Finite Group Databasebeta

← #21430478

Subgroups — #21430478

Order 7552.

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×#14273713C211yesmaximal, characteristic, complemented
2C2×#14273697C211yesmaximal, characteristic
3#16837330C211yesmaximal, characteristic, complemented
4#16837320C211yesmaximal, characteristic, complemented
5#16837319C211yesmaximal, characteristic, complemented
6#16837315C211yesmaximal, characteristic, complemented
7#16837315C211yesmaximal, characteristic, complemented
8#16837292C211yesmaximal, characteristic, complemented
9#16837291C211yesmaximal, characteristic, complemented
10#16837280C211yesmaximal, characteristic, complemented
11#16837280C211yesmaximal, characteristic, complemented
12#16837278C211yesmaximal, characteristic, complemented
13#16837257C211yesmaximal, characteristic, complemented
14#16837257C211yesmaximal, characteristic, complemented
15C59×#397C211yesmaximal, characteristic, complemented
16C24×D59C2211yescharacteristic
17C22×Dic118C2211yescharacteristic, complemented
18C22×D236C2211yescharacteristic
19C22×D236C2211yescharacteristic
20C22×C22⋊D59C2211yescharacteristic
21C22×C4×D59C2211yescharacteristic, complemented
22#14273713—24no—
23#14273697—24no—
24C2×Dic59⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic59C2211yescharacteristic
26C2×C22⋊Dic59C2211yescharacteristic
27C2×(C2×D59)⋊C4C2211yescharacteristic
28C2×(C2×D59)⋊C4C2211yescharacteristic
29C2×(C2×D59)⋊C4C2211yescharacteristic
30C2×(C2×D59)⋊C4C2211yescharacteristic
31C2×(C2×D59)⋊C4C2211yescharacteristic
32C2×(C2×D59)⋊C4C2211yescharacteristic
33C2×(C2×D59)⋊C4C2211yescharacteristic
34C2×(C2×D59)⋊C4C2211yescharacteristic
35C2×(C2×D59)⋊C4C2211yescharacteristic
36C2×(C2×D59)⋊C4C2211yescharacteristic
37C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
38C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
40C2×C4×Dic59C2211yescharacteristic, complemented
41C59⋊#95C2211yescharacteristic, complemented
42C59⋊#95C2211yescharacteristic, complemented
43C59⋊#95C2211yescharacteristic, complemented
44C59⋊#95C2211yescharacteristic, complemented
45C59⋊#95C2211yescharacteristic, complemented
46C2×C4⋊C4×C59C2211yescharacteristic, complemented
47C2×C22⋊C4×C59C2211yescharacteristic
48C2×C22⋊C4×C59C2211yescharacteristic
49C2×C22⋊C4×C59C2211yescharacteristic
50#95×C59C2211yescharacteristic, complemented
51#95×C59C2211yescharacteristic, complemented
52#95×C59C2211yescharacteristic, complemented
53C24×C59C2311yescharacteristic
54C23×D59—22no—
55C23×D59—22no—
56C23×D59—22no—
57C23×D59—41no—
58C23×D59—41no—
59C23×D59—41no—
60C23×D59—41no—
61C23×D59C2311yescharacteristic
62C23×D59C2311yescharacteristic
63C23×D59C2311yescharacteristic
64C22×C4×C59C2311yescharacteristic
65C22×C4×C59C2311yescharacteristic
66C22×C4×C59C2311yescharacteristic
67C22×C4×C59C2311yescharacteristic
68C22×C4×C59C2311yescharacteristic
69C22×C4×C59C2311yescharacteristic
70C2×C22⋊D59—41no—
