Finite Group Databasebeta

← C2×#21437018 #29469191

Subgroups — C2×#21437018 #29469191

Order 15104.

2006 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838128C211yesmaximal, characteristic, complemented
2C2×D4×Dic118C211yesmaximal, characteristic
3#21437018C2116yesmaximal, direct product factor
4C2×#16837811C211yesmaximal, characteristic, complemented
5C2×#16837810C211yesmaximal, characteristic, complemented
6C2×#16837806C211yesmaximal, characteristic, complemented
7C2×#16837697C211yesmaximal, characteristic, complemented
8C2×#16837695C211yesmaximal, characteristic, complemented
9C2×#16837685C211yesmaximal, characteristic, complemented
10C2×#16837704C211yesmaximal, characteristic
11C2×#16837702C211yesmaximal, characteristic
12C2×#16837680C211yesmaximal, characteristic
13C2×#16837530C211yesmaximal, characteristic, complemented
14C2×#16837503C211yesmaximal, characteristic
15C2×SD16×Dic59C211yesmaximal, characteristic
16C2×C59×#440C211yesmaximal, characteristic
17C23×Dic118—21no—
18#16838128—24no—
19#16838128C2218yescomplemented
20D4×Dic118—24no—
21D4×Dic118C2218yes—
22C2×#14273727C2211yescharacteristic
23C2×#14273726—21no—
24C2×#14273726C2211yescharacteristic
25C2×#14273726C2211yescharacteristic
26C2×#14273726C2211yescharacteristic
27C2×#14273719—21no—
28C2×#14273719C2211yescharacteristic
29C2×#14273718—21no—
30C2×#14273718C2211yescharacteristic
31C2×#14273706—21no—
32C2×#14273704—21no—
33C2×#14273704—21no—
34C2×Q8×Dic59C2211yescharacteristic
35C2×Q8×Dic59C2211yescharacteristic
36C2×C4×Dic118—21no—
37C2×C4×Dic118C2211yescharacteristic
38C2×D4×Dic59C2211yescharacteristic
39C2×D4×Dic59C2211yescharacteristic
40#16837811C2218yescomplemented
41#16837810C2218yescomplemented
42#16837806C2218yescomplemented
43#16837704C2218yes—
44#16837702C2218yes—
45#16837697C2218yescomplemented
46#16837695C2218yescomplemented
47#16837685C2218yescomplemented
48#16837680C2218yes—
49#16837530C2218yescomplemented
50#16837503C2218yes—
51SD16×Dic59C2218yes—
52C2×#14273661C2211yescharacteristic
53C2×#14273661C2211yescharacteristic
54C2×#14273660C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273659C2211yescharacteristic
58C2×#14273659C2211yescharacteristic
59C2×#14273658C2211yescharacteristic
60C2×C4⋊(C59⋊C8)C2211yescharacteristic
61C2×Dic59⋊C8C2211yescharacteristic
62C2×Dic59⋊C8C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273651C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×#14273648C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C59×#440C2218yes—
73C2×#107×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118—21no—
80C22×Dic118—21no—
81C22×Dic118—28no—
82C22×Dic118—48no—
83C22×Dic118D411yescharacteristic
84C23×Dic59—21no—
