Finite Group Databasebeta

← C2×#21435732 #29463824

Subgroups — C2×#21435732 #29463824

Order 15104.

2902 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273760C211yesmaximal, characteristic, complemented
2C22×#14273755C211yesmaximal, characteristic, complemented
3C2×#16838061C211yesmaximal, characteristic, complemented
4C2×#16838048C211yesmaximal, characteristic, complemented
5#21435732C2116yesmaximal, direct product factor
6C2×#16837786C211yesmaximal, characteristic, complemented
7C2×#16837660C211yesmaximal, characteristic, complemented
8C2×#16837655C211yesmaximal, characteristic, complemented
9C2×#16837625C211yesmaximal, characteristic, complemented
10C2×#16837618C211yesmaximal, characteristic, complemented
11C2×#16837566C211yesmaximal, characteristic, complemented
12C2×#16837549C211yesmaximal, characteristic, complemented
13C2×#16837543C211yesmaximal, characteristic, complemented
14C2×#16837555C211yesmaximal, characteristic, complemented
15C2×C4×#11745660C211yesmaximal, characteristic, complemented
16C2×C59×#436C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C22×#11745685C2211yescharacteristic
19C23×Dic118C2211yescharacteristic, complemented
20C23×D236C2211yescharacteristic
21C2×#14273760—28no—
22C2×#14273760C2218yescomplemented
23C2×#14273755—28no—
24C2×#14273755C2218yescomplemented
25C22×Dic236C2211yescharacteristic, complemented
26C22×Dic236C2211yescharacteristic, complemented
27C22×#11745660C2211yescharacteristic
28C22×#11745660C2211yescharacteristic
29C22×#11745660C2211yescharacteristic
30C22×#11745660C2211yescharacteristic
31C22×#11745660C2211yescharacteristic, complemented
32C22×D472C2211yescharacteristic
33C22×D472C2211yescharacteristic
34#16838061—24no—
35#16838061C2218yescomplemented
36#16838048—24no—
37#16838048C2218yescomplemented
38C2×#14273715C2211yescharacteristic
39C2×#14273715C2211yescharacteristic, complemented
40C2×#14273713—21no—
41C2×#14273712—21no—
42C2×#14273706C2211yescharacteristic
43C2×#14273706C2211yescharacteristic
44C2×#14273705—21no—
45C2×#14273701C2211yescharacteristic
46C2×#14273701C2211yescharacteristic, complemented
47C2×#14273700—21no—
48C2×#14273699—21no—
49C2×#14273695—21no—
50C2×C4×Dic118C2211yescharacteristic, complemented
51C2×C4×D236C2211yescharacteristic
52C2×(C22⋊D59)⋊C4—21no—
53C2×C22⋊C4×D59—21no—
54#16837786C2218yescomplemented
55#16837660C2218yescomplemented
56#16837655C2218yescomplemented
57#16837625C2218yescomplemented
58#16837618C2218yescomplemented
59#16837566C2218yescomplemented
60#16837555C2218yescomplemented
61#16837549C2218yescomplemented
62#16837543C2218yescomplemented
63C4×#11745660C2218yescomplemented
64C2×#14273659C2211yescharacteristic, complemented
65C2×#14273652C2211yescharacteristic, complemented
66C2×#14273652C2211yescharacteristic, complemented
67C2×#14273652C2211yescharacteristic, complemented
