Finite Group Databasebeta

← #18074224

Subgroups — #18074224

Order 4864.

818 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11927252C211yesmaximal, characteristic
2#14563726C211yesmaximal, characteristic, complemented
3#14563723C211yesmaximal, characteristic, complemented
4#14563620C211yesmaximal, characteristic
5#14562207C211yesmaximal, characteristic, complemented
6#14561951C211yesmaximal, characteristic
7C19×#1520C211yesmaximal, characteristic, complemented
8#11927252—22no—
9#11927252—22no—
10#11927252—22no—
11#11927252—22no—
12C2×#10597334C411yescharacteristic, complemented
13C2×#10597335—21no—
14C2×#10597343—21no—
15C2×#10597324—21no—
16C2×#10597392C411yescharacteristic, complemented
17C2×Q8×Dic19C411yescharacteristic, complemented
18C2×C4×C22⋊D19C2211yescharacteristic
19C2×(C22⋊D19)⋊C4—21no—
20C22×C4⋊Dic19C2211yescharacteristic
21C2×C4⋊C4×D19C411yescharacteristic, complemented
22C2×#10597263—21no—
23C2×C22⋊(C19⋊C8)C2211yescharacteristic
24#11926404C2211yescharacteristic
25#11926310—21no—
26#11926307—22no—
27#11926306—22no—
28#11926281—22no—
29#11926269—21no—
30#11926267—21no—
31C2×C19×C22⋊Q8C2211yescharacteristic
32C2×C19×C22⋊C8C2211yescharacteristic
33C19×#380C2211yescharacteristic
34C19×#328—22no—
35C22×Q8×C19C2×C411yescharacteristic
36C23×C4×C19C2311yescharacteristic
37C22×C22⋊D19D411yescharacteristic
38C23×Dic19—21no—
39C22×C4×D19—21no—
40C22×C4×D19C2×C411yescharacteristic
41C22×Dic38—21no—
42C22×C8×C19—21no—
43C19×C22⋊Q8—21no—
44C19×C22⋊Q8—21no—
45C19×C22⋊Q8D412yes—
46C19×C22⋊Q8D412yes—
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19—21no—
49C2×C4⋊C4×C19C2×C411yescharacteristic
50C2×C22⋊C4×C19—21no—
51C2×C22⋊C4×C19—21no—
52C2×C22⋊Dic19—21no—
53C2×C22⋊Dic19D411yescharacteristic
54#10597392—22no—
55#10597392—22no—
56Q8×Dic19—22no—
57Q8×Dic19—22no—
58C4×C22⋊D19—21no—
59C4×C22⋊D19—21no—
60C4×C22⋊D19—21no—
61C4×C22⋊D19—21no—
62C2×(C2×D19)⋊C4—21no—
63C2×(C2×D19)⋊C4D411yescharacteristic
64C2×C4⋊Dic19—21no—
65C2×C4⋊Dic19—21no—
66C2×C4⋊Dic19—21no—
67C2×C4⋊Dic19—21no—
68C2×C4⋊Dic19—21no—
69C2×C4⋊Dic19C2×C411yescharacteristic
70C2×C4⋊Dic19C2×C411yescharacteristic
71C2×C4⋊Dic19D412yes—
72C2×C4⋊Dic19D412yes—
73C2×Dic19⋊C4—21no—
74C2×Dic19⋊C4—21no—
75C2×Dic19⋊C4—21no—
76C2×Dic19⋊C4D411yescharacteristic
77C2×C4×Dic19—21no—
78C2×C4×Dic19C2×C411yescharacteristic
79C22×C19⋊C8—21no—
80#10597343—24no—
81#10597343—24no—
82C4⋊C4×D19—22no—
83C4⋊C4×D19—22no—
84#10597335—24no—
85#10597335—24no—
86#10597334—22no—
87#10597334—22no—
88(C22⋊D19)⋊C4—24no—
89(C22⋊D19)⋊C4—24no—
90#10597324—24no—
91#10597324—24no—
92C19×C22⋊C8—21no—
93C19×C22⋊C8—21no—
94C19×#95—21no—
95C19⋊#95—21no—
96C22⋊(C19⋊C8)—21no—
97C22⋊(C19⋊C8)—21no—
98#10597263—42no—
99C24×C19C2×D411yescharacteristic
100C23×D19C22⋊C411yescharacteristic
101C2×Q8×C19—21no—
102C2×Q8×C19—42no—
103C2×Q8×C19C22⋊C412yes—
104C22×C4×C19—21no—
105C22×C4×C19—21no—
106C22×C4×C19—42no—
107C22×C4×C19—41no—
108C22×C4×C19C22×C411yescharacteristic
109C22×C4×C19C2×D411yescharacteristic
110C22×C4×C19C2×D411yescharacteristic
