Finite Group Databasebeta

← #34055505

Subgroups — #34055505

Order 19072.

466 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 121 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#23750136C211yesmaximal, characteristic, complemented
2#23749955C211yesmaximal, characteristic, complemented
3#23749946C212yesmaximal, complemented
4#23749938C211yesmaximal, characteristic, complemented
5#23749876C212yesmaximal, complemented
6#23749869C212yesmaximal, complemented
7#23749776C211yesmaximal, characteristic, complemented
8#23749768C212yesmaximal, complemented
9#23749759C211yesmaximal, characteristic, complemented
10#23749589C211yesmaximal, characteristic, complemented
11C2×#121×C149C211yesmaximal, characteristic, complemented
12C2×#14558736C2211yescharacteristic, complemented
13C2×#14558724C2212yescomplemented
14C2×#14558721C2212yescomplemented
15C2×#14558720C2212yescomplemented
16#18011894—21no—
17#18011890C2211yescharacteristic
18#18011890C2211yescharacteristic, complemented
19#18011885C2211yescharacteristic
20#18011885C2211yescharacteristic, complemented
21#18011880—21no—
22C4×C22⋊D149—21no—
23C4×C22⋊D149—21no—
24#18011870C2211yescharacteristic, complemented
25#18011844C2212yescomplemented
26#18011842C2212yescomplemented
27#18011834C2212yescomplemented
28#18011832C2212yescomplemented
29#18011832C2212yescomplemented
30#18011831C2212yescomplemented
31C22⋊#11924746C2211yescharacteristic
32C22⋊#11924746C2211yescharacteristic
33C22⋊#11924746C2212yescomplemented
34C22×D4×C149—21no—
35C22×D4×C149C2211yescharacteristic
36C23×C4×C149C2211yescharacteristic
37#121×C149—21no—
38#121×C149—21no—
39#121×C149C2212yes—
40#121×C149C2212yes—
41C2×C4⋊C4×C149C2211yescharacteristic
42C2×C22⋊C4×C149—21no—
43#14558736—42no—
44C2×Dic298C2311yescharacteristic
45C2×D596C2311yescharacteristic
46C2×C22⋊D149—21no—
47C2×C22⋊D149—21no—
48C2×C22⋊D149—21no—
49C2×C4×D149—21no—
50#14558724—42no—
51#14558721—42no—
52#14558720—42no—
53C2×#11924746C2312yes—
54C2×#11924746C2312yes—
55C4⋊Dic149C2311yescharacteristic
56C4⋊Dic149C2311yescharacteristic
57#14558715—21no—
58#14558715—21no—
59C22⋊Dic149—21no—
60C22⋊Dic149—21no—
61C22⋊Dic149—21no—
62#14558713—21no—
63#14558713—21no—
64C4×Dic149—21no—
65C24×C149—21no—
66C24×C149D411yescharacteristic
67C2×D4×C149—22no—
68C2×D4×C149—22no—
69C2×D4×C149—21no—
70C2×D4×C149—42no—
71C2×D4×C149—44no—
72C2×D4×C149C2312yes—
73C22×C4×C149—21no—
74C22×C4×C149—42no—
75C22×C4×C149D411yescharacteristic
76C22×C4×C149D411yescharacteristic
77C22×C4×C149D411yescharacteristic
78C22×C4×C149C2311yescharacteristic
79C22×C4×C149C2311yescharacteristic
80C22×C4×C149C2311yescharacteristic
81C4⋊C4×C149—21no—
82C4⋊C4×C149C2312yes—
83C22⋊C4×C149—22no—
84C22⋊C4×C149—22no—
85C22×D149—21no—
86Dic298—22no—
87D596—22no—
88C22⋊D149—42no—
89C22⋊D149—42no—
90C22⋊D149—42no—
91C2×Dic149—21no—
92C2×Dic149—21no—
93C2×Dic149—21no—
94C4×D149—42no—
95#11924746—22no—
96#11924746—22no—
97C23×C149—22no—
98C23×C149—22no—
99C23×C149—41no—
100C23×C149—41no—
101C23×C149—42no—
102C23×C149—42no—
103C23×C149—42no—
104C23×C149C2×D411yescharacteristic
105C23×C149C2×D411yescharacteristic
106C23×C149C2×D411yescharacteristic
107D4×C149—22no—
108D4×C149—22no—
109D4×C149—42no—
110D4×C149—44no—
111D4×C149—44no—
112C2×C4×C149—22no—
113C2×C4×C149—22no—
114C2×C4×C149—22no—
115C2×C4×C149—22no—
116C2×C4×C149—41no—
117C2×C4×C149—41no—
118C2×C4×C149—41no—
119C2×C4×C149—42no—
120C2×C4×C149C2×D411yescharacteristic
121C2×C4×C149C2×D411yescharacteristic
122C2×C4×C149C2×D411yescharacteristic
123C2×C4×C149C2411yescharacteristic
124C22×C149—21no—
125C22×C149—21no—
126C22×C149—21no—
127C22×C149—21no—
128C22×C149—21no—
129C22×C149—21no—
130C22×C149—21no—
131C22×C149—21no—
132C22×C149—44no—
133C22×C149—42no—
134C22×C149—42no—
135C22×C149—42no—
136C22×C149—84no—
137C22×C149AGL(1,ℤ/8)12yes—
138C22×C149C22×D411yescharacteristic
139C2×D149—41no—
140C2×D149—41no—
141C2×D149—41no—
142C4×C149—21no—
143C4×C149—21no—
144C4×C149—21no—
145C4×C149—42no—
146C4×C149H(5,𝔽2)12yes—
147Dic149—41no—
148Dic149—41no—
149Dic149—41no—
150C2×C149—22no—
151C2×C149—41no—
152C2×C149—41no—
153C2×C149—82no—
