Finite Group Databasebeta

← #14573177

Subgroups — #14573177

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×#10597365C211yesmaximal, characteristic, complemented
3#11927112C211yesmaximal, characteristic, complemented
4#11927026C211yesmaximal, characteristic, complemented
5#11926768C211yesmaximal, characteristic, complemented
6#11926762C211yesmaximal, characteristic, complemented
7#11926756C211yesmaximal, characteristic, complemented
8#11926744C211yesmaximal, characteristic, complemented
9#11926742C211yesmaximal, characteristic, complemented
10#11926740C211yesmaximal, characteristic, complemented
11#11926738C211yesmaximal, characteristic, complemented
12#11926569C211yesmaximal, characteristic, complemented
13#11926544C211yesmaximal, characteristic, complemented
14#102×D19C211yesmaximal, characteristic, complemented
15C19×#464C211yesmaximal, characteristic, complemented
16C2×#64545C2211yescharacteristic
17C2×#64545C2211yescharacteristic
18C2×D4×D19C2211yescharacteristic
19C2×Q16×C19C2211yescharacteristic, complemented
20C2×SD16×C19C2211yescharacteristic
21C19×#124C2211yescharacteristic
22C4×Q8×C19C2211yescharacteristic, complemented
23#10597393C2211yescharacteristic
24Q8×Dic19C2211yescharacteristic, complemented
25C2×#64527C2211yescharacteristic
26C2×#64527C2211yescharacteristic, complemented
27C2×#64527C2211yescharacteristic, complemented
28#10597386C2211yescharacteristic
29C2×#64525C2211yescharacteristic
30#10597365—24no—
31#10597360—24no—
32C2×D152C2211yescharacteristic
33C2×D152C2211yescharacteristic, complemented
34C2×#64515C2211yescharacteristic
35C2×C8×D19C2211yescharacteristic
36#10597339—21no—
37#10597339C2211yescharacteristic, complemented
38C4⋊C4×D19—21no—
39C4⋊C4×D19C2211yescharacteristic
40#10597330—21no—
41#10597330—21no—
42#10597328—21no—
43#10597328—21no—
44#10597320C2211yescharacteristic
45C4×D76—21no—
46C4×D76C2211yescharacteristic, complemented
47#10597318—21no—
48#10597318C2211yescharacteristic
49C19×C4⋊C8C2211yescharacteristic, complemented
50C19×#103C2211yescharacteristic, complemented
51C19×#102C2211yescharacteristic
52#10597292C2211yescharacteristic, complemented
53#10597289C2211yescharacteristic
54#10597278C2211yescharacteristic
55#10597278C2211yescharacteristic, complemented
56Dic19⋊C8C2211yescharacteristic, complemented
57Dic19⋊C8C2211yescharacteristic, complemented
58#10597266C2211yescharacteristic
59#10597266C2211yescharacteristic, complemented
60C4⋊(C19⋊C8)C2211yescharacteristic, complemented
61C23×D19—21no—
62C2×Q8×C19C2311yescharacteristic
63C2×Q8×C19C2311yescharacteristic
64C2×D4×C19C2311yescharacteristic
65C2×C22⋊D19—21no—
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68#64545—22no—
69#64545—22no—
70#64545—22no—
71#64545D414yescomplemented
72D4×D19—22no—
73D4×D19—22no—
74C2×D76—21no—
75C2×D76—21no—
76C2×D76—21no—
77C2×D76—21no—
78C2×D76C2311yescharacteristic
79C2×D76C2311yescharacteristic
80C2×D76C2311yescharacteristic
81C2×C4×D19—21no—
82C2×C4×D19—21no—
83C2×C4×D19—21no—
