Finite Group Databasebeta

← C2×#21434720 #29458495

Subgroups — C2×#21434720 #29458495

Order 15104.

1970 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838010C211yesmaximal, characteristic, complemented
2C2×#16838003C211yesmaximal, characteristic
3#21434720C2116yesmaximal, direct product factor
4C2×#16837802C211yesmaximal, characteristic, complemented
5C2×#16837773C211yesmaximal, characteristic, complemented
6C2×#16837769C211yesmaximal, characteristic, complemented
7C2×#16837765C211yesmaximal, characteristic, complemented
8C2×#16837651C211yesmaximal, characteristic, complemented
9C2×#16837647C211yesmaximal, characteristic, complemented
10C2×#16837632C211yesmaximal, characteristic, complemented
11C2×#16837628C211yesmaximal, characteristic, complemented
12C2×#16837502C211yesmaximal, characteristic, complemented
13C2×#16837500C211yesmaximal, characteristic, complemented
14C2×C4×#11745660C211yesmaximal, characteristic, complemented
15C2×#16837356C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C59C211yesmaximal, characteristic, complemented
17C22×#11745660C2211yescharacteristic
18C22×#11745670C2211yescharacteristic
19C22×#11745671C2211yescharacteristic
20C22×#11745659C2211yescharacteristic
21C22×C8×D59C2211yescharacteristic
22#16838010—24no—
23#16838010C2218yescomplemented
24#16838003—24no—
25#16838003C2218yes—
26C2×#14273725C2211yescharacteristic
27C2×#14273723C2211yescharacteristic
28C2×#14273722—21no—
29C2×#14273721—21no—
30C2×#14273719—21no—
31C2×#14273718C2211yescharacteristic
32C2×#14273718C2211yescharacteristic
33C2×#14273717—21no—
34C2×#14273710—21no—
35C2×#14273709—21no—
36C2×#14273707C2211yescharacteristic
37C2×#14273703C2211yescharacteristic
38C2×#14273702C2211yescharacteristic
39C2×#14273701—21no—
40C2×#14273700—21no—
41C2×#14273698C2211yescharacteristic
42C2×C4×Dic118C2211yescharacteristic
43C2×C4×D236C2211yescharacteristic
44C2×#14273684C2211yescharacteristic
45#16837802C2218yescomplemented
46#16837773C2218yescomplemented
47#16837769C2218yescomplemented
48#16837765C2218yescomplemented
49#16837651C2218yescomplemented
50#16837647C2218yescomplemented
51#16837632C2218yescomplemented
52#16837628C2218yescomplemented
53#16837502C2218yescomplemented
54#16837500C2218yescomplemented
55C4×#11745660C2218yescomplemented
56C2×#14273660C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58C2×#14273659C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273651C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273649C2211yescharacteristic
63C2×#14273648C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65#16837356C2218yescomplemented
66C2×#14273638C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C4×SD16×C59C2218yescomplemented
73C2×#106×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic
77C22×Dic118C2311yescharacteristic
78C22×D236—21no—
79C22×D236C2311yescharacteristic
80C22×C22⋊D59—21no—
81C22×C22⋊D59—21no—
82C22×C22⋊D59—21no—
83C22×C4×D59—21no—
84C22×C4×D59C2311yescharacteristic
85C2×#11745660—24no—
86C2×#11745660C2314yes—
87C2×#11745670—24no—
88C2×#11745670C2314yes—
89C2×#11745671—24no—
90C2×#11745671C2314yes—
91C2×#11745659—24no—
92C2×#11745659C2314yes—
93C22×C59⋊C8C2311yescharacteristic
94C22×C59⋊C8C2311yescharacteristic
95C2×C8×D59—24no—
