Finite Group Databasebeta

← #14573171

Subgroups — #14573171

Order 2432.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597360C211yesmaximal, characteristic, complemented
2C2×#10597362C211yesmaximal, characteristic, complemented
3#11927107C211yesmaximal, characteristic, complemented
4#11927026C211yesmaximal, characteristic, complemented
5#11926766C211yesmaximal, characteristic, complemented
6#11926764C211yesmaximal, characteristic, complemented
7#11926760C211yesmaximal, characteristic, complemented
8#11926758C211yesmaximal, characteristic, complemented
9#11926742C211yesmaximal, characteristic, complemented
10#11926738C211yesmaximal, characteristic, complemented
11#11926736C211yesmaximal, characteristic, complemented
12#11926569C211yesmaximal, characteristic, complemented
13#11926542C211yesmaximal, characteristic, complemented
14#102×D19C211yesmaximal, characteristic, complemented
15C19×#460C211yesmaximal, characteristic, complemented
16C2×#64545C2211yescharacteristic
17C2×#64543C2211yescharacteristic
18C2×D4×D19C2211yescharacteristic
19C2×SD16×C19C2211yescharacteristic
20C2×SD16×C19C2211yescharacteristic, complemented
21C19×#127C2211yescharacteristic
22C4×Q8×C19C2211yescharacteristic, complemented
23Q8×Dic19C2211yescharacteristic, complemented
24C2×#64528C2211yescharacteristic, complemented
25C2×#64527C2211yescharacteristic
26#10597386C2211yescharacteristic
27#10597385—21no—
28#10597385—21no—
29#10597383—21no—
30#10597383—21no—
31#10597382C2211yescharacteristic
32C2×#64525C2211yescharacteristic
33C2×#64525C2211yescharacteristic, complemented
34#10597362—24no—
35#10597360—24no—
36C2×D152C2211yescharacteristic
37C2×#64516C2211yescharacteristic, complemented
38C2×#64515C2211yescharacteristic
39C2×C8×D19C2211yescharacteristic
40#10597339—21no—
41#10597339C2211yescharacteristic, complemented
42C4⋊C4×D19—21no—
43C4⋊C4×D19C2211yescharacteristic
44#10597321C2211yescharacteristic
45C4×D76—21no—
46C4×D76C2211yescharacteristic, complemented
47#10597318—21no—
48#10597318C2211yescharacteristic
49C19×C4⋊C8C2211yescharacteristic, complemented
50C19×#102C2211yescharacteristic
51C19×#102C2211yescharacteristic, complemented
52#10597289C2211yescharacteristic
53#10597289C2211yescharacteristic, complemented
54#10597278C2211yescharacteristic
55#10597273C2211yescharacteristic, complemented
56Dic19⋊C8C2211yescharacteristic, complemented
57Dic19⋊C8C2211yescharacteristic, complemented
58#10597267C2211yescharacteristic, complemented
59#10597266C2211yescharacteristic
60C4⋊(C19⋊C8)C2211yescharacteristic, complemented
61C23×D19—21no—
62C2×Q8×C19C2311yescharacteristic
63C2×D4×C19—21no—
64C2×D4×C19—21no—
65C2×D4×C19C2311yescharacteristic
66C2×D4×C19C2311yescharacteristic
67C2×C22⋊D19—21no—
68C2×C22⋊D19—21no—
69C2×C22⋊D19—21no—
70C2×C22⋊D19—21no—
71C22×Dic19—21no—
72#64545—22no—
73#64545D414yescomplemented
74#64543—22no—
75#64543—22no—
76D4×D19—22no—
77D4×D19—22no—
78C2×D76—21no—
79C2×D76C2311yescharacteristic
80C2×D76C2311yescharacteristic
81C2×C4×D19—21no—
82C2×C4×D19—21no—
83C2×C4×D19—21no—
84C2×C4×D19—21no—
85C2×C4×D19C2311yescharacteristic
86C2×Dic38C2311yescharacteristic
87SD16×C19—22no—
88SD16×C19—22no—
89C2×C8×C19C2311yescharacteristic
90C2×C8×C19C2311yescharacteristic
91C4⋊C4×C19—21no—
92C4⋊C4×C19C2311yescharacteristic
93C42×C19—21no—
94C42×C19C2311yescharacteristic
95C22⋊Dic19—21no—
96C22⋊Dic19—21no—
97#64528—22no—
98#64527—22no—
99#64525—22no—
100#64525—22no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4—21no—
103(C2×D19)⋊C4—21no—
104(C2×D19)⋊C4—21no—
