Finite Group Databasebeta

← #14566955

Subgroups — #14566955

Order 2432.

1056 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 159 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×#64545C211yesmaximal, characteristic, complemented
2C2×#10597328C212yesmaximal, complemented
3C2×C22⋊C4×D19C211yesmaximal, characteristic, complemented
4#11926455C211yesmaximal, characteristic, complemented
5#11926454C211yesmaximal, characteristic, complemented
6#11926453C211yesmaximal, characteristic, complemented
7#11926422C212yesmaximal, complemented
8#11926422C212yesmaximal, complemented
9#11926420C212yesmaximal, complemented
10#11926406C211yesmaximal, characteristic, complemented
11C19×#393C211yesmaximal, characteristic, complemented
12C24×D19C2211yescharacteristic
13C22×Q8×C19C2211yescharacteristic, complemented
14C22×C22⋊D19C2212yes—
15C2×#64545—28no—
16C2×#64545—24no—
17C22×D76C2212yes—
18C22×D76C2212yes—
19C22×D76C2211yescharacteristic, complemented
20C22×C4×D19C2211yescharacteristic
21C22×C4×D19C2211yescharacteristic
22C22×C4×D19C2212yescomplemented
23C2×C22⋊C4×C19C2212yes—
24C2×C22⋊C4×C19C2211yescharacteristic
25C2×C22⋊Dic19C2211yescharacteristic
26C2×(C2×D19)⋊C4C2212yes—
27C2×(C2×D19)⋊C4C2211yescharacteristic
28C2×(C2×D19)⋊C4C2212yes—
29C2×(C2×D19)⋊C4C2211yescharacteristic
30C2×(C2×D19)⋊C4C2212yescomplemented
31C2×(C2×D19)⋊C4C2212yescomplemented
32#10597328—28no—
33C22⋊C4×D19—24no—
34C19×#95C2211yescharacteristic, complemented
35C19×#95C2212yescomplemented
36C19⋊#95C2212yescomplemented
37C19⋊#95C2211yescharacteristic, complemented
38C19⋊#95C2212yescomplemented
39C24×C19C2311yescharacteristic
40C23×D19—22no—
41C23×D19—22no—
42C23×D19—22no—
43C23×D19—24no—
44C23×D19—42no—
45C23×D19C2312yes—
46C23×D19C2311yescharacteristic
47C23×D19C2311yescharacteristic
48C2×Q8×C19—24no—
49C2×Q8×C19—22no—
50C22×C4×C19C2311yescharacteristic
51C22×C4×C19C2312yes—
52C22×C4×C19C2311yescharacteristic
53C22×C4×C19C2312yes—
54C2×C22⋊D19—24no—
55C2×C22⋊D19—24no—
56C2×C22⋊D19—42no—
57C22×Dic19C2311yescharacteristic
58C22×Dic19C2312yes—
59C22×Dic19C2311yescharacteristic
60#64545—232no—
61C2×D76—24no—
62C2×D76—24no—
63C2×D76—24no—
64C2×D76—22no—
65C2×D76—24no—
66C2×D76—24no—
67C2×D76—42no—
68C2×D76D418yescomplemented
69C2×C4×D19—24no—
70C2×C4×D19—24no—
71C2×C4×D19—24no—
72C2×C4×D19—24no—
73C2×C4×D19—22no—
74C2×C4×D19—42no—
75C2×C4×D19D414yescomplemented
76C22⋊C4×C19—22no—
77C22⋊C4×C19—24no—
78C22⋊Dic19—22no—
79(C2×D19)⋊C4—24no—
80(C2×D19)⋊C4—22no—
81(C2×D19)⋊C4—24no—
82(C2×D19)⋊C4—22no—
83(C2×D19)⋊C4—42no—
84(C2×D19)⋊C4—42no—
85C23×C19—21no—
86C23×C19—22no—
87C23×C19—21no—
88C23×C19—22no—
89C23×C19#4112yescomplemented
90C23×C19C2411yescharacteristic
91C22×D19—21no—
92C22×D19—21no—
93C22×D19—22no—
94C22×D19—28no—
95C22×D19—21no—
96C22×D19—22no—
97C22×D19—22no—
98C22×D19—22no—
99C22×D19—22no—
100C22×D19—22no—
101C22×D19—21no—
102C22×D19—22no—
103C22×D19—22no—
