Finite Group Databasebeta

← #18082777

Subgroups — #18082777

Order 4864.

856 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926862C211yesmaximal, characteristic, complemented
2#14569369C211yesmaximal, characteristic
3#14563725C211yesmaximal, characteristic, complemented
4C2×#11926277C211yesmaximal, characteristic, complemented
5C2×#11926268C211yesmaximal, characteristic, complemented
6#14561514C211yesmaximal, characteristic, complemented
7C2×C19×#399C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9C2×#10597399—21no—
10#11926862—22no—
11#11926862—22no—
12C2×#10597265—21no—
13C2×#10597266—21no—
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16#11926469—21no—
17#11926460—22no—
18#11926453—21no—
19#11926423—21no—
20#11926404C2211yescharacteristic
21#11926306—22no—
22#11926277—22no—
23#11926268—22no—
24C22×C4⋊C4×C19—21no—
25C22×C4⋊C4×C19C2211yescharacteristic
26C22×C22⋊C4×C19—21no—
27C22×C22⋊C4×C19C2211yescharacteristic
28C19×#399—22no—
29C19×#399—22no—
30C2×C19×#95C2211yescharacteristic
31C25×C19D411yescharacteristic
32C23×C4×C19—21no—
33C23×C4×C19—21no—
34C23×C4×C19D411yescharacteristic
35C23×C4×C19C2311yescharacteristic
36C22×C22⋊D19—21no—
37C22×C22⋊D19—22no—
38C22×D76D411yescharacteristic
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—24no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—44no—
46C2×C4⋊C4×C19D412yescomplemented
47C2×C22⋊C4×C19—24no—
48C2×C22⋊C4×C19—21no—
49C2×C22⋊C4×C19—21no—
50C2×C22⋊C4×C19—21no—
51C2×C22⋊C4×C19—21no—
52C2×C22⋊C4×C19—21no—
53C2×C22⋊C4×C19—21no—
54C2×C22⋊C4×C19—44no—
55#10597399—42no—
56#10597399—42no—
57C2×C22⋊Dic19—22no—
58C2×C22⋊Dic19—21no—
59#10597376—21no—
60#10597376—21no—
61#10597376—21no—
62#10597376—21no—
63C2×(C2×D19)⋊C4—21no—
64C2×(C2×D19)⋊C4—22no—
65C2×C4⋊Dic19D411yescharacteristic
66C2×C4⋊Dic19D412yes—
67C22×C19⋊C8—21no—
68C22×C19⋊C8—21no—
69C19×#95—21no—
70C19×#95D412yescomplemented
71C19⋊#95—22no—
72C19⋊#95—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)D412yescomplemented
77#10597266—24no—
78#10597265—24no—
79C24×C19—21no—
80C24×C19—21no—
81C24×C19—21no—
82C24×C19—21no—
83C24×C19—21no—
84C24×C19—21no—
85C24×C19—42no—
86C24×C19—42no—
87C24×C19SD1612yes—
88C24×C19C2×D411yescharacteristic
89C23×D19—21no—
90C22×C4×C19—24no—
91C22×C4×C19—22no—
92C22×C4×C19—21no—
93C22×C4×C19—22no—
94C22×C4×C19—21no—
95C22×C4×C19—21no—
96C22×C4×C19—42no—
97C22×C4×C19—42no—
98C22×C4×C19—41no—
99C22×C4×C19—41no—
100C22×C4×C19—42no—
101C22×C4×C19—42no—
102C22×C4×C19—42no—
103C22×C4×C19—41no—
104C22×C4×C19—41no—
105C22×C4×C19C2×D411yescharacteristic
106C22×C4×C19C2×D411yescharacteristic
107C22×C4×C19C2×D411yescharacteristic
108C22×C4×C19C2×D411yescharacteristic
109C22×C4×C19C2×D411yescharacteristic
110C22×C4×C19#4111yescharacteristic
