Finite Group Databasebeta

← #18074327

Subgroups — #18074327

Order 4864.

858 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14563938C212yesmaximal, complemented
2#14563933C211yesmaximal, characteristic, complemented
3C4×#10597291C211yesmaximal, characteristic, complemented
4#14562126C212yesmaximal, complemented
5C19×#3460C211yesmaximal, characteristic
6C22×#64520C2211yescharacteristic
7C2×#10597294—22no—
8C2×#10597291—21no—
9C2×C22⋊(C19⋊C8)—21no—
10C2×C22⋊(C19⋊C8)C2211yescharacteristic
11C4×C22⋊Dic19C2212yes—
12#11926311—21no—
13#11926303—22no—
14#11926299—21no—
15#11926281—22no—
16#11926278—22no—
17C19×#544C411yescharacteristic, complemented
18C19×#542—22no—
19C19×#540—22no—
20C19×#538—21no—
21C19×#538C412yescomplemented
22C19×#537C411yescharacteristic, complemented
23C19×#535—21no—
24C19×#532—22no—
25C19×#529—22no—
26C19×#525—21no—
27C19×#525C2212yes—
28C4×#41×C19—21no—
29C2×C4×D4×C19C2211yescharacteristic
30C2×#41×C19—21no—
31C2×#41×C19—21no—
32C2×#41×C19D412yes—
33C22×D4×C19D411yescharacteristic
34C23×C4×C19D411yescharacteristic
35C23×C4×C19C2311yescharacteristic
36C19×C4⋊Q8—22no—
37C19×#127—22no—
38C19×#126—22no—
39C19×#126—22no—
40C19×#125—22no—
41C19×#124—22no—
42C19×#124—22no—
43C19×#124—22no—
44C19×#123—22no—
45C19×#123—22no—
46C19×#123—22no—
47C19×#123—22no—
48C19×C22⋊Q8—21no—
49C19×C22⋊Q8—21no—
50C19×C22⋊Q8—22no—
51C19×C22⋊Q8C2×C412yes—
52C19×C22⋊Q8D412yes—
53C19×#121—21no—
54C19×#121—22no—
55C19×#121—22no—
56C19×#121—22no—
57C19×#121—22no—
58C19×#121—22no—
59C19×#121—21no—
60C19×#121C2×C412yes—
61C19×#121D412yes—
62C19×#120—22no—
63C19×#120—22no—
64C4×Q8×C19—21no—
65C4×Q8×C19—21no—
66C4×D4×C19—21no—
67C4×D4×C19—21no—
68C4×D4×C19—22no—
69C4×D4×C19—22no—
70C4×D4×C19—22no—
71C4×D4×C19—22no—
72C4×D4×C19—22no—
73C4×D4×C19—22no—
74C19×#117—22no—
75C19×#117—21no—
76C19×#117—21no—
77C19×#117D412yes—
78C2×C4⋊C4×C19C2×C411yescharacteristic
79C2×C22⋊C4×C19C2×C411yescharacteristic
80C2×C22⋊C4×C19D411yescharacteristic
81C2×C42×C19—22no—
82C2×C42×C19D411yescharacteristic
83C2×C22⋊Dic19—22no—
84C2×C4×Dic19—22no—
85C2×#64520—22no—
86C2×#64520—42no—
87C22×C19⋊C8—21no—
88C22×C19⋊C8—21no—
89#10597294—44no—
90#10597291—24no—
91C19⋊#95—22no—
92C22⋊(C19⋊C8)—22no—
93C22⋊(C19⋊C8)—42no—
94C24×C19C22⋊C411yescharacteristic
95C24×C19C2×D411yescharacteristic
96#41×C19—42no—
97#41×C19—42no—
98#41×C19—42no—
99#41×C19—42no—
100#41×C19—81no—
101#41×C19—81no—
102C2×Q8×C19—21no—
103C2×Q8×C19—21no—
104C2×Q8×C19C22⋊C412yes—
105C2×D4×C19—21no—
106C2×D4×C19—22no—
107C2×D4×C19—22no—
108C2×D4×C19—22no—
109C2×D4×C19—22no—
110C2×D4×C19—21no—
111C2×D4×C19—22no—
112C2×D4×C19—22no—
113C2×D4×C19—22no—
114C2×D4×C19—41no—
115C2×D4×C19C22⋊C412yes—
