Finite Group Databasebeta

← #24911708

Subgroups — #24911708

Order 10624.

664 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581785C211yesmaximal, characteristic, complemented
2C22×C22⋊Dic83C211yesmaximal, characteristic
3#19127629C211yesmaximal, characteristic, complemented
4#19127629C211yesmaximal, characteristic, complemented
5#19127626C211yesmaximal, characteristic, complemented
6#19127624C211yesmaximal, characteristic, complemented
7#19127595C211yesmaximal, characteristic, complemented
8#19127594C211yesmaximal, characteristic, complemented
9#19127589C211yesmaximal, characteristic, complemented
10#19127576C211yesmaximal, characteristic, complemented
11#19127573C211yesmaximal, characteristic, complemented
12#19127559C211yesmaximal, characteristic, complemented
13#19127557C211yesmaximal, characteristic
14C22⋊C4×Dic83C211yesmaximal, characteristic, complemented
15#379×C83C211yesmaximal, characteristic
16C23×Dic83C2211yescharacteristic
17C23×Dic83C2211yescharacteristic
18#14581785—24no—
19C2×C4⋊Dic83C2211yescharacteristic, complemented
20C2×C4⋊Dic83C2211yescharacteristic, complemented
21C2×Dic83⋊C4C2211yescharacteristic, complemented
22C2×Dic83⋊C4C2211yescharacteristic, complemented
23C2×Dic83⋊C4C2211yescharacteristic, complemented
24C2×Dic83⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic83—24no—
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×C22⋊Dic83C2211yescharacteristic
36C2×C4×Dic83C2211yescharacteristic, 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
53C22×Dic83—22no—
54C22×Dic83—22no—
55C22×Dic83—22no—
56C22×Dic83—22no—
57C22×Dic83—41no—
58C22×Dic83—41no—
59C22×Dic83C2311yescharacteristic
60C22×Dic83C2311yescharacteristic
61C22×Dic83C2311yescharacteristic
62C22×Dic83C2311yescharacteristic
63C22×Dic83C2311yescharacteristic
64C22×Dic83C2311yescharacteristic
65C22×Dic83C2311yescharacteristic
66C22×Dic83C2311yescharacteristic
67C4⋊Dic83—22no—
68C4⋊Dic83—41no—
69Dic83⋊C4—22no—
70Dic83⋊C4—22no—
71Dic83⋊C4—41no—
72Dic83⋊C4—41no—
73C22⋊Dic83—22no—
74C22⋊Dic83—22no—
75C22⋊Dic83—22no—
76C22⋊Dic83—22no—
77C22⋊Dic83—22no—
78C22⋊Dic83—22no—
79C22⋊Dic83—22no—
80C22⋊Dic83—41no—
81C22⋊Dic83—41no—
82C22⋊Dic83D414yes—
83C4×Dic83—22no—
84C4×Dic83—41no—
85C24×C83—22no—
86C24×C83—22no—
87C24×C83—22no—
88C24×C83—22no—
89C24×C83—22no—
90C24×C83—41no—
91C24×C83—41no—
92C24×C83C2311yescharacteristic
93C24×C83C2311yescharacteristic
94C24×C83C2311yescharacteristic
95C22×C4×C83C2311yescharacteristic
96C22×C4×C83C2311yescharacteristic
97C22×C4×C83C2311yescharacteristic
98C22×C4×C83C2311yescharacteristic
99C22⋊C4×C83—22no—
100C22⋊C4×C83—22no—
101C22⋊C4×C83—22no—
102C22⋊C4×C83—22no—
103C22⋊C4×C83—41no—
104C22⋊C4×C83—41no—
105C23×C83—21no—
106C23×C83—21no—
107C23×C83—21no—
108C23×C83—21no—
109C23×C83—28no—
110C23×C83—21no—
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—44no—
123C23×C83—44no—
124C23×C83—44no—
125C23×C83—44no—
126C23×C83—44no—
127C23×C83—44no—
128C23×C83C2×D412yes—
129C23×C83#4112yes—
130C23×C83#4112yes—
131C23×C83#4112yes—
132C23×C83#4112yes—
133C23×C83C2411yescharacteristic
134C2×C4×C83—21no—
135C2×C4×C83—21no—
136C2×C4×C83—21no—
137C2×C4×C83—21no—
138C2×C4×C83—21no—
139C2×C4×C83—21no—
140C2×C4×C83—21no—
141C2×C4×C83—21no—
