Finite Group Databasebeta

← #18074945

Subgroups — #18074945

Order 4864.

736 conjugacy classes of subgroups.

The subgroup lattice has 570 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#14562182C211yesmaximal, characteristic, complemented
5#14562182C211yesmaximal, characteristic, complemented
6#14562104C211yesmaximal, characteristic, complemented
7C19×#3546C211yesmaximal, characteristic
8#11926601C2211yescharacteristic, complemented
9#11926601C2211yescharacteristic, complemented
10#11926597C2211yescharacteristic, complemented
11#11926412C2211yescharacteristic, complemented
12#11926290—21no—
13#11926288—21no—
14#11926286—21no—
15#11926284—21no—
16#11926281—21no—
17#11926278—21no—
18#11926278—21no—
19#11926278—22no—
20#11926278—21no—
21D4⋊(C19⋊C8)—22no—
22C19×#560—22no—
23C19×#556C411yescharacteristic, complemented
24C19×#553—21no—
25C19×#550—21no—
26C19×#550C411yescharacteristic, complemented
27C19×#547C411yescharacteristic, complemented
28C19×#546—21no—
29C19×#546—21no—
30D42×C19C411yescharacteristic, complemented
31C19×#542—21no—
32C19×#538—22no—
33C19×#537—21no—
34C19×#535—21no—
35C19×#535—21no—
36C19×#532C2211yescharacteristic
37C19×#532C2211yescharacteristic
38C19×#529C2211yescharacteristic
39C2×#41×C19—21no—
40C2×#41×C19—21no—
41C2×#41×C19—21no—
42C2×#41×C19—21no—
43C22×D4×C19—21no—
44C22×D4×C19—21no—
45C19×C4⋊Q8C2×C411yescharacteristic
46C19×C4⋊Q8D411yescharacteristic
47C19×#127—22no—
48C19×#127—21no—
49C19×#127C2×C411yescharacteristic
50C19×#127D411yescharacteristic
51C19×#126—22no—
52C19×#126—22no—
53C19×#126—21no—
54C19×#125D411yescharacteristic
55C19×#124—22no—
56C19×#124—21no—
57C19×#124—21no—
58C19×#124—21no—
59C19×#124D411yescharacteristic
60C19×#123—22no—
61C19×#123—22no—
62C19×#123—21no—
63C19×#123—22no—
64C19×C22⋊Q8—22no—
65C19×C22⋊Q8—21no—
66C19×C22⋊Q8—21no—
67C19×C22⋊Q8D411yescharacteristic
68C19×#121—22no—
69C19×#121—22no—
70C19×#121—22no—
71C19×#121—22no—
72C19×#121—22no—
73C19×#121—21no—
74C19×#121—22no—
75C19×#121—21no—
76C19×#121—21no—
77C19×#121—21no—
78C19×#121—21no—
79C19×#121—21no—
80C19×#121D411yescharacteristic
81C19×#121D411yescharacteristic
82C19×#121D411yescharacteristic
83C19×#121D412yes—
84C19×#120—22no—
85C19×#120—22no—
86C19×#120—22no—
87C19×#120—22no—
88C4×Q8×C19—21no—
89C4×Q8×C19C2×C411yescharacteristic
90C4×D4×C19—22no—
91C4×D4×C19—21no—
92C4×D4×C19—21no—
93C4×D4×C19—21no—
94C4×D4×C19—21no—
95C4×D4×C19C2×C411yescharacteristic
96C4×D4×C19C2×C411yescharacteristic
97C4×D4×C19C2×C411yescharacteristic
98C4×D4×C19D412yes—
99C19×#117—21no—
100C19×#117—21no—
101C2×C4⋊C4×C19—21no—
102C2×C22⋊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—
116C24×C19—22no—
117#41×C19—82no—
118#41×C19—82no—
119#41×C19—82no—
120#41×C19—82no—
121C2×Q8×C19—21no—
122C2×Q8×C19—21no—
123C2×Q8×C19C22⋊C411yescharacteristic
124C2×D4×C19—22no—
125C2×D4×C19—22no—
126C2×D4×C19—22no—
127C2×D4×C19—22no—
128C2×D4×C19—22no—
