Finite Group Databasebeta

← #14575241

Subgroups — #14575241

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×#10597357C211yesmaximal, characteristic, complemented
3#11927189C211yesmaximal, characteristic, complemented
4#11927187C211yesmaximal, characteristic, complemented
5#11926926C211yesmaximal, characteristic, complemented
6#11926793C211yesmaximal, characteristic, complemented
7#11926789C211yesmaximal, characteristic, complemented
8#11926760C211yesmaximal, characteristic, complemented
9#11926709C211yesmaximal, characteristic, complemented
10#11926703C211yesmaximal, characteristic, complemented
11#11926679C211yesmaximal, characteristic, complemented
12#11926676C211yesmaximal, characteristic, complemented
13C4×#64525C211yesmaximal, characteristic, complemented
14#11926621C211yesmaximal, characteristic, complemented
15C19×#463C211yesmaximal, characteristic, complemented
16C2×#64545C2211yescharacteristic
17C2×#64543C2211yescharacteristic
18C2×D4×D19C2211yescharacteristic, complemented
19C2×D4×D19C2211yescharacteristic, complemented
20C2×SD16×C19C2211yescharacteristic, complemented
21C2×D8×C19C2211yescharacteristic
22C19×#124C2211yescharacteristic, complemented
23C4×D4×C19C2211yescharacteristic, complemented
24#10597392C2211yescharacteristic, complemented
25C2×#64528C2211yescharacteristic, complemented
26C2×#64527C2211yescharacteristic, complemented
27#10597384C2211yescharacteristic
28C2×#64526C2211yescharacteristic, complemented
29C2×#64525C2211yescharacteristic
30C2×#64525C2211yescharacteristic
31#10597376—21no—
32C2×(C2×D19)⋊C4—21no—
33#10597360—24no—
34#10597357—24no—
35C2×D152C2211yescharacteristic
36C2×#64516C2211yescharacteristic, complemented
37C2×#64515C2211yescharacteristic, complemented
38C2×#64515C2211yescharacteristic, complemented
39#10597343C2211yescharacteristic, complemented
40#10597341C2211yescharacteristic
41#10597332—21no—
42#10597330—21no—
43#10597329—21no—
44#10597328—21no—
45#10597328—21no—
46C22⋊C4×D19—21no—
47#10597321C2211yescharacteristic, complemented
48C4×D76C2211yescharacteristic
49C4×D76C2211yescharacteristic, complemented
50C19×C4⋊C8C2211yescharacteristic, complemented
51C19×#103C2211yescharacteristic, complemented
52C19×#102C2211yescharacteristic, complemented
53#10597289C2211yescharacteristic, complemented
54#10597278C2211yescharacteristic, complemented
55(C2×D19)⋊C8C2211yescharacteristic, complemented
56(C2×D19)⋊C8C2211yescharacteristic, complemented
57#10597273C2211yescharacteristic, complemented
58#10597266C2211yescharacteristic, complemented
59#10597264C2211yescharacteristic, complemented
60C4×C19⋊C8C2211yescharacteristic, complemented
61C23×D19—21no—
62C23×D19—21no—
63C2×Q8×C19C2311yescharacteristic
64C2×D4×C19C2311yescharacteristic
65C2×D4×C19C2311yescharacteristic
66C22×C4×C19—21no—
67C2×C22⋊D19—21no—
68C2×C22⋊D19—21no—
69C2×C22⋊D19—21no—
70C2×C22⋊D19—21no—
71C22×Dic19—21no—
72#64545—22no—
73#64545—41no—
74#64543—22no—
75#64543—41no—
76D4×D19—22no—
77D4×D19—22no—
78D4×D19—41no—
79D4×D19—41no—
80C2×D76—21no—
81C2×D76—21no—
82C2×D76D411yescharacteristic
83C2×D76C2311yescharacteristic
84C2×D76C2311yescharacteristic
85C2×C4×D19—21no—
86C2×C4×D19—21no—
87C2×C4×D19C2311yescharacteristic
88C2×C4×D19C2311yescharacteristic
89C2×Dic38C2311yescharacteristic
90SD16×C19—22no—
91D8×C19—22no—
92C2×C8×C19C2311yescharacteristic
93C2×C8×C19C2311yescharacteristic
94C4⋊C4×C19C2311yescharacteristic
95C22⋊C4×C19—21no—
96C22⋊C4×C19—21no—
97C22⋊C4×C19—21no—
98C42×C19C2311yescharacteristic
99C22⋊Dic19—21no—
100#64528—41no—
101#64527—22no—
102#64526—22no—
103#64525—41no—
104#64525D414yescomplemented
