Finite Group Databasebeta

← C4×#16837600 #28594883

Subgroups — C4×#16837600 #28594883

Order 15104.

1152 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837600C211yesmaximal, characteristic
2C2×C4×#11745671C211yesmaximal, characteristic, complemented
3C4×#14273723C211yesmaximal, characteristic
4C4×Q8×Dic59C211yesmaximal, characteristic, complemented
5#21425021C211yesmaximal, characteristic
6#21424856C211yesmaximal, characteristic, complemented
7#21424726C211yesmaximal, characteristic, complemented
8#21424722C211yesmaximal, characteristic, complemented
9#21424453C211yesmaximal, characteristic, complemented
10#21424449C211yesmaximal, characteristic, complemented
11#21424099C211yesmaximal, characteristic, complemented
12C4×Dic59⋊C8C211yesmaximal, characteristic, complemented
13C4×#14273649C211yesmaximal, characteristic, complemented
14C4×#14273648C211yesmaximal, characteristic, complemented
15C2×C4×SD16×C59C211yesmaximal, characteristic, complemented
16C22×#11745671C2211yescharacteristic
17C2×#14273723C2211yescharacteristic
18C2×Q8×Dic59C2211yescharacteristic
19C2×Q8×Dic59C2211yescharacteristic
20C2×C4×D236C2211yescharacteristic
21C2×C4×C22⋊D59—21no—
22C2×C4×C22⋊D59—21no—
23#16837600C418yesdirect product factor
24C4×#11745671—24no—
25C2×#14273658C2211yescharacteristic
26C2×Dic59⋊C8C2211yescharacteristic
27C2×Dic59⋊C8C2211yescharacteristic
28C2×#14273651C2211yescharacteristic
29C2×#14273649C2211yescharacteristic
30C2×#14273649C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×C4×C59⋊C8C2211yescharacteristic
35#16837305C2211yescharacteristic
36#16837303C2211yescharacteristic
37#16837302—21no—
38#16837302—21no—
39#16837271C2211yescharacteristic
40C4⋊C4×Dic59—21no—
41C4⋊C4×Dic59—21no—
42C4⋊C4×Dic59C2211yescharacteristic
43C4⋊C4×Dic59C2211yescharacteristic
44C4×C4⋊Dic59—21no—
45C4×C4⋊Dic59C2211yescharacteristic
46C42×Dic59—21no—
47C42×Dic59C2211yescharacteristic
48#16837165C2211yescharacteristic
49#16837165C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837164C2211yescharacteristic
52#16837156C2211yescharacteristic
53#16837156C2211yescharacteristic
54C22×SD16×C59C2211yescharacteristic
55C2×C4×Q8×C59C2211yescharacteristic
56C2×C4×D4×C59C2211yescharacteristic
57C4×SD16×C59—24no—
58C2×#106×C59C2211yescharacteristic
59C2×#103×C59C2211yescharacteristic
60C2×#102×C59C2211yescharacteristic
61C2×C4×C8×C59C2211yescharacteristic
62C22×D236C2311yescharacteristic
63C22×C22⋊D59—21no—
64C22×C22⋊D59—21no—
65C22×C4×D59—21no—
66C2×#11745671—22no—
67C2×#11745671—22no—
68C2×#11745671C2×C414yescomplemented
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71#14273723—22no—
72#14273723C2×C414yes—
73Q8×Dic59—22no—
74Q8×Dic59—22no—
75Q8×Dic59—22no—
76Q8×Dic59C2×C414yescomplemented
77C4×D236—22no—
78C4×D236—22no—
79C4×C22⋊D59—44no—
80C4×C22⋊D59—44no—
81C2×C4⋊Dic59—21no—
