Finite Group Databasebeta

← #18085415

Subgroups — #18085415

Order 4864.

664 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 101 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#14574392C211yesmaximal, characteristic
2#14571975C211yesmaximal, characteristic, complemented
3#14571961C211yesmaximal, characteristic
4#14563701C211yesmaximal, characteristic, complemented
5#14562208C211yesmaximal, characteristic, complemented
6#14561502C211yesmaximal, characteristic, complemented
7C19×#1519C211yesmaximal, characteristic
8C2×#10597381—21no—
9C2×#10597370C2211yescharacteristic
10C22×C4×Dic19C2211yescharacteristic
11#11926874—21no—
12#11926860—21no—
13#11926771—22no—
14#11926695—21no—
15#11926682—21no—
16C2×C22⋊(C19⋊C8)C2211yescharacteristic
17#11926449—21no—
18#11926447—21no—
19#11926443—21no—
20#11926440—21no—
21#11926432—22no—
22#11926429—22no—
23#11926424—21no—
24#11926419—21no—
25#11926405—21no—
26#11926404C2211yescharacteristic
27#11926298—22no—
28#11926282—22no—
29C2×C19×#121C2211yescharacteristic
30C2×C19×C22⋊C8C2211yescharacteristic
31C19×#380C2211yescharacteristic
32C19×#327—22no—
33C22×D4×C19—21no—
34C22×D4×C19D411yescharacteristic
35C23×C4×C19C2311yescharacteristic
36C23×Dic19D411yescharacteristic
37C23×Dic19D411yescharacteristic
38C22×Dic38D411yescharacteristic
39C22×C8×C19—21no—
40C19×#121—21no—
41C19×#121—21no—
42C19×#121—21no—
43C19×#121—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19D411yescharacteristic
46C2×C22⋊C4×C19—21no—
47C2×C22⋊C4×C19—21no—
48C2×C22⋊Dic19—22no—
49C2×C22⋊Dic19—22no—
50C2×C22⋊Dic19—21no—
51C2×C22⋊Dic19—21no—
52#10597381—42no—
53#10597381—42no—
54C2×#64526—22no—
55C2×C4⋊Dic19—22no—
56C2×C4⋊Dic19—21no—
57C2×C4⋊Dic19D411yescharacteristic
58#10597370—21no—
59#10597370—21no—
60#10597370—21no—
61#10597370—21no—
62C2×Dic19⋊C4—22no—
63C2×Dic19⋊C4—21no—
64C2×C4×Dic19—21no—
65C2×C4×Dic19—21no—
66C2×C4×Dic19—21no—
67C2×C4×Dic19—21no—
68C2×C4×Dic19—21no—
69C2×C4×Dic19—21no—
70C22×C19⋊C8D412yes—
71C19×C22⋊C8—21no—
72C19×C22⋊C8—21no—
73C19×#95D412yes—
74#10597289—22no—
75C19⋊#95—22no—
76C19⋊#95—22no—
77C19⋊#95—22no—
78C19⋊#95—22no—
79C19⋊#95D412yes—
80C22⋊(C19⋊C8)—21no—
81C22⋊(C19⋊C8)—21no—
82#10597267—22no—
83#10597265—22no—
84C24×C19—21no—
85C24×C19C2×D411yescharacteristic
86C2×D4×C19—21no—
87C2×D4×C19—21no—
88C2×D4×C19—42no—
89C2×D4×C19—41no—
90C2×D4×C19—41no—
91C2×D4×C19—41no—
92C2×D4×C19—41no—
93C2×D4×C19—41no—
94C2×D4×C19—41no—
95C22×C4×C19—22no—
96C22×C4×C19—21no—
97C22×C4×C19—42no—
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19C2×D411yescharacteristic
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19#4111yescharacteristic
104C22×Dic19—21no—
105C22×Dic19—21no—
106C22×Dic19—21no—
107C22×Dic19—21no—
108C22×Dic19—21no—
109C22×Dic19—21no—
110C22×Dic19—21no—
111C22×Dic19—21no—
112C22×Dic19—21no—
113C22×Dic19—22no—
114C22×Dic19—21no—
115C22×Dic19—21no—
116C22×Dic19—42no—
117C22×Dic19SD1612yescomplemented
118C2×Dic38—21no—
119C2×Dic38—21no—
120C2×Dic38—42no—
121C2×C8×C19—42no—
122C2×C8×C19—41no—
123C4⋊C4×C19—21no—
124C4⋊C4×C19—21no—
125C4⋊C4×C19—42no—
126C22⋊C4×C19—41no—
127C22⋊C4×C19—41no—
128C22⋊C4×C19—41no—
129C22⋊C4×C19—41no—
130C22⋊Dic19—44no—
131C22⋊Dic19—44no—
132C22⋊Dic19—41no—
133C22⋊Dic19—41no—
134C22⋊Dic19—41no—
135C22⋊Dic19—41no—
136#64526—82no—
137C4⋊Dic19—21no—
138C4⋊Dic19—21no—
139C4⋊Dic19—44no—
140C4⋊Dic19—42no—
141Dic19⋊C4—44no—
142Dic19⋊C4—41no—
143Dic19⋊C4—41no—
144C4×Dic19—41no—
145C4×Dic19—41no—
146C4×Dic19—41no—
147C4×Dic19—41no—
148C2×C19⋊C8—22no—
149C2×C19⋊C8—42no—
