Finite Group Databasebeta

← #18080588

Subgroups — #18080588

Order 4864.

742 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 742 conjugacy classes of subgroups — too many to draw. Only its 103 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#14566402C211yesmaximal, characteristic, complemented
2#14563579C211yesmaximal, characteristic, complemented
3#14563553C211yesmaximal, characteristic, complemented
4#14562164C211yesmaximal, characteristic, complemented
5#14561544C211yesmaximal, characteristic, complemented
6#14561489C211yesmaximal, characteristic, complemented
7C19×#3006C211yesmaximal, characteristic
8C2×#10597294—21no—
9C2×#10597294—21no—
10C2×#10597291—21no—
11C2×#10597291—21no—
12#11926508C2211yescharacteristic
13#11926447—21no—
14#11926437—21no—
15#11926430—21no—
16#11926424—21no—
17#11926424—21no—
18#11926407C2211yescharacteristic
19#11926407C2211yescharacteristic
20C22⋊C4×Dic19—21no—
21C4×C22⋊Dic19C2211yescharacteristic
22#11926278—22no—
23C22×#41×C19C2211yescharacteristic
24C2×C19×AGL(1,ℤ/8)—21no—
25C2×C19×#121C2211yescharacteristic
26C19×#449—22no—
27C19×#448C412yescomplemented
28C19×#447C412yescomplemented
29C19×#417—21no—
30C19×#407C2211yescharacteristic
31C2×#41×C19—21no—
32C2×#41×C19—21no—
33C2×#41×C19—21no—
34C2×#41×C19—21no—
35C2×#41×C19—42no—
36C2×#41×C19—42no—
37C22×Q8×C19C2×C411yescharacteristic, complemented
38C22×D4×C19—21no—
39C22×D4×C19—21no—
40C22×D4×C19C2×C411yescharacteristic, complemented
41C22×D4×C19D411yescharacteristic
42C23×C4×C19—21no—
43C23×C4×C19C2311yescharacteristic
44C23×Dic19—21no—
45C19×AGL(1,ℤ/8)—42no—
46C19×AGL(1,ℤ/8)—42no—
47C2×SD16×C19—22no—
48C2×D8×C19—22no—
49C2×M16×C19—21no—
50C19×#121—21no—
51C19×#121—21no—
52C19×#121C2×C412yes—
53C19×#121D412yes—
54C2×C4⋊C4×C19D411yescharacteristic
55C2×C22⋊C4×C19—21no—
56C2×C22⋊Dic19—21no—
57C2×C22⋊Dic19—21no—
58C2×C22⋊Dic19—21no—
59C2×C22⋊Dic19—21no—
60C2×C22⋊Dic19—21no—
61C2×C22⋊Dic19D411yescharacteristic
62C2×C22⋊Dic19D411yescharacteristic
63C2×C4⋊Dic19—21no—
64C2×C4×Dic19—21no—
65C2×C4×Dic19D411yescharacteristic
66C2×C4×Dic19D411yescharacteristic
67C2×#64520—21no—
68C19×#103—22no—
69C19×#102—22no—
70C19×C22⋊C8—21no—
71C19×C22⋊C8C2×C412yescomplemented
72#10597294—42no—
73#10597294—42no—
74#10597291—42no—
75#10597291—42no—
76C19⋊#95—21no—
77C19⋊#95—21no—
78C19⋊#95—21no—
79C19⋊#95—21no—
80C19⋊#95—21no—
81C19⋊#95—21no—
82C19⋊#95—21no—
83C22⋊(C19⋊C8)—21no—
84C22⋊(C19⋊C8)—21no—
85C24×C19—21no—
86C24×C19—21no—
87C24×C19C2×D411yescharacteristic
88#41×C19—22no—
89#41×C19—22no—
90#41×C19—22no—
91#41×C19—22no—
92#41×C19—41no—
93#41×C19—41no—
94#41×C19—41no—
95#41×C19—41no—
96#41×C19—42no—
97#41×C19—42no—
98#41×C19—42no—
99#41×C19—42no—
100C2×Q8×C19—21no—
101C2×Q8×C19—21no—
102C2×Q8×C19—42no—
103C2×D4×C19—22no—
104C2×D4×C19—22no—
105C2×D4×C19—22no—
106C2×D4×C19—22no—
107C2×D4×C19—21no—
108C2×D4×C19—21no—
109C2×D4×C19—21no—
110C2×D4×C19—41no—
