Finite Group Databasebeta

← #18082763

Subgroups — #18082763

Order 4864.

812 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926857C211yesmaximal, characteristic, complemented
2#14569369C211yesmaximal, characteristic
3#14563721C211yesmaximal, characteristic, complemented
4C2×#11926277C211yesmaximal, characteristic, complemented
5C2×#11926268C211yesmaximal, characteristic, complemented
6#14561514C211yesmaximal, characteristic, complemented
7C2×C19×#397C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9C2×#10597399—21no—
10#11926857—22no—
11#11926857—22no—
12C2×#10597264—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×C19C2211yescharacteristic
25C22×C22⋊C4×C19—21no—
26C22×C22⋊C4×C19C2211yescharacteristic
27C19×#397—22no—
28C19×#397—22no—
29C2×C19×#95—21no—
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—21no—
44C2×C4⋊C4×C19D412yescomplemented
45C2×C22⋊C4×C19—24no—
46C2×C22⋊C4×C19—21no—
47C2×C22⋊C4×C19—21no—
48C2×C22⋊C4×C19—21no—
49C2×C22⋊C4×C19—21no—
50C2×C22⋊C4×C19—21no—
51C2×C22⋊C4×C19—21no—
52C2×C22⋊C4×C19—42no—
53C2×C22⋊C4×C19—42no—
54#10597399—42no—
55#10597399—42no—
56C2×C22⋊Dic19—22no—
57C2×C22⋊Dic19—21no—
58#10597376—21no—
59#10597376—21no—
60#10597376—21no—
61#10597376—21no—
62C2×(C2×D19)⋊C4—21no—
63C2×(C2×D19)⋊C4—22no—
64C2×C4⋊Dic19D411yescharacteristic
65C2×C4⋊Dic19D412yes—
66C22×C19⋊C8—21no—
67C22×C19⋊C8—21no—
68C19×#95—24no—
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#10597264—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×C19D812yes—
88C24×C19C2×D411yescharacteristic
89C23×D19—21no—
90C22×C4×C19—22no—
91C22×C4×C19—22no—
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—42no—
99C22×C4×C19—41no—
100C22×C4×C19—41no—
101C22×C4×C19—41no—
102C22×C4×C19—41no—
103C22×C4×C19—41no—
104C22×C4×C19—41no—
105C22×C4×C19—41no—
106C22×C4×C19—41no—
107C22×C4×C19C2×D411yescharacteristic
108C22×C4×C19C2×D411yescharacteristic
109C22×C4×C19C2×D411yescharacteristic
110C22×C4×C19C2×D411yescharacteristic
111C22×C4×C19C2×D411yescharacteristic
112C22×C4×C19#4111yescharacteristic
113C2×C22⋊D19—44no—
114C2×C22⋊D19—41no—
115C2×C22⋊D19—41no—
116C2×C22⋊D19—41no—
117C2×C22⋊D19—41no—
118C2×C22⋊D19—41no—
119C2×C22⋊D19—41no—
120C2×C22⋊D19—82no—
121C2×C22⋊D19—82no—
122C22×Dic19—21no—
123C22×Dic19—22no—
124C2×D76—21no—
125C2×D76—21no—
126C2×D76—42no—
127C4⋊C4×C19—22no—
128C4⋊C4×C19—22no—
129C4⋊C4×C19—41no—
130C4⋊C4×C19—41no—
131C22⋊C4×C19—48no—
132C22⋊C4×C19—41no—
133C22⋊C4×C19—41no—
134C22⋊C4×C19—41no—
135C22⋊C4×C19—41no—
136C22⋊Dic19—44no—
137C22⋊Dic19—41no—
138C22⋊Dic19—41no—
139(C2×D19)⋊C4—41no—
140(C2×D19)⋊C4—41no—
141(C2×D19)⋊C4—82no—
142C4⋊Dic19—21no—
143C4⋊Dic19—21no—
144C4⋊Dic19—42no—
145C2×C19⋊C8—22no—
146C2×C19⋊C8—42no—
147C2×C19⋊C8—42no—
148C2×C19⋊C8—41no—
149#9918—191nomaximal, Sylow
150C23×C19—22no—
151C23×C19—22no—
152C23×C19—22no—
153C23×C19—22no—
154C23×C19—22no—
155C23×C19—44no—
156C23×C19—44no—
157C23×C19—42no—
158C23×C19—42no—
159C23×C19—41no—
160C23×C19—41no—
161C23×C19—41no—
162C23×C19—42no—
163C23×C19—42no—
164C23×C19—41no—
165C23×C19—82no—
166C23×C19—82no—
167C23×C19—81no—
168C23×C19—81no—
169C23×C19#12011yescharacteristic
170C23×C19#12011yescharacteristic
171C23×C19#12111yescharacteristic
172C23×C19C2×D811yescharacteristic
173C23×C19#13511yescharacteristic
174C23×C19AGL(1,ℤ/8)11yescharacteristic
175C23×C19AGL(1,ℤ/8)11yescharacteristic
176C22×D19—41no—
177C22×D19—41no—
178C22×D19—41no—
179C22×D19—42no—
180C22×D19—42no—
