Finite Group Databasebeta

← C2×#21434386 #29457034

Subgroups — C2×#21434386 #29457034

Order 15104.

2122 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838003C211yesmaximal, characteristic
2C2×#16837878C211yesmaximal, characteristic, complemented
3#21434386C2116yesmaximal, direct product factor
4C2×#16837729C211yesmaximal, characteristic, complemented
5C2×#16837724C211yesmaximal, characteristic, complemented
6C2×#16837711C211yesmaximal, characteristic, complemented
7C2×#16837708C211yesmaximal, characteristic, complemented
8C2×#16837601C211yesmaximal, characteristic, complemented
9C2×#16837600C211yesmaximal, characteristic, complemented
10C2×#16837542C211yesmaximal, characteristic, complemented
11C2×#16837539C211yesmaximal, characteristic, complemented
12C2×#16837504C211yesmaximal, characteristic, complemented
13C2×C4×#11745671C211yesmaximal, characteristic, complemented
14C2×C4×#11745670C211yesmaximal, characteristic, complemented
15C2×#16837464C211yesmaximal, characteristic, complemented
16C2×C59×#440C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×#11745660C2211yescharacteristic
19C22×#11745670C2211yescharacteristic
20C22×#11745671C2211yescharacteristic
21#16838003—24no—
22#16838003C2218yes—
23C2×#14273723C2211yescharacteristic
24C2×#14273718C2211yescharacteristic
25C2×#14273710—21no—
26C2×#14273709—21no—
27C2×#14273702C2211yescharacteristic
28C2×#14273701—21no—
29C2×#14273700—21no—
30C2×#14273698C2211yescharacteristic
31#16837878—24no—
32#16837878C2218yescomplemented
33C2×Q8×Dic59C2211yescharacteristic
34C2×C4×Dic118—21no—
35C2×C4×Dic118C2211yescharacteristic
36C2×#14273692—21no—
37C2×#14273692C2211yescharacteristic
38C2×C4×D236C2211yescharacteristic
39C2×#14273685—21no—
40C2×#14273685C2211yescharacteristic
41C2×#14273684—21no—
42C2×#14273684C2211yescharacteristic
43#16837729C2218yescomplemented
44#16837724C2218yescomplemented
45#16837711C2218yescomplemented
46#16837708C2218yescomplemented
47#16837601C2218yescomplemented
48#16837600C2218yescomplemented
49#16837542C2218yescomplemented
50#16837539C2218yescomplemented
51#16837504C2218yescomplemented
52C4×#11745671C2218yescomplemented
53C4×#11745670C2218yescomplemented
54#16837464C2218yescomplemented
55C2×#14273661C2211yescharacteristic
56C2×#14273658C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C4×C59⋊C8C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C59×#440C2218yescomplemented
73C2×#107×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C2×Q8×D59—24no—
80C2×Q8×D59—22no—
81C2×Q8×D59—24no—
82C2×Q8×D59C2314yes—
83C22×D236—21no—
84C22×D236C2311yescharacteristic
85C22×C22⋊D59—21no—
86C22×C22⋊D59—21no—
87C22×C22⋊D59—21no—
88C22×C4×D59—21no—
89C22×C4×D59—21no—
90C22×C4×D59C2311yescharacteristic
91C2×#11745660—24no—
92C2×#11745660C2314yes—
93C2×#11745670—24no—
