Finite Group Databasebeta

← #18074966

Subgroups — #18074966

Order 4864.

672 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14562345C211yesmaximal, characteristic, complemented
2#14562266C211yesmaximal, characteristic, complemented
3#14562212C211yesmaximal, characteristic, complemented
4#14562186C211yesmaximal, characteristic, complemented
5#14562182C211yesmaximal, characteristic, complemented
6#14562104C211yesmaximal, characteristic, complemented
7C19×#3554C211yesmaximal, characteristic
8#11926601C2211yescharacteristic
9#11926601C2211yescharacteristic
10#11926597C2211yescharacteristic
11#11926412C2211yescharacteristic
12#11926293—21no—
13#11926290—21no—
14#11926286—21no—
15#11926284—21no—
16#11926281—21no—
17#11926281—21no—
18#11926281—21no—
19#11926278—22no—
20#11926278—21no—
21D4⋊(C19⋊C8)—22no—
22C19×#562—22no—
23C19×#559—21no—
24C19×#559C411yescharacteristic, complemented
25C19×#557C411yescharacteristic, complemented
26C19×#554—21no—
27C19×#550C411yescharacteristic, complemented
28D4×Q8×C19C411yescharacteristic, complemented
29C19×#548—21no—
30C19×#547—21no—
31C19×#542—21no—
32C19×#542—21no—
33C19×#540—21no—
34C19×#539—22no—
35C19×#536—21no—
36C19×#533C2211yescharacteristic
37C19×#532C2211yescharacteristic
38C19×#529C2211yescharacteristic
39C2×#41×C19—21no—
40C2×#41×C19—21no—
41C22×Q8×C19—21no—
42C19×C4⋊Q8—21no—
43C19×C4⋊Q8—21no—
44C19×C4⋊Q8C2×C411yescharacteristic
45C19×C4⋊Q8D411yescharacteristic
46C19×C4⋊Q8D411yescharacteristic
47C19×#127—21no—
48C19×#127C2×C411yescharacteristic
49C19×#126—22no—
50C19×#126—21no—
51C19×#125—22no—
52C19×#125—21no—
53C19×#125—21no—
54C19×#125D411yescharacteristic
55C19×#124—22no—
56C19×#124—22no—
57C19×#124—21no—
58C19×#124—21no—
59C19×#124—21no—
60C19×#124D411yescharacteristic
61C19×#123—22no—
62C19×#123—22no—
63C19×#123—22no—
64C19×#123—22no—
65C19×#123—22no—
66C19×#123—22no—
67C19×#123—21no—
68C19×C22⋊Q8—22no—
69C19×C22⋊Q8—22no—
70C19×C22⋊Q8—22no—
71C19×C22⋊Q8—22no—
72C19×C22⋊Q8—21no—
73C19×C22⋊Q8—22no—
74C19×C22⋊Q8—21no—
75C19×C22⋊Q8D411yescharacteristic
76C19×C22⋊Q8D411yescharacteristic
77C19×C22⋊Q8D411yescharacteristic
78C19×#121—22no—
79C19×#121—22no—
80C19×#121—22no—
81C19×#121—21no—
82C19×#121—21no—
83C19×#121D411yescharacteristic
84C19×#121D412yes—
85C4×Q8×C19—21no—
86C4×Q8×C19—21no—
87C4×Q8×C19—21no—
88C4×Q8×C19C2×C411yescharacteristic
89C4×Q8×C19C2×C411yescharacteristic
90C4×Q8×C19C2×C411yescharacteristic
91C4×D4×C19—22no—
92C4×D4×C19—21no—
93C4×D4×C19—21no—
94C4×D4×C19—21no—
95C4×D4×C19—21no—
96C4×D4×C19—21no—
97C4×D4×C19—21no—
98C4×D4×C19C2×C411yescharacteristic
99C4×D4×C19D412yes—
100C19×#117—21no—
101C19×#117—21no—
102C2×C4⋊C4×C19—22no—
103C2×C42×C19C2311yescharacteristic
104C19⋊#95—21no—
105C19⋊#95—21no—
106C19⋊#95—21no—
107C22⋊(C19⋊C8)—21no—
108C22⋊(C19⋊C8)—21no—
109C22⋊(C19⋊C8)—21no—
110C4⋊(C19⋊C8)—21no—
111C4⋊(C19⋊C8)—21no—
112C4⋊(C19⋊C8)—21no—
113#10597260—21no—
