Finite Group Databasebeta

← #14572890

Subgroups — #14572890

Order 2432.

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

normal subgroups only

This group has 754 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
1C22×#64543C211yesmaximal, characteristic
2C2×#10597361C212yesmaximal, complemented
3C22⋊Q8×D19C211yesmaximal, characteristic, complemented
4#11926707C212yesmaximal, complemented
5#11926703C212yesmaximal, complemented
6#11926702C211yesmaximal, characteristic, complemented
7#11926699C211yesmaximal, characteristic, complemented
8#11926695C211yesmaximal, characteristic, complemented
9#11926542C212yesmaximal, complemented
10#11926506C211yesmaximal, characteristic, complemented
11C19×#450C211yesmaximal, characteristic, complemented
12C22×D4×C19C2211yescharacteristic
13C22×C22⋊D19—21no—
14C23×Dic19—21no—
15C2×Q8×D19C2211yescharacteristic, complemented
16C2×#64543—28no—
17C2×#64543—21no—
18C2×#64543—21no—
19C2×#64543C2212yes—
20C2×#64543C2212yes—
21C22×C4×D19C2211yescharacteristic
22C22×Dic38C2211yescharacteristic
23C2×SD16×C19C2212yescomplemented
24C19×C22⋊Q8C2211yescharacteristic
25#10597392C2211yescharacteristic, complemented
26C2×#64528C2212yescomplemented
27C2×#64526C2212yescomplemented
28#10597370C2211yescharacteristic
29#10597361—28no—
30C2×Dic76C2212yescomplemented
31C2×#64515C2212yescomplemented
32#10597343C2211yescharacteristic, complemented
33#10597342—21no—
34C4⋊C4×D19—21no—
35C4⋊C4×D19C2211yescharacteristic, complemented
36C22⋊C4×D19—21no—
37#10597324—21no—
38C19×#102C2212yescomplemented
39C19×C22⋊C8C2211yescharacteristic
40#10597289C2212yescomplemented
41C22⋊(C19⋊C8)C2211yescharacteristic
42(C2×D19)⋊C8C2212yescomplemented
43#10597273C2212yescomplemented
44#10597267C2212yescomplemented
45C24×C19—21no—
46C23×D19D411yescharacteristic
47C2×Q8×C19C2311yescharacteristic
48C2×D4×C19—24no—
49C2×D4×C19—21no—
50C2×D4×C19C2312yes—
51C22×C4×C19C2311yescharacteristic
52C2×C22⋊D19—28no—
53C2×C22⋊D19—22no—
54C2×C22⋊D19—22no—
55C22×Dic19—28no—
56C22×Dic19—21no—
57C22×Dic19—22no—
58C22×Dic19—22no—
59C22×Dic19D411yescharacteristic
60Q8×D19—24no—
61#64543—28no—
62#64543—28no—
63#64543—24no—
64#64543—24no—
65#64543—24no—
66#64543D418yes—
67C2×C4×D19—24no—
68C2×C4×D19—21no—
69C2×C4×D19—21no—
70C2×C4×D19D411yescharacteristic
71C2×C4×D19D411yescharacteristic
72C2×C4×D19C2311yescharacteristic
73C2×C4×D19C2311yescharacteristic
74C2×Dic38—21no—
75C2×Dic38—24no—
76C2×Dic38—21no—
77C2×Dic38C2311yescharacteristic
78C2×Dic38C2312yes—
79SD16×C19—24no—
80C2×C8×C19C2312yes—
81C4⋊C4×C19—21no—
82C4⋊C4×C19C2311yescharacteristic
83C22⋊C4×C19—21no—
84C22⋊Dic19—21no—
85#64528—24no—
86#64526—24no—
87(C2×D19)⋊C4—21no—
88(C2×D19)⋊C4—21no—
89C4⋊Dic19—21no—
90C4⋊Dic19C2311yescharacteristic
91Dic19⋊C4—21no—
92Dic19⋊C4—21no—
93Dic19⋊C4—21no—
94C2×C19⋊C8C2312yes—
95Dic76—24no—
96#64515—24no—
97C23×C19—24no—
