Finite Group Databasebeta

← #34054212

Subgroups — #34054212

Order 19072.

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

normal subgroups only

This group has 490 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×#18011942C211yesmaximal, characteristic, complemented
2C22×#14558723C211yesmaximal, characteristic, complemented
3#23750194C211yesmaximal, characteristic
4#23749847C214yesmaximal, complemented
5#23749825C214yesmaximal, complemented
6#23749652C211yesmaximal, characteristic, complemented
7#23749629C211yesmaximal, characteristic, complemented
8#23749619C211yesmaximal, characteristic, complemented
9#519×C149C211yesmaximal, characteristic, complemented
10C2×#14558736C2211yescharacteristic
11C22×D596C2211yescharacteristic
12#18011942—24no—
13C2×#14558726C2212yescomplemented
14C2×#14558723—24no—
15C2×#14558723C2214yes—
16C2×#14558723C2212yescomplemented
17C2×#14558720C2211yescharacteristic
18C22×#11924746C2211yescharacteristic
19#18011908C2212yes—
20#18011899C2212yes—
21#18011886—22no—
22#18011881—22no—
23C4⋊#11924746C2214yescomplemented
24#18011834C2212yescomplemented
25#18011831C2214yes—
26#18011831C2212yescomplemented
27C22×Q8×C149C2211yescharacteristic
28C4×Q8×C149—22no—
29C4×Q8×C149C2214yescomplemented
30#117×C149—22no—
31#117×C149C2211yescharacteristic
32#117×C149C2211yescharacteristic
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#14558726—24no—
46#14558723—28no—
47#14558723—24no—
48#14558720—22no—
49C2×#11924746—22no—
50C2×#11924746C2312yes—
51C2×#11924746C2312yes—
52#14558713—24no—
53C2×Q8×C149—21no—
54C2×Q8×C149—22no—
55C2×Q8×C149D414yescomplemented
56C2×Q8×C149C2312yes—
57C22×C4×C149—21no—
58C22×C4×C149C2311yescharacteristic
59C4⋊C4×C149—24no—
60C4⋊C4×C149D412yes—
61C4⋊C4×C149C2312yes—
62C22⋊C4×C149—21no—
63C22⋊C4×C149D412yes—
64C42×C149—24no—
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×C149C2×D411yescharacteristic
85Q8×C149—24no—
86Q8×C149—22no—
87Q8×C149C2×D414yes—
88C2×C4×C149—24no—
89C2×C4×C149—22no—
90C2×C4×C149—22no—
91C2×C4×C149C2×D414yes—
92C2×C4×C149C2×D411yescharacteristic
93C2×C4×C149C2×D412yes—
94C2×C4×C149#4112yes—
95C2×C4×C149C2411yescharacteristic
96C22×C149—22no—
97C22×C149#12112yes—
98C22×C149C22×D411yescharacteristic
99C2×D149—41no—
100C2×D149—42no—
101C2×D149—42no—
102C2×D149—44no—
103C2×D149—84no—
104C4×C149—24no—
105C4×C149—24no—
106C4×C149—42no—
107C4×C149#12112yes—
108C4×C149C22×D411yescharacteristic
109C4×C149C2×#4111yescharacteristic
110Dic149—41no—
111C2×C149—22no—
112C2×C149C2×#12111yescharacteristic
113C2×C149#57712yes—
114D149—81no—
115D149—82no—
116C149#304311yescharacteristic, complemented, Sylow
117#3043—1491nomaximal, Sylow
118C2×#137—1491no—
119C22×SD16—1491no—
120#535—1491no—
121#519D14911yescharacteristic, complemented
122#464—1494no—
123#460—1494no—
124#424—1491no—
125#418—1491no—
126#416—1491no—
127C2×#41—1491no—
128C22×Q8C2×D14911yescharacteristic
