Finite Group Databasebeta

← #18075084

Subgroups — #18075084

Order 4864.

728 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564447C211yesmaximal, characteristic, complemented
2#14562259C211yesmaximal, characteristic, complemented
3#14562173C212yesmaximal, complemented
4#14562095C212yesmaximal, complemented
5C19×#3545C211yesmaximal, characteristic
6#11926601C2212yescomplemented
7C2×#10597292—21no—
8C2×#10597289—21no—
9C2×C4×C19⋊C8C2211yescharacteristic, complemented
10#11926410C2211yescharacteristic, complemented
11#11926284—21no—
12#11926284—21no—
13#11926281—22no—
14#11926278—22no—
15Q8⋊(C19⋊C8)—22no—
16D4⋊(C19⋊C8)—22no—
17C19×#563C411yescharacteristic, complemented
18C19×#562C412yescomplemented
19C19×H(3,𝔽4)C411yescharacteristic, complemented
20C19×#555—21no—
21C19×#551—21no—
22C19×#551—22no—
23C19×#546—22no—
24C19×#542—22no—
25C19×#538—22no—
26C19×#536—21no—
27C19×#534—21no—
28C19×#529C2212yes—
29C2×C19×#124C2211yescharacteristic
30C2×#41×C19—21no—
31C22×Q8×C19D411yescharacteristic
32C22×D4×C19—21no—
33C22×D4×C19D411yescharacteristic
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C19×#126—22no—
37C19×#126—22no—
38C19×#126—22no—
39C19×#125C2×C412yes—
40C19×#124—21no—
41C19×#124—22no—
42C19×#124—21no—
43C19×#124—22no—
44C19×#124—22no—
45C19×#124C2×C411yescharacteristic
46C19×#124C2×C411yescharacteristic
47C19×#124C2×C412yes—
48C19×#124D411yescharacteristic
49C19×#124D411yescharacteristic
50C19×#123—21no—
51C19×#123—22no—
52C19×#123—22no—
53C19×#123—21no—
54C19×#123—22no—
55C19×#123—22no—
56C19×#123—22no—
57C19×C22⋊Q8—22no—
58C19×C22⋊Q8—22no—
59C19×C22⋊Q8—22no—
60C19×C22⋊Q8—22no—
61C19×C22⋊Q8D412yes—
62C19×#121—22no—
63C19×#121—22no—
64C19×#121—22no—
65C19×#121—22no—
66C19×#121D412yes—
67C19×#120—21no—
68C19×#120—22no—
69C19×#120—21no—
70C19×#120—22no—
71C4×Q8×C19D412yes—
72C4×D4×C19—22no—
73C4×D4×C19—22no—
74C4×D4×C19—22no—
75C4×D4×C19D412yes—
76C19×#117—21no—
77C19×#117—22no—
78C19×#117—22no—
79C2×C22⋊C4×C19—21no—
80C2×C22⋊C4×C19—22no—
81C2×C22⋊C4×C19—22no—
82C2×C42×C19C2311yescharacteristic
83C2×C4⋊Dic19—21no—
84C22×C19⋊C8—21no—
85#10597292—42no—
86#10597289—42no—
87C19⋊#95—22no—
88C22⋊(C19⋊C8)—22no—
89C4⋊(C19⋊C8)—22no—
90#10597260—22no—
91C4×C19⋊C8—22no—
92C24×C19—21no—
93C24×C19—21no—
94#41×C19—81no—
95#41×C19—81no—
96C2×Q8×C19—21no—
97C2×Q8×C19—21no—
98C2×Q8×C19—41no—
99C2×Q8×C19—41no—
100C2×Q8×C19C22⋊C412yes—
101C2×Q8×C19C22⋊C411yescharacteristic
102C2×Q8×C19C22⋊C411yescharacteristic
103C2×D4×C19—22no—
104C2×D4×C19—22no—
105C2×D4×C19—22no—
106C2×D4×C19—21no—
107C2×D4×C19—22no—
108C2×D4×C19—21no—
109C2×D4×C19—41no—
110C2×D4×C19—41no—
111C2×D4×C19—81no—
112C2×D4×C19—81no—
113C2×D4×C19C22⋊C412yes—
114C2×D4×C19C22⋊C411yescharacteristic
115C2×D4×C19C22⋊C411yescharacteristic
116C22×C4×C19—21no—
117C22×C4×C19—22no—
118C22×C4×C19—22no—
119C22×C4×C19—21no—
120C22×C4×C19—22no—
121C22×C4×C19C2×D411yescharacteristic
122C22×C4×C19C2×D412yes—
123C22×Dic19—41no—
124C4⋊C4×C19—22no—
125C4⋊C4×C19—22no—
126C4⋊C4×C19—22no—
127C4⋊C4×C19—22no—
128C4⋊C4×C19—22no—
129C4⋊C4×C19—22no—
130C4⋊C4×C19—22no—
131C4⋊C4×C19C22⋊C412yes—
132C4⋊C4×C19C22⋊C412yes—
133C22⋊C4×C19—22no—
134C22⋊C4×C19—21no—
135C22⋊C4×C19—21no—
136C22⋊C4×C19—22no—
137C22⋊C4×C19—22no—
138C22⋊C4×C19—22no—
139C22⋊C4×C19—22no—
140C22⋊C4×C19—22no—
141C22⋊C4×C19—22no—
142C22⋊C4×C19—22no—
