Finite Group Databasebeta

← #14568565

Subgroups — #14568565

Order 2432.

900 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 900 conjugacy classes of subgroups — too many to draw. Only its 169 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×#10597375C211yesmaximal, characteristic, complemented
2C2×#10597385C211yesmaximal, characteristic, complemented
3C2×#10597328C211yesmaximal, characteristic, complemented
4C2×#10597383C211yesmaximal, characteristic, complemented
5C22×(C2×D19)⋊C4C211yesmaximal, characteristic, complemented
6#11926479C212yesmaximal, complemented
7#11926453C212yesmaximal, complemented
8#11926445C212yesmaximal, complemented
9#11926444C212yesmaximal, complemented
10C22⋊C4×Dic19C211yesmaximal, characteristic, complemented
11C2×C19×#123C211yesmaximal, characteristic, complemented
12C24×D19C2211yescharacteristic
13C22×D4×C19C2211yescharacteristic
14C23×C4×C19C2211yescharacteristic
15C22×C22⋊D19C2211yescharacteristic
16C22×C22⋊D19C2212yes—
17C22×C22⋊D19C2211yescharacteristic, complemented
18C23×Dic19C2211yescharacteristic
19C22×D76C2212yes—
20C19×#123—24no—
21C2×C4⋊C4×C19C2212yescomplemented
22C2×C22⋊C4×C19C2211yescharacteristic
23C2×C22⋊C4×C19C2212yescomplemented
24C2×C22⋊Dic19C2211yescharacteristic
25C2×C22⋊Dic19C2211yescharacteristic, complemented
26#10597385—24no—
27#10597383—24no—
28#10597375—24no—
29C2×(C2×D19)⋊C4—24no—
30C2×(C2×D19)⋊C4C2212yes—
31C2×(C2×D19)⋊C4C2212yes—
32C2×(C2×D19)⋊C4C2212yes—
33C2×(C2×D19)⋊C4C2212yes—
34C2×(C2×D19)⋊C4C2212yescomplemented
35C2×(C2×D19)⋊C4C2211yescharacteristic, complemented
36C2×Dic19⋊C4C2212yescomplemented
37C2×Dic19⋊C4C2211yescharacteristic, complemented
38C2×C4×Dic19C2212yescomplemented
39#10597328—24no—
40C19⋊#95C2212yescomplemented
41C24×C19C2311yescharacteristic
42C24×C19C2311yescharacteristic
43C23×D19—22no—
44C23×D19—24no—
45C23×D19—22no—
46C23×D19—22no—
47C23×D19—42no—
48C23×D19C2311yescharacteristic
49C23×D19C2312yes—
50C2×D4×C19—22no—
51C2×D4×C19—22no—
52C2×D4×C19—22no—
53C22×C4×C19—22no—
54C22×C4×C19—22no—
55C22×C4×C19—22no—
56C22×C4×C19C2312yes—
57C22×C4×C19C2311yescharacteristic
58C22×C4×C19C2312yes—
59C2×C22⋊D19—22no—
60C2×C22⋊D19—22no—
61C2×C22⋊D19—22no—
62C2×C22⋊D19—24no—
63C2×C22⋊D19—24no—
64C2×C22⋊D19—22no—
65C2×C22⋊D19—42no—
66C2×C22⋊D19—42no—
67C22×Dic19—42no—
68C22×Dic19D414yescomplemented
69C22×Dic19C2311yescharacteristic
70C22×Dic19C2312yes—
71C22×Dic19C2311yescharacteristic
72C22×Dic19C2311yescharacteristic
73C2×D76—24no—
74C2×D76—24no—
75C2×D76—42no—
76C4⋊C4×C19—24no—
77C22⋊C4×C19—24no—
78C22⋊C4×C19D414yescomplemented
79C22⋊Dic19—22no—
80C22⋊Dic19D414yescomplemented
81(C2×D19)⋊C4—24no—
82(C2×D19)⋊C4—24no—
83(C2×D19)⋊C4—22no—
84(C2×D19)⋊C4—24no—
85(C2×D19)⋊C4—24no—
86(C2×D19)⋊C4—24no—
87Dic19⋊C4—22no—
88Dic19⋊C4—24no—
89C4×Dic19—42no—
90C23×C19—22no—
91C23×C19—22no—
92C23×C19—21no—
93C23×C19—21no—
94C23×C19—21no—
95C23×C19—22no—
96C23×C19—22no—
97C23×C19C2×D412yes—
98C23×C19C2×D412yes—
99C23×C19C2×D412yes—
100C23×C19C2411yescharacteristic
101C22×D19—28no—