84C2×C4×D19—21no—
85C2×C4×D19—21no—
86C2×C4×D19C2311yescharacteristic
87Q16×C19—22no—
88SD16×C19—22no—
89C2×C8×C19C2311yescharacteristic
90C2×C8×C19C2311yescharacteristic
91C4⋊C4×C19—21no—
92C4⋊C4×C19C2311yescharacteristic
93C22⋊C4×C19—21no—
94C22⋊C4×C19—21no—
95C42×C19—21no—
96C42×C19C2311yescharacteristic
97#64527—22no—
98#64527—22no—
99#64527—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—
117D152—22no—
118#64515—22no—
119C8×D19—22no—
120C23×C19—21no—
121C22×D19—21no—
122C22×D19—21no—
123C22×D19—21no—
124C22×D19—42no—
125C22×D19—81no—
126C22×D19—81no—
127C22×D19C2×D411yescharacteristic
128Q8×C19—21no—
129Q8×C19—21no—
130Q8×C19—21no—
131Q8×C19C2×D412yes—
132D4×C19—21no—
133D4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19C2×D411yescharacteristic
138C2×C4×C19C2×D411yescharacteristic
139C2×C4×C19C2411yescharacteristic
140C22⋊D19—42no—
141C22⋊D19—81no—
142C22⋊D19—81no—
143C2×Dic19—21no—
144C2×Dic19C2×D411yescharacteristic
145C2×Dic19C2×D411yescharacteristic
146C2×Dic19C2×D411yescharacteristic
147D76—24no—
148D76—21no—
149D76—21no—
150D76—21no—
151D76—21no—
152D76—21no—
153D76—42no—
154D76—81no—
155D76—81no—
156D76C2×D412yes—
157C4×D19—24no—
158C4×D19—42no—
159C4×D19—81no—
160C4×D19—81no—
161C4×D19—81no—
162C4×D19C2×D412yes—
163C4×D19#4112yes—
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×C19C22×D411yescharacteristic
173C2×D19—21no—
174C2×D19—21no—
175C2×D19—22no—
176C2×D19—41no—
177C2×D19—41no—
178C2×D19—41no—
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×C19—41no—
191C4×C19C22×D411yescharacteristic
192C4×C19C2×#4111yescharacteristic
193Dic19—21no—
194Dic19—21no—
195Dic19—41no—
196Dic19#12112yes—
197C2×AGL(1,ℤ/8)—191no—
198C2×#135—191no—
199#535—191no—
200#520—191no—
201#464—191no—
202#464D1911yescharacteristic, complemented
203#463—191no—
204#463—191no—
205#460—191no—
206#460—191no—
207#459—191no—
208#459—191no—
209#424—191no—
210#417—191no—
211C2×#102—191no—
212C2×C19—81no—
213C2×C19C2×#12111yescharacteristic
214C2×C19#57611yescharacteristic
215C2×C19#57711yescharacteristic
216D19—22no—
217D19—42no—
218D19—81no—
219D19—81no—
220C2×#41—191no—
221C2×#41—191no—
222C22×D4—191no—
223AGL(1,ℤ/8)—384no—
224#135—384no—
225C2×Q16C2×D1911yescharacteristic, complemented
226C2×SD16—191no—
227C2×SD16—191no—
228C2×SD16—191no—
229C2×SD16C2×D1911yescharacteristic
230C2×D8—191no—
231C2×D8—191no—
232C2×D8—191no—
233C2×M16—191no—
234C22×C8—191no—
235#127—191no—
236#127—191no—
237#124—191no—
238#124C2×D1911yescharacteristic
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#103C2×D1911yescharacteristic, complemented
259#102—191no—
260#102—191no—
261#102—191no—
262#102—191no—
263#102—191no—
264#102C2×D1911yescharacteristic
265C19#304511yescharacteristic, complemented, Sylow
266C24—381no—
267#41—194no—
268#41—382no—
269#41—382no—
270#41—382no—
271C2×Q8C22×D1911yescharacteristic
272C2×Q8C22×D1911yescharacteristic
273C2×D4—191no—
274C2×D4—191no—
275C2×D4—191no—
276C2×D4—381no—
277C2×D4—381no—
