Finite Group Databasebeta

← C2×#21433445 #29455317

Subgroups — C2×#21433445 #29455317

Order 15104.

4850 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838200C212yesmaximal, complemented
2C2×#16837948C211yesmaximal, characteristic, complemented
3#21433445C2116yesmaximal, direct product factor
4C2×#16837585C212yesmaximal, complemented
5C2×#16837575C212yesmaximal, complemented
6C2×#16837580C212yesmaximal, complemented
7C2×#16837570C212yesmaximal, complemented
8C22×#14273654C212yesmaximal, complemented
9C2×#16837386C211yesmaximal, characteristic, complemented
10C2×C59×#585C211yesmaximal, characteristic, complemented
11C22×#11745685C2211yescharacteristic, complemented
12#16838200—28no—
13#16838200C22116yescomplemented
14C2×#14273758—22no—
15C2×#14273757C2214yescomplemented
16C2×#14273753—22no—
17C2×#14273752C2214yescomplemented
18C2×#14273747—24no—
19C22×#11745664C2212yescomplemented
20#16837948—24no—
21#16837948C2218yescomplemented
22C2×#14273725C2211yescharacteristic, complemented
23C2×#14273723C2211yescharacteristic, complemented
24C2×#14273716C2211yescharacteristic, complemented
25C2×#14273714C2211yescharacteristic, complemented
26C2×#14273699—22no—
27C2×C4×C22⋊D59—22no—
28C22×C4×Dic59C2211yescharacteristic, complemented
29#16837585C22116yescomplemented
30#16837580C22116yescomplemented
31#16837575C22116yescomplemented
32#16837570C22116yescomplemented
33C2×#14273654C2214yescomplemented
34C2×#14273654C2214yescomplemented
35C2×#14273654C22116yescomplemented
36#16837386C2218yescomplemented
37C2×#14273646C2212yescomplemented
38C2×#14273644C2212yescomplemented
39C59×#585—24no—
40C59×#585—28no—
41C59×#585C2218yescomplemented
42C2×2−1+4×C59—22no—
43C2×2−1+4×C59C2212yes—
44C2×H(5,𝔽2)×C59—22no—
45C2×H(5,𝔽2)×C59—22no—
46C2×H(5,𝔽2)×C59C2212yes—
47C22×#41×C59—24no—
48C22×#41×C59—22no—
49C22×#41×C59C2212yes—
50C22×#41×C59C2211yescharacteristic
51C2×#11745685—22no—
52C2×#11745685—22no—
53C2×#11745685—22no—
54C2×#11745685—24no—
55C2×#11745685C2314yescomplemented
56C22×Dic118C2311yescharacteristic
57C22×D236C2311yescharacteristic
58C22×C22⋊D59—21no—
59C22×C22⋊D59—22no—
60C23×Dic59—21no—
61C22×C4×D59—21no—
62#14273758—216no—
63#14273757—28no—
64#14273757C23116yescomplemented
65#14273753—216no—
66#14273752—28no—
67#14273752C23116yescomplemented
68#14273747—232no—
69C2×#11745672—24no—
70C2×#11745670—24no—
71C2×#11745671—24no—
72C2×#11745669—24no—
73C2×#11745664—22no—
74C2×#11745664—24no—
75C2×#11745664C2314yes—
76C2×#11745664C2318yescomplemented
77C22×C59⋊C8—22no—
78#14273725—22no—
79#14273725C2314yescomplemented
80#14273723—22no—
81#14273723C2314yescomplemented
82#14273716—22no—
83#14273716C2314yescomplemented