85C23×Dic59—21no—
86C22×C59⋊C8C2311yescharacteristic
87C22×C59⋊C8C2311yescharacteristic
88#14273727—22no—
89#14273727C2314yes—
90#14273726—28no—
91#14273726—22no—
92#14273726—22no—
93#14273726—22no—
94#14273726C2314yes—
95#14273726C2314yes—
96#14273726C2314yes—
97#14273719—22no—
98#14273719—28no—
99#14273719C2314yes—
100#14273718—28no—
101#14273718—22no—
102#14273718C2314yes—
103#14273706—28no—
104#14273704—28no—
105#14273704—28no—
106Q8×Dic59—22no—
107Q8×Dic59—22no—
108Q8×Dic59C2314yes—
109Q8×Dic59C2314yes—
110C4×Dic118—28no—
111C4×Dic118D414yes—
112C4×Dic118C2314yes—
113D4×Dic59—22no—
114D4×Dic59—22no—
115D4×Dic59C2314yes—
116D4×Dic59C2314yes—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59D411yescharacteristic
122C2×C4⋊Dic59C2311yescharacteristic
123C2×C4⋊Dic59C2311yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4D411yescharacteristic
133C2×Dic59⋊C4D411yescharacteristic
134C2×C22⋊Dic59—21no—
135C2×C22⋊Dic59—21no—
136C2×C4×Dic59—21no—
137C2×C4×Dic59—21no—
138C2×C4×Dic59C2311yescharacteristic
139C2×C4×Dic59C2311yescharacteristic
140#14273661C2314yes—
141#14273661C2314yes—
142#14273660C2314yes—
143#14273660C2314yes—
144#14273660C2314yes—
145#14273659C2314yes—
146#14273659C2314yes—
147#14273658C2314yes—
148C4⋊(C59⋊C8)C2314yes—
149Dic59⋊C8C2314yes—
150Dic59⋊C8C2314yes—
151#14273651C2314yes—
152#14273651C2314yes—
153#14273648C2314yes—
154#14273648C2314yes—
155#14273637C2314yes—
156C8×Dic59C2314yes—
157C22×Q8×C59C2311yescharacteristic
158C22×D4×C59C2311yescharacteristic
159C23×C4×C59—21no—
160C2×SD16×C59Q818yescomplemented
161C2×SD16×C59C2314yes—
162C22×C8×C59C2311yescharacteristic
163C22×C8×C59C2311yescharacteristic
164C4×Q8×C59—22no—
165C4×Q8×C59C2314yes—
166C4×D4×C59—22no—
167C4×D4×C59C2314yes—
168C2×C4⋊C4×C59—21no—
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C22⋊C4×C59—21no—
172C2×C42×C59—21no—
173C2×C42×C59C2311yescharacteristic
174#107×C59C2314yes—
175#103×C59C2314yes—
176#102×C59C2314yes—
177#97×C59C2314yes—
178C24×C59—21no—
179C2×Q8×C59—21no—
180C2×Q8×C59—22no—
181C2×Q8×C59C2×Q814yescomplemented
182C2×Q8×C59C2412yes—
183C2×D4×C59—21no—
184C2×D4×C59—22no—
185C2×D4×C59C2×Q814yes—
186C2×D4×C59C2412yes—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—24no—
191C22×C4×C59—44no—
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2411yescharacteristic
195C22×Dic59—21no—
196C22×Dic59—21no—
197C22×Dic59—21no—
198C22×Dic59—21no—
199C22×Dic59—24no—
200C22×Dic59—24no—
201C22×Dic59—44no—
202C22×Dic59—44no—
203C22×Dic59C2×D411yescharacteristic
204C22×Dic59C2×D411yescharacteristic
205C22×Dic59C2×D411yescharacteristic
206C22×Dic59C2×D411yescharacteristic
207C2×Dic118—24no—
208C2×Dic118—24no—
209C2×Dic118—24no—
210C2×Dic118—24no—
