Finite Group Databasebeta

← #18074938

Subgroups — #18074938

Order 4864.

676 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564609C211yesmaximal, characteristic, complemented
2#14562352C211yesmaximal, characteristic, complemented
3#14562255C211yesmaximal, characteristic, complemented
4#14562255C211yesmaximal, characteristic, complemented
5#14562173C211yesmaximal, characteristic, complemented
6#14562173C211yesmaximal, characteristic, complemented
7C19×#3552C211yesmaximal, characteristic
8#11926601C2211yescharacteristic
9#11926601C2211yescharacteristic
10C2×#10597260C2211yescharacteristic
11#11926410C2211yescharacteristic
12#11926306—22no—
13#11926290—22no—
14#11926286—21no—
15#11926286—21no—
16#11926284—21no—
17#11926284—21no—
18#11926281—21no—
19#11926281—21no—
20#11926278—21no—
21#11926278—21no—
22C19×#563—22no—
23C19×#557C411yescharacteristic, complemented
24C19×#556C411yescharacteristic, complemented
25C19×#554—21no—
26C19×#553—21no—
27D4×Q8×C19—21no—
28D4×Q8×C19C411yescharacteristic, complemented
29C19×#548—21no—
30C19×#547C411yescharacteristic, complemented
31C19×#544—21no—
32C19×#542—21no—
33C19×#541—21no—
34C19×#539—22no—
35C19×#536—21no—
36C2×C19×C4⋊Q8C2211yescharacteristic
37C19×#529C2211yescharacteristic
38C19×#529C2211yescharacteristic
39C2×#41×C19—21no—
40C22×Q8×C19—21no—
41C22×Q8×C19—21no—
42C19×C4⋊Q8—22no—
43C19×C4⋊Q8—21no—
44C19×C4⋊Q8—21no—
45C19×C4⋊Q8—21no—
46C19×C4⋊Q8—21no—
47C19×C4⋊Q8C2×C411yescharacteristic
48C19×C4⋊Q8C2×C411yescharacteristic
49C19×C4⋊Q8D412yes—
50C19×#126—22no—
51C19×#126—22no—
52C19×#126—22no—
53C19×#126—21no—
54C19×#126—21no—
55C19×#125—22no—
56C19×#125—22no—
57C19×#125—22no—
58C19×#125—21no—
59C19×#125D411yescharacteristic
60C19×#125D411yescharacteristic
61C19×#124—22no—
62C19×#124—21no—
63C19×#124D411yescharacteristic
64C19×#124D411yescharacteristic
65C19×#123—22no—
66C19×#123—22no—
67C19×#123—21no—
68C19×#123—21no—
69C19×#123—22no—
70C19×C22⋊Q8—22no—
71C19×C22⋊Q8—22no—
72C19×C22⋊Q8—22no—
73C19×C22⋊Q8—22no—
74C19×C22⋊Q8—22no—
75C19×C22⋊Q8—21no—
76C19×C22⋊Q8—22no—
77C19×C22⋊Q8—21no—
78C19×C22⋊Q8—21no—
79C19×C22⋊Q8D411yescharacteristic
80C19×C22⋊Q8D411yescharacteristic
81C19×#121—22no—
82C19×#121—21no—
83C19×#121D411yescharacteristic
84C19×#121D411yescharacteristic
85C4×Q8×C19—21no—
86C4×Q8×C19—21no—
87C4×Q8×C19—21no—
88C4×Q8×C19C2×C411yescharacteristic
89C4×Q8×C19C2×C411yescharacteristic
90C4×D4×C19—22no—
91C4×D4×C19—22no—
92C4×D4×C19—21no—
93C4×D4×C19—21no—
94C4×D4×C19—21no—
95C4×D4×C19C2×C411yescharacteristic
96C4×D4×C19C2×C411yescharacteristic
97C19×#117—21no—
98C19×#117—21no—
99C19×#117—21no—
100C2×C4⋊C4×C19—21no—
101C2×C4⋊C4×C19—21no—
102C2×C4⋊C4×C19D412yes—
103C2×C42×C19C2311yescharacteristic
104C2×C4⋊Dic19—21no—
105C22×C19⋊C8—21no—
106C19⋊#95—21no—
107C19⋊#95—21no—
108C22⋊(C19⋊C8)—21no—
109C22⋊(C19⋊C8)—21no—
110C4⋊(C19⋊C8)—21no—
111C4⋊(C19⋊C8)—21no—
112#10597260—21no—
113#10597260—21no—
