Finite Group Databasebeta

← #18079021

Subgroups — #18079021

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#14574396C211yesmaximal, characteristic
2#14562139C211yesmaximal, characteristic, complemented
3C2×#11926279C211yesmaximal, characteristic, complemented
4#14561994C211yesmaximal, characteristic, complemented
5#14561523C211yesmaximal, characteristic, complemented
6#14561477C211yesmaximal, characteristic, complemented
7C19×#2977C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9#11926877C411yescharacteristic, complemented
10#11926868—21no—
11#11926860C411yescharacteristic, complemented
12#11926778—21no—
13#11926775—21no—
14#11926694C411yescharacteristic, complemented
15#11926689—21no—
16#11926677C411yescharacteristic, complemented
17#11926508C2211yescharacteristic
18C2×C22⋊(C19⋊C8)C2211yescharacteristic
19C2×C19⋊#95C2211yescharacteristic
20#11926281—21no—
21#11926279—21no—
22#11926279—21no—
23#11926278—21no—
24#11926267—21no—
25#11926267—21no—
26C19×#525C2211yescharacteristic
27C19×#435—21no—
28C19×#435—21no—
29C8×D4×C19—21no—
30C8×D4×C19—21no—
31C19×#433—21no—
32C19×#408—21no—
33C2×C19×C22⋊C8C2211yescharacteristic
34C2×C19×C22⋊C8C2211yescharacteristic
35C2×#41×C19D411yescharacteristic
36C23×C4×C19C2311yescharacteristic
37C22×C22⋊D19—21no—
38C23×Dic19—21no—
39C22×D76C2×C411yescharacteristic
40C2×M16×C19—21no—
41C22×C8×C19—21no—
42C22×C8×C19—21no—
43C22×C8×C19—21no—
44C19×#123—21no—
45C19×C22⋊Q8C2×C411yescharacteristic
46C19×C22⋊Q8D411yescharacteristic
47C19×#121C2×C411yescharacteristic
48C19×#121D411yescharacteristic
49C19×#120—21no—
50C4×D4×C19—21no—
51C4×D4×C19—21no—
52C19×#117D411yescharacteristic
53C2×#64527—21no—
54C2×#64525—21no—
55#10597376—21no—
56#10597376—21no—
57#10597376—21no—
58#10597376—21no—
59C2×(C2×D19)⋊C4—21no—
60C2×C4⋊Dic19C2×C411yescharacteristic
61C2×#64520—21no—
62C22×C19⋊C8—21no—
63C19×C4⋊C8—21no—
64C19×C4⋊C8—21no—
65C19×C22⋊C8—21no—
66C19×C22⋊C8—21no—
67C19×C22⋊C8—21no—
68C19×C22⋊C8—21no—
69C19×C22⋊C8D411yescharacteristic
70C19×C22⋊C8D411yescharacteristic
71C19×C22⋊C8D411yescharacteristic
72C19×C22⋊C8D411yescharacteristic
73C19×#97—21no—
74C4×C8×C19—21no—
75#10597292—21no—
76#10597289—21no—
77C19⋊#95—21no—
78C19⋊#95—21no—
79C22⋊(C19⋊C8)—21no—
80C22⋊(C19⋊C8)—21no—
81C22⋊(C19⋊C8)—21no—
82C22⋊(C19⋊C8)C2×C411yescharacteristic
83C22⋊(C19⋊C8)C2×C411yescharacteristic
84#10597266—21no—
85#10597266—21no—
86#10597265—21no—
87#10597264—21no—
88C24×C19#4111yescharacteristic
89C23×D19—21no—
90#41×C19—81no—
91C2×Q8×C19C22⋊C411yescharacteristic
92C2×D4×C19—21no—
93C2×D4×C19—21no—
94C2×D4×C19—21no—
95C2×D4×C19C22⋊C411yescharacteristic
96C22×C4×C19—21no—
97C22×C4×C19—81no—
98C22×C4×C19C22×C411yescharacteristic
99C22×C4×C19C2×D411yescharacteristic
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19#4111yescharacteristic
104C2×C22⋊D19—41no—
105C2×C22⋊D19—41no—
106C2×C22⋊D19—81no—
107C2×C22⋊D19—81no—
108C22×Dic19—22no—
109C22×Dic19—21no—
110C22×Dic19—41no—
111C22×Dic19—41no—
112C22×Dic19—81no—
113C22×Dic19—81no—
114C2×D76—21no—
115C2×D76—21no—
116C2×D76—81no—
117M16×C19—81no—
118C2×C8×C19—21no—
119C2×C8×C19—21no—
120C2×C8×C19—21no—
121C2×C8×C19—21no—
122C2×C8×C19—81no—
123C2×C8×C19—81no—
124C2×C8×C19—81no—
125C4⋊C4×C19—21no—
126C4⋊C4×C19—21no—
127C4⋊C4×C19C22⋊C411yescharacteristic
128C4⋊C4×C19C22⋊C411yescharacteristic
129C22⋊C4×C19—21no—
