Finite Group Databasebeta

← #18076607

Subgroups — #18076607

Order 4864.

658 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566338C211yesmaximal, characteristic
2#14563952C211yesmaximal, characteristic
3#14563823C211yesmaximal, characteristic, complemented
4C2×#11926277C211yesmaximal, characteristic
5#14561514C211yesmaximal, characteristic, complemented
6#14561478C211yesmaximal, characteristic, complemented
7C19×#1442C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9C2×C4×C22⋊D19—21no—
10C2×#10597264—21no—
11C2×#10597266—21no—
12C2×C22⋊(C19⋊C8)C2211yescharacteristic
13C2×C22⋊(C19⋊C8)C2211yescharacteristic
14#11926436—21no—
15#11926429—21no—
16#11926423—21no—
17#11926422—21no—
18#11926418—21no—
19#11926404C2211yescharacteristic
20#11926306—21no—
21#11926306—21no—
22#11926277C414yescomplemented
23C22×C4⋊C4×C19C2211yescharacteristic
24C2×C19×#95—21no—
25C2×C19×#95—21no—
26C2×C19×#95C2211yescharacteristic
27C2×C19×#95C2211yescharacteristic
28C23×C4×C19—21no—
29C23×C4×C19—21no—
30C23×C4×C19D411yescharacteristic
31C23×C4×C19D411yescharacteristic
32C23×C4×C19C2311yescharacteristic
33C22×C22⋊D19—21no—
34C22×D76D411yescharacteristic
35C22×C4×D19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19—42no—
39C2×C22⋊Dic19—21no—
40#10597376—21no—
41#10597376—21no—
42#10597376C2×C412yes—
43#10597376Q812yes—
44C4×C22⋊D19—42no—
45C4×C22⋊D19—42no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4—21no—
49C2×(C2×D19)⋊C4—21no—
50C2×C4⋊Dic19D411yescharacteristic
51C2×C4⋊Dic19D411yescharacteristic
52C2×C4⋊Dic19D411yescharacteristic
53C2×Dic19⋊C4—21no—
54C2×C4×Dic19—21no—
55C22×C19⋊C8—21no—
56C22×C19⋊C8—21no—
57C19×#95—21no—
58C19×#95—21no—
59C19×#95—21no—
60C19×#95—42no—
61C19×#95—42no—
62C19×#95C2×C412yescomplemented
63C19⋊#95—21no—
64C19⋊#95—21no—
65C19⋊#95—21no—
66C22⋊(C19⋊C8)—21no—
67C22⋊(C19⋊C8)—21no—
68C22⋊(C19⋊C8)—21no—
69C22⋊(C19⋊C8)C2×C412yescomplemented
70#10597266—42no—
71#10597264—42no—
72C24×C19C2×D411yescharacteristic
73C23×D19—21no—
74C22×C4×C19—21no—
75C22×C4×C19—21no—
76C22×C4×C19—22no—
77C22×C4×C19—22no—
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—41no—
82C22×C4×C19—41no—
83C22×C4×C19—41no—
84C22×C4×C19—41no—
85C22×C4×C19—41no—
86C22×C4×C19—41no—
87C22×C4×C19—41no—
88C22×C4×C19—41no—
89C22×C4×C19—41no—
90C22×C4×C19—41no—
91C22×C4×C19—41no—
92C22×C4×C19—41no—
93C22×C4×C19—41no—
94C22×C4×C19—41no—
95C22×C4×C19—41no—
96C22×C4×C19—41no—
97C22×C4×C19—41no—
98C22×C4×C19—41no—
99C22×C4×C19D812yes—
100C22×C4×C19C22×C411yescharacteristic
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19C2×Q811yescharacteristic
104C22×C4×C19#4111yescharacteristic
105C22×C4×C19#4111yescharacteristic
106C2×C22⋊D19—22no—
107C2×C22⋊D19—22no—
108C2×C22⋊D19—41no—
109C2×C22⋊D19—41no—
110C2×C22⋊D19—41no—
111C2×C22⋊D19—41no—
