Finite Group Databasebeta

← C2×#21436569 #29467255

Subgroups — C2×#21436569 #29467255

Order 15104.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838096C211yesmaximal, characteristic, complemented
2C2×#16838052C211yesmaximal, characteristic, complemented
3#21436569C2116yesmaximal, direct product factor
4C2×#16837810C211yesmaximal, characteristic, complemented
5C2×#16837721C211yesmaximal, characteristic, complemented
6C2×#16837719C211yesmaximal, characteristic, complemented
7C2×#16837717C211yesmaximal, characteristic, complemented
8C2×#16837704C211yesmaximal, characteristic, complemented
9C2×#16837691C211yesmaximal, characteristic, complemented
10C2×#16837653C211yesmaximal, characteristic, complemented
11C2×#16837637C211yesmaximal, characteristic, complemented
12C2×#16837511C211yesmaximal, characteristic, complemented
13C2×#16837476C211yesmaximal, characteristic, complemented
14C2×#16837445C211yesmaximal, characteristic, complemented
15C2×#106×D59C211yesmaximal, characteristic, complemented
16C2×C59×#482C211yesmaximal, characteristic, complemented
17C22×#11745687—21no—
18C22×#11745669C2211yescharacteristic
19C22×#11745664C2211yescharacteristic
20C22×C8×D59C2211yescharacteristic
21#16838096—24no—
22#16838096C2218yescomplemented
23#16838052—24no—
24#16838052C2218yescomplemented
25C2×#14273726C2211yescharacteristic
26C2×#14273721—21no—
27C2×#14273718C2211yescharacteristic
28C2×#14273709—21no—
29C2×#14273709—21no—
30C2×#14273708—21no—
31C2×#14273704—21no—
32C2×#14273702C2211yescharacteristic
33C2×#14273701C2211yescharacteristic
34C2×#14273700—21no—
35C2×#14273698C2211yescharacteristic
36C2×C4×D236—21no—
37C2×D4×Dic59C2211yescharacteristic
38C2×#14273689C2211yescharacteristic
39C2×C4×C22⋊D59C2211yescharacteristic
40C22×C4⋊Dic59C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic
42C2×C4⋊C4×D59C2211yescharacteristic
43#16837810C2218yescomplemented
44#16837721C2218yescomplemented
45#16837719C2218yescomplemented
46#16837717C2218yescomplemented
47#16837704C2218yescomplemented
48#16837691C2218yescomplemented
49#16837653C2218yescomplemented
50#16837637C2218yescomplemented
51#16837511C2218yescomplemented
52#16837476C2218yescomplemented
53#16837445C2218yescomplemented
54C2×#14273660C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273659C2211yescharacteristic
57C2×#14273659C2211yescharacteristic
58C2×#14273658C2211yescharacteristic
59C2×#14273658C2211yescharacteristic
60C2×#14273658C2211yescharacteristic
61#106×D59C2218yescomplemented
62C2×Dic59⋊C8C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×#14273647C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C2×#121×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C59×#482C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#106×C59C2211yescharacteristic
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C2×#11745687—28no—
78C2×#11745687—48no—
79C22×Dic118—21no—
80C22×D236—21no—
