Finite Group Databasebeta

← #18079117

Subgroups — #18079117

Order 4864.

564 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574388C211yesmaximal, characteristic
2#14566720C211yesmaximal, characteristic, complemented
3#14564470C211yesmaximal, characteristic
4C2×#11926279C211yesmaximal, characteristic
5#14561513C211yesmaximal, characteristic, complemented
6#14561482C211yesmaximal, characteristic, complemented
7C19×#1520C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9#11926872C412yescomplemented
10#11926862—21no—
11#11926775—22no—
12#11926694C412yescomplemented
13#11926683—21no—
14C2×#10597263—21no—
15C2×#10597263—21no—
16C2×C22⋊(C19⋊C8)C2211yescharacteristic
17#11926451—21no—
18#11926430—21no—
19#11926430—21no—
20#11926419—21no—
21C4⋊C4×Dic19—21no—
22C22⋊C4×Dic19—21no—
23C4×C22⋊Dic19C2211yescharacteristic
24C2×C19⋊#95C2211yescharacteristic
25#11926279—21no—
26#11926279—21no—
27C2×C19×C22⋊Q8C2211yescharacteristic
28C2×C19×C22⋊C8C2211yescharacteristic
29C19×#380C2211yescharacteristic
30C19×#328—22no—
31C22×Q8×C19D411yescharacteristic
32C23×C4×C19C2311yescharacteristic
33C22×C22⋊D19—21no—
34C23×Dic19—21no—
35C22×D76C2×C411yescharacteristic
36C22×C8×C19—21no—
37C19×C22⋊Q8—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8C2×C412yes—
40C19×C22⋊Q8D412yes—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19D411yescharacteristic
44C2×C22⋊C4×C19—21no—
45C2×C22⋊C4×C19—21no—
46C2×C22⋊Dic19D411yescharacteristic
47C2×C22⋊Dic19D411yescharacteristic
48C2×#64527—22no—
49#10597376—21no—
50#10597376—21no—
51#10597376—21no—
52#10597376—21no—
53C2×(C2×D19)⋊C4—21no—
54C2×C4⋊Dic19—21no—
55C2×C4⋊Dic19—21no—
56C2×C4⋊Dic19C2×C411yescharacteristic
57C2×C4×Dic19—21no—
58C2×C4×Dic19—21no—
59C2×C4×Dic19—21no—
60C22×C19⋊C8—21no—
61C19×C22⋊C8—21no—
62C19×C22⋊C8—21no—
63C19×#95—21no—
64#10597292—22no—
65C19⋊#95—21no—
66C19⋊#95—21no—
67C19⋊#95—21no—
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95D411yescharacteristic
72C19⋊#95D411yescharacteristic
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)C2×C412yes—
75#10597266—22no—
76#10597265—22no—
77#10597263—42no—
78#10597263—42no—
79C24×C19C2×D411yescharacteristic
80C23×D19—21no—
81C2×Q8×C19—21no—
82C2×Q8×C19—81no—
83C2×Q8×C19C22⋊C412yes—
84C22×C4×C19—21no—
85C22×C4×C19—21no—
86C22×C4×C19—41no—
87C22×C4×C19—81no—
88C22×C4×C19C22×C411yescharacteristic
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19#4111yescharacteristic
93C22×C4×C19#4111yescharacteristic
94C2×C22⋊D19—41no—
95C2×C22⋊D19—41no—
96C2×C22⋊D19—41no—
97C2×C22⋊D19—41no—
98C2×C22⋊D19—41no—
99C2×C22⋊D19—41no—
100C22×Dic19—21no—
101C22×Dic19—21no—
102C22×Dic19—21no—
103C22×Dic19—21no—
104C22×Dic19—21no—
105C22×Dic19—42no—
106C22×Dic19—41no—
107C22×Dic19—41no—
108C22×Dic19—81no—
109C2×D76—21no—
110C2×D76—21no—
111C2×D76—81no—
112C2×C8×C19—41no—
113C2×C8×C19—81no—
114C4⋊C4×C19—22no—
115C4⋊C4×C19—22no—
116C4⋊C4×C19—21no—
117C4⋊C4×C19—81no—
118C4⋊C4×C19C22⋊C412yes—
119C22⋊C4×C19—22no—
120C22⋊C4×C19—22no—
121C22⋊C4×C19—41no—
122C22⋊C4×C19—41no—
123C22⋊Dic19—21no—
124C22⋊Dic19—21no—
125C22⋊Dic19—21no—
126C22⋊Dic19SD1612yescomplemented
127#64527—82no—
128(C2×D19)⋊C4—41no—
129(C2×D19)⋊C4—41no—
130C4⋊Dic19—21no—
131C4⋊Dic19—21no—
132C4⋊Dic19—42no—
133C4⋊Dic19—81no—
134C4×Dic19—42no—
135C4×Dic19—81no—
136C4×Dic19—81no—
137C2×C19⋊C8—22no—
138C2×C19⋊C8—81no—
139#9278—191nomaximal, Sylow
140C23×C19—41no—
141C23×C19—41no—
142C23×C19C4×D411yescharacteristic
143C23×C19#12011yescharacteristic