71C2×C22⋊D59—41no—
72C2×C22⋊D59D414yes—
73C22×Dic59C2311yescharacteristic
74C22×Dic59C2311yescharacteristic
75C22×Dic59C2311yescharacteristic
76C22×Dic59C2311yescharacteristic
77C22×Dic59C2311yescharacteristic
78C2×D236—22no—
79C2×D236—22no—
80C2×D236—22no—
81C2×D236—22no—
82C2×D236—41no—
83C2×D236—41no—
84C2×C4×D59—41no—
85C2×C4×D59—41no—
86C2×C4×D59—41no—
87C2×Dic118—22no—
88C2×Dic118—41no—
89C2×Dic118—41no—
90C4⋊C4×C59—41no—
91C22⋊C4×C59—22no—
92C22⋊C4×C59—22no—
93C22⋊C4×C59—41no—
94C22⋊Dic59—22no—
95C22⋊Dic59—41no—
96(C2×D59)⋊C4—22no—
97(C2×D59)⋊C4—22no—
98(C2×D59)⋊C4—22no—
99(C2×D59)⋊C4—22no—
100(C2×D59)⋊C4—22no—
101(C2×D59)⋊C4—22no—
102(C2×D59)⋊C4—41no—
103(C2×D59)⋊C4—41no—
104(C2×D59)⋊C4—41no—
105(C2×D59)⋊C4—41no—
106(C2×D59)⋊C4—41no—
107(C2×D59)⋊C4—41no—
108(C2×D59)⋊C4—41no—
109Dic59⋊C4—41no—
110C4×Dic59—22no—
111C23×C59—21no—
112C23×C59—21no—
113C23×C59—21no—
114C23×C59—21no—
115C23×C59—21no—
116C23×C59—21no—
117C23×C59C2×D412yes—
118C23×C59C2411yescharacteristic
119C22×D59—21no—
120C22×D59—21no—
121C22×D59—21no—
122C22×D59—21no—
123C22×D59—21no—
124C22×D59—21no—
125C22×D59—21no—
126C22×D59—21no—
127C22×D59—21no—
128C22×D59—21no—
129C22×D59—21no—
130C22×D59—21no—
131C22×D59—21no—
132C22×D59—21no—
133C22×D59—21no—
134C22×D59—21no—
135C22×D59—21no—
136C22×D59—21no—
137C22×D59—44no—
138C22×D59—44no—
139C22×D59—44no—
140C22×D59—44no—
141C22×D59—44no—
142C22×D59—44no—
143C22×D59—44no—
144C22×D59C2×D412yes—
145C22×D59#4112yes—
146C22×D59#4112yes—
147C2×C4×C59—21no—
148C2×C4×C59—21no—
149C2×C4×C59—21no—
150C2×C4×C59—21no—
151C2×C4×C59—21no—
152C2×C4×C59—21no—
153C2×C4×C59—21no—
154C2×C4×C59—21no—
155C2×C4×C59—21no—
156C2×C4×C59—21no—
157C2×C4×C59—21no—
158C2×C4×C59—21no—
159C2×C4×C59—21no—
160C2×C4×C59—21no—
161C2×C4×C59—21no—
162C2×C4×C59—21no—
163C2×C4×C59—21no—
164C2×C4×C59—21no—
165C22⋊D59—44no—
166C2×Dic59—21no—
167C2×Dic59—21no—
168C2×Dic59—21no—
169C2×Dic59—21no—
170C2×Dic59—21no—
171C2×Dic59—21no—
172C2×Dic59—21no—
173C2×Dic59—21no—
174C2×Dic59—21no—
175C2×Dic59—21no—
176C2×Dic59—21no—
177C2×Dic59—21no—
178C2×Dic59—21no—
179C2×Dic59—21no—
180C2×Dic59C2×D412yes—
181D236—44no—
182D236—44no—
183C4×D59—44no—
184Dic118—44no—
185C22×C59—22no—
186C22×C59—22no—
187C22×C59—22no—
188C22×C59—41no—
189C22×C59—41no—
190C22×C59—41no—
191C22×C59—41no—
192C22×C59C22×D411yescharacteristic
193C22×C59C2×#4111yescharacteristic
194C22×C59C2×#4111yescharacteristic
195C22×C59H(5,𝔽2)11yescharacteristic
196C22×C59H(5,𝔽2)11yescharacteristic
197C22×C59H(5,𝔽2)11yescharacteristic
198C22×C59H(5,𝔽2)11yescharacteristic
199C2×D59—22no—
200C2×D59—22no—
201C2×D59—22no—
202C2×D59—22no—
203C2×D59—22no—
204C2×D59—22no—
205C2×D59—22no—
206C2×D59—22no—
207C2×D59—22no—
208C2×D59—416no—
209C2×D59—41no—
210C2×D59—41no—
211C2×D59—41no—
212C2×D59—41no—
213C2×D59—41no—
214C2×D59—41no—
215C2×D59—41no—
216C2×D59—41no—
217C2×D59—41no—
218C2×D59—41no—
219C2×D59—41no—
220C2×D59—41no—
