Finite Group Databasebeta

← #34055173

Subgroups — #34055173

Order 19072.

596 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 137 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×#18011938C212yesmaximal, complemented
2C2×#18011934C211yesmaximal, characteristic, complemented
3C2×D8×D149C211yesmaximal, characteristic, complemented
4#23750193C212yesmaximal, complemented
5#23750015C212yesmaximal, complemented
6#23750011C212yesmaximal, complemented
7#23750010C211yesmaximal, characteristic, complemented
8#23750002C211yesmaximal, characteristic, complemented
9#23750000C211yesmaximal, characteristic, complemented
10#23749579C211yesmaximal, characteristic, complemented
11#495×C149C211yesmaximal, characteristic, complemented
12C2×#14558737C2212yes—
13C2×D4×D149C2212yes—
14#18011938—28no—
15#18011934—24no—
16C2×#14558723C2212yescomplemented
17C2×#14558723C2212yescomplemented
18C2×D1192C2211yescharacteristic
19C2×D1192C2211yescharacteristic, complemented
20C2×D1192C2212yescomplemented
21C2×#14558721C2212yes—
22C2×#14558721C2212yescomplemented
23D8×D149—24no—
24C2×#14558719C2211yescharacteristic
25C2×C8×D149C2211yescharacteristic
26#18011908C2212yescomplemented
27#18011907C2212yescomplemented
28#18011900C2212yescomplemented
29#18011884—24no—
30#18011881—24no—
31#18011868C2211yescharacteristic
32#18011822C2211yescharacteristic, complemented
33#18011821C2211yescharacteristic, complemented
34C8×Dic149C2211yescharacteristic, complemented
35C2×Q16×C149C2211yescharacteristic, complemented
36C2×SD16×C149C2212yescomplemented
37C2×D8×C149C2211yescharacteristic
38#124×C149C2212yescomplemented
39C4×C8×C149C2211yescharacteristic, complemented
40C23×D149—22no—
41#14558737—24no—
42#14558737—24no—
43C2×D596—22no—
44C2×D596—24no—
45C2×D596C2312yes—
46C2×D596C2312yes—
47C2×C22⋊D149—22no—
48C2×C22⋊D149—24no—
49D4×D149—24no—
50D4×D149—24no—
51C2×C4×D149—22no—
52C2×C4×D149C2311yescharacteristic
53#14558723—24no—
54#14558723—24no—
55D1192—22no—
56D1192—22no—
57D1192—24no—
58#14558721—24no—
59#14558721—24no—
60#14558719D414yescomplemented
61C2×#11924746C2311yescharacteristic
62C2×#11924746C2311yescharacteristic
63C8×D149D414yescomplemented
64#14558715D412yes—
65#14558713—24no—
66#14558713D412yes—
67C4×Dic149C2311yescharacteristic
68C2×Q8×C149C2312yes—
69C2×D4×C149C2312yes—
70Q16×C149—22no—
71SD16×C149—24no—
72D8×C149—22no—
73C2×C8×C149C2311yescharacteristic
74C2×C8×C149C2311yescharacteristic
75C22⋊C4×C149—24no—
76C42×C149C2311yescharacteristic
77C22×D149—22no—
78C22×D149—22no—
79C22×D149—44no—
80C22×D149—84no—
81C22×D149C2×D411yescharacteristic
82D596—22no—
83D596—22no—
84D596—22no—
85D596—22no—
86D596—44no—
87D596—84no—
88C22⋊D149—44no—
89C22⋊D149—84no—
90C2×Dic149C2×D412yes—
91C2×Dic149C2×D411yescharacteristic
92C4×D149—44no—
93C4×D149C2×D412yes—
94C4×D149C2×D412yes—
95#11924746C2×D412yes—
96#11924746C2×D412yes—
97C23×C149—22no—
98Q8×C149—22no—
99Q8×C149—22no—
100D4×C149—22no—
101D4×C149—22no—
102C2×C4×C149—22no—
103C2×C4×C149C2×D412yes—
104C2×C4×C149C2411yescharacteristic
105C8×C149C2×D412yes—
106C8×C149C2×D412yes—
107C22×C149—42no—
108C22×C149—44no—
109C22×C149C22×D411yescharacteristic
110C2×D149—22no—
111C2×D149—42no—
112C2×D149—42no—
113C2×D149—44no—
114C2×D149—44no—
115C2×D149—88no—
116C2×D149#12712yes—
117C4×C149—22no—
118C4×C149—42no—
119C4×C149C22×D411yescharacteristic
120C4×C149C22×D411yescharacteristic
121Dic149—22no—
122Dic149#12712yes—
123C2×C149—82no—
124C2×C149C2×#12711yescharacteristic
125C2×C149#57612yes—
126D149—22no—
127D149—82no—
128D149—82no—
129C149#315511yescharacteristic, complemented, Sylow
130#3155—1491nomaximal, Sylow
