Finite Group Databasebeta

← #34054825

Subgroups — #34054825

Order 19072.

450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4×D596C211yesmaximal, characteristic, complemented
2#23749953C211yesmaximal, characteristic, complemented
3#23749936C211yesmaximal, characteristic, complemented
4#23749922C212yesmaximal, complemented
5#23749837C212yesmaximal, complemented
6#23749775C211yesmaximal, characteristic, complemented
7#23749758C211yesmaximal, characteristic
8#23749735C212yesmaximal, complemented
9#23749723C212yesmaximal, complemented
10#23749682C211yesmaximal, characteristic, complemented
11#529×C149C211yesmaximal, characteristic, complemented
12C22×D596C2211yescharacteristic
13C22×C4×D149—21no—
14C2×#14558723C2212yes—
15C2×#14558721C2212yes—
16C4×D596—21no—
17C4×D596—21no—
18C4×D596C2212yes—
19C4×D596C2212yes—
20C2×C4⋊Dic149C2211yescharacteristic
21C2×#14558713—21no—
22#18011844C2212yescomplemented
23#18011842C2212yescomplemented
24C4⋊#11924746C2212yescomplemented
25#18011835C2212yescomplemented
26#18011832C2212yescomplemented
27#18011831C2212yes—
28#18011831C2212yes—
29C22⋊#11924746C2211yescharacteristic
30C22⋊#11924746C2211yescharacteristic
31#18011822C2212yescomplemented
32#126×C149—21no—
33#125×C149C2211yescharacteristic, complemented
34#124×C149C2211yescharacteristic, complemented
35#123×C149—21no—
36C22⋊Q8×C149C2211yescharacteristic
37#121×C149C2211yescharacteristic
38C4×Q8×C149C2211yescharacteristic, complemented
39C4×D4×C149—21no—
40C4×D4×C149C2211yescharacteristic, complemented
41#117×C149—21no—
42C2×C42×C149C2211yescharacteristic
43C23×D149—21no—
44C2×D596—24no—
45C2×D596—21no—
46C2×D596C2312yes—
47C22×Dic149—21no—
48C2×C4×D149—22no—
49C2×C4×D149—22no—
50C2×C4×D149—44no—
51#14558723—24no—
52#14558721—24no—
53C2×#11924746C2312yes—
54C2×#11924746C2312yes—
55C4⋊Dic149—21no—
56C4⋊Dic149C2312yes—
57#14558713—22no—
58#14558713—22no—
59C2×Q8×C149C2311yescharacteristic
60C2×D4×C149—21no—
61C2×D4×C149C2311yescharacteristic
62C22×C4×C149—21no—
63C22×C4×C149D411yescharacteristic
64C22×C4×C149D411yescharacteristic
65C22×C4×C149C2311yescharacteristic
66C4⋊C4×C149—21no—
67C4⋊C4×C149—21no—
68C4⋊C4×C149—21no—
69C4⋊C4×C149—21no—
70C4⋊C4×C149C2311yescharacteristic
71C4⋊C4×C149C2311yescharacteristic
72C22⋊C4×C149—21no—
73C22⋊C4×C149—21no—
74C22⋊C4×C149—21no—
75C22⋊C4×C149—21no—
76C22⋊C4×C149—21no—
77C42×C149—21no—
78C42×C149D411yescharacteristic
79C42×C149D411yescharacteristic
80C42×C149C2311yescharacteristic
81C42×C149C2311yescharacteristic
82C22×D149—24no—
83C22×D149—22no—
84C22×D149—42no—
85C22×D149—42no—
86D596—24no—
87D596—22no—
88D596#4114yes—
89C2×Dic149—22no—
90C2×Dic149—42no—
91C4×D149—44no—
92C4×D149—44no—
93#11924746—22no—
94#11924746—22no—
95C23×C149—21no—
96C23×C149C2×D411yescharacteristic
97Q8×C149—22no—
98D4×C149—22no—
99D4×C149—42no—
100C2×C4×C149—22no—
101C2×C4×C149—22no—
102C2×C4×C149—21no—
103C2×C4×C149—21no—
104C2×C4×C149—21no—
105C2×C4×C149—41no—
106C2×C4×C149—42no—
107C2×C4×C149C2×D411yescharacteristic
108C2×C4×C149C2×D411yescharacteristic
109C2×C4×C149C2×D411yescharacteristic
110C2×C4×C149C2×D411yescharacteristic
111C2×C4×C149C2×D411yescharacteristic
112C2×C4×C149C2411yescharacteristic
113C22×C149—21no—
114C22×C149—21no—
115C22×C149—41no—
116C22×C149—41no—
117C22×C149—41no—
118C22×C149AGL(1,ℤ/8)12yes—
119C22×C149C22×D411yescharacteristic
120C2×D149—24no—
121C2×D149—48no—
122C2×D149—42no—
123C2×D149—42no—
124C4×C149—21no—
125C4×C149—21no—
126C4×C149—21no—
127C4×C149—21no—
128C4×C149—21no—
129C4×C149—41no—
130C4×C149—41no—
131C4×C149—41no—
132C4×C149C2×#4112yes—
133Dic149—42no—
134C2×C149—22no—
135C2×C149—81no—
136C2×C149#52511yescharacteristic
137C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C149#57511yescharacteristic
139D149—44no—
140C149#311411yescharacteristic, complemented, Sylow
