Finite Group Databasebeta

← #18075020

Subgroups — #18075020

Order 4864.

724 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564593C211yesmaximal, characteristic, complemented
2#14564555C211yesmaximal, characteristic, complemented
3#14562330C211yesmaximal, characteristic, complemented
4#14562237C211yesmaximal, characteristic, complemented
5#14562160C211yesmaximal, characteristic, complemented
6#14562048C211yesmaximal, characteristic, complemented
7C19×#3559C211yesmaximal, characteristic
8#11926601C2211yescharacteristic
9C2×C4⋊(C19⋊C8)C2211yescharacteristic
10C2×#10597294—22no—
11C4×#64520C2211yescharacteristic
12C4×C4⋊Dic19C2211yescharacteristic
13#11926306—21no—
14#11926306—21no—
15#11926293—21no—
16#11926288—21no—
17#11926286—22no—
18#11926281—21no—
19#11926278—21no—
20Q8⋊(C19⋊C8)—21no—
21D4⋊(C19⋊C8)—21no—
22C19×#563C412yescomplemented
23C19×#562C412yescomplemented
24C19×#554—21no—
25C19×#553—21no—
26C19×#553—21no—
27C19×#547—22no—
28C19×#547—21no—
29C19×#544—21no—
30C19×#540—21no—
31C19×#539—22no—
32C19×#539—21no—
33C19×#537—21no—
34C19×#532C2211yescharacteristic
35C19×#529C2211yescharacteristic
36C2×C19×#125C2211yescharacteristic
37C2×#41×C19—22no—
38C2×#41×C19D412yes—
39C19×C4⋊Q8—21no—
40C19×C4⋊Q8—22no—
41C19×C4⋊Q8D411yescharacteristic
42C19×#127D411yescharacteristic
43C19×#126—22no—
44C19×#126—22no—
45C19×#126—21no—
46C19×#125—22no—
47C19×#125—21no—
48C19×#125—21no—
49C19×#125—21no—
50C19×#125C2×C412yes—
51C19×#125C2×C411yescharacteristic
52C19×#125D412yes—
53C19×#124C2×C411yescharacteristic
54C19×#124C2×C412yes—
55C19×#123—22no—
56C19×#123—22no—
57C19×#123—22no—
58C19×#123—22no—
59C19×#123—21no—
60C19×#123—22no—
61C19×#123—22no—
62C19×C22⋊Q8—22no—
63C19×C22⋊Q8—22no—
64C19×C22⋊Q8—22no—
65C19×C22⋊Q8—22no—
66C19×C22⋊Q8—22no—
67C19×C22⋊Q8—22no—
68C19×C22⋊Q8D411yescharacteristic
69C19×#121—22no—
70C19×#121—22no—
71C19×#121—21no—
72C19×#121—21no—
73C19×#121—22no—
74C19×#121—22no—
75C19×#121—21no—
76C19×#121—21no—
77C19×#121D411yescharacteristic
78C4×Q8×C19D411yescharacteristic
79C4×D4×C19—22no—
80C4×D4×C19—22no—
81C4×D4×C19—21no—
82C4×D4×C19—21no—
83C4×D4×C19—21no—
84C4×D4×C19—21no—
85C4×D4×C19—21no—
86C4×D4×C19D411yescharacteristic
87C19×#117—21no—
88C19×#117—21no—
89C2×C4⋊C4×C19—22no—
90C2×C4⋊C4×C19—21no—
91C2×C4⋊C4×C19—21no—
92C2×C4⋊C4×C19—21no—
93C2×C4⋊C4×C19D411yescharacteristic
94C2×C4⋊C4×C19D411yescharacteristic
95C2×C42×C19C2311yescharacteristic
96C2×C4⋊Dic19—21no—
97C2×C4×Dic19—21no—
98C2×#64520—21no—
99C22×C19⋊C8—21no—
100#10597294—44no—
101C19⋊#95—21no—
102C22⋊(C19⋊C8)—21no—
103C4⋊(C19⋊C8)—21no—
104C4⋊(C19⋊C8)—21no—
105C4⋊(C19⋊C8)—21no—
106#10597260—21no—
107#10597260—21no—
108C4×C19⋊C8—21no—
109#41×C19—42no—
110#41×C19—42no—