116C22×C4×C19—22no—
117C22×C4×C19—22no—
118C22×C4×C19—22no—
119C22×C4×C19—21no—
120C22×C4×C19—21no—
121C22×C4×C19—41no—
122C22×C4×C19—41no—
123C22×C4×C19—41no—
124C22×C4×C19—41no—
125C22×C4×C19C22⋊C411yescharacteristic
126C22×C4×C19C22⋊C411yescharacteristic
127C22×C4×C19C22⋊C411yescharacteristic
128C22×C4×C19C22×C411yescharacteristic
129C22×C4×C19C2×D412yes—
130C22×C4×C19C2×D411yescharacteristic
131C22×C4×C19C2×D412yes—
132C22×Dic19—42no—
133C4⋊C4×C19—21no—
134C4⋊C4×C19—21no—
135C4⋊C4×C19—22no—
136C4⋊C4×C19—21no—
137C4⋊C4×C19—21no—
138C4⋊C4×C19—22no—
139C4⋊C4×C19—22no—
140C4⋊C4×C19—22no—
141C4⋊C4×C19—22no—
142C4⋊C4×C19C22⋊C412yes—
143C4⋊C4×C19C22⋊C412yes—
144C22⋊C4×C19—22no—
145C22⋊C4×C19—22no—
146C22⋊C4×C19—22no—
147C22⋊C4×C19—22no—
148C22⋊C4×C19—22no—
149C22⋊C4×C19—22no—
150C22⋊C4×C19—22no—
151C22⋊C4×C19—22no—
152C22⋊C4×C19—22no—
153C22⋊C4×C19—22no—
154C22⋊C4×C19—22no—
155C42×C19—22no—
156C42×C19—22no—
157C42×C19—21no—
158C42×C19—22no—
159C42×C19—21no—
160C22⋊Dic19—24no—
161C22⋊Dic19—42no—
162C4×Dic19—42no—
163C4×Dic19—42no—
164#64520—24no—
165#64520—42no—
166C2×C19⋊C8—22no—
167C2×C19⋊C8—41no—
168C2×C19⋊C8—41no—
169C2×C19⋊C8—41no—
170C2×C19⋊C8—41no—
171C2×C19⋊C8—41no—
172#8400—191nomaximal, Sylow
173C23×C19—21no—
174C23×C19—21no—
175C23×C19—21no—
176C23×C19—22no—
177C23×C19—21no—
178C23×C19—21no—
179C23×C19—41no—
180C23×C19—41no—
181C23×C19—41no—
182C23×C19—41no—
183C23×C19C2×C22⋊C411yescharacteristic
184C23×C19#12012yes—
185Q8×C19—42no—
186Q8×C19—42no—
187Q8×C19—81no—
188D4×C19—44no—
189D4×C19—42no—
190D4×C19—42no—
191D4×C19—42no—
192D4×C19—42no—
193D4×C19—82no—
194D4×C19—82no—
195D4×C19—82no—
196D4×C19—81no—
197D4×C19—82no—
198C2×C4×C19—21no—
199C2×C4×C19—21no—
200C2×C4×C19—21no—
201C2×C4×C19—22no—
202C2×C4×C19—21no—
203C2×C4×C19—22no—
204C2×C4×C19—21no—
205C2×C4×C19—22no—
206C2×C4×C19—22no—
207C2×C4×C19—22no—
208C2×C4×C19—21no—
209C2×C4×C19—41no—
210C2×C4×C19—42no—
211C2×C4×C19—44no—
212C2×C4×C19—41no—
213C2×C4×C19—42no—
214C2×C4×C19—41no—
215C2×C4×C19—42no—
216C2×C4×C19—41no—
217C2×C4×C19—41no—
218C2×C4×C19—81no—
219C2×C4×C19—82no—
220C2×C4×C19#10412yescomplemented
221C2×C4×C19C2×C22⋊C412yes—
222C2×C4×C19#12011yescharacteristic
223C2×C4×C19#12011yescharacteristic
224C2×Dic19—44no—
225C2×Dic19—82no—
226C2×Dic19—82no—
227C19⋊C8—42no—
228C19⋊C8—81no—
229#3460D1911yescharacteristic
230#1871—192no—
231#1870—191no—
232C4×#99—191no—
233#1501—192no—
234C22×C19—21no—
235C22×C19—21no—
236C22×C19—22no—
237C22×C19—22no—
238C22×C19—22no—
239C22×C19—42no—
240C22×C19—42no—
241C22×C19—41no—
242C22×C19—42no—
243C22×C19—41no—
244C22×C19—41no—
245C22×C19—42no—
246C22×C19—81no—
247C22×C19—81no—
248C22×C19—81no—
249C22×C19#37911yescharacteristic
