Finite Group Databasebeta

← #18077396

Subgroups — #18077396

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#14573635C211yesmaximal, characteristic
2D4×#64520C211yesmaximal, characteristic, complemented
3#14564553C211yesmaximal, characteristic, complemented
4#14562087C211yesmaximal, characteristic, complemented
5#14561538C211yesmaximal, characteristic, complemented
6#14561472C211yesmaximal, characteristic, complemented
7C4×C19×#102C211yesmaximal, characteristic, complemented
8C22×#64520—21no—
9#11927094C2211yescharacteristic
10#11926857—21no—
11#11926824C411yescharacteristic, complemented
12#11926824C411yescharacteristic, complemented
13#11926739C411yescharacteristic, complemented
14#11926739C411yescharacteristic, complemented
15#11926678—21no—
16C4×#64525—21no—
17C4×#64525—21no—
18#11926622—21no—
19#11926616—22no—
20D4×C19⋊C8—21no—
21#11926597C2211yescharacteristic
22#11926568C2211yescharacteristic
23C2×#10597262—21no—
24C2×#10597262—21no—
25#11926508—21no—
26C4×#64520C2211yescharacteristic
27#11926273—22no—
28C2×C4×D4×C19C2211yescharacteristic
29C2×C19×#102—21no—
30C2×C4×C8×C19C2211yescharacteristic
31C4×C4⋊C4×C19C2211yescharacteristic
32C19×#340—21no—
33C22×D4×C19D411yescharacteristic
34C23×C4×C19—21no—
35C2×#64541—21no—
36C22×C8×C19—21no—
37C4×D4×C19—21no—
38C4×D4×C19—21no—
39C4×D4×C19C2×C411yescharacteristic
40C4×D4×C19C2×C411yescharacteristic
41C4×D4×C19D411yescharacteristic
42C4×D4×C19D411yescharacteristic
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19D411yescharacteristic
45C2×C22⋊C4×C19—21no—
46C2×C42×C19—21no—
47C2×C42×C19C2311yescharacteristic
48C2×#64525—21no—
49C2×#64525—21no—
50#10597376—21no—
51#10597376—21no—
52C2×#64520—22no—
53C2×#64520—21no—
54C2×#64520—42no—
55C2×#64520—42no—
56C2×#64520D411yescharacteristic
57C2×#64520D411yescharacteristic
58C22×C19⋊C8—22no—
59#10597321—21no—
60#10597320C2×C411yescharacteristic
61C4×D76—21no—
62C4×D76—21no—
63#10597315C2×C411yescharacteristic
64C19×#102—24no—
65C4×C8×C19—21no—
66C4×C8×C19—21no—
67C19×#95—21no—
68#10597289—21no—
69#10597289—21no—
70C22⋊(C19⋊C8)—22no—
71C22⋊(C19⋊C8)—22no—
72C22⋊(C19⋊C8)—21no—
73#10597266—21no—
74#10597266—21no—
75#10597264—21no—
76#10597264—21no—
77#10597262—42no—
78#10597262—42no—
79C4⋊(C19⋊C8)—21no—
80C4⋊(C19⋊C8)C2×C411yescharacteristic
81C4⋊(C19⋊C8)C2×C411yescharacteristic
82C4⋊(C19⋊C8)D412yes—
83#10597260—21no—
84C4×C19⋊C8—21no—
85C4×C19⋊C8—21no—
86C24×C19—21no—
87C2×D4×C19—22no—
88C2×D4×C19—21no—
89C2×D4×C19—41no—
90C2×D4×C19C22⋊C411yescharacteristic
91C2×D4×C19C22⋊C411yescharacteristic
92C22×C4×C19—21no—
93C22×C4×C19—21no—
94C22×C4×C19—21no—
95C22×C4×C19—21no—
96C22×C4×C19—21no—
97C22×C4×C19—41no—
98C22×C4×C19—41no—
99C22×C4×C19—41no—
100C22×C4×C19—41no—
101C22×C4×C19—41no—
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19C2×D411yescharacteristic
104C22×C4×C19#4111yescharacteristic
105C2×C22⋊D19—41no—
106#64541—41no—
107#64541—41no—
108#64541—41no—
109#64541—41no—
110C2×D76—21no—
111C2×D76—21no—
112C2×D76—21no—
113C2×C4×D19—41no—
114C2×Dic38—21no—
115C2×C8×C19—22no—
116C2×C8×C19—41no—
117C2×C8×C19—41no—
118C4⋊C4×C19—21no—
119C4⋊C4×C19—22no—
120C4⋊C4×C19—41no—
121C4⋊C4×C19C22⋊C411yescharacteristic
122C4⋊C4×C19C22⋊C411yescharacteristic
123C22⋊C4×C19—21no—
124C22⋊C4×C19—21no—
125C22⋊C4×C19—21no—
126C22⋊C4×C19—21no—
127C42×C19—41no—
128C42×C19—41no—
129C42×C19C22×C411yescharacteristic
130C42×C19C2×D411yescharacteristic
131C42×C19C2×D411yescharacteristic
132C42×C19#4111yescharacteristic
133#64525—42no—
134#64525—42no—
135(C2×D19)⋊C4—41no—
136(C2×D19)⋊C4—41no—
137C4⋊Dic19—21no—
138C4⋊Dic19—21no—
