Finite Group Databasebeta

← #18074959

Subgroups — #18074959

Order 4864.

672 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
1#14562340C211yesmaximal, characteristic, complemented
2#14562266C211yesmaximal, characteristic, complemented
3#14562212C211yesmaximal, characteristic, complemented
4#14562186C211yesmaximal, characteristic, complemented
5#14562182C211yesmaximal, characteristic, complemented
6#14562108C211yesmaximal, characteristic, complemented
7C19×#3547C211yesmaximal, characteristic
8#11926601C2211yescharacteristic
9#11926601C2211yescharacteristic
10#11926597C2211yescharacteristic
11#11926412C2211yescharacteristic
12#11926290—21no—
13#11926288—21no—
14#11926286—21no—
15#11926284—21no—
16#11926281—22no—
17#11926281—21no—
18#11926278—21no—
19#11926278—21no—
20#11926278—21no—
21Q8⋊(C19⋊C8)—22no—
22C19×#562—22no—
23C19×#555—21no—
24C19×#555C411yescharacteristic, complemented
25C19×#554C411yescharacteristic, complemented
26C19×#553—21no—
27C19×#552—21no—
28D4×Q8×C19C411yescharacteristic, complemented
29C19×#548—21no—
30C19×#547C411yescharacteristic, complemented
31C19×#544—21no—
32C19×#542—22no—
33C19×#540—21no—
34C19×#537—21no—
35C19×#536—21no—
36C19×#533C2211yescharacteristic
37C19×#532C2211yescharacteristic
38C19×#529C2211yescharacteristic
39C2×#41×C19—21no—
40C2×#41×C19—21no—
41C22×Q8×C19—21no—
42C19×C4⋊Q8—22no—
43C19×C4⋊Q8—21no—
44C19×C4⋊Q8C2×C411yescharacteristic
45C19×C4⋊Q8C2×C411yescharacteristic
46C19×C4⋊Q8D411yescharacteristic
47C19×#127D411yescharacteristic
48C19×#126—22no—
49C19×#126—21no—
50C19×#125—22no—
51C19×#125—21no—
52C19×#125—21no—
53C19×#125D411yescharacteristic
54C19×#124—22no—
55C19×#124—22no—
56C19×#124—22no—
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—22no—
66C19×C22⋊Q8—21no—
67C19×C22⋊Q8—22no—
68C19×C22⋊Q8—21no—
69C19×C22⋊Q8—21no—
70C19×C22⋊Q8—21no—
71C19×C22⋊Q8—22no—
72C19×C22⋊Q8D411yescharacteristic
73C19×C22⋊Q8D412yes—
74C19×#121—22no—
75C19×#121—22no—
76C19×#121—22no—
77C19×#121—22no—
78C19×#121—21no—
79C19×#121—21no—
80C19×#121—21no—
81C19×#121—21no—
82C19×#121D411yescharacteristic
83C19×#121D411yescharacteristic
84C19×#121D411yescharacteristic
85C4×Q8×C19—21no—
86C4×Q8×C19C2×C411yescharacteristic
87C4×Q8×C19D412yes—
88C4×D4×C19—22no—
89C4×D4×C19—21no—
90C4×D4×C19—21no—
91C4×D4×C19—21no—
92C4×D4×C19—21no—
93C4×D4×C19C2×C411yescharacteristic
94C4×D4×C19C2×C411yescharacteristic
95C4×D4×C19C2×C411yescharacteristic
96C19×#117—22no—
97C19×#117—21no—
98C19×#117—21no—
99C19×#117—21no—
100C19×#117—21no—
101C2×C4⋊C4×C19—21no—
102C2×C4⋊C4×C19—21no—
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⋊C412yes—
124C2×D4×C19—22no—
125C2×D4×C19—22no—
126C2×D4×C19—21no—
127C2×D4×C19—21no—
128C2×D4×C19—21no—
129C2×D4×C19—21no—
130C2×D4×C19—21no—
131C2×D4×C19C22⋊C411yescharacteristic
132C2×D4×C19C22⋊C411yescharacteristic
133C2×D4×C19C22⋊C411yescharacteristic
134C22×C4×C19—22no—
135C22×C4×C19—22no—
136C22×C4×C19—22no—
137C22×C4×C19—21no—
138C22×C4×C19—21no—
139C22×C4×C19—21no—
140C22×C4×C19C2×D411yescharacteristic
141C22×C4×C19C2×D411yescharacteristic
142C22×C4×C19C2×D411yescharacteristic
143C22×Dic19—41no—
144C4⋊C4×C19—22no—
145C4⋊C4×C19—22no—
146C4⋊C4×C19—22no—
147C4⋊C4×C19—22no—
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—22no—
157C4⋊C4×C19—22no—
158C4⋊C4×C19C22⋊C411yescharacteristic
159C4⋊C4×C19C22⋊C411yescharacteristic
160C4⋊C4×C19C22⋊C411yescharacteristic
161C4⋊C4×C19C22⋊C411yescharacteristic
162C4⋊C4×C19C22⋊C412yes—
163C22⋊C4×C19—22no—
164C22⋊C4×C19—22no—
165C22⋊C4×C19—22no—
166C22⋊C4×C19—22no—
167C22⋊C4×C19—22no—
168C22⋊C4×C19—22no—