84#14273714—22no—
85#14273714C2314yescomplemented
86#14273699—216no—
87C4×C22⋊D59—216no—
88C2×Dic59⋊C4—22no—
89C2×C22⋊Dic59—22no—
90C2×(C2×D59)⋊C4—22no—
91C2×C4×Dic59—22no—
92C2×C4×Dic59—21no—
93C2×C4×Dic59C2311yescharacteristic
94C2×C4×Dic59C2311yescharacteristic
95C2×C4×Dic59C2314yescomplemented
96#14273654C23116yescomplemented
97#14273654C23116yescomplemented
98#14273646C2318yescomplemented
99#14273644C2318yescomplemented
1002−1+4×C59—216no—
1012−1+4×C59—28no—
1022−1+4×C59—24no—
1032−1+4×C59—216no—
1042−1+4×C59C2318yes—
105H(5,𝔽2)×C59—216no—
106H(5,𝔽2)×C59—216no—
107H(5,𝔽2)×C59—28no—
108H(5,𝔽2)×C59—216no—
109H(5,𝔽2)×C59—24no—
110H(5,𝔽2)×C59—216no—
111H(5,𝔽2)×C59C2318yes—
112C2×#41×C59—24no—
113C2×#41×C59—28no—
114C2×#41×C59—24no—
115C2×#41×C59—232no—
116C2×#41×C59—216no—
117C2×#41×C59—232no—
118C2×#41×C59—24no—
119C2×#41×C59—24no—
120C2×#41×C59—22no—
121C2×#41×C59—22no—
122C2×#41×C59—24no—
123C2×#41×C59—216no—
124C2×#41×C59—22no—
125C2×#41×C59—22no—
126C2×#41×C59—24no—
127C2×#41×C59—24no—
128C2×#41×C59—24no—
129C2×#41×C59D414yes—
130C2×#41×C59D414yescomplemented
131C2×#41×C59D418yescomplemented
132C2×#41×C59C2314yes—
133C2×#41×C59C2318yes—
134C2×#41×C59C2314yes—
135C22×Q8×C59—22no—
136C22×Q8×C59—24no—
137C22×Q8×C59D412yescomplemented
138C22×Q8×C59C2311yescharacteristic
139C22×D4×C59—28no—
140C22×D4×C59—22no—
141C22×D4×C59—24no—
142C22×D4×C59—22no—
143C22×D4×C59—24no—
144C22×D4×C59D412yes—
145C22×D4×C59D412yescomplemented
146C22×D4×C59C2311yescharacteristic
147C23×C4×C59—24no—
148C23×C4×C59—22no—
149C23×C4×C59D412yes—
150C23×C4×C59C2311yescharacteristic
151C24×C59—24no—
152C24×C59—22no—
153C24×C59C2×D412yes—
154C24×C59C2×D411yescharacteristic
155C23×D59—21no—
156#41×C59—232no—
157#41×C59—264no—
158#41×C59—216no—
159#41×C59—216no—
160#41×C59—216no—
161#41×C59—232no—
162#41×C59—216no—
163#41×C59—216no—
164#41×C59—28no—
165#41×C59—28no—
166#41×C59—28no—
167#41×C59—28no—
168#41×C59—28no—
169#41×C59—28no—
170#41×C59—28no—
171#41×C59—216no—
172#41×C59—24no—
173#41×C59—28no—
174#41×C59—24no—
175#41×C59—28no—
176#41×C59C2×D418yes—
177#41×C59C2×D4116yescomplemented
178#41×C59C2418yes—
179C2×Q8×C59—24no—
180C2×Q8×C59—216no—
181C2×Q8×C59—216no—
182C2×Q8×C59—216no—
183C2×Q8×C59—22no—
184C2×Q8×C59—24no—
185C2×Q8×C59—22no—
186C2×Q8×C59—22no—
187C2×Q8×C59C2×D414yes—
188C2×Q8×C59C2×D412yes—
189C2×Q8×C59C2×D418yescomplemented
190C2×Q8×C59C2412yes—
191C2×D4×C59—28no—
192C2×D4×C59—24no—
193C2×D4×C59—216no—
194C2×D4×C59—264no—
195C2×D4×C59—216no—
196C2×D4×C59—216no—
197C2×D4×C59—24no—
198C2×D4×C59—24no—
199C2×D4×C59—28no—
200C2×D4×C59—24no—
201C2×D4×C59—24no—
202C2×D4×C59—216no—
203C2×D4×C59—28no—
204C2×D4×C59—216no—
