Finite Group Databasebeta

← #34054215

Subgroups — #34054215

Order 19072.

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

normal subgroups only

This group has 490 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×#18011941C211yesmaximal, characteristic, complemented
2C22×#14558725C211yesmaximal, characteristic, complemented
3#23750189C211yesmaximal, characteristic
4#23750102C211yesmaximal, characteristic, complemented
5#23749850C214yesmaximal, complemented
6#23749824C214yesmaximal, complemented
7#23749651C211yesmaximal, characteristic, complemented
8#23749629C211yesmaximal, characteristic, complemented
9#416×C149C211yesmaximal, characteristic, complemented
10C22×Dic298C2211yescharacteristic
11C22×D596C2211yescharacteristic
12#18011941—24no—
13C2×#14558726C2212yescomplemented
14C2×#14558725—24no—
15C2×#14558725C2214yes—
16C2×#14558724C2212yescomplemented
17C2×#14558720C2211yescharacteristic
18#18011907C2212yes—
19#18011900C2212yes—
20#18011885—22no—
21#18011879—22no—
22C4×Dic298—22no—
23#18011876C2214yescomplemented
24#18011870C2211yescharacteristic
25#18011867—22no—
26#18011840C2214yescomplemented
27#18011831C2214yes—
28C2×#41×C149C2211yescharacteristic
29C22×C8×C149C2211yescharacteristic
30#117×C149C2211yescharacteristic
31#103×C149C2212yescomplemented
32#102×C149C2212yescomplemented
33C23×D149—21no—
34C2×Dic298—21no—
35C2×Dic298—22no—
36C2×Dic298D414yescomplemented
37C2×Dic298C2312yes—
38C2×D596—22no—
39C2×D596—21no—
40C2×D596—22no—
41C2×D596C2312yes—
42C2×C22⋊D149—24no—
43C22×Dic149—21no—
44#14558726—24no—
45#14558725—28no—
46#14558724—24no—
47#14558720—22no—
48C2×#11924746C2312yes—
49C4⋊Dic149D412yes—
50#14558715—24no—
51C22⋊Dic149D412yes—
52#14558713—24no—
53C4×Dic149—24no—
54C4×Dic149C2312yes—
55#41×C149—22no—
56#41×C149—22no—
57C2×Q8×C149C2311yescharacteristic
58C2×D4×C149—21no—
59C2×D4×C149C2311yescharacteristic
60C22×C4×C149—21no—
61C22×C4×C149C2311yescharacteristic
62C2×C8×C149—22no—
63C2×C8×C149C2312yes—
64C4⋊C4×C149C2312yes—
65C22⋊C4×C149—21no—
66C42×C149—21no—
67C22×D149—22no—
68C22×D149—42no—
69C22×D149—82no—
70Dic298—24no—
71Dic298—22no—
72Dic298C2×D414yes—
73D596—22no—
74D596—22no—
75D596—42no—
76C22⋊D149—84no—
77C2×Dic149—24no—
78C2×Dic149—22no—
79C2×Dic149C2×D414yes—
80#11924746—22no—
81C23×C149—21no—
82C23×C149C2×D411yescharacteristic
83Q8×C149—21no—
84Q8×C149—21no—
85D4×C149—21no—
86D4×C149—21no—
87D4×C149—42no—
88C2×C4×C149—22no—
89C2×C4×C149—21no—
90C2×C4×C149—42no—
91C2×C4×C149C2×D411yescharacteristic
92C2×C4×C149C2×D412yes—
93C2×C4×C149#4112yes—
94C2×C4×C149C2411yescharacteristic
95C8×C149—22no—
96C22×C149—22no—
97C22×C149—41no—
98C22×C149—42no—
99C22×C149#12112yes—
100C22×C149C22×D411yescharacteristic
101C2×D149—42no—
102C2×D149—44no—
103C2×D149—84no—
104C4×C149—41no—
105C4×C149—42no—
106C4×C149#12112yes—
107C4×C149C22×D411yescharacteristic
108C4×C149C2×#4111yescharacteristic
109Dic149—24no—
110Dic149—24no—
111C2×C149—22no—
112C2×C149—81no—
113C2×C149C2×#12111yescharacteristic