143C22⋊C4×C19—22no—
144C22⋊C4×C19—22no—
145C22⋊C4×C19—22no—
146C22⋊C4×C19—22no—
147C22⋊C4×C19—22no—
148C42×C19—21no—
149C42×C19—21no—
150C42×C19—22no—
151C42×C19C22×C411yescharacteristic
152C42×C19C2×D411yescharacteristic
153C42×C19C2×D412yes—
154C4⋊Dic19—41no—
155C4⋊Dic19—41no—
156C2×C19⋊C8—22no—
157C2×C19⋊C8—41no—
158C2×C19⋊C8—41no—
159C2×C19⋊C8—42no—
160#8528—191nomaximal, Sylow
161C23×C19—21no—
162C23×C19—22no—
163C23×C19—21no—
164C23×C19—41no—
165C23×C19—41no—
166C23×C19—82no—
167C23×C19—81no—
168C23×C19—82no—
169C23×C19#12011yescharacteristic
170Q8×C19—41no—
171Q8×C19—41no—
172Q8×C19—42no—
173Q8×C19—81no—
174Q8×C19—81no—
175D4×C19—41no—
176D4×C19—41no—
177D4×C19—42no—
178D4×C19—42no—
179D4×C19—42no—
180D4×C19—81no—
181D4×C19—82no—
182D4×C19—82no—
183D4×C19—82no—
184D4×C19—81no—
185C2×C4×C19—21no—
186C2×C4×C19—21no—
187C2×C4×C19—22no—
188C2×C4×C19—21no—
189C2×C4×C19—22no—
190C2×C4×C19—22no—
191C2×C4×C19—21no—
192C2×C4×C19—42no—
193C2×C4×C19—41no—
194C2×C4×C19—41no—
195C2×C4×C19—82no—
196C2×C4×C19—82no—
197C2×C4×C19—81no—
198C2×C4×C19—82no—
199C2×C4×C19C2×C22⋊C412yes—
200C2×C4×C19C2×C22⋊C411yescharacteristic
201C2×C4×C19#12012yes—
202C2×C4×C19#12011yescharacteristic
203C2×Dic19—82no—
204C2×Dic19—81no—
205C19⋊C8—42no—
206C19⋊C8—82no—
207#3545D1911yescharacteristic
208#1958—191no—
209#1533—191no—
210#1512—192no—
211#1494—192no—
212C22×C19—22no—
213C22×C19—42no—
214C22×C19—41no—
215C22×C19—41no—
216C22×C19—42no—
217C22×C19—42no—
218C22×C19—42no—
219C22×C19—42no—
220C22×C19—161no—
221C22×C19—161no—
222C22×C19—162no—
223C22×C19#37911yescharacteristic
224C22×C19#45311yescharacteristic
225C22×C19#45511yescharacteristic
226C4×C19—21no—
227C4×C19—21no—
228C4×C19—22no—
229C4×C19—22no—
230C4×C19—41no—
231C4×C19—41no—
232C4×C19—42no—
233C4×C19—42no—
234C4×C19—42no—
235Dic19—161no—
236#563Dic1911yescharacteristic, complemented
237#562Dic1912yescomplemented
238H(3,𝔽4)Dic1911yescharacteristic, complemented
239#555—21no—
240#551—21no—
241#551—22no—
242#546—22no—
243#542—22no—
244#538—22no—
245#536—21no—
246#534—21no—
247#529C2×D1912yes—
248C2×#124C2×D1911yescharacteristic
249#432—192no—
250C2×#103—381no—
251C2×#102—381no—
252C2×C4×C8—191no—
253#382—191no—
254#329—381no—
255#329—381no—
256#328—382no—
257#327—382no—
258Q8⋊C8—382no—
259D4⋊C8—382no—
260C2×C19—21no—
261C2×C19—21no—
262C2×C19—82no—
263C2×C19—81no—
264C2×C19—81no—
265C2×C19#179211yescharacteristic
266C2×C19#179412yes—
267C2×#41—21no—
268C22×Q8C22⋊D1911yescharacteristic
269C22×D4—21no—
270C22×D4C22⋊D1911yescharacteristic
271C22×C8—381no—
272C4⋊Q8—21no—
273C4⋊Q8—21no—
274#126—22no—
275#126—22no—
276#126—22no—
277#125C2×Dic1912yes—
278#124—21no—
279#124—22no—
280#124—21no—
281#124—22no—
282#124—22no—
283#124C2×Dic1911yescharacteristic
284#124C2×Dic1911yescharacteristic
285#124C2×Dic1912yes—
286#124C22⋊D1911yescharacteristic
287#124C22⋊D1911yescharacteristic
288#123—21no—
289#123—22no—
290#123—22no—
291#123—21no—
292#123—22no—
293#123—22no—
294#123—22no—
295C22⋊Q8—22no—
296C22⋊Q8—22no—
297C22⋊Q8—22no—
298C22⋊Q8—22no—
299C22⋊Q8C22⋊D1912yes—
300#121—22no—
301#121—22no—
302#121—22no—
303#121—22no—
304#121C22⋊D1912yes—
305#120—21no—
306#120—22no—
307#120—21no—
308#120—22no—
309C4×Q8C22⋊D1912yes—
310C4×D4—22no—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4C22⋊D1912yes—
314#117—21no—
315#117—22no—
316#117—22no—
