Finite Group Databasebeta

← #18074442

Subgroups — #18074442

Order 4864.

778 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564555C211yesmaximal, characteristic, complemented
2#14563465C211yesmaximal, characteristic, complemented
3#14562246C211yesmaximal, characteristic, complemented
4#14562223C211yesmaximal, characteristic, complemented
5#14562160C211yesmaximal, characteristic, complemented
6#14562082C211yesmaximal, characteristic, complemented
7C19×#3522C211yesmaximal, characteristic
8#11926601C2211yescharacteristic
9C2×#10597294—22no—
10C2×#10597292—21no—
11C4×#64520C2211yescharacteristic
12C2×#10597260C2211yescharacteristic
13C4×C4⋊Dic19C2211yescharacteristic
14#11926306—21no—
15#11926286—21no—
16#11926284—21no—
17#11926284—22no—
18#11926281—21no—
19#11926278—21no—
20Q8⋊(C19⋊C8)—21no—
21Q8⋊(C19⋊C8)—21no—
22C19×#559—21no—
23C19×#559C411yescharacteristic, complemented
24Q82×C19C411yescharacteristic, complemented
25C19×#554—21no—
26C19×#554C411yescharacteristic, complemented
27C19×#550C411yescharacteristic, complemented
28C19×#548—21no—
29C19×#547—22no—
30C19×#547—21no—
31C19×#542—22no—
32C19×#542—21no—
33C19×#532—21no—
34C19×#532C2211yescharacteristic
35C19×#529—21no—
36C19×#529C2211yescharacteristic
37C19×#520—21no—
38C2×C4×Q8×C19C2211yescharacteristic
39C2×#41×C19—22no—
40C2×#41×C19—21no—
41C2×#41×C19D412yes—
42C22×Q8×C19D411yescharacteristic
43C19×C4⋊Q8—22no—
44C19×C4⋊Q8—21no—
45C19×C4⋊Q8—21no—
46C19×C4⋊Q8C2×C411yescharacteristic
47C19×#127—21no—
48C19×#127C2×C411yescharacteristic
49C19×#126—22no—
50C19×#126—21no—
51C19×#125—21no—
52C19×#125D411yescharacteristic
53C19×#124—22no—
54C19×#124—22no—
55C19×#124—21no—
56C19×#124—21no—
57C19×#124D411yescharacteristic
58C19×#124D412yes—
59C19×#123—22no—
60C19×#123—22no—
61C19×#123—22no—
62C19×#123—22no—
63C19×#123—21no—
64C19×C22⋊Q8—22no—
65C19×C22⋊Q8—22no—
66C19×C22⋊Q8—22no—
67C19×C22⋊Q8—22no—
68C19×C22⋊Q8—21no—
69C19×C22⋊Q8D411yescharacteristic
70C19×#121—22no—
71C19×#121—22no—
72C19×#121—21no—
73C19×#121—21no—
74C19×#121—21no—
75C19×#121D411yescharacteristic
76C4×Q8×C19—21no—
77C4×Q8×C19—21no—
78C4×Q8×C19—21no—
79C4×Q8×C19—21no—
80C4×Q8×C19C2×C411yescharacteristic
81C4×Q8×C19C2×C411yescharacteristic
82C4×Q8×C19C2×C411yescharacteristic
83C4×Q8×C19D411yescharacteristic
84C4×Q8×C19D411yescharacteristic
85C4×D4×C19—22no—
86C4×D4×C19—22no—
87C4×D4×C19—22no—
88C4×D4×C19—21no—
89C4×D4×C19—21no—
90C4×D4×C19—21no—
91C4×D4×C19—21no—
92C4×D4×C19—21no—
93C4×D4×C19—21no—
94C4×D4×C19—21no—
95C4×D4×C19C2×C411yescharacteristic
96C19×#117—22no—
97C19×#117—21no—
98C2×C4⋊C4×C19—22no—
99C2×C4⋊C4×C19—21no—
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#10597294—44no—
109#10597292—24no—
110C19⋊#95—21no—
111C22⋊(C19⋊C8)—21no—
112C4⋊(C19⋊C8)—21no—
113#10597260—21no—
114#10597260—21no—
115#10597260—21no—
116#10597260—21no—
117C4×C19⋊C8—21no—
118#41×C19—42no—
119#41×C19—42no—
120#41×C19—42no—
121#41×C19—42no—
122#41×C19—82no—
123#41×C19—82no—
124C2×Q8×C19—22no—
125C2×Q8×C19—21no—
126C2×Q8×C19—22no—
127C2×Q8×C19—41no—
128C2×Q8×C19C22⋊C411yescharacteristic
