Finite Group Databasebeta

← #18074428

Subgroups — #18074428

Order 4864.

706 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564580C211yesmaximal, characteristic, complemented
2#14563465C211yesmaximal, characteristic, complemented
3#14562250C211yesmaximal, characteristic, complemented
4#14562223C211yesmaximal, characteristic
5#14562160C211yesmaximal, characteristic
6#14562082C211yesmaximal, characteristic, complemented
7C19×#3523C211yesmaximal, characteristic
8#11926601C2211yescharacteristic
9C2×#10597292—21no—
10C4×#64520C2211yescharacteristic
11C2×#10597260C2211yescharacteristic
12C4×C4⋊Dic19C2211yescharacteristic
13#11926306—21no—
14#11926303—22no—
15#11926286—21no—
16#11926286—22no—
17#11926284—21no—
18#11926281—21no—
19#11926278—21no—
20Q8⋊(C19⋊C8)—21no—
21Q8⋊(C19⋊C8)—21no—
22C19×#557—21no—
23C19×#557C411yescharacteristic, complemented
24C19×#557C411yescharacteristic, complemented
25C19×#556—21no—
26C19×#556C411yescharacteristic, complemented
27C19×#552—22no—
28C19×#552—21no—
29D4×Q8×C19—21no—
30D4×Q8×C19C411yescharacteristic, complemented
31C19×#541—22no—
32C19×#541—21no—
33C19×#533—21no—
34C19×#533C2211yescharacteristic
35C19×#529—21no—
36C19×#529C2211yescharacteristic
37C19×#519—21no—
38C2×C4×Q8×C19C2211yescharacteristic
39C22×Q8×C19—21no—
40C22×Q8×C19D411yescharacteristic
41C19×C4⋊Q8—22no—
42C19×C4⋊Q8—21no—
43C19×C4⋊Q8—21no—
44C19×C4⋊Q8—21no—
45C19×C4⋊Q8C2×C411yescharacteristic
46C19×C4⋊Q8C2×C411yescharacteristic
47C19×#126—22no—
48C19×#126—22no—
49C19×#126—22no—
50C19×#126—22no—
51C19×#126—21no—
52C19×#125—22no—
53C19×#125—22no—
54C19×#125—22no—
55C19×#125—21no—
56C19×#125—22no—
57C19×#125—22no—
58C19×#125—21no—
59C19×#125D411yescharacteristic
60C19×#125D412yes—
61C19×#124—21no—
62C19×#124D411yescharacteristic
63C19×#123—22no—
64C19×#123—21no—
65C19×C22⋊Q8—22no—
66C19×C22⋊Q8—22no—
67C19×C22⋊Q8—21no—
68C19×C22⋊Q8—21no—
69C19×C22⋊Q8—21no—
70C19×C22⋊Q8—21no—
71C19×C22⋊Q8—22no—
72C19×C22⋊Q8D411yescharacteristic
73C19×#121D411yescharacteristic
74C4×Q8×C19—22no—
75C4×Q8×C19—22no—
76C4×Q8×C19—21no—
77C4×Q8×C19—21no—
78C4×Q8×C19—21no—
79C4×Q8×C19—21no—
80C4×Q8×C19—21no—
81C4×Q8×C19—21no—
82C4×Q8×C19—21no—
83C4×Q8×C19—21no—
84C4×Q8×C19—21no—
85C4×Q8×C19C2×C411yescharacteristic
86C4×Q8×C19C2×C411yescharacteristic
87C4×Q8×C19C2×C411yescharacteristic
88C4×Q8×C19D411yescharacteristic
89C4×Q8×C19D411yescharacteristic
90C4×D4×C19—22no—
91C4×D4×C19—21no—
92C4×D4×C19—21no—
93C4×D4×C19C2×C411yescharacteristic
94C19×#117—22no—
95C19×#117—22no—
96C19×#117—22no—
97C19×#117—21no—
98C19×#117—21no—
99C19×#117D412yes—
100C2×C4⋊C4×C19—21no—
101C2×C4⋊C4×C19D411yescharacteristic
102C2×C42×C19—21no—
103C2×C42×C19C2311yescharacteristic
104C2×C4⋊Dic19—21no—
105C2×C4×Dic19—21no—
106C2×#64520—21no—
107C22×C19⋊C8—21no—
108#10597292—24no—
109C19⋊#95—21no—
110C22⋊(C19⋊C8)—21no—
111C4⋊(C19⋊C8)—21no—
112#10597260—21no—
113#10597260—21no—
114#10597260—21no—
115#10597260—21no—
116C4×C19⋊C8—21no—
117C2×Q8×C19—22no—
118C2×Q8×C19—21no—
