Finite Group Databasebeta

← #18074845

Subgroups — #18074845

Order 4864.

706 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564485C211yesmaximal, characteristic, complemented
2#14562365C211yesmaximal, characteristic, complemented
3#14562242C211yesmaximal, characteristic, complemented
4#14562100C211yesmaximal, characteristic, complemented
5#14562056C211yesmaximal, characteristic, complemented
6#14561987C211yesmaximal, characteristic, complemented
7C19×#3561C211yesmaximal, characteristic
8#11926601C2211yescharacteristic
9#11926597C2211yescharacteristic
10#11926568C2211yescharacteristic
11C2×#10597293—21no—
12C2×#10597290—21no—
13C4×#64520C2211yescharacteristic
14#11926293—21no—
15#11926290—21no—
16#11926286—21no—
17#11926284—21no—
18Q8⋊(C19⋊C8)—22no—
19Q8⋊(C19⋊C8)—21no—
20D4⋊(C19⋊C8)—21no—
21#11926268—22no—
22C19×#563—21no—
23C19×#562—21no—
24C19×#556—21no—
25C19×#551—22no—
26D4×Q8×C19—21no—
27C19×#548—21no—
28C19×#546—21no—
29C19×#543C412yes—
30C19×#542—21no—
31C19×#542—22no—
32C19×#538C412yes—
33C19×#536—21no—
34C19×#533C2211yescharacteristic
35C19×#529C2211yescharacteristic
36C2×C19×#124C2211yescharacteristic
37C2×#41×C19—21no—
38C22×Q8×C19—21no—
39C22×Q8×C19D411yescharacteristic
40C22×D4×C19D411yescharacteristic
41C19×C4⋊Q8—21no—
42C19×C4⋊Q8—22no—
43C19×C4⋊Q8D411yescharacteristic
44C19×C4⋊Q8D411yescharacteristic
45C19×#126—22no—
46C19×#126—22no—
47C19×#126—22no—
48C19×#126—21no—
49C19×#125—21no—
50C19×#125D411yescharacteristic
51C19×#124—21no—
52C19×#124—22no—
53C19×#124—22no—
54C19×#124—21no—
55C19×#124—21no—
56C19×#124—21no—
57C19×#124—21no—
58C19×#124D411yescharacteristic
59C19×#123—22no—
60C19×#123—22no—
61C19×#123—22no—
62C19×#123—21no—
63C19×#123—22no—
64C19×C22⋊Q8—22no—
65C19×C22⋊Q8—21no—
66C19×C22⋊Q8—22no—
67C19×C22⋊Q8—22no—
68C19×C22⋊Q8—22no—
69C19×C22⋊Q8—22no—
70C19×C22⋊Q8—21no—
71C19×C22⋊Q8—22no—
72C19×C22⋊Q8—22no—
73C19×C22⋊Q8C2×C411yescharacteristic
74C19×C22⋊Q8C2×C412yes—
75C19×#121—21no—
76C19×#121—22no—
77C19×#121—22no—
78C19×#121C2×C411yescharacteristic
79C19×#120—22no—
80C4×Q8×C19—21no—
81C4×Q8×C19—21no—
82C4×Q8×C19D411yescharacteristic
83C4×Q8×C19D412yes—
84C4×D4×C19—21no—
85C4×D4×C19—22no—
86C4×D4×C19—22no—
87C4×D4×C19—21no—
88C4×D4×C19D411yescharacteristic
89C19×#117—22no—
90C19×#117—21no—
91C19×#117—21no—
92C2×C22⋊C4×C19—22no—
93C2×C22⋊C4×C19C2×C412yes—
94C2×C22⋊C4×C19D412yes—
95C2×C42×C19C2311yescharacteristic
96C2×#64520—21no—
97C2×#64520—21no—
98#10597293—42no—
99#10597290—42no—
100C22⋊(C19⋊C8)—21no—
101C22⋊(C19⋊C8)—21no—
102C4⋊(C19⋊C8)—21no—
103C4⋊(C19⋊C8)—21no—
104C4⋊(C19⋊C8)—21no—
105C4⋊(C19⋊C8)—21no—
106#10597260—21no—
107#10597260—21no—
108C4×C19⋊C8—21no—
109C4×C19⋊C8—21no—
110C24×C19C22⋊C412yes—
111#41×C19—81no—
112#41×C19—81no—
