Finite Group Databasebeta

← #14575260

Subgroups — #14575260

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×#10597360C211yesmaximal, characteristic, complemented
2#11927205C211yesmaximal, characteristic, complemented
3#11927182C211yesmaximal, characteristic, complemented
4#11926929C211yesmaximal, characteristic, complemented
5#11926799C211yesmaximal, characteristic, complemented
6#11926797C211yesmaximal, characteristic, complemented
7#11926768C211yesmaximal, characteristic, complemented
8#11926761C211yesmaximal, characteristic, complemented
9#11926705C211yesmaximal, characteristic, complemented
10#11926693C211yesmaximal, characteristic, complemented
11#11926689C211yesmaximal, characteristic, complemented
12#11926683C211yesmaximal, characteristic, complemented
13SD16×Dic19C211yesmaximal, characteristic, complemented
14#11926620C211yesmaximal, characteristic, complemented
15C2×C19×#137C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C22×Q8×C19C2211yescharacteristic, complemented
18C2×#64545C2211yescharacteristic
19C2×D4×D19C2211yescharacteristic
20C19×#137—24no—
21C2×Q16×C19C2211yescharacteristic, complemented
22C2×Q16×C19C2211yescharacteristic, complemented
23C2×SD16×C19C2211yescharacteristic
24C2×SD16×C19C2211yescharacteristic
25C2×M16×C19C2211yescharacteristic, complemented
26#10597393—21no—
27#10597393C2211yescharacteristic
28#10597393C2211yescharacteristic, complemented
29#10597392—21no—
30#10597392C2211yescharacteristic
31#10597392C2211yescharacteristic
32Q8×Dic19C2211yescharacteristic, complemented
33C2×#64527C2211yescharacteristic
34C2×#64527C2211yescharacteristic
35C2×#64527C2211yescharacteristic, complemented
36#10597385—21no—
37#10597383—21no—
38D4×Dic19C2211yescharacteristic
39C2×#64525C2211yescharacteristic
40#10597376—21no—
41#10597376C2211yescharacteristic
42#10597376C2211yescharacteristic, complemented
43#10597375—21no—
44C4×C22⋊D19—21no—
45C4×C22⋊D19C2211yescharacteristic
46C2×(C2×D19)⋊C4—21no—
47#10597360—24no—
48C2×D152C2211yescharacteristic
49C2×#64515C2211yescharacteristic
50#10597292C2211yescharacteristic, complemented
51#10597292C2211yescharacteristic, complemented
52#10597292C2211yescharacteristic, complemented
53#10597289C2211yescharacteristic
54C22⋊(C19⋊C8)C2211yescharacteristic, complemented
55#10597278C2211yescharacteristic
56#10597278C2211yescharacteristic, complemented
57(C2×D19)⋊C8C2211yescharacteristic
58#10597274C2211yescharacteristic, complemented
59Dic19⋊C8C2211yescharacteristic, complemented
60C8×Dic19C2211yescharacteristic, complemented
61C23×D19—21no—
62#41×C19—22no—
63#41×C19—41no—
64C2×Q8×C19—21no—
65C2×Q8×C19—22no—
66C2×Q8×C19—41no—
67C2×Q8×C19C2311yescharacteristic
68C2×Q8×C19C2311yescharacteristic
69C2×Q8×C19C2311yescharacteristic
70C2×D4×C19—21no—
71C2×D4×C19C2311yescharacteristic
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19C2311yescharacteristic
75C2×C22⋊D19—21no—
76C2×C22⋊D19—21no—
77C2×C22⋊D19—21no—
78C2×C22⋊D19D411yescharacteristic
79C22×Dic19—21no—
80#64545—22no—
81#64545—41no—
82D4×D19—22no—
83D4×D19—41no—
84C2×D76—21no—
85C2×D76C2311yescharacteristic
86C2×D76C2311yescharacteristic
87C2×C4×D19—21no—
88C2×C4×D19C2311yescharacteristic
89Q16×C19—22no—
90Q16×C19—22no—
91SD16×C19—22no—
92SD16×C19D414yescomplemented
93M16×C19—22no—
94C2×C8×C19C2311yescharacteristic
