Finite Group Databasebeta

← C2×#21434383 #29457031

Subgroups — C2×#21434383 #29457031

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×#16838005C211yesmaximal, characteristic
2C2×#16837879C211yesmaximal, characteristic, complemented
3#21434383C2116yesmaximal, direct product factor
4C2×#16837726C211yesmaximal, characteristic, complemented
5C2×#16837712C211yesmaximal, characteristic, complemented
6C2×#16837708C211yesmaximal, characteristic, complemented
7C2×#16837601C211yesmaximal, characteristic, complemented
8C2×#16837601C211yesmaximal, characteristic, complemented
9C2×#16837543C211yesmaximal, characteristic, complemented
10C2×#16837540C211yesmaximal, characteristic, complemented
11C2×#16837501C211yesmaximal, characteristic, complemented
12C2×#16837499C211yesmaximal, characteristic, complemented
13C2×#16837493C211yesmaximal, characteristic, complemented
14C2×#16837489C211yesmaximal, characteristic, complemented
15C2×#16837460C211yesmaximal, characteristic, complemented
16C2×C59×#482C211yesmaximal, characteristic, complemented
17C23×Dic118C2211yescharacteristic
18C22×#11745660C2211yescharacteristic
19C22×#11745660C2211yescharacteristic
20C22×#11745670C2211yescharacteristic
21C22×#11745670C2211yescharacteristic
22#16838005—24no—
23#16838005C2218yes—
24C2×#14273723C2211yescharacteristic
25C2×#14273718C2211yescharacteristic
26C2×#14273711—21no—
27C2×#14273709—21no—
28C2×#14273701C2211yescharacteristic
29C2×#14273699—21no—
30C2×#14273698—21no—
31#16837879—24no—
32#16837879C2218yescomplemented
33C2×C4×Dic118—21no—
34C2×C4×Dic118—21no—
35C2×#14273692C2211yescharacteristic
36C2×#14273692C2211yescharacteristic
37C2×#14273692C2211yescharacteristic
38C2×#14273692C2211yescharacteristic
39C2×D4×Dic59C2211yescharacteristic
40C2×#14273689C2211yescharacteristic
41C2×#14273686C2211yescharacteristic
42C2×#14273683—21no—
43C2×#14273683—21no—
44#16837726C2218yescomplemented
45#16837712C2218yescomplemented
46#16837708C2218yescomplemented
47#16837601C2218yescomplemented
48#16837601C2218yescomplemented
49#16837543C2218yescomplemented
50#16837540C2218yescomplemented
51#16837501C2218yescomplemented
52#16837499C2218yescomplemented
53#16837493C2218yescomplemented
54#16837489C2218yescomplemented
55#16837460C2218yescomplemented
56C2×#14273660C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×#121×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C59×#482C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#106×C59C2211yescharacteristic
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—22no—
79C22×Dic118—24no—
80C22×Dic118—24no—
81C22×Dic118C2314yes—
82C22×Dic118C2311yescharacteristic
83C22×Dic118C2311yescharacteristic
84C22×D236C2311yescharacteristic
85C22×C22⋊D59—21no—
86C22×C22⋊D59—21no—
87C22×C22⋊D59—21no—
88C23×Dic59—21no—
89C23×Dic59—21no—
90C22×C4×D59—21no—
91C2×#11745660—24no—
92C2×#11745660—24no—
93C2×#11745660C2314yes—
94C2×#11745660C2314yes—
95C2×#11745670—24no—
96C2×#11745670—24no—
97C2×#11745670C2314yes—
98C2×#11745670C2314yes—
99C22×C59⋊C8C2311yescharacteristic
100C22×C59⋊C8C2311yescharacteristic
101#14273723—22no—
102#14273723C2314yes—
103#14273718—22no—
104#14273718C2314yes—
105#14273711—28no—
106#14273709—28no—
107#14273701—22no—
108#14273701C2314yes—
109#14273699—28no—