112C22×Dic19—21no—
113C22×Dic19—21no—
114C22×Dic19—21no—
115C2×D76—21no—
116C2×D76—41no—
117C2×D76—41no—
118C2×D76C4⋊C412yes—
119C2×C4×D19—42no—
120C2×C4×D19—81no—
121C2×C4×D19—81no—
122C4⋊C4×C19—22no—
123C4⋊C4×C19—22no—
124C4⋊C4×C19—41no—
125C4⋊C4×C19—41no—
126C22⋊Dic19—41no—
127C22⋊Dic19—41no—
128(C2×D19)⋊C4—22no—
129(C2×D19)⋊C4—22no—
130(C2×D19)⋊C4—42no—
131(C2×D19)⋊C4—81no—
132(C2×D19)⋊C4—81no—
133C4⋊Dic19—21no—
134C4⋊Dic19—41no—
135C4⋊Dic19—41no—
136C4⋊Dic19C4⋊C412yes—
137Dic19⋊C4—42no—
138C4×Dic19—42no—
139C2×C19⋊C8—22no—
140C2×C19⋊C8—41no—
141C2×C19⋊C8—41no—
142C2×C19⋊C8—41no—
143C2×C19⋊C8—41no—
144C2×C19⋊C8—41no—
145#8869—191nomaximal, Sylow
146C23×C19—21no—
147C23×C19—21no—
148C23×C19—21no—
149C23×C19—21no—
150C23×C19C4×D411yescharacteristic
151C23×C19#12011yescharacteristic
152C23×C19C22⋊Q811yescharacteristic
153C23×C19C2×D811yescharacteristic
154C23×C19#13511yescharacteristic
155C23×C19AGL(1,ℤ/8)11yescharacteristic
156C23×C19#13711yescharacteristic
157C22×D19—22no—
158C22×D19—41no—
159C22×D19—41no—
160C22×D19—41no—
161C22×D19—41no—
162C22×D19—41no—
163C22×D19—41no—
164C2×C4×C19—21no—
165C2×C4×C19—21no—
166C2×C4×C19—21no—
167C2×C4×C19—21no—
168C2×C4×C19—22no—
169C2×C4×C19—41no—
170C2×C4×C19—41no—
171C2×C4×C19—41no—
172C2×C4×C19—41no—
173C2×C4×C19—41no—
174C2×C4×C19—41no—
175C2×C4×C19—42no—
176C2×C4×C19—42no—
177C2×C4×C19—42no—
178C2×C4×C19—42no—
179C2×C4×C19—42no—
180C2×C4×C19—42no—
181C2×C4×C19—42no—
182C2×C4×C19—41no—
183C2×C4×C19—41no—
184C2×C4×C19—41no—
185C2×C4×C19—42no—
186C2×C4×C19—81no—
187C2×C4×C19—81no—
188C2×C4×C19—81no—
189C2×C4×C19—81no—
190C2×C4×C19—81no—
191C2×C4×C19—81no—
192C2×C4×C19—81no—
193C2×C4×C19—81no—
194C2×C4×C19—81no—
195C2×C4×C19—81no—
196C2×C4×C19C2×C4⋊C411yescharacteristic
197C2×C4×C19C4×D411yescharacteristic
198C2×C4×C19C22⋊Q811yescharacteristic
199C2×C4×C19#12311yescharacteristic
200C22⋊D19—42no—
201C22⋊D19—42no—
202C22⋊D19—42no—
203C22⋊D19—42no—
204C2×Dic19—22no—
205C2×Dic19—41no—
206C2×Dic19—41no—
207C2×Dic19—41no—
208C2×Dic19—41no—
209C2×Dic19—41no—
210C2×Dic19—41no—
211C2×Dic19—41no—
212C2×Dic19—41no—
213D76—42no—
214D76—81no—
215C4×D19—84no—
216C19⋊C8—42no—
217C19⋊C8—81no—
218#2325—191no—
219#1874—191no—
220#1852—191no—
221C2×#327—191no—
222#1442D1911yescharacteristic, complemented
223#1294—191no—
224#1280—191no—
225C22×C19—21no—
226C22×C19—21no—
227C22×C19—21no—
228C22×C19—21no—
229C22×C19—21no—
230C22×C19—21no—
231C22×C19—21no—
232C22×C19—21no—
233C22×C19—21no—
234C22×C19—21no—
235C22×C19—21no—
236C22×C19—21no—
237C22×C19#38511yescharacteristic
238C22×C19C4×D811yescharacteristic
239C22×C19#44011yescharacteristic
240C22×C19#44711yescharacteristic
241C22×C19#45211yescharacteristic
242C22×C19#45411yescharacteristic
243C22×C19#45511yescharacteristic
244C22×C19B(4,𝔽2)11yescharacteristic