129C2×Q8×C19C22⋊C411yescharacteristic
130C2×Q8×C19C22⋊C411yescharacteristic
131C2×Q8×C19C22⋊C412yes—
132C2×D4×C19—22no—
133C2×D4×C19—22no—
134C2×D4×C19—21no—
135C2×D4×C19—22no—
136C2×D4×C19—21no—
137C2×D4×C19—21no—
138C2×D4×C19C22⋊C411yescharacteristic
139C2×D4×C19C22⋊C412yes—
140C22×C4×C19—22no—
141C22×C4×C19—21no—
142C22×C4×C19—21no—
143C22×C4×C19—22no—
144C22×C4×C19—22no—
145C22×C4×C19—21no—
146C22×C4×C19—22no—
147C22×C4×C19C2×D411yescharacteristic
148C22×C4×C19C2×D411yescharacteristic
149C22×C4×C19C2×D411yescharacteristic
150C22×Dic19—41no—
151C4⋊C4×C19—22no—
152C4⋊C4×C19—22no—
153C4⋊C4×C19—22no—
154C4⋊C4×C19—22no—
155C4⋊C4×C19—21no—
156C4⋊C4×C19—21no—
157C4⋊C4×C19—21no—
158C4⋊C4×C19—21no—
159C4⋊C4×C19—21no—
160C4⋊C4×C19—21no—
161C4⋊C4×C19—21no—
162C4⋊C4×C19—21no—
163C4⋊C4×C19—21no—
164C4⋊C4×C19—21no—
165C4⋊C4×C19—21no—
166C4⋊C4×C19C22⋊C411yescharacteristic
167C4⋊C4×C19C22⋊C411yescharacteristic
168C4⋊C4×C19C22⋊C411yescharacteristic
169C4⋊C4×C19C22⋊C411yescharacteristic
170C22⋊C4×C19—22no—
171C22⋊C4×C19—22no—
172C22⋊C4×C19—22no—
173C22⋊C4×C19—22no—
174C22⋊C4×C19—22no—
175C22⋊C4×C19—21no—
176C22⋊C4×C19—21no—
177C22⋊C4×C19—22no—
178C22⋊C4×C19—21no—
179C22⋊C4×C19—21no—
180C22⋊C4×C19—22no—
181C22⋊C4×C19—21no—
182C42×C19—22no—
183C42×C19—21no—
184C42×C19—21no—
185C42×C19—21no—
186C42×C19—21no—
187C42×C19—21no—
188C42×C19C22×C411yescharacteristic
189C42×C19C2×D411yescharacteristic
190C42×C19C2×D411yescharacteristic
191C42×C19C2×D411yescharacteristic
192C4⋊Dic19—22no—
193C4⋊Dic19—41no—
194C4×Dic19—42no—
195#64520—22no—
196#64520—41no—
197C2×C19⋊C8—22no—
198C2×C19⋊C8—41no—
199C2×C19⋊C8—41no—
200C2×C19⋊C8—41no—
201C2×C19⋊C8—41no—
202#8419—191nomaximal, Sylow
203C23×C19—22no—
204C23×C19—21no—
205C23×C19#12011yescharacteristic
206Q8×C19—21no—
207Q8×C19—21no—
208Q8×C19—21no—
209Q8×C19—42no—
210Q8×C19—41no—
211Q8×C19—42no—
212Q8×C19—82no—
213Q8×C19#10412yescomplemented
214D4×C19—41no—
215D4×C19—42no—
216D4×C19—42no—
217D4×C19—44no—
218D4×C19—42no—
219D4×C19—41no—
220D4×C19—42no—
221D4×C19—41no—
222D4×C19—41no—
223D4×C19—41no—
224D4×C19—82no—
225C2×C4×C19—21no—
226C2×C4×C19—21no—
227C2×C4×C19—21no—
228C2×C4×C19—21no—
229C2×C4×C19—21no—
230C2×C4×C19—21no—
231C2×C4×C19—21no—
232C2×C4×C19—21no—
233C2×C4×C19—21no—
234C2×C4×C19—22no—
235C2×C4×C19—21no—
236C2×C4×C19—21no—
237C2×C4×C19—41no—
238C2×C4×C19—42no—
239C2×C4×C19—44no—
240C2×C4×C19—41no—
241C2×C4×C19—41no—
242C2×C4×C19—41no—
243C2×C4×C19—41no—
244C2×C4×C19—82no—
245C2×C4×C19—82no—
246C2×C4×C19—82no—
247C2×C4×C19C2×C22⋊C411yescharacteristic
248C2×C4×C19C2×C22⋊C411yescharacteristic
249C2×C4×C19C2×C22⋊C411yescharacteristic
250C2×C4×C19#12011yescharacteristic
251C2×C4×C19#12011yescharacteristic
252C2×C4×C19#12011yescharacteristic
253C2×Dic19—42no—
254C2×Dic19—81no—
255C2×Dic19—81no—
256C19⋊C8—42no—
257C19⋊C8—42no—
258C19⋊C8—81no—
259#3522D1911yescharacteristic
260#1980—191no—
261#1763—191no—
262#1530—191no—
263#1524—191no—
264#1509—191no—
265#1491—191no—
266C22×C19—21no—
267C22×C19—21no—
268C22×C19—42no—
269C22×C19—41no—
