Finite Group Databasebeta

← C4×#16837617 #28594909

Subgroups — C4×#16837617 #28594909

Order 15104.

1136 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837617C211yesmaximal, characteristic
2C2×C4×#11745670C211yesmaximal, characteristic, complemented
3C2×C4×#11745669C211yesmaximal, characteristic
4C4×#14273715C211yesmaximal, characteristic, complemented
5#21425028C211yesmaximal, characteristic, complemented
6#21424864C211yesmaximal, characteristic, complemented
7#21424737C211yesmaximal, characteristic, complemented
8#21424723C211yesmaximal, characteristic, complemented
9#21424444C211yesmaximal, characteristic
10#21424430C211yesmaximal, characteristic, complemented
11#21424106C211yesmaximal, characteristic, complemented
12C4×C4⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
13C4×#14273650C211yesmaximal, characteristic, complemented
14C4×#14273647C211yesmaximal, characteristic, complemented
15C42×D4×C59C211yesmaximal, characteristic, complemented
16C22×#11745670C2211yescharacteristic
17C22×#11745669C2211yescharacteristic
18C2×#14273715C2211yescharacteristic
19C2×C4×Dic118C2211yescharacteristic
20C2×C4×D236C2211yescharacteristic
21#16837617C418yesdirect product factor
22C4×#11745670—24no—
23C4×#11745669—24no—
24C2×#14273660C2211yescharacteristic
25C2×#14273658C2211yescharacteristic
26C2×C4⋊(C59⋊C8)C2211yescharacteristic
27C2×C4⋊(C59⋊C8)C2211yescharacteristic
28C2×#14273650C2211yescharacteristic
29C2×#14273650C2211yescharacteristic
30C2×#14273650C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×#14273647C2211yescharacteristic
36C2×C4×C59⋊C8C2211yescharacteristic
37C2×C4×C59⋊C8C2211yescharacteristic
38#16837308C2211yescharacteristic
39#16837304C2211yescharacteristic
40#16837293—21no—
41#16837293—21no—
42#16837268C2211yescharacteristic
43C4×(C2×D59)⋊C4—21no—
44C4×(C2×D59)⋊C4—21no—
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837157C2211yescharacteristic
50#16837157C2211yescharacteristic
51C2×C4×D4×C59C2211yescharacteristic
52C2×C4×D4×C59C2211yescharacteristic
53C2×C4×D4×C59C2211yescharacteristic
54C22×C42×C59—21no—
55C4×C4⋊C4×C59C2211yescharacteristic
56C4×C4⋊C4×C59C2211yescharacteristic
57C4×C4⋊C4×C59C2211yescharacteristic
58C4×C22⋊C4×C59—21no—
59C4×C22⋊C4×C59—21no—
60C4×C22⋊C4×C59—21no—
61C43×C59C2211yescharacteristic
62C22×Dic118C2311yescharacteristic
63C22×D236C2311yescharacteristic
64C22×C4×D59—21no—
65C2×#11745670—22no—
66C2×#11745670—22no—
67C2×#11745670C2×C414yescomplemented
68C2×#11745669—22no—
69C2×#11745669—22no—
70C2×#11745669C2×C414yes—
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75#14273715—22no—
76#14273715C2×C414yescomplemented
77C4×Dic118—22no—
78C4×Dic118—22no—
79C4×D236—22no—
80C4×D236—22no—
81C2×C4⋊Dic59C2311yescharacteristic
82C2×C4⋊Dic59C2311yescharacteristic
83C2×Dic59⋊C4—21no—
84C2×(C2×D59)⋊C4—21no—
85C2×(C2×D59)⋊C4—21no—
86C2×(C2×D59)⋊C4—21no—
87C2×(C2×D59)⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×C4×Dic59—21no—
90#14273660—22no—
91#14273658—22no—
92C4⋊(C59⋊C8)—22no—
93C4⋊(C59⋊C8)C2×C414yescomplemented
94#14273650—22no—
95#14273650—22no—
96#14273650C2×C414yescomplemented
