Finite Group Databasebeta

← #18085400

Subgroups — #18085400

Order 4864.

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

normal subgroups only

This group has 726 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#14574383C211yesmaximal, characteristic
2#14571966C211yesmaximal, characteristic, complemented
3#14563703C211yesmaximal, characteristic, complemented
4#14562203C211yesmaximal, characteristic, complemented
5#14562202C211yesmaximal, characteristic, complemented
6#14561502C211yesmaximal, characteristic, complemented
7C19×#2854C211yesmaximal, characteristic, complemented
8C2×#10597375—21no—
9C2×#10597376C2211yescharacteristic
10#11926857—21no—
11#11926855—21no—
12#11926778—22no—
13#11926678—21no—
14#11926677—21no—
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16C2×C22⋊(C19⋊C8)C2211yescharacteristic
17#11926446—21no—
18#11926442—21no—
19#11926435—22no—
20#11926423—21no—
21#11926404C2211yescharacteristic
22#11926299—22no—
23#11926278—22no—
24#11926277—22no—
25C2×C19×#123—21no—
26C2×C19×#121C2211yescharacteristic
27C22×C42×C19C2211yescharacteristic
28C19×#390—21no—
29C19×#389—21no—
30C19×#388—22no—
31C19×#386—21no—
32C19×#380C2211yescharacteristic
33C22×D4×C19—21no—
34C22×D4×C19D411yescharacteristic
35C23×C4×C19D411yescharacteristic
36C23×C4×C19D411yescharacteristic
37C23×C4×C19C2311yescharacteristic
38C22×C22⋊D19—21no—
39C22×D76D411yescharacteristic
40C19×#123—42no—
41C19×#123—42no—
42C19×#121—21no—
43C19×#121—21no—
44C19×#121—21no—
45C19×#121—21no—
46C2×C4⋊C4×C19—22no—
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C22⋊C4×C19—22no—
50C2×C22⋊C4×C19—22no—
51C2×C22⋊C4×C19—21no—
52C2×C22⋊C4×C19—21no—
53C2×C42×C19—21no—
54C2×C42×C19—21no—
55C2×C42×C19—21no—
56C2×C42×C19—21no—
57C2×C42×C19—21no—
58C2×C42×C19—21no—
59C2×C22⋊Dic19—21no—
60C2×#64525—22no—
61#10597376—21no—
62#10597376—21no—
63#10597376—21no—
64#10597376—21no—
65#10597375—42no—
66#10597375—42no—
67C2×(C2×D19)⋊C4—22no—
68C2×(C2×D19)⋊C4—22no—
69C2×(C2×D19)⋊C4—21no—
70C2×C4⋊Dic19—21no—
71C2×C4⋊Dic19D411yescharacteristic
72C2×Dic19⋊C4—22no—
73C22×C19⋊C8—21no—
74C22×C19⋊C8D412yes—
75C19×#95—22no—
76C19×#95D412yes—
77#10597289—22no—
78C19⋊#95—22no—
79C19⋊#95D412yes—
80C22⋊(C19⋊C8)—21no—
81C22⋊(C19⋊C8)—21no—
82C22⋊(C19⋊C8)—21no—
83C22⋊(C19⋊C8)—21no—
84#10597266—22no—
85#10597264—22no—
86C24×C19—21no—
87C24×C19C2×D411yescharacteristic
88C23×D19—21no—
89C2×D4×C19—21no—
90C2×D4×C19—21no—
91C2×D4×C19—42no—
92C2×D4×C19—41no—
93C2×D4×C19—41no—
94C2×D4×C19—41no—
95C2×D4×C19—41no—
96C2×D4×C19—41no—
97C2×D4×C19—41no—
98C22×C4×C19—21no—
99C22×C4×C19—21no—
100C22×C4×C19—21no—
101C22×C4×C19—21no—
102C22×C4×C19—21no—
103C22×C4×C19—21no—
104C22×C4×C19—21no—
105C22×C4×C19—21no—
106C22×C4×C19—21no—
107C22×C4×C19—22no—
108C22×C4×C19—21no—
109C22×C4×C19—42no—
110C22×C4×C19—42no—