205C2×D4×C59—22no—
206C2×D4×C59—24no—
207C2×D4×C59—22no—
208C2×D4×C59—22no—
209C2×D4×C59C2×D418yes—
210C2×D4×C59C2×D412yes—
211C2×D4×C59C2×D414yes—
212C2×D4×C59C2×D418yescomplemented
213C2×D4×C59C2412yes—
214C22×C4×C59—24no—
215C22×C4×C59—28no—
216C22×C4×C59—232no—
217C22×C4×C59—22no—
218C22×C4×C59—24no—
219C22×C4×C59—22no—
220C22×C4×C59—28no—
221C22×C4×C59—22no—
222C22×C4×C59—24no—
223C22×C4×C59—24no—
224C22×C4×C59—28no—
225C22×C4×C59C2×D412yes—
226C22×C4×C59C2×D418yes—
227C22×C4×C59C2×D411yescharacteristic
228C22×C4×C59C2×D412yes—
229C22×C4×C59C2×D412yes—
230C22×C4×C59C2×D412yes—
231C22×C4×C59C2×D414yes—
232C22×C4×C59C2411yescharacteristic
233C22×C4×C59C2412yes—
234C2×C22⋊D59—28no—
235C2×C22⋊D59—24no—
236C2×C22⋊D59—48no—
237C2×C22⋊D59—42no—
238C2×C22⋊D59—42no—
239C22×Dic59—21no—
240C22×Dic59—21no—
241C22×Dic59—24no—
242C22×Dic59—21no—
243C22×Dic59—44no—
244#11745685—28no—
245#11745685—28no—
246#11745685—44no—
247#11745685—44no—
248C2×D236—22no—
249C2×D236—22no—
250C2×D236—21no—
251C2×D236C2412yes—
252C2×C4×D59—24no—
253C2×C4×D59—41no—
254C2×C4×D59—42no—
255C2×C4×D59—41no—
256C2×Dic118—22no—
257C2×Dic118—22no—
258C2×Dic118—21no—
259C2×Dic118C2412yes—
260C22⋊Dic59—28no—
261#11745672—216no—
262#11745671—216no—
263#11745670—216no—
264#11745669—216no—
265(C2×D59)⋊C4—28no—
266Dic59⋊C4—28no—
267C4×Dic59—21no—
268C4×Dic59—21no—
269C4×Dic59—24no—
270C4×Dic59C2412yes—
271C4×Dic59C2412yes—
272#11745664—24no—
273#11745664—28no—
274#11745664C2418yes—
275C2×C59⋊C8—24no—
276C2×C59⋊C8—28no—
277C23×C59—216no—
278C23×C59—22no—
279C23×C59—24no—
280C23×C59—22no—
281C23×C59—28no—
282C23×C59—42no—
283C23×C59—44no—
284C23×C59—84no—
285C23×C59—88no—
286C23×C59#12012yes—
287C23×C59#12012yes—
288C23×C59C22×D411yescharacteristic
289C23×C59C22×D414yes—
290C23×C59C22×D412yes—
291C22×D59—22no—
292C22×D59—44no—
293C22×D59—41no—
294C22×D59—41no—
295Q8×C59—216no—
296Q8×C59—24no—
297Q8×C59—24no—
298Q8×C59—28no—
299Q8×C59—24no—
300Q8×C59C22×D418yes—
301D4×C59—232no—
302D4×C59—216no—
303D4×C59—28no—
304D4×C59—216no—
305D4×C59—216no—
306D4×C59—28no—
307D4×C59—24no—
308D4×C59—24no—
309D4×C59—28no—
310D4×C59—24no—
311D4×C59C22×D418yes—
312C2×C4×C59—216no—
313C2×C4×C59—232no—
314C2×C4×C59—24no—
315C2×C4×C59—22no—
316C2×C4×C59—28no—
317C2×C4×C59—22no—
318C2×C4×C59—216no—
319C2×C4×C59—28no—
320C2×C4×C59—28no—
321C2×C4×C59—28no—
322C2×C4×C59—28no—
323C2×C4×C59#12011yescharacteristic
324C2×C4×C59#12012yes—
325C2×C4×C59#12014yes—
326C2×C4×C59#12014yes—
327C2×C4×C59#12011yescharacteristic
328C2×C4×C59C22×D414yes—
329C2×C4×C59C22×D411yescharacteristic
330C2×C4×C59C22×D412yes—
331C2×C4×C59C22×D412yes—
332C2×C4×C59C22×D414yes—
333C2×C4×C59C22×D412yes—