82C2×C4⋊Dic59—21no—
83C2×C4⋊Dic59C2311yescharacteristic
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C4⋊Dic59C2311yescharacteristic
86C2×Dic59⋊C4—21no—
87C2×Dic59⋊C4—21no—
88C2×C22⋊Dic59—21no—
89C2×C22⋊Dic59—21no—
90C2×(C2×D59)⋊C4—21no—
91C2×(C2×D59)⋊C4—21no—
92C2×(C2×D59)⋊C4—21no—
93C2×C4×Dic59—21no—
94C2×C4×Dic59—21no—
95C2×C4×Dic59—21no—
96C2×C4×Dic59—21no—
97C2×C4×Dic59—21no—
98C2×C4×Dic59D411yescharacteristic
99C2×C4×Dic59D411yescharacteristic
100C2×C4×Dic59D411yescharacteristic
101C2×C4×Dic59D411yescharacteristic
102C2×C4×Dic59C2311yescharacteristic
103C2×C4×Dic59C2311yescharacteristic
104#14273658—22no—
105Dic59⋊C8—22no—
106Dic59⋊C8C2×C414yescomplemented
107#14273651—22no—
108#14273649—22no—
109#14273649C2×C414yescomplemented
110#14273648—22no—
111#14273648C2×C414yescomplemented
112#14273647—22no—
113C4×C59⋊C8—22no—
114C59⋊#95—21no—
115C59⋊#95—21no—
116C59⋊#95—21no—
117C22×Q8×C59C2311yescharacteristic
118C22×D4×C59C2311yescharacteristic
119C23×C4×C59—21no—
120C2×SD16×C59—22no—
121C2×SD16×C59—22no—
122C2×SD16×C59C2×C414yescomplemented
123C22×C8×C59C2311yescharacteristic
124C22×C8×C59C2311yescharacteristic
125C4×Q8×C59—22no—
126C4×Q8×C59D414yescomplemented
127C4×D4×C59—22no—
128C4×D4×C59—22no—
129C2×C4⋊C4×C59—21no—
130C2×C4⋊C4×C59C2311yescharacteristic
131C2×C4⋊C4×C59C2311yescharacteristic
132C2×C22⋊C4×C59—21no—
133C2×C42×C59—21no—
134C2×C42×C59C2311yescharacteristic
135#106×C59—22no—
136#103×C59—22no—
137#102×C59—22no—
138C4×C8×C59—22no—
139C24×C59—21no—
140C23×D59—21no—
141C2×Q8×C59—21no—
142C2×Q8×C59—21no—
143C2×Q8×C59—21no—
144C2×Q8×C59C22×C412yes—
145C2×Q8×C59C2×D412yes—
146C2×Q8×C59#4112yes—
147C2×D4×C59—21no—
148C2×D4×C59—21no—
149C2×D4×C59—21no—
150C2×D4×C59—21no—
151C2×D4×C59—21no—
152C2×D4×C59C22×C412yes—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—42no—
157C22×C4×C59—42no—
158C22×C4×C59—42no—
159C22×C4×C59C2×D411yescharacteristic
160C22×C4×C59C2×D411yescharacteristic
161C22×C4×C59C2411yescharacteristic
162C2×C22⋊D59—24no—
163C2×C22⋊D59—24no—
164C2×C22⋊D59—42no—
165C2×C22⋊D59—42no—
166C2×C22⋊D59—42no—
167C2×C22⋊D59—42no—
168C22×Dic59—21no—
169C22×Dic59—21no—
170C22×Dic59—21no—
171C22×Dic59C2×D411yescharacteristic
172C22×Dic59C2×D411yescharacteristic
173C22×Dic59C2×D411yescharacteristic
174C22×Dic59C2×D411yescharacteristic
175C2×D236—21no—
176C2×D236—21no—
177C2×D236—21no—
178C2×D236—21no—
179C2×D236—21no—
180C2×D236C22×C412yes—
181C2×C4×D59—42no—
182C2×C4×D59—42no—
183C2×C4×D59—42no—
184SD16×C59—28no—
185C2×C8×C59—21no—
186C2×C8×C59—21no—
187C2×C8×C59—21no—
188C2×C8×C59—21no—
189C2×C8×C59—21no—
190C2×C8×C59C22×C412yes—
191C4⋊C4×C59—24no—
192C4⋊C4×C59—21no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—21no—
195C4⋊C4×C59C2×D412yes—
196C22⋊C4×C59—42no—
197C42×C59—24no—
198C42×C59C2×D412yes—
199C42×C59#4112yes—