221C4×C59—41no—
222C4×C59—41no—
223C4×C59—41no—
224C4×C59—41no—
225C4×C59—41no—
226C4×C59—41no—
227Dic59—22no—
228Dic59—41no—
229Dic59—41no—
230Dic59—41no—
231Dic59—41no—
232#2684—591nomaximal, Sylow
233C2×C59—42no—
234C2×C59#53411yescharacteristic
235C2×C59#53811yescharacteristic
236C2×C59#53811yescharacteristic
237C2×C59#54611yescharacteristic
238C2×C59#54611yescharacteristic
239C2×C59#55111yescharacteristic
240C2×C59H(3,𝔽4)11yescharacteristic
241D59—42no—
242D59—42no—
243D59—42no—
244C2×#124—591no—
245C2×#120—591no—
246#397—591no—
247#397D5911yescharacteristic, complemented
248#394—591no—
249#394—591no—
250#393—591no—
251#393—591no—
252#388—591no—
253#388—591no—
254#386—591no—
255#386—591no—
256#386—591no—
257#379—591no—
258#379—591no—
259C59#268411yescharacteristic, complemented, Sylow
260C25—591no—
261C22×Q8—591no—
262C22×D4—591no—
263C22×D4—591no—
264C22×D4—591no—
265C23×C4—591no—
266#124—1184no—
267#120—1184no—
268C2×C4⋊C4—591no—
269C2×C4⋊C4C2×D5911yescharacteristic, complemented
270C2×C22⋊C4—591no—
271C2×C22⋊C4—591no—
272C2×C22⋊C4—591no—
273C2×C22⋊C4—591no—
274C2×C22⋊C4—591no—
275C2×C22⋊C4—591no—
276C2×C22⋊C4—591no—
277C2×C22⋊C4—591no—
278C2×C22⋊C4—591no—
279C2×C22⋊C4—591no—
280C2×C22⋊C4—591no—
281C2×C22⋊C4—591no—
282C2×C22⋊C4—591no—
283C2×C22⋊C4—591no—
284C2×C22⋊C4—591no—
285C2×C22⋊C4C2×D5911yescharacteristic
286C2×C22⋊C4C2×D5911yescharacteristic
287C2×C22⋊C4C2×D5911yescharacteristic
288C2×C42—591no—
289#95—591no—
290#95—591no—
291#95—591no—
292#95—591no—
293#95—591no—
294#95C2×D5911yescharacteristic, complemented
295#95C2×D5911yescharacteristic, complemented
296#95C2×D5911yescharacteristic, complemented
297C24—591no—
298C24—591no—
299C24—591no—
300C24—1182no—
301C24—1182no—
302C24—1182no—
303C24—2361no—
304C24—2361no—
305C24—2361no—
306C24—2361no—
307C24C22×D5911yescharacteristic
308C2×Q8—1182no—
309C2×Q8—2361no—
310C2×Q8—2361no—
311C2×D4—594no—
312C2×D4—1182no—
313C2×D4—1182no—
314C2×D4—1182no—
315C2×D4—1182no—
316C2×D4—2361no—
317C2×D4—2361no—
318C2×D4—2361no—
319C2×D4—2361no—
320C22×C4—591no—
321C22×C4—591no—
322C22×C4—591no—
323C22×C4—591no—
324C22×C4—591no—
325C22×C4—2361no—
326C22×C4—2361no—
327C22×C4—2361no—
328C22×C4C22×D5911yescharacteristic
329C22×C4C22×D5911yescharacteristic
330C22×C4C22×D5911yescharacteristic
331C22×C4C22×D5911yescharacteristic
332C22×C4C22×D5911yescharacteristic
333C22×C4C22×D5911yescharacteristic
334C4⋊C4—41no—
335C4⋊C4—2361no—
336C22⋊C4—22no—
337C22⋊C4—22no—
338C22⋊C4—41no—
339C22⋊C4—1182no—
340C22⋊C4—1182no—
341C22⋊C4—1182no—
342C22⋊C4—1182no—
343C22⋊C4—1182no—
344C22⋊C4—1182no—
345C22⋊C4—1182no—
346C22⋊C4—2361no—
347C22⋊C4—2361no—
348C22⋊C4—2361no—
349C22⋊C4—2361no—
350C22⋊C4—2361no—
351C22⋊C4—2361no—
352C22⋊C4—2361no—
353C22⋊C4—2361no—
354C42—1182no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—592no—
362C23—592no—
363C23—592no—
364C23—1181no—
365C23—1181no—
366C23—1181no—
367C23—1181no—
368C23—1181no—
