Finite Group Databasebeta

← #24911583

Subgroups — #24911583

Order 10624.

786 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581778C211yesmaximal, characteristic, complemented
2C2×#14581771C211yesmaximal, characteristic, complemented
3C2×#14581761C211yesmaximal, characteristic
4#19127629C211yesmaximal, characteristic, complemented
5#19127617C211yesmaximal, characteristic, complemented
6#19127616C211yesmaximal, characteristic, complemented
7#19127613C211yesmaximal, characteristic, complemented
8#19127601C211yesmaximal, characteristic, complemented
9#19127594C211yesmaximal, characteristic, complemented
10#19127589C211yesmaximal, characteristic, complemented
11#19127580C211yesmaximal, characteristic, complemented
12#19127580C211yesmaximal, characteristic, complemented
13#19127557C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic83C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×C83C211yesmaximal, characteristic, complemented
16C22×Dic166C2211yescharacteristic, complemented
17C22×C22⋊D83C2211yescharacteristic
18C22×C22⋊D83C2211yescharacteristic
19C22×C22⋊D83C2211yescharacteristic
20#14581778—24no—
21#14581771—24no—
22#14581761—24no—
23C2×C4⋊Dic83C2211yescharacteristic, complemented
24C2×Dic83⋊C4C2211yescharacteristic, complemented
25C2×Dic83⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic83C2211yescharacteristic
27C2×C22⋊Dic83C2211yescharacteristic
28C2×C22⋊Dic83C2211yescharacteristic
29C2×C22⋊Dic83C2211yescharacteristic
30C2×C22⋊Dic83C2211yescharacteristic
31C2×C22⋊Dic83C2211yescharacteristic
32C2×C22⋊Dic83C2211yescharacteristic
33C2×C22⋊Dic83C2211yescharacteristic
34C2×C22⋊Dic83C2211yescharacteristic
35C2×(C2×D83)⋊C4C2211yescharacteristic, complemented
36C2×(C2×D83)⋊C4C2211yescharacteristic, complemented
37C2×(C2×D83)⋊C4C2211yescharacteristic, complemented
38C2×(C2×D83)⋊C4C2211yescharacteristic, complemented
39C2×C4×Dic83C2211yescharacteristic, complemented
40C2×C4×Dic83C2211yescharacteristic, complemented
41C83⋊#95C2211yescharacteristic, complemented
42C83⋊#95C2211yescharacteristic, complemented
43C83⋊#95C2211yescharacteristic, complemented
44C83⋊#95C2211yescharacteristic, complemented
45C83⋊#95C2211yescharacteristic, complemented
46C83⋊#95C2211yescharacteristic, complemented
47C25×C83C2211yescharacteristic
48C23×C4×C83C2211yescharacteristic
49C23×C4×C83C2211yescharacteristic
50C2×C22⋊C4×C83—24no—
51C2×C22⋊C4×C83C2211yescharacteristic
52C2×C22⋊C4×C83C2211yescharacteristic
53C2×C22⋊C4×C83C2211yescharacteristic
54C2×C22⋊C4×C83C2211yescharacteristic
55C23×D83C2311yescharacteristic
56C2×Dic166—22no—
57C2×Dic166—22no—
58C2×Dic166—41no—
59C2×C22⋊D83—22no—
60C2×C22⋊D83—22no—
61C2×C22⋊D83—22no—
62C2×C22⋊D83—22no—
63C2×C22⋊D83—22no—
64C2×C22⋊D83—22no—
65C2×C22⋊D83—22no—
66C2×C22⋊D83—41no—
67C2×C22⋊D83—41no—
68C22×Dic83C2311yescharacteristic
69C22×Dic83C2311yescharacteristic
70C22×Dic83C2311yescharacteristic
71C22×Dic83C2311yescharacteristic
72C22×Dic83C2311yescharacteristic
73C22×Dic83C2311yescharacteristic
74C22×Dic83C2311yescharacteristic
75C4⋊Dic83—22no—