111#41×C19—82no—
112#41×C19—82no—
113C2×Q8×C19—22no—
114C2×Q8×C19C22⋊C411yescharacteristic
115C2×Q8×C19C22⋊C412yes—
116C2×D4×C19—22no—
117C2×D4×C19—21no—
118C2×D4×C19—22no—
119C2×D4×C19—22no—
120C2×D4×C19—21no—
121C2×D4×C19—21no—
122C2×D4×C19C22⋊C411yescharacteristic
123C2×D4×C19C22⋊C412yes—
124C22×C4×C19—21no—
125C22×C4×C19—22no—
126C22×C4×C19—22no—
127C22×C4×C19—22no—
128C22×C4×C19—21no—
129C22×C4×C19—21no—
130C22×C4×C19—22no—
131C22×C4×C19C2×D411yescharacteristic
132C22×C4×C19C2×D411yescharacteristic
133C22×C4×C19C2×D411yescharacteristic
134C22×Dic19—41no—
135C4⋊C4×C19—22no—
136C4⋊C4×C19—22no—
137C4⋊C4×C19—22no—
138C4⋊C4×C19—22no—
139C4⋊C4×C19—22no—
140C4⋊C4×C19—22no—
141C4⋊C4×C19—21no—
142C4⋊C4×C19—21no—
143C4⋊C4×C19—22no—
144C4⋊C4×C19—21no—
145C4⋊C4×C19—21no—
146C4⋊C4×C19—21no—
147C4⋊C4×C19—22no—
148C4⋊C4×C19—21no—
149C4⋊C4×C19—21no—
150C4⋊C4×C19—21no—
151C4⋊C4×C19C22⋊C412yes—
152C4⋊C4×C19C22⋊C412yes—
153C4⋊C4×C19C22⋊C411yescharacteristic
154C4⋊C4×C19C22⋊C411yescharacteristic
155C22⋊C4×C19—22no—
156C22⋊C4×C19—22no—
157C22⋊C4×C19—22no—
158C22⋊C4×C19—22no—
159C22⋊C4×C19—22no—
160C22⋊C4×C19—21no—
161C22⋊C4×C19—21no—
162C22⋊C4×C19—22no—
163C22⋊C4×C19—22no—
164C22⋊C4×C19—21no—
165C22⋊C4×C19—21no—
166C22⋊C4×C19—21no—
167C42×C19—22no—
168C42×C19—21no—
169C42×C19C22×C411yescharacteristic
170C42×C19C2×D411yescharacteristic
171C42×C19C2×D411yescharacteristic
172C42×C19C2×D411yescharacteristic
173C4⋊Dic19—22no—
174C4⋊Dic19—41no—
175C4×Dic19—42no—
176#64520—22no—
177#64520—41no—
178C2×C19⋊C8—41no—
179C2×C19⋊C8—42no—
180C2×C19⋊C8—41no—
181C2×C19⋊C8—41no—
182#8513—191nomaximal, Sylow
183C23×C19—22no—
184C23×C19—21no—
185C23×C19#12011yescharacteristic
186Q8×C19—41no—
187Q8×C19—42no—
188Q8×C19—82no—
189D4×C19—41no—
190D4×C19—42no—
191D4×C19—42no—
192D4×C19—41no—
193D4×C19—42no—
194D4×C19—41no—
195D4×C19—41no—
196D4×C19—41no—
197D4×C19—81no—
198D4×C19—82no—
199D4×C19—82no—
200C2×C4×C19—21no—
201C2×C4×C19—21no—
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—21no—
209C2×C4×C19—22no—
210C2×C4×C19—41no—
211C2×C4×C19—41no—
212C2×C4×C19—41no—
213C2×C4×C19—41no—
214C2×C4×C19—41no—
215C2×C4×C19—82no—
216C2×C4×C19—81no—
217C2×C4×C19—82no—
218C2×C4×C19—82no—
219C2×C4×C19—82no—
220C2×C4×C19C2×C22⋊C411yescharacteristic
221C2×C4×C19C2×C22⋊C411yescharacteristic
222C2×C4×C19C2×C22⋊C411yescharacteristic
223C2×C4×C19#12011yescharacteristic
224C2×C4×C19#12011yescharacteristic
225C2×C4×C19#12011yescharacteristic
226C2×Dic19—42no—
227C2×Dic19—81no—
228C2×Dic19—81no—
229C19⋊C8—42no—
230C19⋊C8—81no—
231C19⋊C8—81no—
232#3559D1911yescharacteristic
233#1989—191no—
234#1980—191no—
235#1551—191no—
236#1528—191no—
237#1509—191no—
238#1483—191no—
239C22×C19—21no—
240C22×C19—21no—
