Finite Group Databasebeta

← #21427637

Subgroups — #21427637

Order 7552.

922 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273702C211yesmaximal, characteristic, complemented
2C2×#14273700C211yesmaximal, characteristic, complemented
3C2×#14273697C211yesmaximal, characteristic, complemented
4C2×#14273697C211yesmaximal, characteristic, complemented
5C2×C4×D236C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×D59C211yesmaximal, characteristic, complemented
7#16837324C211yesmaximal, characteristic, complemented
8#16837318C211yesmaximal, characteristic, complemented
9#16837318C211yesmaximal, characteristic, complemented
10#16837312C211yesmaximal, characteristic, complemented
11#16837304C211yesmaximal, characteristic, complemented
12#16837280C211yesmaximal, characteristic, complemented
13#16837280C211yesmaximal, characteristic, complemented
14#16837276C211yesmaximal, characteristic, complemented
15C59×#388C211yesmaximal, characteristic, complemented
16C24×D59C2211yescharacteristic
17C22×D236C2211yescharacteristic
18C22×D236C2211yescharacteristic
19C22×D236C2211yescharacteristic
20C22×D236C2211yescharacteristic
21C22×D236C2211yescharacteristic, complemented
22C22×C22⋊D59C2211yescharacteristic
23C22×C22⋊D59C2211yescharacteristic
24C22×C4×D59C2211yescharacteristic
25C22×C4×D59C2211yescharacteristic
26C22×C4×D59C2211yescharacteristic, complemented
27#14273702—24no—
28#14273700—24no—
29#14273697—24no—
30#14273697—24no—
31C4×D236—24no—
32C2×C4⋊Dic59C2211yescharacteristic, complemented
33C2×C4⋊Dic59C2211yescharacteristic, complemented
34C2×Dic59⋊C4C2211yescharacteristic, complemented
35C2×C22⋊Dic59C2211yescharacteristic
36C2×(C2×D59)⋊C4C2211yescharacteristic
37C2×(C2×D59)⋊C4C2211yescharacteristic
38C2×(C2×D59)⋊C4C2211yescharacteristic
39C2×(C2×D59)⋊C4C2211yescharacteristic
40C2×(C2×D59)⋊C4C2211yescharacteristic
41C2×(C2×D59)⋊C4C2211yescharacteristic
42C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
46C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
47C22⋊C4×D59—24no—
48C59⋊#95C2211yescharacteristic, complemented
49C59⋊#95C2211yescharacteristic, complemented
50C2×C4⋊C4×C59C2211yescharacteristic, complemented
51C2×C22⋊C4×C59C2211yescharacteristic
52C2×C22⋊C4×C59C2211yescharacteristic
53C2×C22⋊C4×C59C2211yescharacteristic
54C2×C42×C59C2211yescharacteristic, complemented
55#95×C59C2211yescharacteristic, complemented
56#95×C59C2211yescharacteristic, complemented
57C24×C59C2311yescharacteristic
58C23×D59—22no—
59C23×D59—22no—
60C23×D59—22no—
61C23×D59—22no—
62C23×D59—22no—
63C23×D59—41no—
64C23×D59—41no—
65C23×D59C2311yescharacteristic