144C23×C19#12111yescharacteristic
145C23×C19C2×SD1611yescharacteristic
146C23×C19#13511yescharacteristic
147C23×C19AGL(1,ℤ/8)11yescharacteristic
148C23×C19#13711yescharacteristic
149C22×D19—41no—
150C22×D19—41no—
151C22×D19—41no—
152C22×D19—81no—
153C22×D19—81no—
154Q8×C19—42no—
155Q8×C19—81no—
156C2×C4×C19—22no—
157C2×C4×C19—22no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—41no—
164C2×C4×C19—41no—
165C2×C4×C19—41no—
166C2×C4×C19—41no—
167C2×C4×C19—41no—
168C2×C4×C19—81no—
169C2×C4×C19—81no—
170C2×C4×C19—81no—
171C2×C4×C19C2×C22⋊C411yescharacteristic
172C2×C4×C19C4×D411yescharacteristic
173C2×C4×C19#12111yescharacteristic
174C2×C4×C19#12311yescharacteristic
175C22⋊D19—81no—
176C22⋊D19—81no—
177C22⋊D19—81no—
178C22⋊D19—81no—
179C2×Dic19—22no—
180C2×Dic19—22no—
181C2×Dic19—41no—
182C2×Dic19—41no—
183C2×Dic19—41no—
184C2×Dic19—41no—
185C2×Dic19—41no—
186C2×Dic19—41no—
187C2×Dic19—41no—
188C2×Dic19—41no—
189C2×Dic19—41no—
190C2×Dic19—41no—
191C2×Dic19—41no—
192C2×Dic19—41no—
193C2×Dic19—41no—
194C2×Dic19—82no—
195C2×Dic19—82no—
196D76—42no—
197D76—81no—
198C8×C19—81no—
199C19⋊C8—42no—
200#3187—191no—
201#2368—191no—
202#1964—191no—
203#1520D1911yescharacteristic, complemented
204C2×#327—191no—
205#1294—191no—
206#1282—191no—
207C22×C19—21no—
208C22×C19—21no—
209C22×C19—21no—
210C22×C19—21no—
211C22×C19—21no—
212C22×C19—21no—
213C22×C19—41no—
214C22×C19—41no—
215C22×C19—41no—
216C22×C19—41no—
217C22×C19#38611yescharacteristic
218C22×C19C4×SD1611yescharacteristic
219C22×C19#44011yescharacteristic
220C22×C19#44811yescharacteristic
221C22×C19#44911yescharacteristic
222C22×C19#46011yescharacteristic
223C22×C19#46411yescharacteristic
224C2×D19—81no—
225C2×D19—81no—
226C2×D19—81no—
227C2×D19—161no—
228C2×D19—161no—
229C4×C19—21no—
230C4×C19—21no—
231C4×C19—21no—
232C4×C19—21no—
233C4×C19—42no—
234C4×C19—42no—
235C4×C19—161no—
236Dic19—42no—
237Dic19—42no—
238Dic19—81no—
239Dic19—81no—
240Dic19—81no—
241C2×C22⋊Q8C2×D1911yescharacteristic
242C2×#121—191no—
243#483—192no—
244#481—381no—
245#465—382no—
246#450—192no—
247#448—381no—
248C2×#99—381no—
249C2×#99—381no—
250C2×C22⋊C8—191no—
251C2×C22⋊C8C2×D1911yescharacteristic
252#391—381no—
253#387—381no—
254#387—381no—
255#385—381no—
256#380C2×D1911yescharacteristic
257C4×C4⋊C4—381no—
258C4×C22⋊C4—191no—
259C4×C22⋊C4—381no—
260C2×#95—191no—
261#328—22no—
262#327—381no—
263#327—381no—
264C2×C19—21no—
265C2×C19—21no—
266C2×C19—21no—
267C2×C19—21no—
268C2×C19—21no—
269C2×C19—21no—
270C2×C19#188011yescharacteristic
271C2×C19#190611yescharacteristic
272C2×C19#191311yescharacteristic
273D19—161no—
274C22×Q8D7611yescharacteristic
275C22×D4—191no—
276C22×D4—381no—
277C23×C4—381no—
278C23×C4C22×D1911yescharacteristic
279C2×SD16—382no—
280C22×C8—21no—
281C22×C8—381no—
282C22⋊Q8—21no—
283C22⋊Q8—21no—
284C22⋊Q8C4×D1912yes—
285C22⋊Q8C22⋊D1912yes—
286#121—381no—
287#121—381no—
288#121—381no—
289#121—381no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—191no—
293C2×C4⋊C4—381no—
294C2×C4⋊C4—381no—
295C2×C4⋊C4D7611yescharacteristic
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—191no—
299C2×C22⋊C4—191no—
300C2×C22⋊C4—381no—
301C2×C42—381no—
302C2×C42—381no—
303C2×C42—381no—
304#106—382no—
305#103—382no—
306#102—382no—
307#99—762no—
308#99—762no—
309C22⋊C8—21no—
310C22⋊C8—21no—
311C22⋊C8—192no—
312C22⋊C8—381no—
313#95—21no—
314#95—191no—
315#95—191no—
316#95—381no—
317#95—381no—
318#95—381no—
319#95—381no—
320#95—381no—
321#95—381no—
