Finite Group Databasebeta

← #28598657

Subgroups — #28598657

Order 15104.

1078 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838023C211yesmaximal, characteristic
2C2×#16837429C211yesmaximal, characteristic, complemented
3#21425048C211yesmaximal, characteristic, complemented
4#21425044C211yesmaximal, characteristic, complemented
5#21425028C211yesmaximal, characteristic, complemented
6#21425028C211yesmaximal, characteristic, complemented
7#21424532C211yesmaximal, characteristic
8#21424527C211yesmaximal, characteristic, complemented
9#21424522C211yesmaximal, characteristic
10#21424517C211yesmaximal, characteristic, complemented
11#21424108C211yesmaximal, characteristic, complemented
12#21424103C211yesmaximal, characteristic, complemented
13#21424098C211yesmaximal, characteristic, complemented
14#21424093C211yesmaximal, characteristic, complemented
15C59×#2314C211yesmaximal, characteristic, complemented
16C22×#11745664C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18#16838023—24no—
19#16838023C418yescomplemented
20C2×#14273727C2211yescharacteristic
21C2×#14273722—21no—
22C2×#14273715C2211yescharacteristic
23C2×#14273713—21no—
24C2×#14273709—21no—
25C2×#14273706C2211yescharacteristic
26C2×#14273705—21no—
27C2×#14273701C2211yescharacteristic
28C2×C4×Dic118C2211yescharacteristic
29C2×C4×D236C2211yescharacteristic
30#16837429—24no—
31C2×C4⋊(C59⋊C8)C2211yescharacteristic
32C2×C4⋊(C59⋊C8)C2211yescharacteristic
33C2×C4⋊(C59⋊C8)C2211yescharacteristic
34C2×C4⋊(C59⋊C8)C2211yescharacteristic
35C2×#14273650C2211yescharacteristic
36C2×#14273650C2211yescharacteristic
37C2×#14273650C2211yescharacteristic
38C2×#14273650C2211yescharacteristic
39C2×#14273647C2211yescharacteristic
40C2×#14273647C2211yescharacteristic
41C2×#14273647C2211yescharacteristic
42C2×#14273647C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51C2×#117×C59C2211yescharacteristic
52C59×#388—21no—
53C59×#388—21no—
54C59×#387—21no—
55C59×#387—21no—
56C59×#384C2211yescharacteristic
57C59×#382C2211yescharacteristic
58C59×#380C2211yescharacteristic
59C59×#380C2211yescharacteristic
60C4×C4⋊C4×C59C2211yescharacteristic
61C4×C4⋊C4×C59C2211yescharacteristic
62C22×Dic118—21no—
63C22×Dic118C2311yescharacteristic
64C22×D236C2311yescharacteristic
65C22×C22⋊D59—21no—
66C22×C4×D59—21no—
67C2×#11745664—22no—
68C2×#11745664—41no—
69C2×#11745664—41no—
70C22×C59⋊C8—22no—
71C22×C59⋊C8—41no—
72C22×C59⋊C8—41no—
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75C22×C59⋊C8C2311yescharacteristic
76C22×C59⋊C8C2311yescharacteristic
77#14273727—22no—
78#14273727C2×C414yes—
79#14273722—28no—
80#14273715—22no—
81#14273715C2×C414yes—
82#14273713—28no—
83#14273709—28no—
84#14273706—22no—
85#14273706C2×C414yes—
86#14273705—28no—
87#14273701—22no—
88#14273701C2×C414yes—
89C4×Dic118—22no—
90C4×Dic118C2×C414yes—
91C4×D236—22no—
92C4×D236C2×C414yes—
93C2×C4⋊Dic59—21no—
94C2×C4⋊Dic59C2311yescharacteristic
95C2×C4⋊Dic59C2311yescharacteristic
96C2×Dic59⋊C4—21no—
97C2×Dic59⋊C4—21no—
98C2×C22⋊Dic59—21no—
99C2×(C2×D59)⋊C4—21no—
