Finite Group Databasebeta

← #34054191

Subgroups — #34054191

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×#18011937C211yesmaximal, characteristic, complemented
2#23750192C211yesmaximal, characteristic, complemented
3#23750100C211yesmaximal, characteristic, complemented
4#23749838C214yesmaximal, complemented
5#23749818C214yesmaximal, complemented
6#23749651C211yesmaximal, characteristic, complemented
7#23749630C211yesmaximal, characteristic, complemented
8#23749622C211yesmaximal, characteristic, complemented
9C22×D8×C149C211yesmaximal, characteristic, complemented
10C2×#14558736C2211yescharacteristic
11#18011937—24no—
12C2×#14558724C2212yescomplemented
13C2×#14558721C2212yescomplemented
14C2×#14558720C2211yescharacteristic
15#18011907C2212yescomplemented
16#18011898C2212yescomplemented
17#18011882—22no—
18#18011880—22no—
19D4×Dic149—22no—
20D4×Dic149C2214yescomplemented
21#18011870C2211yescharacteristic
22#18011870C2211yescharacteristic
23C2×C22⋊Dic149—22no—
24#18011840C2214yescomplemented
25#18011836C2212yescomplemented
26#18011833C2212yescomplemented
27#18011832C2214yescomplemented
28C22×D4×C149C2211yescharacteristic
29C22×D4×C149C2211yescharacteristic
30C2×D8×C149—24no—
31C2×D8×C149C2214yes—
32C22×C8×C149C2211yescharacteristic
33#14558736—22no—
34#14558736—22no—
35C2×Dic298C2311yescharacteristic
36C2×D596C2311yescharacteristic
37C2×C22⋊D149—24no—
38C2×C22⋊D149—21no—
39C22×Dic149—24no—
40C2×C4×D149—21no—
41#14558724—24no—
42#14558721—24no—
43#14558720—22no—
44C2×#11924746C2312yes—
45C4⋊Dic149D412yes—
46C4⋊Dic149C2312yes—
47C22⋊Dic149—24no—
48C22⋊Dic149—24no—
49C22⋊Dic149—21no—
50C22⋊Dic149D412yes—
51C4×Dic149—21no—
52C4×Dic149C2312yes—
53C24×C149—21no—
54C24×C149—21no—
55C2×D4×C149—21no—
56C2×D4×C149—22no—
57C2×D4×C149—21no—
58C2×D4×C149—22no—
59C2×D4×C149—22no—
60C2×D4×C149D414yescomplemented
61C2×D4×C149C2312yes—
62C2×D4×C149C2312yes—
63C22×C4×C149C2311yescharacteristic
64D8×C149—28no—
65C2×C8×C149—22no—
66C2×C8×C149C2312yes—
67C22×D149—21no—
68Dic298—21no—
69Dic298—21no—
70D596—21no—
71D596—21no—
72C22⋊D149—42no—
73C22⋊D149—84no—
74C2×Dic149—21no—
75C2×Dic149—22no—
76C2×Dic149—84no—
77C2×Dic149C2×D414yes—
78C4×D149—42no—
79#11924746—22no—
80C23×C149—22no—
81C23×C149—24no—
82C23×C149—22no—
83C23×C149—42no—
84C23×C149—82no—
85C23×C149—82no—
86C23×C149C2×D411yescharacteristic
87D4×C149—24no—
88D4×C149—22no—
89D4×C149—22no—
90D4×C149—22no—
91D4×C149—42no—
92D4×C149C2×D414yes—
93C2×C4×C149C2×D411yescharacteristic
94C2×C4×C149C2×D412yes—
95C2×C4×C149#4112yes—
96C2×C4×C149C2411yescharacteristic
97C8×C149—22no—
98C22×C149—22no—
99C22×C149—24no—
100C22×C149—44no—
101C22×C149—42no—
102C22×C149—44no—
103C22×C149—84no—
104C22×C149—84no—
105C22×C149#12112yes—
106C22×C149C22×D411yescharacteristic
107C2×D149—41no—
108C2×D149—42no—
109C4×C149#12112yes—
110C4×C149C22×D411yescharacteristic
111C4×C149C2×#4111yescharacteristic
112Dic149—24no—
113Dic149—41no—
114Dic149—42no—
115C2×C149—22no—
116C2×C149—44no—
117C2×C149—82no—
118C2×C149C2×#12111yescharacteristic
119C2×C149#57612yes—
120D149—81no—
