Finite Group Databasebeta

← #18079023

Subgroups — #18079023

Order 4864.

504 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572691C211yesmaximal, characteristic, complemented
2#14562139C211yesmaximal, characteristic, complemented
3C2×#11926278C211yesmaximal, characteristic, complemented
4#14561995C211yesmaximal, characteristic, complemented
5#14561523C211yesmaximal, characteristic, complemented
6#14561477C211yesmaximal, characteristic, complemented
7C19×#3188C211yesmaximal, characteristic
8#11926616—21no—
9#11926616—21no—
10D4×C19⋊C8—21no—
11D4×C19⋊C8—21no—
12#11926605—21no—
13#11926511—21no—
14#11926508C2211yescharacteristic
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16C2×C22⋊(C19⋊C8)C2211yescharacteristic
17C2×C19⋊#95C2211yescharacteristic
18#11926281—21no—
19#11926278—21no—
20#11926278—21no—
21#11926278—21no—
22#11926268—21no—
23#11926268—21no—
24C19×#525C2211yescharacteristic
25C2×C19×#121C2211yescharacteristic
26C19×#484C411yescharacteristic, complemented
27C19×#482—21no—
28C19×#481C411yescharacteristic, complemented
29C19×#466—21no—
30C19×#465—21no—
31C19×#450C411yescharacteristic, complemented
32C19×#449—21no—
33C19×#447C411yescharacteristic, complemented
34C2×C19×C22⋊C8C2211yescharacteristic
35C2×#41×C19D411yescharacteristic
36C22×D4×C19—21no—
37C22×D4×C19C2×C411yescharacteristic
38C23×C4×C19C2311yescharacteristic
39C23×Dic19—21no—
40C2×SD16×C19—21no—
41C2×D8×C19—21no—
42C22×C8×C19—21no—
43C19×#123—21no—
44C19×C22⋊Q8C2×C411yescharacteristic
45C19×C22⋊Q8D411yescharacteristic
46C19×#121—21no—
47C19×#121—21no—
48C19×#121—21no—
49C19×#121—21no—
50C19×#121C2×C411yescharacteristic
51C19×#121D411yescharacteristic
52C19×#120—21no—
53C4×D4×C19—21no—
54C4×D4×C19—21no—
55C19×#117D411yescharacteristic
56C2×C4⋊C4×C19C2×C411yescharacteristic
57C2×C22⋊C4×C19—21no—
58C2×#64520—21no—
59C2×#64520—21no—
60C22×C19⋊C8—21no—
61C22×C19⋊C8—21no—
62C22×C19⋊C8—21no—
63C19×#107—21no—
64C19×#106—21no—
65C19×#103—21no—
66C19×#102—21no—
67C19×#102—21no—
68C19×#102—21no—
69C19×C22⋊C8—21no—
70C19×C22⋊C8C2×C411yescharacteristic
71C19×C22⋊C8C2×C411yescharacteristic
72C19⋊#95—21no—
73C19⋊#95—21no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)—21no—
77C22⋊(C19⋊C8)—21no—
78C22⋊(C19⋊C8)—21no—
79C22⋊(C19⋊C8)—21no—
80C22⋊(C19⋊C8)D411yescharacteristic
81C22⋊(C19⋊C8)D411yescharacteristic
82C22⋊(C19⋊C8)D411yescharacteristic
83C22⋊(C19⋊C8)D411yescharacteristic
84C4⋊(C19⋊C8)—21no—
85C4⋊(C19⋊C8)—21no—
86#10597260—21no—
87C4×C19⋊C8—21no—
88C24×C19—21no—
89C24×C19#4111yescharacteristic
90#41×C19—81no—
91C2×Q8×C19C22⋊C411yescharacteristic
92C2×D4×C19—21no—
93C2×D4×C19—21no—
94C2×D4×C19—21no—
95C2×D4×C19—21no—
96C2×D4×C19—21no—