94C2×#11745670C2314yes—
95C2×#11745671—24no—
96C2×#11745671C2314yes—
97C22×C59⋊C8C2311yescharacteristic
98C22×C59⋊C8C2311yescharacteristic
99#14273723—22no—
100#14273723C2314yes—
101#14273718—22no—
102#14273718C2314yes—
103#14273710—28no—
104#14273709—28no—
105#14273702—22no—
106#14273702C2314yes—
107#14273701—28no—
108#14273700—28no—
109#14273698—22no—
110#14273698C2314yes—
111Q8×Dic59—22no—
112Q8×Dic59C2314yes—
113C4×Dic118—22no—
114C4×Dic118—28no—
115C4×Dic118C2314yes—
116#14273692—28no—
117#14273692—22no—
118#14273692C2314yes—
119C4×D236—22no—
120C4×D236C2314yes—
121#14273685—22no—
122#14273685—28no—
123#14273685C2314yes—
124#14273684—28no—
125#14273684D414yes—
126#14273684C2314yes—
127C2×C4⋊Dic59—21no—
128C2×C4⋊Dic59—21no—
129C2×C4⋊Dic59C2311yescharacteristic
130C2×C4⋊Dic59C2311yescharacteristic
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4D411yescharacteristic
135C2×Dic59⋊C4D411yescharacteristic
136C2×C22⋊Dic59—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4D411yescharacteristic
141C2×(C2×D59)⋊C4D411yescharacteristic
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59C2311yescharacteristic
147#14273661C2314yes—
148#14273658C2314yes—
149#14273658C2314yes—
150Dic59⋊C8C2314yes—
151Dic59⋊C8C2314yes—
152#14273652C2314yes—
153#14273651C2314yes—
154#14273650C2314yes—
155#14273649C2314yes—
156#14273648C2314yes—
157#14273647C2314yes—
158(C2×D59)⋊C8C2314yes—
159(C2×D59)⋊C8C2314yes—
160C4×C59⋊C8C2314yes—
161C22×Q8×C59C2311yescharacteristic
162C22×D4×C59C2311yescharacteristic
163C23×C4×C59—21no—
164C2×SD16×C59—24no—
165C2×SD16×C59C2314yes—
166C22×C8×C59C2311yescharacteristic
167C22×C8×C59C2311yescharacteristic
168C4×Q8×C59—22no—
169C4×Q8×C59C2314yes—
170C4×D4×C59—22no—
171C4×D4×C59C2314yes—
172C2×C4⋊C4×C59—21no—
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C22⋊C4×C59—21no—
176C2×C42×C59—21no—
177C2×C42×C59C2311yescharacteristic
178#107×C59C2314yes—
179#103×C59C2314yes—
180#102×C59C2314yes—
181#97×C59C2314yes—
182C24×C59—21no—
183C23×D59—21no—
184C23×D59C2×D411yescharacteristic
185C2×Q8×C59—21no—
186C2×Q8×C59—22no—
187C2×Q8×C59#4114yes—
188C2×Q8×C59C2412yes—
189C2×D4×C59—21no—
190C2×D4×C59—22no—
191C2×D4×C59—22no—
192C2×D4×C59C2412yes—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—24no—
197C22×C4×C59—82no—
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2411yescharacteristic
201C2×C22⋊D59—24no—
202C2×C22⋊D59—24no—
203C2×C22⋊D59—24no—
204C2×C22⋊D59—82no—
205C2×C22⋊D59—82no—
206C2×C22⋊D59—82no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59C2×D411yescharacteristic
211C22×Dic59C2×D411yescharacteristic
212C22×Dic59C2×D411yescharacteristic
213Q8×D59—216no—
214Q8×D59—28no—
215Q8×D59—28no—
216C2×D236—22no—
217C2×D236—22no—
218C2×D236—21no—
219C2×D236—24no—
220C2×D236—82no—
221C2×D236C2412yes—