113C2×Q8×C19—22no—
114C2×Q8×C19—21no—
115C2×Q8×C19—21no—
116C2×Q8×C19—21no—
117C2×Q8×C19—41no—
118C2×Q8×C19—41no—
119C2×Q8×C19—81no—
120C2×Q8×C19—81no—
121C2×Q8×C19C22⋊C411yescharacteristic
122C2×Q8×C19C22⋊C412yes—
123C2×D4×C19—21no—
124C2×D4×C19—22no—
125C2×D4×C19—22no—
126C2×D4×C19—21no—
127C2×D4×C19—21no—
128C2×D4×C19—41no—
129C2×D4×C19—41no—
130C2×D4×C19C22⋊C411yescharacteristic
131C22×C4×C19—22no—
132C22×C4×C19—22no—
133C22×C4×C19—22no—
134C22×C4×C19—21no—
135C22×C4×C19C22⋊C412yes—
136C22×C4×C19C22×C411yescharacteristic
137C22×C4×C19C2×D411yescharacteristic
138C22×C4×C19C2×D411yescharacteristic
139C4⋊C4×C19—22no—
140C4⋊C4×C19—22no—
141C4⋊C4×C19—22no—
142C4⋊C4×C19—22no—
143C4⋊C4×C19—21no—
144C4⋊C4×C19—22no—
145C4⋊C4×C19—21no—
146C4⋊C4×C19—21no—
147C4⋊C4×C19—21no—
148C4⋊C4×C19—21no—
149C4⋊C4×C19—21no—
150C4⋊C4×C19—21no—
151C4⋊C4×C19—22no—
152C4⋊C4×C19C22⋊C411yescharacteristic
153C4⋊C4×C19C22⋊C411yescharacteristic
154C4⋊C4×C19C22⋊C412yes—
155C22⋊C4×C19—22no—
156C22⋊C4×C19—22no—
157C22⋊C4×C19—22no—
158C22⋊C4×C19—22no—
159C22⋊C4×C19—22no—
160C22⋊C4×C19—21no—
161C22⋊C4×C19—22no—
162C22⋊C4×C19—22no—
163C22⋊C4×C19—22no—
164C22⋊C4×C19—21no—
165C22⋊C4×C19—22no—
166C22⋊C4×C19—22no—
167C22⋊C4×C19—21no—
168C22⋊C4×C19—21no—
169C22⋊C4×C19—21no—
170C42×C19—22no—
171C42×C19—22no—
172C42×C19—21no—
173C42×C19C2×D411yescharacteristic
174C42×C19C2×D411yescharacteristic
175C42×C19C2×D411yescharacteristic
176C42×C19C2×D411yescharacteristic
177#64520—22no—
178#64520—41no—
179#64520—41no—
180#64520—41no—
181C2×C19⋊C8—41no—
182C2×C19⋊C8—41no—
183C2×C19⋊C8—41no—
184C2×C19⋊C8—41no—
185#8484—191nomaximal, Sylow
186C23×C19—22no—
187C23×C19—21no—
188C23×C19—42no—
189C23×C19—42no—
190C23×C19—42no—
191C23×C19C2×C22⋊C411yescharacteristic
192Q8×C19—41no—
193Q8×C19—42no—
194Q8×C19—41no—
195Q8×C19—41no—
196Q8×C19—41no—
197Q8×C19—41no—
198Q8×C19—81no—
199Q8×C19—82no—
200D4×C19—41no—
201D4×C19—42no—
202D4×C19—41no—
203D4×C19—41no—
204D4×C19—81no—
205D4×C19—82no—
206D4×C19—82no—
207C2×C4×C19—21no—
208C2×C4×C19—21no—
209C2×C4×C19—21no—
210C2×C4×C19—22no—
211C2×C4×C19—21no—
212C2×C4×C19—22no—
213C2×C4×C19—22no—
214C2×C4×C19—21no—
215C2×C4×C19—41no—
216C2×C4×C19—41no—
217C2×C4×C19—41no—
218C2×C4×C19—41no—
219C2×C4×C19—42no—
220C2×C4×C19—82no—
221C2×C4×C19—82no—
222C2×C4×C19—82no—
223C2×C4×C19C2×C22⋊C411yescharacteristic
224C2×C4×C19C2×C22⋊C411yescharacteristic
225C2×C4×C19#12011yescharacteristic
226C2×C4×C19#12011yescharacteristic
227C2×C4×C19#12011yescharacteristic
228C2×C4×C19#12011yescharacteristic
229C19⋊C8—42no—
230C19⋊C8—81no—
231C19⋊C8—81no—
232C19⋊C8—81no—
233#3561D1911yescharacteristic
234#1967—191no—
235#1559—191no—
236#1529—191no—
237#1495—191no—
238#1485—191no—
239#1469—191no—
240C22×C19—21no—
241C22×C19—21no—
