Finite Group Databasebeta

← #28593833

Subgroups — #28593833

Order 15104.

1150 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838023C211yesmaximal, characteristic
2C2×#16837463C211yesmaximal, characteristic, complemented
3#21425048C211yesmaximal, characteristic, complemented
4#21425044C211yesmaximal, characteristic, complemented
5#21425028C211yesmaximal, characteristic, complemented
6#21425028C211yesmaximal, characteristic, complemented
7#21424418C211yesmaximal, characteristic
8#21424413C211yesmaximal, characteristic
9#21424408C211yesmaximal, characteristic, complemented
10#21424403C211yesmaximal, characteristic, complemented
11#21423929C211yesmaximal, characteristic, complemented
12#21423924C211yesmaximal, characteristic, complemented
13C4×#14273650C211yesmaximal, characteristic, complemented
14C4×#14273647C211yesmaximal, characteristic, complemented
15C59×#2274C211yesmaximal, characteristic, complemented
16#16838023—24no—
17#16838023C418yescomplemented
18C2×#14273727C2211yescharacteristic
19C2×#14273722—21no—
20C2×#14273715C2211yescharacteristic
21C2×#14273713—21no—
22C2×#14273709—21no—
23C2×#14273706C2211yescharacteristic
24C2×#14273705—21no—
25C2×#14273701C2211yescharacteristic
26C2×C4×Dic118C2211yescharacteristic
27C2×C4×D236C2211yescharacteristic
28#16837463—24no—
29C2×C4⋊(C59⋊C8)C2211yescharacteristic
30C2×C4⋊(C59⋊C8)C2211yescharacteristic
31C2×#14273650C2211yescharacteristic
32C2×#14273650C2211yescharacteristic
33C2×#14273650C2211yescharacteristic
34C2×#14273650C2211yescharacteristic
35C2×#14273647C2211yescharacteristic
36C2×#14273647C2211yescharacteristic
37C2×#14273647C2211yescharacteristic
38C2×#14273647C2211yescharacteristic
39C2×C22⋊(C59⋊C8)C2211yescharacteristic
40C2×C22⋊(C59⋊C8)C2211yescharacteristic
41C2×#14273638C2211yescharacteristic
42C2×C4×C59⋊C8C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51C2×#117×C59C2211yescharacteristic
52C2×#117×C59C2211yescharacteristic
53C22×C4⋊C4×C59C2211yescharacteristic
54C4×C4⋊C4×C59—21no—
55C4×C4⋊C4×C59—21no—
56C4×C4⋊C4×C59C2211yescharacteristic
57C4×C4⋊C4×C59C2211yescharacteristic
58C4×C4⋊C4×C59C2211yescharacteristic
59C4×C4⋊C4×C59C2211yescharacteristic
60C4×C22⋊C4×C59—21no—
61C4×C22⋊C4×C59—21no—
62C22×Dic118—21no—
63C22×Dic118C2311yescharacteristic
64C22×D236C2311yescharacteristic
65C22×C22⋊D59—21no—
66C22×C4×D59—21no—
67C22×C59⋊C8C2311yescharacteristic
68C22×C59⋊C8C2311yescharacteristic
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71#14273727—22no—
72#14273727C2×C414yescomplemented
73#14273722—28no—
74#14273715—22no—
75#14273715C2×C414yescomplemented
76#14273713—28no—
77#14273709—28no—
78#14273706—22no—
79#14273706C2×C414yes—
80#14273705—28no—
81#14273701—22no—
82#14273701C2×C414yes—
83C4×Dic118—22no—
84C4×Dic118C2×C414yescomplemented
85C4×D236—22no—
86C4×D236C2×C414yescomplemented
87C2×C4⋊Dic59—21no—
88C2×C4⋊Dic59C2311yescharacteristic
89C2×C4⋊Dic59C2311yescharacteristic
90C2×Dic59⋊C4—21no—
91C2×Dic59⋊C4—21no—
92C2×C22⋊Dic59—21no—
93C2×(C2×D59)⋊C4—21no—
94C2×(C2×D59)⋊C4—21no—