66C23×D59C2311yescharacteristic
67C23×D59C2311yescharacteristic
68C23×D59C2311yescharacteristic
69C22×C4×C59C2311yescharacteristic
70C22×C4×C59C2311yescharacteristic
71C22×C4×C59C2311yescharacteristic
72C22×C4×C59C2311yescharacteristic
73C22×C4×C59C2311yescharacteristic
74C22×C4×C59C2311yescharacteristic
75C2×C22⋊D59—22no—
76C2×C22⋊D59—22no—
77C2×C22⋊D59—22no—
78C2×C22⋊D59—22no—
79C2×C22⋊D59—41no—
80C2×C22⋊D59—41no—
81C22×Dic59C2311yescharacteristic
82C22×Dic59C2311yescharacteristic
83C22×Dic59C2311yescharacteristic
84C22×Dic59C2311yescharacteristic
85C2×D236—22no—
86C2×D236—22no—
87C2×D236—22no—
88C2×D236—22no—
89C2×D236—22no—
90C2×D236—22no—
91C2×D236—22no—
92C2×D236—22no—
93C2×D236—22no—
94C2×D236—22no—
95C2×D236—22no—
96C2×D236—41no—
97C2×D236—41no—
98C2×D236—41no—
99C2×D236D414yescomplemented
100C2×C4×D59—22no—
101C2×C4×D59—22no—
102C2×C4×D59—22no—
103C2×C4×D59—22no—
104C2×C4×D59—22no—
105C2×C4×D59—22no—
106C2×C4×D59—41no—
107C2×C4×D59—41no—
108C2×C4×D59—41no—
109C4⋊C4×C59—22no—
110C22⋊C4×C59—22no—
111C22⋊C4×C59—22no—
112C22⋊C4×C59D414yescomplemented
113C42×C59—22no—
114C22⋊Dic59—22no—
115(C2×D59)⋊C4—22no—
116(C2×D59)⋊C4—22no—
117(C2×D59)⋊C4—22no—
118(C2×D59)⋊C4—22no—
119(C2×D59)⋊C4—22no—
120(C2×D59)⋊C4—22no—
121(C2×D59)⋊C4—22no—
122(C2×D59)⋊C4—22no—
123(C2×D59)⋊C4—22no—
124(C2×D59)⋊C4—41no—
125(C2×D59)⋊C4D414yescomplemented
126C4⋊Dic59—22no—
127C4⋊Dic59—41no—
128Dic59⋊C4—22no—
129C23×C59—21no—
130C23×C59—21no—
131C23×C59—21no—
132C23×C59—21no—
133C23×C59—21no—
134C23×C59—21no—
135C23×C59C2×D412yes—
136C23×C59C2411yescharacteristic
137C22×D59—21no—
138C22×D59—21no—
139C22×D59—21no—
140C22×D59—21no—
141C22×D59—28no—
142C22×D59—21no—
143C22×D59—21no—
144C22×D59—21no—
145C22×D59—21no—
146C22×D59—21no—
147C22×D59—21no—
148C22×D59—21no—
149C22×D59—21no—
150C22×D59—21no—
151C22×D59—21no—
152C22×D59—21no—
153C22×D59—21no—
154C22×D59—21no—
155C22×D59—21no—
156C22×D59—21no—
157C22×D59—21no—
158C22×D59—21no—
159C22×D59—21no—
160C22×D59—21no—
161C22×D59—44no—
162C22×D59—44no—
163C22×D59—44no—
164C22×D59—44no—
165C22×D59—44no—
166C22×D59—44no—
167C22×D59C2×D412yes—
168C22×D59C2×D412yes—
169C22×D59C2×D412yes—
170C22×D59#4112yes—
171C22×D59#4112yes—
172C2×C4×C59—21no—
173C2×C4×C59—21no—
174C2×C4×C59—21no—
175C2×C4×C59—21no—
176C2×C4×C59—21no—
177C2×C4×C59—21no—
178C2×C4×C59—21no—
179C2×C4×C59—21no—
180C2×C4×C59—21no—
181C2×C4×C59—21no—
182C2×C4×C59—21no—
183C2×C4×C59—21no—
184C2×C4×C59—21no—
185C2×C4×C59—21no—
186C2×C4×C59C2×D412yes—
187C2×C4×C59C2×D412yes—
188C2×C4×C59C2×D412yes—
189C2×C4×C59C2×D412yes—
190C22⋊D59—44no—
191C22⋊D59—44no—
192C2×Dic59—21no—