211C2×Dic118—24no—
212C2×Dic118—432no—
213C2×Dic118—44no—
214C2×Dic118—44no—
215C2×Dic118—44no—
216C2×Dic118—44no—
217C2×Dic118C2×D414yes—
218SD16×C59C2×Q8116yescomplemented
219C2×C8×C59—22no—
220C2×C8×C59C2×Q814yescomplemented
221C2×C8×C59C2412yes—
222C2×C8×C59C2412yes—
223C4⋊C4×C59—24no—
224C4⋊C4×C59—21no—
225C4⋊C4×C59—21no—
226C4⋊C4×C59C2412yes—
227C4⋊C4×C59C2412yes—
228C22⋊C4×C59—24no—
229C42×C59—24no—
230C42×C59C2×D412yes—
231C42×C59C2412yes—
232C22⋊Dic59—24no—
233C22⋊Dic59—24no—
234C4⋊Dic59—24no—
235C4⋊Dic59—21no—
236C4⋊Dic59—21no—
237C4⋊Dic59—21no—
238C4⋊Dic59—21no—
239C4⋊Dic59—24no—
240C4⋊Dic59—24no—
241C4⋊Dic59—24no—
242C4⋊Dic59C2×D414yes—
243C4⋊Dic59C2412yes—
244C4⋊Dic59C2412yes—
245C4⋊Dic59C2412yes—
246C4⋊Dic59C2412yes—
247Dic59⋊C4—24no—
248Dic59⋊C4—24no—
249Dic59⋊C4—24no—
250Dic59⋊C4—24no—
251Dic59⋊C4—24no—
252Dic59⋊C4—24no—
253Dic59⋊C4C2×D414yes—
254Dic59⋊C4C2×D414yes—
255C4×Dic59—24no—
256C4×Dic59—24no—
257C4×Dic59C2×D412yes—
258C4×Dic59C2×D412yes—
259C4×Dic59C2412yes—
260C4×Dic59C2412yes—
261C2×C59⋊C8—22no—
262C2×C59⋊C8—22no—
263C2×C59⋊C8C2412yes—
264C2×C59⋊C8C2412yes—
265C23×C59—24no—
266C23×C59—22no—
267C23×C59—42no—
268C23×C59—42no—
269C23×C59C22×D411yescharacteristic
270Q8×C59—24no—
271Q8×C59—22no—
272Q8×C59C22×Q814yescomplemented
273D4×C59—24no—
274D4×C59—22no—
275D4×C59C22×Q814yes—
276C2×C4×C59—24no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—48no—
283C2×C4×C59—42no—
284C2×C4×C59—42no—
285C2×C4×C59C22×D412yes—
286C2×C4×C59C22×D412yes—
287C2×C4×C59C22×D411yescharacteristic
288C2×C4×C59C22×Q812yes—
289C2×C4×C592−1+412yes—
290C2×C4×C59C2511yescharacteristic
291C2×Dic59—22no—
292C2×Dic59—22no—
293C2×Dic59—22no—
294C2×Dic59—22no—
295C2×Dic59—22no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—48no—
299C2×Dic59—42no—
300C2×Dic59—42no—
301C2×Dic59—42no—
302C2×Dic59—42no—
303C2×Dic59—48no—
304C2×Dic59AGL(1,ℤ/8)14yes—
305C2×Dic59C22×D412yes—
306C2×Dic59C22×D412yes—
307C2×Dic59C22×D412yes—
308C2×Dic59C22×D412yes—
309Dic118—28no—
310Dic118—48no—
311Dic118—48no—
312Dic118—48no—
313Dic118—48no—
314C8×C59—22no—
315C8×C59C22×Q814yescomplemented
316C59⋊C8—22no—
317C59⋊C8—22no—
318C2×#3386—591nomaximal, Sylow
319C22×C59—24no—
320C22×C59—48no—
321C22×C59—42no—
322C22×C59—42no—
323C22×C59D4×Q812yes—
324C22×C59C2×AGL(1,ℤ/8)12yes—
325C22×C59#57812yes—
326C22×C59C23×D411yescharacteristic
327C4×C59—24no—
328C4×C59—22no—
329C4×C59—22no—
330C4×C59—42no—
331C4×C59—42no—
332C4×C59D4×Q812yes—
333C4×C59C23×Q811yescharacteristic
334C4×C59C2×2−1+411yescharacteristic
335Dic59—22no—
336Dic59—22no—
337Dic59—22no—
338Dic59—42no—
339Dic59—42no—
340Dic59—42no—
341Dic59—42no—
342Dic59C2×AGL(1,ℤ/8)14yes—
343C2×#557—591no—
344C2×D4×Q8—591no—