95C2×(C2×D59)⋊C4—21no—
96C2×(C2×D59)⋊C4—21no—
97C2×C4×Dic59—21no—
98C4⋊(C59⋊C8)—22no—
99C4⋊(C59⋊C8)—22no—
100#14273650—22no—
101#14273650—22no—
102#14273650—22no—
103#14273650—22no—
104#14273647—22no—
105#14273647—22no—
106#14273647—22no—
107#14273647—22no—
108C22⋊(C59⋊C8)—22no—
109C22⋊(C59⋊C8)—22no—
110#14273638—22no—
111C4×C59⋊C8—22no—
112C23×C4×C59—21no—
113C23×C4×C59C2311yescharacteristic
114#117×C59—22no—
115#117×C59—22no—
116#117×C59C2×C414yes—
117#117×C59D414yes—
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59—22no—
120C2×C4⋊C4×C59—22no—
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×C59D411yescharacteristic
129C2×C22⋊C4×C59D411yescharacteristic
130C2×C42×C59—21no—
131C2×C42×C59—21no—
132C2×C42×C59—21no—
133C2×C42×C59—21no—
134C2×C42×C59—21no—
135C2×C42×C59C2311yescharacteristic
136C2×C42×C59C2311yescharacteristic
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×C59—24no—
152C22×C4×C59—81no—
153C22×C4×C59—81no—
154C22×C4×C59C22×C412yes—
155C22×C4×C59C2×D411yescharacteristic
156C22×C4×C59C2×D411yescharacteristic
157C22×C4×C59C2×D411yescharacteristic
158C22×C4×C59C2×D411yescharacteristic
159C22×C4×C59C2×D411yescharacteristic
160C22×C4×C59C2×D412yes—
161C22×C4×C59C2411yescharacteristic
162C2×C22⋊D59—24no—
163C2×C22⋊D59—81no—
164C2×C22⋊D59—81no—
165C22×Dic59—21no—
166C22×Dic59—21no—
167C22×Dic59—21no—
168C2×D236—21no—
169C2×D236—21no—
170C2×D236—21no—
171C2×D236—21no—
172C2×D236—21no—
173C2×D236C22×C412yes—
174C2×C4×D59—24no—
175C2×C4×D59—81no—
176C2×C4×D59—81no—
177C2×Dic118—21no—
178C2×Dic118—21no—
179C2×Dic118—21no—
180C2×Dic118—21no—
181C2×Dic118—21no—
182C2×Dic118—24no—
183C2×Dic118—81no—
184C2×Dic118—81no—
185C2×Dic118C22×C412yes—
186C4⋊C4×C59—24no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59C22⋊C414yes—
192C4⋊C4×C59C22⋊C414yes—
193C4⋊C4×C59#4112yes—
194C4⋊C4×C59#4112yes—
195C4⋊C4×C59#4112yes—
196C4⋊C4×C59#4112yes—
197C22⋊C4×C59—24no—
198C22⋊C4×C59C22⋊C414yes—
199C22⋊C4×C59C22⋊C414yes—
200C42×C59—24no—
201C42×C59—81no—
202C42×C59—81no—
203C42×C59—81no—
204C42×C59—81no—
205C42×C59C22×C412yes—
206C42×C59C22×C412yes—
207C42×C59C2×D412yes—
208C42×C59C2×D412yes—
209C22⋊Dic59—24no—
210(C2×D59)⋊C4—24no—
211(C2×D59)⋊C4—24no—
212(C2×D59)⋊C4—24no—
213(C2×D59)⋊C4—24no—
214C4⋊Dic59—24no—
215C4⋊Dic59—21no—
216C4⋊Dic59—21no—
217C4⋊Dic59C22×C412yes—
218C4⋊Dic59C22×C412yes—
219Dic59⋊C4—24no—
220Dic59⋊C4—24no—
221C4×Dic59—24no—
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—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—21no—
240C23×C59C2×C22⋊C412yes—
241C23×C59C22×D411yescharacteristic
242C22×D59—22no—
243C22×D59—41no—
244C22×D59—41no—
245C22×D59—41no—
246C22×D59—41no—
247C22×D59—41no—
248C22×D59—41no—
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—21no—
258C2×C4×C59—21no—
259C2×C4×C59—22no—
260C2×C4×C59—22no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—22no—
264C2×C4×C59—22no—
265C2×C4×C59—22no—
266C2×C4×C59—22no—
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×C59—41no—
274C2×C4×C59—41no—
275C2×C4×C59—84no—