95C2×C8×C19C2311yescharacteristic
96C22⋊Dic19—21no—
97C22⋊Dic19D411yescharacteristic
98#64527—22no—
99#64527—41no—
100#64527—41no—
101#64525—22no—
102(C2×D19)⋊C4—21no—
103(C2×D19)⋊C4—21no—
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)⋊C4D411yescharacteristic
111C4⋊Dic19—21no—
112C4⋊Dic19C2311yescharacteristic
113C4⋊Dic19C2311yescharacteristic
114Dic19⋊C4—21no—
115Dic19⋊C4—21no—
116Dic19⋊C4D411yescharacteristic
117C4×Dic19—21no—
118C4×Dic19C2311yescharacteristic
119C2×C19⋊C8C2311yescharacteristic
120C2×C19⋊C8C2311yescharacteristic
121D152—22no—
122#64515—22no—
123C23×C19—21no—
124C23×C19C2×D411yescharacteristic
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—
135Q8×C19—21no—
136Q8×C19—42no—
137Q8×C19C2×D412yes—
138D4×C19—21no—
139D4×C19—42no—
140D4×C19C2×D412yes—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—42no—
147C2×C4×C19—42no—
148C2×C4×C19C2×D411yescharacteristic
149C2×C4×C19C2411yescharacteristic
150C22⋊D19—41no—
151C22⋊D19—42no—
152C22⋊D19—42no—
153C22⋊D19—81no—
154C2×Dic19—21no—
155C2×Dic19—21no—
156C2×Dic19—81no—
157C2×Dic19C2×D411yescharacteristic
158C2×Dic19C2×D411yescharacteristic
159C2×Dic19C2×D411yescharacteristic
160D76—21no—
161D76—21no—
162D76—21no—
163D76—21no—
164D76—42no—
165C4×D19—21no—
166C4×D19—21no—
167C4×D19—42no—
168C8×C19—21no—
169C8×C19C2×D412yes—
170C19⋊C8—21no—
171C19⋊C8—21no—
172#3275—191nomaximal, Sylow
173C22×C19—22no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—41no—
178C22×C19—41no—
179C22×C19C22×D411yescharacteristic
180C2×D19—21no—
181C2×D19—21no—
182C2×D19—21no—
183C2×D19—41no—
184C2×D19—41no—
185C2×D19—41no—
186C2×D19—41no—
187C2×D19—41no—
188C2×D19—41no—
189C2×D19—84no—
190C4×C19—22no—
191C4×C19—21no—
192C4×C19—41no—
193C4×C19—41no—
194C4×C19C22×D411yescharacteristic
195C4×C19H(5,𝔽2)11yescharacteristic
196Dic19—21no—
197Dic19—21no—
198Dic19—21no—
199Dic19—41no—
200Dic19—41no—
201C2×#137D1911yescharacteristic, complemented
202C2×AGL(1,ℤ/8)—191no—
203#548—191no—
204#546—191no—
205#495—191no—
206#470—191no—
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—42no—
217C2×C19—41no—
218C2×C19D4211yescharacteristic
219C2×C19#57511yescharacteristic
220C2×C19#57711yescharacteristic
221D19—41no—
222D19—81no—
223D19—81no—
224C2×#41—191no—
225C2×#41C2×D1911yescharacteristic
226C22×Q8C2×D1911yescharacteristic, complemented
227C22×D4—191no—
228#137—24no—
229AGL(1,ℤ/8)—384no—
230C2×Q16C2×D1911yescharacteristic, complemented
231C2×Q16C2×D1911yescharacteristic, complemented
232C2×SD16—191no—
233C2×SD16—191no—
234C2×SD16—191no—
235C2×SD16C2×D1911yescharacteristic
236C2×SD16C2×D1911yescharacteristic
237C2×D8—191no—
238C2×D8—191no—
239C2×M16—191no—
240C2×M16C2×D1911yescharacteristic, complemented
241#124—191no—
242#124—191no—
243#124—381no—
244#123—381no—
245C22⋊Q8—191no—
246C22⋊Q8—191no—
247C22⋊Q8—381no—
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#106—191no—
259C4⋊C8—191no—
260#103—191no—
261#103—191no—
262#103—191no—
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—22no—
272#41—41no—
273#41—382no—
274#41—761no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8C22×D1911yescharacteristic
279C2×Q8C22×D1911yescharacteristic
280C2×Q8C22×D1911yescharacteristic
281C2×D4—21no—
282C2×D4—191no—
283C2×D4—191no—
284C2×D4—191no—
285C2×D4—381no—
286C2×D4—381no—
287C2×D4—382no—
288C2×D4—381no—
