Finite Group Databasebeta

← #18074952

Subgroups — #18074952

Order 4864.

616 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14562345C211yesmaximal, characteristic, complemented
2#14562266C211yesmaximal, characteristic
3#14562212C211yesmaximal, characteristic
4#14562186C211yesmaximal, characteristic, complemented
5#14562186C211yesmaximal, characteristic, complemented
6#14562108C211yesmaximal, characteristic, complemented
7C19×#3555C211yesmaximal, 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—22no—
19#11926281—21no—
20#11926278—21no—
21Q8⋊(C19⋊C8)—22no—
22C19×#563—22no—
23Q82×C19C411yescharacteristic, complemented
24C19×#557—21no—
25C19×#557C411yescharacteristic, complemented
26C19×#556—21no—
27C19×#556—21no—
28C19×#556C411yescharacteristic, complemented
29C19×#554C411yescharacteristic, complemented
30C19×#552—21no—
31C19×#544—21no—
32C19×#542—21no—
33C19×#541—21no—
34C19×#541—21no—
35C19×#541—22no—
36C19×#533C2211yescharacteristic
37C19×#533C2211yescharacteristic
38C19×#529C2211yescharacteristic
39C19×C4⋊Q8—22no—
40C19×C4⋊Q8—21no—
41C19×C4⋊Q8—22no—
42C19×C4⋊Q8—21no—
43C19×C4⋊Q8—21no—
44C19×C4⋊Q8C2×C411yescharacteristic
45C19×C4⋊Q8C2×C411yescharacteristic
46C19×C4⋊Q8D411yescharacteristic
47C19×C4⋊Q8D411yescharacteristic
48C19×#126—22no—
49C19×#126—22no—
50C19×#126—22no—
51C19×#126—22no—
52C19×#126—22no—
53C19×#126—22no—
54C19×#126—21no—
55C19×#125—22no—
56C19×#125—22no—
57C19×#125—22no—
58C19×#125—22no—
59C19×#125—21no—
60C19×#125—22no—
61C19×#125—21no—
62C19×#125—21no—
63C19×#125—21no—
64C19×#125D411yescharacteristic
65C19×#124—22no—
66C19×#124—21no—
67C19×#124D411yescharacteristic
68C19×#123—22no—
69C19×#123—21no—
70C19×C22⋊Q8—22no—
71C19×C22⋊Q8—22no—
72C19×C22⋊Q8—21no—
73C19×C22⋊Q8—21no—
74C19×C22⋊Q8—22no—
75C19×C22⋊Q8—21no—
76C19×C22⋊Q8—21no—
77C19×C22⋊Q8D411yescharacteristic
78C19×C22⋊Q8D411yescharacteristic
79C19×C22⋊Q8D411yescharacteristic
80C19×C22⋊Q8D412yes—
81C19×#121D411yescharacteristic
82C4×Q8×C19—22no—
83C4×Q8×C19—21no—
84C4×Q8×C19—21no—
85C4×Q8×C19—21no—
86C4×Q8×C19—21no—
87C4×Q8×C19—21no—
88C4×Q8×C19—21no—
89C4×Q8×C19—21no—
90C4×Q8×C19C2×C411yescharacteristic
91C4×Q8×C19C2×C411yescharacteristic
92C4×Q8×C19C2×C411yescharacteristic
93C4×Q8×C19D412yes—
94C4×D4×C19—21no—
95C4×D4×C19—21no—
96C4×D4×C19C2×C411yescharacteristic
97C19×#117—22no—
98C19×#117—21no—
99C19×#117—21no—
100C19×#117—21no—
101C19×#117—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—
116C2×Q8×C19—22no—
117C2×Q8×C19—21no—
118C2×Q8×C19—21no—
119C2×Q8×C19C22⋊C411yescharacteristic
120C2×Q8×C19C22⋊C411yescharacteristic
121C2×Q8×C19C22⋊C411yescharacteristic
122C2×Q8×C19C22⋊C412yes—
123C2×D4×C19—21no—
124C2×D4×C19C22⋊C411yescharacteristic
125C22×C4×C19—22no—
126C22×C4×C19—21no—
127C22×C4×C19C2×D411yescharacteristic
128C22×C4×C19C2×D411yescharacteristic
129C22×C4×C19C2×D411yescharacteristic
130C22×Dic19—41no—
131C4⋊C4×C19—22no—
132C4⋊C4×C19—22no—
133C4⋊C4×C19—22no—
134C4⋊C4×C19—22no—
135C4⋊C4×C19—22no—
136C4⋊C4×C19—22no—
137C4⋊C4×C19—22no—
138C4⋊C4×C19—22no—
139C4⋊C4×C19—21no—
140C4⋊C4×C19—21no—
141C4⋊C4×C19—21no—
142C4⋊C4×C19—21no—
143C4⋊C4×C19—21no—
144C4⋊C4×C19—21no—
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—21no—
152C4⋊C4×C19—22no—
153C4⋊C4×C19—21no—
154C4⋊C4×C19—22no—
155C4⋊C4×C19C22⋊C411yescharacteristic
156C4⋊C4×C19C22⋊C411yescharacteristic
157C4⋊C4×C19C22⋊C411yescharacteristic
158C4⋊C4×C19C22⋊C411yescharacteristic
159C4⋊C4×C19C22⋊C412yes—
160C22⋊C4×C19—22no—
161C22⋊C4×C19—22no—
162C22⋊C4×C19—22no—
163C22⋊C4×C19—21no—
