Finite Group Databasebeta

← #24913843

Subgroups — #24913843

Order 10624.

688 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
1C2×#14581778C211yesmaximal, characteristic, complemented
2C2×#14581761C211yesmaximal, characteristic
3#19127629C211yesmaximal, characteristic, complemented
4#19127626C211yesmaximal, characteristic, complemented
5#19127617C211yesmaximal, characteristic, complemented
6#19127616C211yesmaximal, characteristic, complemented
7#19127613C211yesmaximal, characteristic, complemented
8#19127613C211yesmaximal, characteristic, complemented
9#19127595C211yesmaximal, characteristic, complemented
10#19127594C211yesmaximal, characteristic, complemented
11#19127577C211yesmaximal, characteristic, complemented
12#19127577C211yesmaximal, characteristic, complemented
13#19127577C211yesmaximal, characteristic, complemented
14#19127557C211yesmaximal, characteristic, complemented
15#379×C83C211yesmaximal, characteristic, complemented
16C22×Dic166C2211yescharacteristic, complemented
17C22×C22⋊D83C2211yescharacteristic
18C22×C22⋊D83C2211yescharacteristic
19C22×C22⋊D83C2211yescharacteristic
20C22×C4×D83C2211yescharacteristic, complemented
21#14581778—24no—
22#14581761—24no—
23C2×C4⋊Dic83C2211yescharacteristic, complemented
24C2×Dic83⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic83C2211yescharacteristic
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×(C2×D83)⋊C4C2211yescharacteristic, complemented
35C2×(C2×D83)⋊C4C2211yescharacteristic, complemented
36C2×(C2×D83)⋊C4C2211yescharacteristic, complemented
37C2×C4×Dic83C2211yescharacteristic, complemented
38C83⋊#95C2211yescharacteristic, complemented
39C83⋊#95C2211yescharacteristic, complemented
40C83⋊#95C2211yescharacteristic, complemented
41C83⋊#95C2211yescharacteristic, complemented
42C83⋊#95C2211yescharacteristic, complemented
43C83⋊#95C2211yescharacteristic, complemented
44C83⋊#95C2211yescharacteristic, complemented
45C83⋊#95C2211yescharacteristic, complemented
46C25×C83C2211yescharacteristic
47C2×C22⋊C4×C83C2211yescharacteristic
48C2×C22⋊C4×C83C2211yescharacteristic
49C2×C22⋊C4×C83C2211yescharacteristic
50C2×C22⋊C4×C83C2211yescharacteristic
51C2×C22⋊C4×C83C2211yescharacteristic
52C2×C22⋊C4×C83C2211yescharacteristic
53C23×D83C2311yescharacteristic
54C2×Dic166—22no—
55C2×Dic166—41no—
56C2×Dic166—41no—
57C2×C22⋊D83—22no—
58C2×C22⋊D83—22no—
59C2×C22⋊D83—22no—
60C2×C22⋊D83—22no—
61C2×C22⋊D83—41no—
62C2×C22⋊D83—41no—
63C2×C22⋊D83—41no—
64C2×C22⋊D83—41no—
65C2×C22⋊D83D414yes—
66C22×Dic83C2311yescharacteristic
67C22×Dic83C2311yescharacteristic
68C22×Dic83C2311yescharacteristic
69C22×Dic83C2311yescharacteristic
70C22×Dic83C2311yescharacteristic
71C22×Dic83C2311yescharacteristic
72C22×Dic83C2311yescharacteristic
73C2×C4×D83—41no—
74C2×C4×D83—41no—
75C2×C4×D83—41no—
76C4⋊Dic83—41no—
77Dic83⋊C4—41no—
78C22⋊Dic83—22no—
79C22⋊Dic83—22no—
80C22⋊Dic83—22no—
81C22⋊Dic83—22no—
82C22⋊Dic83—22no—
83C22⋊Dic83—41no—
84C22⋊Dic83—41no—
85C22⋊Dic83—41no—
86C22⋊Dic83—41no—
87(C2×D83)⋊C4—22no—
88(C2×D83)⋊C4—22no—
89(C2×D83)⋊C4—41no—
90C4×Dic83—22no—
91C24×C83—22no—
92C24×C83—22no—
93C24×C83—22no—
94C24×C83—41no—
95C24×C83—41no—
96C24×C83—41no—
97C24×C83—41no—
98C24×C83C2311yescharacteristic
99C24×C83C2311yescharacteristic
100C24×C83C2311yescharacteristic
101C22×C4×C83C2311yescharacteristic
102C22×C4×C83C2311yescharacteristic
103C22×C4×C83C2311yescharacteristic
104C22×C4×C83C2311yescharacteristic
105C22⋊C4×C83—22no—
106C22⋊C4×C83—22no—
107C22⋊C4×C83—41no—
108C22⋊C4×C83—41no—
109C22⋊C4×C83—41no—
110C22⋊C4×C83—41no—
111C23×C83—21no—
112C23×C83—21no—
113C23×C83—21no—
114C23×C83—21no—
