Finite Group Databasebeta

← #34054193

Subgroups — #34054193

Order 19072.

526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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×#18011939C211yesmaximal, characteristic, complemented
2C22×#14558721C211yesmaximal, characteristic, complemented
3#23750192C211yesmaximal, characteristic, complemented
4#23750099C211yesmaximal, characteristic, complemented
5#23749839C214yesmaximal, complemented
6#23749819C214yesmaximal, complemented
7#23749653C211yesmaximal, characteristic, complemented
8#23749619C211yesmaximal, characteristic, complemented
9#418×C149C211yesmaximal, characteristic, complemented
10C2×#14558736C2211yescharacteristic
11C22×D596C2211yescharacteristic
12#18011939—24no—
13C2×#14558725C2212yescomplemented
14C2×D1192C2212yescomplemented
15C2×#14558721—24no—
16C2×#14558721C2214yes—
17C22×#11924746C2211yescharacteristic
18#18011907C2212yescomplemented
19#18011898C2212yescomplemented
20#18011882—22no—
21#18011880—22no—
22C4×D596—22no—
23#18011873C2214yescomplemented
24#18011870C2211yescharacteristic
25C22⋊C4×D149—22no—
26#18011840C2214yescomplemented
27#18011834C2212yescomplemented
28#18011831C2212yescomplemented
29C22×D4×C149C2211yescharacteristic
30C2×M16×C149C2211yescharacteristic
31#117×C149C2211yescharacteristic
32#102×C149C2214yescomplemented
33C23×D149—21no—
34#14558736—22no—
35#14558736—22no—
36C2×Dic298C2311yescharacteristic
37C2×D596—21no—
38C2×D596—22no—
39C2×D596D414yescomplemented
40C2×D596C2311yescharacteristic
41C2×D596C2312yes—
42C2×C22⋊D149—24no—
43C2×C22⋊D149—21no—
44C2×C4×D149—24no—
45C2×C4×D149—21no—
46#14558725—24no—
47D1192—24no—
48#14558721—28no—
49C2×#11924746—22no—
50C2×#11924746C2312yes—
51C4⋊Dic149D412yes—
52C22⋊Dic149—24no—
53C22⋊Dic149D412yes—
54#14558713—24no—
55C4×Dic149C2312yes—
56C24×C149—21no—
57C2×D4×C149—22no—
58C2×D4×C149—21no—
59C2×D4×C149—22no—
60C2×D4×C149C2312yes—
61C22×C4×C149C2311yescharacteristic
62M16×C149—22no—
63C2×C8×C149C2312yes—
64C4⋊C4×C149C2312yes—
65C22⋊C4×C149—21no—
66C42×C149—21no—
67C22×D149—22no—
68C22×D149—24no—
69C22×D149—21no—
70C22×D149—82no—
71Dic298—21no—
72Dic298—21no—
73D596—24no—
74D596—21no—
75D596—22no—
76D596—21no—
77D596C2×D414yes—
78C22⋊D149—42no—
79C22⋊D149—84no—
80C2×Dic149—21no—
81C2×Dic149C2×D414yes—
82C4×D149—42no—
83C4×D149—84no—
84#11924746—22no—
85C23×C149—22no—
86C23×C149—42no—
87C23×C149—82no—
88C23×C149C2×D411yescharacteristic
89D4×C149—22no—
90D4×C149—22no—
91D4×C149—42no—
92C2×C4×C149—22no—
93C2×C4×C149C2×D411yescharacteristic
94C2×C4×C149C2×D412yes—
95C2×C4×C149#4112yes—
96C2×C4×C149C2411yescharacteristic
97C8×C149—22no—
98C22×C149—22no—
99C22×C149—42no—
100C22×C149—44no—
101C22×C149—84no—
102C22×C149#12112yes—
103C22×C149C22×D411yescharacteristic
104C2×D149—24no—
105C2×D149—44no—
106C2×D149—41no—
107C2×D149—42no—
108C2×D149—84no—
109C4×C149—42no—
110C4×C149#12112yes—
111C4×C149C22×D411yescharacteristic
112C4×C149C2×#4111yescharacteristic
113Dic149—24no—
114Dic149—41no—
115C2×C149—22no—
116C2×C149—82no—
117C2×C149C2×#12111yescharacteristic
118C2×C149#57612yes—
119D149—44no—
120D149—81no—
121C149#304111yescharacteristic, complemented, Sylow