278C2×D4—382no—
279C2×D4—382no—
280C2×D4—381no—
281C2×D4—381no—
282C2×D4—381no—
283C2×D4—381no—
284C2×D4—381no—
285C2×D4C22×D1911yescharacteristic
286C22×C4—191no—
287C22×C4—381no—
288C22×C4—381no—
289C22×C4—381no—
290C22×C4—381no—
291C22×C4—381no—
292Q16—22no—
293SD16—22no—
294SD16—382no—
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—21no—
314C22⋊C4—21no—
315C22⋊C4—191no—
316C22⋊C4—191no—
317C22⋊C4—381no—
318C22⋊C4—381no—
319C22⋊C4—381no—
320C22⋊C4—381no—
321C42—21no—
322C42—191no—
323C42—381no—
324C42C22×D1911yescharacteristic
325C23—21no—
326C23—191no—
327C23—381no—
328C23—381no—
329C23—381no—
330C23—762no—
331C23—1521no—
332C23—1521no—
333Q8—21no—
334Q8—21no—
335Q8—21no—
336Q8D4×D1912yes—
337D4—21no—
338D4—21no—
339D4—192no—
340D4—384no—
341D4—381no—
342D4—381no—
343D4—381no—
344D4—381no—
345D4—381no—
346D4—762no—
347D4—762no—
348D4—1521no—
349D4—1521no—
350D4—1521no—
351D4—1521no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—191no—
356C2×C4—192no—
357C2×C4—192no—
358C2×C4—191no—
359C2×C4—191no—
360C2×C4—384no—
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—192no—
377C22—381no—
378C22—381no—
379C22—382no—
380C22—761no—
381C22—761no—
382C22—761no—
383C22—761no—
384C22—761no—
385C22—761no—
386C22—761no—
387C22—761no—
388C22—1524no—
389C22C2×D4×D1911yescharacteristic
390C4—21no—
391C4—21no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—192no—
396C4—381no—
397C4—381no—
398C4—761no—
399C4C2×D4×D1911yescharacteristic
400C4#41×D1911yescharacteristic
401C2—81no—
402C2—382no—
403C2—762no—
404C2—1521no—
405C2—1521no—
406C2#121×D1911yescharacteristic
407C2#1192734611yescharacteristic
408C2#1192735311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#464C2
socleC22×C19C22×D4
hypercenter#464D19
hypocenterC19#3045
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#10597360C2semidirect
2. C2×#10597365C2semidirect
3. #11927112C2semidirect
4. #11927026C2semidirect
5. #11926768C2semidirect
6. #11926762C2semidirect
7. #11926756C2semidirect
8. #11926744C2semidirect
9. #11926742C2semidirect
10. #11926740C2semidirect
11. #11926738C2semidirect
12. #11926569C2semidirect
13. #11926544C2semidirect
14. #102×D19C2semidirect
15. C19×#464C2semidirect
19. C2×Q16×C19C22semidirect
22. C4×Q8×C19C22semidirect
24. Q8×Dic19C22semidirect
26. C2×#64527C22semidirect
27. C2×#64527C22semidirect
33. C2×D152C22semidirect
37. #10597339C22semidirect
46. C4×D76C22semidirect
49. C19×C4⋊C8C22semidirect
50. C19×#103C22semidirect
52. #10597292C22semidirect
55. #10597278C22semidirect
56. Dic19⋊C8C22semidirect
57. Dic19⋊C8C22semidirect
59. #10597266C22semidirect
60. C4⋊(C19⋊C8)C22semidirect
71. #64545D4semidirect
202. #464D19semidirect
225. C2×Q16C2×D19semidirect
244. C4×Q8C2×D19semidirect
256. C4⋊C8C2×D19semidirect
258. #103C2×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×#105973652
#119271122
#119270262
#119267682
#119267622
#119267562
#119267442
#119267422
#119267402
#119267382
#119265692
#119265442
#102×D192
C19×#4642
#304519