96C2×C8×D59C2314yes—
97#14273725—22no—
98#14273725C2314yes—
99#14273723—22no—
100#14273723C2314yes—
101#14273722—28no—
102#14273721—28no—
103#14273719—28no—
104#14273718—22no—
105#14273718—22no—
106#14273718C2314yes—
107#14273718C2314yes—
108#14273717—28no—
109#14273710—28no—
110#14273709—28no—
111#14273707—22no—
112#14273707C2314yes—
113#14273703—22no—
114#14273703C2314yes—
115#14273702—22no—
116#14273702C2314yes—
117#14273701—28no—
118#14273700—28no—
119#14273698—22no—
120#14273698C2314yes—
121C4×Dic118—22no—
122C4×Dic118C2314yes—
123C4×D236—22no—
124C4×D236C2314yes—
125#14273684D414yes—
126#14273684C2314yes—
127C2×C4⋊Dic59—21no—
128C2×C4⋊Dic59—21no—
129C2×C4⋊Dic59—21no—
130C2×C4⋊Dic59C2311yescharacteristic
131C2×C4⋊Dic59C2311yescharacteristic
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4D411yescharacteristic
139C2×Dic59⋊C4D411yescharacteristic
140C2×C22⋊Dic59—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4—21no—
144C2×(C2×D59)⋊C4—21no—
145C2×(C2×D59)⋊C4D411yescharacteristic
146C2×(C2×D59)⋊C4D411yescharacteristic
147C2×C4×Dic59—21no—
148C2×C4×Dic59C2311yescharacteristic
149#14273660C2314yes—
150#14273660C2314yes—
151#14273659C2314yes—
152#14273652C2314yes—
153#14273651C2314yes—
154#14273650C2314yes—
155#14273649C2314yes—
156#14273648C2314yes—
157#14273647C2314yes—
158#14273638C2314yes—
159#14273637C2314yes—
160C8×Dic59C2314yes—
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#106×C59C2314yes—
179#103×C59C2314yes—
180#102×C59C2314yes—
181C4×C8×C59C2314yes—
182C24×C59—21no—
183C23×D59—21no—
184C23×D59C2×D411yescharacteristic
185C2×Q8×C59—21no—
186C2×Q8×C59—22no—
187C2×Q8×C59—22no—
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
213C2×D236—22no—
214C2×D236—22no—
215C2×D236—21no—
216C2×D236—24no—
217C2×D236—82no—
218C2×D236C2412yes—
219C2×C4×D59—22no—
220C2×C4×D59—22no—
221C2×C4×D59—24no—
222C2×C4×D59—82no—
223C2×C4×D59C2×D412yes—
224C2×C4×D59C2412yes—
225C2×Dic118—22no—
226C2×Dic118—22no—
227C2×Dic118—21no—
228C2×Dic118C2412yes—
229SD16×C59—28no—
230C2×C8×C59—22no—
231C2×C8×C59#4114yes—
232C2×C8×C59C2412yes—
233C2×C8×C59C2412yes—
234C4⋊C4×C59—24no—
235C4⋊C4×C59—21no—
236C4⋊C4×C59—21no—
237C4⋊C4×C59C2412yes—
238C4⋊C4×C59C2412yes—
239C22⋊C4×C59—24no—
240C42×C59—24no—
241C42×C59C2×D412yes—
242C42×C59C2412yes—
243C22⋊Dic59—24no—
244#11745671—28no—
245#11745670—28no—
246(C2×D59)⋊C4—24no—
247(C2×D59)⋊C4—24no—
248(C2×D59)⋊C4—24no—
249(C2×D59)⋊C4—24no—
250(C2×D59)⋊C4C2×D414yes—
251(C2×D59)⋊C4C2×D414yes—
252C4⋊Dic59—21no—
253C4⋊Dic59—21no—
254C4⋊Dic59—24no—
255C4⋊Dic59—24no—
256C4⋊Dic59—24no—
257C4⋊Dic59C2412yes—
258C4⋊Dic59C2412yes—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265Dic59⋊C4C2×D414yes—
266Dic59⋊C4C2×D414yes—
267C4×Dic59—24no—
268C4×Dic59C2×D412yes—
269C4×Dic59C2412yes—
270C2×C59⋊C8—22no—
271C2×C59⋊C8#4114yes—
272C2×C59⋊C8C2412yes—
273C2×C59⋊C8C2412yes—
274#11745660—28no—
275#11745659—28no—
276C8×D59—28no—
277C23×C59—22no—
278C23×C59—42no—
279C23×C59—42no—
280C23×C59—42no—
281C23×C59C22×D411yescharacteristic
282C22×D59—22no—
283C22×D59—22no—
284C22×D59—22no—
285C22×D59—22no—
286C22×D59—42no—
287C22×D59—42no—
288C22×D59—42no—
289C22×D59C22×D412yes—
290Q8×C59—22no—
291Q8×C59—22no—
292Q8×C59—42no—
293D4×C59—22no—
294D4×C59—22no—