276C2×C4×C59C2×C22⋊C412yes—
277C2×C4×C59C2×C22⋊C412yes—
278C2×C4×C59C2×C22⋊C412yes—
279C2×C4×C59C2×C22⋊C412yes—
280C2×C4×C59C2×C22⋊C412yes—
281C2×C4×C59C23×C411yescharacteristic
282C2×C4×C59C22×D411yescharacteristic
283C2×C4×C59C2×#4111yescharacteristic
284C2×C4×C59C2×#4111yescharacteristic
285C2×C4×C59C2×#4111yescharacteristic
286C2×C4×C59C2×#4111yescharacteristic
287C22⋊D59—84no—
288C2×Dic59—22no—
289C2×Dic59—22no—
290C2×Dic59—22no—
291C2×Dic59—41no—
292C2×Dic59—41no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297D236—22no—
298D236—22no—
299D236—41no—
300D236—41no—
301C4×D59—84no—
302Dic118—22no—
303Dic118—22no—
304Dic118—41no—
305Dic118—41no—
306Dic118—84no—
307C59⋊C8—41no—
308C59⋊C8—41no—
309C59⋊C8—41no—
310C59⋊C8—41no—
311#21397—591nomaximal, Sylow
312C22×C59—22no—
313C22×C59—22no—
314C22×C59—22no—
315C22×C59—41no—
316C22×C59—41no—
317C22×C59—41no—
318C22×C59—41no—
319C22×C59C22×C22⋊C411yescharacteristic
320C22×C59#52511yescharacteristic
321C22×C59#52511yescharacteristic
322C22×C59#57611yescharacteristic
323C22×C59#57711yescharacteristic
324C22×C59#57711yescharacteristic
325C22×C59#57811yescharacteristic
326C2×D59—42no—
327C2×D59—42no—
328C2×D59—42no—
329C2×D59—81no—
330C2×D59—81no—
331C2×D59—81no—
332C2×D59—81no—
333C4×C59—22no—
334C4×C59—22no—
335C4×C59—22no—
336C4×C59—22no—
337C4×C59—22no—
338C4×C59—42no—
339C4×C59—42no—
340C4×C59—42no—
341C4×C59—42no—
342C4×C59C4×#4111yescharacteristic
343C4×C59C4×#4111yescharacteristic
344C4×C59#53211yescharacteristic
345C4×C59#53211yescharacteristic
346Dic59—42no—
347Dic59—42no—
348Dic59—42no—
349C2×#542—591no—
350C2×#433—591no—
351#2274D5911yescharacteristic, complemented
352#1988—591no—
353#1987—591no—
354#1983—591no—
355#1983—591no—
356#1875—591no—
357#1874—591no—
358#1873—591no—
359#1872—591no—
360#1763—591no—
361#1762—591no—
362C4×#103—591no—
363C4×#102—591no—
364C2×C59—42no—
365C2×C59#229711yescharacteristic
366C2×C59#289711yescharacteristic
367C2×C59#289811yescharacteristic
368C2×C59#311811yescharacteristic
369C2×C59#312111yescharacteristic
370C2×C59#312411yescharacteristic
371C2×C59#312511yescharacteristic
372D59—82no—
373#542—598no—
374#542—1184no—
375C2×C4⋊Q8—591no—
376C2×#126—1181no—
377C2×#124—591no—
378C2×#124—1181no—
379C2×#123—1181no—
380C2×C22⋊Q8—591no—
381C2×C22⋊Q8—1181no—
382C2×#121—591no—
383C2×C4×Q8—591no—
384C2×C4×D4—591no—
385C2×#117C2×D5911yescharacteristic
386C2×#117C2×D5911yescharacteristic
387C22×C4⋊C4C2×D5911yescharacteristic
388#433—1184no—
389C2×C4⋊C8—591no—
390C2×C4⋊C8—591no—
391C2×#103—591no—
392C2×#103—591no—
393C2×#103—591no—
394C2×#103—591no—
395C2×#102—591no—
396C2×#102—591no—
397C2×#102—591no—
398C2×#102—591no—
399C2×C22⋊C8—591no—
400C2×C22⋊C8—591no—
401C2×#97—591no—
402C2×C4×C8—591no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4C2×D5911yescharacteristic
406C4×C4⋊C4C2×D5911yescharacteristic
407C4×C4⋊C4C2×D5911yescharacteristic
408C4×C4⋊C4C2×D5911yescharacteristic
409C4×C22⋊C4—21no—
410C4×C22⋊C4—21no—
411#340—591no—
412#340—591no—
413#340—591no—
414#340—591no—
415#340—591no—