334C2×C4×C59C22×D414yes—
335C2×C4×C59C2511yescharacteristic
336C22⋊D59—416no—
337C22⋊D59—48no—
338C2×Dic59—24no—
339C2×Dic59—22no—
340C2×Dic59—22no—
341C2×Dic59—22no—
342C2×Dic59—48no—
343C2×Dic59—42no—
344C2×Dic59—41no—
345C2×Dic59—41no—
346D236—24no—
347D236—42no—
348C4×D59—44no—
349C4×D59—44no—
350Dic118—24no—
351Dic118—42no—
352C59⋊C8—28no—
353C2×#3018—591nomaximal, Sylow
354C22×C59—22no—
355C22×C59—24no—
356C22×C59—24no—
357C22×C59—28no—
358C22×C59—42no—
359C22×C59—42no—
360C22×C59—44no—
361C22×C59—44no—
362C22×C59—48no—
363C22×C59—82no—
364C22×C59—88no—
365C22×C59—816no—
366C22×C59C2×#12011yescharacteristic
367C22×C59C2×#12014yes—
368C22×C59C2×#12011yescharacteristic
369C22×C59C23×D411yescharacteristic
370C2×D59—44no—
371C2×D59—42no—
372C2×D59—82no—
373C2×D59—82no—
374C4×C59—28no—
375C4×C59—24no—
376C4×C59C2×#12012yes—
377C4×C59C2×#12012yes—
378C4×C59C2×#12012yes—
379C4×C59C23×D412yes—
380Dic59—24no—
381Dic59—42no—
382Dic59—42no—
383C2×#585D5911yescharacteristic, complemented
384C2×#575—592no—
385C2×#532—591no—
386#3018—5916no—
387C2×#456—592no—
388C2×#454—592no—
389C2×#455—592no—
390C2×#453—592no—
391C22×#104—592no—
392C2×#413—591no—
393C2×C59—21no—
394C2×C59—21no—
395C2×C59—24no—
396C2×C59—44no—
397C2×C59—48no—
398C2×C59#301812yescomplemented
399C2×C59C22×#12011yescharacteristic
400D59—82no—
401#585—24no—
402#585—28no—
403#585C2×D5918yescomplemented
404C2×2−1+4—22no—
405C2×2−1+4C2×D5912yes—
406C2×H(5,𝔽2)—22no—
407C2×H(5,𝔽2)—22no—
408C2×H(5,𝔽2)C2×D5912yes—
409C22×#41—24no—
410C22×#41—22no—
411C22×#41—591no—
412C22×#41C2×D5912yes—
413C22×#41C2×D5911yescharacteristic
414#575—5916no—
415#575—1188no—
416C2×#137—594no—
417C2×#137—1182no—
418C2×AGL(1,ℤ/8)—594no—
419C2×AGL(1,ℤ/8)—1182no—
420C2×#135—1184no—
421C22×M16—592no—
422#532—598no—
423#532—1184no—
424C2×C4⋊Q8—591no—
425C2×#127—591no—
426C2×#124—591no—
427C2×#124—591no—
428C2×#121—1182no—
429C2×C4×D4—1182no—
430C22×C42—591no—
431#456—5916no—
432#455—5916no—
433#454—5916no—
434#453—5916no—
435C2×#104—594no—
436C2×#104—594no—
437C2×#104—5916no—
438#413—598no—
439C2×#101—592no—
440C2×#100—592no—
441C59C2×#301811yescharacteristic, complemented, Sylow
4422−1+4—216no—
4432−1+4—28no—
4442−1+4—24no—
4452−1+4—216no—
4462−1+4C22×D5918yes—
447H(5,𝔽2)—216no—
448H(5,𝔽2)—216no—
449H(5,𝔽2)—28no—
450H(5,𝔽2)—216no—
451H(5,𝔽2)—24no—
452H(5,𝔽2)—216no—
453H(5,𝔽2)C22×D5918yes—
454C2×#41—24no—
455C2×#41—28no—
456C2×#41—24no—
457C2×#41—232no—
458C2×#41—216no—
459C2×#41—232no—
460C2×#41—24no—
461C2×#41—24no—
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—24no—
465C2×#41—216no—
466C2×#41—22no—
467C2×#41—22no—
468C2×#41—24no—
469C2×#41—24no—
470C2×#41—24no—
