Finite Group Databasebeta

← C2×#21436684 #29467398

Subgroups — C2×#21436684 #29467398

Order 15104.

2146 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×#16838116C211yesmaximal, characteristic, complemented
2C2×#16838053C211yesmaximal, characteristic, complemented
3#21436684C2116yesmaximal, direct product factor
4C2×#16837799C211yesmaximal, characteristic, complemented
5C2×#16837719C211yesmaximal, characteristic, complemented
6C2×#16837728C211yesmaximal, characteristic, complemented
7C2×#16837727C211yesmaximal, characteristic, complemented
8C2×#16837691C211yesmaximal, characteristic, complemented
9C2×#16837680C211yesmaximal, characteristic, complemented
10C2×#16837654C211yesmaximal, characteristic, complemented
11C2×#16837653C211yesmaximal, characteristic, complemented
12C2×#16837482C211yesmaximal, characteristic, complemented
13C2×#16837477C211yesmaximal, characteristic, complemented
14C2×#16837442C211yesmaximal, characteristic, complemented
15C2×#16837441C211yesmaximal, characteristic, complemented
16C2×C59×#481C211yesmaximal, characteristic, complemented
17C22×#11745685—21no—
18C22×#11745669C2211yescharacteristic
19C22×#11745664C2211yescharacteristic
20C22×#11745659C2211yescharacteristic
21#16838116—24no—
22#16838116C2218yescomplemented
23#16838053—24no—
24#16838053C2218yescomplemented
25C2×#14273726C2211yescharacteristic
26C2×#14273726C2211yescharacteristic
27C2×#14273714—21no—
28C2×#14273713—21no—
29C2×#14273712—21no—
30C2×#14273710—21no—
31C2×#14273705—21no—
32C2×#14273702C2211yescharacteristic
33C2×#14273701C2211yescharacteristic
34C2×#14273699—21no—
35C2×#14273698C2211yescharacteristic
36C2×D4×Dic59C2211yescharacteristic
37C2×#14273689C2211yescharacteristic
38C2×C4×C22⋊D59C2211yescharacteristic
39C2×#14273686C2211yescharacteristic
40C2×#14273685C2211yescharacteristic
41C2×#14273683—21no—
42C2×C4⋊C4×D59C2211yescharacteristic
43#16837799C2218yescomplemented
44#16837728C2218yescomplemented
45#16837727C2218yescomplemented
46#16837719C2218yescomplemented
47#16837691C2218yescomplemented
48#16837680C2218yescomplemented
49#16837654C2218yescomplemented
50#16837653C2218yescomplemented
51#16837482C2218yescomplemented
52#16837477C2218yescomplemented
53#16837442C2218yescomplemented
54#16837441C2218yescomplemented
55C2×#14273661C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58C2×#14273659C2211yescharacteristic
59C2×#14273658C2211yescharacteristic
60C2×#14273658C2211yescharacteristic
61C2×#14273658C2211yescharacteristic
62C2×Dic59⋊C8C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×#14273647C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×#121×C59C2211yescharacteristic
70C22×C4⋊C4×C59C2211yescharacteristic
71C59×#481C2218yescomplemented
72C2×#106×C59C2211yescharacteristic
73C2×#106×C59C2211yescharacteristic
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C2×#11745685—28no—
78C2×#11745685—48no—
79C22×Dic118—21no—
80C22×Dic118—21no—
81C22×D236—21no—
82C22×D236C2311yescharacteristic
83C22×C22⋊D59—21no—
84C22×C22⋊D59—21no—
85C22×C22⋊D59D411yescharacteristic