110#14273698—28no—
111C4×Dic118—28no—
112C4×Dic118—28no—
113#14273692—22no—
114#14273692—22no—
115#14273692—22no—
116#14273692—22no—
117#14273692C2314yes—
118#14273692C2314yes—
119#14273692C2314yes—
120#14273692C2314yes—
121D4×Dic59—22no—
122D4×Dic59C2314yes—
123#14273689—22no—
124#14273689C2314yes—
125#14273686D414yes—
126#14273686C2314yes—
127#14273683—28no—
128#14273683—28no—
129C2×C4⋊Dic59—21no—
130C2×C4⋊Dic59D411yescharacteristic
131C2×C4⋊Dic59D411yescharacteristic
132C2×C4⋊Dic59C2311yescharacteristic
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C2×C22⋊Dic59—21no—
139C2×C22⋊Dic59D411yescharacteristic
140C2×C22⋊Dic59D411yescharacteristic
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59—21no—
147C2×C4×Dic59C2311yescharacteristic
148C2×C4×Dic59C2311yescharacteristic
149#14273660C2314yes—
150#14273658C2314yes—
151Dic59⋊C8C2314yes—
152Dic59⋊C8C2314yes—
153#14273652C2314yes—
154#14273652C2314yes—
155#14273650C2314yes—
156#14273650C2314yes—
157#14273647C2314yes—
158#14273647C2314yes—
159C22⋊(C59⋊C8)C2314yes—
160#14273637C2314yes—
161C8×Dic59C2314yes—
162C22×D4×C59—21no—
163C22×D4×C59C2311yescharacteristic
164C23×C4×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167#121×C59—22no—
168#121×C59C2314yes—
169#117×C59—22no—
170#117×C59C2314yes—
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59—21no—
176C2×C42×C59—21no—
177#107×C59C2314yes—
178#106×C59C2314yes—
179#102×C59C2314yes—
180#102×C59C2314yes—
181C22⋊C8×C59C2314yes—
182C24×C59—21no—
183C24×C59C2×D411yescharacteristic
184C23×D59—21no—
185C2×D4×C59—24no—
186C2×D4×C59—21no—
187C2×D4×C59—22no—
188C2×D4×C59—22no—
189C2×D4×C59—82no—
190C2×D4×C59C2412yes—
191C22×C4×C59—22no—
192C22×C4×C59—22no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D412yes—
198C22×C4×C59C2412yes—
199C22×C4×C59C2411yescharacteristic
200C2×C22⋊D59—24no—
201C2×C22⋊D59—24no—
202C2×C22⋊D59—24no—
203C2×C22⋊D59—82no—
204C2×C22⋊D59—82no—
205C2×C22⋊D59—82no—
206C22×Dic59—28no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—24no—
210C22×Dic59—21no—
211C22×Dic59—24no—
212C22×Dic59—82no—
213C22×Dic59C2×D411yescharacteristic
214C22×Dic59C2×D411yescharacteristic
215C22×Dic59C2×D411yescharacteristic
216C22×Dic59C2×D411yescharacteristic
217C2×D236—22no—
218C2×D236—22no—
219C2×D236—21no—
220C2×D236C2412yes—
221C2×C4×D59—24no—
222C2×C4×D59—82no—
223C2×Dic118—28no—
224C2×Dic118—216no—
225C2×Dic118—21no—
226C2×Dic118—21no—
227C2×Dic118—24no—
228C2×Dic118—22no—
229C2×Dic118—22no—
230C2×Dic118—28no—
231C2×Dic118—28no—
232C2×Dic118#4114yes—
233C2×Dic118#4114yes—
234C2×Dic118C2412yes—
235C2×Dic118C2412yes—
236C2×C8×C59—22no—
237C2×C8×C59—22no—
238C2×C8×C59C2412yes—
239C2×C8×C59C2412yes—
240C4⋊C4×C59—21no—
241C4⋊C4×C59—21no—
242C4⋊C4×C59—21no—
243C4⋊C4×C59C2412yes—
244C4⋊C4×C59C2412yes—
245C4⋊C4×C59C2412yes—
246C22⋊C4×C59—24no—
247C22⋊C4×C59—24no—
248C42×C59—24no—
249C22⋊Dic59—24no—
250C22⋊Dic59C2×D414yes—
251C22⋊Dic59C2×D414yes—
252#11745670—28no—
253#11745670—28no—
254(C2×D59)⋊C4—24no—
255(C2×D59)⋊C4—24no—
256C4⋊Dic59—21no—
257C4⋊Dic59—24no—
258C4⋊Dic59C2×D414yes—
259C4⋊Dic59C2×D414yes—
260C4⋊Dic59C2412yes—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265Dic59⋊C4—24no—
266C4×Dic59—24no—
267C4×Dic59—24no—
268C4×Dic59—24no—
269C4×Dic59—24no—