100C2×(C2×D59)⋊C4—21no—
101C2×(C2×D59)⋊C4—21no—
102C2×(C2×D59)⋊C4—21no—
103C2×C4×Dic59—21no—
104C4⋊(C59⋊C8)—22no—
105C4⋊(C59⋊C8)—22no—
106C4⋊(C59⋊C8)—22no—
107C4⋊(C59⋊C8)—22no—
108#14273650—41no—
109#14273650—41no—
110#14273650—41no—
111#14273650—41no—
112#14273647—41no—
113#14273647—41no—
114#14273647—41no—
115#14273647—41no—
116C23×C4×C59C2311yescharacteristic
117#117×C59C2×C414yes—
118#117×C59D414yes—
119C2×C4⋊C4×C59—21no—
120C2×C4⋊C4×C59—21no—
121C2×C4⋊C4×C59D411yescharacteristic
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×C59—21no—
133C2×C42×C59C2311yescharacteristic
134C2×C42×C59C2311yescharacteristic
135#95×C59—21no—
136#95×C59—21no—
137#95×C59—21no—
138#95×C59—21no—
139#95×C59—21no—
140#95×C59—21no—
141C24×C59C2×D411yescharacteristic
142C23×D59—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×C59C22×C412yes—
152C22×C4×C59C2×D411yescharacteristic
153C22×C4×C59C2×D411yescharacteristic
154C22×C4×C59C2×D411yescharacteristic
155C22×C4×C59C2×D411yescharacteristic
156C22×C4×C59C2×D411yescharacteristic
157C22×C4×C59C2×D412yes—
158C22×C4×C59C2411yescharacteristic
159C2×C22⋊D59—24no—
160C2×C22⋊D59—81no—
161C2×C22⋊D59—81no—
162C22×Dic59—21no—
163C22×Dic59—21no—
164C22×Dic59—21no—
165C2×D236—21no—
166C2×D236—21no—
167C2×D236—21no—
168C2×D236—21no—
169C2×D236—21no—
170C2×D236C22×C412yes—
171C2×C4×D59—24no—
172C2×C4×D59—81no—
173C2×C4×D59—81no—
174C2×Dic118—21no—
175C2×Dic118—21no—
176C2×Dic118—21no—
177C2×Dic118—21no—
178C2×Dic118—21no—
179C2×Dic118—24no—
180C2×Dic118—81no—
181C2×Dic118—81no—
182C2×Dic118C22×C412yes—
183C4⋊C4×C59—21no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—81no—
192C4⋊C4×C59—81no—
193C4⋊C4×C59C22⋊C414yes—
194C4⋊C4×C59C22⋊C414yes—
195C22⋊C4×C59—81no—
196C22⋊C4×C59—81no—
197C22⋊C4×C59C22⋊C414yes—
198C22⋊C4×C59C22⋊C414yes—
199C42×C59—81no—
200C42×C59—81no—
201C42×C59C22×C412yes—
202C42×C59C22×C412yes—
203C42×C59C2×D412yes—
204C42×C59C2×D412yes—
205C22⋊Dic59—24no—
206(C2×D59)⋊C4—24no—
207(C2×D59)⋊C4—24no—
208(C2×D59)⋊C4—24no—
209(C2×D59)⋊C4—24no—
210C4⋊Dic59—24no—
211C4⋊Dic59—21no—
212C4⋊Dic59—21no—
213C4⋊Dic59C22×C412yes—
214C4⋊Dic59C22×C412yes—
215Dic59⋊C4—24no—
216Dic59⋊C4—24no—
217C4×Dic59—24no—
218#11745664—44no—
219C2×C59⋊C8—21no—
220C2×C59⋊C8—21no—
221C2×C59⋊C8—21no—
222C2×C59⋊C8—21no—
223C2×C59⋊C8—21no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—44no—
232C23×C59—21no—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59C2×C22⋊C412yes—
239C23×C59C22×D411yescharacteristic
240C22×D59—22no—
241C22×D59—41no—
242C22×D59—41no—
243C22×D59—41no—
244C22×D59—41no—
245C22×D59—41no—
246C22×D59—41no—
247C2×C4×C59—21no—
248C2×C4×C59—21no—
249C2×C4×C59—21no—
250C2×C4×C59—21no—
251C2×C4×C59—21no—
252C2×C4×C59—21no—
253C2×C4×C59—21no—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
256C2×C4×C59—21no—
257C2×C4×C59—22no—
258C2×C4×C59—22no—
259C2×C4×C59—22no—
260C2×C4×C59—22no—
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—41no—
268C2×C4×C59—41no—
269C2×C4×C59—41no—
270C2×C4×C59—41no—
271C2×C4×C59—41no—