86C23×Dic59—21no—
87C22×C4×D59—21no—
88C22×C4×D59—21no—
89C22×C4×D59C2311yescharacteristic
90C2×#11745669—24no—
91C2×#11745669C2314yes—
92C2×#11745664—24no—
93C2×#11745664C2314yes—
94C2×#11745659—24no—
95C2×#11745659C2314yes—
96C22×C59⋊C8C2311yescharacteristic
97C22×C59⋊C8C2311yescharacteristic
98#14273726—22no—
99#14273726—22no—
100#14273726C2314yes—
101#14273726C2314yes—
102#14273714—28no—
103#14273713—28no—
104#14273712—28no—
105#14273710—28no—
106#14273705—28no—
107#14273702—22no—
108#14273702C2314yes—
109#14273701—22no—
110#14273701C2314yes—
111#14273699—28no—
112#14273698—22no—
113#14273698C2314yes—
114D4×Dic59—22no—
115D4×Dic59C2314yes—
116#14273689—22no—
117#14273689C2314yes—
118C4×C22⋊D59D414yes—
119C4×C22⋊D59C2314yes—
120#14273686—22no—
121#14273686C2314yes—
122#14273685—22no—
123#14273685C2314yes—
124#14273683—28no—
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×C4⋊Dic59C2311yescharacteristic
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4D411yescharacteristic
132C4⋊C4×D59—22no—
133C4⋊C4×D59C2314yes—
134C2×C22⋊Dic59—21no—
135C2×C22⋊Dic59—21no—
136C2×C22⋊Dic59—21no—
137C2×C22⋊Dic59D411yescharacteristic
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4D411yescharacteristic
143C2×C4×Dic59—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59C2311yescharacteristic
146#14273661C2314yes—
147#14273660C2314yes—
148#14273660C2314yes—
149#14273659C2314yes—
150#14273658C2314yes—
151#14273658C2314yes—
152#14273658C2314yes—
153Dic59⋊C8C2314yes—
154#14273649C2314yes—
155#14273649C2314yes—
156#14273648C2314yes—
157#14273647C2314yes—
158(C2×D59)⋊C8C2314yes—
159C8×Dic59C2314yes—
160C22×D4×C59—21no—
161C22×D4×C59C2311yescharacteristic
162C23×C4×C59—21no—
163C23×C4×C59C2311yescharacteristic
164C22×C8×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166#121×C59—22no—
167#121×C59C2314yes—
168C2×C4⋊C4×C59—21no—
169C2×C4⋊C4×C59—22no—
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2314yes—
174C2×C22⋊C4×C59—21no—
175#106×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—82no—
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×C59—24no—
196C22×C4×C59—44no—
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D412yes—
199C22×C4×C59C2412yes—
200C22×C4×C59C2411yescharacteristic
201C2×C22⋊D59—24no—
202C2×C22⋊D59—24no—
203C2×C22⋊D59—24no—
204C2×C22⋊D59—44no—
205C2×C22⋊D59—82no—
206C2×C22⋊D59C2×D414yes—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59—24no—
211C22×Dic59—44no—
212C22×Dic59C2×D411yescharacteristic
213C22×Dic59C2×D411yescharacteristic
214C22×Dic59C2×D411yescharacteristic
215#11745685—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—44no—
227C2×C4×D59—44no—
228C2×C4×D59C2×D412yes—
229C2×C4×D59C2412yes—
230C2×Dic118—24no—
231C2×Dic118—24no—
232C2×Dic118—44no—
233C2×Dic118—82no—
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—24no—
241C4⋊C4×C59—21no—
242C4⋊C4×C59C2412yes—
243C4⋊C4×C59C2412yes—
244C4⋊C4×C59C2412yes—
245C22⋊C4×C59—24no—
246C22⋊Dic59—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)⋊C4—24no—
