Finite Group Databasebeta

← #34054209

Subgroups — #34054209

Order 19072.

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

normal subgroups only

This group has 490 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×#18011942C211yesmaximal, characteristic, complemented
2#23750192C211yesmaximal, characteristic
3#23750103C211yesmaximal, characteristic, complemented
4#23749845C214yesmaximal, complemented
5#23749823C214yesmaximal, complemented
6#23749651C211yesmaximal, characteristic, complemented
7#23749630C211yesmaximal, characteristic, complemented
8#23749622C211yesmaximal, characteristic, complemented
9C22×SD16×C149C211yesmaximal, characteristic, complemented
10C2×#14558736C2211yescharacteristic
11#18011942—24no—
12C2×#14558726C2212yescomplemented
13C2×#14558723C2212yescomplemented
14C2×#14558720C2211yescharacteristic
15#18011907C2212yes—
16#18011898C2212yes—
17#18011882—22no—
18#18011880—22no—
19Q8×Dic149—22no—
20Q8×Dic149C2214yescomplemented
21#18011870—22no—
22#18011870C2211yescharacteristic
23#18011870C2211yescharacteristic
24#18011840C2214yescomplemented
25#18011836C2212yescomplemented
26#18011833C2212yescomplemented
27#18011832C2214yes—
28C22×Q8×C149C2211yescharacteristic
29C22×D4×C149C2211yescharacteristic
30C2×SD16×C149—24no—
31C2×SD16×C149C2214yes—
32C22×C8×C149C2211yescharacteristic
33#14558736—22no—
34#14558736—22no—
35C2×Dic298C2311yescharacteristic
36C2×D596C2311yescharacteristic
37C2×C22⋊D149—24no—
38C2×C22⋊D149—21no—
39C2×C4×D149—21no—
40#14558726—24no—
41#14558723—24no—
42#14558720—22no—
43C2×#11924746C2312yes—
44C4⋊Dic149—24no—
45C4⋊Dic149D412yes—
46C4⋊Dic149C2312yes—
47C22⋊Dic149—24no—
48C22⋊Dic149—21no—
49C22⋊Dic149D412yes—
50C4×Dic149—24no—
51C4×Dic149—21no—
52C4×Dic149C2312yes—
53C24×C149—21no—
54C2×Q8×C149—21no—
55C2×Q8×C149—22no—
56C2×Q8×C149D414yescomplemented
57C2×Q8×C149C2312yes—
58C2×D4×C149—22no—
59C2×D4×C149—21no—
60C2×D4×C149—22no—
61C2×D4×C149C2312yes—
62C22×C4×C149—21no—
63C22×C4×C149C2311yescharacteristic
64SD16×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×Dic149C2×D414yes—
77C4×D149—42no—
78#11924746—22no—
79C23×C149—22no—
80C23×C149—42no—
81C23×C149—82no—
82C23×C149C2×D411yescharacteristic
83Q8×C149—24no—
84Q8×C149—22no—
85Q8×C149C2×D414yes—
86D4×C149—22no—
87D4×C149—22no—
88D4×C149—42no—
89C2×C4×C149—24no—
90C2×C4×C149—22no—
91C2×C4×C149C2×D411yescharacteristic
92C2×C4×C149C2×D412yes—
93C2×C4×C149#4112yes—
94C2×C4×C149C2411yescharacteristic
95C8×C149—22no—
96C22×C149—22no—
97C22×C149—42no—
98C22×C149—44no—
99C22×C149—84no—
100C22×C149#12112yes—
101C22×C149C22×D411yescharacteristic
102C2×D149—41no—
103C2×D149—42no—
104C4×C149—24no—
105C4×C149#12112yes—
106C4×C149C22×D411yescharacteristic
107C4×C149C2×#4111yescharacteristic
108Dic149—24no—
109Dic149—41no—
110Dic149—42no—
111C2×C149—22no—
112C2×C149—82no—
113C2×C149C2×#12111yescharacteristic
114C2×C149#57712yes—
115D149—81no—
116C149#304311yescharacteristic, complemented, Sylow
117#3043—1491nomaximal, Sylow