76Dic83⋊C4—22no—
77Dic83⋊C4—22no—
78C22⋊Dic83—22no—
79C22⋊Dic83—22no—
80C22⋊Dic83—22no—
81C22⋊Dic83—22no—
82C22⋊Dic83—22no—
83C22⋊Dic83—22no—
84C22⋊Dic83—41no—
85C22⋊Dic83—41no—
86C22⋊Dic83D414yes—
87(C2×D83)⋊C4—22no—
88(C2×D83)⋊C4—22no—
89(C2×D83)⋊C4—41no—
90(C2×D83)⋊C4—41no—
91C4×Dic83—22no—
92C4×Dic83—41no—
93C24×C83—22no—
94C24×C83—22no—
95C24×C83—22no—
96C24×C83—22no—
97C24×C83—22no—
98C24×C83—41no—
99C24×C83—41no—
100C24×C83C2311yescharacteristic
101C24×C83C2311yescharacteristic
102C24×C83C2311yescharacteristic
103C22×C4×C83—22no—
104C22×C4×C83—22no—
105C22×C4×C83—22no—
106C22×C4×C83—22no—
107C22×C4×C83—41no—
108C22×C4×C83—41no—
109C22×C4×C83C2311yescharacteristic
110C22×C4×C83C2311yescharacteristic
111C22×C4×C83C2311yescharacteristic
112C22×C4×C83C2311yescharacteristic
113C22⋊C4×C83—22no—
114C22⋊C4×C83—22no—
115C22⋊C4×C83—22no—
116C22⋊C4×C83D414yescomplemented
117C23×C83—21no—
118C23×C83—21no—
119C23×C83—21no—
120C23×C83—21no—
121C23×C83—28no—
122C23×C83—21no—
123C23×C83—21no—
124C23×C83—21no—
125C23×C83—21no—
126C23×C83—21no—
127C23×C83—21no—
128C23×C83—21no—
129C23×C83—21no—
130C23×C83—21no—
131C23×C83—21no—
132C23×C83—21no—
133C23×C83—21no—
134C23×C83—44no—
135C23×C83—44no—
136C23×C83—44no—
137C23×C83—44no—
138C23×C83—44no—
139C23×C83—44no—
140C23×C83C2×D412yes—
141C23×C83C2×D412yes—
142C23×C83#4112yes—
143C23×C83#4112yes—
144C23×C83#4112yes—
145C23×C83C2411yescharacteristic
146C22×D83—21no—
147C22×D83—21no—
148C22×D83—21no—
149C22×D83—21no—
150C22×D83—21no—
151C22×D83—21no—
152C22×D83—21no—
153C2×C4×C83—21no—
154C2×C4×C83—21no—
155C2×C4×C83—21no—
156C2×C4×C83—21no—
157C2×C4×C83—21no—
158C2×C4×C83—21no—
159C2×C4×C83—21no—
160C2×C4×C83—21no—
161C2×C4×C83—21no—
162C2×C4×C83—21no—
163C2×C4×C83—44no—
164C2×C4×C83—44no—
165C2×C4×C83C2×D412yes—
166C2×C4×C83C2×D412yes—
167C22⋊D83—44no—
168C22⋊D83—44no—
169C22⋊D83—44no—
170C2×Dic83—21no—
171C2×Dic83—21no—
172C2×Dic83—21no—
173C2×Dic83—21no—
174C2×Dic83—21no—
175C2×Dic83—21no—
176C2×Dic83—21no—
177C2×Dic83—21no—
178C2×Dic83—21no—
179C2×Dic83—21no—
180C2×Dic83—21no—
181C2×Dic83—21no—
182C2×Dic83—21no—
183C2×Dic83—21no—
184C2×Dic83—21no—
185C2×Dic83—21no—
186C2×Dic83—21no—
187C2×Dic83—21no—
188C2×Dic83—21no—
189C2×Dic83C2×D412yes—
190C2×Dic83C2×D412yes—
191Dic166—44no—
192C22×C83—22no—
193C22×C83—22no—
194C22×C83—22no—
195C22×C83—22no—
196C22×C83—22no—
197C22×C83—22no—
198C22×C83—22no—
199C22×C83—22no—
200C22×C83—22no—
201C22×C83—22no—
202C22×C83—22no—
203C22×C83—22no—
204C22×C83—416no—
205C22×C83—41no—
206C22×C83—41no—
207C22×C83—41no—
208C22×C83—41no—
209C22×C83—41no—
210C22×C83—41no—
211C22×C83—41no—
212C22×C83—41no—
213C22×C83#12414yescomplemented
214C22×C83C22×D411yescharacteristic
215C22×C83C22×D411yescharacteristic
216C22×C83C2×#4111yescharacteristic
217C22×C83C2×#4111yescharacteristic
218C22×C83C2×#4111yescharacteristic
219C22×C83H(5,𝔽2)11yescharacteristic
220C22×C83H(5,𝔽2)11yescharacteristic
221C2×D83—41no—
222C2×D83—41no—
223C2×D83—41no—
224C2×D83—41no—
225C2×D83—41no—
226C2×D83—41no—
227C2×D83—41no—
228C4×C83—22no—
