Finite Group Databasebeta

← #18079098

Subgroups — #18079098

Order 4864.

606 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574392C211yesmaximal, characteristic
2#14564620C211yesmaximal, characteristic, complemented
3#14562203C211yesmaximal, characteristic
4C2×#11926280C211yesmaximal, characteristic, complemented
5#14561514C211yesmaximal, characteristic, complemented
6#14561483C211yesmaximal, characteristic, complemented
7C19×#2364C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9#11926874—21no—
10#11926860C412yescomplemented
11#11926771—22no—
12#11926695—21no—
13#11926682C412yescomplemented
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16#11926404C2211yescharacteristic
17#11926310—21no—
18#11926310—21no—
19#11926280—21no—
20#11926280—21no—
21#11926278—22no—
22C2×C19×#121C2211yescharacteristic
23C2×C4×D4×C19—21no—
24C19×#388—21no—
25C19×#387—21no—
26C19×#386—21no—
27C19×#386—21no—
28C4×C22⋊C4×C19—21no—
29C4×C22⋊C4×C19C2211yescharacteristic
30C2×C19×#95C2211yescharacteristic
31C22×D4×C19—21no—
32C22×D4×C19D411yescharacteristic
33C23×C4×C19—21no—
34C23×C4×C19—21no—
35C23×C4×C19C2311yescharacteristic
36C22×Dic38C2×C411yescharacteristic, complemented
37C19×#121—21no—
38C19×#121—21no—
39C19×#121C2×C412yes—
40C19×#121D412yes—
41C4×D4×C19—42no—
42C4×D4×C19—42no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19D411yescharacteristic
45C2×C22⋊C4×C19—21no—
46C2×C22⋊C4×C19—21no—
47C2×C22⋊C4×C19—21no—
48C2×C22⋊C4×C19—21no—
49C2×C22⋊C4×C19D411yescharacteristic
50C2×C22⋊C4×C19D411yescharacteristic
51C2×C42×C19—21no—
52C2×C42×C19—21no—
53C2×C22⋊Dic19—21no—
54C2×C22⋊Dic19—21no—
55C2×#64526—22no—
56C2×C4⋊Dic19—21no—
57C2×C4⋊Dic19C2×C411yescharacteristic, complemented
58#10597370—21no—
59#10597370—21no—
60#10597370—21no—
61#10597370—21no—
62C2×Dic19⋊C4—21no—
63C22×C19⋊C8—21no—
64C22×C19⋊C8—21no—
65C19×#95—21no—
66C19×#95—21no—
67C19×#95—21no—
68C19×#95—21no—
69C19×#95D411yescharacteristic
70C19×#95D411yescharacteristic
71#10597289—22no—
72C19⋊#95—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)C2×C412yescomplemented
77#10597267—22no—
78#10597265—22no—
79C24×C19—21no—
80C24×C19C2×D411yescharacteristic
81C2×D4×C19—22no—
82C2×D4×C19—22no—
83C2×D4×C19—21no—
84C2×D4×C19—41no—
85C2×D4×C19—41no—
86C2×D4×C19—41no—
87C2×D4×C19—41no—
88C2×D4×C19—81no—
89C2×D4×C19C22⋊C412yes—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19—21no—
93C22×C4×C19—21no—
94C22×C4×C19—21no—
95C22×C4×C19—42no—
96C22×C4×C19—42no—
97C22×C4×C19—42no—
98C22×C4×C19—41no—
99C22×C4×C19—41no—
100C22×C4×C19—81no—
101C22×C4×C19—81no—
102C22×C4×C19—81no—
103C22×C4×C19C22×C411yescharacteristic
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19C2×D411yescharacteristic
106C22×C4×C19C2×D411yescharacteristic
107C22×C4×C19#4111yescharacteristic
108C22×C4×C19#4111yescharacteristic
109C22×Dic19—21no—
110C22×Dic19—21no—
111C22×Dic19—41no—
112C2×Dic38—21no—
113C2×Dic38—21no—
114C2×Dic38—81no—
115C4⋊C4×C19—21no—
116C4⋊C4×C19—42no—
117C4⋊C4×C19C22⋊C412yes—
118C22⋊C4×C19—21no—
119C22⋊C4×C19—22no—
120C22⋊C4×C19—22no—
121C22⋊C4×C19—21no—
122C22⋊C4×C19—21no—
123C22⋊C4×C19—42no—
124C22⋊C4×C19—42no—
125C22⋊C4×C19—81no—
126C22⋊C4×C19SD1612yescomplemented
127C42×C19—42no—
128C42×C19—81no—
129C22⋊Dic19—41no—
130C22⋊Dic19—41no—
131C22⋊Dic19—41no—
132C22⋊Dic19—41no—
133#64526—82no—
134C4⋊Dic19—21no—
135C4⋊Dic19—21no—
136C4⋊Dic19—81no—
137Dic19⋊C4—41no—
138Dic19⋊C4—41no—
139C2×C19⋊C8—22no—
140C2×C19⋊C8—41no—
141C2×C19⋊C8—81no—
142C2×C19⋊C8—81no—