97C2×D4×C19—41no—
98C2×D4×C19—41no—
99C2×D4×C19—81no—
100C2×D4×C19—81no—
101C2×D4×C19—81no—
102C2×D4×C19C22⋊C411yescharacteristic
103C22×C4×C19—21no—
104C22×C4×C19—21no—
105C22×C4×C19—81no—
106C22×C4×C19C22×C411yescharacteristic
107C22×C4×C19C2×D411yescharacteristic
108C22×C4×C19C2×D411yescharacteristic
109C22×C4×C19C2×D411yescharacteristic
110C22×C4×C19C2×D411yescharacteristic
111C22×C4×C19#4111yescharacteristic
112C22×Dic19—22no—
113C22×Dic19—41no—
114C22×Dic19—41no—
115C22×Dic19—81no—
116C22×Dic19—81no—
117SD16×C19—81no—
118D8×C19—81no—
119C2×C8×C19—21no—
120C2×C8×C19—21no—
121C2×C8×C19—81no—
122C4⋊C4×C19—21no—
123C4⋊C4×C19—21no—
124C4⋊C4×C19—21no—
125C4⋊C4×C19—21no—
126C4⋊C4×C19C22⋊C411yescharacteristic
127C4⋊C4×C19C22⋊C411yescharacteristic
128C22⋊C4×C19—21no—
129C22⋊C4×C19—21no—
130C22⋊C4×C19—21no—
131C22⋊C4×C19—21no—
132C22⋊C4×C19—21no—
133C22⋊C4×C19—41no—
134C22⋊C4×C19—41no—
135C42×C19—21no—
136#64520—81no—
137#64520—81no—
138C2×C19⋊C8—21no—
139C2×C19⋊C8—21no—
140C2×C19⋊C8—21no—
141C2×C19⋊C8—21no—
142C2×C19⋊C8—41no—
143C2×C19⋊C8—81no—
144C2×C19⋊C8—81no—
145C2×C19⋊C8—81no—
146#9264—191nomaximal, Sylow
147C23×C19—21no—
148C23×C19—21no—
149C23×C19—21no—
150C23×C19—21no—
151C23×C19—21no—
152C23×C19—41no—
153C23×C19—41no—
154C23×C19—41no—
155C23×C19—41no—
156C23×C19—81no—
157C23×C19—81no—
158C23×C19C4×D411yescharacteristic
159C23×C19#12111yescharacteristic
160C23×C19#12311yescharacteristic
161Q8×C19—41no—
162D4×C19—41no—
163D4×C19—41no—
164D4×C19—41no—
165D4×C19—41no—
166D4×C19—41no—
167D4×C19—41no—
168D4×C19—41no—
169D4×C19—81no—
170D4×C19—81no—
171D4×C19—82no—
172D4×C19—81no—
173D4×C19—81no—
174C2×C4×C19—21no—
175C2×C4×C19—21no—
176C2×C4×C19—21no—
177C2×C4×C19—41no—
178C2×C4×C19—41no—
179C2×C4×C19—41no—
180C2×C4×C19—41no—
181C2×C4×C19—41no—
182C2×C4×C19—41no—
183C2×C4×C19—41no—
184C2×C4×C19—41no—
185C2×C4×C19—41no—
186C2×C4×C19—81no—
187C2×C4×C19C2×C22⋊C411yescharacteristic
188C2×C4×C19C4×D411yescharacteristic
189C2×C4×C19#12011yescharacteristic
190C2×C4×C19#12111yescharacteristic
191C2×Dic19—42no—
192C2×Dic19—81no—
193C2×Dic19—82no—
194C2×Dic19—81no—
195C2×Dic19—82no—
196C8×C19—41no—
197C8×C19—41no—
198C19⋊C8—41no—
199C19⋊C8—41no—
200C19⋊C8—41no—
201C19⋊C8—41no—
202C19⋊C8—81no—
203#3188D1911yescharacteristic
204#2977—191no—
205#1504—191no—
206C2×#327—191no—
207#1471—191no—
208#1298—191no—
209#1280—191no—
210C22×C19—21no—
211C22×C19—21no—
212C22×C19—21no—
213C22×C19—21no—
214C22×C19—21no—
215C22×C19—21no—
216C22×C19—21no—
217C22×C19—41no—
218C22×C19—41no—
219C22×C19—41no—
220C22×C19—41no—
221C22×C19—41no—
222C22×C19—41no—
223C22×C19—41no—
224C22×C19—81no—
225C22×C19—81no—
226C22×C19—81no—
227C22×C19—161no—
228C22×C19—161no—
