Finite Group Databasebeta

← #14575263

Subgroups — #14575263

Order 2432.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597364C211yesmaximal, characteristic, complemented
2C2×#10597354C211yesmaximal, characteristic, complemented
3#11927204C211yesmaximal, characteristic, complemented
4#11927185C211yesmaximal, characteristic, complemented
5#11926929C211yesmaximal, characteristic, complemented
6#11926798C211yesmaximal, characteristic, complemented
7#11926769C211yesmaximal, characteristic, complemented
8#11926762C211yesmaximal, characteristic, complemented
9#11926704C211yesmaximal, characteristic, complemented
10#11926694C211yesmaximal, characteristic, complemented
11#11926692C211yesmaximal, characteristic, complemented
12#11926684C211yesmaximal, characteristic, complemented
13#11926631C211yesmaximal, characteristic, complemented
14#11926620C211yesmaximal, characteristic, complemented
15C19×#470C211yesmaximal, characteristic, complemented
16C2×#64545C2211yescharacteristic
17C2×Q8×D19C2211yescharacteristic, complemented
18C2×#64541C2211yescharacteristic
19C22×D76C2211yescharacteristic
20C2×Q16×C19C2211yescharacteristic, complemented
21C2×M16×C19C2211yescharacteristic
22C19×C22⋊Q8C2211yescharacteristic
23C19×C22⋊Q8C2211yescharacteristic
24#10597393C2211yescharacteristic
25#10597393C2211yescharacteristic, complemented
26C2×#64528C2211yescharacteristic, complemented
27C2×#64527C2211yescharacteristic
28C2×#64527C2211yescharacteristic
29C2×#64527C2211yescharacteristic, complemented
30C4×C22⋊D19C2211yescharacteristic
31#10597364—24no—
32#10597354—24no—
33C2×D152C2211yescharacteristic
34C2×D152C2211yescharacteristic
35C2×#64516C2211yescharacteristic
36C2×#64516C2211yescharacteristic
37C2×#64515C2211yescharacteristic, complemented
38#10597342—21no—
39#10597341—21no—
40#10597341C2211yescharacteristic
41#10597341C2211yescharacteristic, complemented
42#10597340—21no—
43#10597339—21no—
44#10597339C2211yescharacteristic
45#10597333C2211yescharacteristic, complemented
46#10597331—21no—
47#10597330—21no—
48#10597328—21no—
49C22⋊C4×D19—21no—
50C19×#106C2211yescharacteristic, complemented
51C19×#103C2211yescharacteristic, complemented
52C19×#103C2211yescharacteristic, complemented
53C22⋊(C19⋊C8)C2211yescharacteristic
54(C2×D19)⋊C8C2211yescharacteristic, complemented
55Dic19⋊C8C2211yescharacteristic, complemented
56C8×Dic19C2211yescharacteristic, complemented
57#10597267C2211yescharacteristic, complemented
58#10597266C2211yescharacteristic
59#10597266C2211yescharacteristic
60#10597266C2211yescharacteristic, complemented
61C23×D19—21no—
62C2×Q8×C19C2311yescharacteristic
63C2×Q8×C19C2311yescharacteristic
64C22×C4×C19C2311yescharacteristic
65C2×C22⋊D19—21no—
66C2×C22⋊D19D411yescharacteristic
67#64545—22no—
68#64545—41no—
69Q8×D19—22no—
70Q8×D19—41no—
71#64541—22no—
72#64541—41no—
73C2×D76—22no—
74C2×D76—21no—
75C2×D76—21no—
76C2×D76—21no—
77C2×D76—21no—
78C2×D76—41no—
79C2×D76C2311yescharacteristic
80C2×D76C2311yescharacteristic
81C2×D76C2311yescharacteristic
82C2×C4×D19—21no—
83C2×C4×D19—21no—
84C2×C4×D19—21no—
85C2×C4×D19—21no—
86C2×C4×D19C2311yescharacteristic
87C2×Dic38—21no—
88C2×Dic38C2311yescharacteristic
89Q16×C19—22no—
90M16×C19—22no—
91C2×C8×C19C2311yescharacteristic
92C2×C8×C19C2311yescharacteristic
93C4⋊C4×C19—21no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19C2311yescharacteristic
96C4⋊C4×C19C2311yescharacteristic
97C22⋊C4×C19—21no—
98C22⋊C4×C19—21no—
99C22⋊Dic19D411yescharacteristic
100#64528—22no—
101#64527—22no—
102#64527—41no—
103#64527—41no—