130C22⋊C4×C19—21no—
131C22⋊C4×C19—21no—
132C22⋊C4×C19—21no—
133C22⋊C4×C19—21no—
134C42×C19—21no—
135#64527—81no—
136#64525—81no—
137(C2×D19)⋊C4—41no—
138(C2×D19)⋊C4—41no—
139C4⋊Dic19—21no—
140C4⋊Dic19—21no—
141#64520—81no—
142C2×C19⋊C8—21no—
143C2×C19⋊C8—21no—
144C2×C19⋊C8—41no—
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×C19C4×D411yescharacteristic
154C23×C19#12111yescharacteristic
155C23×C19#12311yescharacteristic
156C22×D19—41no—
157C22×D19—41no—
158C22×D19—41no—
159C22×D19—81no—
160C22×D19—81no—
161Q8×C19—41no—
162D4×C19—41no—
163D4×C19—41no—
164D4×C19—41no—
165D4×C19—41no—
166D4×C19—41no—
167D4×C19—81no—
168C2×C4×C19—21no—
169C2×C4×C19—21no—
170C2×C4×C19—21no—
171C2×C4×C19—41no—
172C2×C4×C19—41no—
173C2×C4×C19—41no—
174C2×C4×C19—41no—
175C2×C4×C19—41no—
176C2×C4×C19—41no—
177C2×C4×C19—41no—
178C2×C4×C19—41no—
179C2×C4×C19C2×C22⋊C411yescharacteristic
180C2×C4×C19C4×D411yescharacteristic
181C2×C4×C19#12011yescharacteristic
182C2×C4×C19#12111yescharacteristic
183C22⋊D19—82no—
184C22⋊D19—81no—
185C22⋊D19—81no—
186C2×Dic19—42no—
187C2×Dic19—41no—
188C2×Dic19—81no—
189C2×Dic19—82no—
190C2×Dic19—81no—
191C2×Dic19—81no—
192C2×Dic19—82no—
193D76—41no—
194D76—41no—
195D76—81no—
196C8×C19—41no—
197C8×C19—41no—
198C8×C19—41no—
199C8×C19—41no—
200C19⋊C8—41no—
201C19⋊C8—41no—
202C19⋊C8—81no—
203#3188—191no—
204#2977D1911yescharacteristic, complemented
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#38611yescharacteristic
225C22×C19#44311yescharacteristic
226C22×C19#44411yescharacteristic
227C22×C19#47111yescharacteristic
228C22×C19#47211yescharacteristic
229C2×D19—81no—
230C2×D19—81no—
231C2×D19—81no—
232C2×D19—161no—
233C2×D19—161no—
234C4×C19—21no—
235C4×C19—21no—
236C4×C19—21no—
237C4×C19—21no—
238C4×C19—41no—
239C4×C19—41no—
240C4×C19—41no—
241Dic19—82no—
242Dic19—81no—
243#525C2×D1911yescharacteristic
244C2×#121—191no—
245#484—191no—
246#482—381no—
247#481—191no—
248#466—381no—
249#465—381no—
250#450—191no—
251#449—381no—
252#447—191no—
253#435—21no—
254#435—21no—
255C8×D4—21no—
256C8×D4—21no—
257#433—21no—
258#408—21no—
259#407—191no—
260C2×C22⋊C8—191no—
261C2×C22⋊C8C2×D1911yescharacteristic
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#187611yescharacteristic
277C2×C19#190711yescharacteristic
278C2×C19#191311yescharacteristic
279D19—161no—
280C2×#41C22⋊D1911yescharacteristic
281C22×D4—191no—
282C22×D4—381no—
283C23×C4—381no—
284C23×C4C22×D1911yescharacteristic
285C2×SD16—381no—
286C2×D8—381no—
287C2×M16—21no—
288C2×M16—381no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—381no—
293#123—21no—
294C22⋊Q8C4×D1911yescharacteristic
295C22⋊Q8D7611yescharacteristic
296#121—381no—
297#121—381no—
298#121—381no—
299#121—381no—
300#121C4×D1911yescharacteristic
301#121D7611yescharacteristic
302#120—21no—
303C4×D4—21no—
304C4×D4—21no—
305#117C22⋊D1911yescharacteristic
306C2×C4⋊C4—191no—
307C2×C22⋊C4—381no—
308#107—381no—
309#106—381no—
310C4⋊C8—21no—
311C4⋊C8—21no—
312#103—381no—
313#102—381no—
314#102—381no—
315#102—381no—
316C22⋊C8—21no—
317C22⋊C8—21no—
318C22⋊C8—21no—
319C22⋊C8—21no—
320C22⋊C8—191no—
321C22⋊C8—191no—
322C22⋊C8—381no—
323C22⋊C8—381no—
324C22⋊C8—381no—
325C22⋊C8C22⋊D1911yescharacteristic
326C22⋊C8C22⋊D1911yescharacteristic
327C22⋊C8C22⋊D1911yescharacteristic
328C22⋊C8C22⋊D1911yescharacteristic
329#97—21no—
330C4×C8—21no—
331#95—381no—
