Finite Group Databasebeta

← #18082816

Subgroups — #18082816

Order 4864.

734 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#14569442C211yesmaximal, characteristic
2C2×#11926470C211yesmaximal, characteristic
3#14563721C211yesmaximal, characteristic, complemented
4C2×#11926281C211yesmaximal, characteristic, complemented
5C2×#11926267C211yesmaximal, characteristic
6#14561515C211yesmaximal, characteristic, complemented
7C2×C19×#483C211yesmaximal, characteristic, complemented
8C22×(C2×D19)⋊C4—21no—
9C22×(C2×D19)⋊C4C2211yescharacteristic
10C2×C22⋊(C19⋊C8)C2211yescharacteristic
11#11926479—21no—
12#11926470—22no—
13#11926470—22no—
14#11926466—22no—
15#11926455—21no—
16#11926416—21no—
17#11926404C2211yescharacteristic
18#11926399—21no—
19C2×C19⋊#95—21no—
20C2×C19⋊#95C2211yescharacteristic
21#11926306—22no—
22#11926281—22no—
23#11926267—22no—
24C2×C19×C22⋊Q8C2211yescharacteristic
25C22×C4⋊C4×C19C2211yescharacteristic
26C19×#483—22no—
27C19×#483—22no—
28C2×C19×#106—21no—
29C2×C19×#103—21no—
30C2×C19×C22⋊C8C2211yescharacteristic
31C24×D19D411yescharacteristic
32C22×Q8×C19D411yescharacteristic
33C23×C4×C19—21no—
34C23×C4×C19C2311yescharacteristic
35C23×Dic19—21no—
36C23×Dic19D411yescharacteristic
37C22×C8×C19—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C19×C22⋊Q8—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—21no—
46C2×C4⋊C4×C19—21no—
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C4⋊C4×C19D412yes—
50C2×C22⋊C4×C19—21no—
51C2×C22⋊Dic19—21no—
52C2×(C2×D19)⋊C4—24no—
53C2×(C2×D19)⋊C4—21no—
54C2×(C2×D19)⋊C4—21no—
55C2×(C2×D19)⋊C4—21no—
56C2×(C2×D19)⋊C4—21no—
57C2×(C2×D19)⋊C4—21no—
58C2×(C2×D19)⋊C4—21no—
59C2×(C2×D19)⋊C4—22no—
60C2×(C2×D19)⋊C4—22no—
61C2×(C2×D19)⋊C4—42no—
62C2×(C2×D19)⋊C4—42no—
63C2×C4⋊Dic19D412yes—
64C2×Dic19⋊C4—22no—
65C22×C19⋊C8—21no—
66C19×#106—24no—
67C19×#103—24no—
68C19×C22⋊C8—21no—
69C19×C22⋊C8D412yes—
70C19⋊#95—24no—
71C19⋊#95—22no—
72C19⋊#95—21no—
73C19⋊#95—21no—
74C19⋊#95D412yes—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)—21no—
77C24×C19C2×D411yescharacteristic
78C23×D19—21no—
79C23×D19—21no—
80C23×D19—21no—
81C23×D19—21no—
82C23×D19—21no—
83C23×D19—21no—
84C23×D19—42no—
85C23×D19—42no—
86C23×D19SD1612yes—
87C2×Q8×C19—21no—
88C2×Q8×C19—21no—
89C2×Q8×C19—42no—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19—22no—
93C22×C4×C19—42no—
94C22×C4×C19—41no—
95C22×C4×C19—41no—
96C22×C4×C19—41no—
97C22×C4×C19—41no—
98C22×C4×C19—41no—
99C22×C4×C19—41no—
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19C2×D411yescharacteristic
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19#4111yescharacteristic
106C22×Dic19—22no—
107C22×Dic19—22no—
108C22×Dic19—21no—
109C22×Dic19—21no—
110C22×Dic19—21no—
111C22×Dic19—42no—
112C22×Dic19—42no—
113C22×Dic19—42no—
114C22×Dic19—41no—
115C22×Dic19—41no—
116C2×C8×C19—22no—
117C2×C8×C19—42no—
118C4⋊C4×C19—22no—
119C4⋊C4×C19—21no—
120C4⋊C4×C19—22no—
121C4⋊C4×C19—21no—
122C4⋊C4×C19—41no—
123C4⋊C4×C19—41no—
124C4⋊C4×C19—41no—
125C4⋊C4×C19—41no—
126C22⋊C4×C19—41no—
127C22⋊C4×C19—41no—
128C22⋊Dic19—41no—
129C22⋊Dic19—41no—
130(C2×D19)⋊C4—48no—
131(C2×D19)⋊C4—41no—
132(C2×D19)⋊C4—41no—
133(C2×D19)⋊C4—41no—
134(C2×D19)⋊C4—41no—
135(C2×D19)⋊C4—82no—
136(C2×D19)⋊C4—82no—
137C4⋊Dic19—42no—
138Dic19⋊C4—82no—
139C2×C19⋊C8—42no—
140C2×C19⋊C8—41no—
141#9926—191nomaximal, Sylow
142C23×C19—22no—
143C23×C19—22no—
144C23×C19#12011yescharacteristic
145C23×C19#12011yescharacteristic
146C23×C19#12111yescharacteristic