114#10597260—21no—
115C4×C19⋊C8—21no—
116#41×C19—82no—
117#41×C19—82no—
118C2×Q8×C19—22no—
119C2×Q8×C19—21no—
120C2×Q8×C19—21no—
121C2×Q8×C19—82no—
122C2×Q8×C19C22⋊C411yescharacteristic
123C2×Q8×C19C22⋊C411yescharacteristic
124C2×Q8×C19C22⋊C411yescharacteristic
125C2×D4×C19—22no—
126C2×D4×C19—22no—
127C2×D4×C19—21no—
128C2×D4×C19—22no—
129C2×D4×C19—21no—
130C2×D4×C19—21no—
131C2×D4×C19C22⋊C411yescharacteristic
132C2×D4×C19C22⋊C412yes—
133C22×C4×C19—22no—
134C22×C4×C19—22no—
135C22×C4×C19—22no—
136C22×C4×C19—21no—
137C22×C4×C19—22no—
138C22×C4×C19C2×D411yescharacteristic
139C22×C4×C19C2×D411yescharacteristic
140C22×C4×C19C2×D411yescharacteristic
141C22×Dic19—41no—
142C4⋊C4×C19—22no—
143C4⋊C4×C19—22no—
144C4⋊C4×C19—22no—
145C4⋊C4×C19—22no—
146C4⋊C4×C19—21no—
147C4⋊C4×C19—21no—
148C4⋊C4×C19—21no—
149C4⋊C4×C19—21no—
150C4⋊C4×C19—21no—
151C4⋊C4×C19—21no—
152C4⋊C4×C19—21no—
153C4⋊C4×C19—21no—
154C4⋊C4×C19—21no—
155C4⋊C4×C19—21no—
156C4⋊C4×C19—21no—
157C4⋊C4×C19—21no—
158C4⋊C4×C19C22⋊C411yescharacteristic
159C4⋊C4×C19C22⋊C411yescharacteristic
160C4⋊C4×C19C22⋊C411yescharacteristic
161C4⋊C4×C19C22⋊C412yes—
162C4⋊C4×C19C22⋊C411yescharacteristic
163C22⋊C4×C19—22no—
164C22⋊C4×C19—22no—
165C22⋊C4×C19—22no—
166C22⋊C4×C19—22no—
167C22⋊C4×C19—22no—
168C22⋊C4×C19—21no—
169C22⋊C4×C19—21no—
170C22⋊C4×C19—21no—
171C22⋊C4×C19—21no—
172C22⋊C4×C19—21no—
173C22⋊C4×C19—21no—
174C22⋊C4×C19—21no—
175C22⋊C4×C19—22no—
176C22⋊C4×C19—22no—
177C42×C19—22no—
178C42×C19—21no—
179C42×C19—21no—
180C42×C19—21no—
181C42×C19C22×C411yescharacteristic
182C42×C19C2×D411yescharacteristic
183C42×C19C2×D411yescharacteristic
184C42×C19C2×D411yescharacteristic
185C2×C19⋊C8—41no—
186C2×C19⋊C8—41no—
187C2×C19⋊C8—41no—
188#8503—191nomaximal, Sylow
189C23×C19—22no—
190C23×C19—21no—
191C23×C19#12011yescharacteristic
192Q8×C19—41no—
193Q8×C19—41no—
194Q8×C19—41no—
195Q8×C19—42no—
196Q8×C19—81no—
197Q8×C19—82no—
198D4×C19—42no—
199D4×C19—41no—
200D4×C19—42no—
201D4×C19—42no—
202D4×C19—81no—
203D4×C19—82no—
204D4×C19—82no—
205D4×C19—82no—
206C2×C4×C19—21no—
207C2×C4×C19—21no—
208C2×C4×C19—21no—
209C2×C4×C19—21no—
210C2×C4×C19—21no—
211C2×C4×C19—22no—
212C2×C4×C19—21no—
213C2×C4×C19—21no—
214C2×C4×C19—41no—
215C2×C4×C19—41no—
216C2×C4×C19—41no—
217C2×C4×C19—42no—
218C2×C4×C19—82no—
219C2×C4×C19—82no—
220C2×C4×C19—82no—
221C2×C4×C19—82no—
222C2×C4×C19C2×C22⋊C411yescharacteristic
223C2×C4×C19C2×C22⋊C411yescharacteristic
224C2×C4×C19C2×C22⋊C411yescharacteristic
225C2×C4×C19#12011yescharacteristic
226C2×C4×C19#12011yescharacteristic
227C2×C4×C19#12011yescharacteristic
228C2×Dic19—81no—
229C2×Dic19—81no—
230C2×Dic19—81no—
231C19⋊C8—81no—
232C19⋊C8—81no—
233C19⋊C8—81no—
234#3554D1911yescharacteristic
235#1554—191no—
236#1535—191no—
237#1521—191no—
238#1515—191no—
239#1514—191no—
240#1496—191no—
241C22×C19—21no—
242C22×C19—21no—
243C22×C19—21no—
244C22×C19—42no—
245C22×C19—41no—
