Finite Group Databasebeta

← #34055501

Subgroups — #34055501

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
1C2×#18011885C211yesmaximal, characteristic, complemented
2#23749953C211yesmaximal, characteristic, complemented
3#23749949C212yesmaximal, complemented
4#23749936C211yesmaximal, characteristic, complemented
5#23749876C212yesmaximal, complemented
6#23749873C212yesmaximal, complemented
7#23749775C211yesmaximal, characteristic, complemented
8#23749770C212yesmaximal, complemented
9#23749758C211yesmaximal, characteristic, complemented
10#23749589C211yesmaximal, characteristic, complemented
11#525×C149C211yesmaximal, characteristic, complemented
12C22×D596C2211yescharacteristic
13C22×C22⋊D149—21no—
14C2×#14558723C2212yescomplemented
15C2×#14558721C2212yescomplemented
16C2×#14558720C2212yescomplemented
17#18011885—21no—
18#18011885—21no—
19#18011885C2212yes—
20#18011885C2212yes—
21C2×C4⋊Dic149C2211yescharacteristic
22C2×#14558713—21no—
23#18011844C2212yescomplemented
24#18011842C2212yescomplemented
25#18011835C2212yescomplemented
26#18011832C2212yescomplemented
27#18011831C2212yescomplemented
28#18011831C2212yescomplemented
29C22⋊#11924746C2211yescharacteristic
30C22⋊#11924746C2211yescharacteristic
31C22⋊#11924746C2212yescomplemented
32C2×#41×C149C2211yescharacteristic, complemented
33C23×C4×C149C2211yescharacteristic
34#123×C149—21no—
35C22⋊Q8×C149C2211yescharacteristic
36C22⋊Q8×C149C2211yescharacteristic, complemented
37#121×C149C2211yescharacteristic
38#121×C149C2211yescharacteristic, complemented
39#120×C149—21no—
40C4×D4×C149—21no—
41C4×D4×C149—21no—
42#117×C149C2211yescharacteristic, complemented
43C23×D149—21no—
44C2×D596—21no—
45C2×D596—42no—
46C2×D596C2312yes—
47C2×C22⋊D149—22no—
48C2×C22⋊D149—22no—
49C2×C22⋊D149—44no—
50C22×Dic149—21no—
51#14558723—42no—
52#14558721—42no—
53#14558720—42no—
54C2×#11924746C2312yes—
55C2×#11924746C2312yes—
56C4⋊Dic149—21no—
57C4⋊Dic149C2312yes—
58#14558713—22no—
59#14558713—22no—
60C24×C149D411yescharacteristic
61#41×C149—42no—
62C2×Q8×C149C2311yescharacteristic
63C2×D4×C149—21no—
64C2×D4×C149—21no—
65C2×D4×C149—21no—
66C2×D4×C149C2311yescharacteristic
67C22×C4×C149—21no—
68C22×C4×C149—42no—
69C22×C4×C149D411yescharacteristic
70C22×C4×C149D411yescharacteristic
71C22×C4×C149D411yescharacteristic
72C22×C4×C149C2311yescharacteristic
73C22×C4×C149C2311yescharacteristic
74C22×C4×C149C2311yescharacteristic
75C4⋊C4×C149—21no—
76C4⋊C4×C149—21no—
77C4⋊C4×C149C2311yescharacteristic
78C4⋊C4×C149C2311yescharacteristic
79C22⋊C4×C149—21no—
80C22⋊C4×C149—21no—
81C22⋊C4×C149—21no—
82C22⋊C4×C149—21no—
83C22⋊C4×C149—21no—
84C42×C149—21no—
85C22×D149—22no—
86C22×D149—42no—
87C22×D149—42no—
88C22×D149—42no—
89D596—22no—
90D596—22no—
91D596—42no—
92C22⋊D149—44no—
93C22⋊D149—44no—
94C2×Dic149—22no—
95C2×Dic149—42no—
96#11924746—22no—
97#11924746—22no—
98C23×C149—22no—
99C23×C149—21no—
100C23×C149—41no—
101C23×C149—41no—
102C23×C149C2×D411yescharacteristic
103C23×C149C2×D411yescharacteristic
104C23×C149C2×D411yescharacteristic
105Q8×C149—22no—
106D4×C149—22no—
107D4×C149—42no—
108D4×C149—42no—
109D4×C149—42no—
110C2×C4×C149—22no—
111C2×C4×C149—22no—
112C2×C4×C149—22no—
113C2×C4×C149—21no—
114C2×C4×C149—21no—
115C2×C4×C149—21no—
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—41no—
134C22×C149—41no—
135C22×C149—41no—
136C22×C149AGL(1,ℤ/8)12yes—
137C22×C149C22×D411yescharacteristic
138C2×D149—42no—
139C2×D149—42no—
140C2×D149—42no—
141C2×D149—84no—
142C4×C149—21no—
143C4×C149—21no—
144C4×C149—21no—
145C4×C149—41no—
146C4×C149—41no—
147C4×C149—41no—
148C4×C149H(5,𝔽2)12yes—
149Dic149—42no—
150C2×C149—22no—