181C2×C4×C19—22no—
182C2×C4×C19—22no—
183C2×C4×C19—41no—
184C2×C4×C19—41no—
185C2×C4×C19—41no—
186C2×C4×C19—41no—
187C2×C4×C19—42no—
188C2×C4×C19—42no—
189C2×C4×C19—42no—
190C2×C4×C19—41no—
191C2×C4×C19—42no—
192C2×C4×C19—42no—
193C2×C4×C19—42no—
194C2×C4×C19—42no—
195C2×C4×C19—42no—
196C2×C4×C19—82no—
197C2×C4×C19—82no—
198C2×C4×C19—81no—
199C2×C4×C19—81no—
200C2×C4×C19—81no—
201C2×C4×C19—81no—
202C2×C4×C19—81no—
203C2×C4×C19#12011yescharacteristic
204C2×C4×C19#12111yescharacteristic
205C2×C4×C19#12111yescharacteristic
206C2×C4×C19#12711yescharacteristic
207C22⋊D19—88no—
208C22⋊D19—81no—
209C22⋊D19—81no—
210C22⋊D19—81no—
211C22⋊D19—81no—
212C2×Dic19—41no—
213C2×Dic19—42no—
214C2×Dic19—41no—
215C2×Dic19—41no—
216C2×Dic19—42no—
217C2×Dic19—42no—
218D76—42no—
219D76—81no—
220C19⋊C8—42no—
221C19⋊C8—81no—
222C2×#480—191no—
223#2617—191no—
224C2×#397D1911yescharacteristic, complemented
225#1823—191no—
226C2×#327—191no—
227C2×#323—191no—
228#1294—191no—
229C22×C19—22no—
230C22×C19—22no—
231C22×C19—22no—
232C22×C19—22no—
233C22×C19—21no—
234C22×C19—21no—
235C22×C19—21no—
236C22×C19—21no—
237C22×C19—44no—
238C22×C19—44no—
239C22×C19—42no—
240C22×C19—82no—
241C22×C19—82no—
242C22×C19—82no—
243C22×C19—82no—
244C22×C19—81no—
245C22×C19—81no—
246C22×C19#39211yescharacteristic
247C22×C19#44711yescharacteristic
248C22×C19#44711yescharacteristic
249C22×C19#44911yescharacteristic
250C22×C19#44911yescharacteristic
251C22×C19#45512yes—
252C22×C19#45812yes—
253C22×C19#46611yescharacteristic
254C22×C19#46911yescharacteristic
255C2×D19—82no—
256C2×D19—82no—
257C2×D19—81no—
258C2×D19—81no—
259C2×D19—81no—
260C4×C19—21no—
261C4×C19—21no—
262C4×C19—21no—
263C4×C19—21no—
264C4×C19—82no—
265C4×C19—82no—
266C4×C19—81no—
267Dic19—82no—
268Dic19—81no—
269C2×#121—191no—
270C2×#120—381no—
271C22×C4⋊C4C2×D1911yescharacteristic
272C22×C22⋊C4—21no—
273C22×C22⋊C4C2×D1911yescharacteristic
274#480—382no—
275#480—382no—
276C2×#107—381no—
277C2×#102—381no—
278C2×C22⋊C8—191no—
279C2×C22⋊C8—191no—
280#397—22no—
281#397—22no—
282#397—381no—
283#394—382no—
284#392—381no—
285#386—381no—
286#380—191no—
287C2×#95—21no—
288C2×#95C2×D1911yescharacteristic
289#340—382no—
290#327—382no—
291#323—382no—
292C2×C19—21no—
293C2×C19—21no—
294C2×C19—21no—
295C2×C19—21no—
296C2×C19—82no—
297C2×C19#160712yes—
298C2×C19#161212yes—
299C2×C19#199911yescharacteristic
300C2×C19#200411yescharacteristic
301C2×C19#202211yescharacteristic
302D19—161no—
303C25C22⋊D1911yescharacteristic
304C22×D4—191no—
305C22×D4—381no—
306C22×D4—382no—
307C23×C4—21no—
308C23×C4—21no—
309C23×C4C22⋊D1911yescharacteristic
310C23×C4C22×D1911yescharacteristic
311C22×C8—381no—
312C22×C8—381no—
313#121—381no—
314#121—381no—
315#121—381no—
316#121—381no—
317#120—762no—
318#120—762no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—191no—
325C2×C4⋊C4—192no—
326C2×C4⋊C4C22⋊D1912yescomplemented
327C2×C22⋊C4—24no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—382no—
337C2×C22⋊C4—381no—
338C2×C22⋊C4—381no—
339C2×C22⋊C4—382no—
340#107—384no—
341#102—384no—
342C22⋊C8—192no—
343C22⋊C8—381no—
344C22⋊C8—381no—
345C22⋊C8—381no—
346#95—24no—
347#95—21no—
348#95—382no—
349#95—381no—
350#95C22⋊D1912yescomplemented
351C19#991811yescharacteristic, complemented, Sylow
352C24—21no—
353C24—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—42no—
359C24—42no—
360C24—381no—
361C24#6452512yes—
362C24C2×C22⋊D1911yescharacteristic
363C2×D4—381no—
364C2×D4—381no—
365C2×D4—762no—