111C22×C4×C19D812yescomplemented
112C22×C4×C19C2×D411yescharacteristic
113C22×C4×C19C2×D411yescharacteristic
114C22×C4×C19C2×D411yescharacteristic
115C22×C4×C19C2×D411yescharacteristic
116C22×C4×C19C2×D411yescharacteristic
117C22×C4×C19#4111yescharacteristic
118C2×C22⋊D19—41no—
119C2×C22⋊D19—41no—
120C2×C22⋊D19—41no—
121C2×C22⋊D19—41no—
122C2×C22⋊D19—41no—
123C2×C22⋊D19—41no—
124C22×Dic19—22no—
125C22×Dic19—21no—
126C2×D76—21no—
127C2×D76—21no—
128C2×D76—42no—
129C4⋊C4×C19—21no—
130C4⋊C4×C19—21no—
131C4⋊C4×C19—42no—
132C4⋊C4×C19—44no—
133C22⋊C4×C19—44no—
134C22⋊C4×C19—44no—
135C22⋊C4×C19—41no—
136C22⋊C4×C19—41no—
137C22⋊C4×C19—41no—
138C22⋊C4×C19—41no—
139C42×C19—41no—
140C42×C19—41no—
141C42×C19—41no—
142C42×C19—41no—
143C22⋊Dic19—41no—
144C22⋊Dic19—41no—
145#64525—82no—
146(C2×D19)⋊C4—44no—
147(C2×D19)⋊C4—44no—
148(C2×D19)⋊C4—41no—
149(C2×D19)⋊C4—41no—
150C4⋊Dic19—21no—
151C4⋊Dic19—21no—
152C4⋊Dic19—42no—
153Dic19⋊C4—44no—
154C2×C19⋊C8—22no—
155C2×C19⋊C8—42no—
156C2×C19⋊C8—42no—
157C2×C19⋊C8—41no—
158#10321—191nomaximal, Sylow
159C23×C19—41no—
160C23×C19—41no—
161C23×C19—42no—
162C23×C19—42no—
163C23×C19—41no—
164C23×C19—41no—
165C23×C19—41no—
166C23×C19#12011yescharacteristic
167C23×C19#12011yescharacteristic
168C23×C19#12111yescharacteristic
169C23×C19C2×D811yescharacteristic
170C23×C19#13511yescharacteristic
171C23×C19AGL(1,ℤ/8)11yescharacteristic
172C23×C19AGL(1,ℤ/8)11yescharacteristic
173C22×D19—42no—
174C22×D19—42no—
175C22×D19—41no—
176C22×D19—41no—
177C22×D19—41no—
178D4×C19—42no—
179D4×C19—81no—
180D4×C19—81no—
181D4×C19—81no—
182D4×C19—81no—
183D4×C19—81no—
184C2×C4×C19—22no—
185C2×C4×C19—22no—
186C2×C4×C19—22no—
187C2×C4×C19—22no—
188C2×C4×C19—22no—
189C2×C4×C19—22no—
190C2×C4×C19—22no—
191C2×C4×C19—22no—
192C2×C4×C19—22no—
193C2×C4×C19—41no—
194C2×C4×C19—41no—
195C2×C4×C19—41no—
196C2×C4×C19—41no—
197C2×C4×C19—41no—
198C2×C4×C19—41no—
199C2×C4×C19—41no—
200C2×C4×C19—41no—
201C2×C4×C19—41no—
202C2×C4×C19—41no—
203C2×C4×C19—41no—
204C2×C4×C19—42no—
205C2×C4×C19—42no—
206C2×C4×C19—41no—
207C2×C4×C19—42no—
208C2×C4×C19—41no—
209C2×C4×C19—41no—
210C2×C4×C19#12011yescharacteristic
211C2×C4×C19#12111yescharacteristic
212C2×C4×C19#12111yescharacteristic
213C2×C4×C19#12711yescharacteristic
214C22⋊D19—81no—
215C22⋊D19—81no—
216C22⋊D19—81no—
217C22⋊D19—81no—
218C2×Dic19—42no—
219C2×Dic19—42no—
220C2×Dic19—41no—
221C2×Dic19—41no—
222C2×Dic19—42no—
223C2×Dic19—41no—
224D76—42no—
225D76—81no—
226C19⋊C8—42no—
227C19⋊C8—81no—
228#3186—191no—
229#2854—191no—
230#2854D1911yescharacteristic, complemented
231#1817—191no—
232#1519—191no—
233#1519—191no—
234#1289—191no—
235C22×C19—21no—
236C22×C19—21no—
237C22×C19—21no—
238C22×C19—21no—
239C22×C19—21no—
240C22×C19—21no—
241C22×C19—41no—
242C22×C19—41no—
243C22×C19—41no—
244C22×C19—41no—
245C22×C19—82no—