270C22×C19—42no—
271C22×C19—41no—
272C22×C19—42no—
273C22×C19—41no—
274C22×C19#37911yescharacteristic
275C22×C19#45311yescharacteristic
276C22×C19#45511yescharacteristic
277C4×C19—21no—
278C4×C19—21no—
279C4×C19—21no—
280C4×C19—21no—
281C4×C19—21no—
282C4×C19—22no—
283C4×C19—41no—
284C4×C19—41no—
285C4×C19—42no—
286C4×C19—41no—
287C4×C19—41no—
288C4×C19—41no—
289C4×C19—41no—
290C4×C19C2×#10411yescharacteristic
291C4×C19#42111yescharacteristic
292Dic19—82no—
293#559—21no—
294#559Dic1911yescharacteristic, complemented
295Q82Dic1911yescharacteristic, complemented
296#554—21no—
297#554Dic1911yescharacteristic, complemented
298#550Dic1911yescharacteristic, complemented
299#548—21no—
300#547—22no—
301#547—21no—
302#542—22no—
303#542—21no—
304#532—21no—
305#532C2×D1911yescharacteristic
306#529—21no—
307#529C2×D1911yescharacteristic
308#520—21no—
309C2×C4×Q8C2×D1911yescharacteristic
310#432—191no—
311C2×#104—382no—
312C2×#103—381no—
313C4×M16—191no—
314C2×#97—191no—
315C4×C4⋊C4—191no—
316#340—381no—
317#330—381no—
318#329—381no—
319#329—382no—
320#328—381no—
321#327—381no—
322Q8⋊C8—381no—
323Q8⋊C8—381no—
324C2×C19—21no—
325C2×C19—21no—
326C2×C19—82no—
327C2×C19—81no—
328C2×C19#178911yescharacteristic
329C2×C19#179211yescharacteristic
330C2×C19#179611yescharacteristic
331C2×#41—22no—
332C2×#41—21no—
333C2×#41C22⋊D1912yes—
334C22×Q8C22⋊D1911yescharacteristic
335C2×M16—381no—
336C22×C8—381no—
337C4⋊Q8—22no—
338C4⋊Q8—21no—
339C4⋊Q8—21no—
340C4⋊Q8C2×Dic1911yescharacteristic
341#127—21no—
342#127C2×Dic1911yescharacteristic
343#126—22no—
344#126—21no—
345#125—21no—
346#125C22⋊D1911yescharacteristic
347#124—22no—
348#124—22no—
349#124—21no—
350#124—21no—
351#124C22⋊D1911yescharacteristic
352#124C22⋊D1912yes—
353#123—22no—
354#123—22no—
355#123—22no—
356#123—22no—
357#123—21no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—21no—
363C22⋊Q8C22⋊D1911yescharacteristic
364#121—22no—
365#121—22no—
366#121—21no—
367#121—21no—
368#121—21no—
369#121C22⋊D1911yescharacteristic
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8C2×Dic1911yescharacteristic
375C4×Q8C2×Dic1911yescharacteristic
376C4×Q8C2×Dic1911yescharacteristic
377C4×Q8C22⋊D1911yescharacteristic
378C4×Q8C22⋊D1911yescharacteristic
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4C2×Dic1911yescharacteristic
390#117—22no—
391#117—21no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—381no—
396C2×C4⋊C4C22⋊D1911yescharacteristic
397C2×C42—21no—
398C2×C42—381no—
399C2×C42C22×D1911yescharacteristic
400C4⋊C8—381no—
401#104—764no—
402#103—384no—
403C22⋊C8—381no—
404#97—381no—
405#97—381no—
406#97—381no—
407#97—381no—
408C4×C8—381no—
409#95—381no—
410C19#841911yescharacteristic, complemented, Sylow
411#41—42no—
412#41—42no—
413#41—42no—
414#41—42no—
415#41—82no—
416#41—82no—
417C2×Q8—22no—
418C2×Q8—21no—
419C2×Q8—22no—
420C2×Q8—41no—
421C2×Q8C22⋊Dic1911yescharacteristic
422C2×Q8C22⋊Dic1911yescharacteristic
423C2×Q8C22⋊Dic1911yescharacteristic
424C2×Q8C22⋊Dic1912yes—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4C22⋊Dic1911yescharacteristic