289C2×D4—381no—
290C2×D4—761no—
291C2×D4C22×D1911yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—191no—
295C22×C4—381no—
296C22×C4—381no—
297C22×C4C22×D1911yescharacteristic
298Q16—22no—
299Q16—22no—
300SD16—22no—
301SD16—382no—
302SD16—761no—
303SD16—761no—
304SD16C22⋊D1914yescomplemented
305D8—382no—
306D8—382no—
307M16—22no—
308M16—382no—
309C2×C8—191no—
310C2×C8—191no—
311C2×C8C22×D1911yescharacteristic
312C2×C8C22×D1911yescharacteristic
313C4⋊C4—191no—
314C4⋊C4—191no—
315C4⋊C4—191no—
316C4⋊C4—381no—
317C4⋊C4—381no—
318C4⋊C4—381no—
319C22⋊C4—191no—
320C22⋊C4—191no—
321C22⋊C4—381no—
322C22⋊C4—381no—
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—21no—
333C23—191no—
334C23—381no—
335C23—381no—
336C23—762no—
337C23—762no—
338C23—1521no—
339C23D4×D1911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—21no—
345Q8—42no—
346Q8C2×C22⋊D1912yes—
347D4—21no—
348D4—42no—
349D4—381no—
350D4—381no—
351D4—381no—
352D4—381no—
353D4—762no—
354D4—761no—
355D4—762no—
356D4—762no—
357D4—1521no—
358D4C2×C22⋊D1912yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—191no—
367C2×C4—191no—
368C2×C4—191no—
369C2×C4—381no—
370C2×C4—381no—
371C2×C4—381no—
372C2×C4—381no—
373C2×C4—762no—
374C2×C4—1521no—
375C2×C4D4×D1911yescharacteristic
376C2×C4C23×D1911yescharacteristic
377C8—21no—
378C8—381no—
379C8—381no—
380C8C2×C22⋊D1912yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—381no—
388C22—381no—
389C22—381no—
390C22—761no—
391C22—761no—
392C22—761no—
393C22—761no—
394C22—761no—
395C22—761no—
396C22—1524no—
397C22C2×D4×D1911yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—381no—
403C4—381no—
404C4—381no—
405C4—761no—
406C4—761no—
407C4#1059743011yescharacteristic
408C4C22×C22⋊D1911yescharacteristic
409C2—41no—
410C2—42no—
411C2—761no—
412C2—1521no—
413C2—1521no—
414C2D4×C22⋊D1911yescharacteristic
415C2#1192734311yescharacteristic
416C2#1192735311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×#137C2
socleC22×C19C22×D4
hypercenterC2×#137D19
hypocenterC19#3275
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#10597360C2semidirect
2. #11927205C2semidirect
3. #11927182C2semidirect
4. #11926929C2semidirect
5. #11926799C2semidirect
6. #11926797C2semidirect
7. #11926768C2semidirect
8. #11926761C2semidirect
9. #11926705C2semidirect
10. #11926693C2semidirect
11. #11926689C2semidirect
12. #11926683C2semidirect
13. SD16×Dic19C2semidirect
14. #11926620C2semidirect
15. C2×C19×#137C2semidirect
17. C22×Q8×C19C22semidirect
21. C2×Q16×C19C22semidirect
22. C2×Q16×C19C22semidirect
25. C2×M16×C19C22semidirect
28. #10597393C22semidirect
32. Q8×Dic19C22semidirect
35. C2×#64527C22semidirect
42. #10597376C22semidirect
50. #10597292C22semidirect
51. #10597292C22semidirect
52. #10597292C22semidirect
54. C22⋊(C19⋊C8)C22semidirect
56. #10597278C22semidirect
58. #10597274C22semidirect
59. Dic19⋊C8C22semidirect
60. C8×Dic19C22semidirect
92. SD16×C19D4semidirect
201. C2×#137D19semidirect
226. C22×Q8C2×D19semidirect
230. C2×Q16C2×D19semidirect
231. C2×Q16C2×D19semidirect
240. C2×M16C2×D19semidirect
269. C19#3275semidirect
304. SD16C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973602
#119272052
#119271822
#119269292
#119267992
#119267972
#119267682
#119267612
#119267052
#119266932
#119266892
#119266832
SD16×Dic192
#119266202
C2×C19×#1372
#327519