129C22×D4—1491no—
130#137—2984no—
131C2×Q16—1492no—
132C2×SD16—2984no—
133C2×SD16—1494no—
134C2×SD16—1492no—
135C2×M16—1491no—
136C22×C8—1491no—
137#127—1492no—
138#124—1492no—
139#121—2982no—
140#120—2982no—
141C4×Q8—22no—
142C4×Q8C2×D14914yescomplemented
143#117—22no—
144#117C2×D14911yescharacteristic
145#117C2×D14911yescharacteristic
146C4⋊C8—1494no—
147#103—1492no—
148#102—1492no—
149#102—1494no—
150C24—2981no—
151#41—2982no—
152#41—2982no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—1491no—
156C2×Q8D59614yescomplemented
157C2×Q8C22×D14912yes—
158C2×D4—2981no—
159C2×D4—2981no—
160C2×D4—2984no—
161C2×D4—2982no—
162C2×D4—2982no—
163C2×D4—1492no—
164C2×D4—1491no—
165C22×C4—21no—
166C22×C4—2981no—
167C22×C4C22×D14911yescharacteristic
168Q16—2984no—
169SD16—2988no—
170SD16—2984no—
171M16—2982no—
172C2×C8—2982no—
173C2×C8—1492no—
174C2×C8—1492no—
175C4⋊C4—24no—
176C4⋊C4C22⋊D14912yes—
177C4⋊C4C22×D14912yes—
178C22⋊C4—21no—
179C22⋊C4—2984no—
180C22⋊C4C22⋊D14912yes—
181C42—24no—
182C42—21no—
183C42C22×D14912yes—
184C23—2982no—
185C23—2981no—
186C23—5962no—
187C23—11922no—
188C23C2×C22⋊D14911yescharacteristic
189Q8—22no—
190Q8—24no—
191Q8—2981no—
192Q8—2981no—
193Q8C2×D59614yes—
194D4—2982no—
195D4—2981no—
196D4—2982no—
197D4—2981no—
198D4—5962no—
199D4—5962no—
200D4—11924no—
201C2×C4—22no—
202C2×C4—24no—
203C2×C4—22no—
204C2×C4—2981no—
205C2×C4—5962no—
206C2×C4C2×C22⋊D14914yes—
207C2×C4C2×C22⋊D14911yescharacteristic
208C2×C4C2×D59612yes—
209C2×C4#1455873612yes—
210C2×C4C23×D14911yescharacteristic
211C8—2982no—
212C8—2982no—
213C22—22no—
214C22—5962no—
215C22—5964no—
216C22—5961no—
217C22—5962no—
218C22—11924no—
219C22#1801188512yes—
220C22C22×C22⋊D14911yescharacteristic
221C4—24no—
222C4—24no—
223C4—42no—
224C4—5961no—
225C4#1801188512yes—
226C4C22×D59611yescharacteristic
227C4C2×#1455873611yescharacteristic
228C2—22no—
229C2—11922no—
230C2—11921no—
231C2C2×#1801188511yescharacteristic
232C2#2375043312yes—
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#519×C149C2
socleC22×C149C22×D4
prime radical#23750194C2
hypercenter#519D149
hypocenterC149#3043
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
1. C2×#18011942C2semidirect
2. C22×#14558723C2semidirect
4. #23749847C2semidirect
5. #23749825C2semidirect
6. #23749652C2semidirect
7. #23749629C2semidirect
8. #23749619C2semidirect
9. #519×C149C2semidirect
13. C2×#14558726C22semidirect
16. C2×#14558723C22semidirect
23. C4⋊#11924746C22semidirect
24. #18011834C22semidirect
26. #18011831C22semidirect
29. C4×Q8×C149C22semidirect
55. C2×Q8×C149D4semidirect
116. C149#3043semidirect
121. #519D149semidirect
142. C4×Q8C2×D149semidirect
156. C2×Q8D596semidirect

Maximal subgroups

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

subgroupindex
C2×#180119422
C22×#145587232
#237501942
#237498472
#237498252
#237496522
#237496292
#237496192
#519×C1492
#3043149