222C2×C4×D59—28no—
223C2×C4×D59—24no—
224C2×C4×D59—22no—
225C2×C4×D59—22no—
226C2×C4×D59—24no—
227C2×C4×D59—82no—
228C2×C4×D59C2×D412yes—
229C2×C4×D59C2412yes—
230C2×Dic118—28no—
231C2×Dic118—21no—
232C2×Dic118—22no—
233C2×Dic118—24no—
234C2×Dic118#4114yes—
235C2×Dic118C2412yes—
236SD16×C59—28no—
237C2×C8×C59—22no—
238C2×C8×C59—22no—
239C2×C8×C59C2412yes—
240C2×C8×C59C2412yes—
241C4⋊C4×C59—24no—
242C4⋊C4×C59—21no—
243C4⋊C4×C59—21no—
244C4⋊C4×C59C2412yes—
245C4⋊C4×C59C2412yes—
246C22⋊C4×C59—24no—
247C42×C59—24no—
248C42×C59C2×D412yes—
249C42×C59C2412yes—
250C22⋊Dic59—24no—
251#11745671—28no—
252#11745670—28no—
253(C2×D59)⋊C4—24no—
254(C2×D59)⋊C4—24no—
255(C2×D59)⋊C4—24no—
256(C2×D59)⋊C4C2×D414yes—
257(C2×D59)⋊C4C2×D414yes—
258C4⋊Dic59—21no—
259C4⋊Dic59—21no—
260C4⋊Dic59—24no—
261C4⋊Dic59—24no—
262C4⋊Dic59C2412yes—
263C4⋊Dic59C2412yes—
264Dic59⋊C4—24no—
265Dic59⋊C4—24no—
266Dic59⋊C4—24no—
267Dic59⋊C4C2×D414yes—
268Dic59⋊C4C2×D414yes—
269C4×Dic59—24no—
270C4×Dic59—24no—
271C4×Dic59—24no—
272C4×Dic59—24no—
273C4×Dic59C2×D412yes—
274C4×Dic59C2412yes—
275C2×C59⋊C8—22no—
276C2×C59⋊C8—22no—
277C2×C59⋊C8C2412yes—
278C2×C59⋊C8C2412yes—
279#11745660—28no—
280C23×C59—22no—
281C23×C59—42no—
282C23×C59—42no—
283C23×C59—42no—
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—
293Q8×C59—24no—
294Q8×C59—22no—
295Q8×C59C2×#4114yes—
296D4×C59—22no—
297D4×C59—22no—
298D4×C59—42no—
299C2×C4×C59—24no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—42no—
306C2×C4×C59—42no—
307C2×C4×C59—84no—
308C2×C4×C59C22×D412yes—
309C2×C4×C59C22×D412yes—
310C2×C4×C59C22×D411yescharacteristic
311C2×C4×C59C2×#4112yes—
312C2×C4×C59C2×#4112yes—
313C2×C4×C59C2511yescharacteristic
314C22⋊D59—84no—
315C22⋊D59—84no—
316C22⋊D59—84no—
317C2×Dic59—22no—
318C2×Dic59—24no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—42no—
325C2×Dic59—42no—
326C2×Dic59C22×D412yes—
327C2×Dic59C22×D412yes—
328C2×Dic59C22×D412yes—
329D236—22no—
330D236—22no—
331D236—42no—
332D236—84no—
333C4×D59—216no—
334C4×D59—24no—
335C4×D59—22no—
336C4×D59—22no—
337C4×D59—84no—
338Dic118—216no—
339Dic118—24no—
340Dic118—22no—
341Dic118C2×#4114yes—
342C8×C59—22no—
343C8×C59—22no—
344C59⋊C8—22no—
345C59⋊C8—22no—
346C2×#3126—591nomaximal, Sylow
347C22×C59—42no—
348C22×C59—42no—
349C22×C59—42no—
350C22×C59—84no—
351C22×C59#52512yes—
352C22×C59#57712yes—
353C22×C59#57712yes—
354C22×C59C23×D411yescharacteristic
355C2×D59—22no—
356C2×D59—22no—
357C2×D59—22no—
358C2×D59—44no—
359C2×D59—42no—
360C2×D59—42no—
361C2×D59—42no—
362C2×D59—84no—
363C4×C59—24no—
364C4×C59—22no—
365C4×C59—22no—
366C4×C59—42no—
367C4×C59—42no—
368C4×C59#52512yes—
369C4×C59C22×#4111yescharacteristic
370C4×C59C22×#4111yescharacteristic
371Dic59—22no—
372Dic59—24no—
373Dic59—22no—
374Dic59—22no—
375Dic59—42no—
376Dic59—42no—