111C22×C4×C19C2×D411yescharacteristic
112C22×C4×C19C2×D411yescharacteristic
113C22×C4×C19C2×D411yescharacteristic
114C2×C22⋊D19—21no—
115C2×C22⋊D19—21no—
116C2×C22⋊D19—21no—
117C2×C22⋊D19—21no—
118C2×C22⋊D19SD1612yes—
119C2×C22⋊D19Q1612yes—
120C22×Dic19—21no—
121C22×Dic19—21no—
122C22×Dic19—22no—
123C22×Dic19—22no—
124C22×Dic19—41no—
125C22×Dic19—82no—
126C22×Dic19C22⋊C411yescharacteristic
127C22×Dic19C22⋊C411yescharacteristic
128C22×Dic19C22⋊C411yescharacteristic
129C2×C4×D19—21no—
130C2×C4×D19—21no—
131C2×C4×D19—24no—
132C2×C4×D19—42no—
133C2×C4×D19—82no—
134C2×Dic38—24no—
135C2×Dic38—82no—
136C2×C8×C19—42no—
137C2×C8×C19—41no—
138C4⋊C4×C19—21no—
139C4⋊C4×C19—22no—
140C4⋊C4×C19—22no—
141C4⋊C4×C19—42no—
142C4⋊C4×C19C22⋊C412yes—
143C22⋊C4×C19—22no—
144C22⋊C4×C19—22no—
145C22⋊C4×C19—41no—
146C22⋊C4×C19—41no—
147C22⋊Dic19—21no—
148C22⋊Dic19—21no—
149C22⋊Dic19—41no—
150C22⋊Dic19—41no—
151(C2×D19)⋊C4—24no—
152(C2×D19)⋊C4—21no—
153(C2×D19)⋊C4—21no—
154C4⋊Dic19—24no—
155C4⋊Dic19—21no—
156C4⋊Dic19—21no—
157C4⋊Dic19—22no—
158C4⋊Dic19—22no—
159C4⋊Dic19—42no—
160C4⋊Dic19C22⋊C412yes—
161C4⋊Dic19C22⋊C412yes—
162Dic19⋊C4—24no—
163Dic19⋊C4—24no—
164Dic19⋊C4—24no—
165Dic19⋊C4—21no—
166Dic19⋊C4—21no—
167C4×Dic19—24no—
168C4×Dic19—21no—
169C4×Dic19—21no—
170C2×C19⋊C8—42no—
171C2×C19⋊C8—41no—
172#8380—191nomaximal, Sylow
173C23×C19—41no—
174C23×C19—41no—
175C23×C19C2×C22⋊C411yescharacteristic
176C23×C19#12011yescharacteristic
177C23×C19#12011yescharacteristic
178C23×C19C2×SD1611yescharacteristic
179C23×C19C2×Q1611yescharacteristic
180C23×C19#13711yescharacteristic
181C23×C19#13711yescharacteristic
182C22×D19—21no—
183C22×D19—21no—
184C22×D19—41no—
185C22×D19—41no—
186C22×D19#10312yes—
187Q8×C19—42no—
188Q8×C19—42no—
189C2×C4×C19—22no—
190C2×C4×C19—22no—
191C2×C4×C19—22no—
192C2×C4×C19—22no—
193C2×C4×C19—22no—
194C2×C4×C19—41no—
195C2×C4×C19—41no—
196C2×C4×C19—41no—
197C2×C4×C19—42no—
198C2×C4×C19—42no—
199C2×C4×C19—81no—
200C2×C4×C19—81no—
201C2×C4×C19—81no—
202C2×C4×C19C2×C22⋊C411yescharacteristic
203C2×C4×C19C2×C22⋊C411yescharacteristic
204C2×C4×C19#12011yescharacteristic
205C2×C4×C19#12011yescharacteristic
206C22⋊D19—22no—
207C22⋊D19—22no—
208C22⋊D19—22no—
209C22⋊D19—22no—
210C2×Dic19—21no—
211C2×Dic19—21no—
212C2×Dic19—22no—
213C2×Dic19—21no—
214C2×Dic19—21no—
215C2×Dic19—22no—
216C2×Dic19—42no—
217C2×Dic19—42no—
218C2×Dic19—41no—
219C2×Dic19—41no—
220C2×Dic19—82no—
221C2×Dic19—82no—
222C2×Dic19—81no—
223C2×Dic19—81no—
224C2×Dic19—81no—
225C2×Dic19#10312yes—
226C4×D19—42no—
227C4×D19—42no—
228C4×D19—84no—
229Dic38—84no—
230C8×C19—81no—
231C19⋊C8—81no—
232C2×#554—191no—
233#1824—191no—
234#1824—191no—
235#1799—191no—
236#1520—191no—
237#1520D1911yescharacteristic, complemented
238#1459—191no—
239C22×C19—21no—
240C22×C19—21no—
241C22×C19—21no—
242C22×C19—21no—
243C22×C19—21no—
244C22×C19—21no—
245C22×C19—41no—
246C22×C19—41no—
247C22×C19—41no—
248C22×C19—41no—
249C22×C19#37911yescharacteristic
250C22×C19C2×#10311yescharacteristic
251C22×C19#41911yescharacteristic
252C22×C19#44811yescharacteristic
