Finite Group Databasebeta

← #14574084

Subgroups — #14574084

Order 2432.

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

normal subgroups only

This group has 656 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×#10597360C212yesmaximal, complemented
2C2×#10597357C212yesmaximal, complemented
3#11927093C211yesmaximal, characteristic, complemented
4#127×D19C211yesmaximal, characteristic, complemented
5#11926934C211yesmaximal, characteristic, complemented
6#11926933C211yesmaximal, characteristic, complemented
7#11926931C211yesmaximal, characteristic, complemented
8#11926919C212yesmaximal, complemented
9#11926915C212yesmaximal, complemented
10#11926496C211yesmaximal, characteristic, complemented
11C19×#496C211yesmaximal, characteristic, complemented
12C2×#64545C2211yescharacteristic
13C2×#64543C2211yescharacteristic
14C2×D4×D19—22no—
15C2×D4×D19C2212yes—
16C2×SD16×C19C2212yescomplemented
17C2×D8×C19C2212yescomplemented
18C19×#127C2211yescharacteristic
19C19×#124C2211yescharacteristic, complemented
20#10597390C2211yescharacteristic, complemented
21C2×#64527C2212yescomplemented
22#10597386—22no—
23#10597386C2212yes—
24#10597386C2211yescharacteristic, complemented
25C2×#64526C2212yescomplemented
26C2×#64525C2212yescomplemented
27C2×#64525C2212yescomplemented
28#10597360—28no—
29#10597357—28no—
30C2×D152C2212yescomplemented
31C2×#64516C2212yescomplemented
32C2×#64515C2212yes—
33#10597330—22no—
34(C22⋊D19)⋊C4—22no—
35#10597321C2211yescharacteristic, complemented
36#10597320C2211yescharacteristic
37C42×D19C2211yescharacteristic
38C19×#97C2211yescharacteristic, complemented
39C8×Dic19C2212yescomplemented
40#10597260C2211yescharacteristic, complemented
41C23×D19—22no—
42C2×Q8×C19C2311yescharacteristic
43C2×D4×C19—22no—
44C2×D4×C19C2311yescharacteristic
45C2×D4×C19C2312yes—
46C2×C22⋊D19—21no—
47C2×C22⋊D19—22no—
48C2×C22⋊D19—24no—
49C2×C22⋊D19—22no—
50C22×Dic19—21no—
51#64545—24no—
52#64543—24no—
53D4×D19—24no—
54D4×D19—24no—
55D4×D19—48no—
56C2×D76—21no—
57C2×D76—22no—
58C2×D76C2311yescharacteristic
59C2×D76C2312yes—
60C2×C4×D19—21no—
61C2×C4×D19D412yes—
62C2×C4×D19C2311yescharacteristic
63C2×Dic38C2311yescharacteristic
64SD16×C19—24no—
65D8×C19—24no—
66C2×C8×C19C2312yes—
67C22⋊C4×C19—22no—
68C42×C19C2311yescharacteristic
69#64527—24no—
70#64526—24no—
71#64525—24no—
72#64525—24no—
73(C2×D19)⋊C4—22no—
74Dic19⋊C4—22no—
75C4×Dic19D412yes—
76C4×Dic19C2311yescharacteristic
77C2×C19⋊C8C2312yes—
78D152—24no—
79#64516—24no—
80#64515D418yescomplemented
81C23×C19—21no—
82C23×C19—22no—
83C22×D19—21no—
84C22×D19—22no—
85C22×D19—48no—
86C22×D19—44no—
87C22×D19C2×D411yescharacteristic
88Q8×C19—22no—
89D4×C19—22no—
90D4×C19—22no—
91D4×C19—22no—
92D4×C19—44no—
93C2×C4×C19—21no—
94C2×C4×C19C2×D412yes—
95C2×C4×C19C2411yescharacteristic
96C22⋊D19—42no—
97C22⋊D19—44no—
98C22⋊D19—48no—
99C22⋊D19—44no—
100C2×Dic19—21no—
101C2×Dic19—42no—
102C2×Dic19C2×D411yescharacteristic
103C2×Dic19C2×D412yes—
104D76—22no—
105D76—22no—
106D76—22no—
107D76—44no—
108D76—42no—
109C4×D19—24no—
110C4×D19—42no—
111C4×D19C2×D414yes—
112Dic38—22no—
113C8×C19C2×D414yescomplemented
114C19⋊C8C2×D414yescomplemented
115#3151—191nomaximal, Sylow
116C22×C19—41no—
117C22×C19—42no—
118C22×C19—44no—
119C22×C19—42no—
120C22×C19C22×D411yescharacteristic
121C2×D19—22no—
122C2×D19—41no—
123C2×D19—42no—
124C2×D19—44no—
125C2×D19—42no—
126C2×D19—88no—
127C2×D19#12712yes—
128C4×C19—22no—
129C4×C19—41no—
130C4×C19C22×D412yes—
131Dic19—41no—
132Dic19#12712yes—
133Dic19AGL(1,ℤ/8)14yescomplemented
134C2×AGL(1,ℤ/8)—192no—
135C2×AGL(1,ℤ/8)—192no—
136#532—191no—
137C2×#127—191no—
138#496—191no—
139#496—191no—
140#496—191no—
141#496D1911yescharacteristic, complemented
142#493—192no—
