Finite Group Databasebeta

← #34054195

Subgroups — #34054195

Order 19072.

526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×D1192C211yesmaximal, characteristic, complemented
3#23750194C211yesmaximal, characteristic, complemented
4#23750099C211yesmaximal, characteristic, complemented
5#23749841C214yesmaximal, complemented
6#23749821C214yesmaximal, complemented
7#23749631C211yesmaximal, characteristic, complemented
8#23749622C211yesmaximal, characteristic, complemented
9#424×C149C211yesmaximal, characteristic, complemented
10C2×#14558736C2211yescharacteristic
11C22×D596C2211yescharacteristic
12C22×D596C2211yescharacteristic
13#18011939—24no—
14C2×#14558725C2212yescomplemented
15C2×D1192—24no—
16C2×D1192C2214yes—
17C2×D1192C2212yescomplemented
18#18011908C2212yescomplemented
19#18011899C2212yescomplemented
20#18011886—22no—
21#18011881—22no—
22C4×D596C2214yescomplemented
23#18011873—22no—
24#18011870C2211yescharacteristic
25C22⋊C4×D149—22no—
26#18011836C2212yescomplemented
27#18011833C2212yescomplemented
28#18011833C2214yescomplemented
29C2×M16×C149C2211yescharacteristic
30C22×C8×C149C2211yescharacteristic
31#117×C149C2211yescharacteristic
32C4⋊C8×C149C2214yescomplemented
33C23×D149—21no—
34C23×D149—21no—
35#14558736—22no—
36#14558736—22no—
37C2×Dic298C2311yescharacteristic
38C2×D596—21no—
39C2×D596—22no—
40C2×D596—21no—
41C2×D596—24no—
42C2×D596—22no—
43C2×D596—22no—
44C2×D596D414yescomplemented
45C2×D596C2311yescharacteristic
46C2×D596C2312yes—
47C2×D596C2312yes—
48C2×C22⋊D149—21no—
49C2×C4×D149—21no—
50C2×C4×D149—24no—
51#14558725—24no—
52D1192—28no—
53D1192—24no—
54C4⋊Dic149C2312yes—
55C22⋊Dic149—21no—
56#14558713—24no—
57#14558713—24no—
58C4×Dic149—21no—
59C22×C4×C149C2311yescharacteristic
60M16×C149—22no—
61C2×C8×C149—22no—
62C2×C8×C149C2312yes—
63C2×C8×C149C2312yes—
64C4⋊C4×C149D412yes—
65C22⋊C4×C149D412yes—
66C42×C149C2312yes—
67C22×D149—22no—
68C22×D149—24no—
69C22×D149—21no—
70C22×D149—22no—
71C22×D149—42no—
72C22×D149—82no—
73C22×D149—82no—
74Dic298—21no—
75Dic298—21no—
76D596—24no—
77D596—22no—
78D596—21no—
79D596—22no—
80D596—22no—
81D596—21no—
82D596—42no—
83D596—84no—
84D596C2×D414yes—
85C22⋊D149—42no—
86C2×Dic149—22no—
87C2×Dic149—21no—
88C4×D149—42no—
89C4×D149—84no—
90C23×C149C2×D411yescharacteristic
91C2×C4×C149C2×D412yes—
92C2×C4×C149C2×D414yes—
93C2×C4×C149C2×D411yescharacteristic
94C2×C4×C149#4112yes—
95C2×C4×C149C2411yescharacteristic
96C8×C149—22no—
97C8×C149—22no—
98C22×C149—22no—
99C22×C149#12112yes—
100C22×C149C22×D411yescharacteristic
101C2×D149—24no—
102C2×D149—44no—
103C2×D149—41no—
104C2×D149—42no—
105C2×D149—42no—
106C2×D149—44no—
107C2×D149—84no—
108C2×D149—84no—
109C4×C149—24no—
110C4×C149#12112yes—
111C4×C149C22×D411yescharacteristic
112C4×C149C2×#4111yescharacteristic
113Dic149—41no—
114Dic149—42no—
115C2×C149—22no—
116C2×C149C2×#12111yescharacteristic
117C2×C149#57612yes—
118D149—44no—
119D149—81no—
120D149—82no—