416#340—591no—
417#340—591no—
418#340—591no—
419C59#2139711yescharacteristic, complemented, Sylow
420C22×Q8—591no—
421C22×Q8—1181no—
422C22×D4—591no—
423C22×D4—1181no—
424C23×C4—21no—
425C23×C4—1181no—
426C23×C4C22×D5911yescharacteristic
427C22×C8—591no—
428C22×C8—591no—
429C22×C8—591no—
430C22×C8—591no—
431C4⋊Q8—594no—
432C4⋊Q8—1182no—
433#126—1188no—
434#124—594no—
435#124—1188no—
436#124—1182no—
437#123—1188no—
438C22⋊Q8—594no—
439C22⋊Q8—1182no—
440C22⋊Q8—1188no—
441#121—594no—
442#121—1182no—
443C4×Q8—594no—
444C4×Q8—1182no—
445C4×D4—594no—
446C4×D4—1182no—
447#117—22no—
448#117—22no—
449#117C4×D5914yes—
450#117D23614yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—591no—
455C2×C4⋊C4—591no—
456C2×C4⋊C4—1181no—
457C2×C4⋊C4—1181no—
458C2×C4⋊C4—1181no—
459C2×C4⋊C4C22⋊D5911yescharacteristic
460C2×C4⋊C4C22⋊D5911yescharacteristic
461C2×C4⋊C4C22×D5911yescharacteristic
462C2×C4⋊C4C22×D5911yescharacteristic
463C2×C4⋊C4C22×D5911yescharacteristic
464C2×C4⋊C4C22×D5911yescharacteristic
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—21no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—1181no—
479C2×C42C22×D5911yescharacteristic
480C2×C42C22×D5911yescharacteristic
481C4⋊C8—1182no—
482C4⋊C8—1182no—
483#103—1182no—
484#103—1182no—
485#103—1182no—
486#103—1182no—
487#102—1182no—
488#102—1182no—
489#102—1182no—
490#102—1182no—
491C22⋊C8—1182no—
492C22⋊C8—1182no—
493#97—1182no—
494C4×C8—1182no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499C24—1181no—
500C24C2×C22⋊D5911yescharacteristic
501C2×Q8—592no—
502C2×Q8—1184no—
503C2×Q8—1181no—
504C2×Q8—1181no—
505C2×Q8—1181no—
506C2×Q8—1181no—
507C2×Q8—1181no—
508C2×Q8—4721no—
509C2×Q8—4721no—
510C2×D4—592no—
511C2×D4—1184no—
512C2×D4—1181no—
513C2×D4—1181no—
514C2×D4—1181no—
515C2×D4—1181no—
516C2×D4—1181no—
517C2×D4—4721no—
518C2×D4—4721no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—24no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—1181no—
531C22×C4—1181no—
532C22×C4—1181no—
533C22×C4—1184no—
534C22×C4—4721no—
535C22×C4—4721no—
536C22×C4C2×C4×D5912yes—
537C22×C4C2×D23612yes—
538C22×C4C2×C22⋊D5911yescharacteristic
539C22×C4C2×C22⋊D5911yescharacteristic
540C22×C4C2×C22⋊D5911yescharacteristic
541C22×C4C2×C22⋊D5911yescharacteristic
542C22×C4C2×C22⋊D5911yescharacteristic
543C22×C4C23×D5911yescharacteristic
544C2×C8—1181no—
545C2×C8—1181no—
546C2×C8—1181no—
547C2×C8—1181no—
548C2×C8—1181no—
549C2×C8—1181no—
550C2×C8—1181no—
551C2×C8—1181no—
552C2×C8—1181no—
553C2×C8—1181no—
554C2×C8—1181no—
555C2×C8—1181no—
556C4⋊C4—24no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—592no—
562C4⋊C4—592no—
563C4⋊C4—1184no—
564C4⋊C4—1184no—
565C4⋊C4—1184no—
566C4⋊C4—1181no—
567C4⋊C4—1181no—
568C4⋊C4(C2×D59)⋊C414yes—
569C4⋊C4(C2×D59)⋊C414yes—
570C4⋊C4#1174568512yes—
571C4⋊C4#1174568512yes—
572C4⋊C4#1174568512yes—
573C4⋊C4#1174568512yes—
574C22⋊C4—24no—
575C22⋊C4—1184no—
576C22⋊C4—1184no—
577C22⋊C4—1184no—
578C22⋊C4—1184no—
579C22⋊C4—1184no—
580C22⋊C4(C2×D59)⋊C414yes—
581C22⋊C4(C2×D59)⋊C414yes—
582C42—24no—