97#14273648—22no—
98#14273648—22no—
99#14273647—22no—
100#14273647—22no—
101#14273647C2×C414yescomplemented
102C4×C59⋊C8—22no—
103C4×C59⋊C8—22no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C22×D4×C59C2311yescharacteristic
109C23×C4×C59—21no—
110C23×C4×C59—21no—
111C23×C4×C59—21no—
112C4×D4×C59—22no—
113C4×D4×C59—22no—
114C4×D4×C59—22no—
115C4×D4×C59—22no—
116C4×D4×C59C2×C414yescomplemented
117C4×D4×C59D414yes—
118C2×C4⋊C4×C59C2311yescharacteristic
119C2×C4⋊C4×C59C2311yescharacteristic
120C2×C4⋊C4×C59C2311yescharacteristic
121C2×C22⋊C4×C59—21no—
122C2×C22⋊C4×C59—21no—
123C2×C22⋊C4×C59—21no—
124C2×C42×C59—21no—
125C2×C42×C59—21no—
126C2×C42×C59—21no—
127C2×C42×C59—44no—
128C2×C42×C59D411yescharacteristic
129C2×C42×C59D411yescharacteristic
130C2×C42×C59D411yescharacteristic
131C2×C42×C59D411yescharacteristic
132C2×C42×C59C2311yescharacteristic
133C2×C42×C59C2311yescharacteristic
134C2×C42×C59C2311yescharacteristic
135#95×C59—21no—
136#95×C59—21no—
137#95×C59—21no—
138C24×C59—21no—
139C23×D59—21no—
140C2×D4×C59—21no—
141C2×D4×C59—21no—
142C2×D4×C59—21no—
143C2×D4×C59C22×C412yes—
144C2×D4×C59C2×D412yes—
145C2×D4×C59#4112yes—
146C22×C4×C59—24no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—24no—
151C22×C4×C59—24no—
152C22×C4×C59—42no—
153C22×C4×C59—42no—
154C22×C4×C59—42no—
155C22×C4×C59—42no—
156C22×C4×C59—42no—
157C22×C4×C59—42no—
158C22×C4×C59C2×D411yescharacteristic
159C22×C4×C59C2×D411yescharacteristic
160C22×C4×C59C2×D411yescharacteristic
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2411yescharacteristic
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—42no—
175C2×C4×D59—42no—
176C2×C4×D59—42no—
177C2×Dic118—21no—
178C2×Dic118—21no—
179C2×Dic118—21no—
180C2×Dic118—21no—
181C2×Dic118—21no—
182C2×Dic118C22×C412yes—
183C4⋊C4×C59—21no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59C22×C412yes—
187C4⋊C4×C59C2×D412yes—
188C4⋊C4×C59#4112yes—
189C22⋊C4×C59—24no—
190C22⋊C4×C59—24no—
191C22⋊C4×C59—24no—
192C42×C59—22no—
193C42×C59—22no—
194C42×C59—22no—
195C42×C59—21no—
196C42×C59—21no—
197C42×C59—41no—
198C42×C59—42no—
199C42×C59—42no—
200C42×C59—42no—
201C42×C59C22×C412yes—
202C42×C59C2×D412yes—
203C42×C59#4112yes—
204C42×C59#4112yes—
205#11745670—28no—
206#11745669—28no—
207(C2×D59)⋊C4—24no—
208(C2×D59)⋊C4—24no—
209(C2×D59)⋊C4—42no—
210(C2×D59)⋊C4—42no—
211(C2×D59)⋊C4—42no—
212C4⋊Dic59—21no—
213C4⋊Dic59—21no—
214C4⋊Dic59—21no—
215C4⋊Dic59—21no—
216Dic59⋊C4—42no—
217C4×Dic59—42no—
218C2×C59⋊C8—21no—
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⋊C8C22×C412yes—
229C2×C59⋊C8C22×C412yes—
230C23×C59—22no—
231C23×C59—22no—
232C23×C59—22no—
233C23×C59—41no—
234C23×C59—41no—
235C23×C59—41no—
236C23×C59—41no—
237C23×C59C22×D411yescharacteristic
238C22×D59—22no—
239C22×D59—41no—
240C22×D59—41no—
241C22×D59—41no—
242C22×D59—41no—
243C22×D59—41no—
244C22×D59—41no—
245D4×C59—22no—
246D4×C59—22no—
247D4×C59—22no—
248D4×C59C4×D414yes—
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—21no—
260C2×C4×C59—22no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—48no—
264C2×C4×C59—48no—