111C2×C22⋊D19—44no—
112C2×C22⋊D19—41no—
113C2×C22⋊D19—41no—
114C2×C22⋊D19—41no—
115C2×C22⋊D19—41no—
116C2×C22⋊D19—41no—
117C2×C22⋊D19—41no—
118C2×C22⋊D19—82no—
119C2×C22⋊D19—82no—
120C22×Dic19—21no—
121C22×Dic19—22no—
122C2×D76—21no—
123C2×D76—21no—
124C2×D76—42no—
125C4⋊C4×C19—22no—
126C4⋊C4×C19—22no—
127C4⋊C4×C19—48no—
128C4⋊C4×C19—41no—
129C4⋊C4×C19—41no—
130C22⋊C4×C19—48no—
131C22⋊C4×C19—41no—
132C22⋊C4×C19—41no—
133C22⋊C4×C19—41no—
134C22⋊C4×C19—41no—
135C22⋊Dic19—44no—
136C22⋊Dic19—41no—
137C22⋊Dic19—41no—
138(C2×D19)⋊C4—41no—
139(C2×D19)⋊C4—41no—
140(C2×D19)⋊C4—82no—
141C4⋊Dic19—21no—
142C4⋊Dic19—21no—
143C4⋊Dic19—42no—
144C2×C19⋊C8—22no—
145C2×C19⋊C8—42no—
146C2×C19⋊C8—42no—
147C2×C19⋊C8—41no—
148#9920—191nomaximal, Sylow
149C23×C19—22no—
150C23×C19—22no—
151C23×C19—22no—
152C23×C19—22no—
153C23×C19—22no—
154C23×C19—44no—
155C23×C19—42no—
156C23×C19—44no—
157C23×C19—42no—
158C23×C19—41no—
159C23×C19—41no—
160C23×C19—41no—
161C23×C19—42no—
162C23×C19—42no—
163C23×C19—41no—
164C23×C19—82no—
165C23×C19—82no—
166C23×C19—81no—
167C23×C19—81no—
168C23×C19#12011yescharacteristic
169C23×C19#12011yescharacteristic
170C23×C19#12111yescharacteristic
171C23×C19C2×SD1611yescharacteristic
172C23×C19#13511yescharacteristic
173C23×C19AGL(1,ℤ/8)11yescharacteristic
174C23×C19#13711yescharacteristic
175C22×D19—41no—
176C22×D19—41no—
177C22×D19—41no—
178C22×D19—42no—
179C22×D19—42no—
180C2×C4×C19—22no—
181C2×C4×C19—22no—
182C2×C4×C19—24no—
183C2×C4×C19—41no—
184C2×C4×C19—41no—
185C2×C4×C19—41no—
186C2×C4×C19—41no—
187C2×C4×C19—44no—
188C2×C4×C19—44no—
189C2×C4×C19—42no—
190C2×C4×C19—42no—
191C2×C4×C19—42no—
192C2×C4×C19—42no—
193C2×C4×C19—42no—
194C2×C4×C19—41no—
195C2×C4×C19—42no—
196C2×C4×C19—42no—
197C2×C4×C19—82no—
198C2×C4×C19—82no—
199C2×C4×C19—81no—
200C2×C4×C19#12011yescharacteristic
201C2×C4×C19#12111yescharacteristic
202C2×C4×C19#12111yescharacteristic
203C2×C4×C19#12711yescharacteristic
204C22⋊D19—88no—
205C22⋊D19—81no—
206C22⋊D19—81no—
207C22⋊D19—81no—
208C22⋊D19—81no—
209C2×Dic19—41no—
210C2×Dic19—42no—
211C2×Dic19—41no—
212C2×Dic19—41no—
213C2×Dic19—42no—
214C2×Dic19—42no—
215D76—42no—
216D76—81no—
217C19⋊C8—42no—
218C19⋊C8—81no—
219C2×#481—191no—
220#2617—191no—
221C2×#399D1911yescharacteristic, complemented
222#1824—191no—
223C2×#327—191no—
224C2×#323—191no—
225#1294—191no—
226C22×C19—22no—
227C22×C19—22no—
228C22×C19—22no—
229C22×C19—22no—
230C22×C19—21no—
231C22×C19—21no—
232C22×C19—21no—
233C22×C19—21no—
234C22×C19—44no—
235C22×C19—44no—
236C22×C19—42no—
237C22×C19—82no—
238C22×C19—82no—
239C22×C19—82no—
240C22×C19—82no—
241C22×C19—81no—
242C22×C19—81no—
243C22×C19#39211yescharacteristic
244C22×C19#44811yescharacteristic
245C22×C19#44911yescharacteristic
246C22×C19#45011yescharacteristic