369C23—1181no—
370C23—1181no—
371C23—1181no—
372C23—1181no—
373C23—1181no—
374C23—1181no—
375C23—1181no—
376C23—1181no—
377C23—1181no—
378C23—1181no—
379C23—1181no—
380C23—1181no—
381C23—1181no—
382C23—2364no—
383C23—2364no—
384C23—2364no—
385C23—2364no—
386C23—2364no—
387C23—2364no—
388C23—2364no—
389C23D4×D5912yes—
390C23C23×D5911yescharacteristic
391Q8—2364no—
392D4—2364no—
393D4—2364no—
394D4—2364no—
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—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—592no—
414C2×C4—1181no—
415C2×C4—1181no—
416C2×C4—1181no—
417C2×C4—1181no—
418C2×C4—1181no—
419C2×C4—1181no—
420C2×C4—1181no—
421C2×C4—1181no—
422C2×C4—1181no—
423C2×C4—1181no—
424C2×C4—1181no—
425C2×C4—1181no—
426C2×C4—1181no—
427C2×C4—1181no—
428C2×C4—2364no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—1182no—
437C22—1182no—
438C22—1182no—
439C22—1182no—
440C22—1182no—
441C22—1182no—
442C22—1182no—
443C22—1182no—
444C22—1182no—
445C22—23616no—
446C22—2361no—
447C22—2361no—
448C22—2361no—
449C22—2361no—
450C22—2361no—
451C22—2361no—
452C22—2361no—
453C22—2361no—
454C22—2361no—
455C22—2361no—
456C22—2361no—
457C22—2361no—
458C22C2×D4×D5911yescharacteristic
459C22#41×D5911yescharacteristic
460C22#41×D5911yescharacteristic
461C22#1427377211yescharacteristic
462C22#1427377311yescharacteristic
463C22#1427377311yescharacteristic
464C22#1427377311yescharacteristic
465C4—41no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—1182no—
472C4—2361no—
473C4—2361no—
474C4—2361no—
475C4—2361no—
476C2—42no—
477C2—2362no—
478C2—2362no—
479C2—2362no—
480C2#1683796311yescharacteristic
481C2#1683798811yescharacteristic
482C2#1683799111yescharacteristic
483C2#1683804111yescharacteristic
484C2#1683804411yescharacteristic
485C2#1683807711yescharacteristic
486C2#1683814411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#397C2
hypercenter#397D59
hypocenterC59#2684
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#14273713C2semidirect
3. #16837330C2semidirect
4. #16837320C2semidirect
5. #16837319C2semidirect
6. #16837315C2semidirect
7. #16837315C2semidirect
8. #16837292C2semidirect
9. #16837291C2semidirect
10. #16837280C2semidirect
11. #16837280C2semidirect
12. #16837278C2semidirect
13. #16837257C2semidirect
14. #16837257C2semidirect
15. C59×#397C2semidirect
17. C22×Dic118C22semidirect
21. C22×C4×D59C22semidirect
24. C2×Dic59⋊C4C22semidirect
37. C2×(C2×D59)⋊C4C22semidirect
38. C2×(C2×D59)⋊C4C22semidirect
39. C2×(C2×D59)⋊C4C22semidirect
40. C2×C4×Dic59C22semidirect
41. C59⋊#95C22semidirect
42. C59⋊#95C22semidirect
43. C59⋊#95C22semidirect
44. C59⋊#95C22semidirect
45. C59⋊#95C22semidirect
46. C2×C4⋊C4×C59C22semidirect
50. #95×C59C22semidirect
51. #95×C59C22semidirect
52. #95×C59C22semidirect
247. #397D59semidirect
259. C59#2684semidirect
269. C2×C4⋊C4C2×D59semidirect
294. #95C2×D59semidirect
295. #95C2×D59semidirect
296. #95C2×D59semidirect