121C149#304111yescharacteristic, complemented, Sylow
122#3041—1491nomaximal, Sylow
123C2×AGL(1,ℤ/8)—1491no—
124C22×D8D14911yescharacteristic, complemented
125#535—1491no—
126#518—1491no—
127#463—1494no—
128#459—1494no—
129#424—1491no—
130#418—1491no—
131#416—1491no—
132C2×#41—1491no—
133C22×D4C2×D14911yescharacteristic
134C22×D4C2×D14911yescharacteristic
135AGL(1,ℤ/8)—2984no—
136C2×SD16—1492no—
137C2×D8—24no—
138C2×D8—1492no—
139C2×D8C2×D14914yes—
140C2×M16—1491no—
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#117—1491no—
150C2×C22⋊C4—2982no—
151C4⋊C8—1494no—
152#103—1492no—
153#102—1494no—
154#102—1492no—
155C24—21no—
156C24—21no—
157#41—2982no—
158#41—2982no—
159C2×Q8—1491no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—22no—
164C2×D4—22no—
165C2×D4—2981no—
166C2×D4—2984no—
167C2×D4—1491no—
168C2×D4C22⋊D14914yescomplemented
169C2×D4C22×D14912yes—
170C2×D4C22×D14912yes—
171C22×C4—2981no—
172C22×C4—2984no—
173C22×C4C22×D14911yescharacteristic
174SD16—2984no—
175D8—28no—
176D8—2984no—
177M16—2982no—
178C2×C8—22no—
179C2×C8—1492no—
180C2×C8C22×D14912yes—
181C4⋊C4—1492no—
182C4⋊C4—1492no—
183C22⋊C4—2981no—
184C22⋊C4—2984no—
185C22⋊C4—2984no—
186C22⋊C4—1492no—
187C42—2981no—
188C42—1492no—
189C23—22no—
190C23—24no—
191C23—22no—
192C23—42no—
193C23—82no—
194C23—82no—
195C23—2981no—
196C23D4×D14911yescharacteristic
197Q8—2981no—
198Q8—2981no—
199D4—22no—
200D4—22no—
201D4—22no—
202D4—24no—
203D4—42no—
204D4—2981no—
205D4—2981no—
206D4—5962no—
207D4—11924no—
208D4C2×C22⋊D14914yes—
209C2×C4—2982no—
210C2×C4—2981no—
211C2×C4—5962no—
212C2×C4—1494no—
213C2×C4—11924no—
214C2×C4D4×D14911yescharacteristic
215C2×C4C2×C22⋊D14912yes—
216C2×C4#1455873512yes—
217C2×C4C23×D14911yescharacteristic
218C8—22no—
219C8—2982no—
220C22—22no—
221C22—24no—
222C22—44no—
223C22—44no—
224C22—42no—
225C22—84no—
226C22—84no—
227C22—5962no—
228C22—5961no—
229C22#1801188312yes—
230C22C2×D4×D14911yescharacteristic
231C4—2984no—
232C4—5962no—
233C4—5961no—
234C4#1801188312yes—
235C4C22×C22⋊D14911yescharacteristic
236C4C2×#1455873511yescharacteristic
237C2—22no—
238C2—44no—
239C2—82no—
240C2—11921no—
241C2C2×#1801188311yescharacteristic
242C2#2375042612yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC22×D8×C149C2
socleC22×C149C22×D4
hypercenterC22×D8D149
hypocenterC149#3041
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#18011937C2semidirect
2. #23750192C2semidirect
3. #23750100C2semidirect
4. #23749838C2semidirect
5. #23749818C2semidirect
6. #23749651C2semidirect
7. #23749630C2semidirect
8. #23749622C2semidirect
9. C22×D8×C149C2semidirect
12. C2×#14558724C22semidirect
13. C2×#14558721C22semidirect
15. #18011907C22semidirect
16. #18011898C22semidirect
20. D4×Dic149C22semidirect
24. #18011840C22semidirect
25. #18011836C22semidirect
26. #18011833C22semidirect
27. #18011832C22semidirect
60. C2×D4×C149D4semidirect
121. C149#3041semidirect
124. C22×D8D149semidirect
168. C2×D4C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119372
#237501922
#237501002
#237498382
#237498182
#237496512
#237496302
#237496222
C22×D8×C1492
#3041149