253C22×C19#44811yescharacteristic
254C22×C19#45111yescharacteristic
255C22×C19#45111yescharacteristic
256C2×D19—22no—
257C2×D19—42no—
258C2×D19—41no—
259C2×D19—41no—
260C2×D19—42no—
261C4×C19—21no—
262C4×C19—21no—
263C4×C19—21no—
264C4×C19—42no—
265C4×C19—42no—
266C4×C19—161no—
267C4×C19#41012yes—
268Dic19—22no—
269Dic19—41no—
270Dic19—42no—
271Dic19—42no—
272Dic19—41no—
273Dic19—161no—
274#554—382no—
275#554—382no—
276#554—382no—
277#554—382no—
278C2×C4⋊Q8—191no—
279C2×#125—381no—
280C2×C22⋊Q8—191no—
281C2×C22⋊Q8—381no—
282C2×C22⋊Q8—381no—
283C2×C22⋊Q8C2×D1911yescharacteristic
284C2×C4×Q8—191no—
285C2×C4×D4—191no—
286C2×C4×D4—381no—
287C22×C4⋊C4—191no—
288C22×C4⋊C4—191no—
289C2×#99—381no—
290C2×C22⋊C8—191no—
291C2×C22⋊C8C2×D1911yescharacteristic
292#380—191no—
293#380C2×D1911yescharacteristic
294#342—381no—
295#340—382no—
296#340—382no—
297#328—22no—
298#328—382no—
299#324—381no—
300#323—381no—
301C2×C19—21no—
302C2×C19—21no—
303C2×C19—21no—
304C2×C19—21no—
305C2×C19—21no—
306C2×C19—21no—
307C2×C19#178211yescharacteristic
308C2×C19#178711yescharacteristic
309C2×C19#179511yescharacteristic
310D19—42no—
311C22×Q8—381no—
312C22×Q8C4×D1911yescharacteristic
313C22×D4—191no—
314C23×C4—191no—
315C23×C4—381no—
316C23×C4—381no—
317C23×C4C22×D1911yescharacteristic
318C22×C8—21no—
319C22×C8—381no—
320C4⋊Q8—382no—
321C4⋊Q8—382no—
322#125—384no—
323#125—384no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—384no—
327C22⋊Q8—384no—
328C22⋊Q8—384no—
329C22⋊Q8—384no—
330C22⋊Q8—382no—
331C22⋊Q8—382no—
332C22⋊Q8D7612yes—
333C22⋊Q8C22⋊D1912yes—
334C4×Q8—382no—
335C4×Q8—382no—
336C4×D4—384no—
337C4×D4—384no—
338C4×D4—381no—
339C4×D4—381no—
340C4×D4—381no—
341C4×D4—381no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—191no—
345C2×C4⋊C4—191no—
346C2×C4⋊C4—192no—
347C2×C4⋊C4—192no—
348C2×C4⋊C4—191no—
349C2×C4⋊C4—382no—
350C2×C4⋊C4—381no—
351C2×C4⋊C4—381no—
352C2×C4⋊C4—381no—
353C2×C4⋊C4—381no—
354C2×C4⋊C4—381no—
355C2×C4⋊C4—381no—
356C2×C4⋊C4—381no—
357C2×C4⋊C4—382no—
358C2×C4⋊C4—381no—
359C2×C4⋊C4C4×D1911yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—191no—
363C2×C22⋊C4—191no—
364C2×C22⋊C4—381no—
365C2×C22⋊C4—381no—
366C2×C42—191no—
367C2×C42—381no—
368#99—762no—
369C22⋊C8—21no—
370C22⋊C8—21no—
371C22⋊C8—381no—
372C22⋊C8—381no—
373#95—21no—
374#95—381no—
375C19#838011yescharacteristic, complemented, Sylow
376C24—191no—
377C24D4×D1911yescharacteristic
378C2×Q8—21no—
379C2×Q8—42no—
380C2×Q8—384no—
381C2×Q8—1522no—
382C2×Q8(C2×D19)⋊C412yes—
383C2×D4—192no—
384C2×D4—192no—
385C2×D4—381no—
386C2×D4—381no—
387C2×D4—381no—
388C2×D4—381no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—42no—
392C22×C4—41no—
393C22×C4—191no—
394C22×C4—191no—
395C22×C4—191no—
396C22×C4—384no—
397C22×C4—381no—
398C22×C4—381no—
399C22×C4—382no—
400C22×C4—382no—
401C22×C4—381no—
402C22×C4—381no—
403C22×C4—762no—
404C22×C4—761no—
405C22×C4—1522no—
406C22×C4—1522no—
407C22×C4C2×C4×D1911yescharacteristic
408C22×C4C2×D7611yescharacteristic
409C22×C4D4×D1911yescharacteristic
