Finite Group Databasebeta

← #18086929

Subgroups — #18086929

Order 4864.

532 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 99 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#14574388C211yesmaximal, characteristic
2#14564471C211yesmaximal, characteristic
3#14564061C211yesmaximal, characteristic
4#14564059C211yesmaximal, characteristic, complemented
5#14563815C211yesmaximal, characteristic, complemented
6#14561502C211yesmaximal, characteristic, complemented
7C19×#1996C211yesmaximal, characteristic, complemented
8C23×C19⋊C8C2211yescharacteristic
9C2×#10597376C2211yescharacteristic
10#11926872—21no—
11#11926862—21no—
12#11926775—21no—
13#11926775—21no—
14#11926694—21no—
15#11926683—21no—
16C2×C4⋊(C19⋊C8)—21no—
17C2×#10597292—21no—
18C2×#10597266—21no—
19C2×#10597263—21no—
20C2×#10597263—21no—
21C2×C22⋊(C19⋊C8)C2211yescharacteristic
22#11926404C2211yescharacteristic
23#11926306—21no—
24#11926306—21no—
25#11926299—21no—
26C2×C19×C22⋊Q8C2211yescharacteristic
27C19×#380C2211yescharacteristic
28C4×C22⋊C4×C19C2211yescharacteristic
29C19×#342—21no—
30C19×#342—21no—
31C22×Q8×C19D411yescharacteristic
32C23×C4×C19C2311yescharacteristic
33C22×C22⋊D19—21no—
34C22×D76D411yescharacteristic
35C19×C22⋊Q8—21no—
36C19×C22⋊Q8—21no—
37C19×C22⋊Q8—21no—
38C19×C22⋊Q8—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19D411yescharacteristic
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19—21no—
44C2×C22⋊C4×C19D411yescharacteristic
45C2×C22⋊C4×C19D411yescharacteristic
46C2×C42×C19—21no—
47C2×C22⋊Dic19—21no—
48C2×#64527—21no—
49C2×#64527—21no—
50#10597376—21no—
51#10597376—21no—
52#10597376—21no—
53#10597376—21no—
54C2×(C2×D19)⋊C4—21no—
55C2×C4⋊Dic19—21no—
56C2×C4⋊Dic19D411yescharacteristic
57C22×C19⋊C8—21no—
58C22×C19⋊C8—21no—
59C22×C19⋊C8—21no—
60C22×C19⋊C8—42no—
61C22×C19⋊C8D411yescharacteristic
62C22×C19⋊C8D411yescharacteristic
63C19×#95—21no—
64C19×#95—21no—
65#10597292—21no—
66#10597292—21no—
67#10597292—42no—
68C19⋊#95—21no—
69C22⋊(C19⋊C8)—21no—
70C22⋊(C19⋊C8)—21no—
71#10597266—21no—
72#10597266—21no—
73#10597266—42no—
74#10597265—21no—
75#10597265—21no—
76#10597263—42no—
77#10597263—42no—
78C4⋊(C19⋊C8)—42no—
79C24×C19C2×D411yescharacteristic
80C23×D19—21no—
81C2×Q8×C19—21no—
82C2×Q8×C19—21no—
83C2×Q8×C19—41no—
84C2×Q8×C19—41no—
85C22×C4×C19—21no—
86C22×C4×C19—21no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—41no—
90C22×C4×C19—41no—
91C22×C4×C19—41no—
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19#4111yescharacteristic
96C22×C4×C19#4111yescharacteristic
97C22×C4×C19#4111yescharacteristic
98C2×C22⋊D19—41no—
99C2×C22⋊D19—41no—
100C2×C22⋊D19—41no—
101C2×C22⋊D19—41no—
102C2×C22⋊D19—41no—
103C2×C22⋊D19—41no—
104C22×Dic19—21no—
105C22×Dic19—41no—
106C2×D76—21no—
107C2×D76—21no—
108C2×D76—41no—
109C2×D76—41no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19—21no—
112C4⋊C4×C19—41no—
113C4⋊C4×C19—41no—
114C4⋊C4×C19—41no—
115C4⋊C4×C19—41no—
116C22⋊C4×C19—21no—
117C22⋊C4×C19—21no—
118C22⋊C4×C19—21no—
119C22⋊C4×C19—41no—
120C22⋊C4×C19—41no—
121C22⋊C4×C19—41no—
122C22⋊C4×C19—41no—
123C22⋊C4×C19SD1612yescomplemented
124C42×C19—41no—
125C42×C19—41no—
126C22⋊Dic19—41no—
127C22⋊Dic19—41no—
128#64527—81no—
129#64527—81no—
130(C2×D19)⋊C4—41no—
131(C2×D19)⋊C4—41no—
132C4⋊Dic19—21no—
133C4⋊Dic19—21no—
134C4⋊Dic19—41no—
135C4⋊Dic19—41no—
136C2×C19⋊C8—22no—
137C2×C19⋊C8—22no—
138C2×C19⋊C8—22no—
139C2×C19⋊C8—21no—
140C2×C19⋊C8—21no—
141C2×C19⋊C8—41no—
142C2×C19⋊C8—41no—
143C2×C19⋊C8—41no—
144C2×C19⋊C8—41no—