141#3114—1491nomaximal, Sylow
142#529D14911yescharacteristic, complemented
143C2×C4×D4—1491no—
144#483—1491no—
145#480—1491no—
146#478—1492no—
147#463—1492no—
148#450—1491no—
149#447—1491no—
150#442—1492no—
151#440—1492no—
152#432—1491no—
153C22×D4—1491no—
154C23×C4—2981no—
155C2×SD16—1492no—
156C2×D8—1492no—
157#126—21no—
158#125C2×D14911yescharacteristic, complemented
159#124C2×D14911yescharacteristic, complemented
160#123—21no—
161C22⋊Q8C2×D14911yescharacteristic
162#121C2×D14911yescharacteristic
163C4×Q8C2×D14911yescharacteristic, complemented
164C4×D4—21no—
165C4×D4—2981no—
166C4×D4—2981no—
167C4×D4—1492no—
168C4×D4—1492no—
169C4×D4C2×D14911yescharacteristic, complemented
170#117—21no—
171C2×C4⋊C4—1491no—
172C2×C22⋊C4—2981no—
173C2×C42C2×D14911yescharacteristic
174#107—1492no—
175#106—1492no—
176C4⋊C8—1492no—
177#103—1492no—
178#102—1492no—
179#102—1492no—
180#102—1492no—
181C22⋊C8—1491no—
182C22⋊C8—1491no—
183#97—1492no—
184C24—2981no—
185C2×Q8C22×D14911yescharacteristic
186C2×D4—21no—
187C2×D4—2984no—
188C2×D4—2981no—
189C2×D4—1492no—
190C2×D4C22×D14911yescharacteristic
191C22×C4—21no—
192C22×C4—2981no—
193C22×C4—2982no—
194C22×C4—2982no—
195C22×C4—5964no—
196C22×C4C22⋊D14911yescharacteristic
197C22×C4C22⋊D14911yescharacteristic
198C22×C4C22×D14911yescharacteristic
199SD16—2984no—
200D8—2984no—
201C2×C8—1492no—
202C2×C8—1492no—
203C4⋊C4—21no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—2981no—
208C4⋊C4—1492no—
209C4⋊C4C22×D14911yescharacteristic
210C4⋊C4C22×D14911yescharacteristic
211C22⋊C4—21no—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—21no—
216C22⋊C4—2982no—
217C22⋊C4—2982no—
218C42—21no—
219C42C22⋊D14911yescharacteristic
220C42C22⋊D14911yescharacteristic
221C42C22×D14911yescharacteristic
222C42C22×D14911yescharacteristic
223C23—21no—
224C23—2984no—
225C23—2982no—
226C23—5962no—
227C23—5962no—
228C23C2×C22⋊D14911yescharacteristic
229Q8—22no—
230D4—22no—
231D4—42no—
232D4—2984no—
233D4—2982no—
234D4—1494no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—2982no—
243C2×C4—5964no—
244C2×C4—5964no—
245C2×C4—5962no—
246C2×C4C2×C22⋊D14911yescharacteristic
247C2×C4C2×C22⋊D14911yescharacteristic
248C2×C4C2×C22⋊D14911yescharacteristic
249C2×C4C2×C22⋊D14911yescharacteristic
250C2×C4C2×C22⋊D14911yescharacteristic
251C2×C4C23×D14911yescharacteristic
252C8—2982no—
253C8—2982no—
254C22—21no—
255C22—21no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—2984no—
260C22—5968no—
261C22—5962no—
262C22—5962no—
263C22#1801193612yes—
264C22C22×C22⋊D14911yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—41no—
271C4—41no—
272C4—41no—
273C4—5962no—
274C4#41×D14912yes—
275C2—22no—
276C2—81no—
277C2—5964no—
278C2#2375013211yescharacteristic
279C2C2×#1801193611yescharacteristic
280C2#2375042311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#529×C149C2
socleC22×C149C22×D4
prime radical#23749758C2
hypercenter#529D149
hypocenterC149#3114
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C2×C4×D596C2semidirect
2. #23749953C2semidirect
3. #23749936C2semidirect
4. #23749922C2semidirect
5. #23749837C2semidirect
6. #23749775C2semidirect
8. #23749735C2semidirect
9. #23749723C2semidirect
10. #23749682C2semidirect
11. #529×C149C2semidirect
22. #18011844C22semidirect
23. #18011842C22semidirect
24. C4⋊#11924746C22semidirect
25. #18011835C22semidirect
26. #18011832C22semidirect
31. #18011822C22semidirect
33. #125×C149C22semidirect
34. #124×C149C22semidirect
38. C4×Q8×C149C22semidirect
40. C4×D4×C149C22semidirect
140. C149#3114semidirect
142. #529D149semidirect
158. #125C2×D149semidirect
159. #124C2×D149semidirect
163. C4×Q8C2×D149semidirect
169. C4×D4C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D5962
#237499532
#237499362
#237499222
#237498372
#237497752
#237497582
#237497352
#237497232
#237496822
#529×C1492
#3114149