272C2×C4×C59—41no—
273C2×C4×C59C2×C22⋊C412yes—
274C2×C4×C59C2×C22⋊C412yes—
275C2×C4×C59C2×C22⋊C412yes—
276C2×C4×C59C2×C22⋊C412yes—
277C2×C4×C59C2×C22⋊C412yes—
278C2×C4×C59C23×C411yescharacteristic
279C2×C4×C59C22×D411yescharacteristic
280C2×C4×C59H(5,𝔽2)11yescharacteristic
281C2×C4×C59H(5,𝔽2)11yescharacteristic
282C2×C4×C592−1+411yescharacteristic
283C2×C4×C592−1+411yescharacteristic
284C22⋊D59—84no—
285C2×Dic59—22no—
286C2×Dic59—22no—
287C2×Dic59—22no—
288C2×Dic59—41no—
289C2×Dic59—41no—
290C2×Dic59—41no—
291C2×Dic59—41no—
292C2×Dic59—41no—
293C2×Dic59—41no—
294D236—22no—
295D236—22no—
296D236—41no—
297D236—41no—
298C4×D59—84no—
299Dic118—22no—
300Dic118—22no—
301Dic118—41no—
302Dic118—41no—
303Dic118—84no—
304C59⋊C8—41no—
305C59⋊C8—41no—
306C59⋊C8—41no—
307C59⋊C8—41no—
308#21896—591nomaximal, Sylow
309C22×C59—22no—
310C22×C59—22no—
311C22×C59—22no—
312C22×C59—41no—
313C22×C59—41no—
314C22×C59—41no—
315C22×C59—41no—
316C22×C59C22×C22⋊C411yescharacteristic
317C22×C59#53711yescharacteristic
318C22×C59#53711yescharacteristic
319C22×C59#57611yescharacteristic
320C22×C59#57711yescharacteristic
321C22×C59#57711yescharacteristic
322C22×C59#57811yescharacteristic
323C2×D59—42no—
324C2×D59—42no—
325C2×D59—42no—
326C2×D59—81no—
327C2×D59—81no—
328C2×D59—81no—
329C2×D59—81no—
330C4×C59—22no—
331C4×C59—22no—
332C4×C59—22no—
333C4×C59—22no—
334C4×C59—22no—
335C4×C59—81no—
336C4×C59—81no—
337C4×C59—81no—
338C4×C59—81no—
339C4×C59#52011yescharacteristic
340C4×C59#52011yescharacteristic
341C4×C59#53511yescharacteristic
342C4×C59#53611yescharacteristic
343Dic59—42no—
344Dic59—42no—
345Dic59—42no—
346C2×#542—591no—
347C2×#424—591no—
348#2314D5911yescharacteristic, complemented
349#1988—591no—
350#1987—591no—
351#1983—591no—
352#1983—591no—
353#1895—591no—
354#1894—591no—
355#1893—591no—
356#1892—591no—
357#1805—591no—
358#1804—591no—
359#1803—591no—
360#1802—591no—
361C2×C59—42no—
362C2×C59#231111yescharacteristic
363C2×C59#289711yescharacteristic
364C2×C59#289811yescharacteristic
365C2×C59#325711yescharacteristic
366C2×C59#325811yescharacteristic
367C2×C59#326211yescharacteristic
368C2×C59#326311yescharacteristic
369D59—82no—
370C22×M16—591no—
371C23×C8—591no—
372#542—598no—
373#542—1184no—
374C2×C4⋊Q8—591no—
375C2×#126—1181no—
376C2×#124—591no—
377C2×#124—1181no—
378C2×#123—1181no—
379C2×C22⋊Q8—591no—
380C2×C22⋊Q8—1181no—
381C2×#121—591no—
382C2×C4×Q8—591no—
383C2×C4×D4—591no—
384C2×#117C2×D5911yescharacteristic
385#424—1184no—
386C2×C4⋊C8—591no—
387C2×C4⋊C8—591no—
388C2×C4⋊C8—591no—
389C2×C4⋊C8—591no—
390C2×#103—591no—
391C2×#103—591no—
392C2×#103—591no—
393C2×#103—591no—
394C2×#102—591no—
395C2×#102—591no—
396C2×#102—591no—
397C2×#102—591no—
398#388—21no—
399#388—21no—
400#387—21no—
401#387—21no—
402#384C2×D5911yescharacteristic
403#382C2×D5911yescharacteristic
404#380C2×D5911yescharacteristic
405#380C2×D5911yescharacteristic
406C4×C4⋊C4C2×D5911yescharacteristic
407C4×C4⋊C4C2×D5911yescharacteristic
408#340—591no—
409#340—591no—
410#340—591no—
411#340—591no—