471C2×#41—594no—
472C2×#41—1182no—
473C2×#41—1182no—
474C2×#41—1182no—
475C2×#41—1184no—
476C2×#41C22⋊D5914yes—
477C2×#41C22⋊D5914yescomplemented
478C2×#41C22⋊D5918yescomplemented
479C2×#41C22×D5914yes—
480C2×#41C22×D5918yes—
481C2×#41C22×D5914yes—
482C22×Q8—22no—
483C22×Q8—24no—
484C22×Q8—591no—
485C22×Q8C22⋊D5912yescomplemented
486C22×Q8C22×D5911yescharacteristic
487C22×D4—28no—
488C22×D4—22no—
489C22×D4—24no—
490C22×D4—22no—
491C22×D4—24no—
492C22×D4—591no—
493C22×D4—1182no—
494C22×D4—1181no—
495C22×D4C22⋊D5912yes—
496C22×D4C22⋊D5912yescomplemented
497C22×D4C22×D5911yescharacteristic
498C23×C4—24no—
499C23×C4—22no—
500C23×C4—1181no—
501C23×C4—1181no—
502C23×C4C22⋊D5912yes—
503C23×C4C22×D5911yescharacteristic
504#137—5916no—
505#137—1188no—
506#137—11816no—
507AGL(1,ℤ/8)—5916no—
508AGL(1,ℤ/8)—1188no—
509AGL(1,ℤ/8)—11816no—
510#135—11832no—
511C2×Q16—1184no—
512C2×SD16—1184no—
513C2×SD16—1184no—
514C2×D8—1184no—
515C2×M16—594no—
516C2×M16—598no—
517C2×M16—1182no—
518C2×M16—1184no—
519C22×C8—1182no—
520C4⋊Q8—594no—
521C4⋊Q8—1182no—
522#127—594no—
523#127—1182no—
524#124—594no—
525#124—594no—
526#124—1182no—
527#124—1182no—
528#121—11816no—
529C4×D4—11816no—
530C2×C4⋊C4—1182no—
531C2×C22⋊C4—1182no—
532C2×C22⋊C4—1182no—
533C2×C42—591no—
534C2×C42—591no—
535C2×C42—594no—
536C2×C42—1181no—
537C2×C42—1182no—
538#104—5916no—
539#104—5916no—
540#101—598no—
541#100—598no—
542C24—24no—
543C24—22no—
544C24—1181no—
545C24C2×C22⋊D5912yes—
546C24C2×C22⋊D5911yescharacteristic
547#41—232no—
548#41—264no—
549#41—216no—
550#41—216no—
551#41—216no—
552#41—232no—
553#41—216no—
554#41—216no—
555#41—28no—
556#41—28no—
557#41—28no—
558#41—28no—
559#41—28no—
560#41—28no—
561#41—28no—
562#41—216no—
563#41—24no—
564#41—28no—
565#41—24no—
566#41—28no—
567#41—1188no—
568#41—1188no—
569#41—2364no—
570#41—2364no—
571#41C2×C22⋊D5918yes—
572#41C2×C22⋊D59116yescomplemented
573#41C23×D5918yes—
574C2×Q8—24no—
575C2×Q8—216no—
576C2×Q8—216no—
577C2×Q8—216no—
578C2×Q8—22no—
579C2×Q8—24no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—592no—
583C2×Q8—1181no—
584C2×Q8—1182no—
585C2×Q8—1182no—
586C2×Q8C2×C22⋊D5914yes—
587C2×Q8C2×C22⋊D5912yes—
588C2×Q8C2×C22⋊D5918yescomplemented
589C2×Q8C23×D5912yes—
590C2×D4—28no—
591C2×D4—24no—
592C2×D4—216no—
593C2×D4—264no—
594C2×D4—216no—
595C2×D4—216no—
596C2×D4—24no—
597C2×D4—24no—
598C2×D4—28no—
599C2×D4—24no—
600C2×D4—24no—
601C2×D4—216no—
602C2×D4—28no—
603C2×D4—216no—
604C2×D4—22no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—592no—
609C2×D4—1188no—
610C2×D4—1184no—
611C2×D4—1182no—
612C2×D4—1182no—
613C2×D4—1181no—
614C2×D4—2368no—
615C2×D4—2362no—
616C2×D4—2362no—
617C2×D4C2×C22⋊D5918yes—