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#424D14911yescharacteristic, complemented
130#418—1491no—
131#416—1491no—
132C2×#41—1491no—
133C22×D4—1491no—
134C22×D4—1491no—
135AGL(1,ℤ/8)—2984no—
136C2×SD16—1492no—
137C2×D8—2984no—
138C2×D8—1494no—
139C2×D8—1492no—
140C2×M16C2×D14911yescharacteristic
141C22×C8C2×D14911yescharacteristic
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⋊C8C2×D14914yescomplemented
152#103—1492no—
153#102—1492no—
154#102—1494no—
155C24—2981no—
156C24—2981no—
157#41—2982no—
158#41—2982no—
159C2×Q8—1491no—
160C2×D4—2981no—
161C2×D4—2982no—
162C2×D4—2981no—
163C2×D4—2981no—
164C2×D4—2984no—
165C2×D4—2982no—
166C2×D4—2982no—
167C2×D4—1494no—
168C2×D4—1492no—
169C2×D4—1491no—
170C2×D4—1492no—
171C22×C4—2981no—
172C22×C4—2984no—
173C22×C4C22×D14911yescharacteristic
174SD16—2984no—
175D8—2988no—
176D8—2984no—
177M16—22no—
178C2×C8—22no—
179C2×C8C22×D14912yes—
180C2×C8C22×D14912yes—
181C4⋊C4—1492no—
182C4⋊C4D59612yes—
183C22⋊C4—2981no—
184C22⋊C4—2984no—
185C22⋊C4—2984no—
186C22⋊C4D59612yes—
187C42—2981no—
188C42C22×D14912yes—
189C23—2982no—
190C23—2984no—
191C23—2982no—
192C23—2981no—
193C23—5962no—
194C23—11922no—
195C23—11922no—
196C23C2×D59611yescharacteristic
197Q8—2981no—
198Q8—2981no—
199D4—2982no—
200D4—2981no—
201D4—2982no—
202D4—2982no—
203D4—2981no—
204D4—2984no—
205D4—5962no—
206D4—5962no—
207D4—1494no—
208D4—11924no—
209C2×C4—2982no—
210C2×C4—2981no—
211C2×C4—5962no—
212C2×C4—11924no—
213C2×C4D4×D14912yes—
214C2×C4C2×D59614yes—
215C2×C4C2×D59611yescharacteristic
216C2×C4#1455873712yes—
217C2×C4C23×D14911yescharacteristic
218C8—22no—
219C8—22no—
220C22—22no—
221C22—2984no—
222C22—5964no—
223C22—5962no—
224C22—5964no—
225C22—5961no—
226C22—5962no—
227C22—11924no—
228C22—11924no—
229C22#1801188612yes—
230C22C22×D59611yescharacteristic
231C4—24no—
232C4—5962no—
233C4—5961no—
234C4#1801188612yes—
235C4C2×D4×D14911yescharacteristic
236C4C2×#1455873711yescharacteristic
237C2—22no—
238C2—5964no—
239C2—11922no—
240C2—11921no—
241C2C2×#1801188611yescharacteristic
242C2#2375043012yes—
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#424×C149C2
socleC22×C149C22×D4
hypercenter#424D149
hypocenterC149#3041
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. C2×#18011939C2semidirect
2. C22×D1192C2semidirect
3. #23750194C2semidirect
4. #23750099C2semidirect
5. #23749841C2semidirect
6. #23749821C2semidirect
7. #23749631C2semidirect
8. #23749622C2semidirect
9. #424×C149C2semidirect
14. C2×#14558725C22semidirect
17. C2×D1192C22semidirect
18. #18011908C22semidirect
19. #18011899C22semidirect
22. C4×D596C22semidirect
26. #18011836C22semidirect
27. #18011833C22semidirect
28. #18011833C22semidirect
32. C4⋊C8×C149C22semidirect
44. C2×D596D4semidirect
121. C149#3041semidirect
129. #424D149semidirect
151. C4⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119392
C22×D11922
#237501942
#237500992
#237498412
#237498212
#237496312
#237496222
#424×C1492
#3041149