104(C2×D19)⋊C4—21no—
105(C2×D19)⋊C4—21no—
106(C2×D19)⋊C4—21no—
107(C2×D19)⋊C4—21no—
108(C2×D19)⋊C4—21no—
109(C2×D19)⋊C4—21no—
110(C2×D19)⋊C4—21no—
111(C2×D19)⋊C4D411yescharacteristic
112Dic19⋊C4—21no—
113Dic19⋊C4D411yescharacteristic
114C4×Dic19—21no—
115C4×Dic19C2311yescharacteristic
116C2×C19⋊C8C2311yescharacteristic
117C2×C19⋊C8C2311yescharacteristic
118D152—22no—
119D152—22no—
120#64516—22no—
121#64516D414yescomplemented
122#64515—22no—
123C23×C19C2×D411yescharacteristic
124C22×D19—21no—
125C22×D19—21no—
126C22×D19—21no—
127C22×D19—42no—
128C22×D19—42no—
129C22×D19—81no—
130C22×D19C2×D411yescharacteristic
131Q8×C19—21no—
132Q8×C19—21no—
133Q8×C19—21no—
134Q8×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19C2×D411yescharacteristic
142C2×C4×C19C2411yescharacteristic
143C22⋊D19—41no—
144C22⋊D19—42no—
145C2×Dic19—21no—
146C2×Dic19C2×D411yescharacteristic
147C2×Dic19C2×D411yescharacteristic
148C2×Dic19C2×D411yescharacteristic
149D76—21no—
150D76—21no—
151D76—21no—
152D76—21no—
153D76—21no—
154D76—42no—
155D76—42no—
156D76—42no—
157D76—81no—
158D76C2×D412yes—
159C4×D19—21no—
160C4×D19—21no—
161C4×D19—42no—
162C4×D19—42no—
163C4×D19—42no—
164C4×D19—81no—
165Dic38—21no—
166Dic38—42no—
167Dic38C2×D412yes—
168C8×C19—21no—
169C8×C19C2×D412yes—
170C19⋊C8—21no—
171C19⋊C8—21no—
172#3275—191nomaximal, Sylow
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19C22×D411yescharacteristic
177C2×D19—21no—
178C2×D19—22no—
179C2×D19—21no—
180C2×D19—21no—
181C2×D19—41no—
182C2×D19—41no—
183C2×D19—41no—
184C2×D19—41no—
185C2×D19—41no—
186C2×D19—41no—
187C2×D19—41no—
188C2×D19—41no—
189C2×D19—84no—
190C4×C19—21no—
191C4×C19—41no—
192C4×C19—41no—
193C4×C19—41no—
194C4×C19—41no—
195C4×C19C22×D411yescharacteristic
196C4×C19H(5,𝔽2)11yescharacteristic
197Dic19—22no—
198Dic19—21no—
199Dic19—21no—
200Dic19—21no—
201C2×#137—191no—
202C2×AGL(1,ℤ/8)—191no—
203#548—191no—
204#546—191no—
205#495—191no—
206#470D1911yescharacteristic, complemented
207#469—191no—
208#464—191no—
209#463—191no—
210#452—191no—
211#450—191no—
212#449—191no—
213#448—191no—
214C4×SD16—191no—
215#436—191no—
216C2×C19—41no—
217C2×C19D4211yescharacteristic
218C2×C19#57511yescharacteristic
219C2×C19#57711yescharacteristic
220D19—41no—
221D19—42no—
222D19—81no—
223D19—81no—
224C2×#41—191no—
225C2×#41—191no—
226C22×Q8—191no—
227C22×D4—191no—
228#137—384no—
229AGL(1,ℤ/8)—384no—
230C2×Q16—191no—
231C2×Q16C2×D1911yescharacteristic, complemented
232C2×SD16—191no—
233C2×SD16—191no—
234C2×SD16—191no—
235C2×SD16—191no—
236C2×SD16—191no—
237C2×D8—191no—
238C2×D8—191no—
239C2×M16—191no—
240C2×M16C2×D1911yescharacteristic
241#124—191no—
242#124—191no—
243#124—381no—
244#123—381no—
245C22⋊Q8—381no—
246C22⋊Q8C2×D1911yescharacteristic
247C22⋊Q8C2×D1911yescharacteristic
248#121—191no—
249#121—191no—
250#121—381no—
251#121—381no—
252#120—381no—
253C4×Q8—191no—
254C4×D4—191no—
255C4×D4—191no—
256C4×D4—381no—
257C2×C22⋊C4—381no—
258#106C2×D1911yescharacteristic, complemented
259C4⋊C8—191no—
260#103—191no—
261#103C2×D1911yescharacteristic, complemented
262#103C2×D1911yescharacteristic, complemented
263#102—191no—
264#102—191no—
265#102—191no—
266C22⋊C8—191no—
267C22⋊C8—191no—
268C4×C8—191no—
269C19#327511yescharacteristic, complemented, Sylow
270C24—381no—
271#41—382no—
272#41—382no—
273#41—761no—
274#41—761no—
275C2×Q8—191no—
276C2×Q8—381no—
277C2×Q8—382no—
278C2×Q8—761no—
279C2×Q8C22×D1911yescharacteristic
280C2×Q8C22×D1911yescharacteristic
281C2×D4—191no—
282C2×D4—191no—
283C2×D4—191no—
284C2×D4—191no—
