Finite Group Databasebeta

← #28606867

Subgroups — #28606867

Order 15104.

1042 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837474C211yesmaximal, characteristic
2C2×#16837442C211yesmaximal, characteristic, complemented
3C22×#14273660C211yesmaximal, characteristic, complemented
4#21427025C211yesmaximal, characteristic
5#21424864C211yesmaximal, characteristic, complemented
6#21424852C211yesmaximal, characteristic, complemented
7#21424293C211yesmaximal, characteristic, complemented
8#21424289C211yesmaximal, characteristic, complemented
9#21424284C211yesmaximal, characteristic, complemented
10#21424283C211yesmaximal, characteristic, complemented
11#21424262C211yesmaximal, characteristic, complemented
12#21424127C211yesmaximal, characteristic, complemented
13#21424119C211yesmaximal, characteristic, complemented
14#21423994C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C59C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18C2×#14273686C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20#16837474C418yescomplemented
21#16837442—24no—
22C2×#14273660—24no—
23C2×#14273660C2211yescharacteristic
24C2×#14273660C2211yescharacteristic
25C2×#14273660C2211yescharacteristic
26C2×#14273660C2211yescharacteristic
27C2×#14273660C2211yescharacteristic
28C2×#14273660C2211yescharacteristic
29C2×#14273658C2211yescharacteristic
30C2×#14273658C2211yescharacteristic
31C2×#14273658C2211yescharacteristic
32C2×#14273658C2211yescharacteristic
33C2×C4⋊(C59⋊C8)C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36C2×#14273638C2211yescharacteristic
37#16837295—21no—
38#16837288—21no—
39#16837282—21no—
40#16837268C2211yescharacteristic
41#16837262C2211yescharacteristic
42#16837262C2211yescharacteristic
43C4×C4⋊Dic59C2211yescharacteristic
44C22⋊C4×Dic59—21no—
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51C2×C4×D4×C59—21no—
52C2×C4×D4×C59C2211yescharacteristic
53C22×C4⋊C4×C59C2211yescharacteristic
54C22×C4⋊C4×C59C2211yescharacteristic
55C59×#389—21no—
56C59×#385—21no—
57C59×#385—21no—
58C59×#384C2211yescharacteristic
59C59×#380C2211yescharacteristic
60C59×#380C2211yescharacteristic
61C4×C4⋊C4×C59C2211yescharacteristic
62C23×Dic59—21no—
63C2×#11745664—22no—
64C2×#11745664—22no—
65C2×#11745664C2×C414yescomplemented
66C22×C59⋊C8—22no—
67C22×C59⋊C8—22no—
68C22×C59⋊C8C2×C414yescomplemented
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73#14273686—22no—
74#14273686—41no—
75C2×C4⋊Dic59—22no—
76C2×C4⋊Dic59—21no—
77C2×C4⋊Dic59—41no—
78C2×C4⋊Dic59C2311yescharacteristic
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C4⋊Dic59C2311yescharacteristic
81C2×C4⋊Dic59C2311yescharacteristic
82C2×C22⋊Dic59—21no—
83C2×C22⋊Dic59—21no—
84C2×C22⋊Dic59—21no—
85C2×C4×Dic59—21no—
86C2×C4×Dic59—21no—
87#14273660—22no—
88#14273660—22no—
89#14273660—22no—
90#14273660—22no—
91#14273660—41no—
92#14273660D414yescomplemented
93#14273658—22no—
94#14273658—22no—
95#14273658—22no—
96#14273658—41no—
97C4⋊(C59⋊C8)C2×C414yescomplemented
98C22⋊(C59⋊C8)C2×C414yescomplemented
99C22⋊(C59⋊C8)C2×C414yescomplemented
