Finite Group Databasebeta

← #14566949

Subgroups — #14566949

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×#64543C211yesmaximal, characteristic, complemented
2C2×#10597383C212yesmaximal, complemented
3C2×C22⋊C4×D19C211yesmaximal, characteristic, complemented
4#11926457C211yesmaximal, characteristic, complemented
5#11926456C211yesmaximal, characteristic, complemented
6#11926452C211yesmaximal, characteristic, complemented
7#11926424C212yesmaximal, complemented
8#11926421C212yesmaximal, complemented
9#11926420C212yesmaximal, complemented
10#11926406C211yesmaximal, characteristic, complemented
11C19×#392C211yesmaximal, characteristic, complemented
12C24×D19C2211yescharacteristic
13C22×D4×C19C2212yes—
14C22×D4×C19C2211yescharacteristic, complemented
15C22×C22⋊D19C2212yes—
16C22×C22⋊D19C2212yes—
17C23×Dic19C2212yescomplemented
18C2×#64543—28no—
19C2×#64543—24no—
20C22×C4×D19C2211yescharacteristic
21C22×C4×D19C2211yescharacteristic
22C22×Dic38C2211yescharacteristic, complemented
23C2×C22⋊C4×C19C2211yescharacteristic
24C2×C22⋊C4×C19C2212yescomplemented
25C2×C22⋊Dic19C2211yescharacteristic
26C2×C22⋊Dic19C2212yes—
27C2×C22⋊Dic19C2212yescomplemented
28#10597383—28no—
29C2×(C2×D19)⋊C4C2212yes—
30C2×(C2×D19)⋊C4C2211yescharacteristic
31C2×(C2×D19)⋊C4C2212yes—
32C2×(C2×D19)⋊C4C2211yescharacteristic
33C22⋊C4×D19—24no—
34C19×#95C2211yescharacteristic, complemented
35C19⋊#95C2212yescomplemented
36C19⋊#95C2211yescharacteristic, complemented
37C19⋊#95C2212yescomplemented
38C19⋊#95C2212yescomplemented
39C24×C19C2312yes—
40C24×C19C2311yescharacteristic
41C23×D19—22no—
42C23×D19—22no—
43C23×D19—22no—
44C23×D19—24no—
45C23×D19—42no—
46C23×D19C2311yescharacteristic
47C23×D19C2311yescharacteristic
48C2×D4×C19—24no—
49C2×D4×C19—24no—
50C2×D4×C19—24no—
51C2×D4×C19—22no—
52C2×D4×C19—42no—
53C22×C4×C19C2311yescharacteristic
54C22×C4×C19C2312yes—
55C22×C4×C19C2311yescharacteristic
56C2×C22⋊D19—24no—
57C2×C22⋊D19—24no—
58C2×C22⋊D19—24no—
59C2×C22⋊D19—24no—
60C2×C22⋊D19—42no—
61C2×C22⋊D19D418yescomplemented
62C22×Dic19—24no—
63C22×Dic19—24no—
64C22×Dic19—24no—
65C22×Dic19C2311yescharacteristic
66C22×Dic19C2312yes—
67C22×Dic19C2312yes—
68C22×Dic19C2311yescharacteristic
69#64543—232no—
70C2×C4×D19—24no—
71C2×C4×D19—22no—
72C2×C4×D19—42no—
73C2×C4×D19D414yescomplemented
74C2×Dic38—22no—
75C2×Dic38—24no—
76C22⋊C4×C19—22no—
77C22⋊C4×C19—42no—
78C22⋊Dic19—24no—
79C22⋊Dic19—22no—
80C22⋊Dic19—42no—
81(C2×D19)⋊C4—24no—
82(C2×D19)⋊C4—22no—
83(C2×D19)⋊C4—24no—
84(C2×D19)⋊C4—22no—
85C23×C19—21no—
86C23×C19—22no—
87C23×C19—22no—
88C23×C19—22no—
89C23×C19—22no—
90C23×C19—22no—
91C23×C19—21no—
92C23×C19—22no—
93C23×C19—22no—
94C23×C19—22no—
95C23×C19C2×D414yes—
96C23×C19#4112yescomplemented
97C23×C19C2411yescharacteristic
98C22×D19—21no—
99C22×D19—21no—
100C22×D19—22no—
101C22×D19—28no—
102C22×D19—21no—
103C22×D19—22no—
104C22×D19—21no—
105C22×D19—22no—