114#10597260—21no—
115#10597260—21no—
116#41×C19—82no—
117C2×Q8×C19—22no—
118C2×Q8×C19—21no—
119C2×Q8×C19—21no—
120C2×Q8×C19—22no—
121C2×Q8×C19—82no—
122C2×Q8×C19—82no—
123C2×Q8×C19C22⋊C411yescharacteristic
124C2×Q8×C19C22⋊C411yescharacteristic
125C2×D4×C19—21no—
126C2×D4×C19—21no—
127C2×D4×C19—22no—
128C2×D4×C19C22⋊C411yescharacteristic
129C2×D4×C19C22⋊C411yescharacteristic
130C22×C4×C19—22no—
131C22×C4×C19—22no—
132C22×C4×C19—22no—
133C22×C4×C19—21no—
134C22×C4×C19—21no—
135C22×C4×C19C2×D411yescharacteristic
136C22×C4×C19C2×D411yescharacteristic
137C22×C4×C19C2×D411yescharacteristic
138C22×Dic19—41no—
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—21no—
146C4⋊C4×C19—21no—
147C4⋊C4×C19—21no—
148C4⋊C4×C19—21no—
149C4⋊C4×C19—22no—
150C4⋊C4×C19—22no—
151C4⋊C4×C19—21no—
152C4⋊C4×C19—21no—
153C4⋊C4×C19—21no—
154C4⋊C4×C19—21no—
155C4⋊C4×C19—21no—
156C4⋊C4×C19—21no—
157C4⋊C4×C19C22⋊C411yescharacteristic
158C4⋊C4×C19C22⋊C412yes—
159C4⋊C4×C19C22⋊C412yes—
160C4⋊C4×C19C22⋊C411yescharacteristic
161C4⋊C4×C19C22⋊C411yescharacteristic
162C4⋊C4×C19C22⋊C411yescharacteristic
163C22⋊C4×C19—22no—
164C22⋊C4×C19—22no—
165C22⋊C4×C19—22no—
166C22⋊C4×C19—22no—
167C22⋊C4×C19—21no—
168C22⋊C4×C19—21no—
169C22⋊C4×C19—21no—
170C22⋊C4×C19—21no—
171C22⋊C4×C19—21no—
172C22⋊C4×C19—21no—
173C22⋊C4×C19—21no—
174C22⋊C4×C19—21no—
175C22⋊C4×C19—21no—
176C22⋊C4×C19—21no—
177C42×C19—22no—
178C42×C19—22no—
179C42×C19—21no—
180C42×C19—21no—
181C42×C19C22×C411yescharacteristic
182C42×C19C2×D411yescharacteristic
183C42×C19C2×D411yescharacteristic
184C42×C19C2×D411yescharacteristic
185C4⋊Dic19—42no—
186C2×C19⋊C8—22no—
187C2×C19⋊C8—41no—
188C2×C19⋊C8—41no—
189C2×C19⋊C8—41no—
190C2×C19⋊C8—41no—
191#8499—191nomaximal, Sylow
192C23×C19—21no—
193C23×C19—21no—
194C23×C19#12011yescharacteristic
195Q8×C19—41no—
196Q8×C19—41no—
197Q8×C19—42no—
198Q8×C19—42no—
199Q8×C19—82no—
200Q8×C19—82no—
201D4×C19—41no—
202D4×C19—41no—
203D4×C19—41no—
204D4×C19—41no—
205D4×C19—41no—
206D4×C19—41no—
207D4×C19—82no—
208C2×C4×C19—21no—
209C2×C4×C19—21no—
210C2×C4×C19—21no—
211C2×C4×C19—21no—
212C2×C4×C19—21no—
213C2×C4×C19—21no—
214C2×C4×C19—21no—
215C2×C4×C19—22no—
216C2×C4×C19—22no—
217C2×C4×C19—21no—
218C2×C4×C19—41no—
219C2×C4×C19—41no—
220C2×C4×C19—42no—
221C2×C4×C19—42no—
222C2×C4×C19—82no—
223C2×C4×C19—82no—
224C2×C4×C19—82no—
225C2×C4×C19C2×C22⋊C411yescharacteristic
226C2×C4×C19C2×C22⋊C411yescharacteristic
227C2×C4×C19C2×C22⋊C411yescharacteristic
228C2×C4×C19#12011yescharacteristic
229C2×C4×C19#12011yescharacteristic
230C2×C4×C19#12011yescharacteristic
231C2×Dic19—81no—
232C2×Dic19—81no—
233C2×Dic19—81no—
234C19⋊C8—42no—
235C19⋊C8—81no—
236C19⋊C8—81no—
237#3552D1911yescharacteristic
238#1993—191no—
239#1556—191no—
240#1532—191no—
241#1532—191no—
242#1512—191no—
243#1512—191no—
244C22×C19—21no—
245C22×C19—21no—
246C22×C19—41no—
247C22×C19—41no—
248C22×C19—41no—
249C22×C19—41no—
250C22×C19—41no—