241C22×C19—42no—
242C22×C19—41no—
243C22×C19—41no—
244C22×C19—42no—
245C22×C19—42no—
246C22×C19—41no—
247C22×C19#37911yescharacteristic
248C22×C19#45311yescharacteristic
249C22×C19#45511yescharacteristic
250C4×C19—21no—
251C4×C19—21no—
252C4×C19—21no—
253C4×C19—21no—
254C4×C19—21no—
255C4×C19—42no—
256C4×C19—42no—
257C4×C19—41no—
258C4×C19—41no—
259C4×C19—42no—
260C4×C19—41no—
261C4×C19#45411yescharacteristic
262C4×C19#45611yescharacteristic
263Dic19—82no—
264#563Dic1912yescomplemented
265#562Dic1912yescomplemented
266#554—21no—
267#553—21no—
268#553—21no—
269#547—22no—
270#547—21no—
271#544—21no—
272#540—21no—
273#539—22no—
274#539—21no—
275#537—21no—
276#532C2×D1911yescharacteristic
277#529C2×D1911yescharacteristic
278C2×#125C2×D1911yescharacteristic
279#432—191no—
280C2×C4⋊C8—191no—
281C2×#104—382no—
282C4×M16—191no—
283C4×C4⋊C4—191no—
284#340—381no—
285#340—381no—
286#333—381no—
287#331—381no—
288#330—382no—
289#328—381no—
290#327—381no—
291Q8⋊C8—381no—
292D4⋊C8—381no—
293C2×C19—21no—
294C2×C19—21no—
295C2×C19—82no—
296C2×C19—81no—
297C2×C19#179211yescharacteristic
298C2×C19#179311yescharacteristic
299C2×C19#179411yescharacteristic
300C2×#41—22no—
301C2×#41C22⋊D1912yes—
302C2×M16—381no—
303C22×C8—381no—
304C4⋊Q8—21no—
305C4⋊Q8—22no—
306C4⋊Q8C22⋊D1911yescharacteristic
307#127C22⋊D1911yescharacteristic
308#126—22no—
309#126—22no—
310#126—21no—
311#125—22no—
312#125—21no—
313#125—21no—
314#125—21no—
315#125C2×Dic1912yes—
316#125C2×Dic1911yescharacteristic
317#125C22⋊D1912yes—
318#124C2×Dic1911yescharacteristic
319#124C2×Dic1912yes—
320#123—22no—
321#123—22no—
322#123—22no—
323#123—22no—
324#123—21no—
325#123—22no—
326#123—22no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8C22⋊D1911yescharacteristic
334#121—22no—
335#121—22no—
336#121—21no—
337#121—21no—
338#121—22no—
339#121—22no—
340#121—21no—
341#121—21no—
342#121C22⋊D1911yescharacteristic
343C4×Q8C22⋊D1911yescharacteristic
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—21no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4C22⋊D1911yescharacteristic
352#117—21no—
353#117—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—381no—
359C2×C4⋊C4C22⋊D1911yescharacteristic
360C2×C4⋊C4C22⋊D1911yescharacteristic
361C2×C42—381no—
362C2×C42C22×D1911yescharacteristic
363C4⋊C8—381no—
364C4⋊C8—381no—
365C4⋊C8—381no—
366#104—764no—
367C22⋊C8—381no—
368#97—381no—
369#97—381no—
370C4×C8—381no—
371#95—381no—
372C19#851311yescharacteristic, complemented, Sylow
373#41—42no—
374#41—42no—
375#41—82no—
376#41—82no—
377C2×Q8—22no—
378C2×Q8C22⋊Dic1911yescharacteristic
379C2×Q8C22⋊Dic1912yes—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4C22⋊Dic1911yescharacteristic
