Finite Group Databasebeta

← #24913235

Subgroups — #24913235

Order 10624.

702 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×#14581760C211yesmaximal, characteristic
2C2×C22⋊C4×D83C211yesmaximal, characteristic, complemented
3#19127630C211yesmaximal, characteristic, complemented
4#19127629C211yesmaximal, characteristic, complemented
5#19127627C211yesmaximal, characteristic, complemented
6#19127626C211yesmaximal, characteristic, complemented
7#19127617C211yesmaximal, characteristic, complemented
8#19127616C211yesmaximal, characteristic, complemented
9#19127615C211yesmaximal, characteristic, complemented
10#19127577C211yesmaximal, characteristic, complemented
11#19127577C211yesmaximal, characteristic, complemented
12#19127575C211yesmaximal, characteristic, complemented
13#19127572C211yesmaximal, characteristic, complemented
14#19127556C211yesmaximal, characteristic, complemented
15#394×C83C211yesmaximal, characteristic, complemented
16C24×D83C2211yescharacteristic
17C22×C22⋊D83C2211yescharacteristic
18C22×C22⋊D83C2211yescharacteristic
19C22×C4×D83C2211yescharacteristic
20C22×C4×D83C2211yescharacteristic
21#14581760—24no—
22C2×C4⋊Dic83C2211yescharacteristic, complemented
23C2×Dic83⋊C4C2211yescharacteristic, complemented
24C2×Dic83⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic83C2211yescharacteristic
26C2×C22⋊Dic83C2211yescharacteristic
27C2×C22⋊Dic83C2211yescharacteristic
28C2×C22⋊Dic83C2211yescharacteristic, complemented
29C2×C22⋊Dic83C2211yescharacteristic, complemented
30C2×(C2×D83)⋊C4C2211yescharacteristic
31C2×(C2×D83)⋊C4C2211yescharacteristic
32C2×(C2×D83)⋊C4C2211yescharacteristic
33C2×(C2×D83)⋊C4C2211yescharacteristic
34C2×(C2×D83)⋊C4C2211yescharacteristic
35C2×(C2×D83)⋊C4C2211yescharacteristic
36C2×(C2×D83)⋊C4C2211yescharacteristic
37C2×(C2×D83)⋊C4C2211yescharacteristic
38C22⋊C4×D83—24no—
39C83⋊#95C2211yescharacteristic, complemented
40C83⋊#95C2211yescharacteristic, complemented
41C83⋊#95C2211yescharacteristic, complemented
42C83⋊#95C2211yescharacteristic, complemented
43C83⋊#95C2211yescharacteristic, complemented
44C83⋊#95C2211yescharacteristic, complemented
45C83⋊#95C2211yescharacteristic, complemented
46C22×D4×C83C2211yescharacteristic
47C2×C4⋊C4×C83C2211yescharacteristic, complemented
48C2×C22⋊C4×C83C2211yescharacteristic
49C2×C22⋊C4×C83C2211yescharacteristic
50C2×C22⋊C4×C83C2211yescharacteristic, complemented
51C2×C22⋊C4×C83C2211yescharacteristic, complemented
52#95×C83C2211yescharacteristic, complemented
53C23×D83—22no—
54C23×D83—22no—
55C23×D83—41no—
56C23×D83—41no—
57C23×D83—41no—
58C23×D83—41no—
59C23×D83D414yes—
60C23×D83C2311yescharacteristic
61C23×D83C2311yescharacteristic
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
74C2×C4×D83—22no—
75C2×C4×D83—22no—
76C2×C4×D83—41no—
77C2×C4×D83—41no—
78C2×C4×D83—41no—
79C2×C4×D83—41no—
80C4⋊Dic83—41no—
81Dic83⋊C4—41no—
82Dic83⋊C4—41no—
83C22⋊Dic83—22no—
84C22⋊Dic83—22no—
85C22⋊Dic83—41no—
86C22⋊Dic83—41no—
87C22⋊Dic83—41no—
88(C2×D83)⋊C4—22no—
89(C2×D83)⋊C4—22no—
90(C2×D83)⋊C4—22no—
91(C2×D83)⋊C4—22no—
92(C2×D83)⋊C4—22no—
93(C2×D83)⋊C4—22no—
94(C2×D83)⋊C4—41no—
95(C2×D83)⋊C4—41no—
96C24×C83C2311yescharacteristic
97C24×C83C2311yescharacteristic
98C2×D4×C83—22no—
99C2×D4×C83—41no—
100C2×D4×C83—41no—
101C22×C4×C83C2311yescharacteristic
102C22×C4×C83C2311yescharacteristic
103C22×C4×C83C2311yescharacteristic
104C22×C4×C83C2311yescharacteristic
105C22×C4×C83C2311yescharacteristic