366C2×D4—764no—
367C2×D4—761no—
368C2×D4—761no—
369C2×D4—761no—
370C2×D4—761no—
371C2×D4—761no—
372C2×D4—761no—
373C2×D4—1522no—
374C2×D4—1522no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—381no—
393C22×C4—382no—
394C22×C4D4×D1911yescharacteristic
395C22×C4D4×D1911yescharacteristic
396C22×C4D4×D1911yescharacteristic
397C22×C4#6454311yescharacteristic
398C22×C4C2×C22⋊D1911yescharacteristic
399C22×C4C2×C22⋊D1911yescharacteristic
400C2×C8—382no—
401C2×C8—762no—
402C2×C8—762no—
403C2×C8—761no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—381no—
409C4⋊C4—381no—
410C4⋊C4—762no—
411C22⋊C4—48no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—764no—
417C22⋊C4—761no—
418C22⋊C4—761no—
419C22⋊C4—761no—
420C22⋊C4—761no—
421C22⋊C4—1522no—
422C23—22no—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—22no—
427C23—44no—
428C23—42no—
429C23—44no—
430C23—42no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—42no—
436C23—42no—
437C23—82no—
438C23—81no—
439C23—82no—
440C23—81no—
441C23—761no—
442C23—761no—
443C23—761no—
444C23—762no—
445C23—762no—
446C23C2×#6452511yescharacteristic
447C23#1059737811yescharacteristic
448C23#1059738311yescharacteristic
449C23#1059738511yescharacteristic
450C23#1059739511yescharacteristic
451C23#1059739611yescharacteristic
452C23#1059739911yescharacteristic
453D4—762no—
454D4—1521no—
455D4—1528no—
456D4—1521no—
457D4—1521no—
458D4—1521no—
459D4—1521no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—82no—
476C2×C4—82no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4—81no—
482C2×C4—761no—
483C2×C4—762no—
484C2×C4—761no—
485C2×C4—761no—
486C2×C4—762no—
487C2×C4—762no—
488C2×C4#1059738311yescharacteristic
489C2×C4#1059738411yescharacteristic
490C2×C4#1059738511yescharacteristic
491C2×C4#1059738611yescharacteristic
492C8—762no—
493C8—1521no—
494C22—21no—
495C22—21no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—21no—
501C22—21no—
502C22—44no—
503C22—42no—
504C22—44no—
505C22—82no—
506C22—82no—
507C22—82no—
508C22—81no—
509C22—82no—
510C22—81no—
511C22—1521no—
512C22—1521no—
513C22—1522no—
514C22—1522no—
515C22—1521no—
516C22#1192645211yescharacteristic
517C22#1192667711yescharacteristic
518C22#1192667811yescharacteristic
519C22#1192668711yescharacteristic
520C22#1192668911yescharacteristic
521C22#1192672112yes—
522C22#1192673312yes—
523C22#1192677811yescharacteristic
524C22#1192679511yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—82no—
530C4—82no—
531C4—81no—
532C4—1521no—
533C4—1522no—
534C2—21no—
535C2—21no—
536C2—21no—
537C2—21no—
538C2—82no—
539C2—3041no—
540C2#1456262012yes—
541C2#1456264712yes—
542C2#1456463111yescharacteristic
543C2#1456466411yescharacteristic
544C2#1456476311yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC2×C19×#397C2
socleC23×C19#120
prime radical#14569369C2
hypercenterC2×#397D19
hypocenterC19#9918
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C2×#11926857C2semidirect
3. #14563721C2semidirect
4. C2×#11926277C2semidirect
5. C2×#11926268C2semidirect
6. #14561514C2semidirect
7. C2×C19×#397C2semidirect
44. C2×C4⋊C4×C19D4semidirect
70. C19×#95D4semidirect
76. C22⋊(C19⋊C8)D4semidirect
224. C2×#397D19semidirect
326. C2×C4⋊C4C22⋊D19semidirect
350. #95C22⋊D19semidirect
351. C19#9918semidirect

Maximal subgroups

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

subgroupindex
C2×#119268572
#145693692
#145637212
C2×#119262772
C2×#119262682
#145615142
C2×C19×#3972
#991819