81C22×D236C2311yescharacteristic
82C22×C22⋊D59—21no—
83C22×C22⋊D59—21no—
84C22×C22⋊D59D411yescharacteristic
85C23×Dic59—21no—
86C23×Dic59—21no—
87C22×C4×D59—21no—
88C22×C4×D59—21no—
89C22×C4×D59—21no—
90C22×C4×D59C2311yescharacteristic
91C2×#11745669—24no—
92C2×#11745669C2314yes—
93C2×#11745664—24no—
94C2×#11745664C2314yes—
95C22×C59⋊C8C2311yescharacteristic
96C22×C59⋊C8C2311yescharacteristic
97C2×C8×D59—24no—
98C2×C8×D59C2314yes—
99#14273726—22no—
100#14273726C2314yes—
101#14273721—28no—
102#14273718—22no—
103#14273718C2314yes—
104#14273709—28no—
105#14273709—28no—
106#14273708—28no—
107#14273704—28no—
108#14273702—22no—
109#14273702C2314yes—
110#14273701—22no—
111#14273701C2314yes—
112#14273700—28no—
113#14273698—22no—
114#14273698C2314yes—
115C4×D236—28no—
116D4×Dic59—22no—
117D4×Dic59C2314yes—
118#14273689—22no—
119#14273689C2314yes—
120C4×C22⋊D59D414yes—
121C4×C22⋊D59C2314yes—
122C2×C4⋊Dic59—21no—
123C2×C4⋊Dic59—22no—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×C4⋊Dic59C2311yescharacteristic
128C2×C4⋊Dic59C2314yes—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4D411yescharacteristic
134C4⋊C4×D59—22no—
135C4⋊C4×D59—22no—
136C4⋊C4×D59C2314yes—
137C4⋊C4×D59C2314yes—
138C2×C22⋊Dic59—21no—
139C2×C22⋊Dic59—21no—
140C2×C22⋊Dic59D411yescharacteristic
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4—21no—
144C2×(C2×D59)⋊C4D411yescharacteristic
145C2×C4×Dic59C2311yescharacteristic
146#14273660C2314yes—
147#14273660C2314yes—
148#14273659C2314yes—
149#14273659C2314yes—
150#14273658C2314yes—
151#14273658C2314yes—
152#14273658C2314yes—
153Dic59⋊C8C2314yes—
154#14273649C2314yes—
155#14273649C2314yes—
156#14273648C2314yes—
157#14273647C2314yes—
158(C2×D59)⋊C8C2314yes—
159#14273637C2314yes—
160C22×D4×C59—21no—
161C22×D4×C59C2311yescharacteristic
162C23×C4×C59C2311yescharacteristic
163C22×C8×C59C2311yescharacteristic
164C22×C8×C59C2311yescharacteristic
165#121×C59—22no—
166#121×C59C2314yes—
167#117×C59—22no—
168#117×C59C2314yes—
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C22⋊C4×C59—21no—
173C2×C22⋊C4×C59—21no—
174C2×C42×C59—21no—
175#107×C59C2314yes—
176#106×C59C2314yes—
177#102×C59C2314yes—
178#102×C59C2314yes—
179C22⋊C8×C59C2314yes—
180C24×C59—21no—
181C24×C59C2×D411yescharacteristic
182C23×D59—21no—
183C23×D59C2×D411yescharacteristic
184C2×D4×C59—24no—
185C2×D4×C59—21no—
186C2×D4×C59—22no—
187C2×D4×C59—22no—
188C2×D4×C59—44no—
189C2×D4×C59C2412yes—
190C22×C4×C59—22no—
191C22×C4×C59—22no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D412yes—
197C22×C4×C59C2412yes—
198C22×C4×C59C2411yescharacteristic
199C2×C22⋊D59—24no—
200C2×C22⋊D59—24no—
201C2×C22⋊D59—24no—
202C2×C22⋊D59—44no—
203C2×C22⋊D59—82no—
204C2×C22⋊D59C2×D414yes—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—24no—
209C22×Dic59—24no—
210C22×Dic59—44no—
211C22×Dic59—44no—
212C22×Dic59C2×D411yescharacteristic
213C22×Dic59C2×D411yescharacteristic
214C22×Dic59C2×D411yescharacteristic