145C2×C19⋊C8—41no—
146C2×C19⋊C8—41no—
147#10565—191nomaximal, Sylow
148C23×C19—41no—
149C23×C19—41no—
150C23×C19#12111yescharacteristic
151C23×C19#12111yescharacteristic
152C23×C19#12111yescharacteristic
153C23×C19C2×SD1611yescharacteristic
154C23×C19#13511yescharacteristic
155C23×C19AGL(1,ℤ/8)11yescharacteristic
156C23×C19#13711yescharacteristic
157C22×D19—41no—
158C22×D19—41no—
159C22×D19—41no—
160C22×D19—81no—
161C22×D19—81no—
162Q8×C19—42no—
163Q8×C19—41no—
164Q8×C19—41no—
165C2×C4×C19—21no—
166C2×C4×C19—21no—
167C2×C4×C19—21no—
168C2×C4×C19—21no—
169C2×C4×C19—21no—
170C2×C4×C19—21no—
171C2×C4×C19—22no—
172C2×C4×C19—41no—
173C2×C4×C19—41no—
174C2×C4×C19—41no—
175C2×C4×C19—41no—
176C2×C4×C19—41no—
177C2×C4×C19—41no—
178C2×C4×C19—41no—
179C2×C4×C19—41no—
180C2×C4×C19—41no—
181C2×C4×C19—41no—
182C2×C4×C19—81no—
183C2×C4×C19—81no—
184C2×C4×C19—81no—
185C2×C4×C19—81no—
186C2×C4×C19—81no—
187C2×C4×C19#12011yescharacteristic
188C2×C4×C19#12311yescharacteristic
189C2×C4×C19#12311yescharacteristic
190C2×C4×C19#12411yescharacteristic
191C22⋊D19—81no—
192C22⋊D19—81no—
193C22⋊D19—81no—
194C22⋊D19—81no—
195C2×Dic19—41no—
196C2×Dic19—41no—
197C2×Dic19—41no—
198C2×Dic19—81no—
199C2×Dic19—81no—
200C2×Dic19—81no—
201D76—42no—
202D76—41no—
203D76—41no—
204C19⋊C8—42no—
205C19⋊C8—41no—
206C19⋊C8—41no—
207#3187—191no—
208#1996D1911yescharacteristic, complemented
209#1964—191no—
210#1893—191no—
211#1892—191no—
212#1850—191no—
213#1289—191no—
214C22×C19—21no—
215C22×C19—21no—
216C22×C19—21no—
217C22×C19—21no—
218C22×C19—21no—
219C22×C19—21no—
220C22×C19—41no—
221C22×C19—41no—
222C22×C19—41no—
223C22×C19—41no—
224C22×C19#39411yescharacteristic
225C22×C19#46011yescharacteristic
226C22×C19#46111yescharacteristic
227C22×C19#46311yescharacteristic
228C22×C19#46411yescharacteristic
229C22×C19#46511yescharacteristic
230C22×C19#46811yescharacteristic
231C2×D19—81no—
232C2×D19—81no—
233C2×D19—81no—
234C2×D19—161no—
235C2×D19—161no—
236C4×C19—21no—
237C4×C19—21no—
238C4×C19—21no—
239C4×C19—42no—
240C4×C19—81no—
241C4×C19—81no—
242C4×C19—81no—
243C4×C19—161no—
244C4×C19B(4,𝔽2)11yescharacteristic
245C4×C19#45811yescharacteristic
246Dic19—81no—
247Dic19—161no—
248C23×C8—191no—
249C2×C22⋊Q8C2×D1911yescharacteristic
250C2×#121—191no—
251#483—381no—
252#481—381no—
253#465—381no—
254#465—381no—
255#450—381no—
256#448—381no—
257C2×C4⋊C8—381no—
258C2×#103—381no—
259C2×#102—381no—
260C2×#99—381no—
261C2×#99—381no—
262C2×C22⋊C8—191no—
263#380—191no—
264#380C2×D1911yescharacteristic
265C4×C22⋊C4C2×D1911yescharacteristic
266#342—21no—
267#342—21no—
268#340—381no—
269#340—381no—
270#336—381no—
271C2×C19—21no—
272C2×C19—21no—
273C2×C19—21no—
274C2×C19—21no—
275C2×C19—21no—
276C2×C19—21no—
277C2×C19#204411yescharacteristic
278C2×C19#205311yescharacteristic
279C2×C19#205511yescharacteristic
280D19—161no—
281C22×Q8D7611yescharacteristic
282C22×D4—191no—
283C22×D4—381no—
284C23×C4C22×D1911yescharacteristic
285C2×SD16—381no—
286C2×SD16—381no—
287C22×C8—191no—
288C22×C8—191no—
289C22×C8—381no—
290C22×C8—381no—
291C22×C8—381no—
292C22×C8—762no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297#121—381no—
298#121—381no—
299#121—381no—
300#121—381no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—191no—
304C2×C4⋊C4—381no—
305C2×C4⋊C4D7611yescharacteristic
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—381no—
309C2×C22⋊C4—381no—
310C2×C22⋊C4C22⋊D1911yescharacteristic
311C2×C22⋊C4C22⋊D1911yescharacteristic
312C2×C42—21no—
313#106—381no—
314#106—381no—