229C22×C19#38611yescharacteristic
230C22×C19#44311yescharacteristic
231C22×C19#44411yescharacteristic
232C22×C19#47111yescharacteristic
233C22×C19#47211yescharacteristic
234C4×C19—21no—
235C4×C19—21no—
236C4×C19—21no—
237C4×C19—21no—
238C4×C19—41no—
239C4×C19—41no—
240C4×C19—41no—
241C4×C19—81no—
242Dic19—82no—
243#525C2×D1911yescharacteristic
244C2×#121C2×D1911yescharacteristic
245#484Dic1911yescharacteristic, complemented
246#482—21no—
247#481Dic1911yescharacteristic, complemented
248#466—21no—
249#465—21no—
250#450Dic1911yescharacteristic, complemented
251#449—21no—
252#447Dic1911yescharacteristic, complemented
253#435—381no—
254#435—381no—
255C8×D4—381no—
256C8×D4—381no—
257#433—381no—
258#408—381no—
259#407—191no—
260C2×C22⋊C8—191no—
261C2×C22⋊C8—191no—
262C2×C22⋊C8C2×D1911yescharacteristic
263C2×#95—191no—
264#328—381no—
265#327—381no—
266#327—381no—
267#327—381no—
268#323—381no—
269#323—381no—
270C2×C19—21no—
271C2×C19—21no—
272C2×C19—21no—
273C2×C19—21no—
274C2×C19—41no—
275C2×C19—81no—
276C2×C19—161no—
277C2×C19#187611yescharacteristic
278C2×C19#190711yescharacteristic
279C2×C19#191311yescharacteristic
280C2×#41C22⋊D1911yescharacteristic
281C22×D4—21no—
282C22×D4C2×Dic1911yescharacteristic
283C23×C4—381no—
284C23×C4C22×D1911yescharacteristic
285C2×SD16—21no—
286C2×D8—21no—
287C2×M16—381no—
288C2×M16—381no—
289C22×C8—21no—
290C22×C8—381no—
291C22×C8—381no—
292C22×C8—381no—
293#123—21no—
294C22⋊Q8C2×Dic1911yescharacteristic
295C22⋊Q8C22⋊D1911yescharacteristic
296#121—21no—
297#121—21no—
298#121—21no—
299#121—21no—
300#121C2×Dic1911yescharacteristic
301#121C22⋊D1911yescharacteristic
302#120—21no—
303C4×D4—21no—
304C4×D4—21no—
305#117C22⋊D1911yescharacteristic
306C2×C4⋊C4C2×Dic1911yescharacteristic
307C2×C22⋊C4—21no—
308#107—21no—
309#106—21no—
310C4⋊C8—381no—
311C4⋊C8—381no—
312#103—21no—
313#102—21no—
314#102—21no—
315#102—21no—
316C22⋊C8—21no—
317C22⋊C8—191no—
318C22⋊C8—191no—
319C22⋊C8—191no—
320C22⋊C8—191no—
321C22⋊C8—381no—
322C22⋊C8—381no—
323C22⋊C8—381no—
324C22⋊C8—381no—
325C22⋊C8—381no—
326C22⋊C8—381no—
327C22⋊C8C2×Dic1911yescharacteristic
328C22⋊C8C2×Dic1911yescharacteristic
329#97—381no—
330C4×C8—381no—
331#95—381no—
332#95—381no—
333C19#926411yescharacteristic, complemented, Sylow
334C24—21no—
335C24#6454311yescharacteristic
336#41—81no—
337C2×Q8C22⋊Dic1911yescharacteristic
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—81no—
346C2×D4—81no—
347C2×D4—81no—
348C2×D4C22⋊Dic1911yescharacteristic
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—81no—
352C22×C4—382no—
353C22×C4—761no—
354C22×C4—761no—
355C22×C4—1521no—
356C22×C4—1521no—
357C22×C4D4×D1911yescharacteristic
358C22×C4D4×D1911yescharacteristic
