Finite Group Databasebeta

← #18077395

Subgroups — #18077395

Order 4864.

578 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573631C211yesmaximal, characteristic
2#14572370C211yesmaximal, characteristic, complemented
3#14564555C211yesmaximal, characteristic, complemented
4C4×#10597278C211yesmaximal, characteristic, complemented
5#14561536C211yesmaximal, characteristic, complemented
6#14561472C211yesmaximal, characteristic, complemented
7C19×#1492C211yesmaximal, characteristic, complemented
8C2×M16×D19—21no—
9C2×C4×D76C2211yescharacteristic
10#11926855—21no—
11#11926821C411yescharacteristic, complemented
12#11926821C411yescharacteristic, complemented
13#11926736C411yescharacteristic, complemented
14#11926736C411yescharacteristic, complemented
15#11926677—21no—
16C4×#64525—21no—
17C4×#64525—21no—
18#11926621—21no—
19#11926614—22no—
20#11926609—21no—
21#11926597C2211yescharacteristic
22C2×#10597294—21no—
23C2×#10597294—21no—
24C2×#10597278—21no—
25#11926507—21no—
26C4×#64520C2211yescharacteristic
27C4×C4⋊Dic19C2211yescharacteristic
28#11926307—21no—
29C19×#532C2211yescharacteristic
30C19×#423C2211yescharacteristic
31C2×C4×C8×C19C2211yescharacteristic
32C19×D4⋊C8—22no—
33C2×#41×C19—21no—
34C22×D76D411yescharacteristic
35C22×C4×D19—21no—
36C2×M16×C19—21no—
37C22×C8×C19—21no—
38C19×C4⋊Q8C2×C411yescharacteristic
39C19×#127C2×C411yescharacteristic
40C19×#124—21no—
41C19×#121—21no—
42C19×#121—21no—
43C4×D4×C19—21no—
44C4×D4×C19—21no—
45C2×C42×C19C2311yescharacteristic
46C2×#64525—21no—
47C2×#64525—21no—
48C2×(C2×D19)⋊C4—21no—
49C2×C4⋊Dic19—21no—
50C2×C4⋊Dic19D411yescharacteristic
51C2×C4×Dic19—21no—
52C2×#64520D411yescharacteristic
53C2×#64520D411yescharacteristic
54M16×D19—42no—
55M16×D19—42no—
56C2×#64515—22no—
57C2×C8×D19—22no—
58C4×D76—21no—
59C4×D76—21no—
60C4×D76C2×C411yescharacteristic
61C4×D76C2×C411yescharacteristic
62C4×D76D411yescharacteristic
63C4×D76D411yescharacteristic
64C19×C4⋊C8—21no—
65C19×C4⋊C8D412yes—
66C4×C8×C19—21no—
67C4×C8×C19—21no—
68#10597294—42no—
69#10597294—42no—
70#10597289—21no—
71#10597289—21no—
72C19⋊#95—21no—
73C22⋊(C19⋊C8)—21no—
74#10597278—24no—
75(C2×D19)⋊C8—22no—
76(C2×D19)⋊C8—22no—
77#10597266—21no—
78#10597266—21no—
79#10597264—21no—
80#10597264—21no—
81C4⋊(C19⋊C8)C2×C411yescharacteristic
82C4⋊(C19⋊C8)C2×C411yescharacteristic
83#10597260—21no—
84C4×C19⋊C8—21no—
85C4×C19⋊C8—21no—
86C23×D19—21no—
87#41×C19—41no—
88#41×C19—41no—
89#41×C19—41no—
90#41×C19—41no—
91C2×Q8×C19—21no—
92C2×D4×C19—21no—
93C2×D4×C19—21no—
94C2×D4×C19—21no—
95C2×D4×C19—41no—
96C22×C4×C19—41no—
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19#4111yescharacteristic
100C22×Dic19—21no—
101C22×Dic19—41no—
102C2×D76—22no—
103C2×D76—21no—
104C2×D76—41no—
105C2×D76C22⋊C411yescharacteristic