193C2×Dic59—21no—
194C2×Dic59—21no—
195C2×Dic59—21no—
196C2×Dic59—21no—
197C2×Dic59—21no—
198C2×Dic59—21no—
199C2×Dic59—21no—
200C2×Dic59—21no—
201C2×Dic59—21no—
202C2×Dic59—21no—
203C2×Dic59C2×D412yes—
204D236—28no—
205D236—44no—
206D236—44no—
207D236—44no—
208D236—44no—
209C4×D59—44no—
210C4×D59—44no—
211C4×D59—44no—
212C22×C59—22no—
213C22×C59—22no—
214C22×C59—22no—
215C22×C59—41no—
216C22×C59—41no—
217C22×C59—41no—
218C22×C59—41no—
219C22×C59C22×D411yescharacteristic
220C22×C59C22×D411yescharacteristic
221C22×C59C22×D411yescharacteristic
222C22×C59C2×#4111yescharacteristic
223C22×C59C2×#4111yescharacteristic
224C22×C59H(5,𝔽2)11yescharacteristic
225C22×C59H(5,𝔽2)11yescharacteristic
226C2×D59—22no—
227C2×D59—22no—
228C2×D59—22no—
229C2×D59—22no—
230C2×D59—22no—
231C2×D59—22no—
232C2×D59—22no—
233C2×D59—22no—
234C2×D59—22no—
235C2×D59—22no—
236C2×D59—22no—
237C2×D59—22no—
238C2×D59—416no—
239C2×D59—41no—
240C2×D59—41no—
241C2×D59—41no—
242C2×D59—41no—
243C2×D59—41no—
244C2×D59—41no—
245C2×D59—41no—
246C2×D59—41no—
247C2×D59—41no—
248C2×D59—41no—
249C2×D59—41no—
250C2×D59—41no—
251C2×D59—41no—
252C2×D59—41no—
253C2×D59—41no—
254C2×D59#12114yescomplemented
255C4×C59—22no—
256C4×C59—22no—
257C4×C59—22no—
258C4×C59—22no—
259C4×C59—41no—
260C4×C59—41no—
261Dic59—22no—
262Dic59—41no—
263Dic59—41no—
264Dic59—41no—
265#2424—591nomaximal, Sylow
266C2×C59—42no—
267C2×C59C2×#12111yescharacteristic
268C2×C59#52511yescharacteristic
269C2×C59#53811yescharacteristic
270C2×C59D4211yescharacteristic
271C2×C59D4211yescharacteristic
272C2×C59#54611yescharacteristic
273C2×C59#54611yescharacteristic
274D59—24no—
275D59—42no—
276D59—42no—
277D59—81no—
278C2×#121—591no—
279C2×#121—591no—
280C2×#120—591no—
281C2×#120—591no—
282C2×C4×D4—591no—
283C22×C22⋊C4—591no—
284#396—591no—
285#394—591no—
286#394—591no—
287#392—591no—
288#390—591no—
289#388D5911yescharacteristic, complemented
290#386—591no—
291#386—591no—
292#385—591no—
293C59#242411yescharacteristic, complemented, Sylow
294C25—591no—
295C22×D4—591no—
296C22×D4—591no—
297C22×D4—591no—
298C22×D4—591no—
299C22×D4—591no—
300C22×D4—591no—
301C22×D4—591no—
302C23×C4—591no—
303C23×C4—591no—
304C23×C4—591no—
305#121—1184no—
306#121—1184no—
307#120—1184no—
308#120—1184no—
309C4×D4—1184no—
310C2×C4⋊C4—591no—
311C2×C4⋊C4—591no—
312C2×C4⋊C4—591no—
313C2×C4⋊C4C2×D5911yescharacteristic, complemented
314C2×C22⋊C4—591no—
315C2×C22⋊C4—591no—
316C2×C22⋊C4—591no—
317C2×C22⋊C4—591no—
318C2×C22⋊C4—591no—
319C2×C22⋊C4—591no—
320C2×C22⋊C4—591no—
321C2×C22⋊C4—591no—
322C2×C22⋊C4—591no—
323C2×C22⋊C4—591no—
324C2×C22⋊C4—591no—
325C2×C22⋊C4—591no—
