Finite Group Databasebeta

← #18074353

Subgroups — #18074353

Order 4864.

1020 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11927170C211yesmaximal, characteristic
2#14563942C212yesmaximal, complemented
3C2×#11926280C212yesmaximal, complemented
4C2×#11926268C211yesmaximal, characteristic
5C19×#1439C211yesmaximal, characteristic
6#11927170—24no—
7#11927170—22no—
8#11927170C414yescomplemented
9C2×#10597370—21no—
10C2×#10597370C2212yes—
11C2×#10597324—22no—
12C2×#10597324—22no—
13C22×C22⋊Dic19—21no—
14C2×#10597267—22no—
15C2×C22⋊(C19⋊C8)C2212yes—
16#11926306—22no—
17#11926280—24no—
18#11926268—22no—
19C22×C4⋊C4×C19C2211yescharacteristic
20C22×C22⋊C4×C19—21no—
21C22×C22⋊C4×C19C2211yescharacteristic
22C2×C19×#95—21no—
23C2×C19×#95C2211yescharacteristic
24C25×C19D411yescharacteristic
25C23×C4×C19—21no—
26C23×C4×C19—21no—
27C23×C4×C19D411yescharacteristic
28C23×C4×C19C2311yescharacteristic
29C23×Dic19—21no—
30C23×Dic19—21no—
31C22×Dic38—21no—
32C22×Dic38D412yes—
33C2×C4⋊C4×C19—22no—
34C2×C4⋊C4×C19—42no—
35C2×C22⋊C4×C19—22no—
36C2×C22⋊C4×C19—22no—
37C2×C22⋊C4×C19—42no—
38C2×C22⋊C4×C19—42no—
39C2×C22⋊C4×C19—42no—
40C2×C22⋊C4×C19C2×C412yes—
41C2×C22⋊C4×C19D412yes—
42C2×C22⋊Dic19—22no—
43C2×C22⋊Dic19—24no—
44C2×C22⋊Dic19—24no—
45C2×C22⋊Dic19—22no—
46C2×C4⋊Dic19—21no—
47C2×C4⋊Dic19D412yes—
48#10597370—24no—
49#10597370—24no—
50#10597370—22no—
51#10597370—22no—
52#10597370C2×C414yes—
53#10597370D414yes—
54C2×Dic19⋊C4—22no—
55C2×Dic19⋊C4—22no—
56C22×C19⋊C8—22no—
57#10597324—28no—
58#10597324—28no—
59#10597324—28no—
60#10597324—28no—
61C19×#95—22no—
62C19×#95—42no—
63C22⋊(C19⋊C8)—22no—
64C22⋊(C19⋊C8)—22no—
65#10597267—44no—
66C24×C19—21no—
67C24×C19—21no—
68C24×C19—21no—
69C24×C19—21no—
70C24×C19—41no—
71C24×C19—41no—
72C24×C19—41no—
73C24×C19—41no—
74C24×C19C22⋊C412yes—
75C24×C19SD1612yes—
76C24×C19Q1612yes—
77C24×C19C2×D411yescharacteristic
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19—22no—
81C22×C4×C19—22no—
82C22×C4×C19—41no—
83C22×C4×C19—41no—
84C22×C4×C19—41no—
85C22×C4×C19—41no—
86C22×C4×C19—41no—
87C22×C4×C19—41no—
88C22×C4×C19—41no—
89C22×C4×C19—41no—
90C22×C4×C19—41no—
91C22×C4×C19—41no—
92C22×C4×C19—41no—
93C22×C4×C19—41no—
94C22×C4×C19—41no—
95C22×C4×C19—41no—
96C22×C4×C19—41no—
97C22×C4×C19—41no—
98C22×C4×C19C22⋊C412yes—
99C22×C4×C19C22×C411yescharacteristic
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19C2×D412yes—
102C22×C4×C19C2×D412yes—
103C22×Dic19—22no—
104C22×Dic19—22no—
105C22×Dic19—24no—
106C22×Dic19—24no—
107C22×Dic19—81no—
108C22×Dic19—81no—
109C22×Dic19—81no—
110C22×Dic19—81no—
111C2×Dic38—24no—
112C2×Dic38—22no—
113C2×Dic38—42no—
114C2×Dic38—42no—
115C2×Dic38—81no—
116C2×Dic38—81no—
117C2×Dic38C22⋊C414yescomplemented
118C4⋊C4×C19—24no—
119C4⋊C4×C19—42no—
120C22⋊C4×C19—24no—
121C22⋊C4×C19—24no—
122C22⋊C4×C19—48no—
123C22⋊Dic19—28no—
124C22⋊Dic19—24no—
125C22⋊Dic19—24no—
126C4⋊Dic19—24no—
127C4⋊Dic19—22no—
128C4⋊Dic19C22⋊C414yescomplemented
129Dic19⋊C4—28no—
130Dic19⋊C4—24no—
131Dic19⋊C4—24no—
132C2×C19⋊C8—42no—
133C2×C19⋊C8—42no—
134C2×C19⋊C8—42no—
135#8405—191nomaximal, Sylow
136C23×C19—21no—
137C23×C19—21no—
138C23×C19—21no—
139C23×C19—21no—
140C23×C19—22no—
141C23×C19—22no—
142C23×C19—22no—
143C23×C19—22no—
144C23×C19—22no—
145C23×C19—22no—
146C23×C19—42no—
147C23×C19—42no—
148C23×C19—42no—
149C23×C19—42no—
150C23×C19—42no—
151C23×C19—42no—
152C23×C19—41no—
153C23×C19—41no—
154C23×C19—41no—
155C23×C19—41no—
156C23×C19—81no—
