Finite Group Databasebeta

← #14575239

Subgroups — #14575239

Order 2432.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597360C211yesmaximal, characteristic, complemented
2C2×#10597395C211yesmaximal, characteristic, complemented
3#11927185C211yesmaximal, characteristic, complemented
4#11927182C211yesmaximal, characteristic, complemented
5#11926929C211yesmaximal, characteristic, complemented
6#11926793C211yesmaximal, characteristic, complemented
7#11926792C211yesmaximal, characteristic, complemented
8#11926762C211yesmaximal, characteristic, complemented
9#11926761C211yesmaximal, characteristic, complemented
10#11926705C211yesmaximal, characteristic, complemented
11#11926680C211yesmaximal, characteristic, complemented
12#11926679C211yesmaximal, characteristic, complemented
13#11926624C211yesmaximal, characteristic, complemented
14#11926619C211yesmaximal, characteristic, complemented
15C19×#452C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C2×#64545C2211yescharacteristic
18C2×D4×D19C2211yescharacteristic, complemented
19C22×D76C2211yescharacteristic, complemented
20C2×Q16×C19C2211yescharacteristic, complemented
21C2×SD16×C19C2211yescharacteristic, complemented
22C19×C22⋊Q8C2211yescharacteristic, complemented
23#10597395—24no—
24#10597393C2211yescharacteristic, complemented
25#10597393C2211yescharacteristic, complemented
26#10597392C2211yescharacteristic, complemented
27C2×#64527C2211yescharacteristic, complemented
28C2×#64527C2211yescharacteristic, complemented
29C2×#64527C2211yescharacteristic, complemented
30#10597385—21no—
31#10597383—21no—
32D4×Dic19C2211yescharacteristic, complemented
33C2×#64525C2211yescharacteristic
34C2×#64525C2211yescharacteristic
35#10597376C2211yescharacteristic
36#10597375—21no—
37C4×C22⋊D19C2211yescharacteristic
38C2×(C2×D19)⋊C4—21no—
39C2×#64520C2211yescharacteristic, complemented
40#10597360—24no—
41C2×D152C2211yescharacteristic
42C2×D152C2211yescharacteristic
43C2×#64515C2211yescharacteristic, complemented
44#10597341—21no—
45#10597341C2211yescharacteristic
46#10597340—21no—
47#10597339C2211yescharacteristic, complemented
48#10597328—21no—
49C22⋊C4×D19—21no—
50C19×#103C2211yescharacteristic, complemented
51C19×#102C2211yescharacteristic, complemented
52C19×C22⋊C8C2211yescharacteristic, complemented
53#10597292C2211yescharacteristic, complemented
54#10597278C2211yescharacteristic, complemented
55#10597278C2211yescharacteristic, complemented
56(C2×D19)⋊C8C2211yescharacteristic, complemented
57Dic19⋊C8C2211yescharacteristic, complemented
58C8×Dic19C2211yescharacteristic, complemented
59#10597266C2211yescharacteristic, complemented
60#10597264C2211yescharacteristic, complemented
61C23×D19—21no—
62C23×D19—21no—
63#41×C19—22no—
64#41×C19—41no—
65C2×Q8×C19C2311yescharacteristic
66C2×Q8×C19C2311yescharacteristic
67C2×D4×C19—21no—
68C2×D4×C19C2311yescharacteristic
69C22×C4×C19—21no—
70C22×C4×C19C2311yescharacteristic
71C2×C22⋊D19—21no—
72C2×C22⋊D19—21no—
73C2×C22⋊D19D411yescharacteristic
74C22×Dic19—21no—
75#64545—22no—
76#64545—41no—
77D4×D19—22no—
78D4×D19—41no—
79C2×D76—22no—
80C2×D76—21no—
81C2×D76—21no—
82C2×D76—21no—
83C2×D76—41no—
84C2×D76C2311yescharacteristic
85C2×D76C2311yescharacteristic
86C2×D76C2311yescharacteristic
87C2×C4×D19—21no—
88C2×C4×D19—21no—
89C2×C4×D19C2311yescharacteristic
90Q16×C19—41no—
91SD16×C19—22no—
92C2×C8×C19C2311yescharacteristic
93C2×C8×C19C2311yescharacteristic
94C4⋊C4×C19—21no—
95C4⋊C4×C19C2311yescharacteristic
96C22⋊C4×C19—21no—
97C22⋊Dic19—21no—
98C22⋊Dic19D411yescharacteristic
99#64527—22no—
100#64527—22no—
101#64527—22no—
102#64525—22no—
103#64525D414yescomplemented
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)⋊C4—21no—
112(C2×D19)⋊C4D411yescharacteristic