245C22×C19#45811yescharacteristic
246C22×C19#47411yescharacteristic
247C22×C19#47811yescharacteristic
248C2×D19—42no—
249C2×D19—42no—
250C2×D19—42no—
251C2×D19—81no—
252C2×D19—81no—
253C2×D19—81no—
254C2×D19—81no—
255C4×C19—21no—
256C4×C19—21no—
257C4×C19—21no—
258C4×C19—21no—
259C4×C19—42no—
260C4×C19—82no—
261C4×C19—82no—
262C4×C19—81no—
263Dic19—42no—
264Dic19—81no—
265Dic19—81no—
266C2×#121—191no—
267C2×C4×D4—381no—
268C22×C4⋊C4C2×D1911yescharacteristic
269C2×#107—381no—
270C2×#102—381no—
271C2×C22⋊C8—191no—
272C2×C22⋊C8—191no—
273#388—381no—
274#387—381no—
275#386—381no—
276#386—381no—
277#385—381no—
278#380—191no—
279C2×#95—21no—
280C2×#95—21no—
281C2×#95C2×D1911yescharacteristic
282C2×#95C2×D1911yescharacteristic
283#340—381no—
284#340—381no—
285#327—194no—
286C2×C19—21no—
287C2×C19—21no—
288C2×C19—21no—
289C2×C19—21no—
290C2×C19#159811yescharacteristic
291C2×C19#160611yescharacteristic
292C2×C19#160711yescharacteristic
293C2×C19#161511yescharacteristic
294C2×C19#186011yescharacteristic
295C2×C19#186211yescharacteristic
296C2×C19#186711yescharacteristic
297D19—82no—
298C22×D4—191no—
299C22×D4—381no—
300C23×C4—21no—
301C23×C4—21no—
302C23×C4—381no—
303C23×C4C22⋊D1911yescharacteristic
304C23×C4C22⋊D1911yescharacteristic
305C23×C4C22×D1911yescharacteristic
306C22×C8—381no—
307C22×C8—381no—
308#121—192no—
309#121—192no—
310#121—381no—
311#121—381no—
312C4×D4—762no—
313C4×D4—762no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—191no—
318C2×C4⋊C4—191no—
319C2×C4⋊C4—191no—
320C2×C4⋊C4—381no—
321C2×C22⋊C4—381no—
322C2×C22⋊C4—381no—
323C2×C22⋊C4—381no—
324C2×C22⋊C4—381no—
325C2×C22⋊C4—381no—
326C2×C42—381no—
327#107—762no—
328#102—762no—
329C22⋊C8—192no—
330C22⋊C8—381no—
331C22⋊C8—381no—
332C22⋊C8—381no—
333#95—21no—
334#95—21no—
335#95—21no—
336#95—42no—
337#95—42no—
338#95—381no—
339#95—381no—
340#95—381no—
341#95C4×D1912yescomplemented
342C19#886911yescharacteristic, complemented, Sylow
343C24—381no—
344C24C2×C22⋊D1911yescharacteristic
345C2×D4—192no—
346C2×D4—382no—
347C2×D4—382no—
348C2×D4—381no—
349C2×D4—761no—
350C2×D4—761no—
351C2×D4—761no—
352C2×D4—761no—
353C2×D4—761no—
354C2×D4—761no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—381no—
381C22×C4—381no—
382C22×C4—381no—
383C22×C4—762no—
384C22×C4—1521no—
385C22×C4—1521no—
386C22×C4#6452512yes—
387C22×C4C2×C4×D1911yescharacteristic
388C22×C4#6454111yescharacteristic
389C22×C4D4×D1911yescharacteristic
390C22×C4D4×D1911yescharacteristic
391C22×C4Q8×D1911yescharacteristic
392C22×C4#6454511yescharacteristic
393C2×C8—382no—
394C2×C8—761no—
395C2×C8—761no—
396C2×C8—761no—
397C2×C8—761no—
398C2×C8—761no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4—192no—
404C4⋊C4—381no—
405C4⋊C4—761no—
406C4⋊C4—761no—
407C4⋊C4—762no—
408C22⋊C4—382no—
409C22⋊C4—382no—
410C22⋊C4—762no—
