Finite Group Databasebeta

← #24910921

Subgroups — #24910921

Order 10624.

800 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×#14581773C211yesmaximal, characteristic, complemented
2C2×D4×Dic83C211yesmaximal, characteristic, complemented
3C22×C22⋊Dic83C211yesmaximal, characteristic, complemented
4#19127637C211yesmaximal, characteristic, complemented
5#19127626C211yesmaximal, characteristic, complemented
6#19127615C211yesmaximal, characteristic, complemented
7#19127615C211yesmaximal, characteristic, complemented
8#19127589C211yesmaximal, characteristic, complemented
9#19127589C211yesmaximal, characteristic, complemented
10#19127581C211yesmaximal, characteristic, complemented
11#19127581C211yesmaximal, characteristic, complemented
12#19127573C211yesmaximal, characteristic, complemented
13#19127559C211yesmaximal, characteristic, complemented
14#19127557C211yesmaximal, characteristic, complemented
15C2×#120×C83C211yesmaximal, characteristic
16C23×Dic83C2211yescharacteristic
17C23×Dic83C2211yescharacteristic
18C23×Dic83C2211yescharacteristic, complemented
19#14581773—24no—
20D4×Dic83—24no—
21C2×C4⋊Dic83C2211yescharacteristic, complemented
22C2×Dic83⋊C4C2211yescharacteristic, complemented
23C2×Dic83⋊C4C2211yescharacteristic, complemented
24C2×Dic83⋊C4C2211yescharacteristic, complemented
25C2×Dic83⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic83—24no—
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×C22⋊Dic83C2211yescharacteristic
36C2×C22⋊Dic83C2211yescharacteristic
37C2×C22⋊Dic83C2211yescharacteristic, complemented
38C2×C22⋊Dic83C2211yescharacteristic, complemented
39C2×C22⋊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
48C22×D4×C83C2211yescharacteristic
49C22×D4×C83C2211yescharacteristic
50C22×D4×C83C2211yescharacteristic
51#120×C83—24no—
52C2×C22⋊C4×C83C2211yescharacteristic
53C2×C22⋊C4×C83C2211yescharacteristic
54C2×C22⋊C4×C83C2211yescharacteristic
55C22×Dic83—22no—
56C22×Dic83—22no—
57C22×Dic83—22no—
58C22×Dic83—22no—
59C22×Dic83—22no—
60C22×Dic83—22no—
61C22×Dic83—41no—
62C22×Dic83—41no—
63C22×Dic83—41no—
64C22×Dic83C2311yescharacteristic
65C22×Dic83C2311yescharacteristic
66C22×Dic83C2311yescharacteristic
67C22×Dic83C2311yescharacteristic
68C22×Dic83C2311yescharacteristic
69C22×Dic83C2311yescharacteristic
70C22×Dic83C2311yescharacteristic
71C22×Dic83C2311yescharacteristic
72C4⋊Dic83—22no—
73Dic83⋊C4—22no—
74Dic83⋊C4—22no—
75Dic83⋊C4—41no—
76Dic83⋊C4—41no—
77C22⋊Dic83—22no—
78C22⋊Dic83—22no—
79C22⋊Dic83—22no—
80C22⋊Dic83—22no—
81C22⋊Dic83—22no—
82C22⋊Dic83—22no—
83C22⋊Dic83—22no—
84C22⋊Dic83—22no—
85C22⋊Dic83—22no—
86C22⋊Dic83—41no—
87C22⋊Dic83—41no—
88C22⋊Dic83—41no—
89C22⋊Dic83D414yescomplemented
90C4×Dic83—22no—
91C24×C83—22no—
92C24×C83—22no—
93C24×C83—22no—
94C24×C83—22no—
95C24×C83—22no—
96C24×C83—41no—
97C24×C83—41no—
98C24×C83C2311yescharacteristic
99C24×C83C2311yescharacteristic
100C24×C83C2311yescharacteristic
101C24×C83C2311yescharacteristic
102C2×D4×C83—22no—
103C2×D4×C83—22no—
104C2×D4×C83—22no—
105C2×D4×C83—22no—
106C2×D4×C83—22no—
107C2×D4×C83—22no—
108C2×D4×C83—41no—
109C2×D4×C83—41no—
110C2×D4×C83D414yes—
111C22×C4×C83C2311yescharacteristic
112C22×C4×C83C2311yescharacteristic
113C22×C4×C83C2311yescharacteristic
114C22⋊C4×C83—22no—
115C22⋊C4×C83—22no—