114C2×C149#57712yes—
115D149—82no—
116C149#304311yescharacteristic, complemented, Sylow
117#3043—1491nomaximal, Sylow
118C2×#137—1491no—
119C22×SD16—1491no—
120#535—1491no—
121#519—1491no—
122#464—1494no—
123#460—1494no—
124#424—1491no—
125#418—1491no—
126#416D14911yescharacteristic, complemented
127C2×#41C2×D14911yescharacteristic
128C22×Q8—1491no—
129C22×D4—1491no—
130#137—2984no—
131C2×Q16—1492no—
132C2×SD16—2984no—
133C2×SD16—1492no—
134C2×SD16—1494no—
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#117C2×D14911yescharacteristic
146C4⋊C8—1494no—
147#103C2×D14912yescomplemented
148#102—1494no—
149#102C2×D14912yescomplemented
150C24—2981no—
151#41—22no—
152#41—22no—
153C2×Q8—2981no—
154C2×Q8—2982no—
155C2×Q8—1494no—
156C2×Q8—1492no—
157C2×Q8C22×D14911yescharacteristic
158C2×D4—21no—
159C2×D4—2984no—
160C2×D4—2982no—
161C2×D4—2981no—
162C2×D4—2982no—
163C2×D4—1492no—
164C2×D4C22×D14911yescharacteristic
165C22×C4—21no—
166C22×C4—2981no—
167C22×C4C22×D14911yescharacteristic
168Q16—2984no—
169SD16—2988no—
170SD16—2984no—
171M16—2982no—
172C2×C8—22no—
173C2×C8—1492no—
174C2×C8C22×D14912yes—
175C4⋊C4—2984no—
176C4⋊C4—1492no—
177C4⋊C4C22×D14912yes—
178C22⋊C4—21no—
179C22⋊C4—2984no—
180C22⋊C4—1492no—
181C42—21no—
182C42—2984no—
183C42—1492no—
184C23—21no—
185C23—2982no—
186C23—5962no—
187C23—11922no—
188C23D4×D14911yescharacteristic
189Q8—21no—
190Q8—21no—
191Q8—2982no—
192Q8—2984no—
193Q8—1494no—
194D4—21no—
195D4—21no—
196D4—42no—
197D4—2982no—
198D4—2982no—
199D4—5962no—
200D4—11924no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—42no—
204C2×C4—2982no—
205C2×C4—2984no—
206C2×C4—1494no—
207C2×C4D4×D14912yes—
208C2×C4D4×D14911yescharacteristic
209C2×C4#1455873612yes—
210C2×C4C23×D14911yescharacteristic
211C8—22no—
212C8—2982no—
213C22—22no—
214C22—42no—
215C22—41no—
216C22—5964no—
217C22—5962no—
218C22—11924no—
219C22#1801188412yes—
220C22C2×D4×D14911yescharacteristic
221C4—42no—
222C4—41no—
223C4—2984no—
224C4—2984no—
225C4#1801188412yes—
226C4C2×D4×D14911yescharacteristic
227C4C2×#1455873611yescharacteristic
228C2—22no—
229C2—81no—
230C2—11922no—
231C2C2×#1801188411yescharacteristic
232C2#2375043212yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#416×C149C2
socleC22×C149C22×D4
prime radical#23750189C2
hypercenter#416D149
hypocenterC149#3043
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#18011941C2semidirect
2. C22×#14558725C2semidirect
4. #23750102C2semidirect
5. #23749850C2semidirect
6. #23749824C2semidirect
7. #23749651C2semidirect
8. #23749629C2semidirect
9. #416×C149C2semidirect
13. C2×#14558726C22semidirect
16. C2×#14558724C22semidirect
23. #18011876C22semidirect
26. #18011840C22semidirect
31. #103×C149C22semidirect
32. #102×C149C22semidirect
36. C2×Dic298D4semidirect
116. C149#3043semidirect
126. #416D149semidirect
147. #103C2×D149semidirect
149. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119412
C22×#145587252
#237501892
#237501022
#237498502
#237498242
#237496512
#237496292
#416×C1492
#3043149