111C2×D4×C19—41no—
112C2×D4×C19—42no—
113C2×D4×C19—41no—
114C2×D4×C19—41no—
115C2×D4×C19—41no—
116C2×D4×C19—41no—
117C2×D4×C19—81no—
118C2×D4×C19—81no—
119C2×D4×C19C22⋊C412yes—
120C22×C4×C19—21no—
121C22×C4×C19—21no—
122C22×C4×C19—41no—
123C22×C4×C19—41no—
124C22×C4×C19—42no—
125C22×C4×C19—42no—
126C22×C4×C19—41no—
127C22×C4×C19—41no—
128C22×C4×C19C22×C411yescharacteristic
129C22×C4×C19C2×D411yescharacteristic
130C22×C4×C19C2×D411yescharacteristic
131C22×C4×C19C2×D411yescharacteristic
132C22×C4×C19#4111yescharacteristic
133C22×C4×C19#4111yescharacteristic
134C22×Dic19—21no—
135C22×Dic19—21no—
136C22×Dic19—21no—
137C22×Dic19—21no—
138C22×Dic19—42no—
139C22×Dic19—41no—
140C22×Dic19—81no—
141C22×Dic19—81no—
142SD16×C19—44no—
143D8×C19—44no—
144M16×C19—41no—
145M16×C19—41no—
146C2×C8×C19—22no—
147C4⋊C4×C19—21no—
148C4⋊C4×C19C22⋊C412yes—
149C22⋊C4×C19—22no—
150C22⋊C4×C19—22no—
151C22⋊Dic19—42no—
152C22⋊Dic19—42no—
153C22⋊Dic19—41no—
154C22⋊Dic19—41no—
155C22⋊Dic19—41no—
156C22⋊Dic19—41no—
157C22⋊Dic19—81no—
158C22⋊Dic19—81no—
159C4⋊Dic19—81no—
160C4×Dic19—41no—
161C4×Dic19—41no—
162C4×Dic19—81no—
163#64520—41no—
164#64520—41no—
165C2×C19⋊C8—41no—
166#9523—191nomaximal, Sylow
167C23×C19—21no—
168C23×C19—21no—
169C23×C19—22no—
170C23×C19—22no—
171C23×C19—41no—
172C23×C19—41no—
173C23×C19—41no—
174C23×C19—41no—
175C23×C19—41no—
176C23×C19—41no—
177C23×C19—41no—
178C23×C19—41no—
179C23×C19—41no—
180C23×C19—41no—
181C23×C19—81no—
182C23×C19—81no—
183C23×C19C4×D411yescharacteristic
184C23×C19#12011yescharacteristic
185C23×C19#12111yescharacteristic
186Q8×C19—22no—
187Q8×C19—22no—
188Q8×C19—41no—
189Q8×C19—41no—
190D4×C19—22no—
191D4×C19—22no—
192D4×C19—42no—
193D4×C19—41no—
194D4×C19—41no—
195D4×C19—42no—
196D4×C19—42no—
197D4×C19—42no—
198D4×C19—42no—
199D4×C19—81no—
200D4×C19—82no—
201D4×C19—82no—
202C2×C4×C19—21no—
203C2×C4×C19—21no—
204C2×C4×C19—21no—
205C2×C4×C19—21no—
206C2×C4×C19—22no—
207C2×C4×C19—22no—
208C2×C4×C19—41no—
209C2×C4×C19—41no—
210C2×C4×C19—41no—
211C2×C4×C19—41no—
212C2×C4×C19—42no—
213C2×C4×C19—42no—
214C2×C4×C19—42no—
215C2×C4×C19—42no—
216C2×C4×C19—41no—
217C2×C4×C19—41no—
218C2×C4×C19—41no—
219C2×C4×C19—41no—
220C2×C4×C19C2×C22⋊C411yescharacteristic
221C2×C4×C19C4×D411yescharacteristic
222C2×C4×C19#12111yescharacteristic
223C2×C4×C19#12311yescharacteristic
224C2×Dic19—22no—
225C2×Dic19—41no—
226C2×Dic19—41no—
227C2×Dic19—41no—
228C2×Dic19—41no—
229C2×Dic19—41no—
230C2×Dic19—41no—
231C2×Dic19—41no—
232C2×Dic19—41no—
233C2×Dic19—41no—
234C2×Dic19—41no—
235C2×Dic19—41no—
236C2×Dic19—84no—
237C2×Dic19—81no—
238C2×Dic19—81no—
239C2×Dic19—81no—
240C8×C19—42no—
241C19⋊C8—81no—
242#3006D1911yescharacteristic
243#2333—191no—
244#1789—191no—
245#1782—191no—
246#1510—191no—
247#1306—191no—
248#1284—191no—
249C22×C19—21no—
250C22×C19—21no—
251C22×C19—21no—
252C22×C19—21no—
253C22×C19—21no—
254C22×C19—21no—
255C22×C19—21no—
256C22×C19—21no—