164C22⋊C4×C19—22no—
165C22⋊C4×C19—21no—
166C22⋊C4×C19—21no—
167C22⋊C4×C19—21no—
168C22⋊C4×C19—21no—
169C22⋊C4×C19—21no—
170C22⋊C4×C19—21no—
171C42×C19—22no—
172C42×C19—22no—
173C42×C19—22no—
174C42×C19—21no—
175C42×C19—21no—
176C42×C19—21no—
177C42×C19—22no—
178C42×C19C22×C411yescharacteristic
179C42×C19C2×D411yescharacteristic
180C42×C19C2×D411yescharacteristic
181C42×C19C2×D411yescharacteristic
182C2×C19⋊C8—41no—
183C2×C19⋊C8—41no—
184C2×C19⋊C8—41no—
185#8501—191nomaximal, Sylow
186C23×C19—21no—
187C23×C19#12011yescharacteristic
188Q8×C19—42no—
189Q8×C19—41no—
190Q8×C19—41no—
191Q8×C19—41no—
192Q8×C19—42no—
193Q8×C19—81no—
194Q8×C19—82no—
195D4×C19—41no—
196D4×C19—81no—
197C2×C4×C19—21no—
198C2×C4×C19—21no—
199C2×C4×C19—21no—
200C2×C4×C19—22no—
201C2×C4×C19—21no—
202C2×C4×C19—21no—
203C2×C4×C19—21no—
204C2×C4×C19—22no—
205C2×C4×C19—21no—
206C2×C4×C19—41no—
207C2×C4×C19—41no—
208C2×C4×C19—41no—
209C2×C4×C19—42no—
210C2×C4×C19—82no—
211C2×C4×C19C2×C22⋊C411yescharacteristic
212C2×C4×C19C2×C22⋊C411yescharacteristic
213C2×C4×C19C2×C22⋊C411yescharacteristic
214C2×C4×C19#12011yescharacteristic
215C2×C4×C19#12011yescharacteristic
216C2×C4×C19#12011yescharacteristic
217C2×Dic19—81no—
218C2×Dic19—81no—
219C2×Dic19—81no—
220C19⋊C8—81no—
221C19⋊C8—81no—
222C19⋊C8—81no—
223#3555D1911yescharacteristic
224#1554—191no—
225#1535—191no—
226#1521—191no—
227#1515—191no—
228#1515—191no—
229#1497—191no—
230C22×C19—21no—
231C22×C19—21no—
232C22×C19—21no—
233C22×C19—41no—
234C22×C19—41no—
235C22×C19—41no—
236C22×C19#37911yescharacteristic
237C4×C19—21no—
238C4×C19—21no—
239C4×C19—21no—
240C4×C19—21no—
241C4×C19—21no—
242C4×C19—21no—
243C4×C19—41no—
244C4×C19—42no—
245C4×C19—41no—
246C4×C19—41no—
247C4×C19—41no—
248C4×C19—41no—
249C4×C19—41no—
250C4×C19—41no—
251C4×C19—42no—
252Dic19—161no—
253#563—22no—
254Q82Dic1911yescharacteristic, complemented
255#557—21no—
256#557Dic1911yescharacteristic, complemented
257#556—21no—
258#556—21no—
259#556Dic1911yescharacteristic, complemented
260#554Dic1911yescharacteristic, complemented
261#552—21no—
262#544—21no—
263#542—21no—
264#541—21no—
265#541—21no—
266#541—22no—
267#533C2×D1911yescharacteristic
268#533C2×D1911yescharacteristic
269#529C2×D1911yescharacteristic
270#432—191no—
271#432—191no—
272#431—191no—
273#383—191no—
274#333—381no—
275#332—381no—
276#330—381no—
277#329—381no—
278#328—381no—
279#328—381no—
280#328—382no—
281#328—381no—
282#327—381no—
283Q8⋊C8—382no—
284C2×C19—41no—
285C2×C19—81no—
286C2×C19#179411yescharacteristic
287C2×C19#179611yescharacteristic
288C2×C19#179611yescharacteristic
289C4⋊Q8—22no—
290C4⋊Q8—21no—
291C4⋊Q8—22no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8C2×Dic1911yescharacteristic
295C4⋊Q8C2×Dic1911yescharacteristic
296C4⋊Q8C22⋊D1911yescharacteristic
297C4⋊Q8C22⋊D1911yescharacteristic
298#126—22no—
299#126—22no—
300#126—22no—
301#126—22no—
302#126—22no—
303#126—22no—
304#126—21no—
305#125—22no—
306#125—22no—
307#125—22no—
308#125—22no—
309#125—21no—
310#125—22no—
311#125—21no—
312#125—21no—
313#125—21no—
314#125C22⋊D1911yescharacteristic
315#124—22no—
316#124—21no—
317#124C22⋊D1911yescharacteristic
318#123—22no—
319#123—21no—
320C22⋊Q8—22no—
321C22⋊Q8—22no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—22no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327C22⋊Q8C22⋊D1911yescharacteristic
328C22⋊Q8C22⋊D1911yescharacteristic
329C22⋊Q8C22⋊D1911yescharacteristic
330C22⋊Q8C22⋊D1912yes—
331#121C22⋊D1911yescharacteristic
332C4×Q8—22no—