345#3386—5916no—
346C2×#501—591no—
347C2×#501—591no—
348C2×#500—591no—
349C2×#477—591no—
350C2×#477—591no—
351C2×#475—591no—
352C2×#478—591no—
353C2×#478—591no—
354C2×#474—591no—
355C2×#446—591no—
356C2×#440—591no—
357C2×#440D5911yescharacteristic
358C2×C4×SD16—591no—
359C2×C59—44no—
360C2×C59#338614yescomplemented
361C2×C59C2×D4×Q811yescharacteristic
362C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
363C2×C59C2×#57811yescharacteristic
364C23×Q8—1181no—
365C22×SD16C2×D5911yescharacteristic
366#557—598no—
367#557—1184no—
368D4×Q8—598no—
369D4×Q8—1184no—
370C2×C4⋊Q8—591no—
371C2×C4⋊Q8—591no—
372C2×C4⋊Q8—591no—
373C2×C4⋊Q8—591no—
374C2×C4⋊Q8—1181no—
375C2×#125—591no—
376C2×#125—591no—
377C2×#125—1181no—
378C2×#125—1181no—
379C2×C22⋊Q8—1181no—
380C2×C22⋊Q8—1181no—
381C2×C22⋊Q8—1181no—
382C2×C4×Q8—591no—
383C2×C4×Q8—591no—
384C2×C4×Q8—591no—
385C2×C4×Q8—1181no—
386C2×C4×Q8C2×D5911yescharacteristic
387C2×C4×D4—591no—
388C2×C4×D4—591no—
389C2×C4×D4C2×D5911yescharacteristic
390#501—598no—
391#501—598no—
392#500—598no—
393#478—598no—
394#478—598no—
395#477—598no—
396#477—598no—
397#475—598no—
398#474—598no—
399#446—598no—
400#440—598no—
401#440C2×D5918yes—
402C4×SD16—598no—
403C2×#107—591no—
404C2×#107—591no—
405C2×#107—591no—
406C2×#107—591no—
407C2×#107—591no—
408C2×#107C2×D5911yescharacteristic
409C2×#106—591no—
410C2×#106—591no—
411C2×#106—591no—
412C2×C4⋊C8—591no—
413C2×C4⋊C8—591no—
414C2×C4⋊C8—591no—
415C2×#103—591no—
416C2×#103—591no—
417C2×#103C2×D5911yescharacteristic
418C2×#102—591no—
419C2×#102—591no—
420C2×#102C2×D5911yescharacteristic
421C2×#97—591no—
422C2×#97C2×D5911yescharacteristic
423C2×C4×C8—591no—
424C59C2×#338611yescharacteristic, complemented, Sylow
425C22×Q8—591no—
426C22×Q8—1181no—
427C22×Q8—1181no—
428C22×Q8—1181no—
429C22×Q8—1188no—
430C22×Q8—1181no—
431C22×Q8—2368no—
432C22×Q8C22×D5911yescharacteristic
433C22×D4C22×D5911yescharacteristic
434C23×C4—21no—
435C23×C4—1181no—
436C23×C4—1181no—
437C2×SD16Dic11818yescomplemented
438C2×SD16C22×D5914yes—
439C22×C8—591no—
440C22×C8—591no—
441C22×C8C22×D5911yescharacteristic
442C22×C8C22×D5911yescharacteristic
443C4⋊Q8—594no—
444C4⋊Q8—594no—
445C4⋊Q8—594no—
446C4⋊Q8—594no—
447C4⋊Q8—1182no—
448C4⋊Q8—1182no—
449C4⋊Q8—1182no—
450C4⋊Q8—1188no—
451C4⋊Q8—1182no—
452#125—594no—
453#125—594no—
454#125—1188no—
455#125—1182no—
456#125—1188no—
457#125—1182no—
458C22⋊Q8—1188no—
459C22⋊Q8—1188no—
460C22⋊Q8—1188no—
461C4×Q8—22no—
462C4×Q8—594no—
463C4×Q8—594no—
464C4×Q8—594no—
465C4×Q8—594no—
466C4×Q8—1188no—
467C4×Q8—1182no—
468C4×Q8—1182no—
469C4×Q8C22×D5914yes—
470C4×D4—22no—
471C4×D4—594no—
472C4×D4—594no—
473C4×D4—1182no—
474C4×D4—1182no—