295D4×C59—42no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—42no—
302C2×C4×C59—42no—
303C2×C4×C59—42no—
304C2×C4×C59—84no—
305C2×C4×C59C22×D412yes—
306C2×C4×C59C22×D412yes—
307C2×C4×C59C22×D411yescharacteristic
308C2×C4×C59C2×#4112yes—
309C2×C4×C59C2×#4112yes—
310C2×C4×C59C2511yescharacteristic
311C22⋊D59—84no—
312C22⋊D59—84no—
313C22⋊D59—84no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—42no—
321C2×Dic59—42no—
322C2×Dic59—42no—
323C2×Dic59C22×D412yes—
324C2×Dic59C22×D412yes—
325C2×Dic59C22×D412yes—
326D236—22no—
327D236—22no—
328D236—42no—
329D236—84no—
330C4×D59—24no—
331C4×D59—22no—
332C4×D59—22no—
333C4×D59—84no—
334Dic118—22no—
335Dic118—22no—
336Dic118—42no—
337C8×C59—22no—
338C8×C59C2×#4114yes—
339C59⋊C8—22no—
340C59⋊C8C2×#4114yes—
341C2×#3174—591nomaximal, Sylow
342C22×C59—42no—
343C22×C59—42no—
344C22×C59—42no—
345C22×C59—84no—
346C22×C59#53212yes—
347C22×C59#57712yes—
348C22×C59#57712yes—
349C22×C59C23×D411yescharacteristic
350C2×D59—22no—
351C2×D59—22no—
352C2×D59—22no—
353C2×D59—44no—
354C2×D59—42no—
355C2×D59—42no—
356C2×D59—42no—
357C2×D59—84no—
358C4×C59—22no—
359C4×C59—22no—
360C4×C59—42no—
361C4×C59—42no—
362C4×C59—42no—
363C4×C59#53212yes—
364C4×C59C22×#4111yescharacteristic
365C4×C59C22×#4111yescharacteristic
366Dic59—22no—
367Dic59—22no—
368Dic59—22no—
369Dic59—42no—
370Dic59—42no—
371Dic59—42no—
372C2×#541—591no—
373C2×#540—591no—
374#3174—5916no—
375C2×#499—591no—
376C2×#492—591no—
377C2×#491—591no—
378C2×#490—591no—
379C2×#468—591no—
380C2×#468—591no—
381C2×#465—591no—
382C2×#465—591no—
383C2×#440—591no—
384C2×#440—591no—
385C2×C4×SD16—591no—
386C2×C4×SD16D5911yescharacteristic, complemented
387C2×#405—591no—
388C2×C59—82no—
389C2×C59#317414yescomplemented
390C2×C59C2×#53211yescharacteristic
391C2×C59C2×#57711yescharacteristic
392C2×C59C2×#57711yescharacteristic
393D59—42no—
394D59—82no—
395C22×SD16—591no—
396C22×SD16—591no—
397C22×SD16—591no—
398C22×SD16C2×D5911yescharacteristic
399C22×M16—591no—
400C23×C8—591no—
401#541—598no—
402#541—1184no—
403#540—598no—
404#540—1184no—
405C2×C4⋊Q8—591no—
406C2×#127—591no—
407C2×#126—1181no—
408C2×#126—1181no—
409C2×#125—591no—
410C2×#125—591no—
411C2×#125—1181no—
412C2×#125—1181no—
413C2×#123—1181no—
414C2×#123—1181no—
415C2×C22⋊Q8—591no—
416C2×C22⋊Q8—591no—
417C2×#121—591no—
418C2×#121—591no—
419C2×#121—1181no—
420C2×#121—1181no—
421C2×C4×Q8—591no—
422C2×C4×Q8C2×D5911yescharacteristic
423C2×C4×D4—591no—
424C2×C4×D4C2×D5911yescharacteristic
425C2×#117—591no—
426#499—598no—
427#492—598no—
428#491—598no—
429#490—598no—
430#468—598no—
431#468—598no—
432#465—598no—
433#465—598no—
434#440—598no—
435#440—598no—
436C4×SD16—598no—
437C4×SD16C2×D5918yescomplemented
438C2×#107—591no—
439C2×#107—591no—
440C2×#106—591no—
441C2×#106C2×D5911yescharacteristic
442C2×#103—591no—
443C2×#103—591no—
444C2×#103—591no—
445C2×#103C2×D5911yescharacteristic
446C2×#102—591no—
447C2×#102—591no—
448C2×#102—591no—
449C2×#102C2×D5911yescharacteristic
450#405—598no—
451C2×#97—591no—
452C2×#97—591no—
453C2×C4×C8—591no—
454C2×C4×C8C2×D5911yescharacteristic
455C59C2×#317411yescharacteristic, complemented, Sylow
456C22×Q8—591no—
457C22×Q8C22×D5911yescharacteristic
458C22×D4—591no—
459C22×D4—1181no—
460C22×D4—1181no—
461C22×D4—1181no—
462C22×D4—1181no—
