Finite Group Databasebeta

← #18080595

Subgroups — #18080595

Order 4864.

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

normal subgroups only

This group has 686 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#14566393C211yesmaximal, characteristic, complemented
2#14563579C211yesmaximal, characteristic
3#14563553C211yesmaximal, characteristic
4#14562168C211yesmaximal, characteristic, complemented
5#14561544C211yesmaximal, characteristic, complemented
6#14561489C211yesmaximal, characteristic, complemented
7C19×#3007C211yesmaximal, characteristic
8C2×#10597294—21no—
9C2×#10597294—21no—
10C2×#10597291—21no—
11C2×#10597291—21no—
12#11926508C2211yescharacteristic
13#11926451—21no—
14#11926437—21no—
15#11926437—21no—
16#11926430—21no—
17#11926430—21no—
18#11926407C2211yescharacteristic
19#11926407C2211yescharacteristic
20C4⋊C4×Dic19—21no—
21C4×C22⋊Dic19C2211yescharacteristic
22#11926281—22no—
23C22×#41×C19C2211yescharacteristic
24C2×C19×#137—21no—
25C2×C19×C22⋊Q8C2211yescharacteristic
26C19×#452—22no—
27C19×#451C412yescomplemented
28C19×#450C412yescomplemented
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
38C22×Q8×C19D411yescharacteristic
39C22×D4×C19—21no—
40C22×D4×C19C2×C411yescharacteristic
41C23×C4×C19—21no—
42C23×C4×C19C2311yescharacteristic
43C19×#137—42no—
44C19×#137—42no—
45C2×Q16×C19—22no—
46C2×SD16×C19—22no—
47C2×M16×C19—21no—
48C19×C22⋊Q8—21no—
49C19×C22⋊Q8—21no—
50C19×C22⋊Q8C2×C412yes—
51C19×C22⋊Q8D412yes—
52C2×C4⋊C4×C19—21no—
53C2×C4⋊C4×C19D411yescharacteristic
54C2×C22⋊C4×C19—21no—
55C2×C22⋊Dic19—21no—
56C2×C22⋊Dic19—21no—
57C2×C22⋊Dic19D411yescharacteristic
58C2×C22⋊Dic19D411yescharacteristic
59C2×C4⋊Dic19—21no—
60C2×C4⋊Dic19—21no—
61C2×C4×Dic19—21no—
62C2×C4×Dic19—21no—
63C2×C4×Dic19D411yescharacteristic
64C2×C4×Dic19D411yescharacteristic
65C2×#64520—21no—
66C19×#103—22no—
67C19×#102—22no—
68C19×C22⋊C8—21no—
69C19×C22⋊C8C2×C412yes—
70#10597294—42no—
71#10597294—42no—
72#10597291—42no—
73#10597291—42no—
74C19⋊#95—21no—
75C19⋊#95—21no—
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×C19C2×D411yescharacteristic
87#41×C19—22no—
88#41×C19—22no—
89#41×C19—22no—
90#41×C19—22no—
91#41×C19—41no—
92#41×C19—41no—
93#41×C19—41no—
94#41×C19—41no—
95#41×C19—42no—
96#41×C19—42no—
97#41×C19—42no—
98#41×C19—42no—
99C2×Q8×C19—21no—
100C2×Q8×C19—21no—
101C2×Q8×C19—21no—
102C2×Q8×C19—42no—
103C2×Q8×C19—41no—
104C2×Q8×C19—41no—
105C2×Q8×C19C22⋊C412yes—
106C2×D4×C19—22no—
107C2×D4×C19—22no—
108C2×D4×C19—21no—
109C2×D4×C19—21no—
110C2×D4×C19—42no—
111C2×D4×C19—41no—
112C2×D4×C19—41no—
113C2×D4×C19—41no—
114C2×D4×C19—41no—
115C22×C4×C19—21no—
116C22×C4×C19—21no—
117C22×C4×C19—21no—
118C22×C4×C19—41no—
119C22×C4×C19—41no—
120C22×C4×C19—42no—
121C22×C4×C19—42no—
122C22×C4×C19—41no—
123C22×C4×C19—41no—
124C22×C4×C19C22×C411yescharacteristic
125C22×C4×C19C2×D411yescharacteristic
126C22×C4×C19C2×D411yescharacteristic
127C22×C4×C19C2×D411yescharacteristic
128C22×C4×C19#4111yescharacteristic
129C22×C4×C19#4111yescharacteristic
130C22×Dic19—21no—
131C22×Dic19—21no—
132C22×Dic19—21no—
133C22×Dic19—21no—
134C22×Dic19—41no—
135Q16×C19—44no—
136SD16×C19—44no—
137M16×C19—41no—
138M16×C19—41no—
139C2×C8×C19—22no—
140C4⋊C4×C19—22no—
141C4⋊C4×C19—22no—
142C4⋊C4×C19—21no—
143C4⋊C4×C19C22⋊C412yes—
144C22⋊C4×C19—22no—
145C22⋊C4×C19—22no—
146C22⋊Dic19—42no—
147C22⋊Dic19—41no—
148C22⋊Dic19—41no—
149C22⋊Dic19—41no—
150C22⋊Dic19—41no—
151C4⋊Dic19—42no—
152C4⋊Dic19—81no—
153C4×Dic19—42no—
154C4×Dic19—41no—