200C22⋊Dic59—42no—
201C22⋊Dic59—42no—
202#11745671—28no—
203(C2×D59)⋊C4—42no—
204(C2×D59)⋊C4—42no—
205(C2×D59)⋊C4—42no—
206C4⋊Dic59—24no—
207C4⋊Dic59—21no—
208C4⋊Dic59—21no—
209C4⋊Dic59—24no—
210C4⋊Dic59—21no—
211C4⋊Dic59—21no—
212C4⋊Dic59C22×C412yes—
213C4⋊Dic59#4112yes—
214Dic59⋊C4—42no—
215Dic59⋊C4—42no—
216C4×Dic59—24no—
217C4×Dic59—22no—
218C4×Dic59—21no—
219C4×Dic59—21no—
220C4×Dic59—24no—
221C4×Dic59—22no—
222C4×Dic59—41no—
223C4×Dic59—42no—
224C4×Dic59—42no—
225C4×Dic59—42no—
226C4×Dic59SD1614yescomplemented
227C4×Dic59C22×C412yes—
228C4×Dic59#4112yes—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8C22×C412yes—
235C23×C59—22no—
236C23×C59—41no—
237C23×C59—41no—
238C23×C59—41no—
239C23×C59—41no—
240C23×C59—41no—
241C23×C59—41no—
242C23×C59C22×D411yescharacteristic
243C22×D59—22no—
244C22×D59—41no—
245C22×D59—41no—
246C22×D59—41no—
247C22×D59—41no—
248C22×D59—41no—
249C22×D59—41no—
250Q8×C59—22no—
251Q8×C59—22no—
252Q8×C59—22no—
253Q8×C59C4×D414yescomplemented
254D4×C59—22no—
255D4×C59—22no—
256D4×C59—41no—
257D4×C59—41no—
258C2×C4×C59—22no—
259C2×C4×C59—22no—
260C2×C4×C59—22no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—22no—
264C2×C4×C59—41no—
265C2×C4×C59—41no—
266C2×C4×C59—41no—
267C2×C4×C59—41no—
268C2×C4×C59—41no—
269C2×C4×C59—84no—
270C2×C4×C59#12112yes—
271C2×C4×C59#12112yes—
272C2×C4×C59C2×SD1612yes—
273C2×C4×C59AGL(1,ℤ/8)12yes—
274C2×C4×C59C23×C411yescharacteristic
275C2×C4×C59C22×D411yescharacteristic
276C2×C4×C59C2×#4111yescharacteristic
277C2×C4×C59C2×#4111yescharacteristic
278C2×C4×C59C2×#4111yescharacteristic
279C2×C4×C59C2×#4111yescharacteristic
280C22⋊D59—48no—
281C22⋊D59—48no—
282C2×Dic59—21no—
283C2×Dic59—21no—
284C2×Dic59—21no—
285C2×Dic59—21no—
286C2×Dic59—22no—
287C2×Dic59—21no—
288C2×Dic59—22no—
289C2×Dic59—21no—
290C2×Dic59—21no—
291C2×Dic59—41no—
292C2×Dic59—41no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59C4×D412yes—
299C2×Dic59C4×D412yes—
300C2×Dic59C2×SD1612yes—
301C2×Dic59C2×SD1612yes—
302C2×Dic59#13512yes—
303D236—22no—
304D236—22no—
305D236—41no—
306D236—41no—
307C4×D59—84no—
308C8×C59—22no—
309C8×C59—41no—
310C59⋊C8—22no—
311C59⋊C8—41no—
312C4×#460—591nomaximal, Sylow
313C22×C59—42no—
314C22×C59—42no—
315C22×C59—42no—
316C22×C59—81no—
317C22×C59—81no—
318C22×C59—81no—
319C22×C59—81no—
320C22×C59C2×C4×D411yescharacteristic
321C22×C59C2×#12111yescharacteristic
322C22×C59#52511yescharacteristic
323C22×C59C22×SD1611yescharacteristic
324C22×C59C2×#13511yescharacteristic
325C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C59#57511yescharacteristic
327C2×D59—42no—
328C2×D59—42no—
329C2×D59—42no—
330C2×D59—81no—
331C2×D59—81no—
332C2×D59—81no—
333C2×D59—81no—
334C4×C59—22no—
335C4×C59—24no—
336C4×C59—42no—
337C4×C59—81no—
338C4×C59#46014yescomplemented
339C4×C59C2×C4×D411yescharacteristic
340C4×C59C4×#4111yescharacteristic
