Finite Group Databasebeta

← #14570020

Subgroups — #14570020

Order 2432.

666 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597328C211yesmaximal, characteristic
2#11926479C211yesmaximal, characteristic, complemented
3#11926466C211yesmaximal, characteristic, complemented
4#11926461C211yesmaximal, characteristic, complemented
5#11926461C211yesmaximal, characteristic, complemented
6#11926459C211yesmaximal, characteristic, complemented
7#11926459C211yesmaximal, characteristic, complemented
8#11926446C211yesmaximal, characteristic, complemented
9#11926445C211yesmaximal, characteristic, complemented
10#11926437C211yesmaximal, characteristic, complemented
11#11926435C211yesmaximal, characteristic, complemented
12#11926434C211yesmaximal, characteristic, complemented
13#11926399C211yesmaximal, characteristic, complemented
14#11926399C211yesmaximal, characteristic, complemented
15C2×C19×#126C211yesmaximal, characteristic, complemented
16C24×D19C2211yescharacteristic
17C22×C22⋊D19C2211yescharacteristic
18C22×D76C2211yescharacteristic
19C22×D76C2211yescharacteristic
20C19×#126—24no—
21C2×C4⋊C4×C19C2211yescharacteristic, complemented
22C2×C4⋊C4×C19C2211yescharacteristic, complemented
23C2×C4⋊C4×C19C2211yescharacteristic, complemented
24C2×C22⋊C4×C19C2211yescharacteristic
25C2×C22⋊C4×C19C2211yescharacteristic
26C2×C22⋊C4×C19C2211yescharacteristic
27C2×C42×C19C2211yescharacteristic, complemented
28C2×C22⋊Dic19C2211yescharacteristic
29C2×C22⋊Dic19C2211yescharacteristic
30C2×(C2×D19)⋊C4C2211yescharacteristic
31C2×(C2×D19)⋊C4C2211yescharacteristic
32C2×(C2×D19)⋊C4C2211yescharacteristic
33C2×(C2×D19)⋊C4C2211yescharacteristic
34C2×(C2×D19)⋊C4C2211yescharacteristic
35C2×(C2×D19)⋊C4C2211yescharacteristic
36C2×(C2×D19)⋊C4C2211yescharacteristic
37C2×(C2×D19)⋊C4C2211yescharacteristic
38C2×(C2×D19)⋊C4C2211yescharacteristic
39C2×(C2×D19)⋊C4C2211yescharacteristic
40C2×(C2×D19)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D19)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D19)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D19)⋊C4C2211yescharacteristic, complemented
44C2×C4⋊Dic19C2211yescharacteristic, complemented
45C2×Dic19⋊C4C2211yescharacteristic, complemented
46C2×Dic19⋊C4C2211yescharacteristic, complemented
47C2×C4×Dic19C2211yescharacteristic, complemented
48#10597328—24no—
49C19⋊#95C2211yescharacteristic, complemented
50C19⋊#95C2211yescharacteristic, complemented
51C19⋊#95C2211yescharacteristic, complemented
52C19⋊#95C2211yescharacteristic, complemented
53C24×C19C2311yescharacteristic
54C23×D19—22no—
55C23×D19—22no—
56C23×D19—22no—
57C23×D19—41no—
58C23×D19—41no—
59C23×D19—41no—
60C23×D19—41no—
61C23×D19C2311yescharacteristic
62C23×D19C2311yescharacteristic
63C23×D19C2311yescharacteristic
64C22×C4×C19C2311yescharacteristic
65C22×C4×C19C2311yescharacteristic
66C22×C4×C19C2311yescharacteristic
67C22×C4×C19C2311yescharacteristic
68C22×C4×C19C2311yescharacteristic
69C22×C4×C19C2311yescharacteristic