475C4×D4C22×D5914yes—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—591no—
478C2×C4⋊C4—591no—
479C2×C4⋊C4—591no—
480C2×C4⋊C4—591no—
481C2×C4⋊C4—591no—
482C2×C4⋊C4—591no—
483C2×C4⋊C4—591no—
484C2×C4⋊C4—1181no—
485C2×C4⋊C4—1181no—
486C2×C4⋊C4—1181no—
487C2×C4⋊C4—1181no—
488C2×C4⋊C4—1181no—
489C2×C4⋊C4—1181no—
490C2×C4⋊C4—1181no—
491C2×C4⋊C4—1181no—
492C2×C4⋊C4—1181no—
493C2×C4⋊C4—1181no—
494C2×C4⋊C4C22×D5911yescharacteristic
495C2×C4⋊C4C22×D5911yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—1181no—
498C2×C22⋊C4—1181no—
499C2×C42—21no—
500C2×C42—591no—
501C2×C42—591no—
502C2×C42—1181no—
503C2×C42—1181no—
504C2×C42C22×D5911yescharacteristic
505#107—594no—
506#107—594no—
507#107—594no—
508#107—594no—
509#107—594no—
510#107C22×D5914yes—
511#106—594no—
512#106—594no—
513#106—594no—
514C4⋊C8—594no—
515C4⋊C8—594no—
516C4⋊C8—594no—
517#103—594no—
518#103—594no—
519#103C22×D5914yes—
520#102—594no—
521#102—594no—
522#102C22×D5914yes—
523#97—594no—
524#97C22×D5914yes—
525C4×C8—594no—
526C24—21no—
527C2×Q8—21no—
528C2×Q8—22no—
529C2×Q8—594no—
530C2×Q8—1184no—
531C2×Q8—1184no—
532C2×Q8—1184no—
533C2×Q8—1184no—
534C2×Q8—1184no—
535C2×Q8—2364no—
536C2×Q8—2364no—
537C2×Q8—2364no—
538C2×Q8—2364no—
539C2×Q8—23632no—
540C2×Q8C2×Dic11814yescomplemented
541C2×Q8C23×D5912yes—
542C2×D4—21no—
543C2×D4—22no—
544C2×D4C2×Dic11814yes—
545C2×D4C23×D5912yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—44no—
551C22×C4—591no—
552C22×C4—591no—
553C22×C4—591no—
554C22×C4—591no—
555C22×C4—1184no—
556C22×C4—1184no—
557C22×C4—1181no—
558C22×C4—1181no—
559C22×C4—1181no—
560C22×C4—1181no—
561C22×C4—2364no—
562C22×C4—2364no—
563C22×C4D4×D5911yescharacteristic
564C22×C4D4×D5911yescharacteristic
565C22×C4C23×D5911yescharacteristic
566SD16C2×Dic118116yescomplemented
567C2×C8—22no—
568C2×C8—592no—
569C2×C8—592no—
570C2×C8—1182no—
571C2×C8—1182no—
572C2×C8C2×Dic11814yescomplemented
573C2×C8C23×D5912yes—
574C2×C8C23×D5912yes—
575C4⋊C4—24no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—594no—
579C4⋊C4—594no—
580C4⋊C4—594no—
581C4⋊C4—592no—
582C4⋊C4—592no—
583C4⋊C4—592no—
584C4⋊C4—592no—
585C4⋊C4—1184no—
586C4⋊C4—1184no—
587C4⋊C4—1184no—
588C4⋊C4—1184no—
589C4⋊C4—1184no—
590C4⋊C4—1184no—
591C4⋊C4—1184no—
592C4⋊C4—1181no—
593C4⋊C4—1181no—
594C4⋊C4—1181no—
595C4⋊C4—1181no—
596C4⋊C4—1184no—
597C4⋊C4—1184no—
598C4⋊C4—1184no—
599C4⋊C4C23×D5912yes—
600C4⋊C4C23×D5912yes—
601C22⋊C4—24no—
602C22⋊C4—1184no—
603C22⋊C4—1184no—
604C42—24no—
605C42—592no—
606C42—592no—
607C42—592no—
608C42—592no—
609C42—1184no—
610C42—1184no—
611C42D4×D5912yes—
612C42C23×D5912yes—
613C23—22no—
614C23—24no—
615C23—42no—
616C23—42no—
617C23C2×D4×D5911yescharacteristic
618Q8—22no—
619Q8—24no—
620Q8—1188no—
621Q8—2368no—