106C2×D76C22⋊C411yescharacteristic
107C2×C4×D19—21no—
108C2×C4×D19—21no—
109C2×C4×D19—21no—
110C2×C4×D19—21no—
111C2×C4×D19—41no—
112C2×C4×D19—41no—
113C2×C4×D19—41no—
114C2×C4×D19—41no—
115M16×C19—41no—
116M16×C19—41no—
117C2×C8×C19—22no—
118C2×C8×C19—22no—
119C2×C8×C19—41no—
120C2×C8×C19—41no—
121C4⋊C4×C19—21no—
122C4⋊C4×C19—21no—
123C22⋊C4×C19—41no—
124C22⋊C4×C19—41no—
125C42×C19C22×C411yescharacteristic
126C42×C19C2×D411yescharacteristic
127C42×C19C2×D411yescharacteristic
128C42×C19#4111yescharacteristic
129#64525—42no—
130#64525—42no—
131(C2×D19)⋊C4—21no—
132(C2×D19)⋊C4—21no—
133(C2×D19)⋊C4—21no—
134(C2×D19)⋊C4—21no—
135C4⋊Dic19—21no—
136C4⋊Dic19—22no—
137C4⋊Dic19—41no—
138C4⋊Dic19C22⋊C411yescharacteristic
139C4⋊Dic19C22⋊C411yescharacteristic
140C4×Dic19—41no—
141C4×Dic19—41no—
142#64520—21no—
143#64520—21no—
144#64520—21no—
145#64520D812yescomplemented
146C2×C19⋊C8—21no—
147C2×C19⋊C8—21no—
148C2×C19⋊C8—21no—
149C2×C19⋊C8—21no—
150#64515—44no—
151C8×D19—44no—
152#8991—191nomaximal, Sylow
153C23×C19—41no—
154C23×C19#12111yescharacteristic
155C22×D19—21no—
156C22×D19—21no—
157C22×D19—42no—
158C22×D19—41no—
159C22×D19—41no—
160C22×D19—81no—
161Q8×C19—41no—
162Q8×C19—41no—
163D4×C19—42no—
164D4×C19—41no—
165D4×C19—41no—
166D4×C19—41no—
167D4×C19—41no—
168D4×C19—81no—
169D4×C19—81no—
170C2×C4×C19—21no—
171C2×C4×C19—21no—
172C2×C4×C19—41no—
173C2×C4×C19—41no—
174C2×C4×C19—81no—
175C2×C4×C19—81no—
176C2×C4×C19C2×C22⋊C411yescharacteristic
177C2×C4×C19C4×D411yescharacteristic
178C2×C4×C19C4×D411yescharacteristic
179C2×C4×C19#12011yescharacteristic
180C2×C4×C19#12111yescharacteristic
181C2×C4×C19#12311yescharacteristic
182C2×C4×C19C2×D811yescharacteristic
183C2×C4×C19#13511yescharacteristic
184C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
186C2×Dic19—21no—
187C2×Dic19—21no—
188C2×Dic19—41no—
189C2×Dic19—41no—
190C2×Dic19—42no—
191C2×Dic19—81no—
192C2×Dic19—81no—
193D76—21no—
194D76—21no—
195D76—21no—
196D76—42no—
197D76#10412yescomplemented
198C4×D19—41no—
199C4×D19—41no—
200C4×D19—41no—
201C4×D19—41no—
202C4×D19—41no—
203C4×D19—41no—
204C4×D19—41no—
205C4×D19—41no—
206C8×C19—42no—
207C8×C19—42no—
208C19⋊C8—22no—
209C19⋊C8—41no—
210C19⋊C8—41no—
211C19⋊C8—41no—
212#3100—191no—
213D4×M16—191no—
214#1980—191no—
215C4×#102—191no—
216#1492D1911yescharacteristic, complemented
217#1303—191no—
218#1278—191no—
219C22×C19—21no—
220C22×C19—21no—
221C22×C19—81no—
222C22×C19—81no—
223C22×C19—81no—
224C22×C19#38611yescharacteristic
225C22×C19#45911yescharacteristic
226C22×C19#46311yescharacteristic
227C2×D19—22no—
228C2×D19—41no—
229C2×D19—41no—
230C2×D19—41no—
231C2×D19—41no—
232C2×D19—41no—
233C2×D19—82no—
234C2×D19—82no—
235C4×C19—21no—
236C4×C19—21no—
237C4×C19—21no—
238C4×C19—81no—
239C4×C19C2×#10411yescharacteristic