100#14273638C2×C414yescomplemented
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C22×D4×C59D411yescharacteristic
107C23×C4×C59—21no—
108C23×C4×C59—21no—
109C23×C4×C59C2311yescharacteristic
110C23×C4×C59C2311yescharacteristic
111C4×D4×C59—44no—
112C4×D4×C59C2×C414yes—
113C4×D4×C59Q814yes—
114C2×C4⋊C4×C59—22no—
115C2×C4⋊C4×C59—22no—
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59—21no—
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59—21no—
120C2×C4⋊C4×C59—41no—
121C2×C4⋊C4×C59—41no—
122C2×C4⋊C4×C59D411yescharacteristic
123C2×C4⋊C4×C59C2311yescharacteristic
124C2×C4⋊C4×C59C2311yescharacteristic
125C2×C4⋊C4×C59C2311yescharacteristic
126C2×C4⋊C4×C59C2311yescharacteristic
127C2×C22⋊C4×C59—21no—
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59D411yescharacteristic
130C2×C22⋊C4×C59D411yescharacteristic
131C2×C42×C59—21no—
132C2×C42×C59C2311yescharacteristic
133#95×C59—21no—
134#95×C59—21no—
135#95×C59—21no—
136C24×C59C2×D411yescharacteristic
137C24×C59C2×D411yescharacteristic
138C2×D4×C59—22no—
139C2×D4×C59—22no—
140C2×D4×C59C4⋊C414yes—
141C22×C4×C59—21no—
142C22×C4×C59—21no—
143C22×C4×C59—21no—
144C22×C4×C59—21no—
145C22×C4×C59—21no—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—42no—
154C22×C4×C59—42no—
155C22×C4×C59—42no—
156C22×C4×C59—42no—
157C22×C4×C59—81no—
158C22×C4×C59—81no—
159C22×C4×C59C22×C412yes—
160C22×C4×C59C22×C412yes—
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59C2×Q812yes—
166C22×C4×C59C2×Q812yes—
167C22×C4×C59C2411yescharacteristic
168C22×Dic59—21no—
169C22×Dic59—21no—
170C22×Dic59—21no—
171C22×Dic59—21no—
172C22×Dic59—42no—
173C22×Dic59—42no—
174C22×Dic59—81no—
175C4⋊C4×C59—21no—
176C4⋊C4×C59—21no—
177C4⋊C4×C59—21no—
178C4⋊C4×C59—21no—
179C4⋊C4×C59—21no—
180C4⋊C4×C59—21no—
181C4⋊C4×C59—21no—
182C4⋊C4×C59—42no—
183C4⋊C4×C59—42no—
184C4⋊C4×C59—42no—
185C4⋊C4×C59—81no—
186C4⋊C4×C59C4⋊C414yes—
187C4⋊C4×C59C2×D412yes—
188C22⋊C4×C59—42no—
189C22⋊C4×C59—42no—
190C22⋊C4×C59C4⋊C414yes—
191C22⋊C4×C59C4⋊C414yes—
192C42×C59—42no—
193C42×C59C22×C412yes—
194C42×C59C2×Q812yes—
195C22⋊Dic59—42no—
196C22⋊Dic59—42no—
197C22⋊Dic59—81no—
198C4⋊Dic59—21no—
199C4⋊Dic59—21no—
200C4⋊Dic59—21no—
201C4⋊Dic59—21no—
202C4⋊Dic59—21no—
203C4⋊Dic59—21no—
204C4⋊Dic59—21no—
205C4⋊Dic59—42no—
206C4⋊Dic59C2×D412yes—
207C4×Dic59—42no—
208C4×Dic59—81no—
209#11745664—28no—
210C2×C59⋊C8—21no—
211C2×C59⋊C8—21no—
212C2×C59⋊C8—21no—
213C2×C59⋊C8—21no—
214C2×C59⋊C8—21no—
215C2×C59⋊C8—21no—
216C2×C59⋊C8—28no—
217C2×C59⋊C8C22×C412yes—
218C2×C59⋊C8C22×C412yes—
219C2×C59⋊C8C22×C412yes—
220C2×C59⋊C8C22×C412yes—
221C2×C59⋊C8C2×D412yes—
222C2×C59⋊C8#4112yes—
223C23×C59—21no—
224C23×C59—21no—
225C23×C59—21no—
226C23×C59—21no—
227C23×C59—21no—
228C23×C59—21no—
229C23×C59—21no—
230C23×C59—21no—
231C23×C59—21no—
232C23×C59—21no—
233C23×C59C2×C4⋊C412yes—
234C23×C59C2×C4⋊C412yes—
235C23×C59AGL(1,ℤ/8)12yes—
236C23×C59#13712yes—
237C23×C59C22×D411yescharacteristic
238D4×C59—28no—
239C2×C4×C59—21no—
240C2×C4×C59—21no—
241C2×C4×C59—21no—
242C2×C4×C59—21no—
243C2×C4×C59—21no—