251C22×C19—41no—
252C22×C19#37911yescharacteristic
253C22×C19#45411yescharacteristic
254C22×C19#45611yescharacteristic
255C4×C19—21no—
256C4×C19—21no—
257C4×C19—21no—
258C4×C19—21no—
259C4×C19—21no—
260C4×C19—21no—
261C4×C19—41no—
262C4×C19—41no—
263C4×C19—41no—
264C4×C19—42no—
265C4×C19—42no—
266C4×C19—41no—
267C4×C19—41no—
268C4×C19—41no—
269Dic19—161no—
270#563—22no—
271#557Dic1911yescharacteristic, complemented
272#556Dic1911yescharacteristic, complemented
273#554—21no—
274#553—21no—
275D4×Q8—21no—
276D4×Q8Dic1911yescharacteristic, complemented
277#548—21no—
278#547Dic1911yescharacteristic, complemented
279#544—21no—
280#542—21no—
281#541—21no—
282#539—22no—
283#536—21no—
284C2×C4⋊Q8C2×D1911yescharacteristic
285#529C2×D1911yescharacteristic
286#529C2×D1911yescharacteristic
287#432—191no—
288#432—191no—
289C2×#97—191no—
290#382—191no—
291#340—382no—
292#332—382no—
293#330—381no—
294#330—381no—
295#329—381no—
296#329—381no—
297#328—381no—
298#328—381no—
299#327—381no—
300#327—381no—
301C2×C19—21no—
302C2×C19—21no—
303C2×C19—81no—
304C2×C19—81no—
305C2×C19#179311yescharacteristic
306C2×C19#179511yescharacteristic
307C2×C19#179611yescharacteristic
308C2×#41—21no—
309C22×Q8—21no—
310C22×Q8—21no—
311C22×C8—381no—
312C4⋊Q8—22no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8C2×Dic1911yescharacteristic
318C4⋊Q8C2×Dic1911yescharacteristic
319C4⋊Q8C22⋊D1912yes—
320#126—22no—
321#126—22no—
322#126—22no—
323#126—21no—
324#126—21no—
325#125—22no—
326#125—22no—
327#125—22no—
328#125—21no—
329#125C22⋊D1911yescharacteristic
330#125C22⋊D1911yescharacteristic
331#124—22no—
332#124—21no—
333#124C22⋊D1911yescharacteristic
334#124C22⋊D1911yescharacteristic
335#123—22no—
336#123—22no—
337#123—21no—
338#123—21no—
339#123—22no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—22no—
345C22⋊Q8—21no—
346C22⋊Q8—22no—
347C22⋊Q8—21no—
348C22⋊Q8—21no—
349C22⋊Q8C22⋊D1911yescharacteristic
350C22⋊Q8C22⋊D1911yescharacteristic
351#121—22no—
352#121—21no—
353#121C22⋊D1911yescharacteristic
354#121C22⋊D1911yescharacteristic
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8—21no—
358C4×Q8C2×Dic1911yescharacteristic
359C4×Q8C2×Dic1911yescharacteristic
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4C2×Dic1911yescharacteristic
366C4×D4C2×Dic1911yescharacteristic
367#117—21no—
368#117—21no—
369#117—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—381no—
373C2×C4⋊C4C22⋊D1912yes—
374C2×C42C22×D1911yescharacteristic
375C4⋊C8—381no—
376C4⋊C8—381no—
377C22⋊C8—381no—
378C22⋊C8—381no—
379#97—381no—
380#97—381no—
381#97—381no—
382#97—381no—
383#95—381no—
384#95—381no—
385C19#849911yescharacteristic, complemented, Sylow
386#41—82no—
387C2×Q8—22no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—22no—
391C2×Q8—82no—
392C2×Q8—82no—
393C2×Q8C22⋊Dic1911yescharacteristic
394C2×Q8C22⋊Dic1911yescharacteristic
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—22no—