106C22×D19—48no—
107C22×D19—48no—
108C22×D19—44no—
109C22×D19—44no—
110C22×D19C2×D414yes—
111C22×D19C2×D412yes—
112C22×D19#4112yescomplemented
113D4×C19—28no—
114D4×C19—48no—
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×C19C2×D412yes—
122C22⋊D19—216no—
123C22⋊D19—48no—
124C2×Dic19—216no—
125C2×Dic19—22no—
126C2×Dic19—22no—
127C2×Dic19—22no—
128C2×Dic19—21no—
129C2×Dic19—22no—
130C2×Dic19—22no—
131C2×Dic19—22no—
132C2×Dic19—22no—
133C2×Dic19C2×D414yes—
134C2×Dic19C2×D412yes—
135C4×D19—28no—
136C4×D19—44no—
137Dic38—28no—
138#2404—191nomaximal, Sylow
139C22×C19—24no—
140C22×C19—22no—
141C22×C19—24no—
142C22×C19—24no—
143C22×C19—24no—
144C22×C19—41no—
145C22×C19—42no—
146C22×C19—41no—
147C22×C19—42no—
148C22×C19—42no—
149C22×C19—42no—
150C22×C19—42no—
151C22×C19C22×D411yescharacteristic
152C22×C19C22×D412yes—
153C22×C19C2×#4111yescharacteristic
154C22×C19C2×#4111yescharacteristic
155C22×C19H(5,𝔽2)12yes—
156C2×D19—22no—
157C2×D19—22no—
158C2×D19—24no—
159C2×D19—24no—
160C2×D19—22no—
161C2×D19—24no—
162C2×D19—416no—
163C2×D19—41no—
164C2×D19—41no—
165C2×D19—42no—
166C2×D19#12014yes—
167C4×C19—22no—
168C4×C19—41no—
169C4×C19—42no—
170Dic19—24no—
171Dic19—22no—
172Dic19—41no—
173Dic19—42no—
174C22×#41—191no—
175C2×#120—192no—
176C22×C22⋊C4—191no—
177#393—191no—
178#393—191no—
179#392—191no—
180#392D1911yescharacteristic, complemented
181#386—192no—
182#386—192no—
183#386—192no—
184#381—191no—
185C2×C19—42no—
186C2×C19—44no—
187C2×C19C2×#12011yescharacteristic
188C2×C19#52511yescharacteristic
189C2×C19#53511yescharacteristic
190C2×C19#54612yes—
191C2×C19#54612yes—
192D19—24no—
193D19—42no—
194C25—191no—
195C2×#41—384no—
196C2×#41—388no—
197C22×Q8—191no—
198C22×D4—192no—
199C22×D4—192no—
200C22×D4C2×D1912yes—
201C22×D4C2×D1911yescharacteristic, complemented
202C23×C4—191no—
203C23×C4—192no—
204C23×C4—191no—
205#120—388no—
206C2×C22⋊C4—191no—
207C2×C22⋊C4—192no—
208C2×C22⋊C4—191no—
209C2×C22⋊C4—191no—
210C2×C22⋊C4—192no—
211C2×C22⋊C4—192no—
212C2×C22⋊C4—192no—
213C2×C22⋊C4—384no—
214C2×C22⋊C4C2×D1911yescharacteristic
215C2×C22⋊C4C2×D1912yescomplemented
216#95—192no—
217#95—191no—
218#95—192no—
219#95—192no—
220#95C2×D1911yescharacteristic, complemented
221C19#240411yescharacteristic, complemented, Sylow
222C24—191no—
223C24—191no—
224C24—382no—
225C24—382no—
226C24—384no—
227C24—382no—
228C24—762no—
229C24C22×D1912yes—
230C24C22×D1911yescharacteristic
231#41—3832no—
232C2×Q8—384no—
233C2×Q8—382no—
234C2×D4—24no—
235C2×D4—24no—
236C2×D4—24no—
237C2×D4—22no—
238C2×D4—42no—
239C2×D4—198no—
240C2×D4—384no—
241C2×D4—384no—
242C2×D4—384no—
243C2×D4—384no—
244C2×D4—762no—
245C22×C4—191no—
246C22×C4—192no—
247C22×C4—194no—
248C22×C4—192no—
249C22×C4—191no—
250C22×C4—384no—
251C22×C4—382no—
252C22×C4—384no—
253C22×C4—384no—
254C22×C4—384no—
255C22×C4—762no—
256C22×C4C22×D1912yes—
257C22×C4C22×D1911yescharacteristic