229C4×C83—22no—
230C4×C83—41no—
231C4×C83—41no—
232Dic83—22no—
233Dic83—22no—
234Dic83—41no—
235Dic83—41no—
236Dic83—41no—
237Dic83—41no—
238Dic83—41no—
239C2×C83—24no—
240C2×C83—42no—
241C2×C83—42no—
242C2×C83#52511yescharacteristic
243C2×C83C2×#12411yescharacteristic
244C2×C83#53811yescharacteristic
245C2×C83D4211yescharacteristic
246C2×C83#54611yescharacteristic
247C2×C83#54611yescharacteristic
248C2×C83#55111yescharacteristic
249D83—81no—
250#2472—831nomaximal, Sylow
251C83#247211yescharacteristic, complemented, Sylow
252C2×#124—831no—
253C2×C22⋊Q8—831no—
254C2×#120—831no—
255C22×C22⋊C4D8311yescharacteristic, complemented
256#397—831no—
257#394—831no—
258#394—831no—
259#393—831no—
260#390—831no—
261#388—831no—
262#388—831no—
263#386—831no—
264#386—831no—
265#379—831no—
266C4×C22⋊C4—831no—
267C25C2×D8311yescharacteristic
268C22×Q8—831no—
269C22×D4—831no—
270C22×D4—831no—
271C22×D4—831no—
272C23×C4C2×D8311yescharacteristic
273C23×C4C2×D8311yescharacteristic
274#124—1664no—
275C22⋊Q8—1664no—
276#120—1664no—
277C2×C4⋊C4—831no—
278C2×C4⋊C4—831no—
279C2×C4⋊C4—831no—
280C2×C22⋊C4—24no—
281C2×C22⋊C4—831no—
282C2×C22⋊C4—831no—
283C2×C22⋊C4—831no—
284C2×C22⋊C4—831no—
285C2×C22⋊C4—831no—
286C2×C22⋊C4—831no—
287C2×C22⋊C4—831no—
288C2×C22⋊C4—831no—
289C2×C22⋊C4—831no—
290C2×C22⋊C4—831no—
291C2×C22⋊C4—831no—
292C2×C22⋊C4—831no—
293C2×C22⋊C4—831no—
294C2×C22⋊C4C2×D8311yescharacteristic
295C2×C22⋊C4C2×D8311yescharacteristic
296C2×C22⋊C4C2×D8311yescharacteristic
297C2×C22⋊C4C2×D8311yescharacteristic
298C2×C42—831no—
299C2×C42—831no—
300#95—831no—
301#95—831no—
302#95—831no—
303#95—831no—
304#95—831no—
305#95—831no—
306C24—22no—
307C24—22no—
308C24—22no—
309C24—22no—
310C24—22no—
311C24—41no—
312C24—41no—
313C24—831no—
314C24C22×D8311yescharacteristic
315C24C22×D8311yescharacteristic
316C24C22×D8311yescharacteristic
317C2×Q8—3321no—
318C2×Q8—1662no—
319C2×Q8—1662no—
320C2×D4—3321no—
321C2×D4—3321no—
322C2×D4—1662no—
323C2×D4—1662no—
324C2×D4—1662no—
325C2×D4—1662no—
326C2×D4—1662no—
327C2×D4—1662no—
328C2×D4—1662no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—831no—
336C22×C4—831no—
337C22×C4—831no—
338C22×C4—831no—
339C22×C4—831no—
340C22×C4—831no—
341C22×C4—831no—
342C22×C4C22×D8311yescharacteristic
343C22×C4C22×D8311yescharacteristic
344C22×C4C22×D8311yescharacteristic
345C22×C4C22×D8311yescharacteristic
346C4⋊C4—1662no—
347C4⋊C4—1662no—
348C4⋊C4—1662no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—3321no—
353C22⋊C4—3321no—
354C22⋊C4—3321no—
355C22⋊C4—3321no—
356C22⋊C4—834no—
357C22⋊C4—1662no—
358C22⋊C4—1662no—
359C22⋊C4—1662no—
360C22⋊C4—1662no—
361C22⋊C4—1662no—
362C22⋊C4—1662no—
363C22⋊C4—1662no—
364C22⋊C4—1662no—
365C22⋊C4C22⋊D8314yescomplemented
366C42—3321no—
367C42—1662no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—28no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—44no—
386C23—44no—
387C23—44no—
388C23—44no—
389C23—44no—
390C23—44no—
391C23—1661no—
392C23—1661no—
393C23—1661no—
394C23—1661no—
395C23—1661no—
396C23—1661no—
397C23—1661no—