154C2×C149#53411yescharacteristic
155C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
156C2×C149#57511yescharacteristic
157D149—81no—
158C149#319411yescharacteristic, complemented, Sylow
159#3194—1491nomaximal, Sylow
160#525—1491no—
161C2×#121D14911yescharacteristic, complemented
162#483—1491no—
163#482—1492no—
164#480—1491no—
165#469—1492no—
166#468—1492no—
167#450—1491no—
168#449—1492no—
169#447—1491no—
170#407—1491no—
171C2×#41—1491no—
172C22×D4—21no—
173C22×D4C2×D14911yescharacteristic
174C23×C4C2×D14911yescharacteristic
175C2×SD16—1492no—
176C2×D8—1492no—
177C2×M16—1492no—
178#123—2981no—
179C22⋊Q8—1491no—
180C22⋊Q8—1491no—
181#121—21no—
182#121—21no—
183#121—1491no—
184#121—1491no—
185#121C2×D14912yes—
186#121C2×D14912yes—
187#120—2981no—
188C4×D4—2981no—
189C4×D4—2981no—
190#117—1491no—
191C2×C4⋊C4C2×D14911yescharacteristic
192C2×C22⋊C4—21no—
193#107—1492no—
194#106—1492no—
195#103—1492no—
196#102—1492no—
197#102—1492no—
198#102—1492no—
199C22⋊C8—1491no—
200C22⋊C8—1491no—
201C22⋊C8—1492no—
202C24—21no—
203C24C22⋊D14911yescharacteristic
204#41—5962no—
205C2×Q8—1491no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—21no—
209C2×D4—42no—
210C2×D4—44no—
211C2×D4—2981no—
212C2×D4—2981no—
213C2×D4—2981no—
214C2×D4—1491no—
215C2×D4C22×D14912yes—
216C22×C4—21no—
217C22×C4—42no—
218C22×C4—2981no—
219C22×C4C22⋊D14911yescharacteristic
220C22×C4C22⋊D14911yescharacteristic
221C22×C4C22⋊D14911yescharacteristic
222C22×C4C22×D14911yescharacteristic
223C22×C4C22×D14911yescharacteristic
224C22×C4C22×D14911yescharacteristic
225SD16—5962no—
226D8—5962no—
227M16—5962no—
228C2×C8—1492no—
229C2×C8—1492no—
230C4⋊C4—21no—
231C4⋊C4—2981no—
232C4⋊C4—2981no—
233C4⋊C4—1491no—
234C4⋊C4—1491no—
235C4⋊C4C22×D14912yes—
236C22⋊C4—22no—
237C22⋊C4—22no—
238C22⋊C4—2981no—
239C22⋊C4—2981no—
240C22⋊C4—2981no—
241C22⋊C4—2981no—
242C22⋊C4—2981no—
243C42—2981no—
244C23—22no—
245C23—22no—
246C23—41no—
247C23—41no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—2981no—
252C23C2×C22⋊D14911yescharacteristic
253C23C2×C22⋊D14911yescharacteristic
254C23C2×C22⋊D14911yescharacteristic
255Q8—2982no—
256D4—22no—
257D4—22no—
258D4—42no—
259D4—44no—
260D4—44no—
261D4—2982no—
262D4—5962no—
263D4—5962no—
264D4—5962no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—2981no—
274C2×C4—2981no—
275C2×C4—2981no—
276C2×C4—5962no—
277C2×C4C2×C22⋊D14911yescharacteristic
278C2×C4C2×C22⋊D14911yescharacteristic
279C2×C4C2×C22⋊D14911yescharacteristic
280C2×C4C23×D14911yescharacteristic
281C8—2982no—
282C8—2982no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—44no—
292C22—42no—
293C22—42no—
294C22—42no—
295C22—84no—
296C22—5961no—
297C22—5961no—
298C22—5961no—
299C22#1801193712yes—
300C22C22×C22⋊D14911yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—42no—
305C4—5961no—
306C4—5961no—
307C4—5961no—
308C4#1801195612yes—
309C2—22no—
310C2—41no—
311C2—41no—
312C2—82no—
313C2—11921no—
314C2#2375018411yescharacteristic
315C2C2×#1801193711yescharacteristic
316C2#2375042311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#121×C149C2
socleC22×C149C22×D4
hypercenterC2×#121D149
hypocenterC149#3194
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. #23750136C2semidirect
2. #23749955C2semidirect
3. #23749946C2semidirect
4. #23749938C2semidirect
5. #23749876C2semidirect
6. #23749869C2semidirect
7. #23749776C2semidirect
8. #23749768C2semidirect
9. #23749759C2semidirect
10. #23749589C2semidirect
11. C2×#121×C149C2semidirect
12. C2×#14558736C22semidirect
13. C2×#14558724C22semidirect
14. C2×#14558721C22semidirect
15. C2×#14558720C22semidirect
18. #18011890C22semidirect
20. #18011885C22semidirect
24. #18011870C22semidirect
25. #18011844C22semidirect
26. #18011842C22semidirect
27. #18011834C22semidirect
28. #18011832C22semidirect
29. #18011832C22semidirect
30. #18011831C22semidirect
33. C22⋊#11924746C22semidirect
158. C149#3194semidirect
161. C2×#121D149semidirect

Maximal subgroups

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

subgroupindex
#237501362
#237499552
#237499462
#237499382
#237498762
#237498692
#237497762
#237497682
#237497592
#237495892
C2×#121×C1492
#3194149