Finite Group Databasebeta

← #18079119

Subgroups — #18079119

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#14564471C211yesmaximal, characteristic
3#14562207C211yesmaximal, characteristic, complemented
4C2×#11926277C211yesmaximal, characteristic
5#14561514C211yesmaximal, characteristic, complemented
6#14561483C211yesmaximal, characteristic, complemented
7C19×#2368C211yesmaximal, 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
17C2×C22⋊(C19⋊C8)C2211yescharacteristic
18#11926404C2211yescharacteristic
19#11926281—22no—
20#11926277—21no—
21#11926277—21no—
22C2×C19×C22⋊Q8C2211yescharacteristic
23C19×#391—21no—
24C19×#387—21no—
25C19×#387—21no—
26C19×#385—21no—
27C4×C4⋊C4×C19—21no—
28C4×C22⋊C4×C19—21no—
29C4×C22⋊C4×C19C2211yescharacteristic
30C2×C19×#95C2211yescharacteristic
31C22×Q8×C19D411yescharacteristic
32C23×C4×C19—21no—
33C23×C4×C19C2311yescharacteristic
34C22×C22⋊D19—21no—
35C22×D76C2×C411yescharacteristic
36C19×C22⋊Q8—21no—
37C19×C22⋊Q8—21no—
38C19×C22⋊Q8C2×C412yes—
39C19×C22⋊Q8D412yes—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19D411yescharacteristic
44C2×C22⋊C4×C19—21no—
45C2×C22⋊C4×C19D411yescharacteristic
46C2×C22⋊C4×C19D411yescharacteristic
47C2×C42×C19—21no—
48C2×C42×C19—21no—
49C2×C42×C19—21no—
50C2×C22⋊Dic19—21no—
51C2×#64527—22no—
52#10597376—21no—
53#10597376—21no—
54#10597376—21no—
55#10597376—21no—
56C2×(C2×D19)⋊C4—21no—
57C2×C4⋊Dic19—21no—
58C2×C4⋊Dic19C2×C411yescharacteristic
59C22×C19⋊C8—21no—
60C22×C19⋊C8—21no—
61C19×#95—21no—
62C19×#95—21no—
63C19×#95—21no—
64C19×#95—21no—
65C19×#95—21no—
66C19×#95—21no—
67C19×#95D411yescharacteristic
68C19×#95D411yescharacteristic
69#10597292—22no—
70C19⋊#95—21no—
71C22⋊(C19⋊C8)—21no—
72C22⋊(C19⋊C8)—21no—
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—21no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—21no—
90C22×C4×C19—42no—
91C22×C4×C19—41no—
92C22×C4×C19—41no—
93C22×C4×C19—81no—
94C22×C4×C19—81no—
95C22×C4×C19C22×C411yescharacteristic
96C22×C4×C19C2×D411yescharacteristic
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19#4111yescharacteristic
100C22×C4×C19#4111yescharacteristic
101C2×C22⋊D19—41no—
102C2×C22⋊D19—41no—
103C2×C22⋊D19—41no—
104C2×C22⋊D19—41no—
105C2×C22⋊D19—41no—
106C2×C22⋊D19—41no—
107C22×Dic19—21no—
108C22×Dic19—41no—
109C2×D76—21no—
110C2×D76—21no—
111C2×D76—81no—
112C4⋊C4×C19—22no—
113C4⋊C4×C19—22no—
114C4⋊C4×C19—21no—
115C4⋊C4×C19—42no—
116C4⋊C4×C19—81no—
117C4⋊C4×C19C22⋊C412yes—
118C22⋊C4×C19—22no—
119C22⋊C4×C19—22no—
120C22⋊C4×C19—21no—
121C22⋊C4×C19—21no—
122C22⋊C4×C19—21no—
123C22⋊C4×C19SD1612yescomplemented
124C42×C19—42no—
125C42×C19—81no—
126C42×C19—81no—
127C22⋊Dic19—41no—
128C22⋊Dic19—41no—
129#64527—82no—
130(C2×D19)⋊C4—41no—
131(C2×D19)⋊C4—41no—
132C4⋊Dic19—21no—
133C4⋊Dic19—21no—
134C4⋊Dic19—81no—
135C2×C19⋊C8—22no—
136C2×C19⋊C8—41no—
137C2×C19⋊C8—81no—
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—22no—
159C2×C4×C19—22no—
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—41no—
169C2×C4×C19—41no—
170C2×C4×C19—41no—
171C2×C4×C19—41no—
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—82no—
181C2×C4×C19—82no—
182C2×C4×C19C2×C22⋊C411yescharacteristic
183C2×C4×C19C4×D411yescharacteristic
184C2×C4×C19#12111yescharacteristic
185C2×C4×C19#12311yescharacteristic
186C22⋊D19—81no—
187C22⋊D19—81no—
188C22⋊D19—81no—
189C22⋊D19—81no—
190C2×Dic19—41no—
191C2×Dic19—41no—
192C2×Dic19—41no—
193C2×Dic19—81no—
194C2×Dic19—81no—
195C2×Dic19—81no—
196D76—42no—
197D76—81no—
198C19⋊C8—42no—
199C19⋊C8—81no—
200#3187—191no—
201#2368D1911yescharacteristic, complemented
202#1964—191no—
203#1520—191no—
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—42no—
236C4×C19—42no—
237C4×C19—81no—
238C4×C19—81no—
239Dic19—81no—
240Dic19—161no—
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⋊C8—191no—
252#391—21no—
253#387—21no—
254#387—21no—
255#385—21no—
256#380—191no—
257C4×C4⋊C4—21no—
258C4×C22⋊C4—21no—
259C4×C22⋊C4C2×D1911yescharacteristic
260C2×#95C2×D1911yescharacteristic
261#328—382no—
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×Q8C22⋊D1911yescharacteristic