113C4⋊Dic19C2311yescharacteristic
114Dic19⋊C4—21no—
115Dic19⋊C4D411yescharacteristic
116C4×Dic19C2311yescharacteristic
117#64520—22no—
118C2×C19⋊C8C2311yescharacteristic
119C2×C19⋊C8C2311yescharacteristic
120D152—22no—
121D152—41no—
122#64515—22no—
123C23×C19—21no—
124C23×C19C2×D411yescharacteristic
125C22×D19—21no—
126C22×D19—21no—
127C22×D19—21no—
128C22×D19—42no—
129C22×D19—42no—
130C22×D19—42no—
131C22×D19—42no—
132C22×D19—81no—
133C22×D19—81no—
134C22×D19C2×D411yescharacteristic
135Q8×C19—21no—
136Q8×C19—21no—
137Q8×C19—21no—
138Q8×C19—21no—
139D4×C19—21no—
140D4×C19—42no—
141D4×C19C2×D412yes—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—21no—
147C2×C4×C19—42no—
148C2×C4×C19C2×D411yescharacteristic
149C2×C4×C19C2411yescharacteristic
150C22⋊D19—41no—
151C22⋊D19—42no—
152C22⋊D19—81no—
153C2×Dic19—21no—
154C2×Dic19—81no—
155C2×Dic19C2×D411yescharacteristic
156C2×Dic19C2×D411yescharacteristic
157C2×Dic19C2×D411yescharacteristic
158D76—21no—
159D76—21no—
160D76—21no—
161D76—21no—
162D76—21no—
163D76—42no—
164D76—42no—
165D76—81no—
166D76C2×D412yes—
167C4×D19—21no—
168C4×D19—21no—
169C4×D19—42no—
170C4×D19—81no—
171C8×C19—21no—
172C8×C19—21no—
173C19⋊C8—21no—
174C19⋊C8C2×D412yes—
175#3273—191nomaximal, Sylow
176C22×C19—22no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—41no—
181C22×C19—41no—
182C22×C19C22×D411yescharacteristic
183C2×D19—21no—
184C2×D19—22no—
185C2×D19—21no—
186C2×D19—21no—
187C2×D19—41no—
188C2×D19—41no—
189C2×D19—41no—
190C2×D19—41no—
191C2×D19—41no—
192C2×D19—41no—
193C2×D19—41no—
194C2×D19—41no—
195C2×D19—84no—
196C2×D19—84no—
197C4×C19—21no—
198C4×C19—41no—
199C4×C19—41no—
200C4×C19—41no—
201C4×C19C22×D411yescharacteristic
202C4×C19H(5,𝔽2)11yescharacteristic
203Dic19—21no—
204Dic19—21no—
205Dic19—21no—
206Dic19—41no—
207C2×AGL(1,ℤ/8)—191no—
208C2×AGL(1,ℤ/8)—191no—
209#546—191no—
210#546—191no—
211#495—191no—
212#468—191no—
213#468—191no—
214#463—191no—
215#463—191no—
216#452—191no—
217#452D1911yescharacteristic, complemented
218#447—191no—
219#447—191no—
220C4×D8—191no—
221#436—191no—
222C2×C19—41no—
223C2×C19—42no—
224C2×C19D4211yescharacteristic
225C2×C19#57511yescharacteristic
226C2×C19#57611yescharacteristic
227D19—41no—
228D19—42no—
229D19—81no—
230D19—81no—
231C2×#41—191no—
232C2×#41C2×D1911yescharacteristic
233C22×D4—191no—
234C22×D4—191no—
235AGL(1,ℤ/8)—384no—
236AGL(1,ℤ/8)—384no—
237C2×Q16C2×D1911yescharacteristic, complemented
238C2×SD16—191no—
239C2×SD16—191no—
240C2×SD16—191no—
241C2×SD16C2×D1911yescharacteristic, complemented
242C2×D8—191no—
243C2×D8—191no—
244C2×D8—191no—
245C2×D8—191no—
246C2×M16—191no—
247C2×M16—191no—
248#124—191no—
249#124—191no—
250#123—381no—
251#123—381no—
252C22⋊Q8—191no—
253C22⋊Q8C2×D1911yescharacteristic, complemented
254#121—191no—
255#121—191no—
256#121—381no—
257#121—381no—
258#120—381no—
259#120—381no—
260C4×D4—191no—
261C4×D4—191no—
262C4×D4—191no—
263C2×C22⋊C4—381no—
264C2×C22⋊C4—381no—
265#107—191no—
266C4⋊C8—191no—
267#103—191no—
268#103C2×D1911yescharacteristic, complemented
269#102—191no—
270#102—191no—
271#102—191no—
272#102C2×D1911yescharacteristic, complemented
273C22⋊C8—191no—
274C22⋊C8C2×D1911yescharacteristic, complemented
275C4×C8—191no—
276C19#327311yescharacteristic, complemented, Sylow
277C24—381no—
278C24—381no—
279#41—22no—
280#41—41no—
281#41—382no—
282#41—761no—
283C2×Q8C22×D1911yescharacteristic
284C2×Q8C22×D1911yescharacteristic
285C2×D4—21no—
286C2×D4—191no—
287C2×D4—191no—
288C2×D4—191no—
289C2×D4—191no—
290C2×D4—382no—
291C2×D4—381no—
292C2×D4—381no—
293C2×D4—381no—
294C2×D4—382no—
295C2×D4—381no—
296C2×D4—381no—
297C2×D4—761no—
298C2×D4—761no—
299C2×D4C22×D1911yescharacteristic
300C22×C4—21no—
301C22×C4—191no—
302C22×C4—381no—
303C22×C4—381no—
304C22×C4—381no—