157C23×C19—81no—
158C23×C19—81no—
159C23×C19—81no—
160C23×C19—81no—
161C23×C19—81no—
162C23×C19#10314yescomplemented
163C23×C19C2×C22⋊C411yescharacteristic
164C23×C19#12011yescharacteristic
165C23×C19#12011yescharacteristic
166C23×C19C2×SD1611yescharacteristic
167C23×C19C2×Q1611yescharacteristic
168C23×C19#13711yescharacteristic
169C23×C19#13711yescharacteristic
170C2×C4×C19—22no—
171C2×C4×C19—22no—
172C2×C4×C19—22no—
173C2×C4×C19—41no—
174C2×C4×C19—41no—
175C2×C4×C19—42no—
176C2×C4×C19—41no—
177C2×C4×C19—41no—
178C2×C4×C19—42no—
179C2×C4×C19—42no—
180C2×C4×C19—42no—
181C2×C4×C19—42no—
182C2×C4×C19—42no—
183C2×C4×C19—42no—
184C2×C4×C19—42no—
185C2×C4×C19—81no—
186C2×C4×C19—81no—
187C2×C4×C19—81no—
188C2×C4×C19—81no—
189C2×C4×C19—81no—
190C2×C4×C19—81no—
191C2×C4×C19—81no—
192C2×C4×C19—81no—
193C2×C4×C19—81no—
194C2×C4×C19C2×C22⋊C412yes—
195C2×C4×C19#12012yes—
196C2×Dic19—24no—
197C2×Dic19—24no—
198C2×Dic19—42no—
199C2×Dic19—42no—
200C2×Dic19—42no—
201C2×Dic19—42no—
202C2×Dic19—84no—
203C2×Dic19—84no—
204Dic38—44no—
205Dic38—82no—
206Dic38—84no—
207C19⋊C8—82no—
208C2×#543—191no—
209#1872—192no—
210C2×#328—192no—
211C2×#323—191no—
212#1439D1911yescharacteristic
213C22×C19—21no—
214C22×C19—21no—
215C22×C19—21no—
216C22×C19—21no—
217C22×C19—21no—
218C22×C19—21no—
219C22×C19—21no—
220C22×C19—21no—
221C22×C19—21no—
222C22×C19—21no—
223C22×C19—21no—
224C22×C19—21no—
225C22×C19—24no—
226C22×C19—44no—
227C22×C19—42no—
228C22×C19—42no—
229C22×C19—42no—
230C22×C19—42no—
231C22×C19—42no—
232C22×C19—42no—
233C22×C19—82no—
234C22×C19—82no—
235C22×C19—82no—
236C22×C19#37911yescharacteristic
237C22×C19C2×#10311yescharacteristic
238C22×C19#41911yescharacteristic
239C22×C19#44811yescharacteristic
240C22×C19#44811yescharacteristic
241C22×C19#45111yescharacteristic
242C22×C19#45111yescharacteristic
243C22×C19#45311yescharacteristic
244C22×C19#45511yescharacteristic
245C22×C19B(4,𝔽2)11yescharacteristic
246C22×C19#45811yescharacteristic
247C4×C19—22no—
248C4×C19—22no—
249C4×C19—42no—
250C4×C19—82no—
251C4×C19—82no—
252Dic19—44no—
253Dic19—44no—
254#543—194no—
255#543—384no—
256#543—382no—
257C2×C22⋊Q8—192no—
258C2×C22⋊Q8—382no—
259C2×C22⋊Q8—382no—
260C2×C22⋊Q8—381no—
261C22×C4⋊C4C2×D1911yescharacteristic
262C22×C22⋊C4—21no—
263C22×C22⋊C4—381no—
264C22×C22⋊C4C2×D1911yescharacteristic
265C2×#103—382no—
266C2×C22⋊C8—192no—
267C2×#95—21no—
268C2×#95C2×D1911yescharacteristic
269#340—382no—
270#328—384no—
271#323—382no—
272C2×C19—21no—
273C2×C19—21no—
274C2×C19—21no—
275C2×C19—21no—
276C2×C19—44no—
277C2×C19#159611yescharacteristic
278C2×C19#160211yescharacteristic
279C2×C19#160811yescharacteristic
280C2×C19#161411yescharacteristic
281C2×C19#178711yescharacteristic
282C2×C19#179011yescharacteristic
283C2×C19#179211yescharacteristic
284C25C22⋊D1911yescharacteristic
285C22×Q8—192no—
286C22×Q8—381no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—381no—
290C23×C4—381no—
291C23×C4C22⋊D1911yescharacteristic
292C23×C4C22×D1911yescharacteristic
293C22×C8—382no—
294C22⋊Q8—194no—
295C22⋊Q8—194no—
296C22⋊Q8—388no—
297C22⋊Q8—388no—
298C22⋊Q8—388no—
299C22⋊Q8—388no—
300C22⋊Q8—384no—
301C22⋊Q8—384no—
302C22⋊Q8—382no—
303C22⋊Q8—382no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—192no—
307C2×C4⋊C4—382no—
308C2×C4⋊C4—381no—
309C2×C4⋊C4—382no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—382no—
316C2×C22⋊C4—384no—
317C2×C22⋊C4—384no—
318C2×C22⋊C4—382no—
319C2×C22⋊C4C4×D1912yes—
320C2×C22⋊C4D7612yes—