116C22⋊C4×C83—22no—
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—21no—
135C23×C83—21no—
136C23×C83—21no—
137C23×C83—21no—
138C23×C83—21no—
139C23×C83—21no—
140C23×C83—44no—
141C23×C83—44no—
142C23×C83—44no—
143C23×C83—44no—
144C23×C83—44no—
145C23×C83—44no—
146C23×C83C2×D412yes—
147C23×C83C2×D412yes—
148C23×C83C2×D412yes—
149C23×C83#4112yes—
150C23×C83#4112yes—
151C23×C83#4112yes—
152C23×C83C2411yescharacteristic
153D4×C83—28no—
154D4×C83—44no—
155D4×C83—44no—
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—21no—
164C2×C4×C83C2×D412yes—
165C2×Dic83—21no—
166C2×Dic83—21no—
167C2×Dic83—21no—
168C2×Dic83—21no—
169C2×Dic83—21no—
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—44no—
188C2×Dic83—44no—
189C2×Dic83—44no—
190C2×Dic83C2×D412yes—
191C2×Dic83C2×D412yes—
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—22no—
205C22×C83—22no—
206C22×C83—22no—
207C22×C83—416no—
208C22×C83—41no—
209C22×C83—41no—
210C22×C83—41no—
211C22×C83—41no—
212C22×C83—41no—
213C22×C83—41no—
214C22×C83—41no—
215C22×C83—41no—
216C22×C83—41no—
217C22×C83—41no—
218C22×C83—41no—
219C22×C83—41no—
220C22×C83#12314yescomplemented
221C22×C83C22×D411yescharacteristic
222C22×C83C22×D411yescharacteristic
223C22×C83C2×#4111yescharacteristic
224C22×C83C2×#4111yescharacteristic
225C22×C83C2×#4111yescharacteristic
226C22×C83H(5,𝔽2)11yescharacteristic
227C22×C83H(5,𝔽2)11yescharacteristic
228C4×C83—22no—
229C4×C83—41no—
230C4×C83—41no—
231Dic83—22no—
232Dic83—22no—
233Dic83—41no—
234Dic83—41no—
235Dic83—41no—
236Dic83—41no—
237Dic83—41no—
238Dic83—41no—
239C2×C83—24no—
240C2×C83—42no—
241C2×C83—42no—
242C2×C83—42no—
243C2×C83C2×#12311yescharacteristic
244C2×C83#52511yescharacteristic
245C2×C83#53811yescharacteristic
246C2×C83D4211yescharacteristic
247C2×C83#54611yescharacteristic
248C2×C83#54611yescharacteristic
249C2×C83#55111yescharacteristic
250#2418—831nomaximal, Sylow
251C83#241811yescharacteristic, complemented, Sylow
252C2×#123—831no—
253C2×#120D8311yescharacteristic
254C2×C4×D4—831no—
255C22×C22⋊C4—831no—
256#399—831no—
257#397—831no—
258#394—831no—
259#394—831no—
260#388—831no—
261#388—831no—
262#386—831no—
263#386—831no—
264#385—831no—
265#380—831no—
266#379—831no—
267C25C2×D8311yescharacteristic
268C22×D4C2×D8311yescharacteristic
269C22×D4C2×D8311yescharacteristic
270C22×D4C2×D8311yescharacteristic
271C23×C4—831no—
272C23×C4—831no—
273C23×C4—831no—
274#123—1664no—
275#120—24no—
276C4×D4—1664no—
277C2×C4⋊C4—831no—
278C2×C4⋊C4—831no—
279C2×C4⋊C4—831no—
280C2×C4⋊C4—831no—
281C2×C4⋊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⋊C4—831no—
295C2×C22⋊C4—1664no—
296C2×C22⋊C4C2×D8311yescharacteristic
297C2×C22⋊C4C2×D8311yescharacteristic
298C2×C22⋊C4C2×D8311yescharacteristic
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—
313C24C22×D8311yescharacteristic
314C24C22×D8311yescharacteristic
315C24C22×D8311yescharacteristic
316C24C22×D8311yescharacteristic
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4C22⋊D8314yes—
326C22×C4—3321no—
327C22×C4—3321no—
328C22×C4—3321no—
329C22×C4—831no—
330C22×C4—831no—
331C22×C4—831no—
332C22×C4—831no—
333C22×C4—831no—
334C22×C4—831no—
335C22×C4—831no—
336C22×C4—831no—
337C22×C4—1662no—
338C22×C4—1662no—
339C22×C4—1662no—
340C22×C4—1662no—
341C22×C4—1662no—
342C22×C4—1662no—
