Finite Group Databasebeta

← #34054607

Subgroups — #34054607

Order 19072.

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

normal subgroups only

This group has 420 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#23750138C211yesmaximal, characteristic
2C2×#18011869C211yesmaximal, characteristic, complemented
3#23749965C212yesmaximal, complemented
4#23749953C211yesmaximal, characteristic, complemented
5#23749952C212yesmaximal, complemented
6#23749943C211yesmaximal, characteristic, complemented
7#23749939C211yesmaximal, characteristic, complemented
8#23749662C212yesmaximal, complemented
9#23749620C212yesmaximal, complemented
10C22⋊C8×D149C211yesmaximal, characteristic, complemented
11#484×C149C211yesmaximal, characteristic, complemented
12C2×#14558737C2211yescharacteristic
13C22×C4×D149C2211yescharacteristic
14C2×C8×D149C2212yes—
15#18011896—21no—
16#18011887C2211yescharacteristic
17#18011886C2211yescharacteristic
18#18011885C2211yescharacteristic
19#18011881—21no—
20#18011873—21no—
21#18011871—21no—
22#18011869—21no—
23#18011869—21no—
24#18011869C2211yescharacteristic
25#18011869C2212yes—
26#18011869C2212yes—
27C2×C4⋊Dic149C2211yescharacteristic
28C2×#14558713—21no—
29C2×C4×Dic149—21no—
30#18011845C2212yescomplemented
31#18011842C2212yescomplemented
32#18011842C2212yescomplemented
33#18011835C2212yescomplemented
34#18011833C2212yescomplemented
35#18011831C2212yescomplemented
36C22⋊#11924746C2211yescharacteristic
37#18011823C2212yes—
38C22⋊Q8×C149C2211yescharacteristic
39C2×C4⋊C4×C149C2211yescharacteristic
40#107×C149C2212yescomplemented
41#103×C149C2212yescomplemented
42C22⋊C8×C149C2211yescharacteristic
43C23×D149D411yescharacteristic
44#14558737—24no—
45C2×D596—21no—
46C2×D596—21no—
47C2×D596C2311yescharacteristic
48C2×C22⋊D149—21no—
49C22×Dic149—21no—
50C22×Dic149D411yescharacteristic
51C2×C4×D149—24no—
52C2×C4×D149—21no—
53C2×C4×D149D411yescharacteristic
54C2×C4×D149D411yescharacteristic
55C2×C4×D149C2311yescharacteristic
56C2×C4×D149C2311yescharacteristic
57C2×#11924746C2312yes—
58C8×D149—24no—
59C4⋊Dic149—21no—
60C4⋊Dic149C2312yes—
61C4⋊Dic149C2311yescharacteristic
62#14558715—21no—
63#14558713—22no—
64#14558713—22no—
65#14558713—21no—
66#14558713—21no—
67#14558713—21no—
68#14558713—21no—
69C4×Dic149—22no—
70C4×Dic149—22no—
71C4×Dic149—21no—
72C2×Q8×C149C2311yescharacteristic
73C22×C4×C149—21no—
74C22×C4×C149C2311yescharacteristic
75C2×C8×C149C2312yes—
76C4⋊C4×C149—21no—
77C4⋊C4×C149—21no—
78C4⋊C4×C149C2312yes—
79C4⋊C4×C149C2311yescharacteristic
80C22⋊C4×C149—21no—
81C22×D149—22no—
82C22×D149—22no—
83C22×D149—21no—
84C22×D149—41no—
85C22×D149C2×D411yescharacteristic
86C22×D149C2×D411yescharacteristic
87D596—22no—
88D596—42no—
89D596—42no—
90C22⋊D149—42no—
91C2×Dic149—22no—
92C2×Dic149—22no—
93C2×Dic149—21no—
94C2×Dic149—42no—
95C2×Dic149C2×D411yescharacteristic
96C2×Dic149C2×D411yescharacteristic
97C4×D149—22no—
98C4×D149—22no—
99C4×D149—22no—
100C4×D149—42no—
101C4×D149#4114yes—
102#11924746—22no—
103C23×C149C2×D411yescharacteristic
104Q8×C149—22no—
105C2×C4×C149—22no—
106C2×C4×C149—21no—
107C2×C4×C149—21no—
108C2×C4×C149—22no—
109C2×C4×C149—42no—
110C2×C4×C149C2×D411yescharacteristic
111C2×C4×C149C2411yescharacteristic
112C8×C149—22no—
113C22×C149—21no—
114C22×C149—21no—
115C22×C149#13512yes—
116C22×C149C22×D411yescharacteristic
117C2×D149—21no—
118C2×D149—21no—
119C2×D149—21no—
120C2×D149—21no—
121C2×D149—21no—
122C2×D149—44no—
123C2×D149—41no—
124C2×D149—41no—
125C2×D149—41no—
126C2×D149#12312yes—
127C4×C149—21no—
128C4×C149—41no—
129C4×C149—42no—
130C4×C149—41no—
131C4×C149C2×#4112yes—
132Dic149—21no—
133Dic149—42no—
134Dic149—41no—
135Dic149#12312yes—
136C2×C149—22no—
137C2×C149C2×#12311yescharacteristic