270C4×Dic59C2×D412yes—
271C4×Dic59C2×D412yes—
272C4×Dic59C2412yes—
273C4×Dic59C2412yes—
274C2×C59⋊C8—22no—
275C2×C59⋊C8—22no—
276C2×C59⋊C8C2412yes—
277C2×C59⋊C8C2412yes—
278#11745660—28no—
279#11745660—28no—
280C23×C59—22no—
281C23×C59—22no—
282C23×C59—22no—
283C23×C59—22no—
284C23×C59—42no—
285C23×C59—42no—
286C23×C59—42no—
287C23×C59C22×D412yes—
288C23×C59C22×D411yescharacteristic
289C22×D59—22no—
290C22×D59—42no—
291C22×D59—42no—
292C22×D59—42no—
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—42no—
305C2×C4×C59—42no—
306C2×C4×C59—42no—
307C2×C4×C59C22×D412yes—
308C2×C4×C59C22×D411yescharacteristic
309C2×C4×C59C2×#4112yes—
310C2×C4×C59C2×#4112yes—
311C2×C4×C59C2511yescharacteristic
312C22⋊D59—84no—
313C22⋊D59—84no—
314C22⋊D59—84no—
315C2×Dic59—216no—
316C2×Dic59—24no—
317C2×Dic59—24no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—42no—
326C2×Dic59—84no—
327C2×Dic59C22×D412yes—
328C2×Dic59C22×D412yes—
329C2×Dic59C22×D412yes—
330C2×Dic59C22×D412yes—
331D236—22no—
332D236—22no—
333D236—42no—
334C4×D59—84no—
335Dic118—216no—
336Dic118—24no—
337Dic118—24no—
338Dic118—22no—
339Dic118—22no—
340Dic118C2×#4114yes—
341Dic118C2×#4114yes—
342C8×C59—22no—
343C8×C59—22no—
344C59⋊C8—22no—
345C59⋊C8—22no—
346C2×#3126—591nomaximal, Sylow
347C22×C59—22no—
348C22×C59—22no—
349C22×C59—22no—
350C22×C59—44no—
351C22×C59—42no—
352C22×C59—42no—
353C22×C59—42no—
354C22×C59—84no—
355C22×C59#52512yes—
356C22×C59#57712yes—
357C22×C59#57712yes—
358C22×C59C23×D411yescharacteristic
359C2×D59—42no—
360C2×D59—42no—
361C2×D59—42no—
362C2×D59—84no—
363C4×C59—22no—
364C4×C59—42no—
365C4×C59—42no—
366C4×C59—42no—
367C4×C59#52512yes—
368C4×C59C22×#4111yescharacteristic
369C4×C59C22×#4111yescharacteristic
370Dic59—24no—
371Dic59—24no—
372Dic59—22no—
373Dic59—22no—
374Dic59—22no—
375Dic59—22no—
376Dic59—42no—
377C2×#540—591no—
378C2×#519—591no—
379#3126—5916no—
380C2×#482—591no—
381C2×#482D5911yescharacteristic, complemented
382C2×#479—591no—
383C2×#479—591no—
384C2×#460—591no—
385C2×#460—591no—
386C2×#448—591no—
387C2×#448—591no—
388C2×#440—591no—
389C2×#440—591no—
390C2×C4×SD16—591no—
391C2×C4×SD16—591no—
392C2×#433—591no—
393C2×C59—42no—
394C2×C59—82no—
395C2×C59#312614yescomplemented
396C2×C59C2×#52511yescharacteristic
397C2×C59C2×#57711yescharacteristic
398C2×C59C2×#57711yescharacteristic
399D59—82no—
400C23×Q8—591no—
401C22×SD16—591no—
402C22×SD16—591no—
403C22×SD16—591no—
404C22×SD16—591no—
405#540—598no—
406#540—1184no—
407C2×#127—591no—
408C2×#125—591no—
409C2×#123—1181no—
410C2×#123—1181no—
411C2×#121—591no—
412C2×#121—1181no—
413C2×#121—1181no—
414C2×#121C2×D5911yescharacteristic
415#519—598no—
416#519—1184no—
417C2×C4×Q8—591no—
418C2×C4×Q8—591no—
419C2×C4×Q8—591no—
420C2×C4×Q8—591no—
421C2×C4×Q8—1181no—
422C2×C4×Q8—1181no—
423C2×C4×D4—591no—
424C2×C4×D4—591no—
425C2×#117—591no—
426C2×#117—1181no—
427C2×#117—1181no—
428C2×#117C2×D5911yescharacteristic
429#482—598no—
430#482C2×D5918yescomplemented
431#479—598no—
432#479—598no—
433#460—598no—
434#460—598no—
435#448—598no—
436#448—598no—
437#440—598no—
438#440—598no—
439C4×SD16—598no—
440C4×SD16—598no—
441#433—598no—
442C2×#107—591no—
443C2×#107C2×D5911yescharacteristic
444C2×#106—591no—
445C2×#106C2×D5911yescharacteristic
446C2×C4⋊C8—591no—