315C4⋊C8—762no—
316#103—381no—
317#103—381no—
318#103—762no—
319#102—381no—
320#102—381no—
321#102—762no—
322#99—762no—
323#99—762no—
324C22⋊C8—381no—
325C22⋊C8—381no—
326#95—21no—
327#95—21no—
328#95—381no—
329C19#1056511yescharacteristic, complemented, Sylow
330C24—381no—
331C24C2×C22⋊D1911yescharacteristic
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—41no—
335C2×Q8—41no—
336C2×D4—381no—
337C2×D4—381no—
338C2×D4—761no—
339C2×D4—761no—
340C2×D4—761no—
341C2×D4—761no—
342C2×D4—761no—
343C2×D4—761no—
344C2×D4—761no—
345C2×D4—761no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—381no—
354C22×C4—761no—
355C22×C4C2×D7611yescharacteristic
356C22×C4#6454111yescharacteristic
357C22×C4D4×D1911yescharacteristic
358C22×C4D4×D1911yescharacteristic
359C22×C4#6454311yescharacteristic
360C22×C4#6454311yescharacteristic
361SD16—1521no—
362SD16—1521no—
363C2×C8—382no—
364C2×C8—382no—
365C2×C8—382no—
366C2×C8—381no—
367C2×C8—381no—
368C2×C8—761no—
369C2×C8—761no—
370C2×C8—761no—
371C2×C8—761no—
372C2×C8—761no—
373C2×C8—761no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—381no—
381C4⋊C4—381no—
382C4⋊C4—761no—
383C4⋊C4—761no—
384C22⋊C4—21no—
385C22⋊C4—21no—
386C22⋊C4—21no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—761no—
392C22⋊C4—761no—
393C22⋊C4—761no—
394C22⋊C4—761no—
395C22⋊C4#6452712yescomplemented
396C42—41no—
397C42—41no—
398C23—41no—
399C23—41no—
400C23—761no—
401C23—761no—
402C23—761no—
403C23—1521no—
404C23—1521no—
405C23#1059737611yescharacteristic
406C23#1059738411yescharacteristic
407C23#1059738511yescharacteristic
408C23C2×#6452711yescharacteristic
409C23#1059738811yescharacteristic
410C23#1059739511yescharacteristic
411C23#1059739611yescharacteristic
412Q8—42no—
413Q8—41no—
414Q8—41no—
415D4—762no—
416D4—761no—
417D4—761no—
418D4—1521no—
419D4—1521no—
420D4—1521no—
421D4—1521no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—761no—
445C2×C4—761no—
446C2×C4—761no—
447C2×C4—1521no—
448C2×C4—1521no—
449C2×C4—1521no—
450C2×C4#1059732811yescharacteristic
451C2×C4#1059732911yescharacteristic
452C2×C4#1059733111yescharacteristic
453C2×C4#1059733211yescharacteristic
454C8—762no—
455C8—761no—
456C8—761no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—3041no—
468C22—3041no—
469C22—1521no—
470C22—1521no—
471C22—1521no—
472C22#1192646011yescharacteristic
473C22#1192674411yescharacteristic
474C22#1192674611yescharacteristic
475C22#1192675611yescharacteristic
476C22#1192676611yescharacteristic
477C22#1192677511yescharacteristic
478C22#1192679211yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—81no—
485C4—81no—
486C4—161no—
487C4—3041no—
488C4—1521no—
489C4#1192673211yescharacteristic
490C4#1192673511yescharacteristic
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—3041no—
498C2#1456488511yescharacteristic
499C2#1456494011yescharacteristic
500C2#1456495011yescharacteristic
subgroupG/H
centerC22#11926460
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1996C2
socleC22×C19#394
prime radicalC2×#10597376C22
hypercenter#1996D19
hypocenterC19#10565
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
4. #14564059C2semidirect
5. #14563815C2semidirect
6. #14561502C2semidirect
7. C19×#1996C2semidirect
123. C22⋊C4×C19SD16semidirect
208. #1996D19semidirect
329. C19#10565semidirect
395. C22⋊C4#64527semidirect

Maximal subgroups

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

subgroupindex
#145743882
#145644712
#145640612
#145640592
#145638152
#145615022
C19×#19962
#1056519