412#340—591no—
413#340—591no—
414#340—591no—
415#340—591no—
416C59#2189611yescharacteristic, complemented, Sylow
417C22×Q8—591no—
418C22×Q8—1181no—
419C22×D4—591no—
420C22×D4—1181no—
421C23×C4—1181no—
422C23×C4C22×D5911yescharacteristic
423C2×M16—1182no—
424C2×M16—2361no—
425C2×M16—2361no—
426C22×C8—591no—
427C22×C8—591no—
428C22×C8—591no—
429C22×C8—591no—
430C22×C8—1182no—
431C22×C8—2361no—
432C22×C8—2361no—
433C4⋊Q8—594no—
434C4⋊Q8—1182no—
435#126—1188no—
436#124—594no—
437#124—1188no—
438#124—1182no—
439#123—1188no—
440C22⋊Q8—594no—
441C22⋊Q8—1182no—
442C22⋊Q8—1188no—
443#121—594no—
444#121—1182no—
445C4×Q8—594no—
446C4×Q8—1182no—
447C4×D4—594no—
448C4×D4—1182no—
449#117C4×D5914yes—
450#117D23614yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—591no—
454C2×C4⋊C4—591no—
455C2×C4⋊C4—1181no—
456C2×C4⋊C4—1181no—
457C2×C4⋊C4—1181no—
458C2×C4⋊C4C22⋊D5911yescharacteristic
459C2×C4⋊C4C22⋊D5911yescharacteristic
460C2×C4⋊C4C22×D5911yescharacteristic
461C2×C4⋊C4C22×D5911yescharacteristic
462C2×C4⋊C4C22×D5911yescharacteristic
463C2×C4⋊C4C22×D5911yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—1181no—
467C2×C22⋊C4—1181no—
468C2×C22⋊C4—1181no—
469C2×C22⋊C4—1181no—
470C2×C22⋊C4—1181no—
471C2×C22⋊C4C22⋊D5911yescharacteristic
472C2×C22⋊C4C22⋊D5911yescharacteristic
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—1181no—
476C2×C42C22×D5911yescharacteristic
477C2×C42C22×D5911yescharacteristic
478C4⋊C8—1182no—
479C4⋊C8—1182no—
480C4⋊C8—1182no—
481C4⋊C8—1182no—
482#103—2361no—
483#103—2361no—
484#103—2361no—
485#103—2361no—
486#102—2361no—
487#102—2361no—
488#102—2361no—
489#102—2361no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496C24—1181no—
497C24C2×C22⋊D5911yescharacteristic
498C2×Q8—592no—
499C2×Q8—1184no—
500C2×Q8—1181no—
501C2×Q8—1181no—
502C2×Q8—1181no—
503C2×Q8—1181no—
504C2×Q8—1181no—
505C2×Q8—4721no—
506C2×Q8—4721no—
507C2×D4—592no—
508C2×D4—1184no—
509C2×D4—1181no—
510C2×D4—1181no—
511C2×D4—1181no—
512C2×D4—1181no—
513C2×D4—1181no—
514C2×D4—4721no—
515C2×D4—4721no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—1181no—
525C22×C4—1181no—
526C22×C4—1181no—
527C22×C4—1184no—
528C22×C4—4721no—
529C22×C4—4721no—
530C22×C4C2×C4×D5912yes—
531C22×C4C2×D23612yes—
532C22×C4C2×C22⋊D5911yescharacteristic
533C22×C4C2×C22⋊D5911yescharacteristic
534C22×C4C2×C22⋊D5911yescharacteristic
535C22×C4C2×C22⋊D5911yescharacteristic
536C22×C4C2×C22⋊D5911yescharacteristic
537C22×C4C23×D5911yescharacteristic
538M16—2364no—
539C2×C8—1181no—
540C2×C8—1181no—
541C2×C8—1181no—
542C2×C8—1181no—
543C2×C8—1181no—
544C2×C8—1181no—
545C2×C8—1181no—
546C2×C8—1181no—
547C2×C8—1181no—
548C2×C8—1181no—
549C2×C8—1181no—
550C2×C8—1181no—
551C2×C8—2364no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—81no—
561C4⋊C4—81no—
562C4⋊C4—592no—
563C4⋊C4—592no—
564C4⋊C4—1184no—
565C4⋊C4—1184no—
566C4⋊C4—1184no—
567C4⋊C4—1181no—
568C4⋊C4—1181no—
569C4⋊C4(C2×D59)⋊C414yes—
570C4⋊C4(C2×D59)⋊C414yes—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C22⋊C4—1184no—
574C22⋊C4—1184no—
