Finite Group Databasebeta

← #18085419

Subgroups — #18085419

Order 4864.

910 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 910 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574407C211yesmaximal, characteristic, complemented
2#14571922C211yesmaximal, characteristic
3#14563545C211yesmaximal, characteristic
4#14562207C211yesmaximal, characteristic, complemented
5#14562206C211yesmaximal, characteristic, complemented
6#14561502C211yesmaximal, characteristic, complemented
7C19×#2848C211yesmaximal, characteristic
8C2×#10597370—21no—
9C2×#10597370C2211yescharacteristic
10#11926879—21no—
11#11926877—21no—
12#11926783—22no—
13#11926700—21no—
14#11926699—21no—
15C2×C22⋊(C19⋊C8)—22no—
16C2×C22⋊(C19⋊C8)C2211yescharacteristic
17C2×C22⋊(C19⋊C8)C2211yescharacteristic
18#11926417—22no—
19#11926417—21no—
20#11926404—21no—
21#11926404C2211yescharacteristic
22#11926400—21no—
23#11926281—22no—
24#11926280—22no—
25C24×C4×C19C2211yescharacteristic
26C2×C19×C22⋊Q8—21no—
27C2×C19×C22⋊Q8C2211yescharacteristic
28C19×#385—22no—
29C19×#385—21no—
30C19×#380—21no—
31C19×#380C2211yescharacteristic
32C19×#379—21no—
33C25×C19D411yescharacteristic
34C22×Q8×C19D411yescharacteristic
35C23×C4×C19—21no—
36C23×C4×C19—21no—
37C23×C4×C19—21no—
38C23×C4×C19—21no—
39C23×C4×C19—21no—
40C23×C4×C19—21no—
41C23×C4×C19—44no—
42C23×C4×C19D411yescharacteristic
43C23×C4×C19C2311yescharacteristic
44C22×Dic38D411yescharacteristic
45C19×C22⋊Q8—21no—
46C19×C22⋊Q8—21no—
47C19×C22⋊Q8—21no—
48C19×C22⋊Q8—21no—
49C19×C22⋊Q8—44no—
50C2×C4⋊C4×C19—22no—
51C2×C4⋊C4×C19—21no—
52C2×C4⋊C4×C19—21no—
53C2×C4⋊C4×C19D411yescharacteristic
54C2×C22⋊C4×C19—22no—
55C2×C22⋊C4×C19—22no—
56C2×C22⋊C4×C19—21no—
57C2×C22⋊C4×C19—21no—
58C2×C22⋊Dic19—22no—
59C2×C22⋊Dic19—22no—
60C2×C22⋊Dic19—21no—
61C2×C22⋊Dic19—21no—
62C2×#64528—22no—
63C2×C4⋊Dic19—21no—
64C2×C4⋊Dic19D411yescharacteristic
65#10597370—21no—
66#10597370—21no—
67#10597370—21no—
68#10597370—21no—
69#10597370—44no—
70C2×Dic19⋊C4—22no—
71C2×Dic19⋊C4—21no—
72C22×C19⋊C8—21no—
73C22×C19⋊C8D412yes—
74C19×#95—22no—
75C19×#95D412yes—
76#10597292—22no—
77C19⋊#95—22no—
78C19⋊#95D412yes—
79C22⋊(C19⋊C8)—21no—
80C22⋊(C19⋊C8)—21no—
81C22⋊(C19⋊C8)—21no—
82C22⋊(C19⋊C8)—21no—
83C22⋊(C19⋊C8)—44no—
84#10597267—22no—
85#10597264—22no—
86C24×C19—21no—
87C24×C19—21no—
88C24×C19—21no—
89C24×C19—21no—
90C24×C19—21no—
91C24×C19—21no—
92C24×C19—42no—
93C24×C19—42no—
94C24×C19Q1612yescomplemented
95C24×C19C2×D411yescharacteristic
96C2×Q8×C19—21no—
97C2×Q8×C19—21no—
98C2×Q8×C19—42no—
99C22×C4×C19—24no—
100C22×C4×C19—24no—
101C22×C4×C19—24no—
102C22×C4×C19—21no—
103C22×C4×C19—21no—
104C22×C4×C19—21no—
105C22×C4×C19—21no—
106C22×C4×C19—22no—
107C22×C4×C19—21no—
108C22×C4×C19—42no—
109C22×C4×C19—42no—
110C22×C4×C19—42no—
111C22×C4×C19—42no—
112C22×C4×C19—42no—
113C22×C4×C19—42no—
114C22×C4×C19—42no—
115C22×C4×C19—42no—