102C22×D19—22no—
103C22×D19—22no—
104C22×D19—22no—
105C22×D19—22no—
106C22×D19—22no—
107C22×D19—22no—
108C22×D19—21no—
109C22×D19—21no—
110C22×D19—21no—
111C22×D19—22no—
112C22×D19—22no—
113C22×D19—48no—
114C22×D19—48no—
115C22×D19—44no—
116C22×D19—44no—
117C22×D19#4114yes—
118D4×C19—44no—
119C2×C4×C19—22no—
120C2×C4×C19—22no—
121C2×C4×C19—22no—
122C2×C4×C19—21no—
123C2×C4×C19—22no—
124C2×C4×C19—21no—
125C2×C4×C19—22no—
126C2×C4×C19—21no—
127C2×C4×C19—44no—
128C2×C4×C19C2×D414yes—
129C22⋊D19—48no—
130C22⋊D19—44no—
131C22⋊D19—44no—
132C2×Dic19—22no—
133C2×Dic19—22no—
134C2×Dic19—22no—
135C2×Dic19—22no—
136C2×Dic19—21no—
137C2×Dic19—21no—
138C2×Dic19—21no—
139C2×Dic19—44no—
140C2×Dic19C2×D414yes—
141C2×Dic19C2×D412yes—
142C2×Dic19C2×D412yes—
143D76—48no—
144#2539—191nomaximal, Sylow
145C22×C19—22no—
146C22×C19—22no—
147C22×C19—24no—
148C22×C19—24no—
149C22×C19—41no—
150C22×C19—41no—
151C22×C19—41no—
152C22×C19—42no—
153C22×C19—42no—
154C22×C19#12714yes—
155C22×C19C22×D411yescharacteristic
156C22×C19C22×D411yescharacteristic
157C22×C19C22×D411yescharacteristic
158C22×C19C2×#4112yes—
159C22×C19H(5,𝔽2)12yes—
160C2×D19—24no—
161C2×D19—24no—
162C2×D19—24no—
163C2×D19—416no—
164C2×D19—42no—
165C2×D19—42no—
166C2×D19—42no—
167C2×D19—42no—
168C2×D19—41no—
169C2×D19—41no—
170C2×D19—41no—
171C2×D19—42no—
172C2×D19—42no—
173C4×C19—24no—
174C4×C19—42no—
175C4×C19—41no—
176Dic19—22no—
177Dic19—22no—
178Dic19—24no—
179Dic19—41no—
180C2×#123—191no—
181C2×#123D1911yescharacteristic, complemented
182C2×#121—191no—
183C2×#120—191no—
184C2×#120—191no—
185C22×C22⋊C4—191no—
186#399—192no—
187#392—192no—
188#390—192no—
189#390—192no—
190C4×C22⋊C4—191no—
191C2×C19—24no—
192C2×C19—81no—
193C2×C19#52511yescharacteristic
194C2×C19C2×#12711yescharacteristic
195C2×C19#53411yescharacteristic
196C2×C19#54612yes—
197C2×C19#54612yes—
198D19—44no—
199D19—81no—
200C25—191no—
201C22×D4—191no—
202C22×D4—192no—
203C22×D4—191no—
204C22×D4—192no—
205C22×D4C2×D1911yescharacteristic
206C23×C4—191no—
207C23×C4C2×D1911yescharacteristic
208#123—24no—
209#123—384no—
210#121—384no—
211#120—384no—
212#120—384no—
213C2×C4⋊C4—191no—
214C2×C4⋊C4—192no—
215C2×C4⋊C4C2×D1912yescomplemented
216C2×C22⋊C4—191no—
217C2×C22⋊C4—191no—
218C2×C22⋊C4—192no—
219C2×C22⋊C4—192no—
220C2×C22⋊C4—192no—
221C2×C22⋊C4—192no—
222C2×C22⋊C4—191no—
223C2×C22⋊C4—192no—
224C2×C22⋊C4—384no—
225C2×C22⋊C4C2×D1911yescharacteristic
226C2×C22⋊C4C2×D1912yescomplemented
227C2×C42—192no—
228#95—192no—
229C19#253911yescharacteristic, complemented, Sylow
230C24—192no—
231C24—191no—
232C24—384no—
233C24—382no—
234C24—382no—
235C24—382no—
236C24—762no—
237C24C22×D1911yescharacteristic
238C24C22×D1911yescharacteristic
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—384no—
243C2×D4—384no—
244C2×D4—382no—
245C2×D4—384no—
246C2×D4—382no—
247C2×D4—382no—
248C2×D4—382no—
249C2×D4—384no—
250C2×D4—762no—
251C2×D4—762no—
252C2×D4—762no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—191no—
257C22×C4—192no—
258C22×C4—191no—
259C22×C4—194no—