398C2×D4C22⋊Dic1911yescharacteristic
399C2×D4C22⋊Dic1911yescharacteristic
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—761no—
406C22×C4C2×C22⋊D1911yescharacteristic
407C22×C4C2×C22⋊D1911yescharacteristic
408C22×C4C2×C22⋊D1911yescharacteristic
409C2×C8—382no—
410C2×C8—761no—
411C2×C8—761no—
412C2×C8—761no—
413C2×C8—761no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—762no—
433C4⋊C4C22⋊Dic1911yescharacteristic
434C4⋊C4C22⋊Dic1912yes—
435C4⋊C4C22⋊Dic1912yes—
436C4⋊C4C22⋊Dic1911yescharacteristic
437C4⋊C4C22⋊Dic1911yescharacteristic
438C4⋊C4C22⋊Dic1911yescharacteristic
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—21no—
444C22⋊C4—21no—
445C22⋊C4—21no—
446C22⋊C4—21no—
447C22⋊C4—21no—
448C22⋊C4—21no—
449C22⋊C4—21no—
450C22⋊C4—21no—
451C22⋊C4—21no—
452C22⋊C4—21no—
453C42—22no—
454C42—22no—
455C42—21no—
456C42—21no—
457C42C22×Dic1911yescharacteristic
458C42C2×C22⋊D1911yescharacteristic
459C42C2×C22⋊D1911yescharacteristic
460C42C2×C22⋊D1911yescharacteristic
461C23—21no—
462C23—21no—
463C23#1059739911yescharacteristic
464Q8—41no—
465Q8—41no—
466Q8—42no—
467Q8—42no—
468Q8—82no—
469Q8—82no—
470D4—41no—
471D4—41no—
472D4—41no—
473D4—41no—
474D4—41no—
475D4—41no—
476D4—82no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—82no—
492C2×C4—82no—
493C2×C4—82no—
494C2×C4—1521no—
495C2×C4—1521no—
496C2×C4—1521no—
497C2×C4C2×C22⋊Dic1911yescharacteristic
498C2×C4C2×C22⋊Dic1911yescharacteristic
499C2×C4C2×C22⋊Dic1911yescharacteristic
500C2×C4#1059739911yescharacteristic
501C2×C4#1059739911yescharacteristic
502C2×C4#1059739911yescharacteristic
503C8—762no—
504C8—1521no—
505C8—1521no—
506C22—21no—
507C22—21no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22#1192640011yescharacteristic
515C22#1192671711yescharacteristic
516C22#1192672711yescharacteristic
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—41no—
524C4—41no—
525C4—41no—
526C4—42no—
527C4—42no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—3041no—
532C2—21no—
533C2—21no—
534C2—81no—
535C2—81no—
536C2#1456359411yescharacteristic
537C2#1456360511yescharacteristic
538C2#1456361011yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3552C2
socleC22×C19#379
cosocleC2×C42×C19C23
hypercenter#3552D19
hypocenterC19#8499
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3552

Complements

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

NH ≅ G/Ntype
1. #14564609C2semidirect
2. #14562352C2semidirect
3. #14562255C2semidirect
4. #14562255C2semidirect
5. #14562173C2semidirect
6. #14562173C2semidirect
23. C19×#557C4semidirect
24. C19×#556C4semidirect
28. D4×Q8×C19C4semidirect
30. C19×#547C4semidirect
271. #557Dic19semidirect
272. #556Dic19semidirect
276. D4×Q8Dic19semidirect
278. #547Dic19semidirect
385. C19#8499semidirect

Maximal subgroups

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

subgroupindex
#145646092
#145623522
#145622552
#145621732
C19×#35522
#849919