432C2×D4C22⋊Dic1912yes—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—761no—
441C22×C4C2×C22⋊D1911yescharacteristic
442C22×C4C2×C22⋊D1911yescharacteristic
443C22×C4C2×C22⋊D1911yescharacteristic
444M16—382no—
445M16—761no—
446C2×C8—382no—
447C2×C8—761no—
448C2×C8—761no—
449C2×C8—761no—
450C2×C8—761no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—382no—
467C4⋊C4—761no—
468C4⋊C4C22⋊Dic1911yescharacteristic
469C4⋊C4C22⋊Dic1911yescharacteristic
470C4⋊C4C22⋊Dic1911yescharacteristic
471C4⋊C4C22⋊Dic1911yescharacteristic
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—22no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—22no—
483C22⋊C4—21no—
484C42—22no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—762no—
491C42C22×Dic1911yescharacteristic
492C42C2×C22⋊D1911yescharacteristic
493C42C2×C22⋊D1911yescharacteristic
494C42C2×C22⋊D1911yescharacteristic
495C23—22no—
496C23—21no—
497C23#1059739911yescharacteristic
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—42no—
502Q8—42no—
503Q8—41no—
504Q8—82no—
505Q8#1059729412yescomplemented
506D4—42no—
507D4—41no—
508D4—44no—
509D4—42no—
510D4—42no—
511D4—41no—
512D4—42no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—82no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4—762no—
540C2×C4—1521no—
541C2×C4—1521no—
542C2×C4C2×C22⋊Dic1911yescharacteristic
543C2×C4C2×C22⋊Dic1911yescharacteristic
544C2×C4C2×C22⋊Dic1911yescharacteristic
545C2×C4#1059739911yescharacteristic
546C2×C4#1059739911yescharacteristic
547C2×C4#1059739911yescharacteristic
548C8—762no—
549C8—762no—
550C8—1521no—
551C22—21no—
552C22—21no—
553C22—42no—
554C22—41no—
555C22—42no—
556C22—41no—
557C22—42no—
558C22—41no—
559C22#1192640011yescharacteristic
560C22#1192671211yescharacteristic
561C22#1192672211yescharacteristic
562C4—21no—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—22no—
568C4—41no—
569C4—41no—
570C4—42no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—1522no—
576C4C2×#1059729411yescharacteristic
577C4#1192656111yescharacteristic
578C2—21no—
579C2—21no—
580C2—82no—
581C2—81no—
582C2#1456357911yescharacteristic
583C2#1456358911yescharacteristic
584C2#1456361011yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3522C2
socleC22×C19#379
cosocleC2×C42×C19C23
hypercenter#3522D19
hypocenterC19#8419
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3522

Complements

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

NH ≅ G/Ntype
1. #14564555C2semidirect
2. #14563465C2semidirect
3. #14562246C2semidirect
4. #14562223C2semidirect
5. #14562160C2semidirect
6. #14562082C2semidirect
23. C19×#559C4semidirect
24. Q82×C19C4semidirect
26. C19×#554C4semidirect
27. C19×#550C4semidirect
213. Q8×C19#104semidirect
294. #559Dic19semidirect
295. Q82Dic19semidirect
297. #554Dic19semidirect
298. #550Dic19semidirect
410. C19#8419semidirect
505. Q8#10597294semidirect

Maximal subgroups

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

subgroupindex
#145645552
#145634652
#145622462
#145622232
#145621602
#145620822
C19×#35222
#841919