255(C2×D59)⋊C4C2×D414yes—
256C4⋊Dic59—21no—
257C4⋊Dic59—21no—
258C4⋊Dic59—21no—
259C4⋊Dic59C2412yes—
260C4⋊Dic59C2412yes—
261C4⋊Dic59C2412yes—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265Dic59⋊C4C2×D414yes—
266C4×Dic59—24no—
267C4×Dic59—24no—
268C4×Dic59C2×D412yes—
269C4×Dic59C2412yes—
270#11745664—28no—
271C2×C59⋊C8—22no—
272C2×C59⋊C8#4114yescomplemented
273C2×C59⋊C8C2412yes—
274C2×C59⋊C8C2412yes—
275#11745659—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—22no—
289C22×D59—42no—
290C22×D59—42no—
291C22×D59—42no—
292C22×D59C22×D412yes—
293D4×C59—22no—
294D4×C59—22no—
295D4×C59—42no—
296D4×C59—84no—
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—48no—
305C2×C4×C59—42no—
306C2×C4×C59—42no—
307C2×C4×C59—42no—
308C2×C4×C59C22×D412yes—
309C2×C4×C59C22×D411yescharacteristic
310C2×C4×C59C2×#4112yes—
311C2×C4×C592−1+412yes—
312C2×C4×C59C2511yescharacteristic
313C22⋊D59—28no—
314C22⋊D59—48no—
315C22⋊D59—84no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—42no—
322C2×Dic59—42no—
323C2×Dic59—42no—
324C2×Dic59—48no—
325C2×Dic59AGL(1,ℤ/8)14yes—
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—48no—
338Dic118—48no—
339Dic118—84no—
340C8×C59—22no—
341C8×C59—22no—
342C59⋊C8—22no—
343C59⋊C8C2×#4114yescomplemented
344C2×#3354—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—22no—
358C2×D59—22no—
359C2×D59—22no—
360C2×D59—44no—
361C2×D59—42no—
362C2×D59—42no—
363C2×D59—42no—
364C2×D59—84no—
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—42no—
375Dic59—42no—
376Dic59—42no—
377Dic59C2×AGL(1,ℤ/8)14yes—
378C2×#555—591no—
379C2×#547—591no—
380#3354—5916no—
381C2×#498—591no—
382C2×#481—591no—
383C2×#481D5911yescharacteristic, complemented
384C2×#482—591no—
385C2×#482—591no—
386C2×#476—591no—
387C2×#474—591no—
388C2×#469—591no—
389C2×#469—591no—
390C2×C4×D8—591no—
391C2×#436—591no—
392C2×#428—591no—
393C2×#428—591no—
394C2×C59—42no—
395C2×C59—82no—
396C2×C59#335414yescomplemented
397C2×C59C2×#54711yescharacteristic
398C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
399C2×C59C2×#57711yescharacteristic
400D59—42no—
401D59—82no—
402C22×#41—1181no—
403C22×D8—591no—
404C22×M16—591no—
405C22×M16—591no—
406#555—598no—
407#555—1184no—
408#547—598no—
409#547—1184no—
410C2×C4⋊Q8—591no—
411C2×C4⋊Q8—591no—
412C2×#124—1181no—
413C2×#124—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×#117—591no—
426C2×#117—591no—
427C2×#117—1181no—
428C22×C4⋊C4—591no—
429C22×C4⋊C4C2×D5911yescharacteristic
430#498—598no—
431#482—598no—
432#482—598no—
433#481—598no—
434#481C2×D5918yescomplemented
435#476—598no—
436#474—598no—
437#469—598no—
438#469—598no—
439C4×D8—598no—
440#436—598no—
441#428—598no—
442#428—598no—
443C2×#107—591no—
444C2×#107—591no—
445C2×#107—591no—
446C2×#106—591no—
447C2×#106—591no—
448C2×#106—591no—
449C2×#106—591no—
450C2×#106C2×D5911yescharacteristic
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×C4×C8—591no—
462C59C2×#335411yescharacteristic, complemented, Sylow
463C2×#41—1188no—
464C2×#41—2368no—
465C22×Q8—1181no—
466C22×Q8—1181no—
467C22×D4—21no—
