Finite Group Databasebeta

← #34054194

Subgroups — #34054194

Order 19072.

526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18011937C211yesmaximal, characteristic, complemented
2C22×#14558721C211yesmaximal, characteristic, complemented
3#23750194C211yesmaximal, characteristic, complemented
4#23749840C214yesmaximal, complemented
5#23749820C214yesmaximal, complemented
6#23749652C211yesmaximal, characteristic, complemented
7#23749629C211yesmaximal, characteristic, complemented
8#23749619C211yesmaximal, characteristic, complemented
9#518×C149C211yesmaximal, characteristic, complemented
10C2×#14558736C2211yescharacteristic
11C22×D596C2211yescharacteristic
12#18011937—24no—
13C2×#14558724C2212yescomplemented
14C2×#14558721—24no—
15C2×#14558721C2214yes—
16C2×#14558721C2212yescomplemented
17C2×#14558720C2211yescharacteristic
18C22×#11924746C2211yescharacteristic
19#18011908C2212yescomplemented
20#18011899C2212yescomplemented
21#18011886—22no—
22#18011881—22no—
23C4⋊#11924746C2214yescomplemented
24#18011834C2212yescomplemented
25#18011831C2212yescomplemented
26#18011831C2214yescomplemented
27C22×D4×C149C2211yescharacteristic
28C4×D4×C149—22no—
29C4×D4×C149C2214yescomplemented
30#117×C149C2211yescharacteristic
31#117×C149C2211yescharacteristic
32C2×C22⋊C4×C149—22no—
33C23×D149—21no—
34#14558736—22no—
35#14558736—22no—
36C2×Dic298C2311yescharacteristic
37C2×D596—22no—
38C2×D596—21no—
39C2×D596—24no—
40C2×D596—22no—
41C2×D596C2311yescharacteristic
42C2×D596C2312yes—
43C2×C22⋊D149—21no—
44C2×C4×D149—21no—
45#14558724—24no—
46#14558721—28no—
47#14558721—24no—
48#14558720—22no—
49C2×#11924746—22no—
50C2×#11924746C2312yes—
51C2×#11924746C2312yes—
52#14558713—24no—
53C24×C149—21no—
54C2×D4×C149—21no—
55C2×D4×C149—22no—
56C2×D4×C149D414yescomplemented
57C2×D4×C149C2312yes—
58C22×C4×C149—24no—
59C22×C4×C149C2311yescharacteristic
60C4⋊C4×C149D412yes—
61C4⋊C4×C149C2312yes—
62C22⋊C4×C149—21no—
63C22⋊C4×C149—24no—
64C22⋊C4×C149D412yes—
65C42×C149—21no—
66C42×C149C2312yes—
67C22×D149—21no—
68C22×D149—22no—
69C22×D149—42no—
70C22×D149—82no—
71Dic298—21no—
72Dic298—21no—
73D596—22no—
74D596—21no—
75D596—22no—
76D596—21no—
77D596—42no—
78D596—84no—
79C22⋊D149—42no—
80C2×Dic149—21no—
81C4×D149—42no—
82#11924746—22no—
83#11924746—22no—
84C23×C149—22no—
85C23×C149—24no—
86C23×C149—82no—
87C23×C149C2×D411yescharacteristic
88D4×C149—24no—
89D4×C149—22no—
90D4×C149C2×D414yes—
91C2×C4×C149—22no—
92C2×C4×C149—84no—
93C2×C4×C149C2×D414yes—
94C2×C4×C149C2×D411yescharacteristic
95C2×C4×C149C2×D412yes—
96C2×C4×C149#4112yes—
97C2×C4×C149C2411yescharacteristic
98C22×C149—22no—
99C22×C149—24no—
100C22×C149—44no—
101C22×C149—84no—
102C22×C149#12112yes—
103C22×C149C22×D411yescharacteristic
104C2×D149—41no—
105C2×D149—42no—
106C2×D149—42no—
107C2×D149—44no—
108C2×D149—84no—
109C4×C149—24no—
110C4×C149—42no—
111C4×C149#12112yes—
112C4×C149C22×D411yescharacteristic
113C4×C149C2×#4111yescharacteristic
114Dic149—41no—
115C2×C149—22no—
116C2×C149—44no—
117C2×C149C2×#12111yescharacteristic
118C2×C149#57612yes—