104C22×D19—22no—
105C22×D19—48no—
106C22×D19—48no—
107C22×D19—44no—
108C22×D19—44no—
109C22×D19C2×D414yes—
110C22×D19C2×D414yes—
111C22×D19C2×D412yes—
112C22×D19#4112yescomplemented
113Q8×C19—28no—
114C2×C4×C19—22no—
115C2×C4×C19—22no—
116C2×C4×C19—22no—
117C2×C4×C19—21no—
118C2×C4×C19—22no—
119C2×C4×C19—22no—
120C2×C4×C19—22no—
121C2×C4×C19—22no—
122C2×C4×C19C2×D414yes—
123C2×C4×C19C2×D412yes—
124C22⋊D19—48no—
125C2×Dic19—22no—
126C2×Dic19—22no—
127C2×Dic19—21no—
128C2×Dic19—22no—
129C2×Dic19—22no—
130C2×Dic19—22no—
131C2×Dic19C2×D412yes—
132D76—28no—
133D76—216no—
134D76—48no—
135C4×D19—216no—
136C4×D19—28no—
137C4×D19—44no—
138#2404—191nomaximal, Sylow
139C22×C19—22no—
140C22×C19—24no—
141C22×C19—41no—
142C22×C19—41no—
143C22×C19—42no—
144C22×C19C22×D411yescharacteristic
145C22×C19C22×D412yes—
146C22×C19C2×#4111yescharacteristic
147C22×C19C2×#4111yescharacteristic
148C22×C19H(5,𝔽2)12yes—
149C2×D19—22no—
150C2×D19—22no—
151C2×D19—24no—
152C2×D19—24no—
153C2×D19—24no—
154C2×D19—22no—
155C2×D19—24no—
156C2×D19—24no—
157C2×D19—24no—
158C2×D19—416no—
159C2×D19—41no—
160C2×D19—42no—
161C2×D19—42no—
162C2×D19—41no—
163C2×D19—42no—
164C2×D19—42no—
165C2×D19—42no—
166C2×D19#12014yes—
167C4×C19—24no—
168C4×C19—22no—
169C4×C19—41no—
170C4×C19—42no—
171Dic19—22no—
172Dic19—41no—
173Dic19—42no—
174C22×#41—191no—
175C2×#120—192no—
176C22×C22⋊C4—191no—
177#393—191no—
178#393D1911yescharacteristic, complemented
179#392—191no—
180#392—191no—
181#386—192no—
182#386—192no—
183#386—192no—
184#381—191no—
185C2×C19—42no—
186C2×C19C2×#12011yescharacteristic
187C2×C19#52511yescharacteristic
188C2×C19#53511yescharacteristic
189C2×C19#54612yes—
190C2×C19#54612yes—
191D19—24no—
192D19—44no—
193D19—42no—
194C25—191no—
195C2×#41—384no—
196C2×#41—388no—
197C22×Q8C2×D1911yescharacteristic, complemented
198C22×D4—192no—
199C22×D4—192no—
200C22×D4—191no—
201C22×D4—192no—
202C23×C4—191no—
203C23×C4—192no—
204C23×C4—191no—
205#120—388no—
206C2×C22⋊C4—191no—
207C2×C22⋊C4—191no—
208C2×C22⋊C4—191no—
209C2×C22⋊C4—192no—
210C2×C22⋊C4—192no—
211C2×C22⋊C4—192no—
212C2×C22⋊C4—192no—
213C2×C22⋊C4—384no—
214C2×C22⋊C4C2×D1911yescharacteristic
215C2×C22⋊C4C2×D1912yes—
216#95—192no—
217#95—191no—
218#95—192no—
219#95C2×D1911yescharacteristic, complemented
220#95C2×D1912yescomplemented
221C19#240411yescharacteristic, complemented, Sylow
222C24—191no—
223C24—191no—
224C24—192no—
225C24—382no—
226C24—382no—
227C24—384no—
228C24—382no—
229C24—762no—
230C24C22×D1911yescharacteristic
231#41—3832no—
232C2×Q8—22no—
233C2×Q8—24no—
234C2×D4—198no—
235C2×D4—384no—
236C2×D4—384no—
237C2×D4—384no—
238C2×D4—384no—
239C2×D4—384no—
240C2×D4—384no—
241C2×D4—384no—
242C2×D4—382no—
243C2×D4—762no—
244C2×D4—762no—
245C22×C4—191no—
246C22×C4—194no—
247C22×C4—192no—
248C22×C4—191no—
249C22×C4—384no—
250C22×C4—384no—
251C22×C4—384no—
252C22×C4—382no—
253C22×C4—384no—
254C22×C4—762no—
255C22×C4C22×D1912yes—