377C2×#540—591no—
378C2×#519—591no—
379#3126—5916no—
380C2×#482—591no—
381C2×#482—591no—
382C2×#479—591no—
383C2×#479—591no—
384C2×#460—591no—
385C2×#460—591no—
386C2×#448—591no—
387C2×#448—591no—
388C2×#440—591no—
389C2×#440D5911yescharacteristic, complemented
390C2×C4×SD16—591no—
391C2×C4×SD16—591no—
392C2×#433—591no—
393C2×C59—82no—
394C2×C59#312614yescomplemented
395C2×C59C2×#52511yescharacteristic
396C2×C59C2×#57711yescharacteristic
397C2×C59C2×#57711yescharacteristic
398D59—42no—
399D59—82no—
400C23×Q8—591no—
401C22×SD16—591no—
402C22×SD16—591no—
403C22×SD16—591no—
404C22×SD16C2×D5911yescharacteristic
405#540—598no—
406#540—1184no—
407C2×#127—591no—
408C2×#125—591no—
409C2×#123—1181no—
410C2×#123—1181no—
411C2×#121—591no—
412C2×#121—591no—
413C2×#121—1181no—
414C2×#121—1181no—
415#519—598no—
416#519—1184no—
417C2×C4×Q8—591no—
418C2×C4×Q8—591no—
419C2×C4×Q8—591no—
420C2×C4×Q8—1181no—
421C2×C4×Q8—1181no—
422C2×C4×Q8C2×D5911yescharacteristic
423C2×C4×D4—591no—
424C2×C4×D4C2×D5911yescharacteristic
425C2×#117—591no—
426C2×#117—591no—
427C2×#117—1181no—
428C2×#117—1181no—
429#482—598no—
430#482—598no—
431#479—598no—
432#479—598no—
433#460—598no—
434#460—598no—
435#448—598no—
436#448—598no—
437#440—598no—
438#440C2×D5918yescomplemented
439C4×SD16—598no—
440C4×SD16—598no—
441#433—598no—
442C2×#107—591no—
443C2×#107C2×D5911yescharacteristic
444C2×#106—591no—
445C2×#106—591no—
446C2×C4⋊C8—591no—
447C2×C4⋊C8—591no—
448C2×#103—591no—
449C2×#103—591no—
450C2×#103—591no—
451C2×#103C2×D5911yescharacteristic
452C2×#102—591no—
453C2×#102—591no—
454C2×#102—591no—
455C2×#102C2×D5911yescharacteristic
456C2×C22⋊C8—591no—
457C2×C22⋊C8—591no—
458C2×#97C2×D5911yescharacteristic
459C2×C4×C8—591no—
460C59C2×#312611yescharacteristic, complemented, Sylow
461C22×Q8—594no—
462C22×Q8—591no—
463C22×Q8—1181no—
464C22×Q8—1182no—
465C22×Q8—1184no—
466C22×Q8—1184no—
467C22×Q8C22×D5911yescharacteristic
468C22×D4—591no—
469C22×D4—1181no—
470C22×D4—1181no—
471C22×D4—1181no—
472C22×D4—1181no—
473C22×D4C22×D5911yescharacteristic
474C23×C4—21no—
475C23×C4—591no—
476C23×C4—1181no—
477C23×C4—1181no—
478C2×SD16—24no—
479C2×SD16—594no—
480C2×SD16—594no—
481C2×SD16—594no—
482C2×SD16—1184no—
483C2×SD16—1184no—
484C2×SD16—1184no—
485C2×SD16C22×D5914yes—
486C22×C8—591no—
487C22×C8—591no—
488C22×C8C22×D5911yescharacteristic
489C22×C8C22×D5911yescharacteristic
490#127—594no—
491#127—1182no—
492#125—594no—
493#125—1182no—
494#123—1188no—
495#123—1188no—
496#121—594no—
497#121—594no—
498#121—1188no—
499#121—1188no—
500#121—1182no—
501#121—1182no—
502C4×Q8—22no—
503C4×Q8—594no—
504C4×Q8—594no—
505C4×Q8—594no—
506C4×Q8—1188no—
507C4×Q8—1182no—
508C4×Q8—1182no—
509C4×Q8—1188no—
510C4×Q8—1182no—
511C4×Q8C22×D5914yes—
512C4×D4—22no—
513C4×D4—594no—
514C4×D4—1182no—
515C4×D4C22×D5914yes—