618C2×D4C2×C22⋊D5912yes—
619C2×D4C2×C22⋊D5914yes—
620C2×D4C2×C22⋊D5918yescomplemented
621C2×D4C23×D5912yes—
622C22×C4—24no—
623C22×C4—28no—
624C22×C4—232no—
625C22×C4—22no—
626C22×C4—28no—
627C22×C4—22no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—22no—
631C22×C4—24no—
632C22×C4—28no—
633C22×C4—1181no—
634C22×C4—1181no—
635C22×C4—1184no—
636C22×C4—1181no—
637C22×C4—1184no—
638C22×C4—2364no—
639C22×C4—2361no—
640C22×C4—2362no—
641C22×C4—2361no—
642C22×C4C2×C22⋊D5912yes—
643C22×C4C2×C22⋊D5918yes—
644C22×C4C2×C22⋊D5912yes—
645C22×C4C2×C22⋊D5911yescharacteristic
646C22×C4C2×C22⋊D5912yes—
647C22×C4C2×C22⋊D5914yes—
648C22×C4C2×C22⋊D5912yes—
649C22×C4C23×D5911yescharacteristic
650C22×C4C23×D5912yes—
651Q16—11816no—
652SD16—11816no—
653SD16—11816no—
654D8—11816no—
655M16—598no—
656M16—1184no—
657M16—1188no—
658C2×C8—1184no—
659C2×C8—1188no—
660C4⋊C4—1188no—
661C22⋊C4—1188no—
662C22⋊C4—1188no—
663C42—592no—
664C42—592no—
665C42—1184no—
666C42—1181no—
667C42—1181no—
668C23—216no—
669C23—22no—
670C23—24no—
671C23—22no—
672C23—28no—
673C23—42no—
674C23—44no—
675C23—84no—
676C23—88no—
677C23—1182no—
678C23—2364no—
679C23—2361no—
680C23—2361no—
681C23#1427369612yes—
682C23#1427369612yes—
683C23C22×C22⋊D5911yescharacteristic
684C23C22×C22⋊D5914yes—
685C23C22×C22⋊D5912yes—
686Q8—216no—
687Q8—24no—
688Q8—24no—
689Q8—28no—
690Q8—24no—
691Q8—1184no—
692Q8—2362no—
693Q8C22×C22⋊D5918yes—
694D4—232no—
695D4—216no—
696D4—28no—
697D4—216no—
698D4—216no—
699D4—28no—
700D4—24no—
701D4—24no—
702D4—28no—
703D4—24no—
704D4—1184no—
705D4—23616no—
706D4—2368no—
707D4—2362no—
708D4C22×C22⋊D5918yes—
709C2×C4—216no—
710C2×C4—232no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—28no—
714C2×C4—22no—
715C2×C4—216no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—1184no—
721C2×C4—1182no—
722C2×C4—1182no—
723C2×C4—1182no—
724C2×C4—2368no—
725C2×C4—2362no—
726C2×C4—2361no—
727C2×C4—2361no—
728C2×C4—2364no—
729C2×C4—2364no—
730C2×C4#1427369611yescharacteristic
731C2×C4#1427369612yes—
732C2×C4#1427369614yes—
733C2×C4#1427369614yes—
734C2×C4#1427369611yescharacteristic
735C2×C4C22×C22⋊D5914yes—
736C2×C4C22×C22⋊D5912yes—
737C2×C4C22×C22⋊D5911yescharacteristic
738C2×C4C22×C22⋊D5912yes—
739C2×C4C22×C22⋊D5914yes—
740C2×C4C22×C22⋊D5912yes—
741C2×C4C22×C22⋊D5914yes—
742C2×C4C24×D5911yescharacteristic
743C8—1188no—
744C22—22no—
745C22—24no—
746C22—24no—
747C22—28no—
748C22—42no—
749C22—42no—
750C22—44no—
751C22—44no—
752C22—48no—
753C22—82no—
754C22—88no—
755C22—816no—
756C22—4722no—
757C22—4722no—
758C22—2364no—
759C22—2362no—
760C22C2×#1427369611yescharacteristic
761C22C2×#1427369614yes—
762C22C2×#1427369611yescharacteristic