246C22×C19—41no—
247C22×C19—42no—
248C22×C19—42no—
249C22×C19—41no—
250C22×C19#37911yescharacteristic
251C4×C19—21no—
252C4×C19—21no—
253C4×C19—21no—
254C4×C19—21no—
255C4×C19—21no—
256C4×C19—21no—
257C4×C19—41no—
258C4×C19—41no—
259C4×C19—41no—
260C4×C19—41no—
261C4×C19—41no—
262C4×C19—42no—
263C4×C19—41no—
264C4×C19—41no—
265Dic19—161no—
266#562—22no—
267#559—21no—
268#559Dic1911yescharacteristic, complemented
269#557Dic1911yescharacteristic, complemented
270#554—21no—
271#550Dic1911yescharacteristic, complemented
272D4×Q8Dic1911yescharacteristic, complemented
273#548—21no—
274#547—21no—
275#542—21no—
276#542—21no—
277#540—21no—
278#539—22no—
279#536—21no—
280#533C2×D1911yescharacteristic
281#532C2×D1911yescharacteristic
282#529C2×D1911yescharacteristic
283#432—191no—
284#432—191no—
285#431—191no—
286#383—191no—
287#333—381no—
288#332—381no—
289#330—381no—
290#329—381no—
291#328—381no—
292#328—381no—
293#328—381no—
294#327—382no—
295#327—381no—
296D4⋊C8—382no—
297C2×C19—41no—
298C2×C19—82no—
299C2×C19—81no—
300C2×C19#179411yescharacteristic
301C2×C19#179511yescharacteristic
302C2×C19#179611yescharacteristic
303C2×#41—21no—
304C2×#41—21no—
305C22×Q8—21no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8C2×Dic1911yescharacteristic
309C4⋊Q8C22⋊D1911yescharacteristic
310C4⋊Q8C22⋊D1911yescharacteristic
311#127—21no—
312#127C2×Dic1911yescharacteristic
313#126—22no—
314#126—21no—
315#125—22no—
316#125—21no—
317#125—21no—
318#125C22⋊D1911yescharacteristic
319#124—22no—
320#124—22no—
321#124—21no—
322#124—21no—
323#124—21no—
324#124C22⋊D1911yescharacteristic
325#123—22no—
326#123—22no—
327#123—22no—
328#123—22no—
329#123—22no—
330#123—22no—
331#123—21no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—21no—
337C22⋊Q8—22no—
338C22⋊Q8—21no—
339C22⋊Q8C22⋊D1911yescharacteristic
340C22⋊Q8C22⋊D1911yescharacteristic
341C22⋊Q8C22⋊D1911yescharacteristic
342#121—22no—
343#121—22no—
344#121—22no—
345#121—21no—
346#121—21no—
347#121C22⋊D1911yescharacteristic
348#121C22⋊D1912yes—
349C4×Q8—21no—
350C4×Q8—21no—
351C4×Q8—21no—
352C4×Q8C2×Dic1911yescharacteristic
353C4×Q8C2×Dic1911yescharacteristic
354C4×Q8C2×Dic1911yescharacteristic
355C4×D4—22no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4C2×Dic1911yescharacteristic
363C4×D4C22⋊D1912yes—
364#117—21no—
365#117—21no—
366C2×C4⋊C4—22no—
367C2×C42C22×D1911yescharacteristic
368C4⋊C8—381no—
369C4⋊C8—381no—
370C4⋊C8—381no—
371C22⋊C8—381no—
372C22⋊C8—381no—
373C22⋊C8—381no—
374#97—381no—
375#97—381no—
376C4×C8—381no—
377#95—381no—
378#95—381no—
379#95—381no—
380C19#850311yescharacteristic, complemented, Sylow
381#41—82no—
382#41—82no—
383C2×Q8—22no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—82no—
387C2×Q8C22⋊Dic1911yescharacteristic
388C2×Q8C22⋊Dic1911yescharacteristic
389C2×Q8C22⋊Dic1911yescharacteristic
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4—22no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4C22⋊Dic1911yescharacteristic