155C4×Dic19—41no—
156C4×Dic19—81no—
157#64520—41no—
158#64520—41no—
159C2×C19⋊C8—41no—
160#9524—191nomaximal, Sylow
161C23×C19—21no—
162C23×C19—21no—
163C23×C19—22no—
164C23×C19—41no—
165C23×C19—41no—
166C23×C19—41no—
167C23×C19—41no—
168C23×C19—81no—
169C23×C19—81no—
170C23×C19C4×D411yescharacteristic
171C23×C19#12011yescharacteristic
172C23×C19#12111yescharacteristic
173Q8×C19—22no—
174Q8×C19—22no—
175Q8×C19—42no—
176Q8×C19—41no—
177Q8×C19—41no—
178Q8×C19—81no—
179D4×C19—22no—
180D4×C19—22no—
181D4×C19—41no—
182D4×C19—41no—
183D4×C19—42no—
184D4×C19—42no—
185D4×C19—42no—
186D4×C19—42no—
187C2×C4×C19—21no—
188C2×C4×C19—21no—
189C2×C4×C19—21no—
190C2×C4×C19—21no—
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—41no—
198C2×C4×C19—42no—
199C2×C4×C19—42no—
200C2×C4×C19—42no—
201C2×C4×C19—42no—
202C2×C4×C19—41no—
203C2×C4×C19—41no—
204C2×C4×C19—41no—
205C2×C4×C19—41no—
206C2×C4×C19—41no—
207C2×C4×C19—41no—
208C2×C4×C19C2×C22⋊C411yescharacteristic
209C2×C4×C19C4×D411yescharacteristic
210C2×C4×C19#12111yescharacteristic
211C2×C4×C19#12311yescharacteristic
212C2×Dic19—22no—
213C2×Dic19—41no—
214C2×Dic19—41no—
215C2×Dic19—41no—
216C2×Dic19—41no—
217C2×Dic19—41no—
218C2×Dic19—41no—
219C2×Dic19—41no—
220C2×Dic19—41no—
221C2×Dic19—41no—
222C2×Dic19—41no—
223C2×Dic19—41no—
224C2×Dic19—81no—
225C2×Dic19—81no—
226C2×Dic19—81no—
227C8×C19—42no—
228C19⋊C8—81no—
229#3007D1911yescharacteristic
230#2332—191no—
231#1789—191no—
232#1782—191no—
233#1511—191no—
234#1306—191no—
235#1284—191no—
236C22×C19—21no—
237C22×C19—21no—
238C22×C19—21no—
239C22×C19—21no—
240C22×C19—21no—
241C22×C19—21no—
242C22×C19—21no—
243C22×C19—21no—
244C22×C19—42no—
245C22×C19—81no—
246C22×C19—81no—
247C22×C19—82no—
248C22×C19—82no—
249C22×C19—81no—
250C22×C19—81no—
251C22×C19#38611yescharacteristic
252C22×C19B(4,𝔽2)11yescharacteristic
253C22×C19B(4,𝔽2)11yescharacteristic
254C4×C19—21no—
255C4×C19—21no—
256C4×C19—21no—
257C4×C19—21no—
258C4×C19—42no—
259C4×C19—42no—
260C4×C19—42no—
261Dic19—42no—
262Dic19—81no—
263Dic19—81no—
264Dic19—81no—
265Dic19—161no—
266C22×#41C2×D1911yescharacteristic
267C2×#137—21no—
268C2×C22⋊Q8C2×D1911yescharacteristic
269#452—22no—
270#451Dic1912yescomplemented
271#450Dic1912yescomplemented
272C2×#104—381no—
273C2×#104—381no—
274#417—21no—
275C2×#99—381no—
276C2×#99—381no—
277#407—191no—
278#407C2×D1911yescharacteristic
279#391—381no—
280#388—381no—
281#388—381no—
282#387—381no—
283#387—381no—
284#381—191no—
285#381—191no—
286C4×C4⋊C4—381no—
287C4×C22⋊C4—191no—
288#328—382no—
289C2×C19—21no—
290C2×C19—21no—
291C2×C19—41no—
292C2×C19—41no—
293C2×C19—82no—
294C2×C19#188911yescharacteristic
295C2×C19#190511yescharacteristic
296C2×C19#190611yescharacteristic
297C2×#41—21no—
298C2×#41—21no—
299C2×#41—21no—
300C2×#41—21no—
301C2×#41—42no—
302C2×#41—42no—
303C22×Q8C2×Dic1911yescharacteristic
304C22×Q8C22⋊D1911yescharacteristic
305C22×D4—21no—
306C22×D4C2×Dic1911yescharacteristic
307C23×C4—21no—
308C23×C4C22×D1911yescharacteristic
309#137—42no—
310#137—42no—
311C2×Q16—22no—
312C2×SD16—22no—
313C2×M16—21no—
314C2×M16—381no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8C2×Dic1912yes—
318C22⋊Q8C22⋊D1912yes—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—381no—
321C2×C4⋊C4—381no—
322C2×C4⋊C4C22⋊D1911yescharacteristic
323C2×C22⋊C4—21no—
324C2×C22⋊C4—191no—
325C2×C22⋊C4—191no—
326C2×C22⋊C4—381no—
327C2×C22⋊C4—381no—
328C2×C42—191no—
329C2×C42—191no—
330C2×C42—381no—
331C2×C42—381no—
332#104—762no—