341C4×C59#52911yescharacteristic
342C4×C59#53211yescharacteristic
343Dic59—22no—
344Dic59—22no—
345Dic59—41no—
346Dic59—42no—
347Dic59—42no—
348Dic59—81no—
349Dic59C4×SD1614yescomplemented
350C2×#460—591no—
351C2×C4×SD16—591no—
352C2×C4×SD16D5911yescharacteristic, complemented
353C4×#127—591no—
354C42×Q8—591no—
355#1982—591no—
356#1948—591no—
357#1926—591no—
358#1926—591no—
359#1880—591no—
360#1880—591no—
361#1803—591no—
362C4×C4⋊C8—591no—
363C4×#102—591no—
364C4×#102—591no—
365C2×C59—82no—
366C2×C59C4×#12111yescharacteristic
367C2×C59C2×C4×SD1611yescharacteristic
368C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
369C2×C59C2×#46011yescharacteristic
370C2×C59#303511yescharacteristic
371C2×C59#310311yescharacteristic
372C2×C59#310611yescharacteristic
373D59—82no—
374C22×SD16—591no—
375C22×SD16C2×D5911yescharacteristic
376C2×#127—591no—
377C2×C4×Q8—591no—
378C2×C4×Q8—591no—
379C2×C4×Q8C2×D5911yescharacteristic
380C2×C4×D4—591no—
381C2×C4×D4—1181no—
382C2×C4×D4—1181no—
383C2×C4×D4C2×D5911yescharacteristic
384#460—598no—
385C4×SD16—24no—
386C4×SD16—1184no—
387C2×#106—591no—
388C2×#106C2×D5911yescharacteristic
389C2×C4⋊C8—591no—
390C2×C4⋊C8—591no—
391C2×#103—591no—
392C2×#103C2×D5911yescharacteristic
393C2×#102—591no—
394C2×#102—591no—
395C2×#102—591no—
396C2×#102—591no—
397C2×#102—591no—
398C2×#102C2×D5911yescharacteristic
399C2×C4×C8—591no—
400C2×C4×C8C2×D5911yescharacteristic
401#390—591no—
402#390—591no—
403#390—1181no—
404#390—1181no—
405#384—591no—
406C4×C4⋊C4—591no—
407C4×C4⋊C4—591no—
408C4×C4⋊C4—591no—
409C4×C4⋊C4—1181no—
410C4×C4⋊C4—1181no—
411C4×C4⋊C4—1181no—
412C43—591no—
413C43—1181no—
414#340—591no—
415#340—591no—
416#340—591no—
417#340—591no—
418#336—591no—
419#336—591no—
420C59C4×#46011yescharacteristic, complemented, Sylow
421C22×Q8C22×D5911yescharacteristic
422C22×D4—591no—
423C22×D4—1181no—
424C22×D4—1181no—
425C22×D4C22×D5911yescharacteristic
426C23×C4—21no—
427C23×C4—1181no—
428C2×SD16—22no—
429C2×SD16—22no—
430C2×SD16—594no—
431C2×SD16—1182no—
432C2×SD16—1182no—
433C2×SD16C4×D5914yescomplemented
434C22×C8—591no—
435C22×C8—591no—
436C22×C8C22×D5911yescharacteristic
437C22×C8C22×D5911yescharacteristic
438#127—594no—
439#127—1182no—
440C4×Q8—22no—
441C4×Q8—594no—
442C4×Q8—1182no—
443C4×Q8—1182no—
444C4×Q8—1182no—
445C4×Q8C22⋊D5914yescomplemented
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—1182no—
449C4×D4—1182no—
450C4×D4—2364no—
451C4×D4—2364no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—591no—
454C2×C4⋊C4—591no—
455C2×C4⋊C4—591no—
456C2×C4⋊C4—1181no—
457C2×C4⋊C4—1181no—
458C2×C4⋊C4—1181no—
459C2×C4⋊C4—1181no—
460C2×C4⋊C4C22×D5911yescharacteristic
461C2×C4⋊C4C22×D5911yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—1181no—
464C2×C22⋊C4—1181no—
465C2×C22⋊C4—1181no—
466C2×C22⋊C4—1181no—
467C2×C22⋊C4—1181no—