244C2×C4×C59—21no—
245C2×C4×C59—21no—
246C2×C4×C59—21no—
247C2×C4×C59—22no—
248C2×C4×C59—22no—
249C2×C4×C59—22no—
250C2×C4×C59—22no—
251C2×C4×C59—22no—
252C2×C4×C59—22no—
253C2×C4×C59—22no—
254C2×C4×C59—22no—
255C2×C4×C59—22no—
256C2×C4×C59—41no—
257C2×C4×C59—41no—
258C2×C4×C59—41no—
259C2×C4×C59—41no—
260C2×C4×C59—41no—
261C2×C4×C59—41no—
262C2×C4×C59—41no—
263C2×C4×C59—41no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—41no—
267C2×C4×C59—84no—
268C2×C4×C59—84no—
269C2×C4×C59C2×C4⋊C412yes—
270C2×C4×C59C2×C4⋊C412yes—
271C2×C4×C59C2×C4⋊C412yes—
272C2×C4×C59C2×C4⋊C412yes—
273C2×C4×C59C23×C411yescharacteristic
274C2×C4×C59C22×D411yescharacteristic
275C2×C4×C59C22×Q811yescharacteristic
276C2×C4×C59C2×#4111yescharacteristic
277C2×C4×C59H(5,𝔽2)11yescharacteristic
278C2×C4×C592−1+411yescharacteristic
279C2×Dic59—22no—
280C2×Dic59—41no—
281C2×Dic59—41no—
282C2×Dic59—41no—
283C2×Dic59—41no—
284C2×Dic59—41no—
285C2×Dic59—41no—
286C2×Dic59—41no—
287C2×Dic59—41no—
288C2×Dic59—41no—
289C2×Dic59—41no—
290C2×Dic59—41no—
291C2×Dic59—84no—
292C59⋊C8—22no—
293C59⋊C8—22no—
294C59⋊C8—22no—
295C59⋊C8C4×D414yescomplemented
296#22661—591nomaximal, Sylow
297C22×C59—22no—
298C22×C59—22no—
299C22×C59—22no—
300C22×C59—22no—
301C22×C59—22no—
302C22×C59—22no—
303C22×C59—22no—
304C22×C59—22no—
305C22×C59—22no—
306C22×C59—41no—
307C22×C59—41no—
308C22×C59—41no—
309C22×C59—41no—
310C22×C59#42814yescomplemented
311C22×C59C22×C4⋊C411yescharacteristic
312C22×C59D4211yescharacteristic
313C22×C59#54711yescharacteristic
314C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
315C22×C59C2×#13711yescharacteristic
316C22×C59#57611yescharacteristic
317C22×C59#57811yescharacteristic
318C4×C59—22no—
319C4×C59—22no—
320C4×C59—22no—
321C4×C59—22no—
322C4×C59—42no—
323C4×C59—81no—
324C4×C59—81no—
325C4×C59—81no—
326C4×C59C2×C4×D411yescharacteristic
327C4×C59#52011yescharacteristic
328C4×C59D4×Q811yescharacteristic
329C4×C59#55411yescharacteristic
330Dic59—42no—
331Dic59—81no—
332Dic59—81no—
333Dic59—81no—
334C2×#435—591no—
335C2×#428—591no—
336C22×#107—591no—
337#2352—591no—
338D4×C4⋊C4D5911yescharacteristic
339#1949—591no—
340#1947—591no—
341#1854—591no—
342#1853—591no—
343#1852—591no—
344#1852—591no—
345#1847—591no—
346#1809—591no—
347#1807—591no—
348#1776—591no—
349C2×C59—24no—
350C2×C59—42no—
351C2×C59D4×C4⋊C411yescharacteristic
352C2×C59C2×#42811yescharacteristic
353C2×C59#291311yescharacteristic
354C2×C59#326411yescharacteristic
355C2×C59#327011yescharacteristic
356C2×C59#334311yescharacteristic
357C2×C59#334611yescharacteristic
358C22×M16—591no—
359C23×C8—591no—
360C2×C4×D4—21no—
361C2×C4×D4C2×D5911yescharacteristic
362C2×#117—591no—
363C22×C4⋊C4—591no—
364C22×C4⋊C4C2×D5911yescharacteristic
365C22×C4⋊C4C2×D5911yescharacteristic
366#435—598no—
367#428—1184no—
368C2×#107—591no—
369C2×#107—591no—
370C2×#107—591no—
371C2×#107—591no—
372C2×#107—591no—
373C2×#107—591no—
374C2×#107—1184no—
375C2×#106—591no—
376C2×#106—591no—
377C2×#106—591no—
378C2×#106—591no—
379C2×C4⋊C8—591no—
380C2×C22⋊C8—591no—
381C2×C22⋊C8—591no—