257C22×C19—42no—
258C22×C19—42no—
259C22×C19—42no—
260C22×C19—42no—
261C22×C19—81no—
262C22×C19—81no—
263C22×C19—81no—
264C22×C19—81no—
265C22×C19—81no—
266C22×C19—81no—
267C22×C19—82no—
268C22×C19—82no—
269C22×C19—81no—
270C22×C19—81no—
271C22×C19#38611yescharacteristic
272C22×C19B(4,𝔽2)11yescharacteristic
273C22×C19B(4,𝔽2)11yescharacteristic
274C4×C19—21no—
275C4×C19—21no—
276C4×C19—21no—
277C4×C19—21no—
278C4×C19—42no—
279C4×C19—42no—
280Dic19—42no—
281Dic19—81no—
282Dic19—81no—
283Dic19—81no—
284Dic19—161no—
285C22×#41C2×D1911yescharacteristic
286C2×AGL(1,ℤ/8)—21no—
287C2×#121C2×D1911yescharacteristic
288#449—22no—
289#448Dic1912yescomplemented
290#447Dic1912yescomplemented
291C2×#104—381no—
292C2×#104—381no—
293#417—21no—
294C2×#99—381no—
295C2×#99—381no—
296#407—191no—
297#407C2×D1911yescharacteristic
298#390—381no—
299#388—381no—
300#387—381no—
301#386—381no—
302#386—381no—
303#381—191no—
304#381—191no—
305C4×C22⋊C4—191no—
306C4×C22⋊C4—381no—
307#327—382no—
308C2×C19—21no—
309C2×C19—21no—
310C2×C19—41no—
311C2×C19—41no—
312C2×C19—82no—
313C2×C19—82no—
314C2×C19#188911yescharacteristic
315C2×C19#190411yescharacteristic
316C2×C19#190611yescharacteristic
317C2×#41—21no—
318C2×#41—21no—
319C2×#41—21no—
320C2×#41—21no—
321C2×#41—42no—
322C2×#41—42no—
323C22×Q8C2×Dic1911yescharacteristic, complemented
324C22×D4—21no—
325C22×D4—21no—
326C22×D4C2×Dic1911yescharacteristic, complemented
327C22×D4C22⋊D1911yescharacteristic
328C23×C4—21no—
329C23×C4—381no—
330C23×C4C22×D1911yescharacteristic
331AGL(1,ℤ/8)—42no—
332AGL(1,ℤ/8)—42no—
333C2×SD16—22no—
334C2×D8—22no—
335C2×M16—21no—
336C2×M16—381no—
337#121—21no—
338#121—21no—
339#121C2×Dic1912yes—
340#121C22⋊D1912yes—
341C2×C4⋊C4—381no—
342C2×C4⋊C4C22⋊D1911yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—191no—
345C2×C22⋊C4—191no—
346C2×C22⋊C4—381no—
347C2×C22⋊C4—381no—
348C2×C22⋊C4—381no—
349C2×C22⋊C4—381no—
350C2×C22⋊C4—381no—
351C2×C42—191no—
352C2×C42—191no—
353C2×C42—381no—
354#104—762no—
355#104—762no—
356#103—22no—
357#102—22no—
358#99—762no—
359#99—762no—
360C22⋊C8—21no—
361C22⋊C8—381no—
362C22⋊C8—381no—
363C22⋊C8C2×Dic1912yescomplemented
364#95—381no—
365#95—381no—
366#95—381no—
367#95—381no—
368#95—381no—
369#95—381no—
370#95—381no—
371C19#952311yescharacteristic, complemented, Sylow
372C24—21no—
373C24—21no—
374C24D4×D1911yescharacteristic
375#41—22no—
376#41—22no—
377#41—22no—
378#41—22no—
379#41—41no—
380#41—41no—
381#41—41no—
382#41—41no—
383#41—42no—
384#41—42no—
385#41—42no—
386#41—42no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—42no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—42no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—81no—
405C2×D4—81no—
406C2×D4C22⋊Dic1912yes—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—381no—
416C22×C4—381no—
417C22×C4—381no—
418C22×C4—381no—
419C22×C4—762no—
420C22×C4—761no—
421C22×C4—1521no—
422C22×C4—1521no—