68C2×#14273649C2211yescharacteristic
69C2×#14273649C2211yescharacteristic
70C2×#14273649C2211yescharacteristic, complemented
71C22×M16×C59C2211yescharacteristic
72C22×M16×C59C2211yescharacteristic, complemented
73C2×C4×D4×C59C2211yescharacteristic
74C59×#436C2218yescomplemented
75C2×C4⋊C8×C59C2211yescharacteristic, complemented
76C2×C22⋊C8×C59C2211yescharacteristic
77C2×C22⋊C8×C59C2211yescharacteristic, complemented
78C2×C4×C8×C59C2211yescharacteristic, complemented
79C24×D59—21no—
80C2×#11745685—22no—
81C2×#11745685—22no—
82C2×#11745685—24no—
83C2×#11745685—24no—
84C2×#11745685—42no—
85C2×#11745685—42no—
86C2×#11745685C2314yes—
87C2×#11745685C2314yes—
88C22×Dic118—24no—
89C22×Dic118—21no—
90C22×Dic118—22no—
91C22×Dic118—42no—
92C22×Dic118C2311yescharacteristic
93C22×Dic118C2311yescharacteristic
94C22×Dic118C2311yescharacteristic
95C22×Dic118C2314yescomplemented
96C22×D236—24no—
97C22×D236—21no—
98C22×D236—22no—
99C22×D236—42no—
100C22×D236C2311yescharacteristic
101C22×D236C2311yescharacteristic
102C22×D236C2314yes—
103C22×D236C2311yescharacteristic
104C22×C22⋊D59—21no—
105C22×C22⋊D59—21no—
106C22×C22⋊D59—21no—
107C22×C22⋊D59—21no—
108C23×Dic59—21no—
109C22×C4×D59—21no—
110C22×C4×D59—21no—
111C22×C4×D59—21no—
112#14273760—232no—
113#14273755—232no—
114C2×Dic236—24no—
115C2×Dic236—24no—
116C2×Dic236C2314yescomplemented
117C2×Dic236C2314yescomplemented
118C2×#11745660—24no—
119C2×#11745660—24no—
120C2×#11745660—42no—
121C2×#11745660—42no—
122C2×#11745660D418yescomplemented
123C2×#11745660C2314yes—
124C2×#11745660C2314yes—
125C2×#11745660C2314yes—
126C2×#11745660C2314yes—
127C2×#11745660C2314yescomplemented
128C2×D472—24no—
129C2×D472—24no—
130C2×D472C2314yes—
131C2×D472C2314yes—
132#14273715—22no—
133#14273715—22no—
134#14273715C2314yes—
135#14273715C2314yescomplemented
136#14273713—28no—
137#14273712—28no—
138#14273706—22no—
139#14273706—22no—
140#14273706C2314yes—
141#14273706C2314yes—
142#14273705—28no—
143#14273701—22no—
144#14273701—22no—
145#14273701C2314yes—
146#14273701C2314yescomplemented
147#14273700—28no—
148#14273699—28no—
149#14273695—28no—
150C4×Dic118—22no—
151C4×Dic118C2314yescomplemented
152C4×D236—22no—
153C4×D236C2314yes—
154(C22⋊D59)⋊C4—28no—
155C2×C4⋊Dic59C2311yescharacteristic
156C2×C4⋊Dic59C2311yescharacteristic
157C2×Dic59⋊C4—21no—
158C2×Dic59⋊C4—21no—
159C2×Dic59⋊C4—21no—
160C2×C22⋊Dic59—21no—
161C2×C22⋊Dic59—21no—
162C2×(C2×D59)⋊C4—21no—
163C2×(C2×D59)⋊C4—21no—
164C2×(C2×D59)⋊C4—21no—
165C2×(C2×D59)⋊C4—21no—
166C2×(C2×D59)⋊C4—21no—
167C2×(C2×D59)⋊C4—21no—
168C2×(C2×D59)⋊C4—21no—
169C22⋊C4×D59—28no—
170C2×C4×Dic59—21no—
171#14273659C2314yescomplemented
172#14273652C2314yescomplemented
173#14273652C2314yescomplemented
174#14273652C2314yescomplemented
175#14273649C2314yes—
176#14273649C2314yes—
177#14273649C2314yescomplemented
