Finite Group Databasebeta

← C2×#21433636 #29455615

Subgroups — C2×#21433636 #29455615

Order 15104.

2934 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273751C211yesmaximal, characteristic, complemented
2C22×#14273748C211yesmaximal, characteristic, complemented
3C2×#16837970C211yesmaximal, characteristic, complemented
4C2×#16837881C211yesmaximal, characteristic, complemented
5#21433636C2116yesmaximal, direct product factor
6C2×#16837627C211yesmaximal, characteristic, complemented
7C2×#16837621C211yesmaximal, characteristic, complemented
8C2×#16837603C211yesmaximal, characteristic, complemented
9C2×#16837601C211yesmaximal, characteristic, complemented
10C2×#16837619C211yesmaximal, characteristic, complemented
11C2×#16837597C211yesmaximal, characteristic, complemented
12C2×#16837595C211yesmaximal, characteristic, complemented
13C2×#16837427C211yesmaximal, characteristic, complemented
14C2×#16837402C211yesmaximal, characteristic, complemented
15C2×#102×D59C211yesmaximal, characteristic, complemented
16C2×C59×#463C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C22×#11745687C2211yescharacteristic
19C22×D4×D59C2211yescharacteristic
20C2×#14273751—28no—
21C2×#14273751C2218yescomplemented
22C2×#14273748—28no—
23C2×#14273748C2218yescomplemented
24C22×#11745672C2211yescharacteristic, complemented
25C22×#11745660C2211yescharacteristic
26C22×#11745660C2211yescharacteristic, complemented
27C22×#11745670C2211yescharacteristic
28C22×#11745669C2211yescharacteristic
29C22×#11745669C2211yescharacteristic, complemented
30C22×#11745659C2211yescharacteristic
31C22×C8×D59C2211yescharacteristic
32#16837970—24no—
33#16837970C2218yescomplemented
34C2×#14273724C2211yescharacteristic
35C2×#14273723C2211yescharacteristic
36C2×#14273716C2211yescharacteristic
37C2×#14273700—21no—
38C2×#14273700—21no—
39C2×#14273697—21no—
40C2×#14273697—21no—
41#16837881—24no—
42#16837881C2218yescomplemented
43C2×C4×Dic118C2211yescharacteristic, complemented
44C2×#14273692C2211yescharacteristic, complemented
45C2×D4×Dic59C2211yescharacteristic, complemented
46C2×C4×C22⋊D59—21no—
47C2×(C22⋊D59)⋊C4—21no—
48C2×#14273684C2211yescharacteristic
49C2×#14273683—21no—
50C22×Dic59⋊C4—21no—
51C2×C4⋊C4×D59C2211yescharacteristic
52#16837627C2218yescomplemented
53#16837621C2218yescomplemented
54#16837619C2218yescomplemented
55#16837603C2218yescomplemented
56#16837601C2218yescomplemented
57#16837597C2218yescomplemented
58#16837595C2218yescomplemented
59#16837427C2218yescomplemented
60C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
61C2×Dic59⋊C8C2211yescharacteristic, complemented
62C2×Dic59⋊C8C2211yescharacteristic, complemented
63#16837402C2218yescomplemented
64C2×#14273651C2211yescharacteristic, complemented
65C2×#14273649C2211yescharacteristic