215#11745687—432no—
216C2×D236—22no—
217C2×D236—22no—
218C2×D236—24no—
219C2×D236—21no—
220C2×D236—44no—
221C2×D236C2412yes—
222C2×C4×D59—22no—
223C2×C4×D59—22no—
224C2×C4×D59—24no—
225C2×C4×D59—24no—
226C2×C4×D59—24no—
227C2×C4×D59—44no—
228C2×C4×D59—82no—
229C2×C4×D59—82no—
230C2×C4×D59C2×D412yes—
231C2×C4×D59C2412yes—
232C2×Dic118—24no—
233C2×Dic118—44no—
234C2×C8×C59—22no—
235C2×C8×C59—22no—
236C2×C8×C59C2412yes—
237C2×C8×C59C2412yes—
238C4⋊C4×C59—21no—
239C4⋊C4×C59—21no—
240C4⋊C4×C59—21no—
241C4⋊C4×C59C2412yes—
242C4⋊C4×C59C2412yes—
243C4⋊C4×C59C2412yes—
244C22⋊C4×C59—24no—
245C22⋊C4×C59—24no—
246C42×C59—24no—
247C22⋊Dic59—24no—
248C22⋊Dic59—24no—
249C22⋊Dic59C2×D414yes—
250#11745669—28no—
251(C2×D59)⋊C4—24no—
252(C2×D59)⋊C4—24no—
253(C2×D59)⋊C4—24no—
254(C2×D59)⋊C4C2×D414yes—
255C4⋊Dic59—21no—
256C4⋊Dic59—21no—
257C4⋊Dic59—21no—
258C4⋊Dic59—24no—
259C4⋊Dic59—24no—
260C4⋊Dic59C2412yes—
261C4⋊Dic59C2412yes—
262C4⋊Dic59C2412yes—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265Dic59⋊C4—24no—
266Dic59⋊C4—24no—
267Dic59⋊C4C2×D414yes—
268C4×Dic59C2×D412yes—
269C4×Dic59C2412yes—
270#11745664—28no—
271C2×C59⋊C8—22no—
272C2×C59⋊C8#4114yescomplemented
273C2×C59⋊C8C2412yes—
274C2×C59⋊C8C2412yes—
275C8×D59—28no—
276C23×C59—22no—
277C23×C59—22no—
278C23×C59—22no—
279C23×C59—22no—
280C23×C59—42no—
281C23×C59—42no—
282C23×C59—42no—
283C23×C59C22×D412yes—
284C23×C59C22×D411yescharacteristic
285C22×D59—22no—
286C22×D59—22no—
287C22×D59—22no—
288C22×D59—42no—
289C22×D59—42no—
290C22×D59—42no—
291C22×D59AGL(1,ℤ/8)14yes—
292C22×D59C22×D412yes—
293D4×C59—22no—
294D4×C59—22no—
295D4×C59—48no—
296D4×C59—42no—
297C2×C4×C59—22no—
298C2×C4×C59—24no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—42no—
305C2×C4×C59—42no—
306C2×C4×C59—42no—
307C2×C4×C59C22×D412yes—
308C2×C4×C59C22×D411yescharacteristic
309C2×C4×C59C2×#4112yes—
310C2×C4×C592−1+412yes—
311C2×C4×C59C2511yescharacteristic
312C22⋊D59—28no—
313C22⋊D59—48no—
314C22⋊D59—84no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—48no—
322C2×Dic59—48no—
323C2×Dic59—42no—
324C2×Dic59—42no—
325C2×Dic59—42no—
326C2×Dic59C22×D412yes—
327C2×Dic59C22×D412yes—
328C2×Dic59C22×D412yes—
329D236—22no—
330D236—22no—
331D236—48no—
332D236—42no—
333C4×D59—24no—
334C4×D59—22no—
335C4×D59—22no—
336C4×D59—48no—
337C4×D59—84no—
338C4×D59—84no—
339Dic118—48no—
340C8×C59—22no—
341C8×C59—22no—
342C59⋊C8—22no—
343C59⋊C8C2×#4114yescomplemented
344C2×#3345—591nomaximal, Sylow
345C22×C59—22no—
346C22×C59—22no—
347C22×C59—22no—
348C22×C59—44no—
349C22×C59—42no—
350C22×C59—42no—
351C22×C59—42no—
352C22×C59—84no—
353C22×C59#54712yes—
354C22×C59C2×AGL(1,ℤ/8)12yes—
355C22×C59#57712yes—
356C22×C59C23×D411yescharacteristic
357C2×D59—28no—
358C2×D59—22no—
359C2×D59—22no—
360C2×D59—42no—
361C2×D59—42no—
362C2×D59—42no—
363C2×D59—84no—
364C2×D59C2×AGL(1,ℤ/8)14yes—
365C4×C59—22no—
366C4×C59—42no—
367C4×C59—42no—
368C4×C59—42no—