359C22×C4#6454311yescharacteristic
360C22×C4C22×Dic1911yescharacteristic
361C22×C4C2×C22⋊D1911yescharacteristic
362C22×C4C2×C22⋊D1911yescharacteristic
363SD16—81no—
364D8—81no—
365M16—1521no—
366M16—1521no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—81no—
370C2×C8—381no—
371C2×C8—381no—
372C2×C8—381no—
373C2×C8—381no—
374C2×C8—761no—
375C2×C8—1521no—
376C2×C8—1521no—
377C2×C8—1521no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4C22⋊Dic1911yescharacteristic
383C4⋊C4C22⋊Dic1911yescharacteristic
384C22⋊C4—21no—
385C22⋊C4—21no—
386C22⋊C4—21no—
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C42—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—81no—
402C23—81no—
403C23D4×Dic1911yescharacteristic
404C23#1059738111yescharacteristic
405C23#1059738511yescharacteristic
406Q8—41no—
407D4—41no—
408D4—41no—
409D4—41no—
410D4—41no—
411D4—41no—
412D4—41no—
413D4—41no—
414D4—81no—
415D4—81no—
416D4—82no—
417D4—81no—
418D4—81no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—81no—
432C2×C4—762no—
433C2×C4—1521no—
434C2×C4—1522no—
435C2×C4—1521no—
436C2×C4—1522no—
437C2×C4D4×Dic1911yescharacteristic
438C2×C4#1059738311yescharacteristic
439C2×C4#1059738511yescharacteristic
440C2×C4C2×C22⋊Dic1911yescharacteristic
441C8—41no—
442C8—41no—
443C8—761no—
444C8—761no—
445C8—761no—
446C8—761no—
447C8—1521no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—161no—
466C22—161no—
467C22#1192642411yescharacteristic
468C22#1192666111yescharacteristic
469C22#1192666611yescharacteristic
470C22#1192680511yescharacteristic
471C22#1192681211yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—41no—
477C4—41no—
478C4—41no—
479C4—81no—
480C4—1522no—
481C2—21no—
482C2—21no—
483C2—21no—
484C2—21no—
485C2—41no—
486C2—81no—
487C2—161no—
488C2#1456396411yescharacteristic
489C2#1456414511yescharacteristic
490C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#3188C2
socleC22×C19#386
cosocleC23×C4×C19C23
hypercenter#3188D19
hypocenterC19#9264
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3188

Complements

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

NH ≅ G/Ntype
1. #14572691C2semidirect
2. #14562139C2semidirect
3. C2×#11926278C2semidirect
4. #14561995C2semidirect
5. #14561523C2semidirect
6. #14561477C2semidirect
26. C19×#484C4semidirect
28. C19×#481C4semidirect
31. C19×#450C4semidirect
33. C19×#447C4semidirect
245. #484Dic19semidirect
247. #481Dic19semidirect
250. #450Dic19semidirect
252. #447Dic19semidirect
333. C19#9264semidirect

Maximal subgroups

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

subgroupindex
#145726912
#145621392
C2×#119262782
#145619952
#145615232
#145614772
C19×#31882
#926419