387C2×D4C22⋊Dic1912yes—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—761no—
396C22×C4C2×C22⋊D1911yescharacteristic
397C22×C4C2×C22⋊D1911yescharacteristic
398C22×C4C2×C22⋊D1911yescharacteristic
399M16—382no—
400M16—761no—
401C2×C8—761no—
402C2×C8—762no—
403C2×C8—761no—
404C2×C8—761no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—382no—
422C4⋊C4—761no—
423C4⋊C4C22⋊Dic1912yes—
424C4⋊C4C22⋊Dic1912yes—
425C4⋊C4C22⋊Dic1911yescharacteristic
426C4⋊C4C22⋊Dic1911yescharacteristic
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—21no—
437C22⋊C4—21no—
438C22⋊C4—21no—
439C42—22no—
440C42—21no—
441C42—762no—
442C42C22×Dic1911yescharacteristic
443C42C2×C22⋊D1911yescharacteristic
444C42C2×C22⋊D1911yescharacteristic
445C42C2×C22⋊D1911yescharacteristic
446C23—22no—
447C23—21no—
448C23#1059739911yescharacteristic
449Q8—42no—
450Q8—41no—
451Q8—82no—
452D4—42no—
453D4—41no—
454D4—42no—
455D4—41no—
456D4—42no—
457D4—41no—
458D4—41no—
459D4—41no—
460D4—81no—
461D4—82no—
462D4—82no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—82no—
479C2×C4—81no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4—82no—
483C2×C4—762no—
484C2×C4—1521no—
485C2×C4—1521no—
486C2×C4C2×C22⋊Dic1911yescharacteristic
487C2×C4C2×C22⋊Dic1911yescharacteristic
488C2×C4C2×C22⋊Dic1911yescharacteristic
489C2×C4#1059739911yescharacteristic
490C2×C4#1059739911yescharacteristic
491C2×C4#1059739911yescharacteristic
492C8—762no—
493C8—1521no—
494C8—1521no—
495C22—21no—
496C22—21no—
497C22—42no—
498C22—41no—
499C22—41no—
500C22—42no—
501C22—42no—
502C22—41no—
503C22#1192640011yescharacteristic
504C22#1192671211yescharacteristic
505C22#1192672211yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—21no—
511C4—42no—
512C4—42no—
513C4—41no—
514C4—41no—
515C4—42no—
516C4—41no—
517C4—1522no—
518C4#1192671711yescharacteristic
519C4#1192672711yescharacteristic
520C2—21no—
521C2—21no—
522C2—82no—
523C2—81no—
524C2#1456358911yescharacteristic
525C2#1456359411yescharacteristic
526C2#1456359911yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3559C2
socleC22×C19#379
cosocleC2×C42×C19C23
hypercenter#3559D19
hypocenterC19#8513
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3559

Complements

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

NH ≅ G/Ntype
1. #14564593C2semidirect
2. #14564555C2semidirect
3. #14562330C2semidirect
4. #14562237C2semidirect
5. #14562160C2semidirect
6. #14562048C2semidirect
22. C19×#563C4semidirect
23. C19×#562C4semidirect
264. #563Dic19semidirect
265. #562Dic19semidirect
372. C19#8513semidirect

Maximal subgroups

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

subgroupindex
#145645932
#145645552
#145623302
#145622372
#145621602
#145620482
C19×#35592
#851319