305C22×C4C22×D1911yescharacteristic
306Q16—41no—
307SD16—22no—
308SD16—382no—
309SD16—382no—
310SD16—382no—
311D8—194no—
312D8—382no—
313D8—382no—
314D8—761no—
315M16—382no—
316M16—382no—
317C2×C8—191no—
318C2×C8—191no—
319C2×C8C22×D1911yescharacteristic
320C2×C8C22×D1911yescharacteristic
321C4⋊C4—21no—
322C4⋊C4—191no—
323C4⋊C4—191no—
324C4⋊C4—381no—
325C4⋊C4C22×D1911yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—191no—
328C22⋊C4—191no—
329C22⋊C4—381no—
330C22⋊C4—381no—
331C22⋊C4—381no—
332C22⋊C4—381no—
333C22⋊C4—381no—
334C22⋊C4—381no—
335C22⋊C4—381no—
336C22⋊C4—381no—
337C22⋊C4—381no—
338C42—191no—
339C23—21no—
340C23—191no—
341C23—381no—
342C23—381no—
343C23—381no—
344C23—762no—
345C23—762no—
346C23—762no—
347C23—762no—
348C23—1521no—
349C23—1521no—
350C23D4×D1911yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—21no—
354Q8—21no—
355D4—21no—
356D4—42no—
357D4—192no—
358D4—381no—
359D4—381no—
360D4—381no—
361D4—381no—
362D4—381no—
363D4—762no—
364D4—762no—
365D4—761no—
366D4—762no—
367D4—1521no—
368D4—1521no—
369D4D4×D1912yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—191no—
377C2×C4—191no—
378C2×C4—191no—
379C2×C4—381no—
380C2×C4—381no—
381C2×C4—381no—
382C2×C4—762no—
383C2×C4—1521no—
384C2×C4—1521no—
385C2×C4D4×D1911yescharacteristic
386C2×C4C23×D1911yescharacteristic
387C8—21no—
388C8—21no—
389C8—192no—
390C8—381no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—381no—
398C22—381no—
399C22—381no—
400C22—382no—
401C22—761no—
402C22—761no—
403C22—761no—
404C22—761no—
405C22—761no—
406C22—761no—
407C22—761no—
408C22—761no—
409C22—1524no—
410C22—1524no—
411C22C2×D4×D1911yescharacteristic
412C4—21no—
413C4—41no—
414C4—41no—
415C4—41no—
416C4—381no—
417C4—381no—
418C4—381no—
419C4—761no—
420C4C2×D4×D1911yescharacteristic
421C4#1059743011yescharacteristic
422C2—41no—
423C2—42no—
424C2—761no—
425C2—762no—
426C2—1521no—
427C2—1521no—
428C2#1192717611yescharacteristic
429C2#1192734311yescharacteristic
430C2#1192734611yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#452C2
socleC22×C19C22×D4
hypercenter#452D19
hypocenterC19#3273
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#10597360C2semidirect
2. C2×#10597395C2semidirect
3. #11927185C2semidirect
4. #11927182C2semidirect
5. #11926929C2semidirect
6. #11926793C2semidirect
7. #11926792C2semidirect
8. #11926762C2semidirect
9. #11926761C2semidirect
10. #11926705C2semidirect
11. #11926680C2semidirect
12. #11926679C2semidirect
13. #11926624C2semidirect
14. #11926619C2semidirect
15. C19×#452C2semidirect
18. C2×D4×D19C22semidirect
19. C22×D76C22semidirect
20. C2×Q16×C19C22semidirect
21. C2×SD16×C19C22semidirect
22. C19×C22⋊Q8C22semidirect
24. #10597393C22semidirect
25. #10597393C22semidirect
26. #10597392C22semidirect
27. C2×#64527C22semidirect
28. C2×#64527C22semidirect
29. C2×#64527C22semidirect
32. D4×Dic19C22semidirect
39. C2×#64520C22semidirect
43. C2×#64515C22semidirect
47. #10597339C22semidirect
50. C19×#103C22semidirect
51. C19×#102C22semidirect
52. C19×C22⋊C8C22semidirect
53. #10597292C22semidirect
54. #10597278C22semidirect
55. #10597278C22semidirect
56. (C2×D19)⋊C8C22semidirect
57. Dic19⋊C8C22semidirect
58. C8×Dic19C22semidirect
59. #10597266C22semidirect
60. #10597264C22semidirect
103. #64525D4semidirect
217. #452D19semidirect
237. C2×Q16C2×D19semidirect
241. C2×SD16C2×D19semidirect
253. C22⋊Q8C2×D19semidirect
268. #103C2×D19semidirect
272. #102C2×D19semidirect
274. C22⋊C8C2×D19semidirect
276. C19#3273semidirect

Maximal subgroups

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

subgroupindex
C2×#105973602
C2×#105973952
#119271852
#119271822
#119269292
#119267932
#119267922
#119267622
#119267612
#119267052
#119266802
#119266792
#119266242
#119266192
C19×#4522
#327319