129C2×D4×C19—21no—
130C2×D4×C19—21no—
131C2×D4×C19—22no—
132C2×D4×C19—21no—
133C2×D4×C19—21no—
134C2×D4×C19—21no—
135C2×D4×C19—21no—
136C2×D4×C19—21no—
137C2×D4×C19—82no—
138C2×D4×C19—82no—
139C2×D4×C19C22⋊C411yescharacteristic
140C2×D4×C19C22⋊C411yescharacteristic
141C2×D4×C19C22⋊C411yescharacteristic
142C2×D4×C19C22⋊C412yes—
143C22×C4×C19—22no—
144C22×C4×C19—22no—
145C22×C4×C19—21no—
146C22×C4×C19—21no—
147C22×C4×C19—21no—
148C22×C4×C19—22no—
149C22×C4×C19C2×D411yescharacteristic
150C22×C4×C19C2×D411yescharacteristic
151C22×C4×C19C2×D411yescharacteristic
152C22×Dic19—41no—
153C4⋊C4×C19—22no—
154C4⋊C4×C19—22no—
155C4⋊C4×C19—21no—
156C4⋊C4×C19—21no—
157C4⋊C4×C19—21no—
158C4⋊C4×C19—21no—
159C4⋊C4×C19—21no—
160C4⋊C4×C19—21no—
161C4⋊C4×C19C22⋊C411yescharacteristic
162C4⋊C4×C19C22⋊C411yescharacteristic
163C4⋊C4×C19C22⋊C411yescharacteristic
164C4⋊C4×C19C22⋊C411yescharacteristic
165C4⋊C4×C19C22⋊C412yes—
166C22⋊C4×C19—22no—
167C22⋊C4×C19—22no—
168C22⋊C4×C19—22no—
169C22⋊C4×C19—22no—
170C22⋊C4×C19—22no—
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—
178C22⋊C4×C19—21no—
179C22⋊C4×C19—21no—
180C22⋊C4×C19—22no—
181C22⋊C4×C19—22no—
182C42×C19—22no—
183C42×C19—21no—
184C42×C19C22×C411yescharacteristic
185C42×C19C2×D411yescharacteristic
186C42×C19C2×D411yescharacteristic
187C42×C19C2×D411yescharacteristic
188C2×C19⋊C8—41no—
189C2×C19⋊C8—41no—
190C2×C19⋊C8—41no—
191#8500—191nomaximal, Sylow
192C23×C19—21no—
193C23×C19—21no—
194C23×C19—22no—
195C23×C19—21no—
196C23×C19—82no—
197C23×C19—82no—
198C23×C19—82no—
199C23×C19#12011yescharacteristic
200Q8×C19—41no—
201Q8×C19—42no—
202Q8×C19—81no—
203D4×C19—41no—
204D4×C19—41no—
205D4×C19—42no—
206D4×C19—41no—
207D4×C19—42no—
208D4×C19—42no—
209D4×C19—81no—
210D4×C19—81no—
211D4×C19—81no—
212D4×C19—81no—
213D4×C19—81no—
214D4×C19—82no—
215D4×C19—82no—
216D4×C19—82no—
217D4×C19—82no—
218D4×C19—82no—
219D4×C19—82no—
220C2×C4×C19—21no—
221C2×C4×C19—21no—
222C2×C4×C19—21no—
223C2×C4×C19—22no—
224C2×C4×C19—21no—
225C2×C4×C19—21no—
226C2×C4×C19—41no—
227C2×C4×C19—41no—
228C2×C4×C19—41no—
229C2×C4×C19—42no—
230C2×C4×C19—42no—
231C2×C4×C19—42no—
232C2×C4×C19—82no—
233C2×C4×C19—82no—
234C2×C4×C19—82no—
235C2×C4×C19C2×C22⋊C411yescharacteristic
236C2×C4×C19C2×C22⋊C411yescharacteristic
237C2×C4×C19C2×C22⋊C411yescharacteristic
238C2×C4×C19#12011yescharacteristic
239C2×C4×C19#12011yescharacteristic
240C2×C4×C19#12011yescharacteristic
241C2×Dic19—81no—
242C2×Dic19—81no—
243C2×Dic19—81no—
244C19⋊C8—81no—
245C19⋊C8—81no—
246C19⋊C8—81no—
247#3546D1911yescharacteristic
248#1553—191no—
249#1535—191no—
250#1521—191no—
251#1514—191no—
252#1514—191no—
253#1496—191no—
254C22×C19—21no—
255C22×C19—21no—
256C22×C19—21no—
257C22×C19—42no—
258C22×C19—41no—
259C22×C19—41no—
260C22×C19—41no—
261C22×C19—41no—
262C22×C19—41no—
263C22×C19—41no—
264C22×C19—41no—
265C22×C19—42no—
266C22×C19—42no—
267C22×C19—41no—
268C22×C19—41no—