333#104—762no—
334#103—22no—
335#102—22no—
336#99—762no—
337#99—762no—
338C22⋊C8—21no—
339C22⋊C8—381no—
340C22⋊C8—381no—
341C22⋊C8C2×Dic1912yes—
342#95—381no—
343#95—381no—
344#95—381no—
345#95—381no—
346#95—381no—
347#95—381no—
348#95—381no—
349#95—381no—
350#95—381no—
351C19#952411yescharacteristic, complemented, Sylow
352C24—21no—
353C24D4×D1911yescharacteristic
354#41—22no—
355#41—22no—
356#41—22no—
357#41—22no—
358#41—41no—
359#41—41no—
360#41—41no—
361#41—41no—
362#41—42no—
363#41—42no—
364#41—42no—
365#41—42no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—42no—
370C2×Q8—41no—
371C2×Q8—41no—
372C2×Q8C22⋊Dic1912yes—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—42no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—381no—
392C22×C4—381no—
393C22×C4—381no—
394C22×C4—381no—
395C22×C4—761no—
396C22×C4D4×D1911yescharacteristic
397C22×C4#6454311yescharacteristic
398C22×C4#6454311yescharacteristic
399C22×C4C22×Dic1911yescharacteristic
400C22×C4C2×C22⋊D1911yescharacteristic
401C22×C4C2×C22⋊D1911yescharacteristic
402Q16—44no—
403SD16—44no—
404M16—41no—
405M16—41no—
406M16—761no—
407M16—761no—
408C2×C8—22no—
409C2×C8—761no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—762no—
414C4⋊C4—1521no—
415C4⋊C4C22⋊Dic1912yes—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—762no—
419C22⋊C4—761no—
420C22⋊C4—761no—
421C22⋊C4—761no—
422C22⋊C4—761no—
423C42—761no—
424C42—761no—
425C42—762no—
426C42—1521no—
427C23—21no—
428C23—21no—
429C23—22no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—81no—
435C23—81no—
436C23D4×Dic1911yescharacteristic
437C23#1059738311yescharacteristic
438C23#1059738511yescharacteristic
439Q8—22no—
440Q8—22no—
441Q8—42no—
442Q8—41no—
443Q8—41no—
444Q8—81no—
445D4—22no—
446D4—22no—
447D4—41no—
448D4—41no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—42no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—382no—
475C2×C4—761no—
476C2×C4—761no—
477C2×C4—761no—
478C2×C4—761no—
479C2×C4—761no—
480C2×C4—761no—
481C2×C4—761no—
482C2×C4—761no—
483C2×C4—761no—
484C2×C4—761no—
485C2×C4—761no—
486C2×C4—1521no—
487C2×C4—1521no—
488C2×C4—1521no—
489C2×C4D4×Dic1911yescharacteristic
490C2×C4#1059738111yescharacteristic
491C2×C4#1059738511yescharacteristic
492C2×C4C2×C22⋊Dic1911yescharacteristic
493C8—42no—
494C8—1521no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—42no—
504C22—81no—
505C22—81no—
506C22—82no—
507C22—82no—
508C22—81no—
509C22—81no—
510C22#1192642411yescharacteristic
511C22#1192673011yescharacteristic
512C22#1192673011yescharacteristic
513C4—21no—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—42no—
518C4—42no—
519C4—42no—
520C4—3041no—
521C4—762no—
522C4—1521no—
523C4—1521no—
524C4—1521no—
525C2—21no—
526C2—21no—
527C2—41no—
528C2—41no—
529C2—82no—
530C2#1456404411yescharacteristic
531C2#1456413111yescharacteristic
532C2#1456413811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#3007C2
socleC22×C19#386
prime radicalC22×#41×C19C22
cosocleC23×C4×C19C23
hypercenter#3007D19
hypocenterC19#9524
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
1. #14566393C2semidirect
4. #14562168C2semidirect
5. #14561544C2semidirect
6. #14561489C2semidirect
27. C19×#451C4semidirect
28. C19×#450C4semidirect
270. #451Dic19semidirect
271. #450Dic19semidirect
351. C19#9524semidirect

Maximal subgroups

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

subgroupindex
#145663932
#145635792
#145635532
#145621682
#145615442
#145614892
C19×#30072
#952419