Finite Group Databasebeta

← #34055679

Subgroups — #34055679

Order 19072.

444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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#23750176C211yesmaximal, characteristic, complemented
2#124×D149C211yesmaximal, characteristic, complemented
3#23750015C211yesmaximal, characteristic, complemented
4#23750014C211yesmaximal, characteristic, complemented
5#23749987C211yesmaximal, characteristic, complemented
6#23749843C212yesmaximal, complemented
7#23749839C212yesmaximal, complemented
8#23749765C212yesmaximal, complemented
9#23749760C212yesmaximal, complemented
10#23749680C211yesmaximal, characteristic, complemented
11#489×C149C211yesmaximal, characteristic, complemented
12C2×#14558737—21no—
13C2×Q8×D149C2211yescharacteristic
14C2×D4×D149C2211yescharacteristic
15C2×#14558725C2212yescomplemented
16C2×#14558723C2212yescomplemented
17C2×D1192C2212yes—
18C2×#14558721C2212yes—
19#18011908C2211yescharacteristic, complemented
20#18011900—21no—
21#18011900C2211yescharacteristic
22#18011899C2211yescharacteristic
23#18011898C2211yescharacteristic
24#18011897—21no—
25#18011897—21no—
26#18011886—21no—
27#18011886C2212yes—
28#18011873—21no—
29#18011873C2212yescomplemented
30C22⋊C4×D149—21no—
31C22⋊C4×D149—21no—
32C42×D149C2211yescharacteristic
33#18011840C2212yescomplemented
34#18011834C2212yescomplemented
35#18011831C2212yes—
36#18011823C2212yes—
37#18011822C2211yescharacteristic, complemented
38C4⋊Q8×C149C2211yescharacteristic, complemented
39#124×C149C2211yescharacteristic
40#103×C149C2212yescomplemented
41#102×C149C2212yes—
42#97×C149C2211yescharacteristic, complemented
43C23×D149—21no—
44#14558737—44no—
45C2×Dic298—21no—
46C2×Dic298C2311yescharacteristic
47Q8×D149—42no—
48C2×D596—22no—
49C2×D596—21no—
50C2×D596—21no—
51C2×D596C2312yes—
52C2×D596C2311yescharacteristic
53C2×C22⋊D149—21no—
54D4×D149—42no—
55C2×C4×D149—21no—
56C2×C4×D149—22no—
57C2×C4×D149D411yescharacteristic
58C2×C4×D149D411yescharacteristic
59C2×C4×D149C2311yescharacteristic
60#14558725—42no—
61#14558723—42no—
62D1192—42no—
63#14558721—42no—
64C2×#11924746C2312yes—
65C22⋊Dic149—21no—
66C22⋊Dic149—21no—
67#14558713—21no—
68#14558713—21no—
69#14558713—22no—
70#14558713—22no—
71#14558713—21no—
72#14558713—21no—
73C4×Dic149D411yescharacteristic
74C4×Dic149D411yescharacteristic
75C4×Dic149C2311yescharacteristic
76C2×Q8×C149—21no—
77C2×Q8×C149C2311yescharacteristic
78C2×D4×C149C2311yescharacteristic
79C2×C8×C149C2312yes—
80C4⋊C4×C149—21no—
81C4⋊C4×C149C2312yes—
82C22⋊C4×C149—21no—
83C22⋊C4×C149—21no—
84C42×C149C2311yescharacteristic
85C22×D149—22no—
86C22×D149—21no—
87C22×D149—42no—
88C22×D149—42no—
89C22×D149—42no—
90C22×D149C2×D411yescharacteristic
91Dic298—22no—
92Dic298—42no—
93D596—22no—
94D596—22no—
95D596—22no—
96D596—42no—
97D596—42no—
98D596—44no—
99C22⋊D149—42no—
100C2×Dic149—21no—
101C2×Dic149C2×D411yescharacteristic
102C2×Dic149C2×D411yescharacteristic
103C2×Dic149C2×D411yescharacteristic
104C4×D149—22no—
105C4×D149—22no—
106C4×D149—41no—
107C4×D149—44no—
108C4×D149—42no—
109#11924746—22no—
110C23×C149—21no—
111Q8×C149—22no—
112Q8×C149—42no—
113D4×C149—22no—
114C2×C4×C149—22no—
115C2×C4×C149—21no—
116C2×C4×C149C2×D411yescharacteristic
117C2×C4×C149C2×D411yescharacteristic
118C2×C4×C149C2411yescharacteristic
119C8×C149—22no—
120C22×C149—41no—
121C22×C149—41no—
122C22×C149—41no—
123C22×C149C22×D411yescharacteristic
124C2×D149—21no—
125C2×D149—21no—
126C2×D149—41no—
127C2×D149—42no—
128C2×D149—42no—
129C2×D149—41no—
130C2×D149—42no—
131C2×D149—41no—
132C2×D149—84no—
133C2×D149AGL(1,ℤ/8)12yes—
134C4×C149—21no—
135C4×C149—21no—
136C4×C149—41no—
137C4×C149—42no—
138C4×C149H(5,𝔽2)12yes—
139Dic149—21no—
140Dic149—21no—
141Dic149—21no—
142Dic149—41no—
143C2×C149—81no—
144C2×C149#53511yescharacteristic
145C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
146C2×C149#57511yescharacteristic