369C4×C59#54712yes—
370C4×C59C22×#4111yescharacteristic
371C4×C59C2×2−1+411yescharacteristic
372Dic59—22no—
373Dic59—22no—
374Dic59—22no—
375Dic59—42no—
376Dic59—42no—
377Dic59—42no—
378C2×#553—591no—
379C2×#547—591no—
380#3345—5916no—
381C2×#501—591no—
382C2×#481—591no—
383C2×#481—591no—
384C2×#482D5911yescharacteristic, complemented
385C2×#480—591no—
386C2×#478—591no—
387C2×#476—591no—
388C2×#469—591no—
389C2×#466—591no—
390C2×#442—591no—
391C2×#435—591no—
392C2×#428—591no—
393C22×#106—591no—
394C2×C59—42no—
395C2×C59—82no—
396C2×C59#334514yescomplemented
397C2×C59C2×#54711yescharacteristic
398C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
399C2×C59C2×#57711yescharacteristic
400D59—24no—
401D59—82no—
402C22×#41—1181no—
403C22×D8—591no—
404C22×M16—591no—
405C23×C8—591no—
406#553—598no—
407#553—1184no—
408#547—598no—
409#547—1184no—
410C2×C4⋊Q8—591no—
411C2×#126—1181no—
412C2×#125—591no—
413C2×#123—1181no—
414C2×#123—1181no—
415C2×#123—1181no—
416C2×C22⋊Q8—1181no—
417C2×#121—591no—
418C2×#121—591no—
419C2×#121—591no—
420C2×#121—1181no—
421C2×#121C2×D5911yescharacteristic
422C2×C4×D4—591no—
423C2×C4×D4—591no—
424C2×C4×D4—591no—
425C2×C4×D4—1181no—
426C2×#117C2×D5911yescharacteristic
427C22×C4⋊C4—591no—
428C22×C4⋊C4—591no—
429C22×C4⋊C4—591no—
430#501—598no—
431#482C2×D5918yescomplemented
432#481—598no—
433#481—598no—
434#480—598no—
435#478—598no—
436#476—598no—
437#469—598no—
438#466—598no—
439#442—598no—
440#435—598no—
441#428—598no—
442C2×#107—591no—
443C2×#107—591no—
444C2×#107C2×D5911yescharacteristic
445C2×#106—591no—
446C2×#106—591no—
447C2×#106—591no—
448C2×#106—591no—
449C2×#106—591no—
450C2×#106—598no—
451C2×#106C2×D5911yescharacteristic
452C2×C4⋊C8—591no—
453C2×#102—591no—
454C2×#102—591no—
455C2×#102—591no—
456C2×#102—591no—
457C2×#102C2×D5911yescharacteristic
458C2×#102C2×D5911yescharacteristic
459C2×C22⋊C8—591no—
460C2×C22⋊C8C2×D5911yescharacteristic
461C2×#97—591no—
462C59C2×#334511yescharacteristic, complemented, Sylow
463C2×#41—1188no—
464C2×#41—2368no—
465C22×Q8—1181no—
466C22×D4—21no—
467C22×D4—591no—
468C22×D4—591no—
469C22×D4—1181no—
470C22×D4—1181no—
471C22×D4—1181no—
472C22×D4C22×D5911yescharacteristic
473C23×C4—591no—
474C23×C4—1181no—
475C23×C4—1181no—
476C23×C4—1181no—
477C23×C4—1181no—
478C23×C4—1181no—
479C23×C4C22×D5911yescharacteristic
480C2×D8—594no—
481C2×D8—1184no—
482C2×M16—594no—
483C2×M16—1184no—
484C22×C8—591no—
485C22×C8—591no—
486C22×C8—594no—
487C22×C8—1184no—
488C22×C8C22×D5911yescharacteristic
489C22×C8C22×D5911yescharacteristic
490C4⋊Q8—594no—
491C4⋊Q8—1182no—
492#126—1188no—
493#125—594no—
494#125—1182no—
495#123—1188no—
496#123—1188no—
497#123—1188no—
498C22⋊Q8—1188no—
499#121—22no—
500#121—594no—
501#121—594no—
502#121—594no—
503#121—1188no—
504#121—1182no—
505#121—1182no—
506#121—1182no—
507#121C22×D5914yes—
508C4×D4—594no—
509C4×D4—594no—
510C4×D4—594no—
511C4×D4—594no—
512C4×D4—1188no—