116C22×C4×C19—42no—
117C22×C4×C19—42no—
118C22×C4×C19—42no—
119C22×C4×C19—41no—
120C22×C4×C19—41no—
121C22×C4×C19—41no—
122C22×C4×C19—41no—
123C22×C4×C19C2×D411yescharacteristic
124C22×C4×C19C2×D411yescharacteristic
125C22×C4×C19C2×D411yescharacteristic
126C22×C4×C19C2×D411yescharacteristic
127C22×C4×C19C2×D411yescharacteristic
128C22×C4×C19#4111yescharacteristic
129C22×Dic19—21no—
130C22×Dic19—21no—
131C22×Dic19—22no—
132C2×Dic38—21no—
133C2×Dic38—21no—
134C2×Dic38—42no—
135C4⋊C4×C19—21no—
136C4⋊C4×C19—21no—
137C4⋊C4×C19—42no—
138C4⋊C4×C19—44no—
139C4⋊C4×C19—41no—
140C4⋊C4×C19—41no—
141C22⋊C4×C19—44no—
142C22⋊C4×C19—44no—
143C22⋊C4×C19—41no—
144C22⋊C4×C19—41no—
145C22⋊C4×C19—41no—
146C22⋊C4×C19—41no—
147C22⋊Dic19—44no—
148C22⋊Dic19—44no—
149C22⋊Dic19—41no—
150C22⋊Dic19—41no—
151C22⋊Dic19—41no—
152C22⋊Dic19—41no—
153#64528—82no—
154C4⋊Dic19—21no—
155C4⋊Dic19—21no—
156C4⋊Dic19—42no—
157Dic19⋊C4—44no—
158Dic19⋊C4—41no—
159Dic19⋊C4—41no—
160C2×C19⋊C8—22no—
161C2×C19⋊C8—42no—
162C2×C19⋊C8—42no—
163C2×C19⋊C8—41no—
164#10324—191nomaximal, Sylow
165C23×C19—22no—
166C23×C19—22no—
167C23×C19—22no—
168C23×C19—22no—
169C23×C19—22no—
170C23×C19—22no—
171C23×C19—22no—
172C23×C19—22no—
173C23×C19—22no—
174C23×C19—41no—
175C23×C19—44no—
176C23×C19—41no—
177C23×C19—41no—
178C23×C19—41no—
179C23×C19—41no—
180C23×C19—41no—
181C23×C19—41no—
182C23×C19—41no—
183C23×C19—44no—
184C23×C19—44no—
185C23×C19—44no—
186C23×C19—41no—
187C23×C19—41no—
188C23×C19—41no—
189C23×C19—41no—
190C23×C19#12011yescharacteristic
191C23×C19#12011yescharacteristic
192C23×C19#12111yescharacteristic
193C23×C19C2×Q1611yescharacteristic
194C23×C19#13511yescharacteristic
195C23×C19#13711yescharacteristic
196C23×C19#13711yescharacteristic
197Q8×C19—42no—
198Q8×C19—81no—
199C2×C4×C19—22no—
200C2×C4×C19—22no—
201C2×C4×C19—22no—
202C2×C4×C19—22no—
203C2×C4×C19—22no—
204C2×C4×C19—22no—
205C2×C4×C19—41no—
206C2×C4×C19—41no—
207C2×C4×C19—41no—
208C2×C4×C19—44no—
209C2×C4×C19—44no—
210C2×C4×C19—44no—
211C2×C4×C19—41no—
212C2×C4×C19—41no—
213C2×C4×C19—41no—
214C2×C4×C19—41no—
215C2×C4×C19—44no—
216C2×C4×C19—42no—
217C2×C4×C19—42no—
218C2×C4×C19—42no—
219C2×C4×C19—42no—
220C2×C4×C19—41no—
221C2×C4×C19—41no—
222C2×C4×C19—42no—
223C2×C4×C19#12011yescharacteristic
224C2×C4×C19#12111yescharacteristic
225C2×C4×C19#12111yescharacteristic
226C2×C4×C19#12711yescharacteristic
227C2×Dic19—42no—
228C2×Dic19—42no—
229C2×Dic19—42no—
230C2×Dic19—42no—
231C2×Dic19—41no—
232C2×Dic19—41no—
233C2×Dic19—42no—
234Dic38—42no—
235Dic38—81no—
236C19⋊C8—42no—
237C19⋊C8—81no—
238#3189—191no—
239#2848—191no—
240#2848D1911yescharacteristic
241#1779—191no—
242#1520—191no—
243#1520—191no—
244#1289—191no—
245C22×C19—21no—
246C22×C19—21no—
247C22×C19—21no—
248C22×C19—21no—
249C22×C19—21no—
250C22×C19—21no—
251C22×C19—24no—
252C22×C19—24no—
253C22×C19—24no—
254C22×C19—41no—