66C2×#14273649C2211yescharacteristic, complemented
67C2×#14273648C2211yescharacteristic
68C2×#14273647C2211yescharacteristic
69C2×#14273647C2211yescharacteristic, complemented
70#102×D59C2218yescomplemented
71C22×SD16×C59C2211yescharacteristic, complemented
72C22×D8×C59C2211yescharacteristic
73C2×#124×C59C2211yescharacteristic
74C2×C4×D4×C59C2211yescharacteristic, complemented
75C59×#463C2218yescomplemented
76C2×C4⋊C8×C59C2211yescharacteristic, complemented
77C2×#103×C59C2211yescharacteristic, complemented
78C2×#102×C59C2211yescharacteristic
79C24×D59—21no—
80C2×#11745689—22no—
81C2×#11745689—24no—
82C2×#11745689—24no—
83C2×#11745689C2314yes—
84C2×#11745687—22no—
85C2×#11745687—24no—
86C2×#11745687D418yescomplemented
87C2×#11745687C2314yes—
88C22×Dic118C2311yescharacteristic
89C22×D236—21no—
90C22×D236—21no—
91C22×D236—21no—
92C22×D236C2311yescharacteristic
93C22×D236C2311yescharacteristic
94C22×C22⋊D59—21no—
95C22×C22⋊D59—21no—
96C22×C22⋊D59—21no—
97C22×C22⋊D59—21no—
98C2×D4×D59—24no—
99C2×D4×D59—22no—
100C2×D4×D59—24no—
101C2×D4×D59C2314yes—
102C23×Dic59—21no—
103C23×Dic59—21no—
104C22×C4×D59—21no—
105C22×C4×D59—21no—
106C22×C4×D59C2311yescharacteristic
107#14273751—232no—
108#14273748—232no—
109C2×#11745672—24no—
110C2×#11745672C2314yescomplemented
111C2×#11745660—24no—
112C2×#11745660—24no—
113C2×#11745660C2314yes—
114C2×#11745660C2314yescomplemented
115C2×#11745670—24no—
116C2×#11745670C2314yes—
117C2×#11745669—24no—
118C2×#11745669—24no—
119C2×#11745669C2314yes—
120C2×#11745669C2314yescomplemented
121C2×#11745659—24no—
122C2×#11745659C2314yes—
123C22×C59⋊C8C2311yescharacteristic
124C22×C59⋊C8C2311yescharacteristic
125C2×C8×D59—24no—
126C2×C8×D59C2314yes—
127#14273724—22no—
128#14273724C2314yes—
129#14273723—22no—
130#14273723C2314yes—
131#14273716—22no—
132#14273716C2314yes—
133#14273700—28no—
134#14273700—28no—
135#14273697—28no—
136#14273697—28no—
137C4×Dic118—22no—
138C4×Dic118C2314yescomplemented
139#14273692—22no—
140#14273692C2314yescomplemented
141D4×Dic59—22no—
142D4×Dic59C2314yescomplemented
143C4×C22⋊D59—28no—
144(C22⋊D59)⋊C4—28no—
145#14273684D414yes—
146#14273684C2314yes—
147#14273683—28no—
148C2×C4⋊Dic59C2311yescharacteristic
149C2×Dic59⋊C4—21no—
150C2×Dic59⋊C4—21no—
151C2×Dic59⋊C4—21no—
152C2×Dic59⋊C4—28no—
153C2×Dic59⋊C4D411yescharacteristic
154C2×Dic59⋊C4D411yescharacteristic
155C4⋊C4×D59—22no—
156C4⋊C4×D59C2314yes—
157C2×C22⋊Dic59—21no—
158C2×(C2×D59)⋊C4—21no—
159C2×(C2×D59)⋊C4—21no—
160C2×(C2×D59)⋊C4D411yescharacteristic
161C2×(C2×D59)⋊C4D411yescharacteristic
162C2×C4×Dic59—21no—
163C2×C4×Dic59—21no—
164C2×C4×Dic59C2311yescharacteristic
165C4⋊(C59⋊C8)C2314yescomplemented
166Dic59⋊C8C2314yescomplemented
167Dic59⋊C8C2314yescomplemented
168#14273651C2314yescomplemented