242C22×C19—21no—
243C22×C19—41no—
244C22×C19—42no—
245C22×C19—41no—
246C22×C19—42no—
247C22×C19—42no—
248C22×C19—41no—
249C22×C19—162no—
250C22×C19#37911yescharacteristic
251C4×C19—21no—
252C4×C19—21no—
253C4×C19—21no—
254C4×C19—21no—
255C4×C19—21no—
256C4×C19—41no—
257C4×C19—42no—
258C4×C19—42no—
259C4×C19—41no—
260C4×C19—41no—
261C4×C19—42no—
262C4×C19#45311yescharacteristic
263C4×C19#45511yescharacteristic
264#563—21no—
265#562—21no—
266#556—21no—
267#551—22no—
268D4×Q8—21no—
269#548—21no—
270#546—21no—
271#543Dic1912yes—
272#542—21no—
273#542—22no—
274#538Dic1912yes—
275#536—21no—
276#533C2×D1911yescharacteristic
277#529C2×D1911yescharacteristic
278C2×#124C2×D1911yescharacteristic
279#432—191no—
280#431—191no—
281#423—191no—
282C2×#101—381no—
283C2×#100—381no—
284C4×M16—191no—
285#333—381no—
286#332—381no—
287#330—381no—
288#329—381no—
289Q8⋊C8—382no—
290Q8⋊C8—381no—
291D4⋊C8—381no—
292#323—382no—
293C2×C19—41no—
294C2×C19—81no—
295C2×C19—82no—
296C2×C19#179111yescharacteristic
297C2×C19#179211yescharacteristic
298C2×C19#179611yescharacteristic
299C2×#41—21no—
300C22×Q8—21no—
301C22×Q8C22⋊D1911yescharacteristic
302C22×D4C22⋊D1911yescharacteristic
303C2×M16—381no—
304C2×M16—381no—
305C4⋊Q8—21no—
306C4⋊Q8—22no—
307C4⋊Q8C22⋊D1911yescharacteristic
308C4⋊Q8C22⋊D1911yescharacteristic
309#126—22no—
310#126—22no—
311#126—22no—
312#126—21no—
313#125—21no—
314#125C22⋊D1911yescharacteristic
315#124—21no—
316#124—22no—
317#124—22no—
318#124—21no—
319#124—21no—
320#124—21no—
321#124—21no—
322#124C22⋊D1911yescharacteristic
323#123—22no—
324#123—22no—
325#123—22no—
326#123—21no—
327#123—22no—
328C22⋊Q8—22no—
329C22⋊Q8—21no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—21no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8C2×Dic1911yescharacteristic
338C22⋊Q8C2×Dic1912yes—
339#121—21no—
340#121—22no—
341#121—22no—
342#121C2×Dic1911yescharacteristic
343#120—22no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8C22⋊D1911yescharacteristic
347C4×Q8C22⋊D1912yes—
348C4×D4—21no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—21no—
352C4×D4C22⋊D1911yescharacteristic
353#117—22no—
354#117—21no—
355#117—21no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4C2×Dic1912yes—
358C2×C22⋊C4C22⋊D1912yes—
359C2×C42C22×D1911yescharacteristic
360C4⋊C8—381no—
361C4⋊C8—381no—
362C4⋊C8—381no—
363C4⋊C8—381no—
364#101—762no—
365#100—762no—
366C22⋊C8—381no—
367C22⋊C8—381no—
368#97—381no—
369#97—381no—
370C4×C8—381no—
371C4×C8—381no—
372C19#848411yescharacteristic, complemented, Sylow
373C24C22⋊Dic1912yes—
374#41—81no—
375#41—81no—
376C2×Q8—22no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—41no—
381C2×Q8—41no—
382C2×Q8—81no—
383C2×Q8—81no—
384C2×Q8C22⋊Dic1911yescharacteristic