269C22×C19—164no—
270C22×C19#37911yescharacteristic
271C4×C19—21no—
272C4×C19—21no—
273C4×C19—21no—
274C4×C19—21no—
275C4×C19—21no—
276C4×C19—21no—
277C4×C19—41no—
278C4×C19—41no—
279C4×C19—41no—
280C4×C19—41no—
281C4×C19—41no—
282C4×C19—42no—
283Dic19—161no—
284#560—22no—
285#556Dic1911yescharacteristic, complemented
286#553—21no—
287#550—21no—
288#550Dic1911yescharacteristic, complemented
289#547Dic1911yescharacteristic, complemented
290#546—21no—
291#546—21no—
292D42Dic1911yescharacteristic, complemented
293#542—21no—
294#538—22no—
295#537—21no—
296#535—21no—
297#535—21no—
298#532C2×D1911yescharacteristic
299#532C2×D1911yescharacteristic
300#529C2×D1911yescharacteristic
301#432—191no—
302#432—191no—
303#431—191no—
304#383—191no—
305#332—381no—
306#331—381no—
307#330—381no—
308#329—381no—
309#328—381no—
310#327—381no—
311#327—381no—
312#327—382no—
313#327—381no—
314D4⋊C8—382no—
315C2×C19—41no—
316C2×C19—81no—
317C2×C19—82no—
318C2×C19—81no—
319C2×C19—81no—
320C2×C19#179411yescharacteristic
321C2×C19#179511yescharacteristic
322C2×C19#179511yescharacteristic
323C2×#41—21no—
324C2×#41—21no—
325C2×#41—21no—
326C2×#41—21no—
327C22×D4—21no—
328C22×D4—21no—
329C4⋊Q8C2×Dic1911yescharacteristic
330C4⋊Q8C22⋊D1911yescharacteristic
331#127—22no—
332#127—21no—
333#127C2×Dic1911yescharacteristic
334#127C22⋊D1911yescharacteristic
335#126—22no—
336#126—22no—
337#126—21no—
338#125C22⋊D1911yescharacteristic
339#124—22no—
340#124—21no—
341#124—21no—
342#124—21no—
343#124C22⋊D1911yescharacteristic
344#123—22no—
345#123—22no—
346#123—21no—
347#123—22no—
348C22⋊Q8—22no—
349C22⋊Q8—21no—
350C22⋊Q8—21no—
351C22⋊Q8C22⋊D1911yescharacteristic
352#121—22no—
353#121—22no—
354#121—22no—
355#121—22no—
356#121—22no—
357#121—21no—
358#121—22no—
359#121—21no—
360#121—21no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121C22⋊D1911yescharacteristic
365#121C22⋊D1911yescharacteristic
366#121C22⋊D1911yescharacteristic
367#121C22⋊D1912yes—
368#120—22no—
369#120—22no—
370#120—22no—
371#120—22no—
372C4×Q8—21no—
373C4×Q8C2×Dic1911yescharacteristic
374C4×D4—22no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4C2×Dic1911yescharacteristic
380C4×D4C2×Dic1911yescharacteristic
381C4×D4C2×Dic1911yescharacteristic
382C4×D4C22⋊D1912yes—
383#117—21no—
384#117—21no—
385C2×C4⋊C4—21no—
386C2×C22⋊C4—22no—
387C2×C42C22×D1911yescharacteristic
388C4⋊C8—381no—
389C4⋊C8—381no—
390C4⋊C8—381no—
391C22⋊C8—381no—
392C22⋊C8—381no—
393C22⋊C8—381no—
394#97—381no—
395#97—381no—
396C4×C8—381no—
397#95—381no—
398#95—381no—
399#95—381no—
400C19#850011yescharacteristic, complemented, Sylow
401C24—22no—
402#41—82no—
403#41—82no—
404#41—82no—
405#41—82no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8C22⋊Dic1911yescharacteristic
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—82no—
423C2×D4—82no—
424C2×D4C22⋊Dic1911yescharacteristic
425C2×D4C22⋊Dic1911yescharacteristic