169#14273649C2314yes—
170#14273649C2314yescomplemented
171#14273648C2314yes—
172#14273647C2314yes—
173#14273647C2314yescomplemented
174C22×Q8×C59C2311yescharacteristic
175C22×D4×C59C2311yescharacteristic
176C22×D4×C59C2311yescharacteristic
177C23×C4×C59—21no—
178C2×SD16×C59—24no—
179C2×SD16×C59C2314yescomplemented
180C2×D8×C59—24no—
181C2×D8×C59C2314yes—
182C22×C8×C59C2311yescharacteristic
183C22×C8×C59C2311yescharacteristic
184#124×C59—22no—
185#124×C59C2314yes—
186C4×D4×C59—22no—
187C4×D4×C59C2314yescomplemented
188C2×C4⋊C4×C59C2311yescharacteristic
189C2×C22⋊C4×C59—21no—
190C2×C22⋊C4×C59—21no—
191C2×C22⋊C4×C59—21no—
192C2×C42×C59C2311yescharacteristic
193C4⋊C8×C59C2314yescomplemented
194#103×C59C2314yescomplemented
195#102×C59C2314yes—
196C24×C59—21no—
197C24×C59—21no—
198C23×D59—21no—
199C23×D59—21no—
200C23×D59—24no—
201C23×D59—44no—
202C23×D59—82no—
203C23×D59—82no—
204C23×D59C2×D411yescharacteristic
205C2×Q8×C59—21no—
206C2×Q8×C59—22no—
207C2×Q8×C59—22no—
208C2×Q8×C59C2412yes—
209C2×D4×C59—21no—
210C2×D4×C59—22no—
211C2×D4×C59—21no—
212C2×D4×C59—22no—
213C2×D4×C59—22no—
214C2×D4×C59C2×D414yes—
215C2×D4×C59C2412yes—
216C2×D4×C59C2412yes—
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—24no—
220C22×C4×C59—82no—
221C22×C4×C59C2×D411yescharacteristic
222C22×C4×C59C2×D411yescharacteristic
223C22×C4×C59C2411yescharacteristic
224C2×C22⋊D59—28no—
225C2×C22⋊D59—24no—
226C2×C22⋊D59—24no—
227C2×C22⋊D59—24no—
228C2×C22⋊D59—24no—
229C2×C22⋊D59—44no—
230C2×C22⋊D59—82no—
231C2×C22⋊D59—82no—
232C22×Dic59—21no—
233C22×Dic59—28no—
234C22×Dic59—24no—
235C22×Dic59—21no—
236C22×Dic59—24no—
237C22×Dic59—82no—
238C22×Dic59C2×D411yescharacteristic
239C22×Dic59C2×D411yescharacteristic
240C22×Dic59C2×D411yescharacteristic
241#11745689—28no—
242#11745689—28no—
243#11745689—48no—
244#11745687—216no—
245#11745687—28no—
246#11745687C2×D4116yescomplemented
247D4×D59—28no—
248D4×D59—28no—
249D4×D59—48no—
250C2×D236—22no—
251C2×D236—22no—
252C2×D236—22no—
253C2×D236—22no—
254C2×D236—24no—
255C2×D236—21no—
256C2×D236—21no—
257C2×D236—24no—
258C2×D236—24no—
259C2×D236—44no—
260C2×D236—82no—
261C2×D236—82no—
262C2×D236C2412yes—
263C2×D236C2412yes—
264C2×C4×D59—24no—
265C2×C4×D59—24no—
266C2×C4×D59—44no—
267C2×C4×D59—82no—
268C2×C4×D59C2×D412yes—
269C2×C4×D59C2×D414yes—
270C2×C4×D59#4114yes—
271C2×C4×D59C2412yes—
272C2×Dic118—21no—
273C2×Dic118—22no—
274C2×Dic118C2×D414yes—
275C2×Dic118C2412yes—
276SD16×C59—28no—
277D8×C59—28no—
278C2×C8×C59—22no—
279C2×C8×C59—22no—
280C2×C8×C59C2412yes—
281C2×C8×C59C2412yes—
282C4⋊C4×C59—21no—
283C4⋊C4×C59C2412yes—
284C22⋊C4×C59—24no—
285C22⋊C4×C59—24no—
286C22⋊C4×C59—24no—
287C42×C59C2×D412yes—
288C42×C59C2412yes—
289C22⋊Dic59—24no—
290#11745672—28no—
291#11745670—28no—