256C22×C4C22×D1911yescharacteristic
257C22×C4C22×D1911yescharacteristic
258C22×C4C22×D1912yes—
259C22⋊C4—22no—
260C22⋊C4—24no—
261C22⋊C4—382no—
262C22⋊C4—384no—
263C22⋊C4—382no—
264C22⋊C4—382no—
265C22⋊C4—384no—
266C22⋊C4—762no—
267C22⋊C4—762no—
268C23—21no—
269C23—22no—
270C23—21no—
271C23—22no—
272C23—194no—
273C23—192no—
274C23—194no—
275C23—192no—
276C23—388no—
277C23—381no—
278C23—381no—
279C23—382no—
280C23—381no—
281C23—382no—
282C23—382no—
283C23—382no—
284C23—382no—
285C23—381no—
286C23—382no—
287C23—382no—
288C23—382no—
289C23—382no—
290C23—768no—
291C23—764no—
292C23—768no—
293C23—764no—
294C23#6454512yescomplemented
295C23C23×D1911yescharacteristic
296Q8—28no—
297D4—3816no—
298D4—388no—
299D4—768no—
300D4—768no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—192no—
310C2×C4—388no—
311C2×C4—3816no—
312C2×C4—382no—
313C2×C4—381no—
314C2×C4—382no—
315C2×C4—382no—
316C2×C4—382no—
317C2×C4—382no—
318C2×C4—764no—
319C2×C4D4×D1912yes—
320C2×C4D4×D1914yes—
321C22—22no—
322C22—24no—
323C22—41no—
324C22—42no—
325C22—41no—
326C22—194no—
327C22—382no—
328C22—382no—
329C22—384no—
330C22—384no—
331C22—382no—
332C22—384no—
333C22—384no—
334C22—384no—
335C22—384no—
336C22—7616no—
337C22—762no—
338C22—761no—
339C22—762no—
340C22—762no—
341C22—762no—
342C22—762no—
343C22—761no—
344C22C2×D4×D1911yescharacteristic
345C22C2×D4×D1912yes—
346C22C2×#6454511yescharacteristic
347C22#41×D1911yescharacteristic
348C22#1059743512yes—
349C4—22no—
350C4—24no—
351C4—41no—
352C4—42no—
353C4—382no—
354C4—761no—
355C4—762no—
356C2—42no—
357C2—384no—
358C2—762no—
359C2—764no—
360C2#120×D1911yescharacteristic
361C2#1192705711yescharacteristic
362C2#1192711211yescharacteristic
363C2#1192718512yes—
364C2#1192718712yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#393C2
hypercenter#393D19
hypocenterC19#2404
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C22×#64545C2semidirect
2. C2×#10597328C2semidirect
3. C2×C22⋊C4×D19C2semidirect
4. #11926455C2semidirect
5. #11926454C2semidirect
6. #11926453C2semidirect
7. #11926422C2semidirect
8. #11926422C2semidirect
9. #11926420C2semidirect
10. #11926406C2semidirect
11. C19×#393C2semidirect
13. C22×Q8×C19C22semidirect
19. C22×D76C22semidirect
22. C22×C4×D19C22semidirect
30. C2×(C2×D19)⋊C4C22semidirect
31. C2×(C2×D19)⋊C4C22semidirect
34. C19×#95C22semidirect
35. C19×#95C22semidirect
36. C19⋊#95C22semidirect
37. C19⋊#95C22semidirect
38. C19⋊#95C22semidirect
68. C2×D76D4semidirect
75. C2×C4×D19D4semidirect
89. C23×C19#41semidirect
112. C22×D19#41semidirect
178. #393D19semidirect
197. C22×Q8C2×D19semidirect
219. #95C2×D19semidirect
220. #95C2×D19semidirect
221. C19#2404semidirect
294. C23#64545semidirect

Maximal subgroups

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

subgroupindex
C22×#645452
C2×#105973282
C2×C22⋊C4×D192
#119264552
#119264542
#119264532
#119264222
#119264202
#119264062
C19×#3932
#240419