147C23×C19C2×SD1611yescharacteristic
148C23×C19#13511yescharacteristic
149C23×C19AGL(1,ℤ/8)11yescharacteristic
150C23×C19#13711yescharacteristic
151C22×D19—22no—
152C22×D19—22no—
153C22×D19—22no—
154C22×D19—44no—
155C22×D19—44no—
156C22×D19—42no—
157C22×D19—42no—
158C22×D19—41no—
159C22×D19—41no—
160C22×D19—41no—
161C22×D19—42no—
162C22×D19—42no—
163C22×D19—41no—
164C22×D19—82no—
165C22×D19—82no—
166C22×D19—81no—
167C22×D19—81no—
168Q8×C19—42no—
169Q8×C19—81no—
170C2×C4×C19—22no—
171C2×C4×C19—22no—
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—42no—
179C2×C4×C19—42no—
180C2×C4×C19—42no—
181C2×C4×C19—42no—
182C2×C4×C19—42no—
183C2×C4×C19—81no—
184C2×C4×C19—81no—
185C2×C4×C19—81no—
186C2×C4×C19—81no—
187C2×C4×C19#12011yescharacteristic
188C2×C4×C19#12111yescharacteristic
189C2×C4×C19#12111yescharacteristic
190C2×C4×C19#12711yescharacteristic
191C2×Dic19—42no—
192C2×Dic19—42no—
193C2×Dic19—42no—
194C2×Dic19—41no—
195C2×Dic19—42no—
196C2×Dic19—42no—
197C2×Dic19—42no—
198C2×Dic19—42no—
199C2×Dic19—42no—
200C2×Dic19—82no—
201C2×Dic19—82no—
202C2×Dic19—81no—
203C8×C19—42no—
204C19⋊C8—81no—
205C2×#483D1911yescharacteristic, complemented
206#2626—191no—
207C2×#397—191no—
208#1823—191no—
209C2×#328—191no—
210C2×#323—191no—
211#1294—191no—
212C22×C19—22no—
213C22×C19—22no—
214C22×C19—22no—
215C22×C19—22no—
216C22×C19—21no—
217C22×C19—21no—
218C22×C19—21no—
219C22×C19—21no—
220C22×C19#39211yescharacteristic
221C22×C19#44811yescharacteristic
222C22×C19#44911yescharacteristic
223C22×C19#45011yescharacteristic
224C22×C19#45211yescharacteristic
225C22×C19#45512yes—
226C22×C19#45812yes—
227C22×C19#46511yescharacteristic
228C22×C19#46811yescharacteristic
229C2×D19—44no—
230C2×D19—44no—
231C2×D19—42no—
232C2×D19—82no—
233C2×D19—82no—
234C2×D19—82no—
235C2×D19—81no—
236C2×D19—81no—
237C2×D19—82no—
238C4×C19—21no—
239C4×C19—21no—
240C4×C19—21no—
241C4×C19—21no—
242C4×C19—82no—
243C4×C19—81no—
244C4×C19—81no—
245Dic19—82no—
246Dic19—82no—
247Dic19—81no—
248C2×C22⋊Q8C2×D1911yescharacteristic
249C22×C4⋊C4C2×D1911yescharacteristic
250C22×C22⋊C4—191no—
251C22×C22⋊C4—381no—
252#483—22no—
253#483—22no—
254C2×#106—21no—
255C2×#103—21no—
256C2×C22⋊C8—191no—
257C2×C22⋊C8C2×D1911yescharacteristic
258#399—381no—
259#397—382no—
260#397—382no—
261#396—382no—
262#393—381no—
263#385—381no—
264#380—191no—
265#379—381no—
266C2×#95—191no—
267C2×#95—381no—
268#340—382no—
269#328—382no—
270#323—382no—
271C2×C19—21no—
272C2×C19—21no—
273C2×C19—21no—
274C2×C19—21no—
275C2×C19#160812yes—
276C2×C19#161212yes—
277C2×C19#200011yescharacteristic
278C2×C19#200411yescharacteristic
279C2×C19#202211yescharacteristic
280D19—82no—
281C25—191no—
282C22×Q8C22⋊D1911yescharacteristic
283C23×C4—21no—
284C23×C4—191no—
285C23×C4—381no—
286C23×C4C22×D1911yescharacteristic
287C22×C8—21no—
288C22×C8—381no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—192no—
300C2×C4⋊C4—382no—
301C2×C4⋊C4C22⋊D1912yes—
302C2×C4⋊C4C22⋊D1911yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—384no—
305C2×C22⋊C4—381no—
306C2×C22⋊C4—381no—
307C2×C22⋊C4—381no—
308C2×C22⋊C4—381no—
309C2×C22⋊C4—381no—
310C2×C22⋊C4—381no—
311C2×C22⋊C4—381no—
312C2×C22⋊C4—382no—
313C2×C22⋊C4—382no—
314C2×C22⋊C4—762no—
315C2×C22⋊C4—762no—
316#106—24no—
317#103—24no—
318C22⋊C8—21no—
319C22⋊C8—381no—
320C22⋊C8—381no—
321C22⋊C8C22⋊D1912yes—
322#95—192no—
323#95—384no—
324#95—382no—
325#95—381no—
326#95—381no—
327C19#992611yescharacteristic, complemented, Sylow
328C24—192no—
329C24—381no—
330C24—381no—