463C22×D4C22×D5911yescharacteristic
464C23×C4—21no—
465C23×C4—591no—
466C23×C4—1181no—
467C2×SD16—24no—
468C2×SD16—594no—
469C2×SD16—594no—
470C2×SD16—594no—
471C2×SD16—1184no—
472C2×SD16—1184no—
473C2×SD16—1184no—
474C2×SD16C22×D5914yes—
475C2×M16—594no—
476C2×M16—1184no—
477C22×C8—591no—
478C22×C8—591no—
479C22×C8—594no—
480C22×C8—1184no—
481C22×C8C22×D5911yescharacteristic
482C22×C8C22×D5911yescharacteristic
483C4⋊Q8—594no—
484C4⋊Q8—1182no—
485#127—594no—
486#127—1182no—
487#126—1188no—
488#126—1188no—
489#125—594no—
490#125—594no—
491#125—1188no—
492#125—1182no—
493#125—1182no—
494#125—1188no—
495#123—1188no—
496#123—1188no—
497C22⋊Q8—594no—
498C22⋊Q8—594no—
499C22⋊Q8—1182no—
500C22⋊Q8—1182no—
501#121—594no—
502#121—594no—
503#121—1188no—
504#121—1188no—
505#121—1182no—
506#121—1182no—
507C4×Q8—22no—
508C4×Q8—594no—
509C4×Q8—1182no—
510C4×Q8C22×D5914yes—
511C4×D4—22no—
512C4×D4—594no—
513C4×D4—1182no—
514C4×D4C22×D5914yes—
515#117—594no—
516#117—594no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—591no—
519C2×C4⋊C4—591no—
520C2×C4⋊C4—591no—
521C2×C4⋊C4—591no—
522C2×C4⋊C4—1181no—
523C2×C4⋊C4—1181no—
524C2×C4⋊C4—1181no—
525C2×C4⋊C4—1181no—
526C2×C4⋊C4—1181no—
527C2×C4⋊C4—1181no—
528C2×C4⋊C4—1181no—
529C2×C4⋊C4—1181no—
530C2×C4⋊C4—1181no—
531C2×C4⋊C4C22×D5911yescharacteristic
532C2×C4⋊C4C22×D5911yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—591no—
535C2×C22⋊C4—591no—
536C2×C22⋊C4—1181no—
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×C42C22×D5911yescharacteristic
545#107—594no—
546#107—594no—
547#106—594no—
548#106C22×D5914yes—
549#103—594no—
550#103—594no—
551#103—594no—
552#103C22×D5914yes—
553#102—594no—
554#102—594no—
555#102—594no—
556#102C22×D5914yes—
557#97—594no—
558#97—594no—
559C4×C8—594no—
560C4×C8C22×D5914yes—
561C24—21no—
562C24—591no—
563C24—1181no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—592no—
568C2×Q8—1181no—
569C2×Q8—1182no—
570C2×Q8—1182no—
571C2×Q8C23×D5912yes—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—592no—
576C2×D4—1184no—
577C2×D4—1184no—
578C2×D4—1184no—
579C2×D4—1184no—
580C2×D4—1181no—
581C2×D4—1182no—
582C2×D4—1182no—
583C2×D4—4722no—
584C2×D4—4722no—
585C2×D4—4722no—
586C2×D4—4722no—
587C2×D4C23×D5912yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—82no—
593C22×C4—591no—
594C22×C4—591no—
595C22×C4—591no—
596C22×C4—592no—
597C22×C4—592no—
598C22×C4—1182no—
599C22×C4—1182no—
600C22×C4—1181no—
601C22×C4—1181no—
602C22×C4—1181no—
603C22×C4—1184no—
604C22×C4—4722no—
605C22×C4D4×D5911yescharacteristic
606C22×C4D4×D5911yescharacteristic
607C22×C4C23×D5911yescharacteristic
608SD16—28no—
609SD16—1188no—
610SD16—1188no—
611SD16—1188no—
612M16—1188no—
613C2×C8—22no—
614C2×C8—594no—
615C2×C8—592no—
616C2×C8—592no—
617C2×C8—1182no—
618C2×C8—1188no—
619C2×C8#1174568514yes—
620C2×C8C23×D5912yes—
621C2×C8C23×D5912yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—594no—
626C4⋊C4—594no—
627C4⋊C4—592no—
628C4⋊C4—592no—
629C4⋊C4—1184no—
630C4⋊C4—1184no—
631C4⋊C4—1184no—
632C4⋊C4—1184no—
633C4⋊C4—1184no—
634C4⋊C4—1184no—
635C4⋊C4—1184no—
636C4⋊C4—1184no—
637C4⋊C4—1181no—
638C4⋊C4—1181no—
639C4⋊C4—1184no—
640C4⋊C4C23×D5912yes—
641C4⋊C4C23×D5912yes—
642C22⋊C4—24no—
643C22⋊C4—594no—
644C22⋊C4—594no—
645C22⋊C4—1184no—