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—21no—
176C22⋊C4×C19—21no—
177C22⋊C4×C19—21no—
178C42×C19—22no—
179C42×C19—21no—
180C42×C19—22no—
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#8502—191nomaximal, Sylow
189C23×C19—21no—
190C23×C19—21no—
191C23×C19—21no—
192C23×C19#12011yescharacteristic
193Q8×C19—41no—
194Q8×C19—42no—
195Q8×C19—42no—
196Q8×C19—81no—
197Q8×C19—82no—
198D4×C19—41no—
199D4×C19—41no—
200D4×C19—41no—
201D4×C19—81no—
202D4×C19—81no—
203D4×C19—81no—
204D4×C19—81no—
205D4×C19—81no—
206D4×C19—82no—
207D4×C19—82no—
208C2×C4×C19—21no—
209C2×C4×C19—22no—
210C2×C4×C19—21no—
211C2×C4×C19—21no—
212C2×C4×C19—21no—
213C2×C4×C19—22no—
214C2×C4×C19—21no—
215C2×C4×C19—41no—
216C2×C4×C19—41no—
217C2×C4×C19—41no—
218C2×C4×C19—42no—
219C2×C4×C19—42no—
220C2×C4×C19—42no—
221C2×C4×C19—82no—
222C2×C4×C19—82no—
223C2×C4×C19—82no—
224C2×C4×C19C2×C22⋊C411yescharacteristic
225C2×C4×C19C2×C22⋊C411yescharacteristic
226C2×C4×C19C2×C22⋊C411yescharacteristic
227C2×C4×C19#12011yescharacteristic
228C2×C4×C19#12011yescharacteristic
229C2×C4×C19#12011yescharacteristic
230C2×Dic19—81no—
231C2×Dic19—81no—
232C2×Dic19—81no—
233C19⋊C8—81no—
234C19⋊C8—81no—
235C19⋊C8—81no—
236#3547D1911yescharacteristic
237#1553—191no—
238#1535—191no—
239#1521—191no—
240#1515—191no—
241#1514—191no—
242#1497—191no—
243C22×C19—21no—
244C22×C19—21no—
245C22×C19—21no—
246C22×C19—41no—
247C22×C19—41no—
248C22×C19—41no—
249C22×C19—41no—
250C22×C19—41no—
251C22×C19—41no—
252C22×C19—41no—
253C22×C19—41no—
254C22×C19—41no—
255C22×C19#37911yescharacteristic
256C4×C19—21no—
257C4×C19—21no—
258C4×C19—21no—
259C4×C19—21no—
260C4×C19—21no—
261C4×C19—21no—
262C4×C19—41no—
263C4×C19—42no—
264C4×C19—41no—
265C4×C19—41no—
266C4×C19—42no—
267C4×C19—41no—
268C4×C19—41no—
269Dic19—161no—
270#562—22no—
271#555—21no—
272#555Dic1911yescharacteristic, complemented
273#554Dic1911yescharacteristic, complemented
274#553—21no—
275#552—21no—
276D4×Q8Dic1911yescharacteristic, complemented
277#548—21no—
278#547Dic1911yescharacteristic, complemented
279#544—21no—
280#542—22no—
281#540—21no—
282#537—21no—
283#536—21no—
284#533C2×D1911yescharacteristic
285#532C2×D1911yescharacteristic
286#529C2×D1911yescharacteristic
287#432—191no—
288#432—191no—
289#431—191no—
290#383—191no—
291#332—381no—
292#331—381no—
293#330—381no—
294#329—381no—
295#328—382no—
296#328—381no—
297#327—381no—
298#327—381no—
299#327—381no—
300Q8⋊C8—382no—
301C2×C19—41no—
302C2×C19—81no—
303C2×C19—81no—
304C2×C19—81no—
305C2×C19#179411yescharacteristic
306C2×C19#179511yescharacteristic
307C2×C19#179611yescharacteristic
308C2×#41—21no—
309C2×#41—21no—
310C22×Q8—21no—
311C4⋊Q8—22no—
312C4⋊Q8—21no—
313C4⋊Q8C2×Dic1911yescharacteristic
314C4⋊Q8C2×Dic1911yescharacteristic
315C4⋊Q8C22⋊D1911yescharacteristic
316#127C22⋊D1911yescharacteristic
317#126—22no—
318#126—21no—
319#125—22no—
320#125—21no—
321#125—21no—
322#125C22⋊D1911yescharacteristic
323#124—22no—
324#124—22no—
325#124—22no—
326#124—21no—
327#124C22⋊D1911yescharacteristic
328#123—22no—
329#123—22no—
330#123—22no—
331#123—21no—
332#123—22no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—21no—
336C22⋊Q8—22no—
337C22⋊Q8—21no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340C22⋊Q8—22no—
341C22⋊Q8C22⋊D1911yescharacteristic
342C22⋊Q8C22⋊D1912yes—
343#121—22no—
344#121—22no—
345#121—22no—
346#121—22no—
347#121—21no—
348#121—21no—
349#121—21no—
350#121—21no—
351#121C22⋊D1911yescharacteristic
352#121C22⋊D1911yescharacteristic
353#121C22⋊D1911yescharacteristic
354C4×Q8—21no—
355C4×Q8C2×Dic1911yescharacteristic