275C22×D4—191no—
276C22×D4—381no—
277C23×C4—21no—
278C23×C4C22×D1911yescharacteristic
279C2×SD16—382no—
280C22×C8—381no—
281C22×C8—381no—
282C22⋊Q8—21no—
283C22⋊Q8—21no—
284C22⋊Q8C4×D1912yes—
285C22⋊Q8D7612yes—
286#121—381no—
287#121—381no—
288#121—381no—
289#121—381no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—191no—
294C2×C4⋊C4—381no—
295C2×C4⋊C4C22⋊D1911yescharacteristic
296C2×C22⋊C4—21no—
297C2×C22⋊C4—381no—
298C2×C22⋊C4—381no—
299C2×C22⋊C4C22⋊D1911yescharacteristic
300C2×C22⋊C4C22⋊D1911yescharacteristic
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304#106—382no—
305#103—382no—
306#102—382no—
307#99—762no—
308#99—762no—
309C22⋊C8—192no—
310C22⋊C8—381no—
311C22⋊C8—381no—
312C22⋊C8—381no—
313#95—21no—
314#95—21no—
315#95—21no—
316#95—21no—
317#95—21no—
318#95—21no—
319#95—381no—
320#95C22⋊D1911yescharacteristic
321#95C22⋊D1911yescharacteristic
322C19#927811yescharacteristic, complemented, Sylow
323C24—381no—
324C24C2×C22⋊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—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—42no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—81no—
347C22×C4—81no—
348C22×C4—381no—
349C22×C4—761no—
350C22×C4C2×C4×D1911yescharacteristic
351C22×C4C2×D7611yescharacteristic
352C22×C4#6454111yescharacteristic
353C22×C4#6454111yescharacteristic
354C22×C4C2×C22⋊D1911yescharacteristic
355C22×C4C2×C22⋊D1911yescharacteristic
356SD16—1522no—
357C2×C8—382no—
358C2×C8—761no—
359C2×C8—1521no—
360C2×C8—1521no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—21no—
364C4⋊C4—42no—
365C4⋊C4—81no—
366C4⋊C4—381no—
367C4⋊C4—381no—
368C4⋊C4—1521no—
369C4⋊C4(C2×D19)⋊C412yes—
370C22⋊C4—22no—
371C22⋊C4—21no—
372C22⋊C4—22no—
373C22⋊C4—21no—
374C22⋊C4—21no—
375C22⋊C4—761no—
376C22⋊C4—761no—
377C22⋊C4—761no—
378C22⋊C4—761no—
379C22⋊C4#6452712yescomplemented
380C42—42no—
381C42—81no—
382C42—81no—
383C23—41no—
384C23—41no—
385C23—761no—
386C23—761no—
387C23—761no—
388C23—1521no—
389C23—1521no—
390C23C4×C22⋊D1911yescharacteristic
391C23#1059737611yescharacteristic
392C23C2×#6452711yescharacteristic
393C23#1059738811yescharacteristic
394C23#1059739511yescharacteristic
395C23#1059739611yescharacteristic
396C23#1059739911yescharacteristic
397Q8—42no—
398Q8—81no—
399D4—762no—
400D4—1521no—
401D4—1521no—
402D4—1521no—
403D4—1521no—
404D4—1521no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
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—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4—761no—
432C2×C4—761no—
433C2×C4—761no—
434C2×C4—1521no—
435C2×C4—1521no—
436C2×C4—1521no—
437C2×C4C2×(C2×D19)⋊C411yescharacteristic
438C2×C4C4×C22⋊D1911yescharacteristic
439C2×C4#1059737511yescharacteristic
440C2×C4#1059737611yescharacteristic
441C8—762no—
442C8—1521no—
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#1192642311yescharacteristic
459C22C4×#6452711yescharacteristic
460C22#1192664211yescharacteristic
461C22#1192668311yescharacteristic
462C22#1192668911yescharacteristic
463C22#1192674411yescharacteristic
464C22#1192676611yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—42no—
470C4—42no—
471C4—42no—
472C4—42no—
473C4—81no—
474C4—81no—
475C4—3041no—
476C4—1521no—
477C2—21no—
478C2—21no—
479C2—21no—
480C2—21no—
481C2—21no—
482C2—21no—
483C2—3041no—
484C2#1456399011yescharacteristic
485C2#1456413611yescharacteristic
486C2#1456417711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2368C2
socleC22×C19#386
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#2368D19
hypocenterC19#9278
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2368

Complements

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

NH ≅ G/Ntype
3. #14562207C2semidirect
5. #14561514C2semidirect
6. #14561483C2semidirect
7. C19×#2368C2semidirect
9. #11926872C4semidirect
12. #11926694C4semidirect
123. C22⋊C4×C19SD16semidirect
201. #2368D19semidirect
322. C19#9278semidirect
379. 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
#145622072
C2×#119262772
#145615142
#145614832
C19×#23682
#927819