142C2×C4×C83—21no—
143C2×C4×C83—21no—
144C2×C4×C83—21no—
145C2×C4×C83—21no—
146C2×Dic83—21no—
147C2×Dic83—21no—
148C2×Dic83—21no—
149C2×Dic83—21no—
150C2×Dic83—21no—
151C2×Dic83—21no—
152C2×Dic83—21no—
153C2×Dic83—21no—
154C2×Dic83—21no—
155C2×Dic83—21no—
156C2×Dic83—21no—
157C2×Dic83—21no—
158C2×Dic83—21no—
159C2×Dic83—21no—
160C2×Dic83—21no—
161C2×Dic83—21no—
162C2×Dic83—21no—
163C2×Dic83—21no—
164C2×Dic83—21no—
165C2×Dic83—21no—
166C2×Dic83—21no—
167C2×Dic83—21no—
168C2×Dic83—44no—
169C2×Dic83—44no—
170C2×Dic83C2×D412yes—
171C2×Dic83C2×D412yes—
172C22×C83—22no—
173C22×C83—22no—
174C22×C83—22no—
175C22×C83—22no—
176C22×C83—22no—
177C22×C83—22no—
178C22×C83—22no—
179C22×C83—22no—
180C22×C83—22no—
181C22×C83—22no—
182C22×C83—22no—
183C22×C83—22no—
184C22×C83—416no—
185C22×C83—41no—
186C22×C83—41no—
187C22×C83—41no—
188C22×C83—41no—
189C22×C83—41no—
190C22×C83—41no—
191C22×C83—41no—
192C22×C83—41no—
193C22×C83#12614yescomplemented
194C22×C83C22×D411yescharacteristic
195C22×C83C2×#4111yescharacteristic
196C22×C83C2×#4111yescharacteristic
197C22×C83C2×#4111yescharacteristic
198C22×C83C2×#4111yescharacteristic
199C22×C83H(5,𝔽2)11yescharacteristic
200C22×C83H(5,𝔽2)11yescharacteristic
201C4×C83—41no—
202C4×C83—41no—
203C4×C83—41no—
204C4×C83—41no—
205Dic83—22no—
206Dic83—22no—
207Dic83—41no—
208Dic83—41no—
209Dic83—41no—
210Dic83—41no—
211Dic83—41no—
212Dic83—41no—
213C2×C83—24no—
214C2×C83—42no—
215C2×C83—42no—
216C2×C83#52511yescharacteristic
217C2×C83C2×#12611yescharacteristic
218C2×C83#53811yescharacteristic
219C2×C83#54611yescharacteristic
220C2×C83#54611yescharacteristic
221C2×C83#55111yescharacteristic
222C2×C83#55111yescharacteristic
223#2480—831nomaximal, Sylow
224C83#248011yescharacteristic, complemented, Sylow
225C2×#126—831no—
226C22×C22⋊C4—831no—
227#397—831no—
228#397—831no—
229#397—831no—
230#396—831no—
231#388—831no—
232#388—831no—
233#388—831no—
234#385—831no—
235#385—831no—
236#380—831no—
237#379—831no—
238#379D8311yescharacteristic
239C4×C22⋊C4—831no—
240C25C2×D8311yescharacteristic
241C23×C4—831no—
242C23×C4—831no—
243#126—1664no—
244C2×C4⋊C4—831no—
245C2×C4⋊C4—831no—
246C2×C4⋊C4—831no—
247C2×C4⋊C4—831no—
248C2×C4⋊C4—831no—
249C2×C4⋊C4—831no—
250C2×C22⋊C4—831no—
251C2×C22⋊C4—831no—
252C2×C22⋊C4—831no—
253C2×C22⋊C4—831no—
254C2×C22⋊C4—831no—
255C2×C22⋊C4—831no—
256C2×C22⋊C4—831no—
257C2×C22⋊C4—831no—
258C2×C22⋊C4—831no—
259C2×C22⋊C4—831no—
260C2×C22⋊C4—1664no—
261C2×C22⋊C4C2×D8311yescharacteristic
262C2×C22⋊C4C2×D8311yescharacteristic
263C2×C22⋊C4C2×D8311yescharacteristic
264C2×C22⋊C4C2×D8311yescharacteristic
265C2×C22⋊C4C2×D8311yescharacteristic
266C2×C22⋊C4C2×D8311yescharacteristic
267C2×C42—831no—
268C2×C42—831no—
269#95—831no—
270#95—831no—
271#95—831no—
272#95—831no—
273#95—831no—
274#95—831no—
275#95—831no—
276#95—831no—
277C24—22no—
278C24—22no—
279C24—22no—
280C24—22no—
281C24—22no—
282C24—41no—
283C24—41no—
284C24C22×D8311yescharacteristic
285C24C22×D8311yescharacteristic
286C24C22×D8311yescharacteristic
287C22×C4—3321no—
288C22×C4—3321no—
289C22×C4—831no—
290C22×C4—831no—
291C22×C4—831no—
292C22×C4—831no—
293C22×C4—831no—
294C22×C4—831no—
295C22×C4—831no—
296C22×C4—831no—
297C22×C4—1662no—
298C22×C4—1662no—
299C22×C4—1662no—