70C2×C22⋊D19—22no—
71C2×C22⋊D19—41no—
72C2×C22⋊D19—41no—
73C22×Dic19C2311yescharacteristic
74C22×Dic19C2311yescharacteristic
75C22×Dic19C2311yescharacteristic
76C22×Dic19C2311yescharacteristic
77C22×Dic19C2311yescharacteristic
78C2×D76—22no—
79C2×D76—22no—
80C2×D76—22no—
81C2×D76—22no—
82C2×D76—41no—
83C2×D76—41no—
84C4⋊C4×C19—22no—
85C4⋊C4×C19—22no—
86C4⋊C4×C19—22no—
87C22⋊C4×C19—22no—
88C22⋊C4×C19—22no—
89C22⋊C4×C19D414yes—
90C42×C19—22no—
91C22⋊Dic19—41no—
92C22⋊Dic19—41no—
93(C2×D19)⋊C4—22no—
94(C2×D19)⋊C4—22no—
95(C2×D19)⋊C4—22no—
96(C2×D19)⋊C4—22no—
97(C2×D19)⋊C4—41no—
98(C2×D19)⋊C4—41no—
99(C2×D19)⋊C4—41no—
100(C2×D19)⋊C4—41no—
101(C2×D19)⋊C4—41no—
102(C2×D19)⋊C4—41no—
103(C2×D19)⋊C4—41no—
104(C2×D19)⋊C4—41no—
105(C2×D19)⋊C4—41no—
106(C2×D19)⋊C4—41no—
107C4⋊Dic19—41no—
108Dic19⋊C4—41no—
109Dic19⋊C4—41no—
110C4×Dic19—41no—
111C23×C19—21no—
112C23×C19—21no—
113C23×C19—21no—
114C23×C19—21no—
115C23×C19—21no—
116C23×C19—21no—
117C23×C19C2×D412yes—
118C23×C19C2411yescharacteristic
119C22×D19—21no—
120C22×D19—21no—
121C22×D19—21no—
122C22×D19—21no—
123C22×D19—21no—
124C22×D19—21no—
125C22×D19—21no—
126C22×D19—21no—
127C22×D19—21no—
128C22×D19—21no—
129C22×D19—21no—
130C22×D19—21no—
131C22×D19—21no—
132C22×D19—21no—
133C22×D19—21no—
134C22×D19—21no—
135C22×D19—21no—
136C22×D19—21no—
137C22×D19—21no—
138C22×D19—44no—
139C22×D19—44no—
140C22×D19—44no—
141C22×D19—44no—
142C22×D19—44no—
143C22×D19—44no—
144C22×D19—44no—
145C22×D19#4112yes—
146C22×D19#4112yes—
147C2×C4×C19—21no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—21no—
152C2×C4×C19—21no—
153C2×C4×C19—21no—
154C2×C4×C19—21no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19—21no—
158C2×C4×C19—21no—
159C2×C4×C19—21no—
160C2×C4×C19—21no—
161C2×C4×C19—21no—
162C2×C4×C19—21no—
163C2×C4×C19C2×D412yes—
164C2×C4×C19C2×D412yes—
165C22⋊D19—44no—
166C2×Dic19—21no—
167C2×Dic19—21no—
168C2×Dic19—21no—
169C2×Dic19—21no—
170C2×Dic19—21no—
171C2×Dic19—21no—
172C2×Dic19—21no—
173C2×Dic19—21no—
174C2×Dic19—21no—
175C2×Dic19—21no—
176C2×Dic19—21no—
177C2×Dic19—21no—
178C2×Dic19—21no—
179C2×Dic19—21no—
180C2×Dic19—21no—
181D76—44no—
182D76—44no—
183#2685—191nomaximal, Sylow
184C22×C19—22no—
185C22×C19—22no—
186C22×C19—22no—
187C22×C19—41no—
188C22×C19—41no—
189C22×C19—41no—
190C22×C19—41no—
191C22×C19C22×D411yescharacteristic
192C22×C19C2×#4111yescharacteristic
193C22×C19C2×#4111yescharacteristic
194C22×C19H(5,𝔽2)11yescharacteristic
195C22×C19H(5,𝔽2)11yescharacteristic
196C22×C19H(5,𝔽2)11yescharacteristic
197C22×C19H(5,𝔽2)11yescharacteristic
198C2×D19—22no—
199C2×D19—22no—
200C2×D19—22no—
201C2×D19—22no—
202C2×D19—22no—
203C2×D19—22no—
204C2×D19—416no—
205C2×D19—41no—
206C2×D19—41no—
207C2×D19—41no—
208C2×D19—41no—
209C2×D19—41no—
210C2×D19—41no—
211C2×D19—41no—
212C2×D19—41no—
213C2×D19—41no—
214C2×D19—41no—
215C2×D19—41no—
216C2×D19—41no—
217C2×D19—41no—
218C2×D19—41no—
219C2×D19—41no—
220C4×C19—22no—
221C4×C19—22no—
222C4×C19—41no—
223C4×C19—41no—