178C22×D4×C59D411yescharacteristic
179C23×C4×C59C2311yescharacteristic
180C23×C4×C59C2311yescharacteristic
181C2×M16×C59—24no—
182C2×M16×C59—24no—
183C2×M16×C59C2314yes—
184C2×M16×C59C2314yescomplemented
185C22×C8×C59C2311yescharacteristic
186C22×C8×C59C2311yescharacteristic
187C22×C8×C59C2311yescharacteristic
188C22×C8×C59C2311yescharacteristic
189C4×D4×C59D414yes—
190C4×D4×C59C2314yes—
191C2×C4⋊C4×C59D411yescharacteristic
192C2×C22⋊C4×C59D411yescharacteristic
193C2×C22⋊C4×C59D411yescharacteristic
194C2×C42×C59C2311yescharacteristic
195C4⋊C8×C59C2314yescomplemented
196C22⋊C8×C59C2314yes—
197C22⋊C8×C59C2314yescomplemented
198C4×C8×C59C2314yescomplemented
199C24×C59C2×D411yescharacteristic
200C24×C59C2×D411yescharacteristic
201C23×D59—21no—
202C23×D59—21no—
203C23×D59—21no—
204C23×D59—24no—
205C23×D59—44no—
206C23×D59—44no—
207C23×D59—82no—
208C2×D4×C59—42no—
209C2×D4×C59C2×D414yes—
210C22×C4×C59—22no—
211C22×C4×C59—22no—
212C22×C4×C59—22no—
213C22×C4×C59—22no—
214C22×C4×C59C2×D411yescharacteristic
215C22×C4×C59C2×D411yescharacteristic
216C22×C4×C59C2×D411yescharacteristic
217C22×C4×C59C2×D411yescharacteristic
218C22×C4×C59C2×D412yes—
219C22×C4×C59C2×D412yes—
220C22×C4×C59C2412yes—
221C22×C4×C59C2412yes—
222C22×C4×C59C2411yescharacteristic
223C2×C22⋊D59—24no—
224C2×C22⋊D59—24no—
225C2×C22⋊D59—24no—
226C2×C22⋊D59—24no—
227C2×C22⋊D59—44no—
228C2×C22⋊D59—44no—
229C2×C22⋊D59—44no—
230C2×C22⋊D59—82no—
231C22×Dic59—21no—
232C22×Dic59—21no—
233C22×Dic59—21no—
234C22×Dic59—21no—
235C22×Dic59—21no—
236C22×Dic59—24no—
237C22×Dic59—44no—
238#11745685—28no—
239#11745685—28no—
240#11745685—44no—
241#11745685—44no—
242#11745685—48no—
243#11745685—48no—
244C2×D236—21no—
245C2×D236—22no—
246C2×D236—22no—
247C2×D236—22no—
248C2×D236—22no—
249C2×D236—22no—
250C2×D236—28no—
251C2×D236—24no—
252C2×D236—21no—
253C2×D236—21no—
254C2×D236—44no—
255C2×D236—48no—
256C2×D236—44no—
257C2×D236C2×D414yes—
258C2×D236C2412yes—
259C2×D236C2412yes—
260C2×D236C2412yes—
261C2×C4×D59—24no—
262C2×C4×D59—24no—
263C2×C4×D59—24no—
264C2×C4×D59—44no—
265C2×C4×D59—44no—
266C2×C4×D59—82no—
267C2×Dic118—21no—
268C2×Dic118—22no—
269C2×Dic118—22no—
270C2×Dic118—22no—
271C2×Dic118—22no—
272C2×Dic118—22no—
273C2×Dic118—28no—
274C2×Dic118—24no—
275C2×Dic118—21no—
276C2×Dic118—21no—
277C2×Dic118—44no—
278C2×Dic118—48no—
279C2×Dic118—44no—
280C2×Dic118C2×D414yes—
281C2×Dic118C2412yes—
282C2×Dic118C2412yes—
283C2×Dic118C2412yes—
284M16×C59—28no—
285M16×C59—28no—
286C2×C8×C59—22no—
287C2×C8×C59—22no—
288C2×C8×C59—22no—
289C2×C8×C59C2×D414yes—
290C2×C8×C59C2412yes—
291C2×C8×C59C2412yes—
292C2×C8×C59C2412yes—
293C2×C8×C59C2412yes—
294C4⋊C4×C59C2×D414yes—
295C22⋊C4×C59C2×D414yes—
296C22⋊C4×C59C2×D414yes—
297C42×C59C2×D412yes—
298C42×C59C2412yes—
299C22⋊Dic59—24no—
300C22⋊Dic59—24no—
301(C2×D59)⋊C4—24no—