332#95—381no—
333C19#926411yescharacteristic, complemented, Sylow
334C24—381no—
335C24#6454111yescharacteristic
336#41—81no—
337C2×Q8(C2×D19)⋊C411yescharacteristic
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—381no—
342C2×D4—381no—
343C2×D4—761no—
344C2×D4—761no—
345C2×D4—1521no—
346C2×D4—1521no—
347C2×D4—1521no—
348C2×D4(C2×D19)⋊C411yescharacteristic
349C22×C4—21no—
350C22×C4—81no—
351C22×C4—382no—
352C22×C4—381no—
353C22×C4—761no—
354C22×C4—761no—
355C22×C4—1521no—
356C22×C4—1521no—
357C22×C4C2×C4×D1911yescharacteristic
358C22×C4C2×D7611yescharacteristic
359C22×C4#6454111yescharacteristic
360C22×C4C2×C22⋊D1911yescharacteristic
361C22×C4C2×C22⋊D1911yescharacteristic
362C22×C4C2×C22⋊D1911yescharacteristic
363SD16—1521no—
364D8—1521no—
365M16—81no—
366M16—1521no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—81no—
372C2×C8—81no—
373C2×C8—81no—
374C2×C8—381no—
375C2×C8—381no—
376C2×C8—761no—
377C2×C8—1521no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—381no—
381C4⋊C4—381no—
382C4⋊C4(C2×D19)⋊C411yescharacteristic
383C4⋊C4(C2×D19)⋊C411yescharacteristic
384C22⋊C4—21no—
385C22⋊C4—21no—
386C22⋊C4—21no—
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—761no—
390C22⋊C4—761no—
391C42—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—41no—
398C23—761no—
399C23—761no—
400C23—761no—
401C23—1521no—
402C23—1521no—
403C23C4×C22⋊D1911yescharacteristic
404C23#1059737511yescharacteristic
405C23#1059737611yescharacteristic
406Q8—41no—
407D4—41no—
408D4—41no—
409D4—41no—
410D4—41no—
411D4—41no—
412D4—81no—
413D4—761no—
414D4—761no—
415D4—1521no—
416D4—1522no—
417D4—1521no—
418D4—1521no—
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—762no—
431C2×C4—761no—
432C2×C4—1521no—
433C2×C4—1522no—
434C2×C4—1521no—
435C2×C4—1521no—
436C2×C4—1522no—
437C2×C4C2×(C2×D19)⋊C411yescharacteristic
438C2×C4C4×C22⋊D1911yescharacteristic
439C2×C4#1059737611yescharacteristic
440C2×C4#1059739911yescharacteristic
441C8—41no—
442C8—41no—
443C8—41no—
444C8—41no—
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—3041no—
463C22—3041no—
464C22—1521no—
465C22—1521no—
466C22—1521no—
467C22#1192642311yescharacteristic
468C22#1192665911yescharacteristic
469C22#1192666411yescharacteristic
470C22#1192680711yescharacteristic
471C22#1192681411yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—41no—
477C4—41no—
478C4—41no—
479C4—1522no—
480C4—1521no—
481C2—21no—
482C2—21no—
483C2—21no—
484C2—21no—
485C2—41no—
486C2—81no—
487C2—3041no—
488C2#1456396211yescharacteristic
489C2#1456414311yescharacteristic
490C2#1456417711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2977C2
socleC22×C19#386
prime radical#14574396C2
cosocleC23×C4×C19C23
hypercenter#2977D19
hypocenterC19#9264
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2977

Complements

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

NH ≅ G/Ntype
2. #14562139C2semidirect
3. C2×#11926279C2semidirect
4. #14561994C2semidirect
5. #14561523C2semidirect
6. #14561477C2semidirect
7. C19×#2977C2semidirect
9. #11926877C4semidirect
11. #11926860C4semidirect
14. #11926694C4semidirect
16. #11926677C4semidirect
204. #2977D19semidirect
333. C19#9264semidirect

Maximal subgroups

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

subgroupindex
#145743962
#145621392
C2×#119262792
#145619942
#145615232
#145614772
C19×#29772
#926419