516#117—594no—
517#117—594no—
518#117—594no—
519#117—1188no—
520#117—1188no—
521#117—1182no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—591no—
524C2×C4⋊C4—591no—
525C2×C4⋊C4—591no—
526C2×C4⋊C4—591no—
527C2×C4⋊C4—1181no—
528C2×C4⋊C4—1181no—
529C2×C4⋊C4—1181no—
530C2×C4⋊C4—1181no—
531C2×C4⋊C4—1181no—
532C2×C4⋊C4C22×D5911yescharacteristic
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×C42—21no—
542C2×C42—591no—
543C2×C42—1181no—
544C2×C42—1181no—
545C2×C42—1181no—
546C2×C42—1181no—
547C2×C42C22×D5911yescharacteristic
548#107—594no—
549#107C22×D5914yes—
550#106—594no—
551#106—594no—
552C4⋊C8—594no—
553C4⋊C8—594no—
554#103—594no—
555#103—594no—
556#103—594no—
557#103C22×D5914yes—
558#102—594no—
559#102—594no—
560#102—594no—
561#102C22×D5914yes—
562C22⋊C8—594no—
563C22⋊C8—594no—
564#97C22×D5914yes—
565C4×C8—594no—
566C24—21no—
567C24—591no—
568C24—1181no—
569C2×Q8—21no—
570C2×Q8—22no—
571C2×Q8—594no—
572C2×Q8—592no—
573C2×Q8—1184no—
574C2×Q8—1188no—
575C2×Q8—1188no—
576C2×Q8—11816no—
577C2×Q8—1188no—
578C2×Q8—1181no—
579C2×Q8—1182no—
580C2×Q8#1174568514yes—
581C2×Q8C23×D5912yes—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—592no—
586C2×D4—1184no—
587C2×D4—1184no—
588C2×D4—1184no—
589C2×D4—1184no—
590C2×D4—1181no—
591C2×D4—1182no—
592C2×D4—1182no—
593C2×D4—4722no—
594C2×D4—4722no—
595C2×D4—4722no—
596C2×D4—4722no—
597C2×D4C23×D5912yes—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—82no—
603C22×C4—591no—
604C22×C4—591no—
605C22×C4—591no—
606C22×C4—592no—
607C22×C4—592no—
608C22×C4—1184no—
609C22×C4—1188no—
610C22×C4—1181no—
611C22×C4—1182no—
612C22×C4—1182no—
613C22×C4—1181no—
614C22×C4—1181no—
615C22×C4—1184no—
616C22×C4—4722no—
617C22×C4D4×D5911yescharacteristic
618C22×C4D4×D5911yescharacteristic
619C22×C4C23×D5911yescharacteristic
620SD16—28no—
621SD16—1188no—
622SD16—1188no—
623SD16—1188no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—592no—
627C2×C8—592no—
628C2×C8—1182no—
629C2×C8—1182no—
630C2×C8C23×D5912yes—
631C2×C8C23×D5912yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—594no—
636C4⋊C4—594no—
637C4⋊C4—592no—
638C4⋊C4—592no—
639C4⋊C4—1184no—
640C4⋊C4—1184no—
641C4⋊C4—1184no—
642C4⋊C4—1184no—
643C4⋊C4—1181no—
644C4⋊C4—1181no—
645C4⋊C4—1184no—
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—
655C42—24no—
656C42—592no—
657C42—592no—
658C42—1184no—
659C42—1184no—
660C42—1184no—
661C42—1184no—
662C42D4×D5912yes—
663C42C23×D5912yes—
664C23—22no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—592no—
669C23—1182no—
670C23—1182no—
671C23—1182no—
672C23—1182no—
673C23—2362no—
674C23—2362no—
675C23—2362no—
676C23C2×D4×D5911yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—594no—
680Q8—11816no—
681Q8—1184no—
682Q8—1182no—
683Q8C2×#1174568514yes—
684D4—22no—
685D4—22no—