397C2×D4C22⋊Dic1912yes—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—761no—
404C22×C4C2×C22⋊D1911yescharacteristic
405C22×C4C2×C22⋊D1911yescharacteristic
406C22×C4C2×C22⋊D1911yescharacteristic
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—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4C22⋊Dic1911yescharacteristic
427C4⋊C4C22⋊Dic1911yescharacteristic
428C4⋊C4C22⋊Dic1911yescharacteristic
429C4⋊C4C22⋊Dic1912yes—
430C4⋊C4C22⋊Dic1911yescharacteristic
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—21no—
437C22⋊C4—21no—
438C22⋊C4—21no—
439C22⋊C4—21no—
440C22⋊C4—21no—
441C22⋊C4—21no—
442C22⋊C4—21no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C42—22no—
446C42—21no—
447C42—21no—
448C42—21no—
449C42C22×Dic1911yescharacteristic
450C42C2×C22⋊D1911yescharacteristic
451C42C2×C22⋊D1911yescharacteristic
452C42C2×C22⋊D1911yescharacteristic
453C23—22no—
454C23—21no—
455C23#1059739911yescharacteristic
456Q8—41no—
457Q8—41no—
458Q8—41no—
459Q8—42no—
460Q8—81no—
461Q8—82no—
462D4—42no—
463D4—41no—
464D4—42no—
465D4—42no—
466D4—82no—
467D4—81no—
468D4—82no—
469D4—82no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—82no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4—82no—
486C2×C4—1521no—
487C2×C4—1521no—
488C2×C4—1521no—
489C2×C4C2×C22⋊Dic1911yescharacteristic
490C2×C4C2×C22⋊Dic1911yescharacteristic
491C2×C4C2×C22⋊Dic1911yescharacteristic
492C2×C4#1059739911yescharacteristic
493C2×C4#1059739911yescharacteristic
494C2×C4#1059739911yescharacteristic
495C8—1521no—
496C8—1521no—
497C8—1521no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—42no—
502C22—41no—
503C22—41no—
504C22—42no—
505C22—42no—
506C22—41no—
507C22#1192640011yescharacteristic
508C4—21no—
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—41no—
515C4—41no—
516C4—41no—
517C4—41no—
518C4—41no—
519C4—42no—
520C4—41no—
521C4—41no—
522C4—3041no—
523C2—41no—
524C2—82no—
525C2—81no—
526C2#1456359911yescharacteristic
527C2#1456360511yescharacteristic
528C2#1456361011yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3554C2
socleC22×C19#379
cosocleC2×C42×C19C23
hypercenter#3554D19
hypocenterC19#8503
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3554

Complements

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

NH ≅ G/Ntype
1. #14562345C2semidirect
2. #14562266C2semidirect
3. #14562212C2semidirect
4. #14562186C2semidirect
5. #14562182C2semidirect
6. #14562104C2semidirect
24. C19×#559C4semidirect
25. C19×#557C4semidirect
27. C19×#550C4semidirect
28. D4×Q8×C19C4semidirect
268. #559Dic19semidirect
269. #557Dic19semidirect
271. #550Dic19semidirect
272. D4×Q8Dic19semidirect
380. C19#8503semidirect

Maximal subgroups

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

subgroupindex
#145623452
#145622662
#145622122
#145621862
#145621822
#145621042
C19×#35542
#850319