292#11745669—28no—
293#11745669—28no—
294(C2×D59)⋊C4—24no—
295(C2×D59)⋊C4—24no—
296(C2×D59)⋊C4C2×D414yes—
297(C2×D59)⋊C4C2×D414yes—
298C4⋊Dic59—21no—
299C4⋊Dic59C2412yes—
300Dic59⋊C4—24no—
301Dic59⋊C4—24no—
302Dic59⋊C4—24no—
303Dic59⋊C4C2×D414yes—
304Dic59⋊C4C2×D414yes—
305C4×Dic59—24no—
306C4×Dic59—24no—
307C4×Dic59C2×D412yes—
308C4×Dic59C2412yes—
309C2×C59⋊C8—22no—
310C2×C59⋊C8—22no—
311C2×C59⋊C8C2412yes—
312C2×C59⋊C8C2412yes—
313#11745660—28no—
314#11745660—28no—
315#11745659—28no—
316C8×D59—28no—
317C23×C59—24no—
318C23×C59—22no—
319C23×C59—22no—
320C23×C59—42no—
321C23×C59—42no—
322C23×C59—42no—
323C23×C59—42no—
324C23×C59—42no—
325C23×C59C22×D411yescharacteristic
326C22×D59—22no—
327C22×D59—22no—
328C22×D59—22no—
329C22×D59—22no—
330C22×D59—42no—
331C22×D59—42no—
332C22×D59—42no—
333C22×D59—42no—
334C22×D59—42no—
335C22×D59—42no—
336C22×D59—48no—
337C22×D59—84no—
338C22×D59—84no—
339C22×D59—816no—
340C22×D59#12114yes—
341C22×D59C22×D412yes—
342Q8×C59—22no—
343Q8×C59—22no—
344Q8×C59—42no—
345D4×C59—24no—
346D4×C59—22no—
347D4×C59—22no—
348D4×C59—22no—
349D4×C59—42no—
350D4×C59C22×D414yes—
351C2×C4×C59—22no—
352C2×C4×C59—22no—
353C2×C4×C59—22no—
354C2×C4×C59—22no—
355C2×C4×C59—42no—
356C2×C4×C59—42no—
357C2×C4×C59—84no—
358C2×C4×C59C22×D412yes—
359C2×C4×C59C22×D412yes—
360C2×C4×C59C22×D411yescharacteristic
361C2×C4×C59C22×D412yes—
362C2×C4×C59C2×#4112yes—
363C2×C4×C59C2511yescharacteristic
364C22⋊D59—216no—
365C22⋊D59—48no—
366C22⋊D59—84no—
367C22⋊D59—84no—
368C2×Dic59—24no—
369C2×Dic59—22no—
370C2×Dic59—22no—
371C2×Dic59—22no—
372C2×Dic59—216no—
373C2×Dic59—22no—
374C2×Dic59—42no—
375C2×Dic59—84no—
376C2×Dic59#12114yes—
377C2×Dic59C22×D412yes—
378C2×Dic59C22×D412yes—
379C2×Dic59C22×D412yes—
380D236—22no—
381D236—22no—
382D236—22no—
383D236—22no—
384D236—48no—
385D236—42no—
386D236—42no—
387D236—84no—
388D236—84no—
389C4×D59—48no—
390C4×D59—84no—
391C4×D59#12118yes—
392C4×D59C22×D414yes—
393C4×D59C2×#4114yes—
394Dic118—24no—
395Dic118—22no—
396Dic118C22×D414yes—
397C8×C59—22no—
398C8×C59—22no—
399C59⋊C8—22no—
400C59⋊C8—22no—
401C2×#3045—591nomaximal, Sylow
402C22×C59—24no—
403C22×C59—48no—
404C22×C59—42no—
405C22×C59—42no—
406C22×C59—42no—
407C22×C59—42no—
408C22×C59—42no—
409C22×C59—84no—
410C22×C59C2×#12112yes—
411C22×C59#57612yes—
412C22×C59#57712yes—
413C22×C59C23×D411yescharacteristic
414C2×D59—28no—
415C2×D59—22no—
416C2×D59—22no—
417C2×D59—42no—
418C2×D59—42no—
419C2×D59—42no—
420C2×D59—42no—
421C2×D59—42no—
422C2×D59—42no—
423C2×D59—816no—
424C2×D59—84no—
425C2×D59—84no—
426C2×D59C2×#12114yes—
427C4×C59—22no—
428C4×C59—22no—
429C4×C59—42no—
430C4×C59—42no—
431C4×C59C2×#12112yes—
432C4×C59C23×D411yescharacteristic
433C4×C59C22×#4111yescharacteristic
434Dic59—24no—
435Dic59—22no—
436Dic59—22no—