356C4×Q8C22⋊D1912yes—
357C4×D4—22no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4C2×Dic1911yescharacteristic
363C4×D4C2×Dic1911yescharacteristic
364C4×D4C2×Dic1911yescharacteristic
365#117—22no—
366#117—21no—
367#117—21no—
368#117—21no—
369#117—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C42C22×D1911yescharacteristic
373C4⋊C8—381no—
374C4⋊C8—381no—
375C4⋊C8—381no—
376C22⋊C8—381no—
377C22⋊C8—381no—
378C22⋊C8—381no—
379#97—381no—
380#97—381no—
381C4×C8—381no—
382#95—381no—
383#95—381no—
384#95—381no—
385C19#850211yescharacteristic, complemented, Sylow
386#41—82no—
387#41—82no—
388C2×Q8—22no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—82no—
392C2×Q8C22⋊Dic1911yescharacteristic
393C2×Q8C22⋊Dic1912yes—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4C22⋊Dic1911yescharacteristic
402C2×D4C22⋊Dic1911yescharacteristic
403C2×D4C22⋊Dic1911yescharacteristic
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—761no—
411C22×C4C2×C22⋊D1911yescharacteristic
412C22×C4C2×C22⋊D1911yescharacteristic
413C22×C4C2×C22⋊D1911yescharacteristic
414C2×C8—761no—
415C2×C8—761no—
416C2×C8—761no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4C22⋊Dic1911yescharacteristic
432C4⋊C4C22⋊Dic1911yescharacteristic
433C4⋊C4C22⋊Dic1911yescharacteristic
434C4⋊C4C22⋊Dic1911yescharacteristic
435C4⋊C4C22⋊Dic1912yes—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—21no—
443C22⋊C4—21no—
444C22⋊C4—21no—
445C22⋊C4—21no—
446C22⋊C4—21no—
447C22⋊C4—21no—
448C22⋊C4—21no—
449C22⋊C4—21no—
450C22⋊C4—21no—
451C42—22no—
452C42—21no—
453C42—22no—
454C42C22×Dic1911yescharacteristic
455C42C2×C22⋊D1911yescharacteristic
456C42C2×C22⋊D1911yescharacteristic
457C42C2×C22⋊D1911yescharacteristic
458C23—21no—
459C23—21no—
460C23—21no—
461C23#1059739911yescharacteristic
462Q8—41no—
463Q8—42no—
464Q8—42no—
465Q8—81no—
466Q8—82no—
467D4—41no—
468D4—41no—
469D4—41no—
470D4—81no—
471D4—81no—
472D4—81no—
473D4—81no—
474D4—81no—
475D4—82no—
476D4—82no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—82no—
491C2×C4—82no—
492C2×C4—82no—
493C2×C4—1521no—
494C2×C4—1521no—
495C2×C4—1521no—
496C2×C4C2×C22⋊Dic1911yescharacteristic
497C2×C4C2×C22⋊Dic1911yescharacteristic
498C2×C4C2×C22⋊Dic1911yescharacteristic
499C2×C4#1059739911yescharacteristic
500C2×C4#1059739911yescharacteristic
501C2×C4#1059739911yescharacteristic
502C8—1521no—
503C8—1521no—
504C8—1521no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22#1192640011yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—41no—
525C4—42no—
526C4—41no—
527C4—41no—
528C4—42no—
529C4—41no—
530C4—41no—
531C4—3041no—
532C2—41no—
533C2—81no—
534C2—81no—
535C2—81no—
536C2#1456359911yescharacteristic
537C2#1456360511yescharacteristic
538C2#1456361011yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3547C2
socleC22×C19#379
cosocleC2×C42×C19C23
hypercenter#3547D19
hypocenterC19#8502
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3547

Complements

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

NH ≅ G/Ntype
1. #14562340C2semidirect
2. #14562266C2semidirect
3. #14562212C2semidirect
4. #14562186C2semidirect
5. #14562182C2semidirect
6. #14562108C2semidirect
24. C19×#555C4semidirect
25. C19×#554C4semidirect
28. D4×Q8×C19C4semidirect
30. C19×#547C4semidirect
272. #555Dic19semidirect
273. #554Dic19semidirect
276. D4×Q8Dic19semidirect
278. #547Dic19semidirect
385. C19#8502semidirect

Maximal subgroups

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

subgroupindex
#145623402
#145622662
#145622122
#145621862
#145621822
#145621082
C19×#35472
#850219