646C22⋊C4—1184no—
647C22⋊C4—1184no—
648C22⋊C4—1184no—
649C22⋊C4—1184no—
650C42—24no—
651C42—592no—
652C42—592no—
653C42—1184no—
654C42D4×D5912yes—
655C42C23×D5912yes—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—592no—
661C23—1182no—
662C23—1182no—
663C23—1182no—
664C23—1182no—
665C23—2362no—
666C23—2362no—
667C23—2362no—
668C23C2×D4×D5911yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—1182no—
673Q8—1182no—
674Q8—2362no—
675D4—22no—
676D4—22no—
677D4—42no—
678D4—1182no—
679D4—1182no—
680D4—4724no—
681D4—4724no—
682D4—4724no—
683D4—4724no—
684D4—2362no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—84no—
694C2×C4—592no—
695C2×C4—592no—
696C2×C4—592no—
697C2×C4—1182no—
698C2×C4—1182no—
699C2×C4—1182no—
700C2×C4—1184no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—1182no—
704C2×C4—1182no—
705C2×C4—1182no—
706C2×C4—4724no—
707C2×C4—2362no—
708C2×C4—2362no—
709C2×C4—2362no—
710C2×C4C2×D4×D5912yes—
711C2×C4C2×D4×D5912yes—
712C2×C4C2×D4×D5911yescharacteristic
713C2×C4#41×D5912yes—
714C2×C4C2×#1174568512yes—
715C2×C4C24×D5911yescharacteristic
716C8—22no—
717C8—594no—
718C8—1182no—
719C8C2×#1174568514yes—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—84no—
724C22—1182no—
725C22—1182no—
726C22—1182no—
727C22—4724no—
728C22—2362no—
729C22—2362no—
730C22—2362no—
731C22—2364no—
732C22#1683794912yes—
733C22#1683820812yes—
734C22#1683820912yes—
735C22C22×D4×D5911yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—1182no—
742C4—1182no—
743C4—1182no—
744C4—2362no—
745C4—2362no—
746C4—2362no—
747C4#1683794912yes—
748C4C2×#41×D5911yescharacteristic
749C4C22×#1174568511yescharacteristic
750C2—82no—
751C2—4722no—
752C2—2362no—
753C2#2143472014yesdirect product factor
754C2C2×#1683794911yescharacteristic
755C2C2×#1683820811yescharacteristic
756C2C2×#1683820911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C4×SD16×C59C2
socleC23×C59C22×D4
prime radicalC2×#16838003C2
hypercenterC2×C4×SD16D59
hypocenterC59C2×#3174
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#16838010C2semidirect
3. #21434720C2direct (N × H)
4. C2×#16837802C2semidirect
5. C2×#16837773C2semidirect
6. C2×#16837769C2semidirect
7. C2×#16837765C2semidirect
8. C2×#16837651C2semidirect
9. C2×#16837647C2semidirect
10. C2×#16837632C2semidirect
11. C2×#16837628C2semidirect
12. C2×#16837502C2semidirect
13. C2×#16837500C2semidirect
14. C2×C4×#11745660C2semidirect
15. C2×#16837356C2semidirect
16. C2×C4×SD16×C59C2semidirect
23. #16838010C22semidirect
45. #16837802C22semidirect
46. #16837773C22semidirect
47. #16837769C22semidirect
48. #16837765C22semidirect
49. #16837651C22semidirect
50. #16837647C22semidirect
51. #16837632C22semidirect
52. #16837628C22semidirect
53. #16837502C22semidirect
54. #16837500C22semidirect
55. C4×#11745660C22semidirect
65. #16837356C22semidirect
72. C4×SD16×C59C22semidirect
386. C2×C4×SD16D59semidirect
389. C2×C59#3174semidirect
437. C4×SD16C2×D59semidirect
455. C59C2×#3174semidirect
753. C2#21434720direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380102
C2×#168380032
#214347202
C2×#168378022
C2×#168377732
C2×#168377692
C2×#168377652
C2×#168376512
C2×#168376472
C2×#168376322
C2×#168376282
C2×#168375022
C2×#168375002
C2×C4×#117456602
C2×#168373562
C2×C4×SD16×C592
C2×#317459