317C2×C4⋊C4—381no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C42C22×D1911yescharacteristic
322C4⋊C8—382no—
323#103—762no—
324#102—762no—
325C22⋊C8—382no—
326#97—382no—
327C4×C8—382no—
328#95—382no—
329C19#852811yescharacteristic, complemented, Sylow
330C24—21no—
331C24—21no—
332#41—81no—
333#41—81no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—41no—
337C2×Q8—41no—
338C2×Q8C22⋊Dic1912yes—
339C2×Q8C22⋊Dic1911yescharacteristic
340C2×Q8C22⋊Dic1911yescharacteristic
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—21no—
345C2×D4—22no—
346C2×D4—21no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—81no—
350C2×D4—81no—
351C2×D4C22⋊Dic1912yes—
352C2×D4C22⋊Dic1911yescharacteristic
353C2×D4C22⋊Dic1911yescharacteristic
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—761no—
360C22×C4C2×C22⋊D1911yescharacteristic
361C22×C4C2×C22⋊D1912yes—
362C2×C8—382no—
363C2×C8—761no—
364C2×C8—761no—
365C2×C8—762no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—761no—
374C4⋊C4—761no—
375C4⋊C4C22⋊Dic1912yes—
376C4⋊C4C22⋊Dic1912yes—
377C22⋊C4—22no—
378C22⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—22no—
381C22⋊C4—22no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C42—21no—
393C42—21no—
394C42—22no—
395C42C22×Dic1911yescharacteristic
396C42C2×C22⋊D1912yes—
397C42C2×C22⋊D1911yescharacteristic
398C23—21no—
399C23—22no—
400C23—21no—
401C23—41no—
402C23—41no—
403C23—82no—
404C23—81no—
405C23—82no—
406C23#1059739911yescharacteristic
407Q8—41no—
408Q8—41no—
409Q8—42no—
410Q8—81no—
411Q8—81no—
412D4—41no—
413D4—41no—
414D4—42no—
415D4—42no—
416D4—42no—
417D4—81no—
418D4—82no—
419D4—81no—
420D4—82no—
421D4—82no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—21no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—82no—
433C2×C4—81no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4—1522no—
437C2×C4—1521no—
438C2×C4C2×C22⋊Dic1912yes—
439C2×C4C2×C22⋊Dic1911yescharacteristic
440C2×C4#1059739912yes—
441C2×C4#1059739911yescharacteristic
442C8—762no—
443C8—1522no—
444C22—22no—
445C22—42no—
446C22—41no—
447C22—41no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—161no—
453C22—161no—
454C22—162no—
455C22#1192640011yescharacteristic
456C22#1192671211yescharacteristic
457C22#1192672211yescharacteristic
458C4—21no—
459C4—21no—
460C4—22no—
461C4—22no—
462C4—41no—
463C4—41no—
464C4—42no—
465C4—42no—
466C4—42no—
467C4—3041no—
468C2—21no—
469C2—21no—
470C2—81no—
471C2—82no—
472C2—81no—
473C2#1456358911yescharacteristic
474C2#1456359912yes—
subgroupG/H
centerC22#11926400
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3545C2
socleC22×C19#379
cosocleC2×C42×C19C23
hypercenter#3545D19
hypocenterC19#8528
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3545

Complements

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

NH ≅ G/Ntype
1. #14564447C2semidirect
2. #14562259C2semidirect
3. #14562173C2semidirect
4. #14562095C2semidirect
6. #11926601C22semidirect
9. C2×C4×C19⋊C8C22semidirect
10. #11926410C22semidirect
17. C19×#563C4semidirect
18. C19×#562C4semidirect
19. C19×H(3,𝔽4)C4semidirect
236. #563Dic19semidirect
237. #562Dic19semidirect
238. H(3,𝔽4)Dic19semidirect
329. C19#8528semidirect

Maximal subgroups

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

subgroupindex
#145644472
#145622592
#145621732
#145620952
C19×#35452
#852819