250C22×C19C2×#10411yescharacteristic
251C22×C19#42111yescharacteristic
252C4×C19—22no—
253C4×C19—21no—
254C4×C19—22no—
255C4×C19—41no—
256C4×C19—42no—
257C4×C19—42no—
258C4×C19—41no—
259C4×C19—42no—
260C4×C19B(4,𝔽2)11yescharacteristic
261C4×C19#45811yescharacteristic
262Dic19—84no—
263C22×M16—191no—
264#544Dic1911yescharacteristic, complemented
265#542—22no—
266#540—22no—
267#538—21no—
268#538Dic1912yescomplemented
269#537Dic1911yescharacteristic, complemented
270#535—21no—
271#532—22no—
272#529—22no—
273#525—21no—
274#525C2×D1912yes—
275C4×#41—21no—
276C2×C4×D4C2×D1911yescharacteristic
277C2×#104—382no—
278C2×#99—381no—
279C2×C22⋊C8—191no—
280C2×C22⋊C8—381no—
281C4×C22⋊C4—192no—
282#342—381no—
283#339—382no—
284#336—381no—
285#328—382no—
286#327—382no—
287C2×C19—21no—
288C2×C19—21no—
289C2×C19—42no—
290C2×C19—82no—
291C2×C19—81no—
292C2×C19#178911yescharacteristic
293C2×C19#179011yescharacteristic
294C2×C19#179411yescharacteristic
295C2×#41—21no—
296C2×#41—21no—
297C2×#41C22⋊D1912yes—
298C22×D4C22⋊D1911yescharacteristic
299C23×C4C22⋊D1911yescharacteristic
300C23×C4C22×D1911yescharacteristic
301C2×M16—382no—
302C2×M16—762no—
303C22×C8—381no—
304C22×C8—381no—
305C4⋊Q8—22no—
306#127—22no—
307#126—22no—
308#126—22no—
309#125—22no—
310#124—22no—
311#124—22no—
312#124—22no—
313#123—22no—
314#123—22no—
315#123—22no—
316#123—22no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—22no—
320C22⋊Q8C2×Dic1912yes—
321C22⋊Q8C22⋊D1912yes—
322#121—21no—
323#121—22no—
324#121—22no—
325#121—22no—
326#121—22no—
327#121—22no—
328#121—21no—
329#121C2×Dic1912yes—
330#121C22⋊D1912yes—
331#120—22no—
332#120—22no—
333C4×Q8—21no—
334C4×Q8—21no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—22no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4—22no—
342C4×D4—22no—
343#117—22no—
344#117—21no—
345#117—21no—
346#117C22⋊D1912yes—
347C2×C4⋊C4C2×Dic1911yescharacteristic
348C2×C22⋊C4—382no—
349C2×C22⋊C4C2×Dic1911yescharacteristic
350C2×C22⋊C4C22⋊D1911yescharacteristic
351C2×C42—22no—
352C2×C42—382no—
353C2×C42C22⋊D1911yescharacteristic
354#104—764no—
355#99—384no—
356C22⋊C8—382no—
357C22⋊C8—762no—
358#95—382no—
359C19#840011yescharacteristic, complemented, Sylow
360C24C22⋊Dic1911yescharacteristic
361C24C2×C22⋊D1911yescharacteristic
362#41—42no—
363#41—42no—
364#41—42no—
365#41—42no—
366#41—81no—
367#41—81no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8C22⋊Dic1912yes—
371C2×D4—21no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—21no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—41no—
381C2×D4C22⋊Dic1912yes—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—762no—
392C22×C4C22⋊Dic1911yescharacteristic