300C22×C4—1662no—
301C22×C4C22×D8311yescharacteristic
302C22×C4C22×D8311yescharacteristic
303C22×C4C22×D8311yescharacteristic
304C22×C4C22×D8311yescharacteristic
305C4⋊C4—3321no—
306C4⋊C4—3321no—
307C4⋊C4—3321no—
308C4⋊C4—1662no—
309C4⋊C4—1662no—
310C4⋊C4—1662no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—3321no—
318C22⋊C4—3321no—
319C22⋊C4—834no—
320C22⋊C4—1662no—
321C22⋊C4—1662no—
322C22⋊C4—1662no—
323C22⋊C4—1662no—
324C22⋊C4—1662no—
325C22⋊C4—1662no—
326C22⋊C4—1662no—
327C42—3321no—
328C42—1662no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—28no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—44no—
347C23—44no—
348C23—44no—
349C23—44no—
350C23—44no—
351C23—44no—
352C23D4×D8312yes—
353C23#1305058912yes—
354C23#1305058912yes—
355C23#1305058912yes—
356C23#1305059012yes—
357C23C23×D8311yescharacteristic
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—3324no—
371C2×C4—3324no—
372C2×C4—832no—
373C2×C4—832no—
374C2×C4—1661no—
375C2×C4—1661no—
376C2×C4—1661no—
377C2×C4—1661no—
378C2×C4—1661no—
379C2×C4—1661no—
380C2×C4—1661no—
381C2×C4—1661no—
382C2×C4—1661no—
383C2×C4—1661no—
384C2×C4—1661no—
385C2×C4—1661no—
386C2×C4—1661no—
387C2×C4—1661no—
388C2×C4—1661no—
389C2×C4—1661no—
390C2×C4—1661no—
391C2×C4—1661no—
392C2×C4—1661no—
393C2×C4—1661no—
394C2×C4—1661no—
395C2×C4—1661no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—416no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22#1458178514yescomplemented
418C22C2×D4×D8311yescharacteristic
419C22C2×#1305058911yescharacteristic
420C22C2×#1305058911yescharacteristic
421C22C2×#1305058911yescharacteristic
422C22C2×#1305059011yescharacteristic
423C22#1458183711yescharacteristic
424C22#1458183711yescharacteristic
425C4—41no—
426C4—41no—
427C4—41no—
428C4—41no—
429C4—3321no—
430C4—3321no—
431C4—3321no—
432C4—3321no—
433C4—3321no—
434C4—3321no—
435C4—1662no—
436C4—1662no—
437C2—24no—
438C2—42no—
439C2—42no—
440C2#1912820711yescharacteristic
441C2C2×#1458178511yescharacteristic
442C2#1912828611yescharacteristic
443C2#1912833811yescharacteristic
444C2#1912834111yescharacteristic
445C2#1912837711yescharacteristic
446C2#1912838211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#379×C83C2
prime radicalC25×C83C22
hypercenter#379D83
hypocenterC83#2480
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#14581785C2semidirect
3. #19127629C2semidirect
4. #19127629C2semidirect
5. #19127626C2semidirect
6. #19127624C2semidirect
7. #19127595C2semidirect
8. #19127594C2semidirect
9. #19127589C2semidirect
10. #19127576C2semidirect
11. #19127573C2semidirect
12. #19127559C2semidirect
14. C22⋊C4×Dic83C2semidirect
19. C2×C4⋊Dic83C22semidirect
20. C2×C4⋊Dic83C22semidirect
21. C2×Dic83⋊C4C22semidirect
22. C2×Dic83⋊C4C22semidirect
23. C2×Dic83⋊C4C22semidirect
24. C2×Dic83⋊C4C22semidirect
36. C2×C4×Dic83C22semidirect
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
193. C22×C83#126semidirect
224. C83#2480semidirect
417. C22#14581785semidirect

Maximal subgroups

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

subgroupindex
C2×#145817852
C22×C22⋊Dic832
#191276292
#191276262
#191276242
#191275952
#191275942
#191275892
#191275762
#191275732
#191275592
#191275572
C22⋊C4×Dic832
#379×C832
#248083