138C2×C149C2×#13511yescharacteristic
139C2×C149#57511yescharacteristic
140D149—22no—
141D149—41no—
142D149—81no—
143C149#309111yescharacteristic, complemented, Sylow
144#3091—1491nomaximal, Sylow
145#525—1491no—
146C2×#117—1491no—
147#485—1492no—
148#484D14911yescharacteristic, complemented
149#483—1491no—
150#482—1492no—
151#481—1491no—
152#480—1491no—
153#427—1492no—
154#416—1492no—
155C2×C22⋊C8—1491no—
156C2×#41—1491no—
157C23×C4—1491no—
158C22×C8—1492no—
159#123—2981no—
160C22⋊Q8—1491no—
161C22⋊Q8C2×D14911yescharacteristic
162#121—1491no—
163#121—1491no—
164#120—2981no—
165C4×D4—2981no—
166C4×D4—2981no—
167#117—2981no—
168#117—2981no—
169#117—1492no—
170#117—1492no—
171#117—1491no—
172C2×C4⋊C4—1491no—
173C2×C4⋊C4C2×D14911yescharacteristic
174C2×C22⋊C4—2981no—
175C2×C42—2981no—
176#107—1492no—
177#107C2×D14912yescomplemented
178#106—1492no—
179#106—1492no—
180#103—1492no—
181#103C2×D14912yescomplemented
182#102—1492no—
183#102—1492no—
184C22⋊C8—1491no—
185C22⋊C8—1492no—
186C22⋊C8C2×D14911yescharacteristic
187C24—1491no—
188#41—2984no—
189C2×Q8C22×D14911yescharacteristic
190C2×D4—2981no—
191C2×D4—2981no—
192C2×D4—2981no—
193C2×D4—1491no—
194C22×C4—21no—
195C22×C4—2984no—
196C22×C4—2981no—
197C22×C4—2981no—
198C22×C4—1491no—
199C22×C4—1491no—
200C22×C4—1491no—
201C22×C4—1491no—
202C22×C4—1491no—
203C22×C4C22×D14911yescharacteristic
204C2×C8—2984no—
205C2×C8—1492no—
206C2×C8C22×D14912yes—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—2981no—
210C4⋊C4—2981no—
211C4⋊C4—1492no—
212C4⋊C4—1491no—
213C4⋊C4C22×D14912yes—
214C4⋊C4C22×D14911yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—2982no—
217C22⋊C4—2982no—
218C22⋊C4—2981no—
219C22⋊C4—2981no—
220C22⋊C4—2981no—
221C22⋊C4—2981no—
222C42—2982no—
223C42—2982no—
224C42—2981no—
225C23—2982no—
226C23—2982no—
227C23—2981no—
228C23—5961no—
229C23—1491no—
230C23—1491no—
231C23D4×D14911yescharacteristic
232Q8—22no—
233D4—2982no—
234D4—5962no—
235D4—5962no—
236D4—5962no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—2982no—
243C2×C4—2982no—
244C2×C4—2982no—
245C2×C4—2982no—
246C2×C4—2982no—
247C2×C4—2981no—
248C2×C4—5962no—
249C2×C4—5962no—
250C2×C4—1491no—
251C2×C4—1491no—
252C2×C4—1494no—
253C2×C4D4×D14911yescharacteristic
254C2×C4C23×D14911yescharacteristic
255C8—22no—
256C8—2982no—
257C22—21no—
258C22—21no—
259C22—2981no—
260C22—2981no—
261C22—2981no—
262C22—2981no—
263C22—2981no—
264C22—5964no—
265C22—5961no—
266C22—5961no—
267C22—5961no—
268C22—1492no—
269C22#1801193412yes—
270C22C2×D4×D14911yescharacteristic
271C4—21no—
272C4—42no—
273C4—41no—
274C4—41no—
275C4—2981no—
276C4—5962no—
277C4—5961no—
278C4—1492no—
279C4#41×D14912yes—
280C2—22no—
281C2—2982no—
282C2—5961no—
283C2—11921no—
284C2#123×D14911yescharacteristic
285C2C2×#1801193411yescharacteristic
286C2#2375042111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#484×C149C2
socleC22×C149C22×D4
prime radical#23750138C2
hypercenter#484D149
hypocenterC149#3091
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×#18011869C2semidirect
3. #23749965C2semidirect
4. #23749953C2semidirect
5. #23749952C2semidirect
6. #23749943C2semidirect
7. #23749939C2semidirect
8. #23749662C2semidirect
9. #23749620C2semidirect
10. C22⋊C8×D149C2semidirect
11. #484×C149C2semidirect
30. #18011845C22semidirect
31. #18011842C22semidirect
32. #18011842C22semidirect
33. #18011835C22semidirect
34. #18011833C22semidirect
35. #18011831C22semidirect
40. #107×C149C22semidirect
41. #103×C149C22semidirect
143. C149#3091semidirect
148. #484D149semidirect
177. #107C2×D149semidirect
181. #103C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501382
C2×#180118692
#237499652
#237499532
#237499522
#237499432
#237499392
#237496622
#237496202
C22⋊C8×D1492
#484×C1492
#3091149