105(C2×D19)⋊C4D411yescharacteristic
106(C2×D19)⋊C4D411yescharacteristic
107C4⋊Dic19—21no—
108C4⋊Dic19C2311yescharacteristic
109Dic19⋊C4—21no—
110Dic19⋊C4D411yescharacteristic
111Dic19⋊C4D411yescharacteristic
112C4×Dic19—21no—
113C4×Dic19C2311yescharacteristic
114C2×C19⋊C8C2311yescharacteristic
115C2×C19⋊C8C2311yescharacteristic
116D152—22no—
117#64516—22no—
118#64515—22no—
119C8×D19—22no—
120C23×C19—21no—
121C23×C19—21no—
122C22×D19—21no—
123C22×D19—21no—
124C22×D19—42no—
125C22×D19—81no—
126C22×D19—81no—
127C22×D19C2×D411yescharacteristic
128Q8×C19—21no—
129Q8×C19C2×D412yes—
130D4×C19—21no—
131D4×C19—21no—
132D4×C19—21no—
133D4×C19—21no—
134D4×C19—81no—
135D4×C19—81no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19C2×D411yescharacteristic
139C2×C4×C19C2×D411yescharacteristic
140C2×C4×C19C2411yescharacteristic
141C22⋊D19—42no—
142C22⋊D19—42no—
143C22⋊D19—81no—
144C22⋊D19—81no—
145C2×Dic19—21no—
146C2×Dic19—21no—
147C2×Dic19—42no—
148C2×Dic19C2×D411yescharacteristic
149C2×Dic19C2×D411yescharacteristic
150C2×Dic19C2×D411yescharacteristic
151D76—24no—
152D76—21no—
153D76—21no—
154D76—21no—
155D76C2×D412yes—
156C4×D19—24no—
157C4×D19—81no—
158C4×D19—81no—
159C4×D19—81no—
160C4×D19C2×D412yes—
161C4×D19#4112yes—
162Dic38—21no—
163Dic38—21no—
164C8×C19—21no—
165C8×C19—21no—
166C19⋊C8—21no—
167C19⋊C8—21no—
168#3045—191nomaximal, Sylow
169C22×C19—41no—
170C22×C19—41no—
171C22×C19—41no—
172C22×C19—41no—
173C22×C19—41no—
174C22×C19—41no—
175C22×C19C22×D411yescharacteristic
176C2×D19—21no—
177C2×D19—21no—
178C2×D19—22no—
179C2×D19—41no—
180C2×D19—41no—
181C2×D19—41no—
182C2×D19—41no—
183C2×D19—41no—
184C2×D19—84no—
185C2×D19#12112yes—
186C4×C19—22no—
187C4×C19—21no—
188C4×C19—21no—
189C4×C19—41no—
190C4×C19C22×D411yescharacteristic
191C4×C19C2×#4111yescharacteristic
192Dic19—21no—
193Dic19—21no—
194Dic19—41no—
195Dic19—41no—
196Dic19#12112yes—
197C2×AGL(1,ℤ/8)—191no—
198C2×#135—191no—
199#535—191no—
200#520—191no—
201#464—191no—
202#464—191no—
203#463—191no—
204#463—191no—
205#460—191no—
206#460D1911yescharacteristic, complemented
207#459—191no—
208#459—191no—
209#424—191no—
210#417—191no—
211C2×#102—191no—
212C2×C19—81no—
213C2×C19—81no—
214C2×C19C2×#12111yescharacteristic
215C2×C19#57611yescharacteristic
216C2×C19#57711yescharacteristic
217D19—22no—
218D19—42no—
219D19—81no—
220C2×#41—191no—
221C2×#41—191no—
222C22×D4—191no—
223AGL(1,ℤ/8)—384no—
224#135—384no—
225C2×Q16—191no—
226C2×SD16—191no—
227C2×SD16—191no—
228C2×SD16C2×D1911yescharacteristic
229C2×SD16C2×D1911yescharacteristic, complemented
230C2×D8—191no—
231C2×D8—191no—
232C2×D8—191no—
233C2×M16—191no—
234C22×C8—191no—
235#127—191no—
236#127C2×D1911yescharacteristic
237#124—191no—
238#124—191no—
239#121—381no—
240#121—381no—
241#120—381no—
242#120—381no—
243C4×Q8—191no—
244C4×Q8C2×D1911yescharacteristic, complemented
245C4×D4—191no—
246C4×D4—191no—
247C4×D4—381no—
248C4×D4—381no—
249#117—191no—
250#117—381no—
251C2×C4⋊C4—191no—
252C2×C4⋊C4—381no—
253C4⋊C8—191no—
254C4⋊C8—191no—
255C4⋊C8—191no—
256C4⋊C8C2×D1911yescharacteristic, complemented
257#103—191no—
258#103—191no—
259#102—191no—
260#102—191no—
261#102—191no—
262#102—191no—
263#102C2×D1911yescharacteristic
264#102C2×D1911yescharacteristic, complemented
265C19#304511yescharacteristic, complemented, Sylow
266C24—381no—
267#41—194no—
268#41—382no—
269#41—382no—
270#41—382no—
271C2×Q8—191no—
272C2×Q8C22×D1911yescharacteristic
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—191no—
276C2×D4—191no—
277C2×D4—381no—
278C2×D4—382no—
279C2×D4—382no—
280C2×D4—381no—
281C2×D4—381no—