106C4⋊C4×C83—41no—
107C22⋊C4×C83—22no—
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×C83C2×D412yes—
125C23×C83C2411yescharacteristic
126C22×D83—21no—
127C22×D83—21no—
128C22×D83—21no—
129C22×D83—21no—
130C22×D83—21no—
131C22×D83—21no—
132C22×D83—21no—
133C22×D83—21no—
134C22×D83—21no—
135C22×D83—21no—
136C22×D83—28no—
137C22×D83—44no—
138C22×D83—44no—
139C22×D83—44no—
140C22×D83—44no—
141C22×D83—44no—
142C22×D83—44no—
143C22×D83C2×D412yes—
144C22×D83C2×D412yes—
145C22×D83#4112yes—
146C22×D83#4112yes—
147D4×C83—44no—
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—
159C2×C4×C83—21no—
160C2×C4×C83—21no—
161C2×C4×C83—21no—
162C2×C4×C83—21no—
163C22⋊D83—44no—
164C22⋊D83—44no—
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—
183C4×D83—44no—
184C4×D83—44no—
185C22×C83—22no—
186C22×C83—22no—
187C22×C83—22no—
188C22×C83—41no—
189C22×C83—41no—
190C22×C83—41no—
191C22×C83—41no—
192C22×C83—41no—
193C22×C83—41no—
194C22×C83—41no—
195C22×C83—41no—
196C22×C83—41no—
197C22×C83—41no—
198C22×C83—41no—
199C22×C83C22×D411yescharacteristic
200C22×C83C2×#4111yescharacteristic
201C22×C83C2×#4111yescharacteristic
202C22×C83H(5,𝔽2)11yescharacteristic
203C22×C83H(5,𝔽2)11yescharacteristic
204C22×C83H(5,𝔽2)11yescharacteristic
205C22×C83H(5,𝔽2)11yescharacteristic
206C2×D83—22no—
207C2×D83—22no—
208C2×D83—22no—
209C2×D83—22no—
210C2×D83—22no—
211C2×D83—22no—
212C2×D83—22no—
213C2×D83—22no—
214C2×D83—22no—
215C2×D83—416no—
216C2×D83—41no—
217C2×D83—41no—
218C2×D83—41no—
219C2×D83—41no—
220C2×D83#12314yes—
221C4×C83—41no—
222C4×C83—41no—
223C4×C83—41no—
224C4×C83—41no—
225C4×C83—41no—
226Dic83—41no—
227Dic83—41no—
228Dic83—41no—
229Dic83—41no—
230Dic83—41no—
231Dic83—41no—
232C2×C83—42no—
233C2×C83—81no—
234C2×C83C2×#12311yescharacteristic
235C2×C83#53411yescharacteristic
236C2×C83#53411yescharacteristic
237C2×C83#53811yescharacteristic
238C2×C83#53811yescharacteristic
239C2×C83#53811yescharacteristic
240C2×C83#53811yescharacteristic
241D83—24no—
242D83—42no—
243#2622—831nomaximal, Sylow
244C83#262211yescharacteristic, complemented, Sylow
245C2×#120—831no—
246C22×C22⋊C4—831no—
247#397—831no—
248#397—831no—
249#397—831no—
250#397—831no—
251#394—831no—
252#394—831no—
253#394—831no—
254#394D8311yescharacteristic, complemented
255#386—831no—
256#386—831no—
257#385—831no—
258#385—831no—
259#379—831no—
260C25—831no—
261C22×D4—831no—
262C22×D4—831no—
263C22×D4C2×D8311yescharacteristic
264C23×C4—831no—
265C23×C4—831no—
266#120—1664no—
267C2×C4⋊C4—831no—
268C2×C4⋊C4—831no—
269C2×C4⋊C4—831no—
270C2×C4⋊C4C2×D8311yescharacteristic, complemented
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⋊C4—831no—
283C2×C22⋊C4—831no—
284C2×C22⋊C4—1664no—
285C2×C22⋊C4C2×D8311yescharacteristic
286C2×C22⋊C4C2×D8311yescharacteristic
287C2×C22⋊C4C2×D8311yescharacteristic, complemented
288C2×C22⋊C4C2×D8311yescharacteristic, complemented
289#95—831no—
290#95—831no—
291#95—831no—
292#95—831no—
293#95—831no—
294#95—831no—
295#95—831no—
296#95C2×D8311yescharacteristic, complemented
297C24—3321no—
298C24—3321no—
299C24—3321no—
300C24—3321no—
301C24—834no—
302C24—831no—
303C24—831no—
304C24—1662no—
305C24—1662no—
306C24C22×D8311yescharacteristic
307C24C22×D8311yescharacteristic
308C2×D4—22no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—3321no—
312C2×D4—3321no—
313C2×D4—1662no—
314C2×D4—1662no—
315C2×D4—1662no—
316C2×D4—1662no—
317C22×C4—3321no—
318C22×C4—3321no—
