Finite Group Databasebeta

← C2×#21424587 #28590576

Subgroups — C2×#21424587 #28590576

Order 15104.

1678 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
1C22×#14273757C211yesmaximal, characteristic
2C2×#16837879C211yesmaximal, characteristic, complemented
3C2×#16837412C211yesmaximal, characteristic, complemented
4C2×#16837376C211yesmaximal, characteristic
5#21424587C218yesmaximal, direct product factor
6C2×#16837174C211yesmaximal, characteristic, complemented
7C2×#16837158C211yesmaximal, characteristic, complemented
8C2×C59×#421C211yesmaximal, characteristic
9C23×Dic118C2211yescharacteristic
10C2×#14273757—22no—
11C2×#14273757—22no—
12C2×#14273757—22no—
13C2×#14273757—22no—
14C2×#14273757C414yescomplemented
15C2×#14273757C2214yes—
16C22×#11745672C412yescomplemented
17C22×#11745670C412yescomplemented
18C22×#11745664C2211yescharacteristic
19#16837879—22no—
20#16837879—22no—
21#16837879—22no—
22#16837879C2214yescomplemented
23C2×C4×Dic118—22no—
24C2×#14273692—22no—
25C2×#14273686C2211yescharacteristic
26C2×#14273686C2211yescharacteristic
27C2×#14273683—22no—
28#16837412—22no—
29#16837412C2214yescomplemented
30C2×#14273652—22no—
31#16837376—22no—
32#16837376C2214yes—
33C2×#14273642—22no—
34#16837174C2214yescomplemented
35#16837158C2214yescomplemented
36C22×#41×C59C2211yescharacteristic
37C22×M16×C59C2211yescharacteristic
38C2×#117×C59C2211yescharacteristic
39C59×#421—22no—
40C59×#421C2214yes—
41C2×#104×C59—22no—
42C22×Dic118—21no—
43C22×Dic118—21no—
44C22×Dic118—21no—
45C22×Dic118—21no—
46C22×Dic118—21no—
47C22×Dic118—21no—
48C22×Dic118—21no—
49C22×Dic118C2×C412yes—
50C22×Dic118C2×C412yes—
51C22×Dic118D412yes—
52C22×Dic118D412yes—
53C22×Dic118D412yes—
54C22×Dic118D412yes—
55C22×Dic118C2312yes—
56C23×Dic59—21no—
57#14273757—28no—
58#14273757—28no—
59#14273757—28no—
60#14273757—28no—
61C2×#11745672—24no—
62C2×#11745672—24no—
63C2×#11745672C2×C418yescomplemented
64C2×#11745670—24no—
65C2×#11745670—24no—
66C2×#11745670C2×C418yescomplemented
67C2×#11745664—21no—
68C2×#11745664—21no—
69C2×#11745664—21no—
70C2×#11745664—21no—
71C2×#11745664C2×C412yes—
72C2×#11745664C2312yes—
73C22×C59⋊C8C2×C412yes—
74C4×Dic118—28no—
75C4×Dic118—28no—
76#14273692—28no—
77#14273692—28no—
78#14273686—21no—
79#14273686—21no—
80#14273686—21no—
81#14273686—21no—
82#14273686—21no—
83#14273686D412yes—
84#14273686C2312yes—
85#14273686C2312yes—
86#14273683—28no—
87#14273683—28no—
88C2×C4⋊Dic59—21no—
89C2×C4⋊Dic59—21no—
90C2×Dic59⋊C4—24no—
91C2×C22⋊Dic59—21no—
92C2×C22⋊Dic59D412yes—
93C2×C4×Dic59—24no—
94C2×C4×Dic59—21no—
95C2×C4×Dic59—21no—
96#14273652—28no—
97#14273642—28no—
98C2×#41×C59—21no—