411C22⋊C4—761no—
412C22⋊C4—761no—
413C22⋊C4—1521no—
414C22⋊C4—1521no—
415C42—762no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—382no—
421C23—761no—
422C23—761no—
423C23—761no—
424C23—761no—
425C23—761no—
426C23—761no—
427C23C4×C22⋊D1911yescharacteristic
428C23C2×#6452511yescharacteristic
429C23#1059738311yescharacteristic
430C23#1059738811yescharacteristic
431C23#1059739211yescharacteristic
432C23#1059739511yescharacteristic
433C23#1059739611yescharacteristic
434D4—762no—
435D4—762no—
436D4—762no—
437D4—762no—
438D4—762no—
439D4—1521no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—81no—
463C2×C4—81no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4—81no—
469C2×C4—81no—
470C2×C4—81no—
471C2×C4—81no—
472C2×C4—382no—
473C2×C4—761no—
474C2×C4—761no—
475C2×C4—761no—
476C2×C4—761no—
477C2×C4—761no—
478C2×C4—761no—
479C2×C4—761no—
480C2×C4—761no—
481C2×C4—1524no—
482C2×C4C4⋊C4×D1911yescharacteristic
483C2×C4#1059733911yescharacteristic
484C2×C4#1059734011yescharacteristic
485C2×C4#1059734211yescharacteristic
486C8—762no—
487C8—1521no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—762no—
501C22—762no—
502C22—762no—
503C22—1521no—
504C22—1521no—
505C22—1521no—
506C22—1521no—
507C22#1192641511yescharacteristic
508C22C4×#6452511yescharacteristic
509C22#1192664211yescharacteristic
510C22#1192667711yescharacteristic
511C22#1192670411yescharacteristic
512C22#1192671611yescharacteristic
513C22#1192672111yescharacteristic
514C22#1192673011yescharacteristic
515C22#1192673311yescharacteristic
516C22#1192682111yescharacteristic
517C22#1192684111yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—82no—
524C4—82no—
525C4—81no—
526C4—762no—
527C4—1521no—
528C4—1521no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—21no—
533C2—1522no—
534C2#1456256911yescharacteristic
535C2#1456261311yescharacteristic
536C2#1456262011yescharacteristic
537C2#1456266411yescharacteristic
538C2#1456386711yescharacteristic
539C2#1456388111yescharacteristic
540C2#1456391411yescharacteristic
subgroupG/H
centerC23#10597383
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1442C2
socleC23×C19#120
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1442D19
hypocenterC19#8869
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1442

Complements

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

NH ≅ G/Ntype
3. #14563823C2semidirect
5. #14561514C2semidirect
6. #14561478C2semidirect
7. C19×#1442C2semidirect
22. #11926277C4semidirect
62. C19×#95C2×C4semidirect
69. C22⋊(C19⋊C8)C2×C4semidirect
222. #1442D19semidirect
341. #95C4×D19semidirect
342. C19#8869semidirect

Maximal subgroups

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

subgroupindex
#145663382
#145639522
#145638232
C2×#119262772
#145615142
#145614782
C19×#14422
#886919