468C22×D4—591no—
469C22×D4—591no—
470C22×D4—1181no—
471C22×D4—1181no—
472C22×D4—1181no—
473C22×D4C22×D5911yescharacteristic
474C23×C4—21no—
475C23×C4—591no—
476C23×C4—1181no—
477C23×C4—1181no—
478C23×C4—1181no—
479C23×C4C22×D5911yescharacteristic
480C2×D8—594no—
481C2×D8—1184no—
482C2×M16—594no—
483C2×M16—594no—
484C2×M16—1184no—
485C2×M16—1184no—
486C22×C8—591no—
487C22×C8—591no—
488C22×C8C22×D5911yescharacteristic
489C22×C8C22×D5911yescharacteristic
490C4⋊Q8—594no—
491C4⋊Q8—594no—
492C4⋊Q8—1182no—
493C4⋊Q8—1182no—
494#124—1188no—
495#124—1188no—
496#123—1188no—
497#123—1188no—
498C22⋊Q8—1188no—
499#121—22no—
500#121—594no—
501#121—594no—
502#121—594no—
503#121—1182no—
504#121—1182no—
505#121—1188no—
506#121—1182no—
507#121C22×D5914yes—
508C4×D4—594no—
509C4×D4—594no—
510C4×D4—594no—
511C4×D4—594no—
512C4×D4—1182no—
513C4×D4—1182no—
514#117—594no—
515#117—594no—
516#117—1188no—
517#117—1182no—
518#117—1182no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—591no—
522C2×C4⋊C4—591no—
523C2×C4⋊C4—591no—
524C2×C4⋊C4—591no—
525C2×C4⋊C4—594no—
526C2×C4⋊C4—1182no—
527C2×C4⋊C4—1181no—
528C2×C4⋊C4—1181no—
529C2×C4⋊C4—1181no—
530C2×C4⋊C4C22×D5911yescharacteristic
531C2×C4⋊C4C22×D5911yescharacteristic
532C2×C4⋊C4C22×D5914yes—
533C2×C4⋊C4C22×D5911yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—591no—
536C2×C22⋊C4—591no—
537C2×C22⋊C4—1181no—
538C2×C22⋊C4—1181no—
539C2×C22⋊C4—1181no—
540C2×C22⋊C4—1181no—
541C2×C22⋊C4—1181no—
542C2×C22⋊C4—1181no—
543C2×C22⋊C4—1181no—
544C2×C42—591no—
545C2×C42—1181no—
546C2×C42—1181no—
547#107—594no—
548#107—594no—
549#107—594no—
550#106—594no—
551#106—594no—
552#106—594no—
553#106—594no—
554#106C22×D5914yes—
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—
565C4×C8—594no—
566C24—21no—
567C24—591no—
568C24—1181no—
569C24D4×D5911yescharacteristic
570#41—23632no—
571C2×Q8—1184no—
572C2×Q8—1184no—
573C2×Q8—4722no—
574C2×Q8—2364no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—82no—
580C2×D4—594no—
581C2×D4—592no—
582C2×D4—1184no—
583C2×D4—1184no—
584C2×D4—1184no—
585C2×D4—1184no—
586C2×D4—1181no—
587C2×D4—1182no—
588C2×D4—1182no—
589C2×D4—4722no—
590C2×D4—2364no—
591C2×D4—2364no—
592C2×D4C23×D5912yes—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—44no—
600C22×C4—591no—
601C22×C4—591no—
602C22×C4—591no—
603C22×C4—592no—
604C22×C4—592no—
605C22×C4—1184no—
606C22×C4—1184no—
607C22×C4—1184no—
608C22×C4—1182no—
609C22×C4—1182no—
610C22×C4—1181no—
611C22×C4—1181no—
612C22×C4—1181no—
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—
622M16—1188no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—594no—
626C2×C8—592no—
627C2×C8—592no—
628C2×C8—1182no—
629C2×C8C23×D5912yes—
630C2×C8C23×D5912yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—594no—
636C4⋊C4—592no—
637C4⋊C4—592no—
638C4⋊C4—592no—
639C4⋊C4—1184no—
640C4⋊C4—1184no—
641C4⋊C4—1184no—
642C4⋊C4—1181no—
643C4⋊C4—1181no—
644C4⋊C4—1181no—
645C4⋊C4C23×D5912yes—
646C4⋊C4C23×D5912yes—
647C4⋊C4C23×D5912yes—
648C22⋊C4—24no—
649C22⋊C4—594no—
650C22⋊C4—594no—
651C22⋊C4—1184no—