143#9275—191nomaximal, Sylow
144C23×C19—22no—
145C23×C19—41no—
146C23×C19—41no—
147C23×C19—41no—
148C23×C19—41no—
149C23×C19—41no—
150C23×C19—41no—
151C23×C19—41no—
152C23×C19—41no—
153C23×C19C4×D411yescharacteristic
154C23×C19#12011yescharacteristic
155C23×C19#12111yescharacteristic
156C23×C19C2×SD1611yescharacteristic
157C23×C19#13511yescharacteristic
158C23×C19AGL(1,ℤ/8)11yescharacteristic
159C23×C19#13711yescharacteristic
160D4×C19—42no—
161D4×C19—42no—
162D4×C19—42no—
163D4×C19—42no—
164D4×C19—42no—
165D4×C19—81no—
166C2×C4×C19—22no—
167C2×C4×C19—22no—
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—41no—
176C2×C4×C19—41no—
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—41no—
187C2×C4×C19—84no—
188C2×C4×C19—82no—
189C2×C4×C19—82no—
190C2×C4×C19C2×C22⋊C411yescharacteristic
191C2×C4×C19C4×D411yescharacteristic
192C2×C4×C19#12111yescharacteristic
193C2×C4×C19#12311yescharacteristic
194C2×Dic19—41no—
195C2×Dic19—41no—
196C2×Dic19—81no—
197C2×Dic19—81no—
198C2×Dic19—81no—
199C2×Dic19—81no—
200C2×Dic19—81no—
201Dic38—42no—
202Dic38—81no—
203C19⋊C8—42no—
204C19⋊C8—81no—
205#3187—191no—
206#2364D1911yescharacteristic
207#1996—191no—
208#1519—191no—
209C2×#328—191no—
210#1294—191no—
211#1282—191no—
212C22×C19—21no—
213C22×C19—21no—
214C22×C19—21no—
215C22×C19—21no—
216C22×C19—21no—
217C22×C19—21no—
218C22×C19—41no—
219C22×C19—41no—
220C22×C19—41no—
221C22×C19—41no—
222C22×C19—42no—
223C22×C19—42no—
224C22×C19—42no—
225C22×C19—81no—
226C22×C19—81no—
227C22×C19—81no—
228C22×C19—81no—
229C22×C19#38611yescharacteristic
230C22×C19C4×SD1611yescharacteristic
231C22×C19#44011yescharacteristic
232C22×C19#45011yescharacteristic
233C22×C19#45211yescharacteristic
234C22×C19#46111yescharacteristic
235C22×C19#46311yescharacteristic
236C4×C19—21no—
237C4×C19—21no—
238C4×C19—21no—
239C4×C19—21no—
240C4×C19—42no—
241C4×C19—42no—
242C4×C19—42no—
243C4×C19—81no—
244C4×C19—81no—
245Dic19—81no—
246Dic19—81no—
247Dic19—161no—
248C2×C22⋊Q8—191no—
249C2×#121C2×D1911yescharacteristic
250C2×C4×D4—21no—
251#483—381no—
252#481—192no—
253#465—382no—
254#450—381no—
255#448—192no—
256C2×C22⋊C8—191no—
257C2×C22⋊C8—191no—
258#388—21no—
259#387—21no—
260#386—21no—
261#386—21no—
262#380—191no—
263C4×C22⋊C4—21no—
264C4×C22⋊C4C2×D1911yescharacteristic
265C2×#95C2×D1911yescharacteristic
266#342—381no—
267#342—381no—
268#328—381no—
269#328—381no—
270#327—382no—
271C2×C19—21no—
272C2×C19—21no—
273C2×C19—21no—
274C2×C19—21no—
275C2×C19—21no—
276C2×C19—21no—
277C2×C19—82no—
278C2×C19#187711yescharacteristic
279C2×C19#190611yescharacteristic
280C2×C19#191311yescharacteristic
281C22×Q8—191no—
282C22×D4—21no—
283C22×D4C22⋊D1911yescharacteristic
284C23×C4—21no—
285C23×C4—21no—
286C23×C4C22×D1911yescharacteristic
287C2×SD16—382no—
288C22×C8—381no—
289C22×C8—381no—
290C22⋊Q8—381no—
291C22⋊Q8—381no—
292C22⋊Q8—381no—
293C22⋊Q8—381no—
294#121—21no—
295#121—21no—
296#121C4×D1912yes—
297#121D7612yes—
298C4×D4—42no—
299C4×D4—42no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—191no—
302C2×C4⋊C4—381no—
303C2×C4⋊C4—381no—
304C2×C4⋊C4C22⋊D1911yescharacteristic
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—381no—
310C2×C22⋊C4—381no—
311C2×C22⋊C4C22⋊D1911yescharacteristic
312C2×C22⋊C4C22⋊D1911yescharacteristic
313C2×C42—21no—
314C2×C42—21no—
315#106—382no—
316#103—382no—
317#102—382no—
318C22⋊C8—192no—
319C22⋊C8—381no—
320C22⋊C8—381no—
321C22⋊C8—381no—
322#95—21no—
323#95—21no—
324#95—21no—
325#95—21no—
326#95—381no—
327#95C22⋊D1911yescharacteristic