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
112(C2×D19)⋊C4D411yescharacteristic
113C4⋊Dic19—21no—
114C4⋊Dic19D411yescharacteristic
115C4⋊Dic19C2311yescharacteristic
116Dic19⋊C4—21no—
117C2×C19⋊C8C2311yescharacteristic
118C2×C19⋊C8C2311yescharacteristic
119D152—22no—
120#64516—22no—
121#64515—22no—
122#64515—22no—
123C23×C19—21no—
124C23×C19—21no—
125C22×D19—21no—
126C22×D19—21no—
127C22×D19—42no—
128C22×D19—42no—
129C22×D19—42no—
130C22×D19—42no—
131C22×D19—81no—
132C22×D19—81no—
133C22×D19C2×D411yescharacteristic
134C22×D19C2×D411yescharacteristic
135Q8×C19—21no—
136Q8×C19—21no—
137D4×C19—21no—
138D4×C19—21no—
139D4×C19—21no—
140D4×C19C2×D412yes—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—81no—
144C2×C4×C19C2×D411yescharacteristic
145C2×C4×C19C2×D411yescharacteristic
146C2×C4×C19C2411yescharacteristic
147C22⋊D19—42no—
148C22⋊D19—42no—
149C22⋊D19—42no—
150C22⋊D19—81no—
151C2×Dic19—21no—
152C2×Dic19—21no—
153C2×Dic19—42no—
154C2×Dic19C2×D411yescharacteristic
155C2×Dic19C2×D411yescharacteristic
156D76—21no—
157D76—21no—
158D76—21no—
159D76—41no—
160D76—42no—
161D76—81no—
162D76C2×D412yes—
163C4×D19—21no—
164C4×D19—21no—
165C4×D19—21no—
166C4×D19—21no—
167C4×D19—42no—
168C4×D19—81no—
169Dic38—21no—
170Dic38—21no—
171C8×C19—21no—
172C8×C19—21no—
173C19⋊C8—21no—
174C19⋊C8C2×D412yes—
175#3273—191nomaximal, Sylow
176C22×C19—22no—
177C22×C19—41no—
178C22×C19—41no—
179C22×C19—41no—
180C22×C19—41no—
181C22×C19—41no—
182C22×C19C22×D411yescharacteristic
183C2×D19—21no—
184C2×D19—21no—
185C2×D19—22no—
186C2×D19—21no—
187C2×D19—21no—
188C2×D19—21no—
189C2×D19—21no—
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—21no—
199C4×C19—41no—
200C4×C19—41no—
201C4×C19C22×D411yescharacteristic
202C4×C19H(5,𝔽2)11yescharacteristic
203Dic19—21no—
204Dic19—21no—
205Dic19—41no—
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#463D1911yescharacteristic, complemented
216#452—191no—
217#452—191no—
218#447—191no—
219#447—191no—
220C4×D8—191no—
221#436—191no—
222C2×C19—42no—
223C2×C19—81no—
224C2×C19D4211yescharacteristic
225C2×C19#57511yescharacteristic
226C2×C19#57611yescharacteristic
227D19—41no—
228D19—41no—
229D19—42no—
230D19—81no—
231C2×#41—191no—
232C2×#41—191no—
233C22×D4—191no—
234C22×D4—191no—
235AGL(1,ℤ/8)—384no—
236AGL(1,ℤ/8)—384no—
237C2×Q16—191no—
238C2×SD16—191no—
239C2×SD16—191no—
240C2×SD16—191no—
241C2×SD16C2×D1911yescharacteristic, complemented
242C2×D8—191no—
243C2×D8—191no—
244C2×D8—191no—
245C2×D8C2×D1911yescharacteristic
246C2×M16—191no—
247C2×M16—191no—
248#124—191no—
249#124C2×D1911yescharacteristic, complemented
250#123—381no—
251#123—381no—
252C22⋊Q8—191no—
253C22⋊Q8—191no—
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×D4C2×D1911yescharacteristic, complemented
263C2×C22⋊C4—381no—
264C2×C22⋊C4—381no—
265#107—191no—
266C4⋊C8C2×D1911yescharacteristic, complemented
267#103—191no—
268#103C2×D1911yescharacteristic, complemented
269#102—191no—
270#102—191no—
271#102—191no—
272#102C2×D1911yescharacteristic, complemented
273C22⋊C8—191no—
274C22⋊C8—191no—
275C4×C8—191no—
276C19#327311yescharacteristic, complemented, Sylow
277C24—381no—
278C24—381no—
279#41—382no—
280#41—382no—
281#41—761no—
282#41—761no—
283C2×Q8—191no—
284C2×Q8C22×D1911yescharacteristic
285C2×D4—191no—
286C2×D4—191no—
287C2×D4—191no—
288C2×D4—381no—
289C2×D4—381no—
290C2×D4—381no—
291C2×D4—381no—
292C2×D4—382no—
293C2×D4—382no—
294C2×D4—381no—
295C2×D4—381no—
296C2×D4—761no—
297C2×D4—761no—
298C2×D4C22×D1911yescharacteristic
299C2×D4C22×D1911yescharacteristic
300C22×C4—21no—
301C22×C4—191no—
302C22×C4—191no—
303C22×C4—381no—
304C22×C4—381no—
305C22×C4—381no—
306Q16—761no—