119C2×Q8×C19—21no—
120C2×Q8×C19—21no—
121C2×Q8×C19—22no—
122C2×Q8×C19—41no—
123C2×Q8×C19—42no—
124C2×Q8×C19—42no—
125C2×Q8×C19C22⋊C411yescharacteristic
126C2×Q8×C19C22⋊C411yescharacteristic
127C2×Q8×C19C22⋊C411yescharacteristic
128C2×D4×C19—21no—
129C2×D4×C19C22⋊C411yescharacteristic
130C22×C4×C19—22no—
131C22×C4×C19—21no—
132C22×C4×C19—21no—
133C22×C4×C19—21no—
134C22×C4×C19C2×D411yescharacteristic
135C22×C4×C19C2×D411yescharacteristic
136C22×C4×C19C2×D411yescharacteristic
137C22×Dic19—41no—
138C4⋊C4×C19—22no—
139C4⋊C4×C19—22no—
140C4⋊C4×C19—22no—
141C4⋊C4×C19—22no—
142C4⋊C4×C19—22no—
143C4⋊C4×C19—22no—
144C4⋊C4×C19—22no—
145C4⋊C4×C19—22no—
146C4⋊C4×C19—21no—
147C4⋊C4×C19—21no—
148C4⋊C4×C19—21no—
149C4⋊C4×C19—21no—
150C4⋊C4×C19—21no—
151C4⋊C4×C19—21no—
152C4⋊C4×C19—21no—
153C4⋊C4×C19—21no—
154C4⋊C4×C19—22no—
155C4⋊C4×C19—21no—
156C4⋊C4×C19—21no—
157C4⋊C4×C19—21no—
158C4⋊C4×C19—22no—
159C4⋊C4×C19C22⋊C411yescharacteristic
160C4⋊C4×C19C22⋊C411yescharacteristic
161C4⋊C4×C19C22⋊C412yes—
162C4⋊C4×C19C22⋊C412yes—
163C4⋊C4×C19C22⋊C411yescharacteristic
164C4⋊C4×C19C22⋊C411yescharacteristic
165C22⋊C4×C19—22no—
166C22⋊C4×C19—22no—
167C22⋊C4×C19—22no—
168C22⋊C4×C19—21no—
169C22⋊C4×C19—22no—
170C22⋊C4×C19—21no—
171C22⋊C4×C19—21no—
172C22⋊C4×C19—21no—
173C22⋊C4×C19—21no—
174C42×C19—22no—
175C42×C19—22no—
176C42×C19—22no—
177C42×C19—21no—
178C42×C19—21no—
179C42×C19—21no—
180C42×C19—21no—
181C42×C19—21no—
182C42×C19—22no—
183C42×C19C22×C411yescharacteristic
184C42×C19C2×D411yescharacteristic
185C42×C19C2×D411yescharacteristic
186C42×C19C2×D411yescharacteristic
187C4⋊Dic19—22no—
188C4⋊Dic19—41no—
189C4×Dic19—42no—
190#64520—22no—
191#64520—41no—
192C2×C19⋊C8—22no—
193C2×C19⋊C8—41no—
194C2×C19⋊C8—41no—
195C2×C19⋊C8—41no—
196C2×C19⋊C8—41no—
197#8417—191nomaximal, Sylow
198C23×C19—21no—
199C23×C19#12011yescharacteristic
200Q8×C19—21no—
201Q8×C19—21no—
202Q8×C19—21no—
203Q8×C19—42no—
204Q8×C19—41no—
205Q8×C19—42no—
206Q8×C19—44no—
207Q8×C19—41no—
208Q8×C19—41no—
209Q8×C19#10412yes—
210D4×C19—41no—
211D4×C19—41no—
212D4×C19—41no—
213C2×C4×C19—21no—
214C2×C4×C19—21no—
215C2×C4×C19—21no—
216C2×C4×C19—21no—
217C2×C4×C19—21no—
218C2×C4×C19—21no—
219C2×C4×C19—21no—
220C2×C4×C19—22no—
221C2×C4×C19—21no—
222C2×C4×C19—21no—
223C2×C4×C19—21no—
224C2×C4×C19—21no—
225C2×C4×C19—22no—
226C2×C4×C19—41no—
227C2×C4×C19—42no—
228C2×C4×C19—44no—
229C2×C4×C19—41no—
230C2×C4×C19—41no—
231C2×C4×C19—41no—
232C2×C4×C19—41no—
233C2×C4×C19C2×C22⋊C411yescharacteristic
234C2×C4×C19C2×C22⋊C411yescharacteristic
235C2×C4×C19C2×C22⋊C411yescharacteristic
236C2×C4×C19#12011yescharacteristic
237C2×C4×C19#12011yescharacteristic
238C2×C4×C19#12011yescharacteristic
239C2×Dic19—42no—
240C2×Dic19—81no—
241C2×Dic19—81no—
242C19⋊C8—42no—
243C19⋊C8—42no—
244C19⋊C8—81no—
245#3523D1911yescharacteristic
246#1986—191no—
247#1763—191no—
248#1531—191no—
249#1524—191no—
250#1509—191no—
251#1491—191no—
252C22×C19—21no—
253C22×C19—21no—
254C22×C19—41no—
255C22×C19—41no—
256C22×C19—41no—