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—48no—
272C2×C4×C59C4×D412yes—
273C2×C4×C59C4×D412yes—
274C2×C4×C59#12112yes—
275C2×C4×C59#12112yes—
276C2×C4×C59#13512yes—
277C2×C4×C59#13512yes—
278C2×C4×C59AGL(1,ℤ/8)12yes—
279C2×C4×C59C23×C411yescharacteristic
280C2×C4×C59C22×D411yescharacteristic
281C2×C4×C59C2×#4111yescharacteristic
282C2×C4×C59C2×#4111yescharacteristic
283C2×C4×C59C2×#4111yescharacteristic
284C2×C4×C59C2×#4111yescharacteristic
285C2×Dic59—22no—
286C2×Dic59—41no—
287C2×Dic59—41no—
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—
303C59⋊C8—22no—
304C59⋊C8—22no—
305C59⋊C8—41no—
306C59⋊C8—41no—
307C4×#463—591nomaximal, Sylow
308C22×C59—24no—
309C22×C59—42no—
310C22×C59—42no—
311C22×C59—42no—
312C22×C59—42no—
313C22×C59—42no—
314C22×C59—42no—
315C22×C59C2×C4×D411yescharacteristic
316C22×C59C2×#12111yescharacteristic
317C22×C59#52511yescharacteristic
318C22×C59C2×#13511yescharacteristic
319C22×C59C2×#13511yescharacteristic
320C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C59#57511yescharacteristic
322C2×D59—42no—
323C2×D59—42no—
324C2×D59—42no—
325C2×D59—81no—
326C2×D59—81no—
327C2×D59—81no—
328C2×D59—81no—
329C4×C59—22no—
330C4×C59—22no—
331C4×C59—22no—
332C4×C59—22no—
333C4×C59—41no—
334C4×C59—42no—
335C4×C59—42no—
336C4×C59—42no—
337C4×C59#46314yescomplemented
338C4×C59C2×C4×D411yescharacteristic
339C4×C59C4×#4111yescharacteristic
340C4×C59#52911yescharacteristic
341C4×C59#53211yescharacteristic
342Dic59—42no—
343Dic59—81no—
344Dic59—81no—
345C2×#463—591no—
346C2×C4×SD16—591no—
347C2×C4×D8—591no—
348C4×#124—591no—
349C42×D4D5911yescharacteristic, complemented
350#1983—591no—
351#1949—591no—
352#1928—591no—
353#1926—591no—
354#1879—591no—
355#1877—591no—
356#1804—591no—
357C4×C4⋊C8—591no—
358C4×#103—591no—
359C4×#102—591no—
360C2×C59—44no—
361C2×C59C4×#12111yescharacteristic
362C2×C59C4×#13511yescharacteristic
363C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
364C2×C59C2×#46311yescharacteristic
365C2×C59#303511yescharacteristic
366C2×C59#310211yescharacteristic
367C2×C59#310511yescharacteristic
368D59—82no—
369C22×SD16—591no—
370C22×D8—591no—
371C2×#124—591no—
372C2×C4×Q8—591no—
373C2×C4×D4—591no—
374C2×C4×D4C2×D5911yescharacteristic
375C2×C4×D4C2×D5911yescharacteristic
376C2×C4×D4C2×D5911yescharacteristic
377C22×C42—21no—
378#463—598no—
379C4×SD16—1184no—
380C4×D8—1184no—
381C2×#107—591no—
382C2×#106—591no—
383C2×C4⋊C8—591no—
384C2×C4⋊C8—591no—
385C2×#103—591no—
386C2×#103—591no—
387C2×#103—591no—
388C2×#102—591no—
389C2×#102—591no—
390C2×#102—591no—
391C2×#102—591no—
392C2×#102—591no—
393C2×C4×C8—591no—
394C2×C4×C8—591no—
395#391—591no—
396#390—591no—
397#388—1181no—
398#388—1181no—
399#382—591no—
400C4×C4⋊C4C2×D5911yescharacteristic
401C4×C4⋊C4C2×D5911yescharacteristic
402C4×C4⋊C4C2×D5911yescharacteristic
403C4×C22⋊C4—21no—
404C4×C22⋊C4—21no—
405C4×C22⋊C4—21no—
406C4×C22⋊C4—1181no—
407C4×C22⋊C4—1181no—
408C43C2×D5911yescharacteristic
409#340—591no—
410#340—591no—
411#340—591no—
412#340—591no—
413#336—591no—
414#336—591no—
415C59C4×#46311yescharacteristic, complemented, Sylow
416C22×Q8—591no—
417C22×D4—591no—