131C2×AGL(1,ℤ/8)—1492no—
132C2×#135—1491no—
133C22×D8—1491no—
134#535—1492no—
135#496—1492no—
136#496—1492no—
137#495—1491no—
138#495D14911yescharacteristic, complemented
139#493—1491no—
140#493—1491no—
141#405—1491no—
142C2×#41—1492no—
143C22×D4—1492no—
144AGL(1,ℤ/8)—2988no—
145#135—2984no—
146C2×Q16C2×D14911yescharacteristic, complemented
147C2×SD16—1492no—
148C2×SD16—1492no—
149C2×SD16C2×D14912yescomplemented
150C2×D8—2984no—
151C2×D8—1492no—
152C2×D8—1492no—
153C2×D8—1491no—
154C2×D8—1491no—
155C2×D8—1492no—
156C2×D8C2×D14911yescharacteristic
157C2×M16—1491no—
158C22×C8—1491no—
159#127—1492no—
160#127—1492no—
161#124—1492no—
162#124C2×D14912yescomplemented
163#121—2984no—
164#120—2984no—
165#117—1491no—
166#97—1491no—
167#97—1491no—
168C4×C8—1491no—
169C4×C8C2×D14911yescharacteristic, complemented
170C24—2982no—
171#41—2984no—
172#41—2984no—
173C2×Q8C22×D14912yes—
174C2×D4—2982no—
175C2×D4—2984no—
176C2×D4—2984no—
177C2×D4—2982no—
178C2×D4—2984no—
179C2×D4—2984no—
180C2×D4—1492no—
181C2×D4—1492no—
182C2×D4C22×D14912yes—
183C22×C4—2982no—
184C22×C4—1491no—
185Q16—22no—
186SD16—24no—
187SD16—2984no—
188SD16—2984no—
189D8—22no—
190D8—2984no—
191D8—2984no—
192D8—2982no—
193D8—2982no—
194D8—2984no—
195M16—1494no—
196C2×C8—1491no—
197C2×C8—1491no—
198C2×C8—1494no—
199C2×C8C22×D14911yescharacteristic
200C2×C8C22×D14911yescharacteristic
201C4⋊C4—1492no—
202C22⋊C4—24no—
203C22⋊C4—2984no—
204C22⋊C4—1492no—
205C42—1491no—
206C42C22×D14911yescharacteristic
207C23—22no—
208C23—2982no—
209C23—2982no—
210C23—5964no—
211C23—1491no—
212C23—11924no—
213Q8—22no—
214Q8—22no—
215D4—22no—
216D4—22no—
217D4—2982no—
218D4—2982no—
219D4—2982no—
220D4—2982no—
221D4—5964no—
222D4—5964no—
223D4—11924no—
224D4—11924no—
225C2×C4—22no—
226C2×C4—5964no—
227C2×C4—1492no—
228C2×C4—1491no—
229C2×C4—1492no—
230C2×C4—1492no—
231C2×C4D4×D14912yes—
232C2×C4C23×D14911yescharacteristic
233C8—1492no—
234C8—1492no—
235C8D4×D14912yes—
236C8D4×D14912yes—
237C22—42no—
238C22—44no—
239C22—2982no—
240C22—5962no—
241C22—5962no—
242C22—5964no—
243C22—5964no—
244C22—1492no—
245C22—11928no—
246C22C2×D4×D14911yescharacteristic
247C4—22no—
248C4—42no—
249C4—2982no—
250C4—1492no—
251C4C2×D4×D14911yescharacteristic
252C4C2×D4×D14911yescharacteristic
253C2—82no—
254C2—2982no—
255C2—11922no—
256C2—11922no—
257C2#127×D14911yescharacteristic
258C2#2375042712yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#495×C149C2
socleC22×C149C22×D4
hypercenter#495D149
hypocenterC149#3155
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#18011938C2semidirect
2. C2×#18011934C2semidirect
3. C2×D8×D149C2semidirect
4. #23750193C2semidirect
5. #23750015C2semidirect
6. #23750011C2semidirect
7. #23750010C2semidirect
8. #23750002C2semidirect
9. #23750000C2semidirect
10. #23749579C2semidirect
11. #495×C149C2semidirect
16. C2×#14558723C22semidirect
17. C2×#14558723C22semidirect
19. C2×D1192C22semidirect
20. C2×D1192C22semidirect
22. C2×#14558721C22semidirect
26. #18011908C22semidirect
27. #18011907C22semidirect
28. #18011900C22semidirect
32. #18011822C22semidirect
33. #18011821C22semidirect
34. C8×Dic149C22semidirect
35. C2×Q16×C149C22semidirect
36. C2×SD16×C149C22semidirect
38. #124×C149C22semidirect
39. C4×C8×C149C22semidirect
60. #14558719D4semidirect
63. C8×D149D4semidirect
129. C149#3155semidirect
138. #495D149semidirect
146. C2×Q16C2×D149semidirect
149. C2×SD16C2×D149semidirect
162. #124C2×D149semidirect
169. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119382
C2×#180119342
C2×D8×D1492
#237501932
#237500152
#237500112
#237500102
#237500022
#237500002
#237495792
#495×C1492
#3155149