258C22×C4C22×D1911yescharacteristic
259C22⋊C4—22no—
260C22⋊C4—42no—
261C22⋊C4—382no—
262C22⋊C4—384no—
263C22⋊C4—384no—
264C22⋊C4—382no—
265C22⋊C4—384no—
266C22⋊C4—382no—
267C22⋊C4—762no—
268C23—21no—
269C23—22no—
270C23—22no—
271C23—22no—
272C23—22no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—21no—
278C23—194no—
279C23—192no—
280C23—192no—
281C23—388no—
282C23—381no—
283C23—382no—
284C23—381no—
285C23—381no—
286C23—382no—
287C23—381no—
288C23—382no—
289C23—768no—
290C23—764no—
291C23—768no—
292C23—764no—
293C23D4×D1914yes—
294C23#6454312yescomplemented
295C23C23×D1911yescharacteristic
296Q8—388no—
297D4—28no—
298D4—48no—
299D4—3816no—
300D4—768no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—192no—
308C2×C4—194no—
309C2×C4—388no—
310C2×C4—3816no—
311C2×C4—382no—
312C2×C4—382no—
313C2×C4—382no—
314C2×C4—381no—
315C2×C4—382no—
316C2×C4—382no—
317C2×C4—382no—
318C2×C4—382no—
319C2×C4—764no—
320C2×C4D4×D1912yes—
321C22—22no—
322C22—24no—
323C22—24no—
324C22—24no—
325C22—24no—
326C22—42no—
327C22—41no—
328C22—42no—
329C22—42no—
330C22—42no—
331C22—42no—
332C22—41no—
333C22—194no—
334C22—382no—
335C22—382no—
336C22—384no—
337C22—384no—
338C22—382no—
339C22—384no—
340C22—7616no—
341C22—761no—
342C22—762no—
343C22—761no—
344C22C2×D4×D1911yescharacteristic
345C22C2×D4×D1912yes—
346C22C2×#6454311yescharacteristic
347C22#1059743012yes—
348C22#41×D1911yescharacteristic
349C4—22no—
350C4—41no—
351C4—42no—
352C4—382no—
353C4—384no—
354C4—761no—
355C4—762no—
356C2—42no—
357C2—44no—
358C2—384no—
359C2—762no—
360C2#120×D1911yescharacteristic
361C2#1192705411yescharacteristic
362C2#1192710711yescharacteristic
363C2#1192718112yes—
364C2#1192718312yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#392C2
hypercenter#392D19
hypocenterC19#2404
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×#64543C2semidirect
2. C2×#10597383C2semidirect
3. C2×C22⋊C4×D19C2semidirect
4. #11926457C2semidirect
5. #11926456C2semidirect
6. #11926452C2semidirect
7. #11926424C2semidirect
8. #11926421C2semidirect
9. #11926420C2semidirect
10. #11926406C2semidirect
11. C19×#392C2semidirect
14. C22×D4×C19C22semidirect
17. C23×Dic19C22semidirect
22. C22×Dic38C22semidirect
24. C2×C22⋊C4×C19C22semidirect
27. C2×C22⋊Dic19C22semidirect
34. C19×#95C22semidirect
35. C19⋊#95C22semidirect
36. C19⋊#95C22semidirect
37. C19⋊#95C22semidirect
38. C19⋊#95C22semidirect
61. C2×C22⋊D19D4semidirect
73. C2×C4×D19D4semidirect
96. C23×C19#41semidirect
112. C22×D19#41semidirect
180. #392D19semidirect
201. C22×D4C2×D19semidirect
215. C2×C22⋊C4C2×D19semidirect
220. #95C2×D19semidirect
221. C19#2404semidirect
294. C23#64543semidirect

Maximal subgroups

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

subgroupindex
C22×#645432
C2×#105973832
C2×C22⋊C4×D192
#119264572
#119264562
#119264522
#119264242
#119264212
#119264202
#119264062
C19×#3922
#240419