423C22×C4D4×D1911yescharacteristic
424C22×C4#6454311yescharacteristic
425C22×C4#6454311yescharacteristic
426C22×C4C22×Dic1911yescharacteristic
427C22×C4C2×C22⋊D1911yescharacteristic
428C22×C4C2×C22⋊D1911yescharacteristic
429SD16—44no—
430D8—44no—
431M16—41no—
432M16—41no—
433M16—761no—
434M16—761no—
435C2×C8—22no—
436C2×C8—761no—
437C4⋊C4—21no—
438C4⋊C4—1521no—
439C4⋊C4C22⋊Dic1912yes—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—762no—
443C22⋊C4—762no—
444C22⋊C4—761no—
445C22⋊C4—761no—
446C22⋊C4—761no—
447C22⋊C4—761no—
448C22⋊C4—1521no—
449C22⋊C4—1521no—
450C42—761no—
451C42—761no—
452C42—1521no—
453C23—21no—
454C23—21no—
455C23—22no—
456C23—22no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—81no—
468C23—81no—
469C23D4×Dic1911yescharacteristic
470C23#1059738311yescharacteristic
471C23#1059738511yescharacteristic
472Q8—22no—
473Q8—22no—
474Q8—41no—
475Q8—41no—
476D4—22no—
477D4—22no—
478D4—42no—
479D4—41no—
480D4—41no—
481D4—42no—
482D4—42no—
483D4—42no—
484D4—42no—
485D4—81no—
486D4—82no—
487D4—82no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—382no—
507C2×C4—761no—
508C2×C4—761no—
509C2×C4—761no—
510C2×C4—761no—
511C2×C4—761no—
512C2×C4—761no—
513C2×C4—761no—
514C2×C4—761no—
515C2×C4—761no—
516C2×C4—761no—
517C2×C4—761no—
518C2×C4—1521no—
519C2×C4—1521no—
520C2×C4—1521no—
521C2×C4—1524no—
522C2×C4D4×Dic1911yescharacteristic
523C2×C4#1059738111yescharacteristic
524C2×C4#1059738511yescharacteristic
525C2×C4C2×C22⋊Dic1911yescharacteristic
526C8—42no—
527C8—1521no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—82no—
547C22—82no—
548C22—81no—
549C22—81no—
550C22#1192642411yescharacteristic
551C22#1192673011yescharacteristic
552C22#1192673011yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—42no—
558C4—42no—
559C4—3041no—
560C4—762no—
561C4—1521no—
562C4—1521no—
563C4—1521no—
564C2—21no—
565C2—21no—
566C2—41no—
567C2—41no—
568C2—82no—
569C2—82no—
570C2#1456404411yescharacteristic
571C2#1456412411yescharacteristic
572C2#1456413811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#3006C2
socleC22×C19#386
cosocleC23×C4×C19C23
hypercenter#3006D19
hypocenterC19#9523
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3006

Complements

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

NH ≅ G/Ntype
1. #14566402C2semidirect
2. #14563579C2semidirect
3. #14563553C2semidirect
4. #14562164C2semidirect
5. #14561544C2semidirect
6. #14561489C2semidirect
27. C19×#448C4semidirect
28. C19×#447C4semidirect
37. C22×Q8×C19C2×C4semidirect
40. C22×D4×C19C2×C4semidirect
71. C19×C22⋊C8C2×C4semidirect
289. #448Dic19semidirect
290. #447Dic19semidirect
323. C22×Q8C2×Dic19semidirect
326. C22×D4C2×Dic19semidirect
363. C22⋊C8C2×Dic19semidirect
371. C19#9523semidirect

Maximal subgroups

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

subgroupindex
#145664022
#145635792
#145635532
#145621642
#145615442
#145614892
C19×#30062
#952319