285C2×D4—382no—
286C2×D4—381no—
287C2×D4—381no—
288C2×D4—381no—
289C2×D4—381no—
290C2×D4—381no—
291C2×D4—761no—
292C22×C4—191no—
293C22×C4—381no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4—381no—
297C22×C4C22×D1911yescharacteristic
298Q16—22no—
299Q16—382no—
300SD16—194no—
301SD16—382no—
302SD16—382no—
303SD16—761no—
304SD16—761no—
305D8—382no—
306D8—382no—
307M16—22no—
308M16—382no—
309C2×C8—191no—
310C2×C8—191no—
311C2×C8C22×D1911yescharacteristic
312C2×C8C22×D1911yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—191no—
316C4⋊C4—381no—
317C4⋊C4C22×D1911yescharacteristic
318C4⋊C4C22×D1911yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—191no—
322C22⋊C4—191no—
323C22⋊C4—381no—
324C22⋊C4—381no—
325C22⋊C4—381no—
326C22⋊C4—381no—
327C22⋊C4—381no—
328C22⋊C4—381no—
329C22⋊C4—381no—
330C42—191no—
331C42—381no—
332C23—191no—
333C23—381no—
334C23—381no—
335C23—381no—
336C23—762no—
337C23—762no—
338C23—1521no—
339C23D4×D1911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—192no—
345Q8—381no—
346Q8—762no—
347D4—192no—
348D4—381no—
349D4—381no—
350D4—381no—
351D4—381no—
352D4—381no—
353D4—762no—
354D4—762no—
355D4—762no—
356D4—761no—
357D4—762no—
358D4—1521no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—191no—
366C2×C4—191no—
367C2×C4—191no—
368C2×C4—381no—
369C2×C4—381no—
370C2×C4—381no—
371C2×C4—762no—
372C2×C4—762no—
373C2×C4—762no—
374C2×C4—1521no—
375C2×C4D4×D1911yescharacteristic
376C2×C4C23×D1911yescharacteristic
377C8—21no—
378C8—381no—
379C8—381no—
380C8D4×D1912yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—381no—
385C22—381no—
386C22—381no—
387C22—382no—
388C22—761no—
389C22—761no—
390C22—761no—
391C22—761no—
392C22—761no—
393C22—761no—
394C22—761no—
395C22—761no—
396C22—1524no—
397C22C2×D4×D1911yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—381no—
404C4—381no—
405C4—381no—
406C4—382no—
407C4C2×D4×D1911yescharacteristic
408C4#1059743511yescharacteristic
409C2—41no—
410C2—761no—
411C2—762no—
412C2—1521no—
413C2—1521no—
414C2#1192717811yescharacteristic
415C2#1192734311yescharacteristic
416C2#1192735311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#470C2
socleC22×C19C22×D4
hypercenter#470D19
hypocenterC19#3275
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. C2×#10597364C2semidirect
2. C2×#10597354C2semidirect
3. #11927204C2semidirect
4. #11927185C2semidirect
5. #11926929C2semidirect
6. #11926798C2semidirect
7. #11926769C2semidirect
8. #11926762C2semidirect
9. #11926704C2semidirect
10. #11926694C2semidirect
11. #11926692C2semidirect
12. #11926684C2semidirect
13. #11926631C2semidirect
14. #11926620C2semidirect
15. C19×#470C2semidirect
17. C2×Q8×D19C22semidirect
20. C2×Q16×C19C22semidirect
25. #10597393C22semidirect
26. C2×#64528C22semidirect
29. C2×#64527C22semidirect
37. C2×#64515C22semidirect
41. #10597341C22semidirect
45. #10597333C22semidirect
50. C19×#106C22semidirect
51. C19×#103C22semidirect
52. C19×#103C22semidirect
54. (C2×D19)⋊C8C22semidirect
55. Dic19⋊C8C22semidirect
56. C8×Dic19C22semidirect
57. #10597267C22semidirect
60. #10597266C22semidirect
121. #64516D4semidirect
206. #470D19semidirect
231. C2×Q16C2×D19semidirect
258. #106C2×D19semidirect
261. #103C2×D19semidirect
262. #103C2×D19semidirect
269. C19#3275semidirect

Maximal subgroups

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

subgroupindex
C2×#105973642
C2×#105973542
#119272042
#119271852
#119269292
#119267982
#119267692
#119267622
#119267042
#119266942
#119266922
#119266842
#119266312
#119266202
C19×#4702
#327519