246C22×C19—82no—
247C22×C19—81no—
248C22×C19—81no—
249C22×C19—81no—
250C22×C19#39211yescharacteristic
251C22×C19#44711yescharacteristic
252C22×C19#44711yescharacteristic
253C22×C19#44911yescharacteristic
254C22×C19#44911yescharacteristic
255C22×C19#46611yescharacteristic
256C22×C19#46911yescharacteristic
257C2×D19—82no—
258C2×D19—82no—
259C2×D19—81no—
260C2×D19—81no—
261C2×D19—81no—
262C4×C19—21no—
263C4×C19—21no—
264C4×C19—21no—
265C4×C19—42no—
266C4×C19—42no—
267C4×C19—82no—
268C4×C19—81no—
269C4×C19#45812yes—
270Dic19—82no—
271Dic19—81no—
272C2×#123—21no—
273C2×#123—381no—
274C2×#121—191no—
275C2×#121C2×D1911yescharacteristic
276C22×C42C2×D1911yescharacteristic
277#480—381no—
278#480—381no—
279#466—382no—
280#447—381no—
281#447—381no—
282C2×C22⋊C8—191no—
283C2×C22⋊C8—191no—
284#390—21no—
285#390—381no—
286#389—21no—
287#389—381no—
288#388—22no—
289#388—382no—
290#386—21no—
291#386—381no—
292#380—191no—
293#380C2×D1911yescharacteristic
294#336—382no—
295#327—382no—
296#327—382no—
297C2×C19—21no—
298C2×C19—21no—
299C2×C19—21no—
300C2×C19—21no—
301C2×C19—21no—
302C2×C19—21no—
303C2×C19—161no—
304C2×C19#199911yescharacteristic
305C2×C19#201011yescharacteristic
306C2×C19#202211yescharacteristic
307D19—161no—
308C22×D4—21no—
309C22×D4—191no—
310C22×D4—381no—
311C22×D4C22⋊D1911yescharacteristic
312C23×C4C22⋊D1911yescharacteristic
313C23×C4C22⋊D1911yescharacteristic
314C23×C4C22×D1911yescharacteristic
315C2×D8—382no—
316C22×C8—192no—
317C22×C8—381no—
318#123—42no—
319#123—42no—
320#123—762no—
321#123—762no—
322#121—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121—381no—
327#121—381no—
328#121—381no—
329#121—381no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—191no—
333C2×C4⋊C4—382no—
334C2×C4⋊C4—381no—
335C2×C4⋊C4C22⋊D1911yescharacteristic
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—382no—
341C2×C22⋊C4—382no—
342C2×C22⋊C4—381no—
343C2×C22⋊C4—381no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350#107—382no—
351#102—382no—
352#102—382no—
353C22⋊C8—381no—
354C22⋊C8—381no—
355C22⋊C8—381no—
356C22⋊C8—381no—
357#95—22no—
358#95—192no—
359#95—382no—
360#95C22⋊D1912yes—
361C19#1032111yescharacteristic, complemented, Sylow
362C24—21no—
363C24—381no—
364C24C2×C22⋊D1911yescharacteristic
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—42no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—381no—
375C2×D4—381no—
376C2×D4—762no—
377C2×D4—761no—
378C2×D4—761no—
379C2×D4—761no—
380C2×D4—761no—
381C2×D4—761no—
382C2×D4—761no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—382no—
397C22×C4—381no—
398C22×C4#6452512yescomplemented
399C22×C4D4×D1911yescharacteristic
400C22×C4D4×D1911yescharacteristic
401C22×C4D4×D1911yescharacteristic
402C22×C4#6454311yescharacteristic
403C22×C4C2×C22⋊D1911yescharacteristic