150#10323—191nomaximal, Sylow
151C23×C19—41no—
152C23×C19—41no—
153C23×C19—42no—
154C23×C19—42no—
155C23×C19—41no—
156C23×C19—41no—
157C23×C19—41no—
158C23×C19#12011yescharacteristic
159C23×C19#12011yescharacteristic
160C23×C19#12111yescharacteristic
161C23×C19C2×SD1611yescharacteristic
162C23×C19#13511yescharacteristic
163C23×C19AGL(1,ℤ/8)11yescharacteristic
164C23×C19#13711yescharacteristic
165D4×C19—42no—
166D4×C19—81no—
167D4×C19—81no—
168D4×C19—81no—
169D4×C19—81no—
170D4×C19—81no—
171C2×C4×C19—22no—
172C2×C4×C19—22no—
173C2×C4×C19—22no—
174C2×C4×C19—41no—
175C2×C4×C19—41no—
176C2×C4×C19—41no—
177C2×C4×C19—42no—
178C2×C4×C19—42no—
179C2×C4×C19—41no—
180C2×C4×C19—42no—
181C2×C4×C19—41no—
182C2×C4×C19—41no—
183C2×C4×C19#12011yescharacteristic
184C2×C4×C19#12111yescharacteristic
185C2×C4×C19#12111yescharacteristic
186C2×C4×C19#12711yescharacteristic
187C2×Dic19—22no—
188C2×Dic19—22no—
189C2×Dic19—22no—
190C2×Dic19—22no—
191C2×Dic19—22no—
192C2×Dic19—22no—
193C2×Dic19—41no—
194C2×Dic19—41no—
195C2×Dic19—41no—
196C2×Dic19—41no—
197C2×Dic19—41no—
198C2×Dic19—41no—
199C2×Dic19—41no—
200C2×Dic19—41no—
201C2×Dic19—42no—
202C2×Dic19—42no—
203C2×Dic19—42no—
204C2×Dic19—42no—
205C2×Dic19—41no—
206C2×Dic19—41no—
207C2×Dic19—42no—
208Dic38—42no—
209Dic38—81no—
210C8×C19—81no—
211C19⋊C8—42no—
212#3187—191no—
213#2855—191no—
214#2854—191no—
215#1817—191no—
216#1520—191no—
217#1519D1911yescharacteristic
218#1289—191no—
219C22×C19—21no—
220C22×C19—21no—
221C22×C19—21no—
222C22×C19—21no—
223C22×C19—21no—
224C22×C19—21no—
225C22×C19—41no—
226C22×C19—41no—
227C22×C19—41no—
228C22×C19—41no—
229C22×C19—82no—
230C22×C19—82no—
231C22×C19—81no—
232C22×C19—81no—
233C22×C19—81no—
234C22×C19#39211yescharacteristic
235C22×C19#44811yescharacteristic
236C22×C19#44911yescharacteristic
237C22×C19#45011yescharacteristic
238C22×C19#45211yescharacteristic
239C22×C19#46511yescharacteristic
240C22×C19#46811yescharacteristic
241C4×C19—21no—
242C4×C19—21no—
243C4×C19—21no—
244C4×C19—82no—
245C4×C19—81no—
246C4×C19#45812yes—
247Dic19—42no—
248Dic19—42no—
249Dic19—82no—
250Dic19—81no—
251Dic19—81no—
252C2×#123—381no—
253C2×C22⋊Q8—191no—
254C2×#121C2×D1911yescharacteristic
255C22×C42—191no—
256#483—381no—
257#481—381no—
258#465—382no—
259#450—381no—
260#448—381no—
261C2×C22⋊C8—191no—
262C2×C22⋊C8C2×D1911yescharacteristic
263#391—381no—
264#390—381no—
265#389—381no—
266#389—381no—
267#388—382no—
268#387—382no—
269#386—381no—
270#385—381no—
271#381—381no—
272#380—191no—
273#380C2×D1911yescharacteristic
274#336—382no—
275#328—382no—
276#327—22no—
277C2×C19—21no—
278C2×C19—21no—
279C2×C19—21no—
280C2×C19—21no—
281C2×C19—21no—
282C2×C19—21no—
283C2×C19—161no—
284C2×C19#200011yescharacteristic
285C2×C19#201011yescharacteristic
286C2×C19#202211yescharacteristic
287C22×Q8—191no—
288C22×D4—21no—
289C22×D4D7611yescharacteristic
290C23×C4—191no—
291C23×C4—191no—
292C23×C4C22×D1911yescharacteristic
293C2×SD16—382no—
294C22×C8—21no—
295C22×C8—192no—
296#123—762no—
297#123—762no—
298C22⋊Q8—381no—
299C22⋊Q8—381no—
300C22⋊Q8—381no—
301C22⋊Q8—381no—
302#121—21no—
303#121—21no—
304#121—21no—
305#121—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—191no—
308C2×C4⋊C4—382no—
309C2×C4⋊C4—382no—
310C2×C4⋊C4—381no—
311C2×C4⋊C4—381no—
312C2×C4⋊C4D7611yescharacteristic
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—382no—
316C2×C22⋊C4—382no—
317C2×C22⋊C4—381no—
318C2×C22⋊C4—381no—
319C2×C42—381no—
320C2×C42—381no—
321C2×C42—381no—
322C2×C42—381no—
323C2×C42—381no—
324C2×C42—381no—
325#106—382no—
326#103—382no—
327#102—382no—