151C2×C149—41no—
152C2×C149—41no—
153C2×C149—81no—
154C2×C149#53411yescharacteristic
155C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
156C2×C149#57511yescharacteristic
157D149—82no—
158C149#319411yescharacteristic, complemented, Sylow
159#3194—1491nomaximal, Sylow
160#525D14911yescharacteristic, complemented
161C2×#121—1491no—
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×#41C2×D14911yescharacteristic, complemented
172C22×D4—2981no—
173C22×D4—1491no—
174C23×C4C2×D14911yescharacteristic
175C2×SD16—1492no—
176C2×D8—1492no—
177C2×M16—1492no—
178#123—21no—
179C22⋊Q8C2×D14911yescharacteristic
180C22⋊Q8C2×D14911yescharacteristic, complemented
181#121—2981no—
182#121—2981no—
183#121—1492no—
184#121—1492no—
185#121C2×D14911yescharacteristic
186#121C2×D14911yescharacteristic, complemented
187#120—21no—
188C4×D4—21no—
189C4×D4—21no—
190#117C2×D14911yescharacteristic, complemented
191C2×C4⋊C4—1491no—
192C2×C22⋊C4—2981no—
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—2981no—
203C24C22⋊D14911yescharacteristic
204#41—42no—
205C2×Q8C22×D14911yescharacteristic
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—21no—
209C2×D4—2982no—
210C2×D4—2982no—
211C2×D4—2981no—
212C2×D4—5962no—
213C2×D4—5964no—
214C2×D4—1492no—
215C2×D4C22×D14911yescharacteristic
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—21no—
232C4⋊C4—2981no—
233C4⋊C4—1492no—
234C4⋊C4C22×D14911yescharacteristic
235C4⋊C4C22×D14911yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—21no—
238C22⋊C4—21no—
239C22⋊C4—21no—
240C22⋊C4—21no—
241C22⋊C4—2982no—
242C22⋊C4—2982no—
243C42—21no—
244C23—22no—
245C23—21no—
246C23—41no—
247C23—41no—
248C23—2982no—
249C23—5962no—
250C23—5962no—
251C23—5962no—
252C23C2×C22⋊D14911yescharacteristic
253C23C2×C22⋊D14911yescharacteristic
254C23C2×C22⋊D14911yescharacteristic
255Q8—22no—
256D4—22no—
257D4—42no—
258D4—42no—
259D4—42no—
260D4—2982no—
261D4—2982no—
262D4—5962no—
263D4—5964no—
264D4—5964no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—2982no—
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—41no—
293C22—41no—
294C22—41no—
295C22—5962no—
296C22—5962no—
297C22—5962no—
298C22—11924no—
299C22#1801193612yes—
300C22C22×C22⋊D14911yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—5962no—
308C4#1801195612yes—
309C2—22no—
310C2—41no—
311C2—41no—
312C2—81no—
313C2—11922no—
314C2#2375018411yescharacteristic
315C2C2×#1801193611yescharacteristic
316C2#2375042311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#525×C149C2
socleC22×C149C22×D4
hypercenter#525D149
hypocenterC149#3194
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#18011885C2semidirect
2. #23749953C2semidirect
3. #23749949C2semidirect
4. #23749936C2semidirect
5. #23749876C2semidirect
6. #23749873C2semidirect
7. #23749775C2semidirect
8. #23749770C2semidirect
9. #23749758C2semidirect
10. #23749589C2semidirect
11. #525×C149C2semidirect
14. C2×#14558723C22semidirect
15. C2×#14558721C22semidirect
16. C2×#14558720C22semidirect
23. #18011844C22semidirect
24. #18011842C22semidirect
25. #18011835C22semidirect
26. #18011832C22semidirect
27. #18011831C22semidirect
28. #18011831C22semidirect
31. C22⋊#11924746C22semidirect
32. C2×#41×C149C22semidirect
36. C22⋊Q8×C149C22semidirect
38. #121×C149C22semidirect
42. #117×C149C22semidirect
158. C149#3194semidirect
160. #525D149semidirect
171. C2×#41C2×D149semidirect
180. C22⋊Q8C2×D149semidirect
186. #121C2×D149semidirect
190. #117C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118852
#237499532
#237499492
#237499362
#237498762
#237498732
#237497752
#237497702
#237497582
#237495892
#525×C1492
#3194149