393C22×C4C22⋊Dic1911yescharacteristic
394C22×C4C22⋊Dic1911yescharacteristic
395C22×C4C22×Dic1911yescharacteristic
396C22×C4C2×C22⋊D1912yes—
397C22×C4C2×C22⋊D1911yescharacteristic
398C22×C4C2×C22⋊D1912yes—
399M16—384no—
400M16—762no—
401C2×C8—382no—
402C2×C8—761no—
403C2×C8—761no—
404C2×C8—761no—
405C2×C8—761no—
406C2×C8—761no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4C22⋊Dic1912yes—
417C4⋊C4C22⋊Dic1912yes—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—384no—
430C22⋊C4—762no—
431C42—22no—
432C42—22no—
433C42—21no—
434C42—21no—
435C42—22no—
436C42—762no—
437C42—762no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—22no—
443C23—21no—
444C23—41no—
445C23—41no—
446C23—41no—
447C23—41no—
448C23C2×C22⋊Dic1911yescharacteristic
449C23#1059739912yes—
450Q8—42no—
451Q8—42no—
452Q8—81no—
453D4—44no—
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—82no—
459D4—82no—
460D4—81no—
461D4—82no—
462D4—82no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—44no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—81no—
484C2×C4—82no—
485C2×C4—764no—
486C2×C4—1522no—
487C2×C4—1522no—
488C2×C4#1059729412yescomplemented
489C2×C4C2×C22⋊Dic1912yes—
490C2×C4#1059739911yescharacteristic
491C2×C4#1059739911yescharacteristic
492C8—762no—
493C8—1521no—
494C22—21no—
495C22—21no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—42no—
500C22—42no—
501C22—41no—
502C22—42no—
503C22—41no—
504C22—41no—
505C22—42no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22#1192640011yescharacteristic
510C22C2×#1059729411yescharacteristic
511C22#1192656111yescharacteristic
512C4—22no—
513C4—21no—
514C4—22no—
515C4—41no—
516C4—42no—
517C4—42no—
518C4—41no—
519C4—42no—
520C4—1524no—
521C4#1192673111yescharacteristic
522C4#1192673411yescharacteristic
523C2—21no—
524C2—21no—
525C2—42no—
526C2—81no—
527C2—82no—
528C2#1456357911yescharacteristic
529C2#1456358311yescharacteristic
530C2#1456359911yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#3460C2
socleC22×C19#379
cosocleC23×C4×C19C23
hypercenter#3460D19
hypocenterC19#8400
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3460

Complements

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

NH ≅ G/Ntype
1. #14563938C2semidirect
2. #14563933C2semidirect
3. C4×#10597291C2semidirect
4. #14562126C2semidirect
17. C19×#544C4semidirect
21. C19×#538C4semidirect
22. C19×#537C4semidirect
220. C2×C4×C19#104semidirect
264. #544Dic19semidirect
268. #538Dic19semidirect
269. #537Dic19semidirect
359. C19#8400semidirect
488. C2×C4#10597294semidirect

Maximal subgroups

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

subgroupindex
#145639382
#145639332
C4×#105972912
#145621262
C19×#34602
#840019