447C2×C4⋊C8—591no—
448C2×#103—591no—
449C2×#103—591no—
450C2×#103—591no—
451C2×#103—591no—
452C2×#102—591no—
453C2×#102—591no—
454C2×#102C2×D5911yescharacteristic
455C2×#102C2×D5911yescharacteristic
456C2×C22⋊C8—591no—
457C2×C22⋊C8C2×D5911yescharacteristic
458C2×#97—591no—
459C2×C4×C8—591no—
460C59C2×#312611yescharacteristic, complemented, Sylow
461C22×Q8—591no—
462C22×Q8—591no—
463C22×Q8—594no—
464C22×Q8—1184no—
465C22×Q8—1184no—
466C22×Q8—1181no—
467C22×Q8—1182no—
468C22×D4—21no—
469C22×D4—591no—
470C22×D4—1181no—
471C22×D4—1181no—
472C22×D4—1181no—
473C22×D4C22×D5911yescharacteristic
474C23×C4—1181no—
475C23×C4—1181no—
476C23×C4—1181no—
477C23×C4C22×D5911yescharacteristic
478C2×SD16—594no—
479C2×SD16—594no—
480C2×SD16—594no—
481C2×SD16—594no—
482C2×SD16—1184no—
483C2×SD16—1184no—
484C2×SD16—1184no—
485C2×SD16—1184no—
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—22no—
497#121—594no—
498#121—1188no—
499#121—1188no—
500#121—1182no—
501#121C22×D5914yes—
502C4×Q8—594no—
503C4×Q8—594no—
504C4×Q8—594no—
505C4×Q8—594no—
506C4×Q8—1188no—
507C4×Q8—1188no—
508C4×Q8—1182no—
509C4×Q8—1182no—
510C4×Q8—1182no—
511C4×Q8—1182no—
512C4×D4—594no—
513C4×D4—594no—
514C4×D4—1182no—
515C4×D4—1182no—
516#117—22no—
517#117—594no—
518#117—594no—
519#117—1188no—
520#117—1188no—
521#117C22×D5914yes—
522C2×C4⋊C4—591no—
523C2×C4⋊C4—591no—
524C2×C4⋊C4—591no—
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×C4⋊C4C22×D5911yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—591no—
537C2×C22⋊C4—591no—
538C2×C22⋊C4—1181no—
539C2×C22⋊C4—1181no—
540C2×C22⋊C4—1181no—
541C2×C42—21no—
542C2×C42—591no—
543C2×C42—591no—
544C2×C42—1181no—
545C2×C42—1181no—
546C2×C42—1181no—
547C2×C42—1181no—
548#107—594no—
549#107C22×D5914yes—
550#106—594no—
551#106C22×D5914yes—
552C4⋊C8—594no—
553C4⋊C8—594no—
554#103—594no—
555#103—594no—
556#103—594no—
557#103—594no—
558#102—594no—
559#102—594no—
560#102C22×D5914yes—
561#102C22×D5914yes—
562C22⋊C8—594no—
563C22⋊C8C22×D5914yes—
564#97—594no—
565C4×C8—594no—
566C24—21no—
567C24—1181no—
568C24D4×D5911yescharacteristic
569C2×Q8—594no—
570C2×Q8—594no—
571C2×Q8—592no—
572C2×Q8—592no—
573C2×Q8—1188no—
574C2×Q8—1188no—
575C2×Q8—1188no—
576C2×Q8—11816no—
577C2×Q8—1184no—
578C2×Q8—1181no—
579C2×Q8—1181no—
580C2×Q8—1182no—
581C2×Q8—1182no—
582C2×D4—24no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—82no—
587C2×D4—592no—
588C2×D4—1184no—
589C2×D4—1184no—
590C2×D4—1184no—
591C2×D4—1181no—
592C2×D4—1182no—
593C2×D4—1182no—
594C2×D4—4722no—
595C2×D4—4722no—
596C2×D4—4722no—
597C2×D4C23×D5912yes—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—591no—
604C22×C4—591no—
605C22×C4—591no—
606C22×C4—591no—
607C22×C4—1184no—
608C22×C4—1184no—
609C22×C4—1188no—
610C22×C4—1184no—
611C22×C4—1181no—
612C22×C4—1181no—
613C22×C4—1181no—
614C22×C4—4722no—
615C22×C4—4722no—
616C22×C4D4×D5912yes—
617C22×C4D4×D5911yescharacteristic
618C22×C4C23×D5912yes—
619C22×C4C23×D5911yescharacteristic
620SD16—1188no—
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—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—594no—
636C4⋊C4—594no—
637C4⋊C4—592no—
638C4⋊C4—1184no—
639C4⋊C4—1184no—
640C4⋊C4—1184no—
641C4⋊C4—1184no—
642C4⋊C4—1184no—
643C4⋊C4—1184no—
644C4⋊C4—1181no—
645C4⋊C4C23×D5912yes—