115C23×C83—21no—
116C23×C83—21no—
117C23×C83—21no—
118C23×C83—21no—
119C23×C83—21no—
120C23×C83—21no—
121C23×C83—21no—
122C23×C83—21no—
123C23×C83—21no—
124C23×C83—21no—
125C23×C83—21no—
126C23×C83—21no—
127C23×C83—21no—
128C23×C83—21no—
129C23×C83—44no—
130C23×C83—44no—
131C23×C83—44no—
132C23×C83—44no—
133C23×C83—44no—
134C23×C83—44no—
135C23×C83—44no—
136C23×C83C2×D412yes—
137C23×C83#4112yes—
138C23×C83#4112yes—
139C23×C83C2411yescharacteristic
140C22×D83—21no—
141C22×D83—21no—
142C22×D83—21no—
143C22×D83—21no—
144C22×D83—21no—
145C22×D83—21no—
146C22×D83C2×D412yes—
147C2×C4×C83—21no—
148C2×C4×C83—21no—
149C2×C4×C83—21no—
150C2×C4×C83—21no—
151C2×C4×C83—21no—
152C2×C4×C83—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—
159C22⋊D83—44no—
160C22⋊D83—44no—
161C22⋊D83—44no—
162C2×Dic83—21no—
163C2×Dic83—21no—
164C2×Dic83—21no—
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×Dic83C2×D412yes—
183C4×D83—44no—
184Dic166—44no—
185C22×C83—22no—
186C22×C83—22no—
187C22×C83—22no—
188C22×C83—22no—
189C22×C83—22no—
190C22×C83—22no—
191C22×C83—22no—
192C22×C83—22no—
193C22×C83—22no—
194C22×C83—416no—
195C22×C83—41no—
196C22×C83—41no—
197C22×C83—41no—
198C22×C83—41no—
199C22×C83—41no—
200C22×C83—41no—
201C22×C83—41no—
202C22×C83—41no—
203C22×C83—41no—
204C22×C83—41no—
205C22×C83—41no—
206C22×C83—41no—
207C22×C83C22×D411yescharacteristic
208C22×C83C2×#4111yescharacteristic
209C22×C83C2×#4111yescharacteristic
210C22×C83H(5,𝔽2)11yescharacteristic
211C22×C83H(5,𝔽2)11yescharacteristic
212C22×C83H(5,𝔽2)11yescharacteristic
213C22×C83H(5,𝔽2)11yescharacteristic
214C2×D83—22no—
215C2×D83—22no—
216C2×D83—22no—
217C2×D83—41no—
218C2×D83—41no—
219C2×D83—41no—
220C2×D83—41no—
221C4×C83—41no—
222C4×C83—41no—
223C4×C83—41no—
224C4×C83—41no—
225Dic83—22no—
226Dic83—41no—
227Dic83—41no—
228Dic83—41no—
229Dic83—41no—
230Dic83—41no—
231Dic83—41no—
232C2×C83—42no—
233C2×C83—42no—
234C2×C83—42no—
235C2×C83#53411yescharacteristic
236C2×C83#53811yescharacteristic
237C2×C83#53811yescharacteristic
238C2×C83#54611yescharacteristic
239C2×C83#54611yescharacteristic
240C2×C83#55111yescharacteristic
241C2×C83H(3,𝔽4)11yescharacteristic
242D83—42no—
243#2684—831nomaximal, Sylow
244C83#268411yescharacteristic, complemented, Sylow
245C2×#124—831no—
246C2×#120—831no—
247#397—831no—
248#397—831no—
249#394—831no—
250#394—831no—
251#393—831no—
252#393—831no—
253#388—831no—
254#388—831no—
255#386—831no—
256#386—831no—
257#386—831no—
258#379—831no—
259#379D8311yescharacteristic, complemented
260C25C2×D8311yescharacteristic
261C22×Q8—831no—
262C22×D4—831no—
263C22×D4—831no—
264C22×D4—831no—
265C23×C4—831no—
266#124—1664no—
267#120—1664no—
268C2×C4⋊C4—831no—
269C2×C4⋊C4—831no—
270C2×C22⋊C4—831no—
271C2×C22⋊C4—831no—
272C2×C22⋊C4—831no—
273C2×C22⋊C4—831no—
274C2×C22⋊C4—831no—
275C2×C22⋊C4—831no—
276C2×C22⋊C4—831no—
277C2×C22⋊C4—831no—
278C2×C22⋊C4—831no—
279C2×C22⋊C4—831no—
280C2×C22⋊C4—831no—
281C2×C22⋊C4—831no—
282C2×C22⋊C4C2×D8311yescharacteristic
283C2×C22⋊C4C2×D8311yescharacteristic
284C2×C22⋊C4C2×D8311yescharacteristic
285C2×C22⋊C4C2×D8311yescharacteristic
286C2×C22⋊C4C2×D8311yescharacteristic
287C2×C22⋊C4C2×D8311yescharacteristic
288C2×C42—831no—
289#95—831no—
290#95—831no—
291#95—831no—
292#95—831no—
293#95—831no—
294#95—831no—
295#95—831no—
296#95—831no—
297C24—22no—
298C24—22no—
299C24—22no—
300C24—41no—
301C24—41no—
302C24—41no—
303C24—41no—
304C24—831no—
305C24C22×D8311yescharacteristic
306C24C22×D8311yescharacteristic
307C24C22×D8311yescharacteristic
308C2×Q8—3321no—
309C2×Q8—3321no—
310C2×Q8—1662no—
311C2×D4—3321no—
312C2×D4—3321no—
313C2×D4—3321no—
314C2×D4—3321no—