260C22×C4—191no—
261C22×C4—762no—
262C22×C4C22×D1912yes—
263C22×C4C22×D1911yescharacteristic
264C22×C4C22×D1912yes—
265C4⋊C4—24no—
266C4⋊C4—382no—
267C4⋊C4—384no—
268C22⋊C4—24no—
269C22⋊C4—194no—
270C22⋊C4—384no—
271C22⋊C4—384no—
272C22⋊C4—384no—
273C22⋊C4—382no—
274C22⋊C4—384no—
275C22⋊C4—382no—
276C22⋊C4—384no—
277C22⋊C4C22⋊D1914yescomplemented
278C42—762no—
279C23—22no—
280C23—22no—
281C23—21no—
282C23—21no—
283C23—22no—
284C23—22no—
285C23—21no—
286C23—194no—
287C23—388no—
288C23—382no—
289C23—382no—
290C23—382no—
291C23—382no—
292C23—382no—
293C23—382no—
294C23—381no—
295C23—381no—
296C23—382no—
297C23—382no—
298C23—381no—
299C23—768no—
300C23—768no—
301C23—764no—
302C23—764no—
303C23D4×D1912yes—
304C23D4×D1912yes—
305C23C2×C22⋊D1912yes—
306C23C23×D1911yescharacteristic
307D4—44no—
308D4—768no—
309D4—768no—
310D4—764no—
311D4—764no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—44no—
321C2×C4—194no—
322C2×C4—192no—
323C2×C4—192no—
324C2×C4—382no—
325C2×C4—382no—
326C2×C4—382no—
327C2×C4—382no—
328C2×C4—381no—
329C2×C4—381no—
330C2×C4—381no—
331C2×C4—764no—
332C2×C4C2×C22⋊D1914yes—
333C22—22no—
334C22—22no—
335C22—24no—
336C22—24no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—42no—
341C22—42no—
342C22—384no—
343C22—384no—
344C22—384no—
345C22—7616no—
346C22—762no—
347C22—762no—
348C22—762no—
349C22—762no—
350C22—761no—
351C22—761no—
352C22—761no—
353C22—762no—
354C22—762no—
355C22#1059738614yes—
356C22C2×D4×D1911yescharacteristic
357C22C2×D4×D1911yescharacteristic
358C22#41×D1912yes—
359C22#1059743512yes—
360C22C22×C22⋊D1911yescharacteristic
361C4—24no—
362C4—42no—
363C4—41no—
364C4—382no—
365C4—382no—
366C4—384no—
367C4—761no—
368C2—24no—
369C2—81no—
370C2—764no—
371C2—1521no—
372C2#1192705211yescharacteristic
373C2C2×#1059738611yescharacteristic
374C2#1192710511yescharacteristic
375C2#1192718212yes—
376C2#1192718612yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#123C2
hypercenterC2×#123D19
hypocenterC19#2539
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#10597375C2semidirect
2. C2×#10597385C2semidirect
3. C2×#10597328C2semidirect
4. C2×#10597383C2semidirect
5. C22×(C2×D19)⋊C4C2semidirect
6. #11926479C2semidirect
7. #11926453C2semidirect
8. #11926445C2semidirect
9. #11926444C2semidirect
10. C22⋊C4×Dic19C2semidirect
11. C2×C19×#123C2semidirect
17. C22×C22⋊D19C22semidirect
21. C2×C4⋊C4×C19C22semidirect
23. C2×C22⋊C4×C19C22semidirect
25. C2×C22⋊Dic19C22semidirect
34. C2×(C2×D19)⋊C4C22semidirect
35. C2×(C2×D19)⋊C4C22semidirect
36. C2×Dic19⋊C4C22semidirect
37. C2×Dic19⋊C4C22semidirect
38. C2×C4×Dic19C22semidirect
40. C19⋊#95C22semidirect
68. C22×Dic19D4semidirect
78. C22⋊C4×C19D4semidirect
80. C22⋊Dic19D4semidirect
181. C2×#123D19semidirect
215. C2×C4⋊C4C2×D19semidirect
226. C2×C22⋊C4C2×D19semidirect
229. C19#2539semidirect
277. C22⋊C4C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973752
C2×#105973852
C2×#105973282
C2×#105973832
C22×(C2×D19)⋊C42
#119264792
#119264532
#119264452
#119264442
C22⋊C4×Dic192
C2×C19×#1232
#253919