Finite Group Databasebeta

← #34054203

Subgroups — #34054203

Order 19072.

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

normal subgroups only

This group has 494 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
2C22×#14558724C211yesmaximal, characteristic, complemented
3#23750201C211yesmaximal, characteristic, complemented
4#23749840C214yesmaximal, complemented
5#23749830C214yesmaximal, complemented
6#23749652C211yesmaximal, characteristic, complemented
7#23749633C211yesmaximal, characteristic, complemented
8#23749619C211yesmaximal, characteristic, complemented
9#518×C149C211yesmaximal, characteristic, complemented
10C2×#14558736C2211yescharacteristic
11C22×Dic298C2211yescharacteristic
12#18011937—24no—
13C2×#14558724—24no—
14C2×#14558724C2212yes—
15C2×#14558724C2214yes—
16C2×#14558721C2212yes—
17C2×#14558720C2211yescharacteristic
18C22×#11924746C2211yescharacteristic
19#18011911C2212yescomplemented
20#18011899C2212yescomplemented
21#18011895—22no—
22#18011891—22no—
23C4⋊#11924746C2214yescomplemented
24#18011834C2214yescomplemented
25#18011834C2212yescomplemented
26#18011831C2212yescomplemented
27C22×D4×C149C2211yescharacteristic
28C4×D4×C149—22no—
29C4×D4×C149C2214yes—
30#117×C149C2211yescharacteristic
31#117×C149C2211yescharacteristic
32C2×C22⋊C4×C149—22no—
33#14558736—22no—
34#14558736—22no—
35C2×Dic298—21no—
36C2×Dic298—22no—
37C2×Dic298—22no—
38C2×Dic298C2311yescharacteristic
39C2×Dic298C2312yes—
40C2×D596C2311yescharacteristic
41C2×C22⋊D149—21no—
42C22×Dic149—21no—
43C2×C4×D149—21no—
44#14558724—28no—
45#14558724—24no—
46#14558721—24no—
47#14558720—22no—
48C2×#11924746—22no—
49C2×#11924746C2312yes—
50C2×#11924746C2312yes—
51C4⋊Dic149—24no—
52#14558713—24no—
53C24×C149—21no—
54C2×D4×C149—21no—
55C2×D4×C149—22no—
56C2×D4×C149D414yes—
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—
68Dic298—22no—
69Dic298—21no—
70Dic298—22no—
71Dic298—21no—
72Dic298—42no—
73D596—21no—
74D596—21no—
75C22⋊D149—42no—
76C2×Dic149—21no—
77C2×Dic149—22no—
78C2×Dic149—42no—
79C4×D149—42no—
80#11924746—22no—
81#11924746—22no—
82C23×C149—22no—
83C23×C149—24no—
84C23×C149—82no—
85C23×C149C2×D411yescharacteristic
86D4×C149—24no—
87D4×C149—22no—
88D4×C149C2×D414yes—
89C2×C4×C149—22no—
90C2×C4×C149—84no—
91C2×C4×C149C2×D414yes—
92C2×C4×C149C2×D411yescharacteristic
93C2×C4×C149C2×D412yes—
94C2×C4×C149#4112yes—
95C2×C4×C149C2411yescharacteristic
96C22×C149—22no—
97C22×C149—24no—
98C22×C149—44no—
99C22×C149—84no—
100C22×C149#12112yes—
101C22×C149C22×D411yescharacteristic
102C2×D149—41no—
103C2×D149—42no—
104C4×C149—24no—
105C4×C149—42no—
106C4×C149#12112yes—
107C4×C149C22×D411yescharacteristic
108C4×C149C2×#4111yescharacteristic
109Dic149—41no—
110Dic149—42no—
111C2×C149—22no—
112C2×C149—44no—
113C2×C149C2×#12111yescharacteristic
114C2×C149#57712yes—
115D149—81no—