139#64520—21no—
140#64520—21no—
141#64520—21no—
142#64520—44no—
143#64520—41no—
144#64520—41no—
145#64520D812yescomplemented
146C2×C19⋊C8—21no—
147C2×C19⋊C8—21no—
148C2×C19⋊C8—21no—
149C2×C19⋊C8—21no—
150C2×C19⋊C8—22no—
151C2×C19⋊C8—44no—
152#8991—191nomaximal, Sylow
153C23×C19—21no—
154C23×C19—21no—
155C23×C19—42no—
156C23×C19—41no—
157C23×C19—41no—
158C23×C19—81no—
159C23×C19#12111yescharacteristic
160C22×D19—41no—
161D4×C19—21no—
162D4×C19—21no—
163D4×C19—21no—
164D4×C19—42no—
165D4×C19#10412yescomplemented
166C2×C4×C19—21no—
167C2×C4×C19—21no—
168C2×C4×C19—21no—
169C2×C4×C19—21no—
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—41no—
181C2×C4×C19—42no—
182C2×C4×C19—81no—
183C2×C4×C19—81no—
184C2×C4×C19C2×C22⋊C411yescharacteristic
185C2×C4×C19C4×D411yescharacteristic
186C2×C4×C19C4×D411yescharacteristic
187C2×C4×C19#12011yescharacteristic
188C2×C4×C19#12111yescharacteristic
189C2×C4×C19#12311yescharacteristic
190C2×C4×C19C2×D811yescharacteristic
191C2×C4×C19#13511yescharacteristic
192C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
194C22⋊D19—81no—
195C22⋊D19—81no—
196C2×Dic19—41no—
197D76—42no—
198D76—41no—
199D76—41no—
200D76—41no—
201D76—41no—
202C4×D19—81no—
203C4×D19—81no—
204Dic38—41no—
205Dic38—41no—
206C8×C19—42no—
207C19⋊C8—22no—
208C19⋊C8—41no—
209C19⋊C8—41no—
210C19⋊C8—42no—
211C19⋊C8—41no—
212#3100—191no—
213D4×M16—191no—
214#1980—191no—
215C4×#102D1911yescharacteristic, complemented
216#1492—191no—
217#1303—191no—
218#1278—191no—
219C22×C19—21no—
220C22×C19—21no—
221C22×C19—22no—
222C22×C19—41no—
223C22×C19—41no—
224C22×C19—41no—
225C22×C19—41no—
226C22×C19—41no—
227C22×C19—82no—
228C22×C19—82no—
229C22×C19#38611yescharacteristic
230C22×C19#45911yescharacteristic
231C22×C19#46311yescharacteristic
232C2×D19—81no—
233C2×D19—81no—
234C2×D19—81no—
235C4×C19—21no—
236C4×C19—21no—
237C4×C19—21no—
238C4×C19—41no—
239C4×C19—41no—
240C4×C19—82no—
241C4×C19C2×#10411yescharacteristic
242C4×C19#42111yescharacteristic
243C4×C19C4×D811yescharacteristic
244C4×C19#44211yescharacteristic
245C4×C19#44711yescharacteristic
246C4×C19#44911yescharacteristic
247Dic19—81no—
248C22×M16—381no—
249#532—191no—
250C2×C4×D4C2×D1911yescharacteristic
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#423—191no—
264C2×#104—381no—
265C2×#104—381no—
266C2×#102—21no—
267#407—381no—
268C4×M16—191no—
269C2×C4×C8C2×D1911yescharacteristic
270C4×C4⋊C4C2×D1911yescharacteristic
271#340—21no—
272D4⋊C8—382no—
273C2×C19—21no—
274C2×C19—21no—
275C2×C19—42no—
276C2×C19—81no—
277C2×C19#187111yescharacteristic
278C2×C19#187911yescharacteristic
279C2×C19#188111yescharacteristic
280D19—161no—
281C2×#41—381no—
282C22×D4C22⋊D1911yescharacteristic
283C23×C4—21no—
284C2×D8—381no—
285C2×D8—381no—
286C2×M16—191no—
287C2×M16—191no—
288C2×M16—382no—
289C2×M16—381no—
290C2×M16—762no—
291C2×M16—762no—
292C22×C8—21no—
293C22×C8—382no—
294C4⋊Q8—191no—
295#127—191no—
296#124—381no—
297#121—381no—
298#121—381no—
299C4×D4—21no—
300C4×D4—21no—
301C4×D4—381no—
302C4×D4—381no—
303C4×D4C4×D1911yescharacteristic
304C4×D4C4×D1911yescharacteristic
305C4×D4D7611yescharacteristic
306C4×D4D7611yescharacteristic
307C2×C4⋊C4—21no—
308C2×C4⋊C4C22⋊D1911yescharacteristic
309C2×C22⋊C4—21no—
310C2×C42—21no—
311C2×C42C22×D1911yescharacteristic
312#107—381no—
313#107—381no—
314C4⋊C8—191no—
315C4⋊C8—191no—
316C4⋊C8—192no—
317C4⋊C8—381no—
318#104—762no—
319#104—762no—
320#102—24no—
321#102—381no—
322#102—381no—
323#102—381no—
324#102—381no—
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—21no—
334C19#899111yescharacteristic, complemented, Sylow