513C4×D4—1182no—
514C4×D4—1182no—
515#117—22no—
516#117C22×D5914yes—
517C2×C4⋊C4—591no—
518C2×C4⋊C4—591no—
519C2×C4⋊C4—591no—
520C2×C4⋊C4—591no—
521C2×C4⋊C4—594no—
522C2×C4⋊C4—594no—
523C2×C4⋊C4—594no—
524C2×C4⋊C4—1182no—
525C2×C4⋊C4—1182no—
526C2×C4⋊C4—1181no—
527C2×C4⋊C4—1181no—
528C2×C4⋊C4—1181no—
529C2×C4⋊C4—1181no—
530C2×C4⋊C4—1181no—
531C2×C4⋊C4—1181no—
532C2×C4⋊C4—1182no—
533C2×C4⋊C4C22×D5911yescharacteristic
534C2×C4⋊C4C22×D5911yescharacteristic
535C2×C4⋊C4C22×D5911yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—591no—
539C2×C22⋊C4—591no—
540C2×C22⋊C4—1181no—
541C2×C22⋊C4—1181no—
542C2×C22⋊C4—1181no—
543C2×C22⋊C4—1181no—
544C2×C22⋊C4—1181no—
545C2×C42—21no—
546C2×C42—591no—
547#107—594no—
548#107—594no—
549#107C22×D5914yes—
550#106—594no—
551#106—594no—
552#106—594no—
553#106—594no—
554#106—594no—
555#106C22×D5914yes—
556C4⋊C8—594no—
557#102—594no—
558#102—594no—
559#102—594no—
560#102—594no—
561#102C22×D5914yes—
562#102C22×D5914yes—
563C22⋊C8—594no—
564C22⋊C8C22×D5914yes—
565#97—594no—
566C24—21no—
567C24—591no—
568C24—1181no—
569C24D4×D5911yescharacteristic
570#41—23632no—
571C2×Q8—1184no—
572C2×Q8—2364no—
573C2×D4—24no—
574C2×D4—21no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—44no—
578C2×D4—594no—
579C2×D4—592no—
580C2×D4—1184no—
581C2×D4—1184no—
582C2×D4—1184no—
583C2×D4—1184no—
584C2×D4—1181no—
585C2×D4—1182no—
586C2×D4—1182no—
587C2×D4—4722no—
588C2×D4—2364no—
589C2×D4—2364no—
590C2×D4C23×D5912yes—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—591no—
597C22×C4—591no—
598C22×C4—591no—
599C22×C4—592no—
600C22×C4—592no—
601C22×C4—1184no—
602C22×C4—1184no—
603C22×C4—1184no—
604C22×C4—1184no—
605C22×C4—1182no—
606C22×C4—1182no—
607C22×C4—1184no—
608C22×C4—1181no—
609C22×C4—1181no—
610C22×C4—1181no—
611C22×C4—4722no—
612C22×C4—4722no—
613C22×C4—2364no—
614C22×C4—2364no—
615C22×C4—2364no—
616C22×C4D4×D5912yes—
617C22×C4D4×D5911yescharacteristic
618C22×C4C23×D5912yes—
619C22×C4C23×D5911yescharacteristic
620D8—1188no—
621M16—1188no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—594no—
625C2×C8—592no—
626C2×C8—592no—
627C2×C8—1188no—
628C2×C8—1182no—
629C2×C8C23×D5912yes—
630C2×C8C23×D5912yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—594no—
635C4⋊C4—592no—
636C4⋊C4—592no—
637C4⋊C4—592no—
638C4⋊C4—1184no—
639C4⋊C4—1184no—
640C4⋊C4—1184no—
641C4⋊C4—1184no—
642C4⋊C4—1184no—
643C4⋊C4—1181no—
644C4⋊C4—1181no—
645C4⋊C4—1181no—
646C4⋊C4—1184no—
647C4⋊C4C23×D5912yes—
648C4⋊C4C23×D5912yes—
649C4⋊C4C23×D5912yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—594no—
653C22⋊C4—594no—
654C22⋊C4—1184no—
655C22⋊C4—1184no—
656C22⋊C4—1184no—
657C22⋊C4—1184no—
658C22⋊C4—1184no—
659C42—24no—
660C42—592no—
661C42—592no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—594no—
670C23—592no—
671C23—1182no—
672C23—1182no—
673C23—1182no—
674C23—2362no—
675C23—2362no—
676C23—2362no—
677C23C2×D4×D5912yes—
678C23C2×D4×D5911yescharacteristic