418C22×D4C22×D5911yescharacteristic
419C23×C4—21no—
420C23×C4—21no—
421C23×C4—21no—
422C23×C4—1181no—
423C2×SD16—594no—
424C2×SD16—1182no—
425C2×SD16—1182no—
426C2×D8—594no—
427C2×D8—1182no—
428C2×D8—1182no—
429C22×C8—591no—
430C22×C8—591no—
431C22×C8—591no—
432C22×C8—591no—
433#124—594no—
434#124—1182no—
435C4×Q8—1182no—
436C4×Q8—1182no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—1182no—
442C4×D4—1182no—
443C4×D4C4×D5914yescomplemented
444C4×D4D23614yes—
445C2×C4⋊C4—591no—
446C2×C4⋊C4—591no—
447C2×C4⋊C4—1181no—
448C2×C4⋊C4C22×D5911yescharacteristic
449C2×C4⋊C4C22×D5911yescharacteristic
450C2×C4⋊C4C22×D5911yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—1181no—
455C2×C22⋊C4—1181no—
456C2×C22⋊C4—1181no—
457C2×C22⋊C4—1181no—
458C2×C22⋊C4—1181no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—44no—
463C2×C42—1181no—
464C2×C42C22⋊D5911yescharacteristic
465C2×C42C22⋊D5911yescharacteristic
466C2×C42C22⋊D5911yescharacteristic
467C2×C42C22⋊D5911yescharacteristic
468C2×C42C22×D5911yescharacteristic
469C2×C42C22×D5911yescharacteristic
470C2×C42C22×D5911yescharacteristic
471#107—1182no—
472#106—1182no—
473C4⋊C8—594no—
474C4⋊C8—1182no—
475#103—594no—
476#103—1182no—
477#103—1182no—
478#102—594no—
479#102—1182no—
480#102—1182no—
481#102—1182no—
482#102—1182no—
483C4×C8—1182no—
484C4×C8—1182no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—1181no—
489#95—1181no—
490#95—1181no—
491#95—1181no—
492C24—21no—
493C24—1181no—
494C2×Q8—592no—
495C2×Q8—1181no—
496C2×Q8—1181no—
497C2×Q8—1181no—
498C2×Q8—1181no—
499C2×Q8—1181no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—592no—
504C2×D4—1181no—
505C2×D4—1181no—
506C2×D4—1181no—
507C2×D4—1181no—
508C2×D4—1181no—
509C2×D4C2×C4×D5912yes—
510C2×D4C2×D23612yes—
511C2×D4#1174568512yes—
512C22×C4—24no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—1181no—
525C22×C4—1181no—
526C22×C4—1181no—
527C22×C4—2362no—
528C22×C4—2362no—
529C22×C4—2362no—
530C22×C4C2×C22⋊D5911yescharacteristic
531C22×C4C2×C22⋊D5911yescharacteristic
532C22×C4C2×C22⋊D5911yescharacteristic
533C22×C4C2×C22⋊D5911yescharacteristic
534C22×C4C2×C22⋊D5911yescharacteristic
535C22×C4C2×C22⋊D5911yescharacteristic
536C22×C4C23×D5911yescharacteristic
537SD16—1188no—
538D8—1188no—
539C2×C8—592no—
540C2×C8—592no—
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—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—1181no—
555C4⋊C4—1181no—
556C4⋊C4—1181no—
557C4⋊C4—1181no—
558C4⋊C4—2362no—
559C4⋊C4C2×C4×D5912yes—
560C4⋊C4C2×D23612yes—
561C4⋊C4#1174568512yes—
562C22⋊C4—24no—
563C22⋊C4—24no—
564C22⋊C4—24no—
565C22⋊C4—1184no—
566C22⋊C4—1184no—
567C22⋊C4—2362no—
568C22⋊C4—2362no—
569C22⋊C4—2362no—
570C42—22no—
571C42—22no—
572C42—22no—
573C42—21no—
574C42—21no—
575C42—41no—
576C42—42no—
577C42—42no—
578C42—42no—
579C42—2362no—
580C42C2×C4×D5912yes—
581C42C2×D23612yes—
582C42#1174568512yes—
583C42#1174568512yes—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—1182no—
592C23—2361no—
593C23—2361no—
594C23—2361no—
595C23—2361no—
596C23—2361no—
597C23—2361no—
598C23C22×C22⋊D5911yescharacteristic
599Q8—1182no—
600Q8—1182no—