404C22×C4C2×C22⋊D1911yescharacteristic
405D8—1522no—
406C2×C8—382no—
407C2×C8—762no—
408C2×C8—762no—
409C2×C8—761no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—42no—
413C4⋊C4—44no—
414C4⋊C4—381no—
415C4⋊C4—381no—
416C4⋊C4—764no—
417C4⋊C4—762no—
418C22⋊C4—44no—
419C22⋊C4—44no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—764no—
425C22⋊C4—764no—
426C22⋊C4—761no—
427C22⋊C4—761no—
428C22⋊C4—761no—
429C22⋊C4—761no—
430C42—41no—
431C42—41no—
432C42—41no—
433C42—41no—
434C23—41no—
435C23—41no—
436C23—42no—
437C23—42no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—762no—
442C23—762no—
443C23—761no—
444C23—761no—
445C23—761no—
446C23C2×#6452511yescharacteristic
447C23#1059737811yescharacteristic
448C23#1059738311yescharacteristic
449C23#1059738511yescharacteristic
450C23#1059739511yescharacteristic
451C23#1059739611yescharacteristic
452C23#1059739911yescharacteristic
453D4—42no—
454D4—81no—
455D4—81no—
456D4—81no—
457D4—81no—
458D4—81no—
459D4—762no—
460D4—1521no—
461D4—1521no—
462D4—1521no—
463D4—1521no—
464D4—1521no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—762no—
492C2×C4—762no—
493C2×C4—762no—
494C2×C4—761no—
495C2×C4—761no—
496C2×C4—761no—
497C2×C4#1059738311yescharacteristic
498C2×C4#1059738411yescharacteristic
499C2×C4#1059738511yescharacteristic
500C2×C4#1059738611yescharacteristic
501C8—762no—
502C8—1521no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—82no—
514C22—82no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—1522no—
519C22—1522no—
520C22—1521no—
521C22—1521no—
522C22—1521no—
523C22#1192645211yescharacteristic
524C22#1192667711yescharacteristic
525C22#1192667811yescharacteristic
526C22#1192668711yescharacteristic
527C22#1192668911yescharacteristic
528C22#1192677811yescharacteristic
529C22#1192679511yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—42no—
534C4—42no—
535C4—82no—
536C4—81no—
537C4—1522no—
538C4—1521no—
539C4#1192673312yes—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—21no—
546C2—161no—
547C2—3041no—
548C2#1456463111yescharacteristic
549C2#1456470011yescharacteristic
550C2#1456476311yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2854C2
socleC22×C19#392
prime radical#14574383C2
hypercenter#2854D19
hypocenterC19#10321
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2854

Complements

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

NH ≅ G/Ntype
2. #14571966C2semidirect
3. #14563703C2semidirect
4. #14562203C2semidirect
5. #14562202C2semidirect
6. #14561502C2semidirect
7. C19×#2854C2semidirect
111. C22×C4×C19D8semidirect
230. #2854D19semidirect
361. C19#10321semidirect
398. C22×C4#64525semidirect

Maximal subgroups

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

subgroupindex
#145743832
#145719662
#145637032
#145622032
#145622022
#145615022
C19×#28542
#1032119