763C22C23×C22⋊D5911yescharacteristic
764C4—28no—
765C4—24no—
766C4—1184no—
767C4—2362no—
768C4—2362no—
769C4C2×#1427369612yes—
770C4C2×#1427369612yes—
771C4C2×#1427369612yes—
772C4C23×C22⋊D5912yes—
773C2—21no—
774C2—21no—
775C2—24no—
776C2—44no—
777C2—48no—
778C2—4722no—
779C2#2143344512yesdirect product factor
780C2C22×#1427369611yescharacteristic
subgroupG/H
centerC2×C4#14273696
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#585C2
socleC22×C59C2×#120
hypercenterC2×#585D59
hypocenterC59C2×#3018
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#585

Complements

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

NH ≅ G/Ntype
1. C2×#16838200C2semidirect
2. C2×#16837948C2semidirect
3. #21433445C2direct (N × H)
4. C2×#16837585C2semidirect
5. C2×#16837575C2semidirect
6. C2×#16837580C2semidirect
7. C2×#16837570C2semidirect
8. C22×#14273654C2semidirect
9. C2×#16837386C2semidirect
10. C2×C59×#585C2semidirect
11. C22×#11745685C22semidirect
13. #16838200C22semidirect
15. C2×#14273757C22semidirect
17. C2×#14273752C22semidirect
19. C22×#11745664C22semidirect
21. #16837948C22semidirect
22. C2×#14273725C22semidirect
23. C2×#14273723C22semidirect
24. C2×#14273716C22semidirect
25. C2×#14273714C22semidirect
28. C22×C4×Dic59C22semidirect
29. #16837585C22semidirect
30. #16837580C22semidirect
31. #16837575C22semidirect
32. #16837570C22semidirect
33. C2×#14273654C22semidirect
34. C2×#14273654C22semidirect
35. C2×#14273654C22semidirect
36. #16837386C22semidirect
37. C2×#14273646C22semidirect
38. C2×#14273644C22semidirect
41. C59×#585C22semidirect
55. C2×#11745685C23semidirect
64. #14273757C23semidirect
67. #14273752C23semidirect
76. C2×#11745664C23semidirect
79. #14273725C23semidirect
81. #14273723C23semidirect
83. #14273716C23semidirect
85. #14273714C23semidirect
95. C2×C4×Dic59C23semidirect
96. #14273654C23semidirect
97. #14273654C23semidirect
98. #14273646C23semidirect
99. #14273644C23semidirect
130. C2×#41×C59D4semidirect
131. C2×#41×C59D4semidirect
137. C22×Q8×C59D4semidirect
145. C22×D4×C59D4semidirect
177. #41×C59C2×D4semidirect
189. C2×Q8×C59C2×D4semidirect
212. C2×D4×C59C2×D4semidirect
383. C2×#585D59semidirect
398. C2×C59#3018semidirect
403. #585C2×D59semidirect
441. C59C2×#3018semidirect
477. C2×#41C22⋊D59semidirect
478. C2×#41C22⋊D59semidirect
485. C22×Q8C22⋊D59semidirect
496. C22×D4C22⋊D59semidirect
572. #41C2×C22⋊D59semidirect
588. C2×Q8C2×C22⋊D59semidirect
620. C2×D4C2×C22⋊D59semidirect
779. C2#21433445direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168382002
C2×#168379482
#214334452
C2×#168375852
C2×#168375752
C2×#168375802
C2×#168375702
C22×#142736542
C2×#168373862
C2×C59×#5852
C2×#301859