326C2×C22⋊C4—1184no—
327C2×C22⋊C4C2×D5911yescharacteristic
328C2×C22⋊C4C2×D5911yescharacteristic
329C2×C22⋊C4C2×D5911yescharacteristic
330C2×C42C2×D5911yescharacteristic, complemented
331#95—591no—
332#95—591no—
333#95C2×D5911yescharacteristic, complemented
334#95C2×D5911yescharacteristic, complemented
335C24—591no—
336C24—591no—
337C24—591no—
338C24—591no—
339C24—1182no—
340C24—1182no—
341C24—1182no—
342C24—1182no—
343C24—1182no—
344C24—2361no—
345C24—2361no—
346C24C22×D5911yescharacteristic
347C2×D4—594no—
348C2×D4—1182no—
349C2×D4—1182no—
350C2×D4—1182no—
351C2×D4—1182no—
352C2×D4—1182no—
353C2×D4—1182no—
354C2×D4—1182no—
355C2×D4—1182no—
356C2×D4—1182no—
357C2×D4—1182no—
358C2×D4—1182no—
359C2×D4—1182no—
360C2×D4—1182no—
361C2×D4—1182no—
362C2×D4—1182no—
363C2×D4—2361no—
364C2×D4—2361no—
365C2×D4—2361no—
366C2×D4—2361no—
367C2×D4—2361no—
368C22×C4—591no—
369C22×C4—591no—
370C22×C4—591no—
371C22×C4—591no—
372C22×C4—1182no—
373C22×C4—1182no—
374C22×C4—1182no—
375C22×C4—1182no—
376C22×C4—1182no—
377C22×C4—1182no—
378C22×C4—2361no—
379C22×C4—2361no—
380C22×C4—2361no—
381C22×C4C22×D5911yescharacteristic
382C22×C4C22×D5911yescharacteristic
383C22×C4C22×D5911yescharacteristic
384C22×C4C22×D5911yescharacteristic
385C22×C4C22×D5911yescharacteristic
386C22×C4C22×D5911yescharacteristic
387C4⋊C4—22no—
388C4⋊C4—1182no—
389C4⋊C4—1182no—
390C4⋊C4—2361no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—594no—
394C22⋊C4—1182no—
395C22⋊C4—1182no—
396C22⋊C4—1182no—
397C22⋊C4—1182no—
398C22⋊C4—1182no—
399C22⋊C4—1182no—
400C22⋊C4—1182no—
401C22⋊C4—1182no—
402C22⋊C4—1182no—
403C22⋊C4—1182no—
404C22⋊C4—2361no—
405C22⋊C4D23614yescomplemented
406C42—22no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—592no—
414C23—592no—
415C23—592no—
416C23—592no—
417C23—592no—
418C23—1188no—
419C23—1181no—
420C23—1181no—
421C23—1181no—
422C23—1181no—
423C23—1181no—
424C23—1181no—
425C23—1181no—
426C23—1181no—
427C23—1181no—
428C23—1181no—
429C23—1181no—
430C23—1181no—
431C23—1181no—
432C23—1181no—
433C23—1181no—
434C23—1181no—
435C23—1181no—
436C23—1181no—
437C23—1181no—
438C23—1181no—
439C23—1181no—
440C23—1181no—
441C23—1181no—
442C23—2364no—
443C23—2364no—
444C23—2364no—
445C23—2364no—
446C23—2364no—
447C23—2364no—
448C23C2×D23612yes—
449C23C23×D5911yescharacteristic
450D4—1188no—
451D4—2364no—
452D4—2364no—
453D4—2364no—
454D4—2364no—
455D4—2364no—
456D4—2364no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—592no—
472C2×C4—1181no—
473C2×C4—1181no—
474C2×C4—1181no—
475C2×C4—1181no—
476C2×C4—1181no—
477C2×C4—1181no—
478C2×C4—1181no—
479C2×C4—1181no—