116C149#304211yescharacteristic, complemented, Sylow
117#3042—1491nomaximal, Sylow
118C2×AGL(1,ℤ/8)—1491no—
119C22×SD16—1491no—
120#536—1491no—
121#518D14911yescharacteristic, complemented
122#463—1494no—
123#461—1494no—
124#424—1491no—
125#419—1491no—
126#416—1491no—
127C2×#41—1491no—
128C22×Q8—1491no—
129C22×D4C2×D14911yescharacteristic
130AGL(1,ℤ/8)—2984no—
131C2×SD16—2984no—
132C2×SD16—1494no—
133C2×SD16—1492no—
134C2×D8—1492no—
135C2×M16—1491no—
136C22×C8—1491no—
137C4⋊Q8—1492no—
138#124—1492no—
139#123—2982no—
140C22⋊Q8—2982no—
141C4×D4—22no—
142C4×D4C2×D14914yes—
143#117C2×D14911yescharacteristic
144#117C2×D14911yescharacteristic
145C2×C22⋊C4—22no—
146C4⋊C8—1494no—
147#103—1492no—
148#103—1494no—
149#102—1492no—
150C24—21no—
151#41—2982no—
152#41—2982no—
153C2×Q8—2981no—
154C2×Q8—2982no—
155C2×Q8—2982no—
156C2×Q8—1492no—
157C2×Q8—1491no—
158C2×D4—21no—
159C2×D4—22no—
160C2×D4—2981no—
161C2×D4—1491no—
162C2×D4D59614yes—
163C2×D4C22×D14912yes—
164C22×C4—24no—
165C22×C4—2981no—
166C22×C4—2981no—
167C22×C4C22×D14911yescharacteristic
168SD16—2988no—
169SD16—2984no—
170D8—2984no—
171M16—2982no—
172C2×C8—2982no—
173C2×C8—1492no—
174C2×C8—1492no—
175C4⋊C4—2984no—
176C4⋊C4C22⋊D14912yes—
177C4⋊C4C22×D14912yes—
178C22⋊C4—21no—
179C22⋊C4—24no—
180C22⋊C4—2984no—
181C22⋊C4C22⋊D14912yes—
182C42—21no—
183C42C22×D14912yes—
184C23—22no—
185C23—24no—
186C23—82no—
187C23—2981no—
188C23C2×C22⋊D14911yescharacteristic
189Q8—2982no—
190Q8—2981no—
191Q8—2982no—
192Q8—2981no—
193Q8—5962no—
194D4—22no—
195D4—24no—
196D4—2981no—
197D4—2981no—
198D4—5962no—
199D4C2×D59614yes—
200C2×C4—22no—
201C2×C4—84no—
202C2×C4—2982no—
203C2×C4—2981no—
204C2×C4—5962no—
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—24no—
215C22—44no—
216C22—84no—
217C22—5962no—
218C22—5961no—
219C22#1801188512yes—
220C22C22×C22⋊D14911yescharacteristic
221C4—24no—
222C4—42no—
223C4—5961no—
224C4—5962no—
225C4#1801188512yes—
226C4C22×D59611yescharacteristic
227C4C2×#1455873611yescharacteristic
228C2—22no—
229C2—44no—
230C2—11921no—
231C2C2×#1801188511yescharacteristic
232C2#2375043612yes—
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#518×C149C2
socleC22×C149C22×D4
prime radicalC2×#18011937C2
hypercenter#518D149
hypocenterC149#3042
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
2. C22×#14558724C2semidirect
3. #23750201C2semidirect
4. #23749840C2semidirect
5. #23749830C2semidirect
6. #23749652C2semidirect
7. #23749633C2semidirect
8. #23749619C2semidirect
9. #518×C149C2semidirect
19. #18011911C22semidirect
20. #18011899C22semidirect
23. C4⋊#11924746C22semidirect
24. #18011834C22semidirect
25. #18011834C22semidirect
26. #18011831C22semidirect
116. C149#3042semidirect
121. #518D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119372
C22×#145587242
#237502012
#237498402
#237498302
#237496522
#237496332
#237496192
#518×C1492
#3042149