328C22⋊C8—21no—
329C22⋊C8—21no—
330C22⋊C8—381no—
331C22⋊C8—381no—
332#95—192no—
333#95—382no—
334#95—382no—
335#95—382no—
336#95—382no—
337#95C22⋊D1912yes—
338C19#1032311yescharacteristic, complemented, Sylow
339C24—21no—
340C24D4×D1911yescharacteristic
341C2×Q8—381no—
342C2×Q8—381no—
343C2×Q8—762no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—42no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—42no—
356C22×C4—192no—
357C22×C4—381no—
358C22×C4—381no—
359C22×C4—381no—
360C22×C4—381no—
361C22×C4—381no—
362C22×C4—381no—
363C22×C4—381no—
364C22×C4—381no—
365C22×C4—381no—
366C22×C4—381no—
367C22×C4—381no—
368C22×C4—382no—
369C22×C4—762no—
370C22×C4C2×D7611yescharacteristic
371C22×C4#6454111yescharacteristic
372C22×C4D4×D1911yescharacteristic
373C22×C4D4×D1911yescharacteristic
374C22×C4D4×D1911yescharacteristic
375C22×C4C2×C22⋊D1911yescharacteristic
376SD16—1522no—
377C2×C8—42no—
378C2×C8—41no—
379C2×C8—382no—
380C2×C8—762no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—42no—
384C4⋊C4—381no—
385C4⋊C4—381no—
386C4⋊C4—762no—
387C4⋊C4—764no—
388C4⋊C4—764no—
389C4⋊C4—761no—
390C4⋊C4—761no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—764no—
396C22⋊C4—764no—
397C22⋊C4—761no—
398C22⋊C4—761no—
399C22⋊C4—761no—
400C22⋊C4—761no—
401C42—761no—
402C42—761no—
403C42—761no—
404C42—761no—
405C23—41no—
406C23—41no—
407C23—42no—
408C23—42no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23#1059732811yescharacteristic
413C23#1059733011yescharacteristic
414C23#1059735711yescharacteristic
415C23#1059735811yescharacteristic
416C23SD16×D1911yescharacteristic
417C23#1059736111yescharacteristic
418C23#1059738311yescharacteristic
419Q8—762no—
420Q8—1521no—
421D4—42no—
422D4—81no—
423D4—81no—
424D4—81no—
425D4—81no—
426D4—81no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—382no—
440C2×C4—382no—
441C2×C4—382no—
442C2×C4—382no—
443C2×C4—382no—
444C2×C4—382no—
445C2×C4—761no—
446C2×C4—761no—
447C2×C4—761no—
448C2×C4—761no—
449C2×C4—761no—
450C2×C4—761no—
451C2×C4—761no—
452C2×C4—761no—
453C2×C4—762no—
454C2×C4—762no—
455C2×C4—762no—
456C2×C4—762no—
457C2×C4—762no—
458C2×C4—761no—
459C2×C4—761no—
460C2×C4#1059732811yescharacteristic
461C2×C4#1059733011yescharacteristic
462C2×C4#1059737611yescharacteristic
463C2×C4#1059738611yescharacteristic
464C8—81no—
465C8—762no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—82no—
477C22—82no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22#1192645311yescharacteristic
482C22#1192668111yescharacteristic
483C22#1192668611yescharacteristic
484C22#1192669611yescharacteristic
485C22#1192670711yescharacteristic
486C22#1192677211yescharacteristic
487C22#1192678911yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—82no—
492C4—81no—
493C4—762no—
494C4—762no—
495C4—1522no—
496C4—1521no—
497C4—1521no—
498C4#1192673512yes—
499C2—21no—
500C2—21no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2—161no—
506C2#1456463911yescharacteristic
507C2#1456470111yescharacteristic
508C2#1456476511yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1519C2
socleC22×C19#392
prime radicalC2×C19×#121C22
hypercenter#1519D19
hypocenterC19#10323
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. #14571975C2semidirect
4. #14563701C2semidirect
5. #14562208C2semidirect
6. #14561502C2semidirect
117. C22×Dic19SD16semidirect
338. C19#10323semidirect

Maximal subgroups

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

subgroupindex
#145743922
#145719752
#145719612
#145637012
#145622082
#145615022
C19×#15192
#1032319