315C2×D4—834no—
316C2×D4—1662no—
317C2×D4—1662no—
318C2×D4—1662no—
319C2×D4—1662no—
320C22×C4—3321no—
321C22×C4—3321no—
322C22×C4—3321no—
323C22×C4—831no—
324C22×C4—831no—
325C22×C4—831no—
326C22×C4—831no—
327C22×C4—831no—
328C22×C4—831no—
329C22×C4—831no—
330C22×C4C22×D8311yescharacteristic
331C22×C4C22×D8311yescharacteristic
332C22×C4C22×D8311yescharacteristic
333C22×C4C22×D8311yescharacteristic
334C4⋊C4—3321no—
335C4⋊C4—3321no—
336C22⋊C4—22no—
337C22⋊C4—22no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—3321no—
343C22⋊C4—3321no—
344C22⋊C4—3321no—
345C22⋊C4—3321no—
346C22⋊C4—3321no—
347C22⋊C4—1662no—
348C22⋊C4—1662no—
349C22⋊C4—1662no—
350C22⋊C4—1662no—
351C22⋊C4—1662no—
352C22⋊C4—1662no—
353C22⋊C4—1662no—
354C42—1662no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—44no—
374C23—44no—
375C23—44no—
376C23—44no—
377C23—44no—
378C23—44no—
379C23—44no—
380C23—832no—
381C23—1661no—
382C23—1661no—
383C23—1661no—
384C23—1661no—
385C23—1661no—
386C23—1661no—
387C23D4×D8312yes—
388C23#1305058912yes—
389C23#1305059012yes—
390C23C23×D8311yescharacteristic
391Q8—3324no—
392D4—3324no—
393D4—3324no—
394D4—3324no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—3324no—
408C2×C4—832no—
409C2×C4—1661no—
410C2×C4—1661no—
411C2×C4—1661no—
412C2×C4—1661no—
413C2×C4—1661no—
414C2×C4—1661no—
415C2×C4—1661no—
416C2×C4—1661no—
417C2×C4—1661no—
418C2×C4—1661no—
419C2×C4—1661no—
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—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—416no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—3321no—
452C22—3321no—
453C22—3321no—
454C22—3321no—
455C22—1662no—
456C22—1662no—
457C22—1662no—
458C22C2×D4×D8311yescharacteristic
459C22C2×#1305058911yescharacteristic
460C22C2×#1305059011yescharacteristic
461C22#1458183711yescharacteristic
462C22#1458183711yescharacteristic
463C22#1458183711yescharacteristic
464C22#1458183711yescharacteristic
465C4—41no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—3321no—
470C4—3321no—
471C4—3321no—
472C4—3321no—
473C4—3321no—
474C4—3321no—
475C4—1662no—
476C2—42no—
477C2—42no—
478C2—42no—
479C2—3322no—
480C2#1912826111yescharacteristic
481C2#1912828611yescharacteristic
482C2#1912828911yescharacteristic
483C2#1912833811yescharacteristic
484C2#1912834111yescharacteristic
485C2#1912837711yescharacteristic
486C2#1912844411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#379×C83C2
prime radicalC2×#14581761C2
hypercenter#379D83
hypocenterC83#2684
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#14581778C2semidirect
3. #19127629C2semidirect
4. #19127626C2semidirect
5. #19127617C2semidirect
6. #19127616C2semidirect
7. #19127613C2semidirect
8. #19127613C2semidirect
9. #19127595C2semidirect
10. #19127594C2semidirect
11. #19127577C2semidirect
12. #19127577C2semidirect
13. #19127577C2semidirect
14. #19127557C2semidirect
15. #379×C83C2semidirect
16. C22×Dic166C22semidirect
20. C22×C4×D83C22semidirect
23. C2×C4⋊Dic83C22semidirect
24. C2×Dic83⋊C4C22semidirect
34. C2×(C2×D83)⋊C4C22semidirect
35. C2×(C2×D83)⋊C4C22semidirect
36. C2×(C2×D83)⋊C4C22semidirect
37. C2×C4×Dic83C22semidirect
38. C83⋊#95C22semidirect
39. C83⋊#95C22semidirect
40. C83⋊#95C22semidirect
41. C83⋊#95C22semidirect
42. C83⋊#95C22semidirect
43. C83⋊#95C22semidirect
44. C83⋊#95C22semidirect
45. C83⋊#95C22semidirect
244. C83#2684semidirect
259. #379D83semidirect

Maximal subgroups

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

subgroupindex
C2×#145817782
C2×#145817612
#191276292
#191276262
#191276172
#191276162
#191276132
#191275952
#191275942
#191275772
#191275572
#379×C832
#268483