149—42no—
118C22×C149—88no—
119C22×C149C2×SD1614yes—
120C22×C149C22×D411yescharacteristic
121C4×C149—22no—
122C4×C149—21no—
123C4×C149—41no—
124C4×C149C2×SD1612yes—
125C4×C149C2×#4111yescharacteristic
126C4×C149H(5,𝔽2)11yescharacteristic
127Dic149—41no—
128Dic149—41no—
129Dic149—42no—
130C2×C149—24no—
131C2×C149—42no—
132C2×C149—82no—
133C2×C149#54611yescharacteristic
134C2×C149C22×SD1611yescharacteristic
135C2×C149#57611yescharacteristic
136C149#329511yescharacteristic, complemented, Sylow
137#3295—1491nomaximal, Sylow
138#554—1491no—
139D42D14911yescharacteristic
140#486—1491no—
141#481—1492no—
142#476—1491no—
143#465—1492no—
144#460—1491no—
145#450—1492no—
146C4×SD16—1491no—
147C8×D4—1491no—
148C2×#102—1492no—
149C22×D4—21no—
150C22×D4C2×D14912yes—
151C2×SD16—1491no—
152C2×SD16—1492no—
153C22×C8—1492no—
154C4⋊Q8—1491no—
155#127C2×D14911yescharacteristic
156#125—2981no—
157C22⋊Q8—2982no—
158C22⋊Q8—1492no—
159#121—21no—
160#121C2×D14912yes—
161#120—22no—
162C4×Q8—1491no—
163C4×D4—2981no—
164C4×D4C2×D14911yescharacteristic
165C4×D4C2×D14911yescharacteristic
166C2×C4⋊C4—1492no—
167#106—1491no—
168#106—1492no—
169C4⋊C8—1491no—
170#103—1491no—
171#102—1491no—
172#102—1492no—
173#102—1492no—
174#102—1492no—
175#102—1492no—
176C22⋊C8—1492no—
177C4×C8—1491no—
178C24—22no—
179C2×Q8—2981no—
180C2×Q8—1491no—
181C2×D4—24no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—42no—
187C2×D4—44no—
188C2×D4C22⋊D14911yescharacteristic
189C2×D4C22×D14912yes—
190C2×D4C22×D14911yescharacteristic
191C22×C4—21no—
192C22×C4—2982no—
193C22×C4C22×D14912yes—
194SD16—2982no—
195SD16—5962no—
196C2×C8—5962no—
197C2×C8—1491no—
198C2×C8—1491no—
199C2×C8—1492no—
200C4⋊C4—2982no—
201C4⋊C4—2981no—
202C4⋊C4—2981no—
203C4⋊C4—2982no—
204C4⋊C4—1491no—
205C4⋊C4—1492no—
206C4⋊C4C22⋊D14911yescharacteristic
207C4⋊C4C22×D14911yescharacteristic
208C22⋊C4—21no—
209C22⋊C4—22no—
210C22⋊C4—2982no—
211C22⋊C4C22⋊D14912yes—
212C42—2981no—
213C42C22×D14911yescharacteristic
214C23—21no—
215C23—22no—
216C23—44no—
217C23—44no—
218C23—82no—
219C23C2×C22⋊D14912yes—
220Q8—2981no—
221Q8—2981no—
222Q8—11921no—
223D4—22no—
224D4—21no—
225D4—22no—
226D4—44no—
227D4—44no—
228D4—42no—
229D4—81no—
230D4#1455872414yescomplemented
231D4#1455873512yes—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—2981no—
237C2×C4—2981no—
238C2×C4—2982no—
239C2×C4—11922no—
240C2×C4C2×C22⋊D14911yescharacteristic
241C2×C4C2×C22⋊D14912yes—
242C2×C4C2×C22⋊D14911yescharacteristic
243C2×C4C23×D14911yescharacteristic
244C8—2981no—
245C8—2981no—
246C8—2982no—
247C22—22no—
248C22—22no—
249C22—22no—
250C22—41no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—88no—
256C22C2×#1455872414yes—
257C22C22×C22⋊D14911yescharacteristic
258C4—21no—
259C4—22no—
260C4—41no—
261C4—5961no—
262C4—5962no—
263C4—5961no—
264C4C2×#1455872412yes—
265C4C2×#1455873511yescharacteristic
266C4#1801195611yescharacteristic
267C2—24no—
268C2—42no—
269C2—82no—
270C2#2375026911yescharacteristic
271C2C22×#1455872411yescharacteristic
272C2#2375042811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting, prime radicalD42×C149C2
socleC22×C149C22×D4
hypercenterD42D149
hypocenterC149#3295
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #23750332C2semidirect
2. #23749971C2semidirect
3. #23749941C2semidirect
4. #23749915C2semidirect
5. #23749852C2semidirect
6. #23749822C2semidirect
7. #23749776C2semidirect
8. C4×#14558724C2semidirect
9. D4×#11924746C2semidirect
10. C2×#18011832C2semidirect
13. C2×#14558724C22semidirect
14. C22×#11924746C22semidirect
15. #18011911C22semidirect
17. #18011890C22semidirect
19. C4×Dic298C22semidirect
21. C2×C4⋊Dic149C22semidirect
22. #18011842C22semidirect
23. #18011842C22semidirect
24. C4⋊#11924746C22semidirect
25. #18011834C22semidirect
28. #18011832C22semidirect
29. #18011832C22semidirect
30. #18011832C22semidirect
31. C22⋊#11924746C22semidirect
32. C4×#11924746C22semidirect
100. D4×C149SD16semidirect
136. C149#3295semidirect
230. D4#14558724semidirect

Maximal subgroups

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

subgroupindex
#237503322
#237499712
#237499412
#237499152
#237498522
#237498222
#237497762
C4×#145587242
D4×#119247462
C2×#180118322
D42×C1492
#3295149