686D4—42no—
687D4—1182no—
688D4—1182no—
689D4—4724no—
690D4—4724no—
691D4—4724no—
692D4—4724no—
693D4—2362no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—84no—
703C2×C4—592no—
704C2×C4—592no—
705C2×C4—592no—
706C2×C4—11816no—
707C2×C4—1182no—
708C2×C4—1184no—
709C2×C4—1182no—
710C2×C4—1182no—
711C2×C4—1182no—
712C2×C4—1184no—
713C2×C4—1182no—
714C2×C4—1182no—
715C2×C4—1182no—
716C2×C4—1182no—
717C2×C4—4724no—
718C2×C4—2362no—
719C2×C4—2362no—
720C2×C4C2×D4×D5912yes—
721C2×C4C2×D4×D5912yes—
722C2×C4C2×D4×D5911yescharacteristic
723C2×C4#41×D5912yes—
724C2×C4C2×#1174568512yes—
725C2×C4C24×D5911yescharacteristic
726C8—22no—
727C8—22no—
728C8—1182no—
729C8—1182no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—1182no—
735C22—1182no—
736C22—1182no—
737C22—4724no—
738C22—2362no—
739C22—2362no—
740C22—2362no—
741C22—2364no—
742C22#1683791112yes—
743C22#1683821112yes—
744C22#1683821212yes—
745C22C22×D4×D5911yescharacteristic
746C4—22no—
747C4—22no—
748C4—24no—
749C4—42no—
750C4—42no—
751C4—1182no—
752C4—1182no—
753C4—1182no—
754C4—1184no—
755C4—2362no—
756C4—2362no—
757C4#1683791112yes—
758C4C2×#41×D5911yescharacteristic
759C4C22×#1174568511yescharacteristic
760C2—82no—
761C2—4722no—
762C2—2362no—
763C2#2143438614yesdirect product factor
764C2C2×#1683791111yescharacteristic
765C2C2×#1683821111yescharacteristic
766C2C2×#1683821211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#440C2
socleC23×C59C22×D4
prime radicalC2×#16838003C2
hypercenterC2×#440D59
hypocenterC59C2×#3126
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
2. C2×#16837878C2semidirect
3. #21434386C2direct (N × H)
4. C2×#16837729C2semidirect
5. C2×#16837724C2semidirect
6. C2×#16837711C2semidirect
7. C2×#16837708C2semidirect
8. C2×#16837601C2semidirect
9. C2×#16837600C2semidirect
10. C2×#16837542C2semidirect
11. C2×#16837539C2semidirect
12. C2×#16837504C2semidirect
13. C2×C4×#11745671C2semidirect
14. C2×C4×#11745670C2semidirect
15. C2×#16837464C2semidirect
16. C2×C59×#440C2semidirect
32. #16837878C22semidirect
43. #16837729C22semidirect
44. #16837724C22semidirect
45. #16837711C22semidirect
46. #16837708C22semidirect
47. #16837601C22semidirect
48. #16837600C22semidirect
49. #16837542C22semidirect
50. #16837539C22semidirect
51. #16837504C22semidirect
52. C4×#11745671C22semidirect
53. C4×#11745670C22semidirect
54. #16837464C22semidirect
72. C59×#440C22semidirect
389. C2×#440D59semidirect
394. C2×C59#3126semidirect
438. #440C2×D59semidirect
460. C59C2×#3126semidirect
763. C2#21434386direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380032
C2×#168378782
#214343862
C2×#168377292
C2×#168377242
C2×#168377112
C2×#168377082
C2×#168376012
C2×#168376002
C2×#168375422
C2×#168375392
C2×#168375042
C2×C4×#117456712
C2×C4×#117456702
C2×#168374642
C2×C59×#4402
C2×#312659