382C2×#97—591no—
383#389—21no—
384#388—1181no—
385#387—1181no—
386#386—1181no—
387#385—21no—
388#385—21no—
389#384C2×D5911yescharacteristic
390#382—591no—
391#380—591no—
392#380—591no—
393#380C2×D5911yescharacteristic
394#380C2×D5911yescharacteristic
395C4×C4⋊C4—591no—
396C4×C4⋊C4C2×D5911yescharacteristic
397C4×C22⋊C4—1181no—
398#340—591no—
399#340—591no—
400#340—591no—
401#340—591no—
402#340—591no—
403#340—591no—
404C59#2266111yescharacteristic, complemented, Sylow
405C22×D4C22⋊D5911yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—1181no—
409C23×C4C22×D5911yescharacteristic
410C23×C4C22×D5911yescharacteristic
411C2×M16—594no—
412C2×M16—1182no—
413C2×M16—1182no—
414C22×C8—591no—
415C22×C8—594no—
416C22×C8—591no—
417C22×C8—591no—
418C22×C8—591no—
419C22×C8—1182no—
420C22×C8—1182no—
421C4×D4—44no—
422C4×D4Dic11814yes—
423C4×D4C4×D5914yes—
424#117—1182no—
425#117—2361no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—41no—
433C2×C4⋊C4—41no—
434C2×C4⋊C4—591no—
435C2×C4⋊C4—591no—
436C2×C4⋊C4—591no—
437C2×C4⋊C4—591no—
438C2×C4⋊C4—1182no—
439C2×C4⋊C4—1181no—
440C2×C4⋊C4—2361no—
441C2×C4⋊C4C22⋊D5911yescharacteristic
442C2×C4⋊C4C22×D5911yescharacteristic
443C2×C4⋊C4C22×D5911yescharacteristic
444C2×C4⋊C4C22×D5911yescharacteristic
445C2×C4⋊C4C22×D5911yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—1181no—
449C2×C22⋊C4—1181no—
450C2×C22⋊C4—1181no—
451C2×C22⋊C4C22⋊D5911yescharacteristic
452C2×C22⋊C4C22⋊D5911yescharacteristic
453C2×C42—21no—
454C2×C42—1181no—
455C2×C42—1181no—
456C2×C42C22×D5911yescharacteristic
457#107—594no—
458#107—1182no—
459#107—1182no—
460#107—1182no—
461#107—1182no—
462#107—2361no—
463#106—1182no—
464#106—1182no—
465#106—1182no—
466#106—2361no—
467C4⋊C8—594no—
468C22⋊C8—594no—
469C22⋊C8—594no—
470#97—594no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—1181no—
475#95—1181no—
476#95—1181no—
477#95—1181no—
478#95—1181no—
479C24C2×C22⋊D5911yescharacteristic
480C24C2×C22⋊D5911yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4Dic59⋊C414yes—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4—1181no—
503C22×C4—1181no—
504C22×C4—1181no—
505C22×C4—1181no—
506C22×C4—4721no—
507C22×C4—2362no—
508C22×C4—2362no—
509C22×C4C2×Dic11812yes—
510C22×C4C2×Dic11812yes—
511C22×C4C2×C4×D5912yes—
512C22×C4C2×C4×D5912yes—
513C22×C4C2×C22⋊D5911yescharacteristic
514C22×C4C2×C22⋊D5911yescharacteristic
515C22×C4C2×C22⋊D5911yescharacteristic
516C22×C4C2×C22⋊D5911yescharacteristic
517C22×C4C23×D5911yescharacteristic
518M16—1188no—
519C2×C8—592no—
520C2×C8—592no—
521C2×C8—592no—
522C2×C8—592no—
523C2×C8—592no—
524C2×C8—592no—
525C2×C8—1188no—
526C2×C8—1181no—
527C2×C8—1181no—
528C2×C8—1181no—
529C2×C8—1181no—
530C2×C8—1181no—
531C2×C8—1181no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—81no—
543C4⋊C4—592no—
544C4⋊C4—1181no—
545C4⋊C4—1181no—
546C4⋊C4—1181no—
547C4⋊C4—1181no—
548C4⋊C4—1181no—
549C4⋊C4—1181no—
550C4⋊C4—1181no—
551C4⋊C4—2362no—
552C4⋊C4Dic59⋊C414yes—
553C4⋊C4D4×D5912yes—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—4721no—
557C22⋊C4—2362no—