302(C2×D59)⋊C4—24no—
303(C2×D59)⋊C4—24no—
304(C2×D59)⋊C4—24no—
305(C2×D59)⋊C4—24no—
306(C2×D59)⋊C4—24no—
307(C2×D59)⋊C4—24no—
308C4⋊Dic59—21no—
309C4⋊Dic59—21no—
310C4⋊Dic59C2412yes—
311C4⋊Dic59C2412yes—
312Dic59⋊C4—24no—
313Dic59⋊C4—24no—
314Dic59⋊C4—24no—
315C4×Dic59—24no—
316Dic236—28no—
317Dic236—28no—
318D472—28no—
319D472—28no—
320#11745660—28no—
321#11745660—28no—
322#11745660—44no—
323#11745660—44no—
324#11745660C2×D4116yescomplemented
325C23×C59—22no—
326C23×C59—22no—
327C23×C59—22no—
328C23×C59—22no—
329C23×C59—22no—
330C23×C59—22no—
331C23×C59C22×D412yes—
332C23×C59C22×D412yes—
333C23×C59C22×D411yescharacteristic
334C22×D59—24no—
335C22×D59—22no—
336C22×D59—22no—
337C22×D59—22no—
338C22×D59—48no—
339C22×D59—42no—
340C22×D59—42no—
341C22×D59—48no—
342C22×D59—42no—
343C22×D59—42no—
344C22×D59—42no—
345C22×D59—42no—
346C22×D59—42no—
347C22×D59—42no—
348C22×D59—84no—
349C22×D59—816no—
350D4×C59—44no—
351C2×C4×C59—22no—
352C2×C4×C59—22no—
353C2×C4×C59—22no—
354C2×C4×C59—22no—
355C2×C4×C59—24no—
356C2×C4×C59—24no—
357C2×C4×C59—22no—
358C2×C4×C59—22no—
359C2×C4×C59—22no—
360C2×C4×C59—22no—
361C2×C4×C59C22×D412yes—
362C2×C4×C59C22×D412yes—
363C2×C4×C59C22×D412yes—
364C2×C4×C59C22×D412yes—
365C2×C4×C59C22×D412yes—
366C2×C4×C59C22×D411yescharacteristic
367C2×C4×C59H(5,𝔽2)12yes—
368C2×C4×C59C2511yescharacteristic
369C22⋊D59—48no—
370C22⋊D59—48no—
371C22⋊D59—48no—
372C22⋊D59—84no—
373C2×Dic59—24no—
374C2×Dic59—22no—
375C2×Dic59—22no—
376C2×Dic59—22no—
377C2×Dic59—22no—
378C2×Dic59—22no—
379C2×Dic59—48no—
380C2×Dic59—42no—
381C2×Dic59—42no—
382C2×Dic59—42no—
383C2×Dic59—42no—
384D236—24no—
385D236—22no—
386D236—22no—
387D236—22no—
388D236—22no—
389D236—22no—
390D236—48no—
391D236—42no—
392D236—42no—
393D236C22×D414yes—
394C4×D59—48no—
395C4×D59—48no—
396C4×D59—84no—
397Dic118—24no—
398Dic118—22no—
399Dic118—22no—
400Dic118—22no—
401Dic118—22no—
402Dic118—22no—
403Dic118—48no—
404Dic118—42no—
405Dic118—42no—
406Dic118C22×D414yes—
407C8×C59—22no—
408C8×C59—22no—
409C8×C59—22no—
410C8×C59C22×D414yes—
411C2×#3275—591nomaximal, Sylow
412C22×C59—22no—
413C22×C59—22no—
414C22×C59—22no—
415C22×C59—22no—
416C22×C59—22no—
417C22×C59—22no—
418C22×C59—44no—
419C22×C59—44no—
420C22×C59D4212yes—
421C22×C59#57512yes—
422C22×C59#57712yes—
423C22×C59C23×D411yescharacteristic
424C2×D59—24no—
425C2×D59—48no—
426C2×D59—42no—
427C2×D59—42no—
428C2×D59—42no—
429C2×D59—42no—
430C2×D59—42no—
431C2×D59—42no—
432C2×D59—42no—
433C2×D59—42no—
434C2×D59—816no—
435C2×D59—84no—
436C2×D59—84no—
437C4×C59—22no—
438C4×C59—22no—
439C4×C59—22no—
440C4×C59—22no—
441C4×C59D4212yes—
442C4×C59C23×D411yescharacteristic
443C4×C59C2×H(5,𝔽2)11yescharacteristic
444Dic59—24no—
445Dic59—42no—
446Dic59—42no—
447Dic59—42no—
448Dic59—42no—
449C22×#137—591no—
450C22×AGL(1,ℤ/8)—591no—
451C2×#548—591no—