679Q8—2368no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—42no—
684D4—1188no—
685D4—1182no—
686D4—1182no—
687D4—4724no—
688D4—2368no—
689D4—2368no—
690D4—2362no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—592no—
702C2×C4—592no—
703C2×C4—592no—
704C2×C4—1182no—
705C2×C4—1182no—
706C2×C4—1182no—
707C2×C4—1182no—
708C2×C4—1182no—
709C2×C4—1184no—
710C2×C4—1182no—
711C2×C4—1182no—
712C2×C4—1182no—
713C2×C4—4724no—
714C2×C4—4724no—
715C2×C4—2368no—
716C2×C4—2368no—
717C2×C4—2368no—
718C2×C4—2362no—
719C2×C4—2362no—
720C2×C4—2362no—
721C2×C4C2×D4×D5912yes—
722C2×C4C2×D4×D5911yescharacteristic
723C2×C4#41×D5912yes—
724C2×C4#1427377412yes—
725C2×C4C24×D5911yescharacteristic
726C8—22no—
727C8—22no—
728C8—594no—
729C8—1182no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—594no—
739C22—1182no—
740C22—1182no—
741C22—1188no—
742C22—4724no—
743C22—2362no—
744C22—2362no—
745C22—2362no—
746C22#1683805012yes—
747C22AGL(1,ℤ/8)×D5912yes—
748C22#1683820912yes—
749C22C22×D4×D5911yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—1182no—
755C4—1182no—
756C4—1182no—
757C4—2362no—
758C4—2362no—
759C4—2362no—
760C4#1683805012yes—
761C4C2×#41×D5911yescharacteristic
762C4C2×#1427377411yescharacteristic
763C2—42no—
764C2—82no—
765C2—1184no—
766C2—4722no—
767C2#2143656914yesdirect product factor
768C2C2×#1683805011yescharacteristic
769C2C2×AGL(1,ℤ/8)×D5911yescharacteristic
770C2C2×#1683820911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#482C2
socleC23×C59C22×D4
hypercenterC2×#482D59
hypocenterC59C2×#3345
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16838096C2semidirect
2. C2×#16838052C2semidirect
3. #21436569C2direct (N × H)
4. C2×#16837810C2semidirect
5. C2×#16837721C2semidirect
6. C2×#16837719C2semidirect
7. C2×#16837717C2semidirect
8. C2×#16837704C2semidirect
9. C2×#16837691C2semidirect
10. C2×#16837653C2semidirect
11. C2×#16837637C2semidirect
12. C2×#16837511C2semidirect
13. C2×#16837476C2semidirect
14. C2×#16837445C2semidirect
15. C2×#106×D59C2semidirect
16. C2×C59×#482C2semidirect
22. #16838096C22semidirect
24. #16838052C22semidirect
43. #16837810C22semidirect
44. #16837721C22semidirect
45. #16837719C22semidirect
46. #16837717C22semidirect
47. #16837704C22semidirect
48. #16837691C22semidirect
49. #16837653C22semidirect
50. #16837637C22semidirect
51. #16837511C22semidirect
52. #16837476C22semidirect
53. #16837445C22semidirect
61. #106×D59C22semidirect
71. C59×#482C22semidirect
272. C2×C59⋊C8#41semidirect
343. C59⋊C8C2×#41semidirect
384. C2×#482D59semidirect
396. C2×C59#3345semidirect
431. #482C2×D59semidirect
462. C59C2×#3345semidirect
767. C2#21436569direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380962
C2×#168380522
#214365692
C2×#168378102
C2×#168377212
C2×#168377192
C2×#168377172
C2×#168377042
C2×#168376912
C2×#168376532
C2×#168376372
C2×#168375112
C2×#168374762
C2×#168374452
C2×#106×D592
C2×C59×#4822
C2×#334559