257C22×C19#37911yescharacteristic
258C22×C19#45411yescharacteristic
259C22×C19#45611yescharacteristic
260C4×C19—21no—
261C4×C19—21no—
262C4×C19—21no—
263C4×C19—21no—
264C4×C19—21no—
265C4×C19—22no—
266C4×C19—41no—
267C4×C19—41no—
268C4×C19—41no—
269C4×C19—41no—
270C4×C19—42no—
271C4×C19—41no—
272C4×C19—42no—
273C4×C19—41no—
274C4×C19C2×#10411yescharacteristic
275C4×C19#42111yescharacteristic
276Dic19—82no—
277#557—21no—
278#557Dic1911yescharacteristic, complemented
279#557Dic1911yescharacteristic, complemented
280#556—21no—
281#556Dic1911yescharacteristic, complemented
282#552—22no—
283#552—21no—
284D4×Q8—21no—
285D4×Q8Dic1911yescharacteristic, complemented
286#541—22no—
287#541—21no—
288#533—21no—
289#533C2×D1911yescharacteristic
290#529—21no—
291#529C2×D1911yescharacteristic
292#519—21no—
293C2×C4×Q8C2×D1911yescharacteristic
294#432—191no—
295C2×#103—381no—
296C4×M16—191no—
297C2×#97—191no—
298C4×C4⋊C4—191no—
299#340—381no—
300#339—382no—
301#330—381no—
302#330—382no—
303#329—381no—
304#328—381no—
305#327—381no—
306Q8⋊C8—381no—
307Q8⋊C8—381no—
308C2×C19—21no—
309C2×C19—21no—
310C2×C19—81no—
311C2×C19#178911yescharacteristic
312C2×C19#179311yescharacteristic
313C2×C19#179611yescharacteristic
314C22×Q8—21no—
315C22×Q8C22⋊D1911yescharacteristic
316C2×M16—381no—
317C22×C8—381no—
318C4⋊Q8—22no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8C2×Dic1911yescharacteristic
323C4⋊Q8C2×Dic1911yescharacteristic
324#126—22no—
325#126—22no—
326#126—22no—
327#126—22no—
328#126—21no—
329#125—22no—
330#125—22no—
331#125—22no—
332#125—21no—
333#125—22no—
334#125—22no—
335#125—21no—
336#125C22⋊D1911yescharacteristic
337#125C22⋊D1912yes—
338#124—21no—
339#124C22⋊D1911yescharacteristic
340#123—22no—
341#123—21no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—21no—
345C22⋊Q8—21no—
346C22⋊Q8—21no—
347C22⋊Q8—21no—
348C22⋊Q8—22no—
349C22⋊Q8C22⋊D1911yescharacteristic
350#121C22⋊D1911yescharacteristic
351C4×Q8—22no—
352C4×Q8—22no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8C2×Dic1911yescharacteristic
363C4×Q8C2×Dic1911yescharacteristic
364C4×Q8C2×Dic1911yescharacteristic
365C4×Q8C22⋊D1911yescharacteristic
366C4×Q8C22⋊D1911yescharacteristic
367C4×D4—22no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4C2×Dic1911yescharacteristic
371#117—22no—
372#117—22no—
373#117—22no—
374#117—21no—
375#117—21no—
376#117C22⋊D1912yes—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—381no—
379C2×C4⋊C4C22⋊D1911yescharacteristic
380C2×C42—21no—
381C2×C42—381no—
382C2×C42C22×D1911yescharacteristic
383C4⋊C8—381no—
384#103—384no—
385C22⋊C8—381no—
386#97—381no—
387#97—381no—
388#97—381no—
389#97—381no—
390C4×C8—381no—
391#95—381no—
392C19#841711yescharacteristic, complemented, Sylow
393C2×Q8—22no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—22no—
398C2×Q8—41no—
399C2×Q8—42no—
400C2×Q8—42no—
401C2×Q8C22⋊Dic1911yescharacteristic
402C2×Q8C22⋊Dic1911yescharacteristic
403C2×Q8C22⋊Dic1911yescharacteristic
404C2×D4—21no—
405C2×D4C22⋊Dic1911yescharacteristic