98C23×C19—22no—
99C23×C19—42no—
100C23×C19—42no—
101C23×C19C2×D411yescharacteristic
102C22×D19—22no—
103C22×D19—22no—
104C22×D19—41no—
105C22×D19C2×D411yescharacteristic
106C22×D19C2×D411yescharacteristic
107Q8×C19—22no—
108D4×C19—24no—
109D4×C19—22no—
110D4×C19C2×D414yes—
111C2×C4×C19—22no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19C2×D411yescharacteristic
115C2×C4×C19C2411yescharacteristic
116C22⋊D19—28no—
117C22⋊D19—28no—
118C2×Dic19—24no—
119C2×Dic19—28no—
120C2×Dic19—22no—
121C2×Dic19—22no—
122C2×Dic19—28no—
123C2×Dic19—21no—
124C2×Dic19—21no—
125C2×Dic19C2×D411yescharacteristic
126C2×Dic19C2×D411yescharacteristic
127C4×D19—22no—
128C4×D19—22no—
129C4×D19—22no—
130C4×D19—42no—
131C4×D19—42no—
132C4×D19C2×D414yes—
133Dic38—24no—
134Dic38—22no—
135Dic38—22no—
136Dic38—42no—
137Dic38C2×D414yes—
138C8×C19—22no—
139C19⋊C8—22no—
140#3007—191nomaximal, Sylow
141C22×C19—21no—
142C22×C19—21no—
143C22×C19—24no—
144C22×C19—48no—
145C22×C19—42no—
146C22×C19—42no—
147C22×C19#13712yescomplemented
148C22×C19C22×D411yescharacteristic
149C2×D19—21no—
150C2×D19—21no—
151C2×D19—21no—
152C2×D19—21no—
153C2×D19—21no—
154C2×D19—44no—
155C2×D19#12012yes—
156C4×C19—21no—
157C4×C19—41no—
158C4×C19—41no—
159C4×C19C22×D412yes—
160Dic19—24no—
161Dic19—21no—
162Dic19—41no—
163Dic19—41no—
164Dic19#12012yes—
165C22×#41—191no—
166C2×#137—192no—
167C2×C22⋊Q8—191no—
168#452—192no—
169#452—192no—
170#451—191no—
171#451—191no—
172#450—191no—
173#450D1911yescharacteristic, complemented
174#417—192no—
175#407—191no—
176C2×C19—22no—
177C2×C19—44no—
178C2×C19C2×#12011yescharacteristic
179C2×C19C2×#13711yescharacteristic
180C2×C19#57511yescharacteristic
181D19—22no—
182D19—41no—
183C2×#41—192no—
184C2×#41—192no—
185C2×#41—381no—
186C2×#41—381no—
187C2×#41—388no—
188C22×Q8—191no—
189C22×Q8—191no—
190C22×D4—381no—
191C22×D4C2×D1911yescharacteristic
192C23×C4—191no—
193C23×C4—381no—
194#137—388no—
195C2×Q16—192no—
196C2×Q16—192no—
197C2×SD16—192no—
198C2×SD16C2×D1912yescomplemented
199C2×M16—192no—
200C22⋊Q8—191no—
201C22⋊Q8—191no—
202C22⋊Q8—191no—
203C22⋊Q8—381no—
204C22⋊Q8—381no—
205C22⋊Q8C2×D1911yescharacteristic
206C2×C4⋊C4—191no—
207C2×C4⋊C4—381no—
208C2×C22⋊C4—381no—
209#103—192no—
210#103—192no—
211#102—192no—
212#102C2×D1912yescomplemented
213C22⋊C8—191no—
214C22⋊C8—192no—
215C22⋊C8C2×D1911yescharacteristic
216C19#300711yescharacteristic, complemented, Sylow
217C24—21no—
218C24—191no—
219#41—198no—
220#41—384no—
221#41—384no—
222#41—388no—
223#41—388no—
224#41—384no—
225C2×Q8—192no—
226C2×Q8—191no—
227C2×Q8—381no—
228C2×Q8—384no—
229C2×Q8—384no—
230C2×Q8—381no—
231C2×Q8C22×D1911yescharacteristic
232C2×D4—24no—
233C2×D4—21no—
234C2×D4—382no—
235C2×D4—382no—
236C2×D4—388no—
237C2×D4C22×D1912yes—
238C22×C4—191no—
239C22×C4—191no—
240C22×C4—191no—
241C22×C4—191no—
242C22×C4—191no—
243C22×C4—384no—