343C22×C4C22×D8311yescharacteristic
344C22×C4C22×D8311yescharacteristic
345C22×C4C22×D8311yescharacteristic
346C4⋊C4—3321no—
347C4⋊C4—3321no—
348C4⋊C4—1662no—
349C4⋊C4—1662no—
350C4⋊C4—1662no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—3321no—
355C22⋊C4—3321no—
356C22⋊C4—3321no—
357C22⋊C4—834no—
358C22⋊C4—1662no—
359C22⋊C4—1662no—
360C22⋊C4—1662no—
361C22⋊C4—1662no—
362C22⋊C4—1662no—
363C22⋊C4—1662no—
364C22⋊C4—1662no—
365C22⋊C4—1662no—
366C22⋊C4—1662no—
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—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—44no—
392C23—44no—
393C23—44no—
394C23—44no—
395C23—44no—
396C23—44no—
397C23D4×D8312yes—
398C23C2×C22⋊D8312yes—
399C23C2×C22⋊D8312yes—
400C23#1305058912yes—
401C23#1305058912yes—
402C23#1305058912yes—
403C23C23×D8311yescharacteristic
404D4—28no—
405D4—44no—
406D4—44no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—3324no—
416C2×C4—3324no—
417C2×C4—3324no—
418C2×C4—832no—
419C2×C4—832no—
420C2×C4—1661no—
421C2×C4—1661no—
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×C4—1661no—
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—22no—
456C22—22no—
457C22—22no—
458C22—416no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22#1458177314yescomplemented
472C22C2×D4×D8311yescharacteristic
473C22C22×C22⋊D8311yescharacteristic
474C22C2×#1305058911yescharacteristic
475C22C2×#1305058911yescharacteristic
476C22C2×#1305058911yescharacteristic
477C22#1458183711yescharacteristic
478C22#1458183711yescharacteristic
479C4—22no—
480C4—41no—
481C4—41no—
482C4—3321no—
483C4—3321no—
484C4—3321no—
485C4—3321no—
486C4—3321no—
487C4—3321no—
488C4—1662no—
489C4—1662no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—42no—
494C2C2×#1458177311yescharacteristic
495C2#1912820711yescharacteristic
496C2#1912828611yescharacteristic
497C2D4×C22⋊D8311yescharacteristic
498C2#1912833811yescharacteristic
499C2#1912834511yescharacteristic
500C2#1912838211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting, prime radicalC2×#120×C83C2
hypercenterC2×#120D83
hypocenterC83#2418
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#14581773C2semidirect
2. C2×D4×Dic83C2semidirect
3. C22×C22⋊Dic83C2semidirect
4. #19127637C2semidirect
5. #19127626C2semidirect
6. #19127615C2semidirect
7. #19127615C2semidirect
8. #19127589C2semidirect
9. #19127589C2semidirect
10. #19127581C2semidirect
11. #19127581C2semidirect
12. #19127573C2semidirect
13. #19127559C2semidirect
14. #19127557C2semidirect
18. C23×Dic83C22semidirect
21. C2×C4⋊Dic83C22semidirect
22. C2×Dic83⋊C4C22semidirect
23. C2×Dic83⋊C4C22semidirect
24. C2×Dic83⋊C4C22semidirect
25. C2×Dic83⋊C4C22semidirect
37. C2×C22⋊Dic83C22semidirect
38. C2×C22⋊Dic83C22semidirect
39. C2×C22⋊Dic83C22semidirect
40. C2×C4×Dic83C22semidirect
41. C83⋊#95C22semidirect
42. C83⋊#95C22semidirect
43. C83⋊#95C22semidirect
44. C83⋊#95C22semidirect
45. C83⋊#95C22semidirect
46. C83⋊#95C22semidirect
89. C22⋊Dic83D4semidirect
220. C22×C83#123semidirect
251. C83#2418semidirect
471. C22#14581773semidirect

Maximal subgroups

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

subgroupindex
C2×#145817732
C2×D4×Dic832
C22×C22⋊Dic832
#191276372
#191276262
#191276152
#191275892
#191275812
#191275732
#191275592
#191275572
C2×#120×C832
#241883