575C22⋊C4—1184no—
576C22⋊C4—1184no—
577C22⋊C4—1184no—
578C22⋊C4(C2×D59)⋊C414yes—
579C22⋊C4(C2×D59)⋊C414yes—
580C42—81no—
581C42—81no—
582C42—1184no—
583C42C2×C4×D5912yes—
584C42C2×C4×D5912yes—
585C42C2×D23612yes—
586C42C2×D23612yes—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—1182no—
594C23—2361no—
595C23—2361no—
596C23—2361no—
597C23—2361no—
598C23—2361no—
599C23—2361no—
600C23C2×(C2×D59)⋊C412yes—
601C23C22×C22⋊D5911yescharacteristic
602Q8—1182no—
603Q8—1182no—
604Q8—4724no—
605Q8—2361no—
606Q8—2361no—
607D4—1182no—
608D4—1182no—
609D4—4724no—
610D4—2361no—
611D4—2361no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—1182no—
639C2×C4—1182no—
640C2×C4—1182no—
641C2×C4—4724no—
642C2×C4—2361no—
643C2×C4—2361no—
644C2×C4—2361no—
645C2×C4—2361no—
646C2×C4—2361no—
647C2×C4—2361no—
648C2×C4C2×(C2×D59)⋊C412yes—
649C2×C4C2×(C2×D59)⋊C412yes—
650C2×C4C2×(C2×D59)⋊C412yes—
651C2×C4C2×(C2×D59)⋊C412yes—
652C2×C4C2×(C2×D59)⋊C412yes—
653C2×C4C22×C4×D5911yescharacteristic
654C2×C4C22×D23611yescharacteristic
655C2×C4#1427377311yescharacteristic
656C2×C4#1427377311yescharacteristic
657C2×C4#1427377411yescharacteristic
658C2×C4#1427377411yescharacteristic
659C8—2361no—
660C8—2361no—
661C8—2361no—
662C8—2361no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—4721no—
671C22—4721no—
672C22—4721no—
673C22—4721no—
674C22—2362no—
675C22—2362no—
676C22—2362no—
677C22C22×(C2×D59)⋊C411yescharacteristic
678C22#1683798011yescharacteristic
679C22#1683798011yescharacteristic
680C22#1683820511yescharacteristic
681C22#1683821011yescharacteristic
682C22#1683821311yescharacteristic
683C22#1683821711yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—22no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4—2362no—
694C4—2362no—
695C4—2362no—
696C4#1683788211yescharacteristic
697C4#1683788211yescharacteristic
698C4#1683797111yescharacteristic
699C4#1683797811yescharacteristic
700C2—42no—
701C2—4722no—
702C2#2142668411yescharacteristic
703C2#2143261911yescharacteristic
704C2#2143262611yescharacteristic
705C2#2143550111yescharacteristic
706C2#2143551611yescharacteristic
707C2#2143555211yescharacteristic
708C2#2143556111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2314C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
cosocleC22×C4×C59C24
hypercenter#2314D59
hypocenterC59#21896
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. C2×#16837429C2semidirect
3. #21425048C2semidirect
4. #21425044C2semidirect
5. #21425028C2semidirect
6. #21425028C2semidirect
8. #21424527C2semidirect
10. #21424517C2semidirect
11. #21424108C2semidirect
12. #21424103C2semidirect
13. #21424098C2semidirect
14. #21424093C2semidirect
15. C59×#2314C2semidirect
19. #16838023C4semidirect
348. #2314D59semidirect
416. C59#21896semidirect

Maximal subgroups

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

subgroupindex
C2×#168380232
C2×#168374292
#214250482
#214250442
#214250282
#214245322
#214245272
#214245222
#214245172
#214241082
#214241032
#214240982
#214240932
C59×#23142
#2189659