335C24—21no—
336#41—761no—
337#41—761no—
338#41—761no—
339#41—761no—
340C2×Q8—381no—
341C2×D4—22no—
342C2×D4—21no—
343C2×D4—41no—
344C2×D4—381no—
345C2×D4—381no—
346C2×D4—381no—
347C2×D4—761no—
348C2×D4(C2×D19)⋊C411yescharacteristic
349C2×D4(C2×D19)⋊C411yescharacteristic
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—761no—
361C22×C4D4×D1911yescharacteristic
362C22×C4#6454311yescharacteristic
363C22×C4C2×C22⋊D1911yescharacteristic
364D8—762no—
365D8—762no—
366M16—192no—
367M16—381no—
368M16—381no—
369M16—381no—
370M16—764no—
371M16—761no—
372M16—761no—
373C2×C8—22no—
374C2×C8—41no—
375C2×C8—41no—
376C2×C8—381no—
377C2×C8—381no—
378C2×C8—382no—
379C2×C8—381no—
380C2×C8—381no—
381C2×C8—764no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—41no—
385C4⋊C4—381no—
386C4⋊C4—381no—
387C4⋊C4(C2×D19)⋊C411yescharacteristic
388C4⋊C4(C2×D19)⋊C411yescharacteristic
389C22⋊C4—21no—
390C22⋊C4—21no—
391C22⋊C4—21no—
392C22⋊C4—21no—
393C22⋊C4—761no—
394C22⋊C4—761no—
395C42—41no—
396C42—41no—
397C42C2×C4×D1911yescharacteristic
398C42C2×D7611yescharacteristic
399C42D4×D1911yescharacteristic
400C42#6454311yescharacteristic
401C23—21no—
402C23—21no—
403C23—42no—
404C23—41no—
405C23—41no—
406C23—81no—
407C23—761no—
408C23#1059738511yescharacteristic
409Q8—761no—
410Q8—761no—
411D4—21no—
412D4—21no—
413D4—21no—
414D4—42no—
415D4—762no—
416D4—761no—
417D4—761no—
418D4—761no—
419D4—761no—
420D4—1521no—
421D4—1521no—
422D4#1059726212yescomplemented
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—41no—
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—42no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—761no—
442C2×C4—1521no—
443C2×C4—1521no—
444C2×C4(C22⋊D19)⋊C411yescharacteristic
445C2×C4(C22⋊D19)⋊C411yescharacteristic
446C2×C4#1059732811yescharacteristic
447C2×C4#1059733211yescharacteristic
448C2×C4D8×D1911yescharacteristic
449C2×C4#1059735711yescharacteristic
450C2×C4#1059736011yescharacteristic
451C2×C4#1059736211yescharacteristic
452C2×C4C2×(C2×D19)⋊C411yescharacteristic
453C2×C4#1059738511yescharacteristic
454C8—42no—
455C8—382no—
456C8—761no—
457C8—761no—
458C8—762no—
459C8—761no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—82no—
469C22—82no—
470C22—1521no—
471C22—1521no—
472C22—1521no—
473C22#1192642111yescharacteristic
474C22#1192673711yescharacteristic
475C22#1192676111yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—41no—
480C4—41no—
481C4—82no—
482C4—1521no—
483C4C2×#1059726211yescharacteristic
484C4#1192656211yescharacteristic
485C4#1192662411yescharacteristic
486C4#1192665311yescharacteristic
487C4#1192667911yescharacteristic
488C4#1192669011yescharacteristic
489C2—21no—
490C2—21no—
491C2—42no—
492C2—81no—
493C2—3041no—
494C2#1456393511yescharacteristic
495C2#1456398111yescharacteristic
496C2#1456399511yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC4×C19×#102C2
socleC22×C19#386
prime radical#14573635C2
cosocleC2×C42×C19C23
hypercenterC4×#102D19
hypocenterC19#8991
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. D4×#64520C2semidirect
3. #14564553C2semidirect
4. #14562087C2semidirect
5. #14561538C2semidirect
6. #14561472C2semidirect
7. C4×C19×#102C2semidirect
11. #11926824C4semidirect
12. #11926824C4semidirect
13. #11926739C4semidirect
14. #11926739C4semidirect
145. #64520D8semidirect
165. D4×C19#104semidirect
215. C4×#102D19semidirect
334. C19#8991semidirect
422. D4#10597262semidirect

Maximal subgroups

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

subgroupindex
#145736352
D4×#645202
#145645532
#145620872
#145615382
#145614722
C4×C19×#1022
#899119