331C24—381no—
332C24—381no—
333C24—381no—
334C24—381no—
335C24—762no—
336C24—762no—
337C24D4×D1911yescharacteristic
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—42no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—42no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—382no—
352C22×C4—381no—
353C22×C4—382no—
354C22×C4—381no—
355C22×C4—381no—
356C22×C4—762no—
357C22×C4—762no—
358C22×C4—762no—
359C22×C4—761no—
360C22×C4—761no—
361C22×C4D4×D1911yescharacteristic
362C22×C4D4×D1911yescharacteristic
363C22×C4#6454311yescharacteristic
364C22×C4C2×C22⋊D1911yescharacteristic
365C22×C4C2×C22⋊D1911yescharacteristic
366C22×C4C2×C22⋊D1911yescharacteristic
367C2×C8—22no—
368C2×C8—42no—
369C2×C8—762no—
370C2×C8—761no—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—21no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—762no—
380C4⋊C4—1522no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—768no—
384C22⋊C4—761no—
385C22⋊C4—761no—
386C22⋊C4—761no—
387C22⋊C4—761no—
388C22⋊C4—761no—
389C22⋊C4—761no—
390C22⋊C4—1522no—
391C22⋊C4—1522no—
392C23—22no—
393C23—22no—
394C23—382no—
395C23—382no—
396C23—382no—
397C23—764no—
398C23—762no—
399C23—764no—
400C23—762no—
401C23—761no—
402C23—761no—
403C23—761no—
404C23—761no—
405C23—762no—
406C23—762no—
407C23—1522no—
408C23—1521no—
409C23—1522no—
410C23—1521no—
411C23SD16×D1911yescharacteristic
412C23#1059736011yescharacteristic
413C23#1059736111yescharacteristic
414C23#1059736211yescharacteristic
415C23#1059738311yescharacteristic
416C23#1059738311yescharacteristic
417C23#1059738411yescharacteristic
418Q8—42no—
419Q8—81no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—81no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—81no—
437C2×C4—762no—
438C2×C4—762no—
439C2×C4—762no—
440C2×C4—762no—
441C2×C4—762no—
442C2×C4—761no—
443C2×C4—762no—
444C2×C4—762no—
445C2×C4—762no—
446C2×C4—1522no—
447C2×C4—1522no—
448C2×C4—1521no—
449C2×C4#1059738511yescharacteristic
450C2×C4#1059738511yescharacteristic
451C2×C4#1059738611yescharacteristic
452C2×C4#1059739911yescharacteristic
453C8—42no—
454C8—1521no—
455C22—21no—
456C22—21no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—21no—
462C22—21no—
463C22—764no—
464C22—762no—
465C22—764no—
466C22—1522no—
467C22—1522no—
468C22—1522no—
469C22—1521no—
470C22—1522no—
471C22—1521no—
472C22#1192645211yescharacteristic
473C22#1192668111yescharacteristic
474C22#1192668811yescharacteristic
475C22#1192669311yescharacteristic
476C22#1192670311yescharacteristic
477C22#1192672012yes—
478C22#1192673312yes—
479C22#1192677011yescharacteristic
480C22#1192678711yescharacteristic
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—82no—
486C4—81no—
487C4—81no—
488C4—1522no—
489C4—1521no—
490C4—1522no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—1522no—
496C2#1456262412yes—
497C2#1456264812yes—
498C2#1456463511yescharacteristic
499C2#1456466111yescharacteristic
500C2#1456476311yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC2×C19×#483C2
socleC23×C19#120
prime radicalC24×D19D4
hypercenterC2×#483D19
hypocenterC19#9926
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
3. #14563721C2semidirect
4. C2×#11926281C2semidirect
6. #14561515C2semidirect
7. C2×C19×#483C2semidirect
205. C2×#483D19semidirect
327. C19#9926semidirect

Maximal subgroups

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

subgroupindex
#145694422
C2×#119264702
#145637212
C2×#119262812
C2×#119262672
#145615152
C2×C19×#4832
#992619