385C2×Q8C22⋊Dic1912yes—
386C2×D4—21no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4C22⋊Dic1911yescharacteristic
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4C22⋊Dic1912yes—
399C22×C4C22×Dic1911yescharacteristic
400C22×C4C2×C22⋊D1911yescharacteristic
401C22×C4C2×C22⋊D1911yescharacteristic
402M16—382no—
403M16—761no—
404M16—761no—
405M16—761no—
406C2×C8—761no—
407C2×C8—761no—
408C2×C8—761no—
409C2×C8—761no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4C22⋊Dic1911yescharacteristic
424C4⋊C4C22⋊Dic1911yescharacteristic
425C4⋊C4C22⋊Dic1912yes—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—21no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—21no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—21no—
439C22⋊C4—21no—
440C22⋊C4—21no—
441C42—22no—
442C42—22no—
443C42—21no—
444C42C2×C22⋊D1911yescharacteristic
445C42C2×C22⋊D1911yescharacteristic
446C42C2×C22⋊D1911yescharacteristic
447C42C2×C22⋊D1911yescharacteristic
448C23—22no—
449C23—21no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23C2×C22⋊Dic1911yescharacteristic
454Q8—41no—
455Q8—42no—
456Q8—41no—
457Q8—41no—
458Q8—41no—
459Q8—41no—
460Q8—81no—
461Q8—82no—
462D4—41no—
463D4—42no—
464D4—41no—
465D4—41no—
466D4—81no—
467D4—82no—
468D4—82no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—82no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4C2×C22⋊Dic1911yescharacteristic
486C2×C4C2×C22⋊Dic1911yescharacteristic
487C2×C4#1059739911yescharacteristic
488C2×C4#1059739911yescharacteristic
489C2×C4#1059739911yescharacteristic
490C2×C4#1059739911yescharacteristic
491C8—762no—
492C8—1521no—
493C8—1521no—
494C8—1521no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—42no—
499C22—41no—
500C22—41no—
501C22—42no—
502C22—41no—
503C22—42no—
504C22—162no—
505C22#1192640011yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—21no—
511C4—41no—
512C4—42no—
513C4—41no—
514C4—42no—
515C4—42no—
516C4—41no—
517C4#1192671211yescharacteristic
518C4#1192672211yescharacteristic
519C2—41no—
520C2—82no—
521C2—81no—
522C2#1456358611yescharacteristic
523C2#1456358911yescharacteristic
524C2#1456361011yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3561C2
socleC22×C19#379
cosocleC2×C42×C19C23
hypercenter#3561D19
hypocenterC19#8484
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3561

Complements

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

NH ≅ G/Ntype
1. #14564485C2semidirect
2. #14562365C2semidirect
3. #14562242C2semidirect
4. #14562100C2semidirect
5. #14562056C2semidirect
6. #14561987C2semidirect
372. C19#8484semidirect

Maximal subgroups

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

subgroupindex
#145644852
#145623652
#145622422
#145621002
#145620562
#145619872
C19×#35612
#848419