282C2×D4—381no—
283C2×D4—381no—
284C2×D4C22×D1911yescharacteristic
285C2×D4C22×D1911yescharacteristic
286C22×C4—191no—
287C22×C4—381no—
288C22×C4—381no—
289C22×C4—381no—
290C22×C4—381no—
291C22×C4—381no—
292Q16—382no—
293SD16—22no—
294SD16—22no—
295SD16—382no—
296SD16—382no—
297D8—382no—
298D8—382no—
299D8—382no—
300M16—382no—
301C2×C8—191no—
302C2×C8—191no—
303C2×C8—382no—
304C2×C8C22×D1911yescharacteristic
305C2×C8C22×D1911yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—191no—
308C4⋊C4—191no—
309C4⋊C4—191no—
310C4⋊C4—381no—
311C4⋊C4—381no—
312C4⋊C4C22×D1911yescharacteristic
313C22⋊C4—191no—
314C22⋊C4—191no—
315C22⋊C4—381no—
316C22⋊C4—381no—
317C22⋊C4—381no—
318C22⋊C4—381no—
319C22⋊C4—381no—
320C22⋊C4—381no—
321C42—21no—
322C42—191no—
323C42—381no—
324C42C22×D1911yescharacteristic
325C23—21no—
326C23—21no—
327C23—191no—
328C23—381no—
329C23—381no—
330C23—762no—
331C23—1521no—
332C23—1521no—
333Q8—21no—
334Q8—381no—
335Q8—381no—
336Q8D4×D1912yes—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—81no—
342D4—81no—
343D4—192no—
344D4—384no—
345D4—381no—
346D4—381no—
347D4—381no—
348D4—762no—
349D4—762no—
350D4—1521no—
351D4—1521no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—191no—
355C2×C4—192no—
356C2×C4—192no—
357C2×C4—191no—
358C2×C4—191no—
359C2×C4—384no—
360C2×C4—381no—
361C2×C4—381no—
362C2×C4—762no—
363C2×C4—1521no—
364C2×C4—1521no—
365C2×C4—1521no—
366C2×C4D4×D1911yescharacteristic
367C2×C4D4×D1911yescharacteristic
368C2×C4C23×D1911yescharacteristic
369C8—21no—
370C8—21no—
371C8—381no—
372C8—381no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—192no—
380C22—381no—
381C22—381no—
382C22—382no—
383C22—761no—
384C22—761no—
385C22—761no—
386C22—761no—
387C22—761no—
388C22—1524no—
389C22C2×D4×D1911yescharacteristic
390C4—21no—
391C4—21no—
392C4—22no—
393C4—41no—
394C4—192no—
395C4—381no—
396C4—381no—
397C4—761no—
398C4—761no—
399C4C2×D4×D1911yescharacteristic
400C4#41×D1911yescharacteristic
401C2—81no—
402C2—81no—
403C2—382no—
404C2—762no—
405C2—1521no—
406C2#121×D1911yescharacteristic
407C2#1192734811yescharacteristic
408C2#1192735011yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#460C2
socleC22×C19C22×D4
hypercenter#460D19
hypocenterC19#3045
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#10597360C2semidirect
2. C2×#10597362C2semidirect
3. #11927107C2semidirect
4. #11927026C2semidirect
5. #11926766C2semidirect
6. #11926764C2semidirect
7. #11926760C2semidirect
8. #11926758C2semidirect
9. #11926742C2semidirect
10. #11926738C2semidirect
11. #11926736C2semidirect
12. #11926569C2semidirect
13. #11926542C2semidirect
14. #102×D19C2semidirect
15. C19×#460C2semidirect
20. C2×SD16×C19C22semidirect
22. C4×Q8×C19C22semidirect
23. Q8×Dic19C22semidirect
24. C2×#64528C22semidirect
33. C2×#64525C22semidirect
37. C2×#64516C22semidirect
41. #10597339C22semidirect
46. C4×D76C22semidirect
49. C19×C4⋊C8C22semidirect
51. C19×#102C22semidirect
53. #10597289C22semidirect
55. #10597273C22semidirect
56. Dic19⋊C8C22semidirect
57. Dic19⋊C8C22semidirect
58. #10597267C22semidirect
60. C4⋊(C19⋊C8)C22semidirect
73. #64545D4semidirect
206. #460D19semidirect
229. C2×SD16C2×D19semidirect
244. C4×Q8C2×D19semidirect
256. C4⋊C8C2×D19semidirect
264. #102C2×D19semidirect
265. C19#3045semidirect

Maximal subgroups

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

subgroupindex
C2×#105973602
C2×#105973622
#119271072
#119270262
#119267662
#119267642
#119267602
#119267582
#119267422
#119267382
#119267362
#119265692
#119265422
#102×D192
C19×#4602
#304519