255C22×C19—41no—
256C22×C19—41no—
257C22×C19—41no—
258C22×C19—42no—
259C22×C19—42no—
260C22×C19—42no—
261C22×C19—42no—
262C22×C19—42no—
263C22×C19—42no—
264C22×C19—42no—
265C22×C19—42no—
266C22×C19—42no—
267C22×C19—42no—
268C22×C19—42no—
269C22×C19—42no—
270C22×C19#39211yescharacteristic
271C22×C19#45111yescharacteristic
272C22×C19#45111yescharacteristic
273C22×C19#45211yescharacteristic
274C22×C19#45211yescharacteristic
275C22×C19#46711yescharacteristic
276C22×C19#47011yescharacteristic
277C4×C19—21no—
278C4×C19—21no—
279C4×C19—21no—
280C4×C19—42no—
281C4×C19—82no—
282C4×C19—81no—
283C4×C19—81no—
284C4×C19B(4,𝔽2)12yes—
285Dic19—82no—
286Dic19—81no—
287Dic19—81no—
288C24×C4C2×D1911yescharacteristic
289C2×C22⋊Q8—21no—
290C2×C22⋊Q8—191no—
291C2×C22⋊Q8—381no—
292C2×C22⋊Q8C2×D1911yescharacteristic
293#484—381no—
294#484—381no—
295#467—382no—
296#451—381no—
297#451—381no—
298C2×C22⋊C8—191no—
299C2×C22⋊C8—191no—
300C2×C22⋊C8—382no—
301#385—21no—
302#385—22no—
303#385—382no—
304#385—381no—
305#380—21no—
306#380—191no—
307#380—381no—
308#380C2×D1911yescharacteristic
309#379—21no—
310#379—381no—
311#328—382no—
312#328—382no—
313C2×C19—21no—
314C2×C19—21no—
315C2×C19—21no—
316C2×C19—21no—
317C2×C19—21no—
318C2×C19—21no—
319C2×C19—44no—
320C2×C19#200111yescharacteristic
321C2×C19#201011yescharacteristic
322C2×C19#202111yescharacteristic
323C25C22⋊D1911yescharacteristic
324C22×Q8—191no—
325C22×Q8C22⋊D1911yescharacteristic
326C23×C4—21no—
327C23×C4—21no—
328C23×C4—21no—
329C23×C4—21no—
330C23×C4—21no—
331C23×C4—21no—
332C23×C4—44no—
333C23×C4C22⋊D1911yescharacteristic
334C23×C4C22×D1911yescharacteristic
335C2×Q16—382no—
336C22×C8—192no—
337C22×C8—381no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340C22⋊Q8—21no—
341C22⋊Q8—21no—
342C22⋊Q8—44no—
343C22⋊Q8—381no—
344C22⋊Q8—381no—
345C22⋊Q8—381no—
346C22⋊Q8—381no—
347C22⋊Q8—764no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—191no—
352C2×C4⋊C4—382no—
353C2×C4⋊C4—381no—
354C2×C4⋊C4—381no—
355C2×C4⋊C4C22⋊D1911yescharacteristic
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—382no—
361C2×C22⋊C4—382no—
362C2×C22⋊C4—381no—
363C2×C22⋊C4—381no—
364#107—382no—
365#103—382no—
366#103—382no—
367C22⋊C8—381no—
368C22⋊C8—381no—
369C22⋊C8—381no—
370C22⋊C8—381no—
371C22⋊C8—764no—
372#95—22no—
373#95—192no—
374#95—382no—
375#95C22⋊D1912yes—
376C19#1032411yescharacteristic, complemented, Sylow
377C24—21no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—42no—
384C24—42no—
385C24#6452812yescomplemented
386C24C2×C22⋊D1911yescharacteristic
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—42no—
390C2×Q8—381no—
391C2×Q8—381no—
392C2×Q8—762no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—382no—
418C22×C4—381no—
419C22×C4—381no—
420C22×C4D4×D1911yescharacteristic
421C22×C4D4×D1911yescharacteristic
422C22×C4D4×D1911yescharacteristic