480C2×C4—1181no—
481C2×C4—1181no—
482C2×C4—1181no—
483C2×C4—2364no—
484C2×C4—2364no—
485C2×C4—2364no—
486C2×C4C2×D23612yes—
487C2×C4C2×D23612yes—
488C2×C4D4×D5912yes—
489C2×C4D4×D5912yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—594no—
498C22—1182no—
499C22—1182no—
500C22—1182no—
501C22—1182no—
502C22—1182no—
503C22—1182no—
504C22—1182no—
505C22—1182no—
506C22—1182no—
507C22—1182no—
508C22—1182no—
509C22—1182no—
510C22—23616no—
511C22—2361no—
512C22—2361no—
513C22—2361no—
514C22—2361no—
515C22—2361no—
516C22—2361no—
517C22—2361no—
518C22—2361no—
519C22—2361no—
520C22—2361no—
521C22—2361no—
522C22—2361no—
523C22—2361no—
524C22—2361no—
525C22—2361no—
526C22C2×D4×D5911yescharacteristic
527C22C2×D4×D5911yescharacteristic
528C22C22×D23611yescharacteristic
529C22#41×D5911yescharacteristic
530C22#41×D5911yescharacteristic
531C22#1427377311yescharacteristic
532C22#1427377311yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—22no—
537C4—41no—
538C4—41no—
539C4—1182no—
540C4—2361no—
541C4—2361no—
542C4—2361no—
543C2—42no—
544C2—1184no—
545C2—4721no—
546C2—2362no—
547C2—2362no—
548C2#121×D5911yescharacteristic
549C2#1683791411yescharacteristic
550C2#1683799111yescharacteristic
551C2D4×D23611yescharacteristic
552C2D4×D23611yescharacteristic
553C2#1683804411yescharacteristic
554C2#1683804511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#388C2
hypercenter#388D59
hypocenterC59#2424
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#14273702C2semidirect
2. C2×#14273700C2semidirect
3. C2×#14273697C2semidirect
4. C2×#14273697C2semidirect
5. C2×C4×D236C2semidirect
6. C2×C22⋊C4×D59C2semidirect
7. #16837324C2semidirect
8. #16837318C2semidirect
9. #16837318C2semidirect
10. #16837312C2semidirect
11. #16837304C2semidirect
12. #16837280C2semidirect
13. #16837280C2semidirect
14. #16837276C2semidirect
15. C59×#388C2semidirect
21. C22×D236C22semidirect
26. C22×C4×D59C22semidirect
32. C2×C4⋊Dic59C22semidirect
33. C2×C4⋊Dic59C22semidirect
34. C2×Dic59⋊C4C22semidirect
42. C2×(C2×D59)⋊C4C22semidirect
43. C2×(C2×D59)⋊C4C22semidirect
44. C2×(C2×D59)⋊C4C22semidirect
45. C2×(C2×D59)⋊C4C22semidirect
46. C2×(C2×D59)⋊C4C22semidirect
48. C59⋊#95C22semidirect
49. C59⋊#95C22semidirect
50. C2×C4⋊C4×C59C22semidirect
54. C2×C42×C59C22semidirect
55. #95×C59C22semidirect
56. #95×C59C22semidirect
99. C2×D236D4semidirect
112. C22⋊C4×C59D4semidirect
125. (C2×D59)⋊C4D4semidirect
254. C2×D59#121semidirect
289. #388D59semidirect
293. C59#2424semidirect
313. C2×C4⋊C4C2×D59semidirect
330. C2×C42C2×D59semidirect
333. #95C2×D59semidirect
334. #95C2×D59semidirect
405. C22⋊C4D236semidirect