244C22×C4—381no—
245C22×C4—381no—
246C22×C4—382no—
247C22×C4—382no—
248C22×C4—388no—
249C22×C4—381no—
250C22×C4C22×D1911yescharacteristic
251Q16—384no—
252Q16—384no—
253SD16—24no—
254SD16—384no—
255M16—384no—
256C2×C8—192no—
257C2×C8C22×D1912yes—
258C4⋊C4—21no—
259C4⋊C4—191no—
260C4⋊C4—381no—
261C4⋊C4—381no—
262C4⋊C4—381no—
263C4⋊C4—381no—
264C4⋊C4C22×D1911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—381no—
267C22⋊C4—381no—
268C22⋊C4—381no—
269C23—24no—
270C23—22no—
271C23—42no—
272C23—42no—
273C23—191no—
274C23—191no—
275C23—382no—
276C23—382no—
277C23—761no—
278C23D4×D1911yescharacteristic
279Q8—22no—
280Q8—194no—
281Q8—384no—
282Q8—382no—
283Q8—382no—
284Q8—762no—
285D4—24no—
286D4—22no—
287D4—388no—
288D4—388no—
289D4D4×D1914yes—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—191no—
294C2×C4—194no—
295C2×C4—191no—
296C2×C4—382no—
297C2×C4—382no—
298C2×C4—382no—
299C2×C4—388no—
300C2×C4—384no—
301C2×C4—388no—
302C2×C4—382no—
303C2×C4—382no—
304C2×C4—381no—
305C2×C4—381no—
306C2×C4—762no—
307C2×C4—762no—
308C2×C4D4×D1911yescharacteristic
309C2×C4C23×D1911yescharacteristic
310C8—22no—
311C8—382no—
312C22—21no—
313C22—21no—
314C22—24no—
315C22—48no—
316C22—42no—
317C22—42no—
318C22—192no—
319C22—381no—
320C22—381no—
321C22—381no—
322C22—381no—
323C22—381no—
324C22—764no—
325C22#1059736112yescomplemented
326C22C2×D4×D1911yescharacteristic
327C4—21no—
328C4—41no—
329C4—41no—
330C4—192no—
331C4—381no—
332C4—384no—
333C4—761no—
334C4—761no—
335C4C2×D4×D1912yes—
336C2—22no—
337C2—44no—
338C2—382no—
339C2—761no—
340C2#120×D1911yescharacteristic
341C2C2×#1059736111yescharacteristic
342C2#1192734011yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#450C2
socleC22×C19C22×D4
prime radicalC22×#64543C2
hypercenter#450D19
hypocenterC19#3007
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
2. C2×#10597361C2semidirect
3. C22⋊Q8×D19C2semidirect
4. #11926707C2semidirect
5. #11926703C2semidirect
6. #11926702C2semidirect
7. #11926699C2semidirect
8. #11926695C2semidirect
9. #11926542C2semidirect
10. #11926506C2semidirect
11. C19×#450C2semidirect
15. C2×Q8×D19C22semidirect
23. C2×SD16×C19C22semidirect
25. #10597392C22semidirect
26. C2×#64528C22semidirect
27. C2×#64526C22semidirect
30. C2×Dic76C22semidirect
31. C2×#64515C22semidirect
32. #10597343C22semidirect
35. C4⋊C4×D19C22semidirect
38. C19×#102C22semidirect
40. #10597289C22semidirect
42. (C2×D19)⋊C8C22semidirect
43. #10597273C22semidirect
44. #10597267C22semidirect
147. C22×C19#137semidirect
173. #450D19semidirect
198. C2×SD16C2×D19semidirect
212. #102C2×D19semidirect
216. C19#3007semidirect
325. C22#10597361semidirect

Maximal subgroups

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

subgroupindex
C22×#645432
C2×#105973612
C22⋊Q8×D192
#119267072
#119267032
#119267022
#119266992
#119266952
#119265422
#119265062
C19×#4502
#300719