437Dic59—42no—
438Dic59C2×#12114yes—
439C22×AGL(1,ℤ/8)—591no—
440C22×#135—591no—
441C2×#535—591no—
442C2×#520—591no—
443#3045—5916no—
444C2×#464—591no—
445C2×#464—591no—
446C2×#460—591no—
447C2×#460—591no—
448C2×#463—591no—
449C2×#463D5911yescharacteristic, complemented
450C2×#459—591no—
451C2×#459—591no—
452C2×#424—591no—
453C2×#417—591no—
454C22×#102—591no—
455C2×C59—44no—
456C2×C59—82no—
457C2×C59#304514yescomplemented
458C2×C59C22×#12111yescharacteristic
459C2×C59C2×#57611yescharacteristic
460C2×C59C2×#57711yescharacteristic
461D59—24no—
462D59—82no—
463D59—82no—
464C22×#41—591no—
465C22×#41—591no—
466C23×D4—591no—
467C2×AGL(1,ℤ/8)—598no—
468C2×AGL(1,ℤ/8)—1188no—
469C2×#135—598no—
470C2×#135—1188no—
471C22×Q16—591no—
472C22×SD16—591no—
473C22×SD16—591no—
474C22×SD16—591no—
475C22×SD16C2×D5911yescharacteristic, complemented
476C22×D8—591no—
477C22×D8—591no—
478C22×D8C2×D5911yescharacteristic
479C22×M16—591no—
480C23×C8—591no—
481#535—598no—
482#535—1184no—
483C2×#127—591no—
484C2×#127—591no—
485C2×#124—591no—
486C2×#124C2×D5911yescharacteristic
487C2×#121—1181no—
488C2×#121—1181no—
489C2×#120—1181no—
490C2×#120—1181no—
491#520—598no—
492#520—1184no—
493C2×C4×Q8—591no—
494C2×C4×Q8—591no—
495C2×C4×D4—591no—
496C2×C4×D4—1181no—
497C2×C4×D4—1181no—
498C2×C4×D4C2×D5911yescharacteristic, complemented
499C2×#117—591no—
500C2×#117—1181no—
501C22×C4⋊C4—591no—
502C22×C4⋊C4—1181no—
503#464—598no—
504#464—598no—
505#463—598no—
506#463C2×D5918yescomplemented
507#460—598no—
508#460—598no—
509#459—598no—
510#459—598no—
511#424—598no—
512C2×C4⋊C8—591no—
513C2×C4⋊C8—591no—
514C2×C4⋊C8—591no—
515C2×C4⋊C8C2×D5911yescharacteristic, complemented
516#417—598no—
517C2×#103—591no—
518C2×#103C2×D5911yescharacteristic, complemented
519C2×#102—591no—
520C2×#102—591no—
521C2×#102—591no—
522C2×#102—591no—
523C2×#102—591no—
524C2×#102—598no—
525C2×#102C2×D5911yescharacteristic
526C59C2×#304511yescharacteristic, complemented, Sylow
527C25—1181no—
528C2×#41—594no—
529C2×#41—598no—
530C2×#41—594no—
531C2×#41—1182no—
532C2×#41—1184no—
533C2×#41—1182no—
534C2×#41—1184no—
535C2×#41—1184no—
536C22×Q8—591no—
537C22×Q8C22×D5911yescharacteristic
538C22×D4—594no—
539C22×D4—591no—
540C22×D4—591no—
541C22×D4—1181no—
542C22×D4—1184no—
543C22×D4—1184no—
544C22×D4—1182no—
545C22×D4—1181no—
546C22×D4—1181no—
547C22×D4—1181no—
548C22×D4—1181no—
549C22×D4—1181no—
550C22×D4—1181no—
551C22×D4C22×D5911yescharacteristic
552C22×D4C22×D5911yescharacteristic
553C23×C4—21no—
554C23×C4—591no—
555C23×C4—1181no—
556C23×C4—1181no—
557C23×C4—1181no—
558C23×C4—1181no—
559AGL(1,ℤ/8)—11832no—
560#135—11832no—
561C2×Q16—594no—
562C2×Q16—1184no—
563C2×SD16—24no—
564C2×SD16—594no—
565C2×SD16—594no—
566C2×SD16—594no—
567C2×SD16—1184no—
568C2×SD16—1184no—