147D149—22no—
148D149—82no—
149D149—81no—
150C149#321311yescharacteristic, complemented, Sylow
151#3213—1491nomaximal, Sylow
152#532—1491no—
153C2×#124—1491no—
154#496—1491no—
155#496—1491no—
156#489—1491no—
157#489D14911yescharacteristic, complemented
158#463—1492no—
159#463—1492no—
160#448—1492no—
161#447—1492no—
162#432—1491no—
163C2×#41—2981no—
164C22×Q8—1491no—
165C22×D4—1491no—
166C2×SD16—1492no—
167C2×SD16—1492no—
168C2×D8—1492no—
169C2×D8—1492no—
170C4⋊Q8C2×D14911yescharacteristic, complemented
171#127—1491no—
172#124—2981no—
173#124—2981no—
174#124—2981no—
175#124—1491no—
176#124—1491no—
177#124—1491no—
178#124C2×D14911yescharacteristic
179#121—2981no—
180#121—1492no—
181C4×D4—2981no—
182C4×D4—1492no—
183C2×C22⋊C4—2981no—
184C2×C22⋊C4—2981no—
185C2×C42—1491no—
186C4⋊C8—1492no—
187#103—1492no—
188#103C2×D14912yescomplemented
189#102—1492no—
190#102C2×D14912yes—
191C22⋊C8—1492no—
192#97—1491no—
193#97C2×D14911yescharacteristic, complemented
194C24—2981no—
195#41—5964no—
196C2×Q8—21no—
197C2×Q8—2981no—
198C2×Q8—5962no—
199C2×Q8—1491no—
200C2×Q8C22×D14911yescharacteristic
201C2×D4—2982no—
202C2×D4—2981no—
203C2×D4—2981no—
204C2×D4—2981no—
205C2×D4—5962no—
206C2×D4—1491no—
207C2×D4—1492no—
208C2×D4C22×D14911yescharacteristic
209C22×C4—2981no—
210C22×C4—2982no—
211C22×C4—1491no—
212C22×C4—1491no—
213C22×C4—1491no—
214SD16—5962no—
215SD16—5962no—
216D8—5962no—
217D8—5962no—
218C2×C8—1492no—
219C2×C8C22×D14912yes—
220C4⋊C4—21no—
221C4⋊C4C22×D14912yes—
222C22⋊C4—21no—
223C22⋊C4—21no—
224C22⋊C4—2981no—
225C22⋊C4—2981no—
226C22⋊C4—2982no—
227C22⋊C4—2982no—
228C22⋊C4—2981no—
229C22⋊C4—2981no—
230C22⋊C4—2981no—
231C22⋊C4—2981no—
232C42—1491no—
233C42—1491no—
234C42—1491no—
235C42C22×D14911yescharacteristic
236C23—21no—
237C23—2981no—
238C23—2982no—
239C23—5962no—
240C23—5962no—
241C23—5962no—
242C23—1491no—
243Q8—22no—
244Q8—42no—
245Q8—2982no—
246Q8—5962no—
247D4—22no—
248D4—2982no—
249D4—2982no—
250D4—2982no—
251D4—5962no—
252D4—5962no—
253D4—5964no—
254D4—5962no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—2982no—
258C2×C4—2982no—
259C2×C4—2981no—
260C2×C4—5961no—
261C2×C4—5964no—
262C2×C4—5962no—
263C2×C4—1491no—
264C2×C4—1491no—
265C2×C4—1491no—
266C2×C4D4×D14911yescharacteristic
267C2×C4D4×D14911yescharacteristic
268C2×C4C23×D14911yescharacteristic
269C8—22no—
270C8—2982no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—2981no—
275C22—2981no—
276C22—5962no—
277C22—5961no—
278C22—5962no—
279C22—5961no—
280C22—5961no—
281C22—5962no—
282C22—1492no—
283C22—11924no—
284C22C2×D4×D14911yescharacteristic
285C4—21no—
286C4—21no—
287C4—42no—
288C4—41no—
289C4—2981no—
290C4—2981no—
291C4—2981no—
292C4—5961no—
293C4#1801195712yes—
294C2—81no—
295C2—2982no—
296C2—11921no—
297C2—11922no—
298C2#2375019311yescharacteristic
299C2AGL(1,ℤ/8)×D14911yescharacteristic
300C2#2375042411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#489×C149C2
socleC22×C149C22×D4
hypercenter#489D149
hypocenterC149#3213
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #23750176C2semidirect
2. #124×D149C2semidirect
3. #23750015C2semidirect
4. #23750014C2semidirect
5. #23749987C2semidirect
6. #23749843C2semidirect
7. #23749839C2semidirect
8. #23749765C2semidirect
9. #23749760C2semidirect
10. #23749680C2semidirect
11. #489×C149C2semidirect
15. C2×#14558725C22semidirect
16. C2×#14558723C22semidirect
19. #18011908C22semidirect
29. #18011873C22semidirect
33. #18011840C22semidirect
34. #18011834C22semidirect
37. #18011822C22semidirect
38. C4⋊Q8×C149C22semidirect
40. #103×C149C22semidirect
42. #97×C149C22semidirect
150. C149#3213semidirect
157. #489D149semidirect
170. C4⋊Q8C2×D149semidirect
188. #103C2×D149semidirect
193. #97C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501762
#124×D1492
#237500152
#237500142
#237499872
#237498432
#237498392
#237497652
#237497602
#237496802
#489×C1492
#3213149