319C22×C4—3321no—
320C22×C4—3321no—
321C22×C4—831no—
322C22×C4—831no—
323C22×C4—831no—
324C22×C4—831no—
325C22×C4—831no—
326C22×C4—831no—
327C22×C4—1662no—
328C22×C4—1662no—
329C22×C4C22×D8311yescharacteristic
330C22×C4C22×D8311yescharacteristic
331C22×C4C22×D8311yescharacteristic
332C22×C4C22×D8311yescharacteristic
333C22×C4C22×D8311yescharacteristic
334C4⋊C4—41no—
335C4⋊C4—3321no—
336C4⋊C4—3321no—
337C4⋊C4—3321no—
338C22⋊C4—22no—
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—
354C22⋊C4—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—3324no—
369C23—3324no—
370C23—3324no—
371C23—3324no—
372C23—3324no—
373C23—3324no—
374C23—832no—
375C23—832no—
376C23—832no—
377C23—832no—
378C23—1668no—
379C23—1661no—
380C23—1661no—
381C23—1661no—
382C23—1661no—
383C23—1661no—
384C23—1661no—
385C23—1661no—
386C23—1661no—
387C23—1661no—
388C23—1661no—
389C23D4×D8312yes—
390C23C23×D8311yescharacteristic
391D4—44no—
392D4—3324no—
393D4—3324no—
394C2×C4—21no—
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—21no—
408C2×C4—21no—
409C2×C4—3324no—
410C2×C4—3324no—
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—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—33216no—
444C22—3321no—
445C22—3321no—
446C22—3321no—
447C22—3321no—
448C22—834no—
449C22—1662no—
450C22—1662no—
451C22—1662no—
452C22—1662no—
453C22—1662no—
454C22—1662no—
455C22—1662no—
456C22—1662no—
457C22—1662no—
458C22C2×D4×D8311yescharacteristic
459C22#41×D8311yescharacteristic
460C22#41×D8311yescharacteristic
461C22#1458183711yescharacteristic
462C22#1458183711yescharacteristic
463C22#1458183711yescharacteristic
464C22#1458183811yescharacteristic
465C4—41no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—41no—
470C4—3321no—
471C4—3321no—
472C4—3321no—
473C4—3321no—
474C4—3321no—
475C4—3321no—
476C2—42no—
477C2—81no—
478C2—3322no—
479C2—1664no—
480C2#123×D8311yescharacteristic
481C2#1912825911yescharacteristic
482C2#1912826111yescharacteristic
483C2#1912828311yescharacteristic
484C2#1912828311yescharacteristic
485C2#1912828511yescharacteristic
486C2#1912828711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#394×C83C2
prime radicalC2×#14581760C2
hypercenter#394D83
hypocenterC83#2622
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×D83C2semidirect
3. #19127630C2semidirect
4. #19127629C2semidirect
5. #19127627C2semidirect
6. #19127626C2semidirect
7. #19127617C2semidirect
8. #19127616C2semidirect
9. #19127615C2semidirect
10. #19127577C2semidirect
11. #19127577C2semidirect
12. #19127575C2semidirect
13. #19127572C2semidirect
14. #19127556C2semidirect
15. #394×C83C2semidirect
22. C2×C4⋊Dic83C22semidirect
23. C2×Dic83⋊C4C22semidirect
24. C2×Dic83⋊C4C22semidirect
28. C2×C22⋊Dic83C22semidirect
29. C2×C22⋊Dic83C22semidirect
39. C83⋊#95C22semidirect
40. C83⋊#95C22semidirect
41. C83⋊#95C22semidirect
42. C83⋊#95C22semidirect
43. C83⋊#95C22semidirect
44. C83⋊#95C22semidirect
45. C83⋊#95C22semidirect
47. C2×C4⋊C4×C83C22semidirect
50. C2×C22⋊C4×C83C22semidirect
51. C2×C22⋊C4×C83C22semidirect
52. #95×C83C22semidirect
244. C83#2622semidirect
254. #394D83semidirect
270. C2×C4⋊C4C2×D83semidirect
287. C2×C22⋊C4C2×D83semidirect
288. C2×C22⋊C4C2×D83semidirect
296. #95C2×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#145817602
C2×C22⋊C4×D832
#191276302
#191276292
#191276272
#191276262
#191276172
#191276162
#191276152
#191275772
#191275752
#191275722
#191275562
#394×C832
#262283