652C22⋊C4—1184no—
653C22⋊C4—1184no—
654C22⋊C4—1184no—
655C22⋊C4—1184no—
656C22⋊C4—1184no—
657C22⋊C4—1184no—
658C42—592no—
659C42—592no—
660C42—1184no—
661C42—1184no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—592no—
670C23—1182no—
671C23—1182no—
672C23—1182no—
673C23—1182no—
674C23—2362no—
675C23—2362no—
676C23—2362no—
677C23C2×D4×D5912yes—
678C23C2×D4×D5911yescharacteristic
679Q8—4724no—
680Q8—2368no—
681D4—22no—
682D4—22no—
683D4—42no—
684D4—84no—
685D4—1188no—
686D4—1182no—
687D4—1182no—
688D4—4724no—
689D4—2368no—
690D4—2368no—
691D4—2362no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—48no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—594no—
704C2×C4—592no—
705C2×C4—592no—
706C2×C4—592no—
707C2×C4—1182no—
708C2×C4—1182no—
709C2×C4—1182no—
710C2×C4—1182no—
711C2×C4—1184no—
712C2×C4—1182no—
713C2×C4—1182no—
714C2×C4—1182no—
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—1182no—
739C22—1182no—
740C22—1182no—
741C22—4724no—
742C22—2362no—
743C22—2362no—
744C22—2362no—
745C22—2364no—
746C22#1683805012yes—
747C22AGL(1,ℤ/8)×D5912yes—
748C22#1683820812yes—
749C22C22×D4×D5911yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—594no—
755C4—1182no—
756C4—1182no—
757C4—2362no—
758C4—2362no—
759C4—2362no—
760C4#1683805012yes—
761C4C2×#41×D5911yescharacteristic
762C4C2×#1427377411yescharacteristic
763C2—42no—
764C2—82no—
765C2—4722no—
766C2—2362no—
767C2#2143668414yesdirect product factor
768C2C2×#1683805011yescharacteristic
769C2C2×AGL(1,ℤ/8)×D5911yescharacteristic
770C2C2×#1683820811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#481C2
socleC23×C59C22×D4
hypercenterC2×#481D59
hypocenterC59C2×#3354
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#16838116C2semidirect
2. C2×#16838053C2semidirect
3. #21436684C2direct (N × H)
4. C2×#16837799C2semidirect
5. C2×#16837719C2semidirect
6. C2×#16837728C2semidirect
7. C2×#16837727C2semidirect
8. C2×#16837691C2semidirect
9. C2×#16837680C2semidirect
10. C2×#16837654C2semidirect
11. C2×#16837653C2semidirect
12. C2×#16837482C2semidirect
13. C2×#16837477C2semidirect
14. C2×#16837442C2semidirect
15. C2×#16837441C2semidirect
16. C2×C59×#481C2semidirect
22. #16838116C22semidirect
24. #16838053C22semidirect
43. #16837799C22semidirect
44. #16837728C22semidirect
45. #16837727C22semidirect
46. #16837719C22semidirect
47. #16837691C22semidirect
48. #16837680C22semidirect
49. #16837654C22semidirect
50. #16837653C22semidirect
51. #16837482C22semidirect
52. #16837477C22semidirect
53. #16837442C22semidirect
54. #16837441C22semidirect
71. C59×#481C22semidirect
272. C2×C59⋊C8#41semidirect
343. C59⋊C8C2×#41semidirect
383. C2×#481D59semidirect
396. C2×C59#3354semidirect
434. #481C2×D59semidirect
462. C59C2×#3354semidirect
767. C2#21436684direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381162
C2×#168380532
#214366842
C2×#168377992
C2×#168377192
C2×#168377282
C2×#168377272
C2×#168376912
C2×#168376802
C2×#168376542
C2×#168376532
C2×#168374822
C2×#168374772
C2×#168374422
C2×#168374412
C2×C59×#4812
C2×#335459