398C23D4×D8312yes—
399C23C2×C22⋊D8312yes—
400C23#1305058912yes—
401C23#1305059012yes—
402C23#1305059012yes—
403C23C23×D8311yescharacteristic
404Q8—3324no—
405D4—3324no—
406D4—3324no—
407D4—3324no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—44no—
419C2×C4—44no—
420C2×C4—832no—
421C2×C4—832no—
422C2×C4—1661no—
423C2×C4—1661no—
424C2×C4—1661no—
425C2×C4—1661no—
426C2×C4—1661no—
427C2×C4—1661no—
428C2×C4—1661no—
429C2×C4—1661no—
430C2×C4—1661no—
431C2×C4—1661no—
432C2×C4—1661no—
433C2×C4—1661no—
434C2×C4—1661no—
435C2×C4—1661no—
436C2×C4—1661no—
437C2×C4—1661no—
438C2×C4—1661no—
439C2×C4—1661no—
440C2×C4—1661no—
441C2×C4C2×C22⋊D8312yes—
442C2×C4C2×C22⋊D8312yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—416no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—3321no—
465C22—3321no—
466C22—3321no—
467C22—3321no—
468C22—3321no—
469C22—3321no—
470C22—3321no—
471C22#1458177814yescomplemented
472C22C2×D4×D8311yescharacteristic
473C22C22×C22⋊D8311yescharacteristic
474C22C2×#1305058911yescharacteristic
475C22C2×#1305059011yescharacteristic
476C22C2×#1305059011yescharacteristic
477C22#1458183711yescharacteristic
478C22#1458183711yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—3321no—
484C4—3321no—
485C4—3321no—
486C4—3321no—
487C4—3321no—
488C4—1662no—
489C4—1662no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—6641no—
494C2#1912821211yescharacteristic
495C2C2×#1458177811yescharacteristic
496C2#1912828911yescharacteristic
497C2D4×C22⋊D8311yescharacteristic
498C2#1912834111yescharacteristic
499C2#1912834511yescharacteristic
500C2#1912837711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
FittingC22×C22⋊C4×C83C2
prime radicalC2×#14581761C2
hypercenterC22×C22⋊C4D83
hypocenterC83#2472
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14581778C2semidirect
2. C2×#14581771C2semidirect
4. #19127629C2semidirect
5. #19127617C2semidirect
6. #19127616C2semidirect
7. #19127613C2semidirect
8. #19127601C2semidirect
9. #19127594C2semidirect
10. #19127589C2semidirect
11. #19127580C2semidirect
12. #19127580C2semidirect
13. #19127557C2semidirect
14. C4×C22⋊Dic83C2semidirect
15. C22×C22⋊C4×C83C2semidirect
16. C22×Dic166C22semidirect
23. C2×C4⋊Dic83C22semidirect
24. C2×Dic83⋊C4C22semidirect
25. C2×Dic83⋊C4C22semidirect
35. C2×(C2×D83)⋊C4C22semidirect
36. C2×(C2×D83)⋊C4C22semidirect
37. C2×(C2×D83)⋊C4C22semidirect
38. C2×(C2×D83)⋊C4C22semidirect
39. C2×C4×Dic83C22semidirect
40. C2×C4×Dic83C22semidirect
41. C83⋊#95C22semidirect
42. C83⋊#95C22semidirect
43. C83⋊#95C22semidirect
44. C83⋊#95C22semidirect
45. C83⋊#95C22semidirect
46. C83⋊#95C22semidirect
116. C22⋊C4×C83D4semidirect
213. C22×C83#124semidirect
251. C83#2472semidirect
255. C22×C22⋊C4D83semidirect
365. C22⋊C4C22⋊D83semidirect
471. C22#14581778semidirect

Maximal subgroups

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

subgroupindex
C2×#145817782
C2×#145817712
C2×#145817612
#191276292
#191276172
#191276162
#191276132
#191276012
#191275942
#191275892
#191275802
#191275572
C4×C22⋊Dic832
C22×C22⋊C4×C832
#247283