321#103—764no—
322C22⋊C8—382no—
323C22⋊C8—382no—
324#95—22no—
325#95—42no—
326C19#840511yescharacteristic, complemented, Sylow
327C24—21no—
328C24—21no—
329C24—21no—
330C24—21no—
331C24—41no—
332C24—41no—
333C24—41no—
334C24—41no—
335C24(C2×D19)⋊C412yes—
336C24#6452612yes—
337C24#6452812yes—
338C24C2×C22⋊D1911yescharacteristic
339C2×Q8—194no—
340C2×Q8—384no—
341C2×Q8—382no—
342C2×Q8—762no—
343C2×Q8—762no—
344C2×Q8—1521no—
345C2×Q8—1521no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—382no—
367C22×C4—382no—
368C22×C4—384no—
369C22×C4—384no—
370C22×C4—1521no—
371C22×C4—1521no—
372C22×C4—1521no—
373C22×C4—1521no—
374C22×C4(C2×D19)⋊C412yes—
375C22×C4C2×C4×D1911yescharacteristic
376C22×C4C2×D7611yescharacteristic
377C22×C4D4×D1912yes—
378C22×C4D4×D1912yes—
379C2×C8—762no—
380C2×C8—762no—
381C2×C8—762no—
382C4⋊C4—24no—
383C4⋊C4—42no—
384C4⋊C4—194no—
385C4⋊C4—388no—
386C4⋊C4—384no—
387C4⋊C4—384no—
388C4⋊C4—384no—
389C4⋊C4—382no—
390C22⋊C4—24no—
391C22⋊C4—24no—
392C22⋊C4—48no—
393C22⋊C4—388no—
394C22⋊C4—384no—
395C22⋊C4—384no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—22no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—81no—
417C23—81no—
418C23—81no—
419C23—81no—
420C23—81no—
421C23—81no—
422C23#1059726714yescomplemented
423C23C2×(C2×D19)⋊C411yescharacteristic
424C23C2×#6452611yescharacteristic
425C23#1059738311yescharacteristic
426C23#1059738311yescharacteristic
427C23C2×#6452811yescharacteristic
428C23#1059739711yescharacteristic
429C23#1059739711yescharacteristic
430Q8—764no—
431Q8—1522no—
432Q8—1524no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4—81no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4—81no—
456C2×C4—81no—
457C2×C4—384no—
458C2×C4—384no—
459C2×C4—762no—
460C2×C4—762no—
461C2×C4—762no—
462C2×C4—762no—
463C2×C4—1524no—
464C2×C4—1524no—
465C2×C4C22⋊C4×D1912yes—
466C2×C4#1059732812yes—
467C8—1522no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—24no—
481C22—44no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—82no—
489C22—82no—
490C22—82no—
491C22#1192639911yescharacteristic
492C22C2×#1059726711yescharacteristic
493C22#1192655211yescharacteristic
494C22#1192668211yescharacteristic
495C22#1192668211yescharacteristic
496C22#1192669911yescharacteristic
497C22#1192669911yescharacteristic
498C22#1192671111yescharacteristic
499C22#1192672111yescharacteristic
500C22#1192673011yescharacteristic
501C22#1192673311yescharacteristic
502C4—22no—
503C4—22no—
504C4—42no—
505C4—82no—
506C4—82no—
507C4—764no—
508C4—764no—
509C2—21no—
510C2—21no—
511C2—21no—
512C2—21no—
513C2—44no—
514C2#1456255711yescharacteristic
515C2#1456259111yescharacteristic
516C2#1456262511yescharacteristic
517C2#1456265911yescharacteristic
518C2#1456356911yescharacteristic
519C2#1456358211yescharacteristic
520C2#1456358811yescharacteristic
subgroupG/H
centerC23#10597383
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1439C2
socleC23×C19#120
prime radicalC25×C19D4
cosocleC23×C4×C19C23
hypercenter#1439D19
hypocenterC19#8405
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. #14563942C2semidirect
3. C2×#11926280C2semidirect
8. #11927170C4semidirect
117. C2×Dic38C22⋊C4semidirect
128. C4⋊Dic19C22⋊C4semidirect
162. C23×C19#103semidirect
326. C19#8405semidirect
422. C23#10597267semidirect

Maximal subgroups

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

subgroupindex
C2×#119271702
#145639422
C2×#119262802
C2×#119262682
C19×#14392
#840519