558C22⋊C4—2362no—
559C22⋊C4Dic59⋊C414yes—
560C22⋊C4Dic59⋊C414yes—
561C42—42no—
562C42—4721no—
563C42—2362no—
564C42C2×Dic11812yes—
565C42C2×C4×D5912yes—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23C2×Dic59⋊C412yes—
577C23C2×Dic59⋊C412yes—
578C23#1427375312yes—
579C23#1427375812yes—
580C23C22×C22⋊D5911yescharacteristic
581D4—28no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—84no—
611C2×C4—84no—
612C2×C4—1182no—
613C2×C4—4724no—
614C2×C4—2361no—
615C2×C4—2361no—
616C2×C4—2361no—
617C2×C4—2361no—
618C2×C4—2361no—
619C2×C4—2361no—
620C2×C4—2361no—
621C2×C4—2361no—
622C2×C4—2361no—
623C2×C4—2361no—
624C2×C4—2361no—
625C2×C4C2×Dic59⋊C412yes—
626C2×C4C2×Dic59⋊C412yes—
627C2×C4C2×Dic59⋊C412yes—
628C2×C4C2×Dic59⋊C412yes—
629C2×C4C22×C4×D5911yescharacteristic
630C2×C4C2×D4×D5911yescharacteristic
631C2×C4C22×Dic11811yescharacteristic
632C2×C4#41×D5911yescharacteristic
633C2×C4#1427377211yescharacteristic
634C2×C4#1427377411yescharacteristic
635C8—594no—
636C8—1182no—
637C8—1182no—
638C8—1182no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22#1683744214yescomplemented
653C22C22×Dic59⋊C411yescharacteristic
654C22D4×C22⋊D5911yescharacteristic
655C22#1683805111yescharacteristic
656C22C2×#1427375311yescharacteristic
657C22C2×#1427375811yescharacteristic
658C22#1683820511yescharacteristic
659C22#1683821711yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—42no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4—4721no—
669C4—4721no—
670C4—4721no—
671C4—2362no—
672C4C4×D4×D5911yescharacteristic
673C4#1683788111yescharacteristic
674C4D4×Dic11811yescharacteristic
675C4#1683811111yescharacteristic
676C2—24no—
677C2—42no—
678C2D4×Dic59⋊C411yescharacteristic
679C2C2×#1683744211yescharacteristic
680C2#2143269411yescharacteristic
681C2#2143557211yescharacteristic
682C2#2143566711yescharacteristic
683C2#2143653011yescharacteristic
684C2#2143657511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingD4×C4⋊C4×C59C2
socleC23×C59C22×D4
prime radicalC22×D4×C59D4
cosocleC22×C4×C59C24
hypercenterD4×C4⋊C4D59
hypocenterC59#22661
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16837442C2semidirect
3. C22×#14273660C2semidirect
5. #21424864C2semidirect
6. #21424852C2semidirect
7. #21424293C2semidirect
8. #21424289C2semidirect
9. #21424284C2semidirect
10. #21424283C2semidirect
11. #21424262C2semidirect
12. #21424127C2semidirect
13. #21424119C2semidirect
14. #21423994C2semidirect
20. #16837474C4semidirect
65. C2×#11745664C2×C4semidirect
68. C22×C59⋊C8C2×C4semidirect
92. #14273660D4semidirect
97. C4⋊(C59⋊C8)C2×C4semidirect
98. C22⋊(C59⋊C8)C2×C4semidirect
99. C22⋊(C59⋊C8)C2×C4semidirect
100. #14273638C2×C4semidirect
295. C59⋊C8C4×D4semidirect
310. C22×C59#428semidirect
404. C59#22661semidirect
652. C22#16837442semidirect

Maximal subgroups

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

subgroupindex
C2×#168374742
C2×#168374422
C22×#142736602
#214270252
#214248642
#214248522
#214242932
#214242892
#214242842
#214242832
#214242622
#214241272
#214241192
#214239942
D4×C4⋊C4×C592
#2266159