Finite Group Databasebeta

← #24913849

Subgroups — #24913849

Order 10624.

666 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581787C211yesmaximal, characteristic, complemented
2C2×#14581760C211yesmaximal, characteristic
3#19127636C211yesmaximal, characteristic, complemented
4#19127624C211yesmaximal, characteristic, complemented
5#19127617C211yesmaximal, characteristic, complemented
6#19127616C211yesmaximal, characteristic, complemented
7#19127616C211yesmaximal, characteristic, complemented
8#19127615C211yesmaximal, characteristic, complemented
9#19127601C211yesmaximal, characteristic, complemented
10#19127595C211yesmaximal, characteristic, complemented
11#19127592C211yesmaximal, characteristic, complemented
12#19127592C211yesmaximal, characteristic, complemented
13#19127556C211yesmaximal, characteristic, complemented
14#19127556C211yesmaximal, characteristic, complemented
15#390×C83C211yesmaximal, characteristic, complemented
16C24×D83C2211yescharacteristic
17C22×C22⋊D83C2211yescharacteristic
18C22×C22⋊D83C2211yescharacteristic
19#14581787—24no—
20#14581760—24no—
21C2×C4⋊Dic83C2211yescharacteristic, complemented
22C2×Dic83⋊C4C2211yescharacteristic, complemented
23C2×Dic83⋊C4C2211yescharacteristic, complemented
24C2×Dic83⋊C4C2211yescharacteristic, complemented
25C2×Dic83⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic83C2211yescharacteristic
27C2×C22⋊Dic83C2211yescharacteristic
28C2×C22⋊Dic83C2211yescharacteristic
29C2×C22⋊Dic83C2211yescharacteristic, complemented
30C2×C22⋊Dic83C2211yescharacteristic, complemented
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
38C2×(C2×D83)⋊C4C2211yescharacteristic
39C2×(C2×D83)⋊C4C2211yescharacteristic
40C2×(C2×D83)⋊C4C2211yescharacteristic
41C2×C4×Dic83C2211yescharacteristic, 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
52C2×C42×C83C2211yescharacteristic, complemented
53C23×D83—22no—
54C23×D83—22no—
55C23×D83—22no—
56C23×D83—41no—
57C23×D83—41no—
58C23×D83—41no—
59C23×D83—41no—
60C23×D83C2311yescharacteristic
61C23×D83C2311yescharacteristic
62C2×C22⋊D83—22no—
63C2×C22⋊D83—22no—
64C2×C22⋊D83—22no—
65C2×C22⋊D83—41no—
66C2×C22⋊D83—41no—
67C2×C22⋊D83—41no—
68C22×Dic83C2311yescharacteristic
69C22×Dic83C2311yescharacteristic
70C22×Dic83C2311yescharacteristic
71C22×Dic83C2311yescharacteristic
72C22×Dic83C2311yescharacteristic
73C22×Dic83C2311yescharacteristic
74C4⋊Dic83—22no—
75Dic83⋊C4—22no—
76Dic83⋊C4—41no—
77Dic83⋊C4—41no—
78Dic83⋊C4—41no—
79C22⋊Dic83—22no—
80C22⋊Dic83—22no—
81C22⋊Dic83—41no—
82C22⋊Dic83—41no—
83C22⋊Dic83—41no—
84(C2×D83)⋊C4—22no—
85(C2×D83)⋊C4—22no—
86(C2×D83)⋊C4—22no—
87(C2×D83)⋊C4—22no—
88(C2×D83)⋊C4—41no—
89(C2×D83)⋊C4—41no—
90(C2×D83)⋊C4—41no—
91(C2×D83)⋊C4—41no—
92(C2×D83)⋊C4—41no—
93(C2×D83)⋊C4D414yes—
94C4×Dic83—22no—
95C24×C83C2311yescharacteristic
96C24×C83C2311yescharacteristic
97C2×D4×C83—22no—
98C2×D4×C83—22no—
99C2×D4×C83—41no—
100C22×C4×C83C2311yescharacteristic
101C22×C4×C83C2311yescharacteristic
102C22×C4×C83C2311yescharacteristic
103C22×C4×C83C2311yescharacteristic
104C22×C4×C83C2311yescharacteristic
105C4⋊C4×C83—22no—
106C22⋊C4×C83—41no—
107C22⋊C4×C83—41no—
108C22⋊C4×C83—41no—
109C22⋊C4×C83—41no—