240C4×C19#42111yescharacteristic
241C4×C19C4×D811yescharacteristic
242C4×C19#44211yescharacteristic
243C4×C19#44711yescharacteristic
244C4×C19#44911yescharacteristic
245Dic19—41no—
246Dic19—41no—
247Dic19—82no—
248C22×M16—381no—
249#532C2×D1911yescharacteristic
250C2×C4×D4—191no—
251#480—381no—
252#474—191no—
253#474—191no—
254#459—191no—
255#459—191no—
256#447—381no—
257C4×D8—381no—
258C4×D8—381no—
259#436—381no—
260#435—382no—
261C8×D4—381no—
262#431—191no—
263#423C2×D1911yescharacteristic
264C2×#104—381no—
265C2×#104—381no—
266C2×#102—381no—
267#407—381no—
268C4×M16—191no—
269C2×C4×C8C2×D1911yescharacteristic
270C4×C4⋊C4—191no—
271#340—381no—
272D4⋊C8—22no—
273C2×C19—21no—
274C2×C19—21no—
275C2×C19—161no—
276C2×C19#187111yescharacteristic
277C2×C19#187911yescharacteristic
278C2×C19#188111yescharacteristic
279D19—42no—
280D19—81no—
281C2×#41—21no—
282C22×D4—191no—
283C23×C4—381no—
284C2×D8—381no—
285C2×D8—381no—
286C2×M16—21no—
287C2×M16—191no—
288C2×M16—191no—
289C2×M16—382no—
290C2×M16—762no—
291C2×M16—762no—
292C22×C8—21no—
293C22×C8—382no—
294C4⋊Q8C4×D1911yescharacteristic
295#127C4×D1911yescharacteristic
296#124—21no—
297#121—21no—
298#121—21no—
299C4×D4—21no—
300C4×D4—21no—
301C4×D4—191no—
302C4×D4—191no—
303C4×D4—191no—
304C4×D4—191no—
305C4×D4—381no—
306C4×D4—381no—
307C2×C4⋊C4—191no—
308C2×C4⋊C4—381no—
309C2×C22⋊C4—381no—
310C2×C42—381no—
311C2×C42C22×D1911yescharacteristic
312#107—381no—
313#107—381no—
314C4⋊C8—21no—
315C4⋊C8—191no—
316C4⋊C8—191no—
317C4⋊C8C22⋊D1912yes—
318#104—762no—
319#104—762no—
320#102—381no—
321#102—381no—
322#102—381no—
323#102—381no—
324#102—384no—
325C22⋊C8—382no—
326C22⋊C8—382no—
327C22⋊C8—381no—
328#97—381no—
329C4×C8—21no—
330C4×C8—21no—
331C4×C8—381no—
332C4×C8—381no—
333#95—381no—
334C19#899111yescharacteristic, complemented, Sylow
335C24—381no—
336#41—41no—
337#41—41no—
338#41—41no—
339#41—41no—
340C2×Q8—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—41no—
345C2×D4—191no—
346C2×D4—191no—
347C2×D4—382no—
348C2×D4—381no—
349C2×D4—761no—
350C22×C4—41no—
351C22×C4—381no—
352C22×C4—381no—
353C22×C4—381no—
354C22×C4—381no—
355C22×C4—381no—
356C22×C4—761no—
357C22×C4—761no—
358C22×C4—761no—
359C22×C4—761no—
360C22×C4—761no—
361C22×C4#6454111yescharacteristic
362C22×C4D4×D1911yescharacteristic
363C22×C4D4×D1911yescharacteristic
364D8—762no—
365D8—762no—
366M16—41no—
367M16—41no—
368M16—192no—
369M16—381no—
370M16—381no—
371M16—381no—
372M16—764no—
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—41no—
376C2×C8—41no—
377C2×C8—381no—
378C2×C8—381no—
379C2×C8—381no—
380C2×C8—381no—
381C2×C8—764no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—191no—
385C4⋊C4—191no—
386C4⋊C4—382no—
387C4⋊C4—381no—
388C4⋊C4—761no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—381no—