307SD16—22no—
308SD16—382no—
309SD16—382no—
310SD16—382no—
311D8—22no—
312D8—194no—
313D8—382no—
314D8—761no—
315M16—382no—
316M16—382no—
317C2×C8—191no—
318C2×C8—191no—
319C2×C8C22×D1911yescharacteristic
320C2×C8C22×D1911yescharacteristic
321C4⋊C4—191no—
322C4⋊C4—191no—
323C4⋊C4—381no—
324C4⋊C4—381no—
325C4⋊C4C22×D1911yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—191no—
330C22⋊C4—191no—
331C22⋊C4—381no—
332C22⋊C4—381no—
333C22⋊C4—381no—
334C22⋊C4—381no—
335C22⋊C4—381no—
336C22⋊C4—381no—
337C22⋊C4—381no—
338C42C22×D1911yescharacteristic
339C23—21no—
340C23—21no—
341C23—191no—
342C23—191no—
343C23—381no—
344C23—381no—
345C23—762no—
346C23—762no—
347C23—762no—
348C23—762no—
349C23—1521no—
350C23—1521no—
351Q8—21no—
352Q8—21no—
353Q8—381no—
354Q8—381no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—192no—
359D4—381no—
360D4—381no—
361D4—381no—
362D4—761no—
363D4—762no—
364D4—762no—
365D4—762no—
366D4—762no—
367D4—1521no—
368D4—1521no—
369D4D4×D1912yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—191no—
374C2×C4—191no—
375C2×C4—381no—
376C2×C4—381no—
377C2×C4—381no—
378C2×C4—381no—
379C2×C4—381no—
380C2×C4—381no—
381C2×C4—762no—
382C2×C4—762no—
383C2×C4—1521no—
384C2×C4D4×D1911yescharacteristic
385C2×C4D4×D1911yescharacteristic
386C2×C4C23×D1911yescharacteristic
387C8—21no—
388C8—21no—
389C8—192no—
390C8—381no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—381no—
398C22—381no—
399C22—381no—
400C22—381no—
401C22—381no—
402C22—381no—
403C22—382no—
404C22—761no—
405C22—761no—
406C22—761no—
407C22—761no—
408C22—761no—
409C22—1524no—
410C22—1524no—
411C22C2×D4×D1911yescharacteristic
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—381no—
417C4—381no—
418C4—761no—
419C4—761no—
420C4C2×D4×D1911yescharacteristic
421C4#1059743511yescharacteristic
422C2—42no—
423C2—81no—
424C2—761no—
425C2—761no—
426C2—762no—
427C2—1521no—
428C2#1192717811yescharacteristic
429C2#1192734111yescharacteristic
430C2#1192734811yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#463C2
socleC22×C19C22×D4
hypercenter#463D19
hypocenterC19#3273
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#10597360C2semidirect
2. C2×#10597357C2semidirect
3. #11927189C2semidirect
4. #11927187C2semidirect
5. #11926926C2semidirect
6. #11926793C2semidirect
7. #11926789C2semidirect
8. #11926760C2semidirect
9. #11926709C2semidirect
10. #11926703C2semidirect
11. #11926679C2semidirect
12. #11926676C2semidirect
13. C4×#64525C2semidirect
14. #11926621C2semidirect
15. C19×#463C2semidirect
18. C2×D4×D19C22semidirect
19. C2×D4×D19C22semidirect
20. C2×SD16×C19C22semidirect
22. C19×#124C22semidirect
23. C4×D4×C19C22semidirect
24. #10597392C22semidirect
25. C2×#64528C22semidirect
26. C2×#64527C22semidirect
28. C2×#64526C22semidirect
36. C2×#64516C22semidirect
37. C2×#64515C22semidirect
38. C2×#64515C22semidirect
39. #10597343C22semidirect
47. #10597321C22semidirect
49. C4×D76C22semidirect
50. C19×C4⋊C8C22semidirect
51. C19×#103C22semidirect
52. C19×#102C22semidirect
53. #10597289C22semidirect
54. #10597278C22semidirect
55. (C2×D19)⋊C8C22semidirect
56. (C2×D19)⋊C8C22semidirect
57. #10597273C22semidirect
58. #10597266C22semidirect
59. #10597264C22semidirect
60. C4×C19⋊C8C22semidirect
104. #64525D4semidirect
215. #463D19semidirect
241. C2×SD16C2×D19semidirect
249. #124C2×D19semidirect
262. C4×D4C2×D19semidirect
266. C4⋊C8C2×D19semidirect
268. #103C2×D19semidirect
272. #102C2×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×#105973572
#119271892
#119271872
#119269262
#119267932
#119267892
#119267602
#119267092
#119267032
#119266792
#119266762
C4×#645252
#119266212
C19×#4632
#327319