99C2×#41×C59—21no—
100C2×#41×C59—21no—
101C2×#41×C59—21no—
102C2×#41×C59—21no—
103C2×#41×C59—21no—
104C2×#41×C59—21no—
105C2×#41×C59—21no—
106C2×#41×C59—21no—
107C2×#41×C59—21no—
108C2×#41×C59C2×C412yes—
109C2×#41×C59C2312yes—
110C22×Q8×C59C2×C411yescharacteristic
111C22×D4×C59—21no—
112C22×D4×C59C2×C411yescharacteristic
113C23×C4×C59—21no—
114C23×C4×C59C2311yescharacteristic
115C2×M16×C59—21no—
116C2×M16×C59—21no—
117C2×M16×C59—21no—
118C2×M16×C59—21no—
119C2×M16×C59—21no—
120C2×M16×C59C2312yes—
121C22×C8×C59—21no—
122#117×C59—21no—
123#117×C59—21no—
124#117×C59D412yes—
125#117×C59C2312yes—
126C2×C4⋊C4×C59—21no—
127C2×C22⋊C4×C59—21no—
128C2×C42×C59D412yes—
129#104×C59—28no—
130C24×C59—21no—
131C24×C59C2×D411yescharacteristic
132#41×C59—22no—
133#41×C59—22no—
134#41×C59—22no—
135#41×C59—22no—
136#41×C59—22no—
137#41×C59—22no—
138#41×C59—22no—
139#41×C59—22no—
140#41×C59—41no—
141#41×C59—41no—
142#41×C59—41no—
143#41×C59—41no—
144#41×C59—41no—
145#41×C59—41no—
146#41×C59—41no—
147#41×C59—41no—
148C2×Q8×C59—21no—
149C2×Q8×C59—21no—
150C2×Q8×C59—21no—
151C2×Q8×C59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59C22×C412yes—
154C2×D4×C59—22no—
155C2×D4×C59—22no—
156C2×D4×C59—21no—
157C2×D4×C59—21no—
158C2×D4×C59—21no—
159C2×D4×C59—21no—
160C2×D4×C59—21no—
161C2×D4×C59—41no—
162C2×D4×C59—41no—
163C2×D4×C59—41no—
164C2×D4×C59—41no—
165C2×D4×C59C22×C412yes—
166C22×C4×C59—21no—
167C22×C4×C59—22no—
168C22×C4×C59—22no—
169C22×C4×C59—22no—
170C22×C4×C59—41no—
171C22×C4×C59—41no—
172C22×C4×C59—41no—
173C22×C4×C59—41no—
174C22×C4×C59C22×C411yescharacteristic
175C22×C4×C59C22×C411yescharacteristic
176C22×C4×C59C2×D411yescharacteristic
177C22×C4×C59C2×D411yescharacteristic
178C22×C4×C59C2×D411yescharacteristic
179C22×C4×C59C2×D411yescharacteristic
180C22×C4×C59C2×D411yescharacteristic
181C22×C4×C59C2×D411yescharacteristic
182C22×C4×C59C2×D411yescharacteristic
183C22×C4×C59#4111yescharacteristic
184C22×C4×C59#4111yescharacteristic
185C22×C4×C59#4111yescharacteristic
186C22×C4×C59#4111yescharacteristic
187C22×C4×C59C2411yescharacteristic
188C22×Dic59—22no—
189C22×Dic59—22no—
190C22×Dic59—22no—
191C22×Dic59—22no—
192C22×Dic59—22no—
193C22×Dic59—22no—
194C22×Dic59—22no—
195C22×Dic59—22no—
196C22×Dic59—41no—
197C2×Dic118—22no—
198C2×Dic118—22no—
199C2×Dic118—22no—
200C2×Dic118—22no—
201C2×Dic118—22no—
202C2×Dic118—22no—
203C2×Dic118—22no—
204C2×Dic118—22no—
205C2×Dic118—22no—
206C2×Dic118—22no—
207C2×Dic118—22no—
208C2×Dic118—22no—
209C2×Dic118—22no—
210C2×Dic118—22no—
211C2×Dic118—22no—
212C2×Dic118—22no—
213C2×Dic118—22no—
214C2×Dic118—22no—
215C2×Dic118—22no—