118C2×#137—1491no—
119C22×SD16D14911yescharacteristic, complemented
120#535—1491no—
121#519—1491no—
122#464—1494no—
123#460—1494no—
124#424—1491no—
125#418—1491no—
126#416—1491no—
127C2×#41—1491no—
128C22×Q8C2×D14911yescharacteristic
129C22×D4C2×D14911yescharacteristic
130#137—2984no—
131C2×Q16—1492no—
132C2×SD16—24no—
133C2×SD16—1492no—
134C2×SD16C2×D14914yes—
135C2×M16—1491no—
136C22×C8C2×D14911yescharacteristic
137#127—1492no—
138#124—1492no—
139#121—2982no—
140#120—2982no—
141C4×Q8—2982no—
142C4×Q8—1494no—
143#117—2982no—
144#117—1491no—
145#117—1491no—
146C4⋊C8—1494no—
147#103—1492no—
148#102—1494no—
149#102—1492no—
150C24—21no—
151#41—2982no—
152#41—2982no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—1491no—
156C2×Q8C22⋊D14914yescomplemented
157C2×Q8C22×D14912yes—
158C2×D4—21no—
159C2×D4—22no—
160C2×D4—22no—
161C2×D4—2981no—
162C2×D4—2984no—
163C2×D4—1491no—
164C2×D4C22×D14912yes—
165C22×C4—21no—
166C22×C4—2981no—
167C22×C4C22×D14911yescharacteristic
168Q16—2984no—
169SD16—28no—
170SD16—2984no—
171M16—2982no—
172C2×C8—22no—
173C2×C8—1492no—
174C2×C8C22×D14912yes—
175C4⋊C4—2984no—
176C4⋊C4—1492no—
177C4⋊C4—1492no—
178C22⋊C4—2981no—
179C22⋊C4—2984no—
180C22⋊C4—1492no—
181C42—2984no—
182C42—2981no—
183C42—1492no—
184C23—22no—
185C23—42no—
186C23—82no—
187C23—2981no—
188C23D4×D14911yescharacteristic
189Q8—22no—
190Q8—24no—
191Q8—2981no—
192Q8—2981no—
193Q8C2×C22⋊D14914yes—
194D4—22no—
195D4—22no—
196D4—42no—
197D4—2981no—
198D4—2981no—
199D4—5962no—
200D4—11924no—
201C2×C4—22no—
202C2×C4—24no—
203C2×C4—2982no—
204C2×C4—2981no—
205C2×C4—5962no—
206C2×C4—1494no—
207C2×C4D4×D14911yescharacteristic
208C2×C4C2×C22⋊D14912yes—
209C2×C4#1455873512yes—
210C2×C4C23×D14911yescharacteristic
211C8—22no—
212C8—2982no—
213C22—22no—
214C22—44no—
215C22—42no—
216C22—84no—
217C22—5962no—
218C22—5961no—
219C22#1801188312yes—
220C22C2×D4×D14911yescharacteristic
221C4—24no—
222C4—2984no—
223C4—5962no—
224C4—5961no—
225C4#1801188312yes—
226C4C22×C22⋊D14911yescharacteristic
227C4C2×#1455873511yescharacteristic
228C2—22no—
229C2—82no—
230C2—11921no—
231C2C2×#1801188311yescharacteristic
232C2#2375043112yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC22×SD16×C149C2
socleC22×C149C22×D4
prime radical#23750192C2
hypercenterC22×SD16D149
hypocenterC149#3043
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#18011942C2semidirect
3. #23750103C2semidirect
4. #23749845C2semidirect
5. #23749823C2semidirect
6. #23749651C2semidirect
7. #23749630C2semidirect
8. #23749622C2semidirect
9. C22×SD16×C149C2semidirect
12. C2×#14558726C22semidirect
13. C2×#14558723C22semidirect
20. Q8×Dic149C22semidirect
24. #18011840C22semidirect
25. #18011836C22semidirect
26. #18011833C22semidirect
56. C2×Q8×C149D4semidirect
116. C149#3043semidirect
119. C22×SD16D149semidirect
156. C2×Q8C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119422
#237501922
#237501032
#237498452
#237498232
#237496512
#237496302
#237496222
C22×SD16×C1492
#3043149