468C2×C42—21no—
469C2×C42—591no—
470C2×C42—591no—
471C2×C42—591no—
472C2×C42—591no—
473C2×C42—591no—
474C2×C42—591no—
475C2×C42—1181no—
476C2×C42—1181no—
477C2×C42—1181no—
478C2×C42—1181no—
479C2×C42—1181no—
480C2×C42C22×D5911yescharacteristic
481#106—22no—
482#106—1182no—
483C4⋊C8—594no—
484C4⋊C8—1182no—
485#103—22no—
486#103—1182no—
487#102—22no—
488#102—594no—
489#102—594no—
490#102—1182no—
491#102—1182no—
492#102—1182no—
493C4×C8—22no—
494C4×C8—1182no—
495#95—1181no—
496#95—1181no—
497#95—1181no—
498C24—21no—
499C24—1181no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8C2×C4×D5912yes—
504C2×Q8#1174568512yes—
505C2×Q8C2×C22⋊D5912yes—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—592no—
512C2×D4—1184no—
513C2×D4—1184no—
514C2×D4—1181no—
515C2×D4—1181no—
516C2×D4—1181no—
517C2×D4—1181no—
518C2×D4—1181no—
519C2×D4—2362no—
520C2×D4—2362no—
521C2×D4—2362no—
522C2×D4—2362no—
523C2×D4C2×C4×D5912yes—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—591no—
531C22×C4—591no—
532C22×C4—591no—
533C22×C4—591no—
534C22×C4—1181no—
535C22×C4—1181no—
536C22×C4—1181no—
537C22×C4—2362no—
538C22×C4—2362no—
539C22×C4—2362no—
540C22×C4D4×D5911yescharacteristic
541C22×C4D4×D5911yescharacteristic
542C22×C4C23×D5911yescharacteristic
543SD16—28no—
544SD16—1188no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—592no—
551C2×C8—1181no—
552C2×C8—1181no—
553C2×C8—1181no—
554C2×C8—1181no—
555C2×C8—1181no—
556C2×C8C2×C4×D5912yes—
557C4⋊C4—24no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—592no—
562C4⋊C4—592no—
563C4⋊C4—1184no—
564C4⋊C4—1184no—
565C4⋊C4—1181no—
566C4⋊C4—1181no—
567C4⋊C4—1181no—
568C4⋊C4—1181no—
569C4⋊C4—2362no—
570C4⋊C4—2362no—
571C4⋊C4C2×C22⋊D5912yes—
572C22⋊C4—42no—
573C22⋊C4—2362no—
574C22⋊C4—2362no—
575C22⋊C4—2362no—
576C22⋊C4—2362no—
577C22⋊C4—2362no—
578C42—24no—
579C42—594no—
580C42—592no—
581C42—592no—
582C42—1182no—
583C42—1184no—
584C42—1184no—
585C42—1182no—
586C42—1181no—
587C42—1181no—
588C42—2361no—
589C42—2362no—
590C42—2362no—
591C42—2362no—
592C42#1174568712yes—
593C42C2×C22⋊D5912yes—
594C23—22no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—1182no—
602C23—2361no—
603C23—2361no—
604C23—2361no—
605C23—2361no—
606C23—2361no—
607C23—2361no—
608C23C2×D4×D5911yescharacteristic
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8C4×C22⋊D5914yescomplemented
613D4—22no—
614D4—22no—
615D4—41no—
616D4—41no—
617D4—1182no—
618D4—1182no—
619D4—2368no—
620D4—2368no—
621D4—2361no—
622D4—2361no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—84no—
635C2×C4—592no—
636C2×C4—592no—
637C2×C4—592no—
638C2×C4—592no—
639C2×C4—592no—
640C2×C4—1181no—
641C2×C4—1181no—
642C2×C4—1181no—
643C2×C4—1181no—
644C2×C4—1182no—
645C2×C4—1181no—
646C2×C4—1181no—
647C2×C4—1181no—
648C2×C4—1182no—
649C2×C4—4724no—
650C2×C4—2361no—