322C19#927811yescharacteristic, complemented, Sylow
323C24—381no—
324C24D4×D1911yescharacteristic
325C2×Q8—21no—
326C2×Q8—81no—
327C2×Q8(C2×D19)⋊C412yes—
328C2×D4—381no—
329C2×D4—381no—
330C2×D4—761no—
331C2×D4—761no—
332C2×D4—761no—
333C2×D4—761no—
334C2×D4—761no—
335C2×D4—761no—
336C2×D4—1521no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—41no—
340C22×C4—81no—
341C22×C4—381no—
342C22×C4—381no—
343C22×C4—381no—
344C22×C4—381no—
345C22×C4—381no—
346C22×C4—762no—
347C22×C4—761no—
348C22×C4—761no—
349C22×C4—1521no—
350C22×C4C2×C4×D1911yescharacteristic
351C22×C4C2×D7611yescharacteristic
352C22×C4D4×D1911yescharacteristic
353C22×C4#6454311yescharacteristic
354C22×C4#6454311yescharacteristic
355C22×C4C2×C22⋊D1911yescharacteristic
356SD16—1522no—
357C2×C8—41no—
358C2×C8—81no—
359C2×C8—382no—
360C2×C8—1521no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—21no—
364C4⋊C4—81no—
365C4⋊C4—381no—
366C4⋊C4—381no—
367C4⋊C4—762no—
368C4⋊C4—1521no—
369C4⋊C4(C2×D19)⋊C412yes—
370C22⋊C4—22no—
371C22⋊C4—22no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—192no—
375C22⋊C4—381no—
376C22⋊C4—381no—
377C22⋊C4—381no—
378C22⋊C4—761no—
379C22⋊C4—761no—
380C42—762no—
381C42—1521no—
382C42—1521no—
383C23—41no—
384C23—41no—
385C23—761no—
386C23—761no—
387C23—761no—
388C23—1521no—
389C23—1521no—
390C23(C22⋊D19)⋊C411yescharacteristic
391C23#1059732811yescharacteristic
392C23SD16×D1911yescharacteristic
393C23#1059736011yescharacteristic
394C23#1059736411yescharacteristic
395C23#1059736511yescharacteristic
396C23#1059738511yescharacteristic
397Q8—42no—
398Q8—81no—
399D4—762no—
400D4—1521no—
401D4—1521no—
402D4—1521no—
403D4—1521no—
404D4—1521no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—382no—
421C2×C4—382no—
422C2×C4—761no—
423C2×C4—761no—
424C2×C4—761no—
425C2×C4—761no—
426C2×C4—761no—
427C2×C4—761no—
428C2×C4—761no—
429C2×C4—761no—
430C2×C4—761no—
431C2×C4—761no—
432C2×C4—761no—
433C2×C4—761no—
434C2×C4—761no—
435C2×C4—1522no—
436C2×C4—1522no—
437C2×C4(C22⋊D19)⋊C411yescharacteristic
438C2×C4#1059733211yescharacteristic
439C2×C4C2×(C2×D19)⋊C411yescharacteristic
440C2×C4#1059738511yescharacteristic
441C8—81no—
442C8—762no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—3041no—
454C22—3041no—
455C22—1521no—
456C22—1521no—
457C22—1521no—
458C22#1192642111yescharacteristic
459C22#1192662911yescharacteristic
460C22#1192664711yescharacteristic
461C22#1192668411yescharacteristic
462C22#1192669211yescharacteristic
463C22#1192674211yescharacteristic
464C22#1192676811yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—42no—
470C4—42no—
471C4—161no—
472C4—762no—
473C4—762no—
474C4—1521no—
475C4—1521no—
476C4—1521no—
477C2—21no—
478C2—21no—
479C2—21no—
480C2—21no—
481C2—21no—
482C2—21no—
483C2—3041no—
484C2#1456398811yescharacteristic
485C2#1456413411yescharacteristic
486C2#1456417511yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1520C2
socleC22×C19#386
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1520D19
hypocenterC19#9278
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
2. #14566720C2semidirect
5. #14561513C2semidirect
6. #14561482C2semidirect
7. C19×#1520C2semidirect
9. #11926872C4semidirect
12. #11926694C4semidirect
126. C22⋊Dic19SD16semidirect
203. #1520D19semidirect
322. C19#9278semidirect

Maximal subgroups

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

subgroupindex
#145743882
#145667202
#145644702
C2×#119262792
#145615132
#145614822
C19×#15202
#927819