247C22×C19#45211yescharacteristic
248C22×C19#45312yes—
249C22×C19#45812yes—
250C22×C19#46511yescharacteristic
251C22×C19#46811yescharacteristic
252C2×D19—82no—
253C2×D19—82no—
254C2×D19—81no—
255C2×D19—81no—
256C2×D19—81no—
257C4×C19—21no—
258C4×C19—21no—
259C4×C19—21no—
260C4×C19—21no—
261C4×C19—44no—
262C4×C19—81no—
263C4×C19—82no—
264Dic19—82no—
265Dic19—81no—
266C2×#121—191no—
267C2×#120—381no—
268C22×C4⋊C4—21no—
269C22×C4⋊C4C2×D1911yescharacteristic
270C22×C22⋊C4—21no—
271C22×C22⋊C4C2×D1911yescharacteristic
272#481—382no—
273#481—382no—
274C2×#106—381no—
275C2×#102—381no—
276C2×C22⋊C8—191no—
277C2×C22⋊C8—191no—
278#399—22no—
279#399—22no—
280#397—381no—
281#394—382no—
282#392—381no—
283#386—381no—
284#380—191no—
285C2×#95C2×D1911yescharacteristic
286#340—382no—
287#327—382no—
288#323—382no—
289C2×C19—21no—
290C2×C19—21no—
291C2×C19—21no—
292C2×C19—21no—
293C2×C19—82no—
294C2×C19#161312yes—
295C2×C19#161812yes—
296C2×C19#200011yescharacteristic
297C2×C19#200211yescharacteristic
298C2×C19#202211yescharacteristic
299D19—161no—
300C25C22⋊D1911yescharacteristic
301C22×D4—191no—
302C22×D4—381no—
303C22×D4—382no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4C22⋊D1911yescharacteristic
307C23×C4C22×D1911yescharacteristic
308C22×C8—381no—
309C22×C8—381no—
310#121—381no—
311#121—381no—
312#121—381no—
313#121—381no—
314#120—762no—
315#120—762no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—191no—
324C2×C4⋊C4—192no—
325C2×C4⋊C4C22⋊D1912yescomplemented
326C2×C22⋊C4—24no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—382no—
335C2×C22⋊C4—381no—
336C2×C22⋊C4—381no—
337C2×C22⋊C4—382no—
338#106—384no—
339#102—384no—
340C22⋊C8—192no—
341C22⋊C8—381no—
342C22⋊C8—381no—
343C22⋊C8—381no—
344#95—21no—
345#95—382no—
346#95—381no—
347#95C22⋊D1912yescomplemented
348C19#992011yescharacteristic, complemented, Sylow
349C24—21no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—21no—
355C24—42no—
356C24—42no—
357C24—381no—
358C24#6452712yes—
359C24C2×C22⋊D1911yescharacteristic
360C2×D4—381no—
361C2×D4—381no—
362C2×D4—762no—
363C2×D4—764no—
364C2×D4—761no—
365C2×D4—761no—
366C2×D4—761no—
367C2×D4—761no—
368C2×D4—761no—
369C2×D4—761no—
370C2×D4—1522no—
371C2×D4—1522no—
372C22×C4—24no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—381no—
388C22×C4—382no—
389C22×C4D4×D1911yescharacteristic
390C22×C4D4×D1911yescharacteristic
391C22×C4D4×D1911yescharacteristic
392C22×C4#6454311yescharacteristic
393C22×C4C2×C22⋊D1911yescharacteristic
394C22×C4C2×C22⋊D1911yescharacteristic
395C2×C8—382no—
396C2×C8—762no—
397C2×C8—762no—
398C2×C8—761no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—48no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—381no—
405C4⋊C4—381no—
406C4⋊C4—762no—
407C22⋊C4—48no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—764no—