328#95C22⋊D1911yescharacteristic
329C19#927511yescharacteristic, complemented, Sylow
330C24—21no—
331C24C2×C22⋊D1911yescharacteristic
332C2×Q8—381no—
333C2×Q8—381no—
334C2×Q8—1521no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—21no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—81no—
343C2×D4(C2×D19)⋊C412yes—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—81no—
355C22×C4—81no—
356C22×C4—81no—
357C22×C4—381no—
358C22×C4—381no—
359C22×C4—761no—
360C22×C4C2×C4×D1911yescharacteristic
361C22×C4C2×D7611yescharacteristic
362C22×C4#6454111yescharacteristic
363C22×C4#6454111yescharacteristic
364C22×C4C2×C22⋊D1911yescharacteristic
365C22×C4C2×C22⋊D1911yescharacteristic
366SD16—1522no—
367C2×C8—382no—
368C2×C8—761no—
369C2×C8—1521no—
370C2×C8—1521no—
371C4⋊C4—21no—
372C4⋊C4—42no—
373C4⋊C4—381no—
374C4⋊C4—381no—
375C4⋊C4—761no—
376C4⋊C4—761no—
377C4⋊C4—1521no—
378C4⋊C4(C2×D19)⋊C412yes—
379C22⋊C4—21no—
380C22⋊C4—22no—
381C22⋊C4—22no—
382C22⋊C4—21no—
383C22⋊C4—21no—
384C22⋊C4—42no—
385C22⋊C4—42no—
386C22⋊C4—81no—
387C22⋊C4—761no—
388C22⋊C4—761no—
389C22⋊C4—761no—
390C22⋊C4—761no—
391C22⋊C4#6452612yescomplemented
392C42—42no—
393C42—81no—
394C23—22no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23C4×C22⋊D1911yescharacteristic
404C23#1059737611yescharacteristic
405C23#1059737811yescharacteristic
406C23C2×#6452611yescharacteristic
407C23#1059739611yescharacteristic
408C23#1059739711yescharacteristic
409C23#1059739911yescharacteristic
410Q8—762no—
411Q8—1521no—
412D4—42no—
413D4—42no—
414D4—42no—
415D4—42no—
416D4—42no—
417D4—81no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—41no—
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—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—84no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—761no—
443C2×C4—761no—
444C2×C4—1521no—
445C2×C4—1521no—
446C2×C4—1521no—
447C2×C4—1521no—
448C2×C4—1521no—
449C2×C4C2×(C2×D19)⋊C411yescharacteristic
450C2×C4C4×C22⋊D1911yescharacteristic
451C2×C4#1059737511yescharacteristic
452C2×C4#1059737611yescharacteristic
453C8—762no—
454C8—1521no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22#1192642311yescharacteristic
473C22C4×#6452611yescharacteristic
474C22#1192664411yescharacteristic
475C22#1192669511yescharacteristic
476C22#1192670611yescharacteristic
477C22#1192674911yescharacteristic
478C22#1192675911yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—42no—
484C4—42no—
485C4—42no—
486C4—81no—
487C4—81no—
488C4—3041no—
489C4—1521no—
490C4—1521no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—82no—
498C2#1456396911yescharacteristic
499C2#1456413611yescharacteristic
500C2#1456417711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2364C2
socleC22×C19#386
prime radicalC2×C19×#121C22
cosocleC23×C4×C19C23
hypercenter#2364D19
hypocenterC19#9275
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2364

Complements

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

NH ≅ G/Ntype
2. #14564620C2semidirect
4. C2×#11926280C2semidirect
5. #14561514C2semidirect
6. #14561483C2semidirect
10. #11926860C4semidirect
13. #11926682C4semidirect
36. C22×Dic38C2×C4semidirect
57. C2×C4⋊Dic19C2×C4semidirect
76. C22⋊(C19⋊C8)C2×C4semidirect
126. C22⋊C4×C19SD16semidirect
329. C19#9275semidirect
391. C22⋊C4#64526semidirect

Maximal subgroups

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

subgroupindex
#145743922
#145646202
#145622032
C2×#119262802
#145615142
#145614832
C19×#23642
#927519