646C4⋊C4C23×D5912yes—
647C4⋊C4C23×D5912yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—594no—
651C22⋊C4—594no—
652C22⋊C4—1184no—
653C22⋊C4—1184no—
654C22⋊C4—1184no—
655C42—24no—
656C42—592no—
657C42—592no—
658C42—592no—
659C42—592no—
660C42—1184no—
661C42—1184no—
662C42—1184no—
663C42—1184no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—1182no—
672C23—2362no—
673C23—2362no—
674C23—2362no—
675C23C2×D4×D5912yes—
676C23C2×D4×D5911yescharacteristic
677Q8—594no—
678Q8—594no—
679Q8—11816no—
680Q8—1184no—
681Q8—1184no—
682Q8—1182no—
683Q8—1182no—
684D4—22no—
685D4—22no—
686D4—42no—
687D4—84no—
688D4—1182no—
689D4—1182no—
690D4—4724no—
691D4—4724no—
692D4—4724no—
693D4—2362no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—592no—
705C2×C4—592no—
706C2×C4—592no—
707C2×C4—592no—
708C2×C4—11816no—
709C2×C4—1184no—
710C2×C4—1184no—
711C2×C4—1182no—
712C2×C4—1182no—
713C2×C4—1182no—
714C2×C4—1182no—
715C2×C4—1182no—
716C2×C4—1182no—
717C2×C4—1182no—
718C2×C4—4724no—
719C2×C4—4724no—
720C2×C4—2362no—
721C2×C4C2×D4×D5912yes—
722C2×C4C2×D4×D5911yescharacteristic
723C2×C4#41×D5912yes—
724C2×C4#41×D5912yes—
725C2×C4C24×D5911yescharacteristic
726C8—22no—
727C8—22no—
728C8—1182no—
729C8—1182no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—4724no—
739C22—2362no—
740C22—2362no—
741C22—2362no—
742C22#1683791012yes—
743C22#1683820912yes—
744C22#1683821212yes—
745C22C22×D4×D5911yescharacteristic
746C4—22no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—1182no—
751C4—1182no—
752C4—1182no—
753C4—1182no—
754C4—1184no—
755C4—1184no—
756C4—2362no—
757C4#1683791012yes—
758C4C2×#41×D5911yescharacteristic
759C4C2×#41×D5911yescharacteristic
760C2—42no—
761C2—82no—
762C2—4722no—
763C2#2143438314yesdirect product factor
764C2C2×#1683791011yescharacteristic
765C2C2×#1683820911yescharacteristic
766C2C2×#1683821211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#482C2
socleC23×C59C22×D4
prime radicalC2×#16838005C2
hypercenterC2×#482D59
hypocenterC59C2×#3126
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
2. C2×#16837879C2semidirect
3. #21434383C2direct (N × H)
4. C2×#16837726C2semidirect
5. C2×#16837712C2semidirect
6. C2×#16837708C2semidirect
7. C2×#16837601C2semidirect
8. C2×#16837601C2semidirect
9. C2×#16837543C2semidirect
10. C2×#16837540C2semidirect
11. C2×#16837501C2semidirect
12. C2×#16837499C2semidirect
13. C2×#16837493C2semidirect
14. C2×#16837489C2semidirect
15. C2×#16837460C2semidirect
16. C2×C59×#482C2semidirect
32. #16837879C22semidirect
44. #16837726C22semidirect
45. #16837712C22semidirect
46. #16837708C22semidirect
47. #16837601C22semidirect
48. #16837601C22semidirect
49. #16837543C22semidirect
50. #16837540C22semidirect
51. #16837501C22semidirect
52. #16837499C22semidirect
53. #16837493C22semidirect
54. #16837489C22semidirect
55. #16837460C22semidirect
71. C59×#482C22semidirect
381. C2×#482D59semidirect
395. C2×C59#3126semidirect
430. #482C2×D59semidirect
460. C59C2×#3126semidirect
763. C2#21434383direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380052
C2×#168378792
#214343832
C2×#168377262
C2×#168377122
C2×#168377082
C2×#168376012
C2×#168375432
C2×#168375402
C2×#168375012
C2×#168374992
C2×#168374932
C2×#168374892
C2×#168374602
C2×C59×#4822
C2×#312659