452C2×#546—591no—
453#3275—5916no—
454C2×#495—591no—
455C2×#470—591no—
456C2×#469—591no—
457C2×#464—591no—
458C2×#463—591no—
459C2×#452—591no—
460C2×#449—591no—
461C2×#448—591no—
462C2×#450—591no—
463C2×C4×SD16—591no—
464C2×#436D5911yescharacteristic, complemented
465C2×C59—42no—
466C2×C59—42no—
467C2×C59#327514yescomplemented
468C2×C59C2×D4211yescharacteristic
469C2×C59C2×#57511yescharacteristic
470C2×C59C2×#57711yescharacteristic
471D59—44no—
472D59—82no—
473D59—82no—
474C22×#41—591no—
475C22×#41—591no—
476C23×Q8—591no—
477C23×D4—591no—
478C2×#137—598no—
479C2×#137—1188no—
480C2×AGL(1,ℤ/8)—598no—
481C2×AGL(1,ℤ/8)—1188no—
482C22×Q16—591no—
483C22×Q16—591no—
484C22×SD16—591no—
485C22×SD16—591no—
486C22×SD16—591no—
487C22×SD16—591no—
488C22×SD16—591no—
489C22×D8—591no—
490C22×D8—591no—
491C22×M16C2×D5911yescharacteristic
492C22×M16C2×D5911yescharacteristic, complemented
493#548—598no—
494#548—1184no—
495#546—598no—
496#546—1184no—
497C2×#124—591no—
498C2×#124—591no—
499C2×#124—1181no—
500C2×#123—1181no—
501C2×C22⋊Q8—591no—
502C2×C22⋊Q8—591no—
503C2×C22⋊Q8—1181no—
504C2×#121—591no—
505C2×#121—591no—
506C2×#121—1181no—
507C2×#121—1181no—
508C2×#120—1181no—
509C2×C4×Q8—591no—
510C2×C4×D4—591no—
511C2×C4×D4—1181no—
512C2×C4×D4C2×D5911yescharacteristic
513C22×C22⋊C4—1181no—
514#495—598no—
515#470—598no—
516#469—598no—
517#464—598no—
518#463—598no—
519#452—598no—
520#450—598no—
521#449—598no—
522#448—598no—
523C4×SD16—598no—
524#436C2×D5918yescomplemented
525C2×#106—591no—
526C2×C4⋊C8C2×D5911yescharacteristic, complemented
527C2×#103—591no—
528C2×#103—591no—
529C2×#103—591no—
530C2×#102—591no—
531C2×#102—591no—
532C2×#102—591no—
533C2×C22⋊C8C2×D5911yescharacteristic
534C2×C22⋊C8C2×D5911yescharacteristic, complemented
535C2×C4×C8C2×D5911yescharacteristic, complemented
536C59C2×#327511yescharacteristic, complemented, Sylow
537C25—1181no—
538C2×#41—594no—
539C2×#41—594no—
540C2×#41—1184no—
541C2×#41—1184no—
542C2×#41—1182no—
543C2×#41—1182no—
544C2×#41—2362no—
545C2×#41—2362no—
546C22×Q8—591no—
547C22×Q8—591no—
548C22×Q8—591no—
549C22×Q8—594no—
550C22×Q8—1184no—
551C22×Q8—1181no—
552C22×Q8—1182no—
553C22×Q8—2362no—
554C22×D4—591no—
555C22×D4—591no—
556C22×D4—591no—
557C22×D4—594no—
558C22×D4—1184no—
559C22×D4—1181no—
560C22×D4—1181no—
561C22×D4—1181no—
562C22×D4—1181no—
563C22×D4—1181no—
564C22×D4—1182no—
565C22×D4—2362no—
566C22×D4D23611yescharacteristic
567C23×C4—1181no—
568C23×C4—1181no—
569C23×C4—1181no—
570C23×C4—1181no—
571C23×C4C22×D5911yescharacteristic
572C23×C4C22×D5911yescharacteristic
573#137—11832no—
574AGL(1,ℤ/8)—11832no—
575C2×Q16—594no—
576C2×Q16—594no—
577C2×Q16—1184no—
578C2×Q16—1184no—
579C2×SD16—598no—
580C2×SD16—594no—
581C2×SD16—594no—
582C2×SD16—594no—
583C2×SD16—594no—
584C2×SD16—594no—
585C2×SD16—1184no—
586C2×SD16—1184no—
587C2×SD16—2362no—