622Q8—2368no—
623Q8—2368no—
624Q8—2368no—
625Q8C22×Dic11814yescomplemented
626D4—22no—
627D4—24no—
628D4C22×Dic11814yes—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—48no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—594no—
639C2×C4—592no—
640C2×C4—592no—
641C2×C4—592no—
642C2×C4—592no—
643C2×C4—1182no—
644C2×C4—1182no—
645C2×C4—1182no—
646C2×C4—1182no—
647C2×C4—1182no—
648C2×C4—1182no—
649C2×C4—1182no—
650C2×C4—2368no—
651C2×C4—2368no—
652C2×C4—2362no—
653C2×C4—2362no—
654C2×C4—2362no—
655C2×C4—2362no—
656C2×C4C2×D4×D5912yes—
657C2×C4C2×D4×D5912yes—
658C2×C4C2×D4×D5911yescharacteristic
659C2×C4C22×Dic11812yes—
660C2×C4#1427377412yes—
661C2×C4C24×D5911yescharacteristic
662C8—22no—
663C8—1182no—
664C8—1182no—
665C8C22×Dic11814yescomplemented
666C22—24no—
667C22—48no—
668C22—42no—
669C22—42no—
670C22D4×Dic11812yes—
671C22AGL(1,ℤ/8)×D5912yes—
672C22#1683821812yes—
673C22C22×D4×D5911yescharacteristic
674C4—22no—
675C4—24no—
676C4—22no—
677C4—42no—
678C4—42no—
679C4—594no—
680C4—1182no—
681C4—1182no—
682C4—1182no—
683C4—2362no—
684C4—2362no—
685C4—2362no—
686C4—2362no—
687C4D4×Dic11812yes—
688C4C23×Dic11811yescharacteristic
689C4C2×#1427377411yescharacteristic
690C2—44no—
691C2#2143701814yesdirect product factor
692C2C2×D4×Dic11811yescharacteristic
693C2C2×AGL(1,ℤ/8)×D5911yescharacteristic
694C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#440C2
socleC23×C59C22×D4
prime radicalC22×D4×C59C23
hypercenterC2×#440D59
hypocenterC59C2×#3386
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#16838128C2semidirect
3. #21437018C2direct (N × H)
4. C2×#16837811C2semidirect
5. C2×#16837810C2semidirect
6. C2×#16837806C2semidirect
7. C2×#16837697C2semidirect
8. C2×#16837695C2semidirect
9. C2×#16837685C2semidirect
13. C2×#16837530C2semidirect
19. #16838128C22semidirect
40. #16837811C22semidirect
41. #16837810C22semidirect
42. #16837806C22semidirect
45. #16837697C22semidirect
46. #16837695C22semidirect
47. #16837685C22semidirect
49. #16837530C22semidirect
160. C2×SD16×C59Q8semidirect
181. C2×Q8×C59C2×Q8semidirect
218. SD16×C59C2×Q8semidirect
220. C2×C8×C59C2×Q8semidirect
272. Q8×C59C22×Q8semidirect
315. C8×C59C22×Q8semidirect
360. C2×C59#3386semidirect
424. C59C2×#3386semidirect
437. C2×SD16Dic118semidirect
540. C2×Q8C2×Dic118semidirect
566. SD16C2×Dic118semidirect
572. C2×C8C2×Dic118semidirect
625. Q8C22×Dic118semidirect
665. C8C22×Dic118semidirect
691. C2#21437018direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381282
C2×D4×Dic1182
#214370182
C2×#168378112
C2×#168378102
C2×#168378062
C2×#168376972
C2×#168376952
C2×#168376852
C2×#168377042
C2×#168377022
C2×#168376802
C2×#168375302
C2×#168375032
C2×SD16×Dic592
C2×C59×#4402
C2×#338659