583C42—81no—
584C42—81no—
585C42—81no—
586C42—81no—
587C42—1184no—
588C42C2×C4×D5912yes—
589C42C2×C4×D5912yes—
590C42C2×D23612yes—
591C42C2×D23612yes—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—1182no—
599C23—2361no—
600C23—2361no—
601C23—2361no—
602C23—2361no—
603C23—2361no—
604C23—2361no—
605C23C2×(C2×D59)⋊C412yes—
606C23C22×C22⋊D5911yescharacteristic
607Q8—1182no—
608Q8—1182no—
609Q8—4724no—
610Q8—2361no—
611Q8—2361no—
612D4—1182no—
613D4—1182no—
614D4—4724no—
615D4—2361no—
616D4—2361no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—84no—
644C2×C4—1182no—
645C2×C4—1182no—
646C2×C4—1182no—
647C2×C4—4724no—
648C2×C4—2361no—
649C2×C4—2361no—
650C2×C4—2361no—
651C2×C4—2361no—
652C2×C4—2361no—
653C2×C4—2361no—
654C2×C4C2×(C2×D59)⋊C412yes—
655C2×C4C2×(C2×D59)⋊C412yes—
656C2×C4C2×(C2×D59)⋊C412yes—
657C2×C4C2×(C2×D59)⋊C412yes—
658C2×C4C2×(C2×D59)⋊C412yes—
659C2×C4C22×C4×D5911yescharacteristic
660C2×C4C22×D23611yescharacteristic
661C2×C4C2×#1174568511yescharacteristic
662C2×C4C2×#1174568511yescharacteristic
663C2×C4C2×#1174568511yescharacteristic
664C2×C4C2×#1174568511yescharacteristic
665C8—2361no—
666C8—2361no—
667C8—2361no—
668C8—2361no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—4721no—
677C22—4721no—
678C22—4721no—
679C22—4721no—
680C22—2362no—
681C22—2362no—
682C22—2362no—
683C22C22×(C2×D59)⋊C411yescharacteristic
684C22#1683791311yescharacteristic
685C22#1683791311yescharacteristic
686C22#1683820511yescharacteristic
687C22#1683821011yescharacteristic
688C22#1683821311yescharacteristic
689C22#1683821711yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—2362no—
700C4—2362no—
701C4—2362no—
702C4C4×#1174568511yescharacteristic
703C4C4×#1174568511yescharacteristic
704C4#1683795211yescharacteristic
705C4#1683795211yescharacteristic
706C2—42no—
707C2—4722no—
708C2#2142658611yescharacteristic
709C2#2143261911yescharacteristic
710C2#2143262611yescharacteristic
711C2#2143428011yescharacteristic
712C2#2143432511yescharacteristic
713C2#2143435811yescharacteristic
714C2#2143437311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2274C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
cosocleC22×C4×C59C24
hypercenter#2274D59
hypocenterC59#21397
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. C2×#16837463C2semidirect
3. #21425048C2semidirect
4. #21425044C2semidirect
5. #21425028C2semidirect
6. #21425028C2semidirect
9. #21424408C2semidirect
10. #21424403C2semidirect
11. #21423929C2semidirect
12. #21423924C2semidirect
13. C4×#14273650C2semidirect
14. C4×#14273647C2semidirect
15. C59×#2274C2semidirect
17. #16838023C4semidirect
72. #14273727C2×C4semidirect
75. #14273715C2×C4semidirect
84. C4×Dic118C2×C4semidirect
86. C4×D236C2×C4semidirect
351. #2274D59semidirect
419. C59#21397semidirect

Maximal subgroups

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

subgroupindex
C2×#168380232
C2×#168374632
#214250482
#214250442
#214250282
#214244182
#214244132
#214244082
#214244032
#214239292
#214239242
C4×#142736502
C4×#142736472
C59×#22742
#2139759