110C42×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#4112yes—
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—21no—
137C22×D83—21no—
138C22×D83—44no—
139C22×D83—44no—
140C22×D83—44no—
141C22×D83—44no—
142C22×D83—44no—
143C22×D83—44no—
144C22×D83—44no—
145C22×D83C2×D412yes—
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×C83C2×D412yes—
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×Dic83C2×D412yes—
183C22×C83—22no—
184C22×C83—22no—
185C22×C83—22no—
186C22×C83—41no—
187C22×C83—41no—
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×C83C22×D411yescharacteristic
198C22×C83C2×#4111yescharacteristic
199C22×C83C2×#4111yescharacteristic
200C22×C83H(5,𝔽2)11yescharacteristic
201C22×C83H(5,𝔽2)11yescharacteristic
202C22×C83H(5,𝔽2)11yescharacteristic
203C22×C83H(5,𝔽2)11yescharacteristic
204C2×D83—22no—
205C2×D83—22no—
206C2×D83—22no—
207C2×D83—22no—
208C2×D83—22no—
209C2×D83—22no—
210C2×D83—416no—
211C2×D83—41no—
212C2×D83—41no—
213C2×D83—41no—
214C2×D83—41no—
215C2×D83—41no—
216C2×D83—41no—
217C2×D83—41no—
218C2×D83—41no—
219C4×C83—22no—
220C4×C83—41no—
221C4×C83—41no—
222C4×C83—41no—
223C4×C83—41no—
224Dic83—22no—
225Dic83—41no—
226Dic83—41no—
227Dic83—41no—
228Dic83—41no—
229Dic83—41no—
230C2×C83—42no—
231C2×C83—81no—
232C2×C83#53511yescharacteristic
233C2×C83#53811yescharacteristic
234C2×C83#53811yescharacteristic
235C2×C83#54611yescharacteristic
236C2×C83#54611yescharacteristic
237C2×C83#55111yescharacteristic
238C2×C83#56011yescharacteristic
239D83—42no—
240D83—42no—
241#2685—831nomaximal, Sylow
242C83#268511yescharacteristic, complemented, Sylow
243C2×#126—831no—
244C2×#120—831no—
245#399—831no—
246#396—831no—
247#394—831no—
248#394—831no—
249#394—831no—
250#394—831no—
251#390—831no—
252#390D8311yescharacteristic, complemented
253#388—831no—
254#388—831no—
255#388—831no—
256#379—831no—
257#379—831no—
258C25—831no—
259C22×D4—831no—
260C22×D4—831no—
261C22×D4C2×D8311yescharacteristic
262#126—1664no—
263#120—1664no—
264C2×C4⋊C4—831no—
265C2×C4⋊C4—831no—
266C2×C4⋊C4—831no—
267C2×C4⋊C4—831no—
268C2×C4⋊C4—831no—
269C2×C4⋊C4C2×D8311yescharacteristic, complemented
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⋊C4—831no—
283C2×C22⋊C4—831no—
284C2×C22⋊C4—831no—
285C2×C22⋊C4C2×D8311yescharacteristic
286C2×C22⋊C4C2×D8311yescharacteristic
287C2×C22⋊C4C2×D8311yescharacteristic, complemented
288C2×C22⋊C4C2×D8311yescharacteristic, complemented
289C2×C42—831no—
290C2×C42C2×D8311yescharacteristic, complemented
291#95—831no—
292#95—831no—
293#95—831no—
294#95—831no—
295C24—3321no—
296C24—3321no—
297C24—3321no—
298C24—3321no—
299C24—831no—
300C24—831no—
301C24—1662no—
302C24—1662no—
303C24—1662no—
304C24C22×D8311yescharacteristic
305C24C22×D8311yescharacteristic
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—41no—
309C2×D4—3321no—
310C2×D4—3321no—
311C2×D4—3321no—
312C2×D4—1662no—
313C2×D4—1662no—
314C2×D4—1662no—
315C22×C4—831no—
316C22×C4—831no—
317C22×C4—831no—
318C22×C4—831no—
319C22×C4—831no—
320C22×C4—831no—
321C22×C4C22×D8311yescharacteristic
322C22×C4C22×D8311yescharacteristic
323C22×C4C22×D8311yescharacteristic
324C22×C4C22×D8311yescharacteristic
325C22×C4C22×D8311yescharacteristic
326C4⋊C4—22no—
327C4⋊C4—3321no—
328C4⋊C4—3321no—