651C2×C4—2361no—
652C2×C4—2361no—
653C2×C4—2361no—
654C2×C4—2361no—
655C2×C4—2361no—
656C2×C4—2361no—
657C2×C4#1427369912yes—
658C2×C4#1427369912yes—
659C2×C4SD16×D5912yes—
660C2×C4#1427375412yes—
661C2×C4C22×C4×D5911yescharacteristic
662C2×C4C22×C22⋊D5911yescharacteristic
663C2×C4#41×D5911yescharacteristic
664C2×C4#41×D5911yescharacteristic
665C2×C4C2×#1174568711yescharacteristic
666C2×C4C2×#1174568511yescharacteristic
667C8—22no—
668C8—41no—
669C8—1182no—
670C8—2361no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—4721no—
679C22—4721no—
680C22—4721no—
681C22—4721no—
682C22—2362no—
683C22—2362no—
684C22—2362no—
685C22C4×D4×D5911yescharacteristic
686C22C2×#1427369911yescharacteristic
687C22#1683791111yescharacteristic
688C22C2×SD16×D5911yescharacteristic
689C22#135×D5911yescharacteristic
690C22C2×#1427375411yescharacteristic
691C22#1683819911yescharacteristic
692C4—24no—
693C4—22no—
694C4—42no—
695C4—81no—
696C4—594no—
697C4—1182no—
698C4—1182no—
699C4—4721no—
700C4—2361no—
701C4—2362no—
702C4—2362no—
703C4#1683760014yesdirect product factor
704C4C2×C4×C22⋊D5911yescharacteristic
705C4C4×#1174568711yescharacteristic
706C4#1683793211yescharacteristic
707C4#1683794811yescharacteristic
708C2—82no—
709C2—4722no—
710C2C4×#1427369911yescharacteristic
711C2C4×SD16×D5911yescharacteristic
712C2C4×#1427375411yescharacteristic
713C2C2×#1683760011yescharacteristic
714C2#2143354711yescharacteristic
715C2#2143412511yescharacteristic
716C2#2143415411yescharacteristic
subgroupG/H
centerC22×C4D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C4×SD16×C59C2
socleC23×C59C22×D4
prime radicalC2×#14273723C22
cosocleC22×C4×C59C24
hypercenterC2×C4×SD16D59
hypocenterC59C4×#460
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11745671C2semidirect
4. C4×Q8×Dic59C2semidirect
6. #21424856C2semidirect
7. #21424726C2semidirect
8. #21424722C2semidirect
9. #21424453C2semidirect
10. #21424449C2semidirect
11. #21424099C2semidirect
12. C4×Dic59⋊C8C2semidirect
13. C4×#14273649C2semidirect
14. C4×#14273648C2semidirect
15. C2×C4×SD16×C59C2semidirect
23. #16837600C4direct (N × H)
68. C2×#11745671C2×C4semidirect
76. Q8×Dic59C2×C4semidirect
106. Dic59⋊C8C2×C4semidirect
109. #14273649C2×C4semidirect
111. #14273648C2×C4semidirect
122. C2×SD16×C59C2×C4semidirect
126. C4×Q8×C59D4semidirect
226. C4×Dic59SD16semidirect
253. Q8×C59C4×D4semidirect
338. C4×C59#460semidirect
349. Dic59C4×SD16semidirect
352. C2×C4×SD16D59semidirect
420. C59C4×#460semidirect
433. C2×SD16C4×D59semidirect
445. C4×Q8C22⋊D59semidirect
612. Q8C4×C22⋊D59semidirect
703. C4#16837600direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168376002
C2×C4×#117456712
C4×#142737232
C4×Q8×Dic592
#214250212
#214248562
#214247262
#214247222
#214244532
#214244492
#214240992
C4×Dic59⋊C82
C4×#142736492
C4×#142736482
C2×C4×SD16×C592
C4×#46059