569C2×SD16—1184no—
570C2×SD16C22×D5914yescomplemented
571C2×D8—24no—
572C2×D8—594no—
573C2×D8—594no—
574C2×D8—1184no—
575C2×D8—1184no—
576C2×D8C22×D5914yes—
577C2×M16—594no—
578C2×M16—1184no—
579C22×C8—591no—
580C22×C8—591no—
581C22×C8—594no—
582C22×C8—1184no—
583C22×C8C22×D5911yescharacteristic
584C22×C8C22×D5911yescharacteristic
585#127—594no—
586#127—594no—
587#127—1182no—
588#127—1182no—
589#124—22no—
590#124—594no—
591#124—1182no—
592#124C22×D5914yes—
593#121—1188no—
594#121—1188no—
595#120—1188no—
596#120—1188no—
597C4×Q8—594no—
598C4×Q8—594no—
599C4×Q8—1182no—
600C4×Q8—1182no—
601C4×D4—22no—
602C4×D4—594no—
603C4×D4—1182no—
604C4×D4—1188no—
605C4×D4—1188no—
606C4×D4C22×D5914yescomplemented
607#117—594no—
608#117—594no—
609#117—1188no—
610C2×C4⋊C4—591no—
611C2×C4⋊C4—591no—
612C2×C4⋊C4—591no—
613C2×C4⋊C4—594no—
614C2×C4⋊C4—1182no—
615C2×C4⋊C4—1188no—
616C2×C4⋊C4—1181no—
617C2×C4⋊C4—1181no—
618C2×C4⋊C4—1181no—
619C2×C4⋊C4C22×D5911yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—591no—
624C2×C22⋊C4—591no—
625C2×C22⋊C4—1181no—
626C2×C22⋊C4—1181no—
627C2×C22⋊C4—1181no—
628C2×C42—591no—
629C2×C42—1181no—
630C2×C42—1181no—
631C2×C42C22×D5911yescharacteristic
632C4⋊C8—594no—
633C4⋊C8—594no—
634C4⋊C8—594no—
635C4⋊C8C22×D5914yescomplemented
636#103—594no—
637#103C22×D5914yescomplemented
638#102—594no—
639#102—594no—
640#102—594no—
641#102—594no—
642#102—594no—
643#102C22×D5914yes—
644C24—21no—
645C24—21no—
646C24—591no—
647C24—1184no—
648C24—1181no—
649C24—1181no—
650C24—4722no—
651C24—4722no—
652C24—2364no—
653#41—5916no—
654#41—11816no—
655#41—1188no—
656#41—1188no—
657#41—1188no—
658#41—2368no—
659C2×Q8—21no—
660C2×Q8—22no—
661C2×Q8—22no—
662C2×Q8—594no—
663C2×Q8—592no—
664C2×Q8—1181no—
665C2×Q8—1182no—
666C2×Q8C23×D5912yes—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—21no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—592no—
673C2×D4—592no—
674C2×D4—1184no—
675C2×D4—1188no—
676C2×D4—1188no—
677C2×D4—1184no—
678C2×D4—1184no—
679C2×D4—1184no—
680C2×D4—1184no—
681C2×D4—1188no—
682C2×D4—1182no—
683C2×D4—1182no—
684C2×D4—1184no—
685C2×D4—1184no—
686C2×D4—1181no—
687C2×D4—1181no—
688C2×D4—1182no—
689C2×D4—1182no—
690C2×D4—4722no—
691C2×D4—4722no—
692C2×D4—4722no—
693C2×D4—4722no—
694C2×D4—2364no—
695C2×D4—2368no—
696C2×D4—2364no—
697C2×D4D4×D5914yes—
698C2×D4C23×D5912yes—
699C2×D4C23×D5912yes—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—24no—
703C22×C4—82no—
704C22×C4—591no—
705C22×C4—592no—
706C22×C4—594no—
707C22×C4—594no—
708C22×C4—592no—
709C22×C4—591no—
710C22×C4—591no—
711C22×C4—1184no—
712C22×C4—1184no—
713C22×C4—1184no—
714C22×C4—1188no—
715C22×C4—1184no—
716C22×C4—1181no—
717C22×C4—1181no—
718C22×C4—4722no—
719C22×C4—4722no—
720C22×C4—2364no—
721C22×C4D4×D5911yescharacteristic