392C22⋊C4—381no—
393C22⋊C4—381no—
394C22⋊C4—381no—
395C42—761no—
396C42—761no—
397C42C2×C4×D1911yescharacteristic
398C42D4×D1911yescharacteristic
399C42#6454311yescharacteristic
400C42C2×C22⋊D1911yescharacteristic
401C23—41no—
402C23—381no—
403C23—381no—
404C23—762no—
405C23—761no—
406C23—761no—
407C23—1521no—
408C23#1059733011yescharacteristic
409Q8—41no—
410Q8—41no—
411D4—42no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—41no—
416D4—81no—
417D4—81no—
418D4—192no—
419D4—381no—
420D4—381no—
421D4—381no—
422D4—762no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—381no—
430C2×C4—381no—
431C2×C4—761no—
432C2×C4—761no—
433C2×C4—761no—
434C2×C4—761no—
435C2×C4—761no—
436C2×C4—761no—
437C2×C4—761no—
438C2×C4—761no—
439C2×C4—761no—
440C2×C4—761no—
441C2×C4—762no—
442C2×C4—1521no—
443C2×C4—1521no—
444C2×C4C22⋊C4×D1911yescharacteristic
445C2×C4(C22⋊D19)⋊C411yescharacteristic
446C2×C4#1059732911yescharacteristic
447C2×C4D8×D1911yescharacteristic
448C2×C4#1059735711yescharacteristic
449C2×C4#1059736011yescharacteristic
450C2×C4#1059736211yescharacteristic
451C2×C4C4×C22⋊D1911yescharacteristic
452C2×C4#1059738311yescharacteristic
453C2×C4#1059738411yescharacteristic
454C8—42no—
455C8—42no—
456C8—382no—
457C8—761no—
458C8—761no—
459C8—761no—
460C22—21no—
461C22—21no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—382no—
466C22—761no—
467C22—761no—
468C22—761no—
469C22—761no—
470C22—761no—
471C22—1522no—
472C22—1522no—
473C22#1192642011yescharacteristic
474C22#1192673811yescharacteristic
475C22#1192675811yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—81no—
480C4—761no—
481C4—761no—
482C4—1522no—
483C4#104×D1911yescharacteristic
484C4#1192655911yescharacteristic
485C4#1192662411yescharacteristic
486C4#1192665311yescharacteristic
487C4#1192667611yescharacteristic
488C4#1192668811yescharacteristic
489C2—21no—
490C2—21no—
491C2—161no—
492C2—762no—
493C2—1521no—
494C2#1456393411yescharacteristic
495C2#1456398011yescharacteristic
496C2#1456400011yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1492C2
socleC22×C19#386
prime radical#14573631C2
cosocleC2×C42×C19C23
hypercenter#1492D19
hypocenterC19#8991
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. #14572370C2semidirect
3. #14564555C2semidirect
4. C4×#10597278C2semidirect
5. #14561536C2semidirect
6. #14561472C2semidirect
7. C19×#1492C2semidirect
11. #11926821C4semidirect
12. #11926821C4semidirect
13. #11926736C4semidirect
14. #11926736C4semidirect
145. #64520D8semidirect
197. D76#104semidirect
216. #1492D19semidirect
334. C19#8991semidirect

Maximal subgroups

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

subgroupindex
#145736312
#145723702
#145645552
C4×#105972782
#145615362
#145614722
C19×#14922
#899119