426C2×D4C22⋊Dic1911yescharacteristic
427C2×D4C22⋊Dic1912yes—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—761no—
435C22×C4C2×C22⋊D1911yescharacteristic
436C22×C4C2×C22⋊D1911yescharacteristic
437C22×C4C2×C22⋊D1911yescharacteristic
438C2×C8—761no—
439C2×C8—761no—
440C2×C8—761no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4C22⋊Dic1911yescharacteristic
450C4⋊C4C22⋊Dic1911yescharacteristic
451C4⋊C4C22⋊Dic1911yescharacteristic
452C4⋊C4C22⋊Dic1911yescharacteristic
453C4⋊C4C22⋊Dic1912yes—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—21no—
460C22⋊C4—21no—
461C22⋊C4—21no—
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C42—22no—
471C42—21no—
472C42C22×Dic1911yescharacteristic
473C42C2×C22⋊D1911yescharacteristic
474C42C2×C22⋊D1911yescharacteristic
475C42C2×C22⋊D1911yescharacteristic
476C23—21no—
477C23—21no—
478C23—22no—
479C23—21no—
480C23—82no—
481C23—82no—
482C23—82no—
483C23#1059739911yescharacteristic
484Q8—41no—
485Q8—42no—
486Q8—81no—
487D4—41no—
488D4—41no—
489D4—41no—
490D4—42no—
491D4—42no—
492D4—42no—
493D4—81no—
494D4—81no—
495D4—81no—
496D4—81no—
497D4—82no—
498D4—81no—
499D4—82no—
500D4—82no—
501D4—82no—
502D4—82no—
503D4—82no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—1521no—
520C2×C4—1521no—
521C2×C4—1521no—
522C2×C4C2×C22⋊Dic1911yescharacteristic
523C2×C4C2×C22⋊Dic1911yescharacteristic
524C2×C4C2×C22⋊Dic1911yescharacteristic
525C2×C4#1059739911yescharacteristic
526C2×C4#1059739911yescharacteristic
527C2×C4#1059739911yescharacteristic
528C8—1521no—
529C8—1521no—
530C8—1521no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—42no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—42no—
543C22—42no—
544C22—41no—
545C22—41no—
546C22—164no—
547C22#1192640011yescharacteristic
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—42no—
559C4—41no—
560C4—3041no—
561C2—41no—
562C2—81no—
563C2—81no—
564C2—82no—
565C2—81no—
566C2#1456359911yescharacteristic
567C2#1456360511yescharacteristic
568C2#1456360511yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3546C2
socleC22×C19#379
cosocleC2×C42×C19C23
hypercenter#3546D19
hypocenterC19#8500
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3546

Complements

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

NH ≅ G/Ntype
1. #14562340C2semidirect
2. #14562266C2semidirect
3. #14562212C2semidirect
4. #14562182C2semidirect
5. #14562182C2semidirect
6. #14562104C2semidirect
8. #11926601C22semidirect
9. #11926601C22semidirect
10. #11926597C22semidirect
11. #11926412C22semidirect
23. C19×#556C4semidirect
26. C19×#550C4semidirect
27. C19×#547C4semidirect
30. D42×C19C4semidirect
285. #556Dic19semidirect
288. #550Dic19semidirect
289. #547Dic19semidirect
292. D42Dic19semidirect
400. C19#8500semidirect

Maximal subgroups

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

subgroupindex
#145623402
#145622662
#145622122
#145621822
#145621042
C19×#35462
#850019