333C4×Q8—21no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8C2×Dic1911yescharacteristic
341C4×Q8C2×Dic1911yescharacteristic
342C4×Q8C2×Dic1911yescharacteristic
343C4×Q8C22⋊D1912yes—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4C2×Dic1911yescharacteristic
347#117—22no—
348#117—21no—
349#117—21no—
350#117—21no—
351#117—21no—
352C2×C4⋊C4—21no—
353C2×C42C22×D1911yescharacteristic
354C4⋊C8—381no—
355C4⋊C8—381no—
356C4⋊C8—381no—
357C22⋊C8—381no—
358C22⋊C8—381no—
359C22⋊C8—381no—
360#97—381no—
361#97—381no—
362C4×C8—381no—
363#95—381no—
364#95—381no—
365#95—381no—
366C19#850111yescharacteristic, complemented, Sylow
367C2×Q8—22no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8C22⋊Dic1911yescharacteristic
371C2×Q8C22⋊Dic1911yescharacteristic
372C2×Q8C22⋊Dic1911yescharacteristic
373C2×Q8C22⋊Dic1912yes—
374C2×D4—21no—
375C2×D4C22⋊Dic1911yescharacteristic
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—761no—
379C22×C4C2×C22⋊D1911yescharacteristic
380C22×C4C2×C22⋊D1911yescharacteristic
381C22×C4C2×C22⋊D1911yescharacteristic
382C2×C8—761no—
383C2×C8—761no—
384C2×C8—761no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4C22⋊Dic1911yescharacteristic
410C4⋊C4C22⋊Dic1911yescharacteristic
411C4⋊C4C22⋊Dic1911yescharacteristic
412C4⋊C4C22⋊Dic1911yescharacteristic
413C4⋊C4C22⋊Dic1912yes—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—21no—
418C22⋊C4—22no—
419C22⋊C4—21no—
420C22⋊C4—21no—
421C22⋊C4—21no—
422C22⋊C4—21no—
423C22⋊C4—21no—
424C22⋊C4—21no—
425C42—22no—
426C42—22no—
427C42—22no—
428C42—21no—
429C42—21no—
430C42—21no—
431C42—22no—
432C42C22×Dic1911yescharacteristic
433C42C2×C22⋊D1911yescharacteristic
434C42C2×C22⋊D1911yescharacteristic
435C42C2×C22⋊D1911yescharacteristic
436C23—21no—
437C23#1059739911yescharacteristic
438Q8—42no—
439Q8—41no—
440Q8—41no—
441Q8—41no—
442Q8—42no—
443Q8—81no—
444Q8—82no—
445D4—41no—
446D4—81no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—22no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—21no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—82no—
461C2×C4—1521no—
462C2×C4—1521no—
463C2×C4—1521no—
464C2×C4C2×C22⋊Dic1911yescharacteristic
465C2×C4C2×C22⋊Dic1911yescharacteristic
466C2×C4C2×C22⋊Dic1911yescharacteristic
467C2×C4#1059739911yescharacteristic
468C2×C4#1059739911yescharacteristic
469C2×C4#1059739911yescharacteristic
470C8—1521no—
471C8—1521no—
472C8—1521no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22#1192640011yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—41no—
487C4—42no—
488C4—41no—
489C4—41no—
490C4—41no—
491C4—42no—
492C4—41no—
493C4—41no—
494C4—41no—
495C4—3041no—
496C2—41no—
497C2—81no—
498C2#1456359911yescharacteristic
499C2#1456361011yescharacteristic
500C2#1456361011yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3555C2
socleC22×C19#379
prime radicalC19×#121D4
cosocleC2×C42×C19C23
hypercenter#3555D19
hypocenterC19#8501
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3555

Complements

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

NH ≅ G/Ntype
1. #14562345C2semidirect
4. #14562186C2semidirect
5. #14562186C2semidirect
6. #14562108C2semidirect
23. Q82×C19C4semidirect
25. C19×#557C4semidirect
28. C19×#556C4semidirect
29. C19×#554C4semidirect
254. Q82Dic19semidirect
256. #557Dic19semidirect
259. #556Dic19semidirect
260. #554Dic19semidirect
366. C19#8501semidirect

Maximal subgroups

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

subgroupindex
#145623452
#145622662
#145622122
#145621862
#145621082
C19×#35552
#850119