Finite Group Databasebeta

← #34055471

Subgroups — #34055471

Order 19072.

420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 115 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#23750135C211yesmaximal, characteristic
2C2×#18011891C211yesmaximal, characteristic, complemented
3#23749968C212yesmaximal, complemented
4#23749955C211yesmaximal, characteristic, complemented
5#23749867C212yesmaximal, complemented
6#23749853C212yesmaximal, complemented
7#23749788C212yesmaximal, complemented
8#23749783C211yesmaximal, characteristic, complemented
9#23749763C211yesmaximal, characteristic, complemented
10C22⋊C8×D149C211yesmaximal, characteristic, complemented
11#480×C149C211yesmaximal, characteristic, complemented
12C2×#14558735C2211yescharacteristic
13C22×Dic298C2211yescharacteristic
14C22×C4×D149C2211yescharacteristic
15C2×Dic596C2212yescomplemented
16C2×#14558724C2212yescomplemented
17C2×C8×D149C2212yes—
18#18011893—21no—
19#18011891—21no—
20#18011891—21no—
21#18011891C2212yes—
22#18011891C2212yes—
23#18011891C2211yescharacteristic
24#18011890C2211yescharacteristic
25#18011882C2211yescharacteristic
26#18011879—21no—
27D4×Dic149—21no—
28#18011871—21no—
29#18011869C2211yescharacteristic
30C2×C4⋊Dic149—21no—
31C2×#14558713—21no—
32#18011842C2212yescomplemented
33#18011836C2212yescomplemented
34#18011834C2212yescomplemented
35#18011834C2212yescomplemented
36C22⋊#11924746C2211yescharacteristic
37#18011823C2212yes—
38#121×C149C2211yescharacteristic
39C2×C4⋊C4×C149C2211yescharacteristic
40#107×C149C2212yescomplemented
41#102×C149C2212yescomplemented
42C22⋊C8×C149C2211yescharacteristic
43C23×D149D411yescharacteristic
44#14558735—42no—
45C2×Dic298—21no—
46C2×Dic298—42no—
47C2×Dic298C2312yes—
48C2×Dic298C2311yescharacteristic
49C2×C22⋊D149—21no—
50C2×C22⋊D149—21no—
51C22×Dic149—21no—
52C22×Dic149—21no—
53C22×Dic149D411yescharacteristic
54C2×C4×D149—42no—
55C2×C4×D149D411yescharacteristic
56C2×C4×D149D411yescharacteristic
57C2×C4×D149C2311yescharacteristic
58C2×C4×D149C2311yescharacteristic
59Dic596—42no—
60#14558724—42no—
61C2×#11924746C2312yes—
62C8×D149—42no—
63C4⋊Dic149—22no—
64C4⋊Dic149—22no—
65C4⋊Dic149—21no—
66C4⋊Dic149C2311yescharacteristic
67#14558715—21no—
68C22⋊Dic149—21no—
69C22⋊Dic149—21no—
70#14558713—22no—
71#14558713—22no—
72#14558713—21no—
73#14558713—21no—
74C4×Dic149—21no—
75C2×D4×C149—21no—
76C2×D4×C149C2311yescharacteristic
77C22×C4×C149—21no—
78C22×C4×C149C2311yescharacteristic
79C2×C8×C149C2312yes—
80C4⋊C4×C149—21no—
81C4⋊C4×C149C2312yes—
82C4⋊C4×C149C2311yescharacteristic
83C22⋊C4×C149—21no—
84C22×D149—22no—
85C22×D149—22no—
86C22×D149—41no—
87C22×D149C2×D411yescharacteristic
88C22×D149C2×D411yescharacteristic
89Dic298—22no—
90Dic298—22no—
91Dic298—22no—
92Dic298—42no—
93C22⋊D149—42no—
94C22⋊D149—42no—
95C2×Dic149—21no—
96C2×Dic149—22no—
97C2×Dic149—21no—
98C2×Dic149—41no—
99C2×Dic149—42no—
100C2×Dic149—42no—
101C2×Dic149C2×D411yescharacteristic
102C2×Dic149C2×D411yescharacteristic
103C4×D149—22no—
104C4×D149—22no—
105C4×D149—41no—
106C4×D149—41no—
107#11924746—22no—
108C23×C149—21no—
109C23×C149C2×D411yescharacteristic
110D4×C149—22no—
111D4×C149—42no—
112C2×C4×C149—22no—
113C2×C4×C149—21no—
114C2×C4×C149—22no—
115C2×C4×C149—42no—
116C2×C4×C149C2×D411yescharacteristic
117C2×C4×C149C2411yescharacteristic
118C8×C149—22no—
119C22×C149—21no—
120C22×C149—21no—
121C22×C149—41no—
122C22×C149—41no—
123C22×C149—41no—
124C22×C149#13512yes—
125C22×C149C22×D411yescharacteristic
126C2×D149—21no—
127C2×D149—21no—
128C2×D149—21no—
129C2×D149—21no—
130C2×D149—21no—
131C2×D149—44no—
132C2×D149#13712yes—
133C4×C149—21no—
134C4×C149—42no—
135C4×C149—41no—
136C4×C149H(5,𝔽2)12yes—
137Dic149—21no—
138Dic149—21no—
139Dic149—41no—
140Dic149—42no—
141Dic149—41no—
142C2×C149—22no—
143C2×C149—81no—
144C2×C149#53411yescharacteristic