329C4⋊C4—3321no—
330C4⋊C4—1662no—
331C4⋊C4—1662no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—3321no—
337C22⋊C4—3321no—
338C22⋊C4—3321no—
339C22⋊C4—3321no—
340C22⋊C4—3321no—
341C22⋊C4—3321no—
342C22⋊C4—3321no—
343C22⋊C4—3321no—
344C22⋊C4—834no—
345C22⋊C4—1662no—
346C22⋊C4—1662no—
347C22⋊C4—1662no—
348C22⋊C4—1662no—
349C22⋊C4—1662no—
350C22⋊C4—1662no—
351C42—41no—
352C42—1662no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—3324no—
367C23—3324no—
368C23—3324no—
369C23—3324no—
370C23—3324no—
371C23—3324no—
372C23—3324no—
373C23—832no—
374C23—832no—
375C23—1661no—
376C23—1661no—
377C23—1661no—
378C23—1661no—
379C23—1661no—
380C23—1661no—
381C23—1661no—
382C23—1661no—
383C23—1661no—
384C23—1661no—
385C23—1661no—
386C23—1661no—
387C23#1305059012yes—
388C23C23×D8311yescharacteristic
389D4—44no—
390D4—3324no—
391D4—3324no—
392C2×C4—21no—
393C2×C4—21no—
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—832no—
407C2×C4—1661no—
408C2×C4—1661no—
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×C4D4×D8312yes—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—33216no—
440C22—3321no—
441C22—3321no—
442C22—3321no—
443C22—3321no—
444C22—3321no—
445C22—3321no—
446C22—3321no—
447C22—3321no—
448C22—1662no—
449C22—1662no—
450C22—1662no—
451C22—1662no—
452C22—1662no—
453C22—1662no—
454C22C2×D4×D8311yescharacteristic
455C22#41×D8311yescharacteristic
456C22C2×#1305059011yescharacteristic
457C22#1458183711yescharacteristic
458C22#1458183711yescharacteristic
459C22#1458183711yescharacteristic
460C22#1458183811yescharacteristic
461C4—22no—
462C4—41no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—3321no—
467C4—3321no—
468C4—3321no—
469C4—3321no—
470C4—3321no—
471C4—1662no—
472C2—42no—
473C2—81no—
474C2—3322no—
475C2—3322no—
476C2#1912826411yescharacteristic
477C2#1912828311yescharacteristic
478C2#1912828411yescharacteristic
479C2#1912834111yescharacteristic
480C2#1912834411yescharacteristic
481C2#1912838011yescharacteristic
482C2#1912843911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#390×C83C2
prime radicalC2×#14581760C2
hypercenter#390D83
hypocenterC83#2685
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14581787C2semidirect
3. #19127636C2semidirect
4. #19127624C2semidirect
5. #19127617C2semidirect
6. #19127616C2semidirect
7. #19127616C2semidirect
8. #19127615C2semidirect
9. #19127601C2semidirect
10. #19127595C2semidirect
11. #19127592C2semidirect
12. #19127592C2semidirect
13. #19127556C2semidirect
14. #19127556C2semidirect
15. #390×C83C2semidirect
21. C2×C4⋊Dic83C22semidirect
22. C2×Dic83⋊C4C22semidirect
23. C2×Dic83⋊C4C22semidirect
24. C2×Dic83⋊C4C22semidirect
25. C2×Dic83⋊C4C22semidirect
29. C2×C22⋊Dic83C22semidirect
30. C2×C22⋊Dic83C22semidirect
41. C2×C4×Dic83C22semidirect
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. C2×C42×C83C22semidirect
242. C83#2685semidirect
252. #390D83semidirect
269. C2×C4⋊C4C2×D83semidirect
287. C2×C22⋊C4C2×D83semidirect
288. C2×C22⋊C4C2×D83semidirect
290. C2×C42C2×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#145817872
C2×#145817602
#191276362
#191276242
#191276172
#191276162
#191276152
#191276012
#191275952
#191275922
#191275562
#390×C832
#268583