224C4×C19—41no—
225C4×C19—41no—
226Dic19—41no—
227Dic19—41no—
228Dic19—41no—
229Dic19—41no—
230Dic19—41no—
231C2×#126D1911yescharacteristic, complemented
232C2×#120—191no—
233#399—191no—
234#396—191no—
235#394—191no—
236#394—191no—
237#394—191no—
238#394—191no—
239#390—191no—
240#390—191no—
241#388—191no—
242#388—191no—
243#388—191no—
244#379—191no—
245#379—191no—
246C2×C19—42no—
247C2×C19#53511yescharacteristic
248C2×C19#53811yescharacteristic
249C2×C19#53811yescharacteristic
250C2×C19#54611yescharacteristic
251C2×C19#54611yescharacteristic
252C2×C19#55111yescharacteristic
253C2×C19#56011yescharacteristic
254D19—42no—
255D19—42no—
256D19—81no—
257C25—191no—
258C22×D4—191no—
259C22×D4—191no—
260C22×D4—191no—
261#126—24no—
262#120—384no—
263C2×C4⋊C4—191no—
264C2×C4⋊C4—191no—
265C2×C4⋊C4—191no—
266C2×C4⋊C4C2×D1911yescharacteristic, complemented
267C2×C4⋊C4C2×D1911yescharacteristic, complemented
268C2×C4⋊C4C2×D1911yescharacteristic, complemented
269C2×C22⋊C4—191no—
270C2×C22⋊C4—191no—
271C2×C22⋊C4—191no—
272C2×C22⋊C4—191no—
273C2×C22⋊C4—191no—
274C2×C22⋊C4—191no—
275C2×C22⋊C4—191no—
276C2×C22⋊C4—191no—
277C2×C22⋊C4—191no—
278C2×C22⋊C4—191no—
279C2×C22⋊C4—191no—
280C2×C22⋊C4—191no—
281C2×C22⋊C4—191no—
282C2×C22⋊C4—191no—
283C2×C22⋊C4—191no—
284C2×C22⋊C4—191no—
285C2×C22⋊C4C2×D1911yescharacteristic
286C2×C22⋊C4C2×D1911yescharacteristic
287C2×C22⋊C4C2×D1911yescharacteristic
288C2×C42—191no—
289C2×C42C2×D1911yescharacteristic, complemented
290#95—191no—
291#95—191no—
292#95—191no—
293#95—191no—
294C19#268511yescharacteristic, complemented, Sylow
295C24—191no—
296C24—191no—
297C24—191no—
298C24—382no—
299C24—382no—
300C24—382no—
301C24—761no—
302C24—761no—
303C24—761no—
304C24—761no—
305C24C22×D1911yescharacteristic
306C2×D4—382no—
307C2×D4—382no—
308C2×D4—382no—
309C2×D4—382no—
310C2×D4—382no—
311C2×D4—761no—
312C2×D4—761no—
313C2×D4—761no—
314C2×D4—761no—
315C22×C4—191no—
316C22×C4—191no—
317C22×C4—191no—
318C22×C4—191no—
319C22×C4—191no—
320C22×C4C22×D1911yescharacteristic
321C22×C4C22×D1911yescharacteristic
322C22×C4C22×D1911yescharacteristic
323C22×C4C22×D1911yescharacteristic
324C22×C4C22×D1911yescharacteristic
325C22×C4C22×D1911yescharacteristic
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—761no—
330C4⋊C4—761no—
331C4⋊C4—761no—
332C22⋊C4—22no—
333C22⋊C4—22no—
334C22⋊C4—382no—
335C22⋊C4—382no—
336C22⋊C4—382no—
337C22⋊C4—382no—
338C22⋊C4—761no—
339C22⋊C4—761no—
340C22⋊C4—761no—
341C22⋊C4—761no—
342C22⋊C4—761no—
343C22⋊C4—761no—
344C22⋊C4—761no—
345C22⋊C4—761no—
346C22⋊C4—761no—
347C22⋊C4—761no—
348C22⋊C4—761no—
349C22⋊C4—761no—
350C22⋊C4C22⋊D1914yes—
351C42—22no—
352C42—761no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—192no—
360C23—192no—
361C23—381no—
362C23—381no—
363C23—381no—
364C23—381no—
365C23—381no—
366C23—381no—
367C23—381no—
368C23—381no—
369C23—381no—
370C23—381no—
371C23—381no—
372C23—381no—
373C23—381no—
374C23—381no—
375C23—381no—
376C23—381no—
377C23—381no—
378C23—381no—