122#3041—1491nomaximal, Sylow
123C2×AGL(1,ℤ/8)—1491no—
124C22×D8—1491no—
125#535—1491no—
126#518—1491no—
127#463—1494no—
128#459—1494no—
129#424—1491no—
130#418D14911yescharacteristic, complemented
131#416—1491no—
132C2×#41—1491no—
133C22×D4—1491no—
134C22×D4C2×D14911yescharacteristic
135AGL(1,ℤ/8)—2984no—
136C2×SD16—1492no—
137C2×D8—2984no—
138C2×D8—1494no—
139C2×D8—1492no—
140C2×M16C2×D14911yescharacteristic
141C22×C8—1491no—
142#127—1492no—
143#124—1492no—
144#121—2982no—
145#120—2982no—
146C4×D4—2982no—
147C4×D4—1494no—
148#117—1491no—
149#117C2×D14911yescharacteristic
150C2×C22⋊C4—2982no—
151C4⋊C8—1494no—
152#103—1492no—
153#102—1492no—
154#102C2×D14914yescomplemented
155C24—21no—
156C24—2981no—
157#41—2982no—
158#41—2982no—
159C2×Q8—1491no—
160C2×D4—22no—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—2981no—
164C2×D4—2984no—
165C2×D4—2981no—
166C2×D4—2982no—
167C2×D4—1494no—
168C2×D4—1491no—
169C2×D4—1492no—
170C2×D4C22×D14912yes—
171C22×C4—2984no—
172C22×C4—2981no—
173C22×C4C22×D14911yescharacteristic
174SD16—2984no—
175D8—2984no—
176D8—2988no—
177M16—22no—
178C2×C8—2982no—
179C2×C8—1492no—
180C2×C8C22×D14912yes—
181C4⋊C4—1492no—
182C4⋊C4C22×D14912yes—
183C22⋊C4—21no—
184C22⋊C4—2984no—
185C22⋊C4—2984no—
186C22⋊C4—1492no—
187C42—21no—
188C42—1492no—
189C23—22no—
190C23—42no—
191C23—82no—
192C23—2982no—
193C23—2984no—
194C23—2981no—
195C23—11922no—
196C23D4×D14911yescharacteristic
197Q8—2981no—
198Q8—2981no—
199D4—22no—
200D4—22no—
201D4—42no—
202D4—2981no—
203D4—2982no—
204D4—2981no—
205D4—2984no—
206D4—5962no—
207D4—1494no—
208D4—11924no—
209C2×C4—22no—
210C2×C4—2981no—
211C2×C4—5962no—
212C2×C4—1494no—
213C2×C4—11924no—
214C2×C4D4×D14912yes—
215C2×C4D4×D14911yescharacteristic
216C2×C4#1455873612yes—
217C2×C4C23×D14911yescharacteristic
218C8—22no—
219C8—2982no—
220C22—22no—
221C22—44no—
222C22—42no—
223C22—84no—
224C22—2984no—
225C22—5964no—
226C22—5962no—
227C22—5961no—
228C22—11924no—
229C22#1801188412yes—
230C22C2×D4×D14911yescharacteristic
231C4—42no—
232C4—2984no—
233C4—5961no—
234C4#1801188412yes—
235C4C2×D4×D14911yescharacteristic
236C4C2×#1455873611yescharacteristic
237C2—22no—
238C2—82no—
239C2—5964no—
240C2—11921no—
241C2C2×#1801188411yescharacteristic
242C2#2375042912yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#418×C149C2
socleC22×C149C22×D4
hypercenter#418D149
hypocenterC149#3041
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#18011939C2semidirect
2. C22×#14558721C2semidirect
3. #23750192C2semidirect
4. #23750099C2semidirect
5. #23749839C2semidirect
6. #23749819C2semidirect
7. #23749653C2semidirect
8. #23749619C2semidirect
9. #418×C149C2semidirect
13. C2×#14558725C22semidirect
14. C2×D1192C22semidirect
18. #18011907C22semidirect
19. #18011898C22semidirect
23. #18011873C22semidirect
26. #18011840C22semidirect
27. #18011834C22semidirect
28. #18011831C22semidirect
32. #102×C149C22semidirect
39. C2×D596D4semidirect
121. C149#3041semidirect
130. #418D149semidirect
154. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119392
C22×#145587212
#237501922
#237500992
#237498392
#237498192
#237496532
#237496192
#418×C1492
#3041149