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—761no—
411C22×C4C2×C22⋊D1911yescharacteristic
412C22×C4C2×C22⋊D1911yescharacteristic
413C22×C4C2×C22⋊D1911yescharacteristic
414M16—382no—
415M16—761no—
416C2×C8—382no—
417C2×C8—761no—
418C2×C8—761no—
419C2×C8—761no—
420C2×C8—761no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—382no—
443C4⋊C4—761no—
444C4⋊C4C22⋊Dic1911yescharacteristic
445C4⋊C4C22⋊Dic1911yescharacteristic
446C4⋊C4C22⋊Dic1912yes—
447C4⋊C4C22⋊Dic1912yes—
448C4⋊C4C22⋊Dic1911yescharacteristic
449C4⋊C4C22⋊Dic1911yescharacteristic
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—21no—
454C22⋊C4—22no—
455C22⋊C4—21no—
456C22⋊C4—21no—
457C22⋊C4—21no—
458C22⋊C4—21no—
459C42—22no—
460C42—22no—
461C42—22no—
462C42—21no—
463C42—21no—
464C42—21no—
465C42—21no—
466C42—21no—
467C42—22no—
468C42—762no—
469C42C22×Dic1911yescharacteristic
470C42C2×C22⋊D1911yescharacteristic
471C42C2×C22⋊D1911yescharacteristic
472C42C2×C22⋊D1911yescharacteristic
473C23—21no—
474C23#1059739911yescharacteristic
475Q8—21no—
476Q8—21no—
477Q8—21no—
478Q8—42no—
479Q8—41no—
480Q8—44no—
481Q8—42no—
482Q8—41no—
483Q8—41no—
484Q8#1059729412yes—
485D4—41no—
486D4—41no—
487D4—41no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—44no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—762no—
509C2×C4—1521no—
510C2×C4—1521no—
511C2×C4C2×C22⋊Dic1911yescharacteristic
512C2×C4C2×C22⋊Dic1911yescharacteristic
513C2×C4C2×C22⋊Dic1911yescharacteristic
514C2×C4#1059739911yescharacteristic
515C2×C4#1059739911yescharacteristic
516C2×C4#1059739911yescharacteristic
517C8—762no—
518C8—762no—
519C8—1521no—
520C22—21no—
521C22—21no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22#1192640011yescharacteristic
526C22#1192671711yescharacteristic
527C22#1192672711yescharacteristic
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—21no—
533C4—22no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—42no—
538C4—41no—
539C4—41no—
540C4—42no—
541C4—41no—
542C4—1522no—
543C4C2×#1059729411yescharacteristic
544C4#1192656111yescharacteristic
545C2—21no—
546C2—21no—
547C2—81no—
548C2#1456357911yescharacteristic
549C2#1456359411yescharacteristic
550C2#1456361011yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3523C2
socleC22×C19#379
prime radicalC19×#121D4
cosocleC2×C42×C19C23
hypercenter#3523D19
hypocenterC19#8417
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3523

Complements

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

NH ≅ G/Ntype
1. #14564580C2semidirect
2. #14563465C2semidirect
3. #14562250C2semidirect
6. #14562082C2semidirect
23. C19×#557C4semidirect
24. C19×#557C4semidirect
26. C19×#556C4semidirect
30. D4×Q8×C19C4semidirect
278. #557Dic19semidirect
279. #557Dic19semidirect
281. #556Dic19semidirect
285. D4×Q8Dic19semidirect
392. C19#8417semidirect

Maximal subgroups

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

subgroupindex
#145645802
#145634652
#145622502
#145622232
#145621602
#145620822
C19×#35232
#841719