216C2×Dic118—22no—
217C2×Dic118—22no—
218C2×Dic118C22⋊C414yes—
219C2×Dic118C22⋊C414yes—
220C2×Dic118C22⋊C414yes—
221C2×Dic118C22⋊C414yes—
222C2×Dic118C22×C414yes—
223C2×Dic118C2×D414yes—
224C2×Dic118C2×D414yes—
225M16×C59—22no—
226M16×C59—22no—
227M16×C59—41no—
228M16×C59—41no—
229C2×C8×C59—22no—
230C2×C8×C59—41no—
231C2×C8×C59—41no—
232C4⋊C4×C59—22no—
233C4⋊C4×C59—22no—
234C22⋊C4×C59—22no—
235C22⋊C4×C59—22no—
236C42×C59—22no—
237C42×C59C2×D414yes—
238C22⋊Dic59—22no—
239C22⋊Dic59—22no—
240C22⋊Dic59—41no—
241C22⋊Dic59C2×D414yes—
242#11745672—216no—
243#11745670—216no—
244C4⋊Dic59—22no—
245C4⋊Dic59—22no—
246C4⋊Dic59—22no—
247C4⋊Dic59—41no—
248Dic59⋊C4—216no—
249C4×Dic59—216no—
250C4×Dic59—22no—
251C4×Dic59—22no—
252C4×Dic59—22no—
253C4×Dic59—41no—
254#11745664—22no—
255#11745664—22no—
256#11745664—22no—
257#11745664—22no—
258C2×C59⋊C8—22no—
259C2×C59⋊C8—22no—
260C2×C59⋊C8C22×C414yes—
261C23×C59—22no—
262C23×C59—42no—
263C23×C59—41no—
264C23×C59—41no—
265C23×C59—82no—
266C23×C59C4×D411yescharacteristic
267C23×C59C4×D411yescharacteristic
268C23×C59#12011yescharacteristic
269C23×C59#12011yescharacteristic
270C23×C59#12111yescharacteristic
271C23×C59#12111yescharacteristic
272C23×C59C22×D411yescharacteristic
273Q8×C59—22no—
274Q8×C59—22no—
275Q8×C59—41no—
276Q8×C59—41no—
277D4×C59—22no—
278D4×C59—22no—
279D4×C59—42no—
280D4×C59—42no—
281D4×C59—42no—
282D4×C59—42no—
283D4×C59—41no—
284D4×C59—41no—
285C2×C4×C59—22no—
286C2×C4×C59—24no—
287C2×C4×C59—44no—
288C2×C4×C59—41no—
289C2×C4×C59—41no—
290C2×C4×C59—42no—
291C2×C4×C59—42no—
292C2×C4×C59—42no—
293C2×C4×C59—42no—
294C2×C4×C59C2×C22⋊C411yescharacteristic
295C2×C4×C59C2×C22⋊C411yescharacteristic
296C2×C4×C59C2×C22⋊C411yescharacteristic
297C2×C4×C59C2×C22⋊C411yescharacteristic
298C2×C4×C59C4×D411yescharacteristic
299C2×C4×C59C4×D411yescharacteristic
300C2×C4×C59C4×D411yescharacteristic
301C2×C4×C59C4×D411yescharacteristic
302C2×C4×C59C4×D411yescharacteristic
303C2×C4×C59C4×D411yescharacteristic
304C2×C4×C59#12011yescharacteristic
305C2×C4×C59#12011yescharacteristic
306C2×C4×C59#12111yescharacteristic
307C2×C4×C59#12111yescharacteristic
308C2×C4×C59#12111yescharacteristic
309C2×C4×C59#12111yescharacteristic
310C2×C4×C59#12111yescharacteristic
311C2×C4×C59#12111yescharacteristic
312C2×C4×C59#12311yescharacteristic
313C2×C4×C59#12311yescharacteristic
314C2×C4×C59#12311yescharacteristic
315C2×C4×C59#12311yescharacteristic
316C2×C4×C59C23×C411yescharacteristic
317C2×C4×C59C22×D411yescharacteristic
318C2×C4×C59C22×D411yescharacteristic
319C2×C4×C59C22×D411yescharacteristic
320C2×C4×C59C2×#4111yescharacteristic