588C2×SD16—2362no—
589C2×D8—594no—
590C2×D8—594no—
591C2×D8—1184no—
592C2×D8—1184no—
593C2×M16—24no—
594C2×M16—24no—
595C2×M16C22×D5914yes—
596C2×M16C22×D5914yescomplemented
597C22×C8C22×D5911yescharacteristic
598C22×C8C22×D5911yescharacteristic
599C22×C8C22×D5911yescharacteristic
600C22×C8C22×D5911yescharacteristic
601#124—594no—
602#124—594no—
603#124—1188no—
604#124—1182no—
605#124—1182no—
606#123—1188no—
607C22⋊Q8—594no—
608C22⋊Q8—594no—
609C22⋊Q8—1182no—
610C22⋊Q8—1182no—
611C22⋊Q8—1188no—
612#121—594no—
613#121—594no—
614#121—1188no—
615#121—1182no—
616#121—1182no—
617#121—1188no—
618#120—1188no—
619C4×Q8—594no—
620C4×Q8—1182no—
621C4×D4—594no—
622C4×D4—1188no—
623C4×D4—1182no—
624C4×D4D23614yes—
625C4×D4C22×D5914yes—
626C2×C4⋊C4—591no—
627C2×C4⋊C4—591no—
628C2×C4⋊C4—1181no—
629C2×C4⋊C4—1181no—
630C2×C4⋊C4—1181no—
631C2×C4⋊C4D23611yescharacteristic
632C2×C22⋊C4—1181no—
633C2×C22⋊C4—1181no—
634C2×C22⋊C4—1181no—
635C2×C22⋊C4—1181no—
636C2×C22⋊C4—1181no—
637C2×C22⋊C4—1181no—
638C2×C22⋊C4—1181no—
639C2×C22⋊C4—1181no—
640C2×C22⋊C4—1181no—
641C2×C22⋊C4—1188no—
642C2×C22⋊C4D23611yescharacteristic
643C2×C22⋊C4D23611yescharacteristic
644C2×C42—1181no—
645C2×C42C22×D5911yescharacteristic
646#106—594no—
647C4⋊C8C22×D5914yescomplemented
648#103—594no—
649#103—594no—
650#103—594no—
651#102—594no—
652#102—594no—
653#102—594no—
654C22⋊C8C22×D5914yes—
655C22⋊C8C22×D5914yescomplemented
656C4×C8C22×D5914yescomplemented
657C24—1181no—
658C24—1184no—
659C24—1181no—
660C24—1181no—
661C24—4722no—
662C24—2364no—
663C24—2364no—
664C24C2×D23611yescharacteristic
665C24C2×D23611yescharacteristic
666#41—1188no—
667#41—1188no—
668#41—2364no—
669#41—2364no—
670#41—2368no—
671#41—2368no—
672C2×Q8—594no—
673C2×Q8—592no—
674C2×Q8—592no—
675C2×Q8—592no—
676C2×Q8—1188no—
677C2×Q8—1181no—
678C2×Q8—1184no—
679C2×Q8—1181no—
680C2×Q8—1181no—
681C2×Q8—1182no—
682C2×Q8—1182no—
683C2×Q8—1182no—
684C2×Q8—1182no—
685C2×Q8—1182no—
686C2×Q8—2364no—
687C2×Q8—2364no—
688C2×Q8—2368no—
689C2×D4—42no—
690C2×D4—594no—
691C2×D4—592no—
692C2×D4—592no—
693C2×D4—592no—
694C2×D4—1188no—
695C2×D4—1184no—
696C2×D4—1184no—
697C2×D4—1184no—
698C2×D4—1184no—
699C2×D4—1182no—
700C2×D4—1182no—
701C2×D4—1181no—
702C2×D4—1184no—
703C2×D4—1181no—
704C2×D4—1181no—
705C2×D4—1182no—
706C2×D4—1182no—
707C2×D4—1182no—
708C2×D4—4722no—
709C2×D4—2364no—
710C2×D4—2368no—
711C2×D4—2364no—
712C2×D4—2364no—
713C2×D4—2364no—
714C2×D4—2364no—
715C2×D4C2×D23614yes—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—1181no—
721C22×C4—1184no—
722C22×C4—1181no—
723C22×C4—1181no—
724C22×C4—1181no—
725C22×C4—1181no—
726C22×C4—1184no—
727C22×C4—1184no—
728C22×C4—1184no—
729C22×C4—4722no—
730C22×C4—2364no—
731C22×C4—2364no—
732C22×C4—2364no—
733C22×C4C2×D23612yes—
734C22×C4C2×D23612yes—
735C22×C4C2×D23611yescharacteristic