410C22×C4D4×D1911yescharacteristic
411C22×C4D4×D1911yescharacteristic
412C22×C4C2×C22⋊D1911yescharacteristic
413C2×C8—42no—
414C2×C8—41no—
415C2×C8—762no—
416C2×C8—761no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—42no—
421C4⋊C4—192no—
422C4⋊C4—192no—
423C4⋊C4—384no—
424C4⋊C4—384no—
425C4⋊C4—384no—
426C4⋊C4—384no—
427C4⋊C4—381no—
428C4⋊C4—382no—
429C4⋊C4—381no—
430C4⋊C4—382no—
431C4⋊C4—381no—
432C4⋊C4—381no—
433C4⋊C4—762no—
434C4⋊C4(C2×D19)⋊C412yes—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—384no—
440C22⋊C4—381no—
441C22⋊C4—381no—
442C22⋊C4—381no—
443C22⋊C4—381no—
444C22⋊C4—761no—
445C22⋊C4—761no—
446C42—384no—
447C42—381no—
448C42—381no—
449C23—41no—
450C23—41no—
451C23—192no—
452C23—381no—
453C23—381no—
454C23—761no—
455C23—761no—
456C23C22⋊C4×D1911yescharacteristic
457C23#1059732811yescharacteristic
458C23SD16×D1911yescharacteristic
459C23#1059736111yescharacteristic
460C23Q16×D1911yescharacteristic
461C23#1059736411yescharacteristic
462C23#1059738311yescharacteristic
463Q8—42no—
464Q8—42no—
465Q8—1524no—
466D4—382no—
467D4—382no—
468D4—382no—
469D4—382no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—81no—
481C2×C4—81no—
482C2×C4—81no—
483C2×C4—192no—
484C2×C4—381no—
485C2×C4—381no—
486C2×C4—381no—
487C2×C4—382no—
488C2×C4—382no—
489C2×C4—381no—
490C2×C4—762no—
491C2×C4—762no—
492C2×C4—762no—
493C2×C4—762no—
494C2×C4—761no—
495C2×C4—761no—
496C2×C4—1524no—
497C2×C4—1521no—
498C2×C4—1521no—
499C2×C4—1521no—
500C2×C4—1522no—
501C2×C4—1522no—
502C2×C4C22⋊C4×D1911yescharacteristic
503C2×C4#1059732811yescharacteristic
504C2×C4C2×(C2×D19)⋊C411yescharacteristic
505C2×C4#1059738311yescharacteristic
506C8—81no—
507C8—1521no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—382no—
519C22—762no—
520C22—762no—
521C22—761no—
522C22—761no—
523C22#1192639911yescharacteristic
524C22#103×D1911yescharacteristic
525C22#1192655111yescharacteristic
526C22#1192668111yescharacteristic
527C22#1192668411yescharacteristic
528C22#1192669811yescharacteristic
529C22#1192670111yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—42no—
534C4—42no—
535C4—161no—
536C4—382no—
537C4—3041no—
538C4—762no—
539C4—762no—
540C4—761no—
541C4—761no—
542C4#1192651612yes—
543C2—21no—
544C2—21no—
545C2—21no—
546C2—21no—
547C2—21no—
548C2—21no—
549C2—762no—
550C2#1456355111yescharacteristic
551C2#1456356811yescharacteristic
552C2#1456360411yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1520C2
socleC22×C19#379
prime radicalC22×C22⋊D19D4
cosocleC23×C4×C19C23
hypercenter#1520D19
hypocenterC19#8380
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
2. #14563726C2semidirect
3. #14563723C2semidirect
5. #14562207C2semidirect
7. C19×#1520C2semidirect
12. C2×#10597334C4semidirect
16. C2×#10597392C4semidirect
17. C2×Q8×Dic19C4semidirect
21. C2×C4⋊C4×D19C4semidirect
237. #1520D19semidirect
375. C19#8380semidirect

Maximal subgroups

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

subgroupindex
C2×#119272522
#145637262
#145637232
#145636202
#145622072
#145619512
C19×#15202
#838019