379C23—381no—
380C23—764no—
381C23—764no—
382C23—764no—
383C23—764no—
384C23—764no—
385C23—764no—
386C23—764no—
387C23C2×C22⋊D1912yes—
388C23C23×D1911yescharacteristic
389D4—764no—
390D4—764no—
391D4—764no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—381no—
409C2×C4—381no—
410C2×C4—381no—
411C2×C4—381no—
412C2×C4—381no—
413C2×C4—381no—
414C2×C4—381no—
415C2×C4—381no—
416C2×C4—381no—
417C2×C4—381no—
418C2×C4—381no—
419C2×C4—381no—
420C2×C4—381no—
421C2×C4—381no—
422C2×C4—381no—
423C2×C4C2×C22⋊D1912yes—
424C2×C4C2×C22⋊D1912yes—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—382no—
433C22—382no—
434C22—382no—
435C22—382no—
436C22—382no—
437C22—382no—
438C22—7616no—
439C22—761no—
440C22—761no—
441C22—761no—
442C22—761no—
443C22—761no—
444C22—761no—
445C22—761no—
446C22—761no—
447C22—761no—
448C22—761no—
449C22—761no—
450C22—761no—
451C22—761no—
452C22—761no—
453C22—761no—
454C22#41×D1911yescharacteristic
455C22#41×D1911yescharacteristic
456C22#1059743511yescharacteristic
457C22#1059743511yescharacteristic
458C22#1059743511yescharacteristic
459C22#1059743511yescharacteristic
460C22C22×C22⋊D1911yescharacteristic
461C4—22no—
462C4—22no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—761no—
468C4—761no—
469C4—761no—
470C4—761no—
471C4—761no—
472C2—42no—
473C2—762no—
474C2—762no—
475C2—1521no—
476C2#1192710811yescharacteristic
477C2#1192713311yescharacteristic
478C2#1192713311yescharacteristic
479C2#1192718211yescharacteristic
480C2#1192718211yescharacteristic
481C2#1192721911yescharacteristic
482C2#1192728511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#126C2
prime radicalC2×#10597328C2
hypercenterC2×#126D19
hypocenterC19#2685
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
2. #11926479C2semidirect
3. #11926466C2semidirect
4. #11926461C2semidirect
5. #11926461C2semidirect
6. #11926459C2semidirect
7. #11926459C2semidirect
8. #11926446C2semidirect
9. #11926445C2semidirect
10. #11926437C2semidirect
11. #11926435C2semidirect
12. #11926434C2semidirect
13. #11926399C2semidirect
14. #11926399C2semidirect
15. C2×C19×#126C2semidirect
21. C2×C4⋊C4×C19C22semidirect
22. C2×C4⋊C4×C19C22semidirect
23. C2×C4⋊C4×C19C22semidirect
27. C2×C42×C19C22semidirect
40. C2×(C2×D19)⋊C4C22semidirect
41. C2×(C2×D19)⋊C4C22semidirect
42. C2×(C2×D19)⋊C4C22semidirect
43. C2×(C2×D19)⋊C4C22semidirect
44. C2×C4⋊Dic19C22semidirect
45. C2×Dic19⋊C4C22semidirect
46. C2×Dic19⋊C4C22semidirect
47. C2×C4×Dic19C22semidirect
49. C19⋊#95C22semidirect
50. C19⋊#95C22semidirect
51. C19⋊#95C22semidirect
52. C19⋊#95C22semidirect
231. C2×#126D19semidirect
266. C2×C4⋊C4C2×D19semidirect
267. C2×C4⋊C4C2×D19semidirect
268. C2×C4⋊C4C2×D19semidirect
289. C2×C42C2×D19semidirect
294. C19#2685semidirect

Maximal subgroups

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

subgroupindex
C2×#105973282
#119264792
#119264662
#119264612
#119264592
#119264462
#119264452
#119264372
#119264352
#119264342
#119263992
C2×C19×#1262
#268519