722C22×C4D4×D5911yescharacteristic
723C22×C4C23×D5911yescharacteristic
724Q16—1188no—
725SD16—28no—
726SD16—1188no—
727SD16—1188no—
728SD16—1188no—
729D8—28no—
730D8—1188no—
731D8—1188no—
732M16—1188no—
733C2×C8—22no—
734C2×C8—22no—
735C2×C8—592no—
736C2×C8—592no—
737C2×C8—1188no—
738C2×C8—1182no—
739C2×C8—1182no—
740C2×C8C23×D5912yes—
741C2×C8C23×D5912yes—
742C4⋊C4—21no—
743C4⋊C4—594no—
744C4⋊C4—594no—
745C4⋊C4—592no—
746C4⋊C4—1184no—
747C4⋊C4—1184no—
748C4⋊C4—1181no—
749C4⋊C4—1184no—
750C4⋊C4C23×D5912yes—
751C22⋊C4—24no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—594no—
755C22⋊C4—594no—
756C22⋊C4—1184no—
757C22⋊C4—1184no—
758C22⋊C4—1184no—
759C42—592no—
760C42—592no—
761C42—1184no—
762C42—1184no—
763C42D4×D5912yes—
764C42C23×D5912yes—
765C23—24no—
766C23—22no—
767C23—22no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—594no—
774C23—592no—
775C23—1182no—
776C23—1182no—
777C23—1182no—
778C23—1182no—
779C23—4724no—
780C23—4724no—
781C23—47216no—
782C23—2368no—
783C23—2362no—
784C23—2362no—
785C23—2362no—
786C23—2362no—
787C23—2362no—
788C23—2362no—
789C23C2×D4×D5911yescharacteristic
790Q8—22no—
791Q8—22no—
792Q8—42no—
793Q8—594no—
794Q8—1184no—
795Q8—1182no—
796D4—24no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—42no—
801D4—11816no—
802D4—1182no—
803D4—1182no—
804D4—1182no—
805D4—1182no—
806D4—4724no—
807D4—4724no—
808D4—4724no—
809D4—4724no—
810D4—2368no—
811D4—2368no—
812D4—2362no—
813D4—2362no—
814D4C2×D4×D5914yes—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—84no—
822C2×C4—594no—
823C2×C4—592no—
824C2×C4—598no—
825C2×C4—594no—
826C2×C4—594no—
827C2×C4—592no—
828C2×C4—592no—
829C2×C4—11816no—
830C2×C4—1184no—
831C2×C4—1182no—
832C2×C4—1182no—
833C2×C4—1182no—
834C2×C4—1182no—
835C2×C4—4724no—
836C2×C4—4724no—
837C2×C4—2368no—
838C2×C4—2362no—
839C2×C4C2×D4×D5912yes—
840C2×C4C2×D4×D5912yes—
841C2×C4C2×D4×D5911yescharacteristic
842C2×C4C2×D4×D5912yes—
843C2×C4#41×D5912yes—
844C2×C4C24×D5911yescharacteristic
845C8—22no—
846C8—22no—
847C8—1182no—
848C8—1182no—
849C22—24no—
850C22—48no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—84no—
857C22—594no—
858C22—1188no—
859C22—1182no—
860C22—1182no—
861C22—47216no—
862C22—4724no—
863C22—4724no—
864C22—2362no—
865C22—2362no—
866C22—2362no—
867C22—2362no—
868C22—2362no—
869C22—2362no—
870C22#121×D5912yes—
871C22#1683820612yes—
872C22#1683820912yes—
873C22C22×D4×D5911yescharacteristic
874C4—22no—
875C4—22no—
876C4—42no—
877C4—42no—
878C4—594no—
879C4—1182no—
880C4—1184no—
881C4—1182no—
882C4—2362no—
883C4#121×D5912yes—
884C4C22×D4×D5911yescharacteristic
885C4C2×#41×D5911yescharacteristic
886C2—44no—
887C2—82no—
888C2—1184no—
889C2—4722no—
890C2—4722no—
891C2#2143363614yesdirect product factor