601Q8—2361no—
602Q8—2361no—
603D4—22no—
604D4—22no—
605D4—22no—
606D4—1182no—
607D4—1182no—
608D4—2361no—
609D4—2361no—
610D4C4×D23614yes—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—48no—
626C2×C4—48no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—48no—
634C2×C4—1182no—
635C2×C4—4724no—
636C2×C4—2361no—
637C2×C4—2361no—
638C2×C4—2361no—
639C2×C4—2361no—
640C2×C4—2361no—
641C2×C4—2361no—
642C2×C4—2361no—
643C2×C4—2361no—
644C2×C4C4×C22⋊D5912yes—
645C2×C4C4×C22⋊D5912yes—
646C2×C4#1427370112yes—
647C2×C4#1427370112yes—
648C2×C4#1427374712yes—
649C2×C4#1427374712yes—
650C2×C4#1427375312yes—
651C2×C4C22×C4×D5911yescharacteristic
652C2×C4C22×D23611yescharacteristic
653C2×C4C2×#1174568511yescharacteristic
654C2×C4C2×#1174568511yescharacteristic
655C2×C4C2×#1174568511yescharacteristic
656C2×C4C2×#1174568511yescharacteristic
657C8—1182no—
658C8—1182no—
659C8—2361no—
660C8—2361no—
661C22—24no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—4721no—
669C22—4721no—
670C22—4721no—
671C22—4721no—
672C22—2362no—
673C22—2362no—
674C22—2362no—
675C22C2×C4×C22⋊D5911yescharacteristic
676C22C2×#1427370111yescharacteristic
677C22#1683791311yescharacteristic
678C22C2×#1427374711yescharacteristic
679C22C2×#1427374711yescharacteristic
680C22C2×#1427375311yescharacteristic
681C22#1683820011yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—41no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—4721no—
691C4—4721no—
692C4—2362no—
693C4#1683761714yesdirect product factor
694C4C2×C4×D23611yescharacteristic
695C4C4×#1174568511yescharacteristic
696C4#1683793611yescharacteristic
697C4#1683795211yescharacteristic
698C2—44no—
699C2—4722no—
700C2C4×#1427370111yescharacteristic
701C2C4×#1427374711yescharacteristic
702C2C4×#1427375311yescharacteristic
703C2C2×#1683761711yescharacteristic
704C2#2143355111yescharacteristic
705C2#2143411411yescharacteristic
706C2#2143414311yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC42×D4×C59C2
socleC23×C59C22×D4
prime radicalC22×#11745669C22
cosocleC22×C4×C59C24
hypercenterC42×D4D59
hypocenterC59C4×#463
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C43 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11745670C2semidirect
4. C4×#14273715C2semidirect
5. #21425028C2semidirect
6. #21424864C2semidirect
7. #21424737C2semidirect
8. #21424723C2semidirect
10. #21424430C2semidirect
11. #21424106C2semidirect
12. C4×C4⋊(C59⋊C8)C2semidirect
13. C4×#14273650C2semidirect
14. C4×#14273647C2semidirect
15. C42×D4×C59C2semidirect
21. #16837617C4direct (N × H)
67. C2×#11745670C2×C4semidirect
76. #14273715C2×C4semidirect
93. C4⋊(C59⋊C8)C2×C4semidirect
96. #14273650C2×C4semidirect
101. #14273647C2×C4semidirect
116. C4×D4×C59C2×C4semidirect
337. C4×C59#463semidirect
349. C42×D4D59semidirect
415. C59C4×#463semidirect
443. C4×D4C4×D59semidirect
693. C4#16837617direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168376172
C2×C4×#117456702
C2×C4×#117456692
C4×#142737152
#214250282
#214248642
#214247372
#214247232
#214244442
#214244302
#214241062
C4×C4⋊(C59⋊C8)2
C4×#142736502
C4×#142736472
C42×D4×C592
C4×#46359