736C22×C4C2×D23611yescharacteristic
737C22×C4C2×D23611yescharacteristic
738C22×C4C2×D23611yescharacteristic
739C22×C4C23×D5912yes—
740C22×C4C23×D5912yes—
741C22×C4C23×D5911yescharacteristic
742Q16—1188no—
743Q16—1188no—
744SD16—5916no—
745SD16—1188no—
746SD16—1188no—
747SD16—2364no—
748SD16—2364no—
749D8—1188no—
750D8—1188no—
751M16—28no—
752M16—28no—
753C2×C8—22no—
754C2×C8—22no—
755C2×C8—22no—
756C2×C8D4×D5914yes—
757C2×C8C23×D5912yes—
758C2×C8C23×D5912yes—
759C2×C8C23×D5912yes—
760C2×C8C23×D5912yes—
761C4⋊C4—592no—
762C4⋊C4—592no—
763C4⋊C4—1181no—
764C4⋊C4—1181no—
765C4⋊C4—1184no—
766C4⋊C4—1184no—
767C4⋊C4—1184no—
768C4⋊C4C2×D23614yes—
769C22⋊C4—1184no—
770C22⋊C4—1184no—
771C22⋊C4—1184no—
772C22⋊C4—1184no—
773C22⋊C4—1184no—
774C22⋊C4—1184no—
775C22⋊C4—1184no—
776C22⋊C4—1184no—
777C22⋊C4—1184no—
778C22⋊C4C2×D23614yes—
779C22⋊C4C2×D23614yes—
780C42—1184no—
781C42C2×D23612yes—
782C42C23×D5912yes—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—1182no—
790C23—1184no—
791C23—1182no—
792C23—1182no—
793C23—4724no—
794C23—47216no—
795C23—2368no—
796C23—2368no—
797C23—2362no—
798C23—2362no—
799C23—2362no—
800C23—2362no—
801C23—2362no—
802C23—2362no—
803C23—2362no—
804C23—2362no—
805C23C22×D23612yes—
806C23C22×D23612yes—
807C23C22×D23611yescharacteristic
808Q8—594no—
809Q8—1182no—
810Q8—1184no—
811Q8—1182no—
812Q8—1182no—
813Q8—1182no—
814Q8—1182no—
815Q8—2368no—
816Q8—2362no—
817Q8—2362no—
818D4—44no—
819D4—594no—
820D4—1182no—
821D4—1182no—
822D4—1182no—
823D4—1182no—
824D4—1182no—
825D4—1184no—
826D4—4724no—
827D4—2368no—
828D4—2368no—
829D4—2368no—
830D4—2368no—
831D4—2362no—
832D4—2362no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—1182no—
844C2×C4—1184no—
845C2×C4—1182no—
846C2×C4—1182no—
847C2×C4—1182no—
848C2×C4—1182no—
849C2×C4—4724no—
850C2×C4—2368no—
851C2×C4—2368no—
852C2×C4—2368no—
853C2×C4—2362no—
854C2×C4—2362no—
855C2×C4—2362no—
856C2×C4—2362no—
857C2×C4C2×D4×D5912yes—
858C2×C4C22×D23612yes—
859C2×C4C22×D23612yes—
860C2×C4C22×D23612yes—
861C2×C4C22×D23612yes—
862C2×C4C22×D23611yescharacteristic
863C2×C4#1427377312yes—
864C2×C4C24×D5911yescharacteristic
865C8—22no—
866C8—22no—
867C8—22no—
868C8C2×D4×D5914yes—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—44no—
876C22—44no—
877C22—1184no—
878C22—47216no—
879C22—4724no—
880C22—4724no—
881C22—2362no—
882C22—2362no—
883C22—2362no—
884C22—2362no—
885C22—2362no—
886C22—2362no—
887C22—2368no—
888C22—2362no—
889C22—2362no—
890C22D4×D23612yes—
891C22#1683820212yes—
892C22#1683821412yes—
893C22C23×D23611yescharacteristic
894C4—22no—
895C4—22no—
896C4—22no—
897C4—22no—
898C4—1184no—
899C4—2362no—
900C4—2362no—
901C4—2362no—
902C4—2362no—
903C4D4×D23612yes—
904C4C22×D4×D5911yescharacteristic
905C4C2×#1427377311yescharacteristic
906C2—42no—
907C2—42no—
908C2—4722no—
909C2—4722no—
910C2—2364no—