892C2C2×#121×D5911yescharacteristic
893C2C2×#1683820611yescharacteristic
894C2C2×#1683820911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#463C2
socleC23×C59C22×D4
hypercenterC2×#463D59
hypocenterC59C2×#3045
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C22×#14273751C2semidirect
2. C22×#14273748C2semidirect
3. C2×#16837970C2semidirect
4. C2×#16837881C2semidirect
5. #21433636C2direct (N × H)
6. C2×#16837627C2semidirect
7. C2×#16837621C2semidirect
8. C2×#16837603C2semidirect
9. C2×#16837601C2semidirect
10. C2×#16837619C2semidirect
11. C2×#16837597C2semidirect
12. C2×#16837595C2semidirect
13. C2×#16837427C2semidirect
14. C2×#16837402C2semidirect
15. C2×#102×D59C2semidirect
16. C2×C59×#463C2semidirect
21. C2×#14273751C22semidirect
23. C2×#14273748C22semidirect
24. C22×#11745672C22semidirect
26. C22×#11745660C22semidirect
29. C22×#11745669C22semidirect
33. #16837970C22semidirect
42. #16837881C22semidirect
43. C2×C4×Dic118C22semidirect
44. C2×#14273692C22semidirect
45. C2×D4×Dic59C22semidirect
52. #16837627C22semidirect
53. #16837621C22semidirect
54. #16837619C22semidirect
55. #16837603C22semidirect
56. #16837601C22semidirect
57. #16837597C22semidirect
58. #16837595C22semidirect
59. #16837427C22semidirect
60. C2×C4⋊(C59⋊C8)C22semidirect
61. C2×Dic59⋊C8C22semidirect
62. C2×Dic59⋊C8C22semidirect
63. #16837402C22semidirect
64. C2×#14273651C22semidirect
66. C2×#14273649C22semidirect
69. C2×#14273647C22semidirect
70. #102×D59C22semidirect
71. C22×SD16×C59C22semidirect
74. C2×C4×D4×C59C22semidirect
75. C59×#463C22semidirect
76. C2×C4⋊C8×C59C22semidirect
77. C2×#103×C59C22semidirect
86. C2×#11745687D4semidirect
110. C2×#11745672C23semidirect
114. C2×#11745660C23semidirect
120. C2×#11745669C23semidirect
138. C4×Dic118C23semidirect
140. #14273692C23semidirect
142. D4×Dic59C23semidirect
165. C4⋊(C59⋊C8)C23semidirect
166. Dic59⋊C8C23semidirect
167. Dic59⋊C8C23semidirect
168. #14273651C23semidirect
170. #14273649C23semidirect
173. #14273647C23semidirect
179. C2×SD16×C59C23semidirect
187. C4×D4×C59C23semidirect
193. C4⋊C8×C59C23semidirect
194. #103×C59C23semidirect
246. #11745687C2×D4semidirect
449. C2×#463D59semidirect
457. C2×C59#3045semidirect
475. C22×SD16C2×D59semidirect
498. C2×C4×D4C2×D59semidirect
506. #463C2×D59semidirect
515. C2×C4⋊C8C2×D59semidirect
518. C2×#103C2×D59semidirect
526. C59C2×#3045semidirect
570. C2×SD16C22×D59semidirect
606. C4×D4C22×D59semidirect
635. C4⋊C8C22×D59semidirect
637. #103C22×D59semidirect
891. C2#21433636direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737512
C22×#142737482
C2×#168379702
C2×#168378812
#214336362
C2×#168376272
C2×#168376212
C2×#168376032
C2×#168376012
C2×#168376192
C2×#168375972
C2×#168375952
C2×#168374272
C2×#168374022
C2×#102×D592
C2×C59×#4632
C2×#304559