413C22⋊C4—761no—
414C22⋊C4—761no—
415C22⋊C4—761no—
416C22⋊C4—761no—
417C22⋊C4—1522no—
418C23—22no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—44no—
424C23—42no—
425C23—44no—
426C23—42no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—42no—
432C23—42no—
433C23—82no—
434C23—81no—
435C23—82no—
436C23—81no—
437C23—761no—
438C23—761no—
439C23—761no—
440C23—762no—
441C23—762no—
442C23#1059738311yescharacteristic
443C23#1059738511yescharacteristic
444C23C2×#6452711yescharacteristic
445C23#1059738811yescharacteristic
446C23#1059739511yescharacteristic
447C23#1059739611yescharacteristic
448C23#1059739911yescharacteristic
449D4—762no—
450D4—1521no—
451D4—1528no—
452D4—1521no—
453D4—1521no—
454D4—1521no—
455D4—1521no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—82no—
474C2×C4—82no—
475C2×C4—81no—
476C2×C4—761no—
477C2×C4—762no—
478C2×C4—761no—
479C2×C4—761no—
480C2×C4—762no—
481C2×C4—762no—
482C2×C4#1059738311yescharacteristic
483C2×C4#1059738411yescharacteristic
484C2×C4#1059738511yescharacteristic
485C2×C4#1059738611yescharacteristic
486C8—762no—
487C8—1521no—
488C22—21no—
489C22—21no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—21no—
495C22—21no—
496C22—44no—
497C22—42no—
498C22—44no—
499C22—82no—
500C22—82no—
501C22—82no—
502C22—81no—
503C22—82no—
504C22—81no—
505C22—1521no—
506C22—1521no—
507C22—1522no—
508C22—1522no—
509C22—1521no—
510C22#1192645211yescharacteristic
511C22#1192668311yescharacteristic
512C22#1192668911yescharacteristic
513C22#1192669411yescharacteristic
514C22#1192670411yescharacteristic
515C22#1192671112yes—
516C22#1192673312yes—
517C22#1192677511yescharacteristic
518C22#1192679211yescharacteristic
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—44no—
524C4—81no—
525C4—82no—
526C4—1521no—
527C4—1522no—
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—82no—
533C2—3041no—
534C2#1456265412yes—
535C2#1456268112yes—
536C2#1456463611yescharacteristic
537C2#1456465011yescharacteristic
538C2#1456476311yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC2×C19×#399C2
socleC23×C19#120
prime radical#14569369C2
hypercenterC2×#399D19
hypocenterC19#9920
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C2×#11926862C2semidirect
3. #14563725C2semidirect
4. C2×#11926277C2semidirect
5. C2×#11926268C2semidirect
6. #14561514C2semidirect
7. C2×C19×#399C2semidirect
46. C2×C4⋊C4×C19D4semidirect
70. C19×#95D4semidirect
76. C22⋊(C19⋊C8)D4semidirect
221. C2×#399D19semidirect
325. C2×C4⋊C4C22⋊D19semidirect
347. #95C22⋊D19semidirect
348. C19#9920semidirect

Maximal subgroups

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

subgroupindex
C2×#119268622
#145693692
#145637252
C2×#119262772
C2×#119262682
#145615142
C2×C19×#3992
#992019