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#518D14911yescharacteristic, complemented
127#463—1494no—
128#459—1494no—
129#424—1491no—
130#418—1491no—
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×M16—1491no—
141C22×C8—1491no—
142#127—1492no—
143#124—1492no—
144#121—2982no—
145#120—2982no—
146C4×D4—22no—
147C4×D4C2×D14914yescomplemented
148#117C2×D14911yescharacteristic
149#117C2×D14911yescharacteristic
150C2×C22⋊C4—22no—
151C4⋊C8—1494no—
152#103—1492no—
153#102—1492no—
154#102—1494no—
155C24—21no—
156C24—2981no—
157#41—2982no—
158#41—2982no—
159C2×Q8—1491no—
160C2×D4—21no—
161C2×D4—22no—
162C2×D4—2981no—
163C2×D4—2981no—
164C2×D4—2984no—
165C2×D4—2982no—
166C2×D4—2982no—
167C2×D4—1492no—
168C2×D4—1491no—
169C2×D4D59614yescomplemented
170C2×D4C22×D14912yes—
171C22×C4—24no—
172C22×C4—2981no—
173C22×C4C22×D14911yescharacteristic
174SD16—2984no—
175D8—2988no—
176D8—2984no—
177M16—2982no—
178C2×C8—2982no—
179C2×C8—1492no—
180C2×C8—1492no—
181C4⋊C4C22⋊D14912yes—
182C4⋊C4C22×D14912yes—
183C22⋊C4—21no—
184C22⋊C4—24no—
185C22⋊C4—2984no—
186C22⋊C4C22⋊D14912yes—
187C42—21no—
188C42C22×D14912yes—
189C23—22no—
190C23—24no—
191C23—82no—
192C23—2982no—
193C23—2981no—
194C23—5962no—
195C23—11922no—
196C23C2×C22⋊D14911yescharacteristic
197Q8—2981no—
198Q8—2981no—
199D4—22no—
200D4—24no—
201D4—2982no—
202D4—2981no—
203D4—2982no—
204D4—2981no—
205D4—5962no—
206D4—5962no—
207D4—11924no—
208D4C2×D59614yes—
209C2×C4—22no—
210C2×C4—84no—
211C2×C4—2981no—
212C2×C4—5962no—
213C2×C4C2×C22⋊D14914yes—
214C2×C4C2×C22⋊D14911yescharacteristic
215C2×C4C2×D59612yes—
216C2×C4#1455873612yes—
217C2×C4C23×D14911yescharacteristic
218C8—2982no—
219C8—2982no—
220C22—22no—
221C22—24no—
222C22—44no—
223C22—84no—
224C22—5962no—
225C22—5964no—
226C22—5961no—
227C22—5962no—
228C22—11924no—
229C22#1801188512yes—
230C22C22×C22⋊D14911yescharacteristic
231C4—24no—
232C4—42no—
233C4—5961no—
234C4#1801188512yes—
235C4C22×D59611yescharacteristic
236C4C2×#1455873611yescharacteristic
237C2—22no—
238C2—44no—
239C2—11922no—
240C2—11921no—
241C2C2×#1801188511yescharacteristic
242C2#2375042812yes—
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#518×C149C2
socleC22×C149C22×D4
hypercenter#518D149
hypocenterC149#3041
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. C2×#18011937C2semidirect
2. C22×#14558721C2semidirect
3. #23750194C2semidirect
4. #23749840C2semidirect
5. #23749820C2semidirect
6. #23749652C2semidirect
7. #23749629C2semidirect
8. #23749619C2semidirect
9. #518×C149C2semidirect
13. C2×#14558724C22semidirect
16. C2×#14558721C22semidirect
19. #18011908C22semidirect
20. #18011899C22semidirect
23. C4⋊#11924746C22semidirect
24. #18011834C22semidirect
25. #18011831C22semidirect
26. #18011831C22semidirect
29. C4×D4×C149C22semidirect
56. C2×D4×C149D4semidirect
121. C149#3041semidirect
126. #518D149semidirect
147. C4×D4C2×D149semidirect
169. C2×D4D596semidirect

Maximal subgroups

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

subgroupindex
C2×#180119372
C22×#145587212
#237501942
#237498402
#237498202
#237496522
#237496292
#237496192
#518×C1492
#3041149