911C2#2143573214yesdirect product factor
912C2C2×D4×D23611yescharacteristic
913C2C2×#1683820211yescharacteristic
914C2C2×#1683821411yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#436C2
socleC23×C59C22×D4
hypercenterC2×#436D59
hypocenterC59C2×#3275
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C22×#14273760C2semidirect
2. C22×#14273755C2semidirect
3. C2×#16838061C2semidirect
4. C2×#16838048C2semidirect
5. #21435732C2direct (N × H)
6. C2×#16837786C2semidirect
7. C2×#16837660C2semidirect
8. C2×#16837655C2semidirect
9. C2×#16837625C2semidirect
10. C2×#16837618C2semidirect
11. C2×#16837566C2semidirect
12. C2×#16837549C2semidirect
13. C2×#16837543C2semidirect
14. C2×#16837555C2semidirect
15. C2×C4×#11745660C2semidirect
16. C2×C59×#436C2semidirect
19. C23×Dic118C22semidirect
22. C2×#14273760C22semidirect
24. C2×#14273755C22semidirect
25. C22×Dic236C22semidirect
26. C22×Dic236C22semidirect
31. C22×#11745660C22semidirect
35. #16838061C22semidirect
37. #16838048C22semidirect
39. C2×#14273715C22semidirect
46. C2×#14273701C22semidirect
50. C2×C4×Dic118C22semidirect
54. #16837786C22semidirect
55. #16837660C22semidirect
56. #16837655C22semidirect
57. #16837625C22semidirect
58. #16837618C22semidirect
59. #16837566C22semidirect
60. #16837555C22semidirect
61. #16837549C22semidirect
62. #16837543C22semidirect
63. C4×#11745660C22semidirect
64. C2×#14273659C22semidirect
65. C2×#14273652C22semidirect
66. C2×#14273652C22semidirect
67. C2×#14273652C22semidirect
70. C2×#14273649C22semidirect
72. C22×M16×C59C22semidirect
74. C59×#436C22semidirect
75. C2×C4⋊C8×C59C22semidirect
77. C2×C22⋊C8×C59C22semidirect
78. C2×C4×C8×C59C22semidirect
95. C22×Dic118C23semidirect
116. C2×Dic236C23semidirect
117. C2×Dic236C23semidirect
122. C2×#11745660D4semidirect
127. C2×#11745660C23semidirect
135. #14273715C23semidirect
146. #14273701C23semidirect
151. C4×Dic118C23semidirect
171. #14273659C23semidirect
172. #14273652C23semidirect
173. #14273652C23semidirect
174. #14273652C23semidirect
177. #14273649C23semidirect
184. C2×M16×C59C23semidirect
195. C4⋊C8×C59C23semidirect
197. C22⋊C8×C59C23semidirect
198. C4×C8×C59C23semidirect
324. #11745660C2×D4semidirect
464. C2×#436D59semidirect
467. C2×C59#3275semidirect
492. C22×M16C2×D59semidirect
524. #436C2×D59semidirect
526. C2×C4⋊C8C2×D59semidirect
534. C2×C22⋊C8C2×D59semidirect
535. C2×C4×C8C2×D59semidirect
536. C59C2×#3275semidirect
596. C2×M16C22×D59semidirect
647. C4⋊C8C22×D59semidirect
655. C22⋊C8C22×D59semidirect
656. C4×C8C22×D59semidirect
911. C2#21435732direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737602
C22×#142737552
C2×#168380612
C2×#168380482
#214357322
C2×#168377862
C2×#168376602
C2×#168376552
C2×#168376252
C2×#168376182
C2×#168375662
C2×#168375492
C2×#168375432
C2×#168375552
C2×C4×#117456602
C2×C59×#4362
C2×#327559