143#492—192no—
144C4×M16—191no—
145C2×C19—82no—
146C2×C19—81no—
147C2×C19C2×#12711yescharacteristic
148C2×C19C2×AGL(1,ℤ/8)12yes—
149D19—22no—
150D19—81no—
151D19—82no—
152C2×#41—191no—
153C2×#41—191no—
154C22×D4—192no—
155C22×D4—382no—
156AGL(1,ℤ/8)—388no—
157AGL(1,ℤ/8)—388no—
158C2×SD16—192no—
159C2×SD16—192no—
160C2×SD16—192no—
161C2×SD16C2×D1912yescomplemented
162C2×D8—192no—
163C2×D8—192no—
164C2×D8—192no—
165C2×D8C2×D1912yescomplemented
166C2×M16—192no—
167C4⋊Q8—191no—
168#127—192no—
169#127—191no—
170#127—191no—
171#127—382no—
172#127C2×D1911yescharacteristic
173#124—191no—
174#124C2×D1911yescharacteristic, complemented
175#121—382no—
176C4×D4—382no—
177C2×C42—191no—
178#97—191no—
179#97C2×D1911yescharacteristic, complemented
180C4×C8—192no—
181C19#315111yescharacteristic, complemented, Sylow
182C24—382no—
183#41—384no—
184#41—384no—
185C2×Q8—191no—
186C2×Q8C22×D1911yescharacteristic
187C2×D4—22no—
188C2×D4—191no—
189C2×D4—192no—
190C2×D4—381no—
191C2×D4—384no—
192C2×D4—384no—
193C2×D4—382no—
194C2×D4—384no—
195C2×D4—382no—
196C2×D4—381no—
197C2×D4—382no—
198C2×D4—768no—
199C2×D4C22×D1911yescharacteristic
200C2×D4C22×D1912yes—
201C22×C4—191no—
202C22×C4—192no—
203C22×C4—381no—
204C22×C4—381no—
205SD16—24no—
206SD16—384no—
207SD16—384no—
208SD16—384no—
209D8—24no—
210D8—384no—
211D8—384no—
212D8—384no—
213M16—198no—
214C2×C8—192no—
215C2×C8C22×D1912yes—
216C4⋊C4—382no—
217C22⋊C4—22no—
218C22⋊C4—382no—
219C42—192no—
220C42—191no—
221C42C22×D1911yescharacteristic
222C23—21no—
223C23—22no—
224C23—191no—
225C23—381no—
226C23—382no—
227C23—764no—
228C23—768no—
229Q8—22no—
230Q8—382no—
231D4—22no—
232D4—22no—
233D4—22no—
234D4—44no—
235D4—382no—
236D4—382no—
237D4—382no—
238D4—764no—
239D4—762no—
240D4—764no—
241D4—768no—
242D4—764no—
243D4—762no—
244C2×C4—21no—
245C2×C4—192no—
246C2×C4—191no—
247C2×C4—194no—
248C2×C4—384no—
249C2×C4—381no—
250C2×C4—762no—
251C2×C4—762no—
252C2×C4D4×D1912yes—
253C2×C4C23×D1911yescharacteristic
254C8—194no—
255C8D4×D1914yescomplemented
256C22—44no—
257C22—42no—
258C22—41no—
259C22—42no—
260C22—192no—
261C22—382no—
262C22—764no—
263C22—762no—
264C22—761no—
265C22—762no—
266C22—1528no—
267C22C2×D4×D1911yescharacteristic
268C4—22no—
269C4—41no—
270C4—194no—
271C4—192no—
272C4—761no—
273C4C2×D4×D1912yes—
274C2—82no—
275C2—81no—
276C2—382no—
277C2—1522no—
278C2—1521no—
279C2#127×D1911yescharacteristic
280C2AGL(1,ℤ/8)×D1912yes—
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#496C2
socleC22×C19C22×D4
hypercenter#496D19
hypocenterC19#3151
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#10597360C2semidirect
2. C2×#10597357C2semidirect
3. #11927093C2semidirect
4. #127×D19C2semidirect
5. #11926934C2semidirect
6. #11926933C2semidirect
7. #11926931C2semidirect
8. #11926919C2semidirect
9. #11926915C2semidirect
10. #11926496C2semidirect
11. C19×#496C2semidirect
16. C2×SD16×C19C22semidirect
17. C2×D8×C19C22semidirect
19. C19×#124C22semidirect
20. #10597390C22semidirect
21. C2×#64527C22semidirect
24. #10597386C22semidirect
25. C2×#64526C22semidirect
26. C2×#64525C22semidirect
27. C2×#64525C22semidirect
30. C2×D152C22semidirect
31. C2×#64516C22semidirect
35. #10597321C22semidirect
38. C19×#97C22semidirect
39. C8×Dic19C22semidirect
40. #10597260C22semidirect
80. #64515D4semidirect
113. C8×C19C2×D4semidirect
114. C19⋊C8C2×D4semidirect
133. Dic19AGL(1,ℤ/8)semidirect
141. #496D19semidirect
161. C2×SD16C2×D19semidirect
165. C2×D8C2×D19semidirect
174. #124C2×D19semidirect
179. #97C2×D19semidirect
181. C19#3151semidirect
255. C8D4×D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973602
C2×#105973572
#119270932
#127×D192
#119269342
#119269332
#119269312
#119269192
#119269152
#119264962
C19×#4962
#315119