423C22×C4#6454311yescharacteristic
424C22×C4C2×C22⋊D1911yescharacteristic
425C22×C4C2×C22⋊D1911yescharacteristic
426Q16—1522no—
427C2×C8—382no—
428C2×C8—762no—
429C2×C8—762no—
430C2×C8—761no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—42no—
434C4⋊C4—44no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—381no—
438C4⋊C4—381no—
439C4⋊C4—764no—
440C4⋊C4—762no—
441C4⋊C4—761no—
442C4⋊C4—761no—
443C22⋊C4—44no—
444C22⋊C4—44no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—764no—
450C22⋊C4—764no—
451C22⋊C4—761no—
452C22⋊C4—761no—
453C22⋊C4—761no—
454C22⋊C4—761no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—22no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—41no—
465C23—44no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—44no—
474C23—44no—
475C23—44no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23#1059738311yescharacteristic
481C23#1059738511yescharacteristic
482C23#1059738811yescharacteristic
483C23C2×#6452811yescharacteristic
484C23#1059739611yescharacteristic
485C23#1059739711yescharacteristic
486C23#1059739911yescharacteristic
487Q8—42no—
488Q8—81no—
489Q8—762no—
490Q8—1521no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—44no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—762no—
516C2×C4—762no—
517C2×C4—762no—
518C2×C4—762no—
519C2×C4—762no—
520C2×C4—761no—
521C2×C4—761no—
522C2×C4#1059738311yescharacteristic
523C2×C4#1059738411yescharacteristic
524C2×C4#1059738511yescharacteristic
525C2×C4#1059738611yescharacteristic
526C8—762no—
527C8—1521no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—24no—
535C22—24no—
536C22—24no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22#1192645211yescharacteristic
554C22#1192669911yescharacteristic
555C22#1192670011yescharacteristic
556C22#1192670411yescharacteristic
557C22#1192670611yescharacteristic
558C22#1192678311yescharacteristic
559C22#1192680011yescharacteristic
560C4—21no—
561C4—21no—
562C4—21no—
563C4—42no—
564C4—82no—
565C4—81no—
566C4—81no—
567C4—1522no—
568C4—1521no—
569C4—1521no—
570C4#1192673012yes—
571C2—21no—
572C2—21no—
573C2—21no—
574C2—21no—
575C2—21no—
576C2—21no—
577C2—44no—
578C2#1456464311yescharacteristic
579C2#1456470011yescharacteristic
580C2#1456475811yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2848C2
socleC22×C19#392
prime radicalC25×C19D4
hypercenter#2848D19
hypocenterC19#10324
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2848

Complements

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

NH ≅ G/Ntype
1. #14574407C2semidirect
4. #14562207C2semidirect
5. #14562206C2semidirect
6. #14561502C2semidirect
94. C24×C19Q16semidirect
376. C19#10324semidirect
385. C24#64528semidirect

Maximal subgroups

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

subgroupindex
#145744072
#145719222
#145635452
#145622072
#145622062
#145615022
C19×#28482
#1032419