145C2×C149C2×#13511yescharacteristic
146C2×C149C2×#13711yescharacteristic
147D149—22no—
148D149—41no—
149C149#319011yescharacteristic, complemented, Sylow
150#3190—1491nomaximal, Sylow
151#525—1491no—
152C2×C22⋊Q8—1491no—
153#485—1492no—
154#483—1491no—
155#480D14911yescharacteristic, complemented
156#467—1492no—
157#465—1492no—
158#452—1492no—
159#451—1491no—
160#448—1491no—
161C2×C22⋊C8—1491no—
162C2×#41—1491no—
163C22×Q8—1491no—
164C23×C4—1491no—
165C2×Q16—1492no—
166C2×SD16—1492no—
167C22×C8—1492no—
168#123—2981no—
169C22⋊Q8—2981no—
170C22⋊Q8—2981no—
171C22⋊Q8—1491no—
172C22⋊Q8—1492no—
173C22⋊Q8—1492no—
174C22⋊Q8—1491no—
175#121—1491no—
176#121C2×D14911yescharacteristic
177#120—2981no—
178C4×D4—2981no—
179C4×D4—2981no—
180#117—1491no—
181C2×C4⋊C4—2981no—
182C2×C4⋊C4C2×D14911yescharacteristic
183C2×C22⋊C4—2981no—
184#107C2×D14912yescomplemented
185#106—1492no—
186#103—1492no—
187#103—1492no—
188#103—1492no—
189#102C2×D14912yescomplemented
190C22⋊C8—1491no—
191C22⋊C8—1492no—
192C22⋊C8C2×D14911yescharacteristic
193C24—1491no—
194#41—5962no—
195C2×Q8—2981no—
196C2×Q8—5962no—
197C2×Q8—1492no—
198C2×Q8—1491no—
199C2×D4—21no—
200C2×D4—2981no—
201C2×D4—2981no—
202C2×D4C22×D14911yescharacteristic
203C22×C4—21no—
204C22×C4—2981no—
205C22×C4—2981no—
206C22×C4—5962no—
207C22×C4—1491no—
208C22×C4—1491no—
209C22×C4—1491no—
210C22×C4—1491no—
211C22×C4—1491no—
212C22×C4C22×D14911yescharacteristic
213Q16—5962no—
214SD16—5962no—
215C2×C8—5962no—
216C2×C8—1492no—
217C2×C8C22×D14912yes—
218C4⋊C4—21no—
219C4⋊C4—2982no—
220C4⋊C4—2982no—
221C4⋊C4—2981no—
222C4⋊C4—2981no—
223C4⋊C4—1491no—
224C4⋊C4C22×D14912yes—
225C4⋊C4C22×D14911yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—2982no—
228C22⋊C4—2982no—
229C22⋊C4—2981no—
230C22⋊C4—2981no—
231C22⋊C4—2981no—
232C22⋊C4—2981no—
233C42—2981no—
234C23—21no—
235C23—2982no—
236C23—2982no—
237C23—5961no—
238C23—1491no—
239C23—1491no—
240C23D4×D14911yescharacteristic
241Q8—2982no—
242Q8—2982no—
243Q8—2982no—
244Q8—5962no—
245D4—22no—
246D4—42no—
247D4—5962no—
248D4—5962no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—2982no—
254C2×C4—2982no—
255C2×C4—2981no—
256C2×C4—2981no—
257C2×C4—2982no—
258C2×C4—5961no—
259C2×C4—5961no—
260C2×C4—5961no—
261C2×C4—5962no—
262C2×C4—5962no—
263C2×C4—1491no—
264C2×C4—1491no—
265C2×C4D4×D14911yescharacteristic
266C2×C4C23×D14911yescharacteristic
267C8—22no—
268C8—2982no—
269C22—21no—
270C22—21no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—2981no—
275C22—2981no—
276C22—2981no—
277C22—2981no—
278C22—2981no—
279C22—5964no—
280C22—1492no—
281C22#1801193012yes—
282C22C2×D4×D14911yescharacteristic
283C4—21no—
284C4—42no—
285C4—41no—
286C4—2981no—
287C4—2981no—
288C4—5961no—
289C4—5961no—
290C4—5962no—
291C4#1801195712yes—
292C2—22no—
293C2—81no—
294C2—2982no—
295C2—5961no—
296C2#2375018611yescharacteristic
297C2C2×#1801193011yescharacteristic
298C2#137×D14911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#480×C149C2
socleC22×C149C22×D4
prime radical#23750135C2
hypercenter#480D149
hypocenterC149#3190
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#18011891C2semidirect
3. #23749968C2semidirect
4. #23749955C2semidirect
5. #23749867C2semidirect
6. #23749853C2semidirect
7. #23749788C2semidirect
8. #23749783C2semidirect
9. #23749763C2semidirect
10. C22⋊C8×D149C2semidirect
11. #480×C149C2semidirect
15. C2×Dic596C22semidirect
16. C2×#14558724C22semidirect
32. #18011842C22semidirect
33. #18011836C22semidirect
34. #18011834C22semidirect
35. #18011834C22semidirect
40. #107×C149C22semidirect
41. #102×C149C22semidirect
149. C149#3190semidirect
155. #480D149semidirect
184. #107C2×D149semidirect
189. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501352
C2×#180118912
#237499682
#237499552
#237498672
#237498532
#237497882
#237497832
#237497632
C22⋊C8×D1492
#480×C1492
#3190149