321C2×C4×C59C2×#4111yescharacteristic
322C2×Dic59—24no—
323C2×Dic59—24no—
324C2×Dic59—24no—
325C2×Dic59—24no—
326C2×Dic59—24no—
327C2×Dic59—24no—
328C2×Dic59—24no—
329C2×Dic59—24no—
330C2×Dic59—44no—
331C2×Dic59—42no—
332C2×Dic59—82no—
333Dic118—24no—
334Dic118—24no—
335Dic118—24no—
336Dic118—24no—
337Dic118—24no—
338Dic118—24no—
339Dic118—24no—
340Dic118C2×C22⋊C418yes—
341C8×C59—42no—
342C59⋊C8—24no—
343C2×#1905—591nomaximal, Sylow
344C22×C59—22no—
345C22×C59—22no—
346C22×C59—22no—
347C22×C59—41no—
348C22×C59—41no—
349C22×C59—41no—
350C22×C59—41no—
351C22×C59—42no—
352C22×C59—82no—
353C22×C59—82no—
354C22×C59—82no—
355C22×C59#38611yescharacteristic
356C22×C59#38611yescharacteristic
357C22×C59#38611yescharacteristic
358C22×C59#38611yescharacteristic
359C22×C59C2×C4×D411yescharacteristic
360C22×C59C2×#12011yescharacteristic
361C22×C59C2×#12111yescharacteristic
362C4×C59—44no—
363C4×C59—42no—
364C4×C59#38611yescharacteristic
365C4×C59#38611yescharacteristic
366C4×C59#38611yescharacteristic
367C4×C59#38611yescharacteristic
368C4×C59C22×C22⋊C411yescharacteristic
369C4×C59C2×C4×D411yescharacteristic
370C4×C59C2×#12111yescharacteristic
371C4×C59C2×#12311yescharacteristic
372Dic59—28no—
373Dic59—44no—
374Dic59—82no—
375C22×#137—591no—
376C2×#519—591no—
377C2×#421D5911yescharacteristic
378C2×#419—591no—
379C2×#410—591no—
380#1905—598no—
381C2×#344—591no—
382C2×H(3,ℤ/4)—591no—
383C2×C59—21no—
384C2×C59—21no—
385C2×C59—21no—
386C2×C59—21no—
387C2×C59—21no—
388C2×C59—21no—
389C2×C59—82no—
390C2×C59#190512yescomplemented
391C2×C59C2×#38611yescharacteristic
392C22×#41C2×D5911yescharacteristic
393C23×Q8—591no—
394C2×#137—594no—
395C2×#137—594no—
396C2×#137—1182no—
397C2×#137—1182no—
398C2×#137—1182no—
399C2×#137—1182no—
400C22×Q16—592no—
401C22×SD16—592no—
402C22×M16—591no—
403C22×M16C2×D5911yescharacteristic
404#519—594no—
405#519—1182no—
406#519—1182no—
407#519—1182no—
408C2×C4×Q8—1182no—
409C2×C4×Q8—1182no—
410C2×#117—591no—
411C2×#117—591no—
412C2×#117—1182no—
413C2×#117C2×D5911yescharacteristic
414#421—22no—
415#421C2×D5914yes—
416C2×#104—22no—
417#419—594no—
418#419—1182no—
419C2×#103—1182no—
420#410—594no—
421#410—1182no—
422C2×#99—1182no—
423#344—594no—
424H(3,ℤ/4)—594no—
425C59C2×#190511yescharacteristic, complemented, Sylow
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41C4×D5912yes—
437C2×#41C22×D5912yes—
438C22×Q8—592no—
439C22×Q8—592no—
440C22×Q8—592no—
441C22×Q8—592no—
442C22×Q8—592no—
443C22×Q8—592no—
444C22×Q8—592no—
445C22×Q8—1181no—
446C22×Q8—1181no—
447C22×Q8—1181no—
448C22×Q8—1181no—
449C22×Q8—1181no—
450C22×Q8—1181no—
451C22×Q8—1181no—
452C22×Q8C4×D5911yescharacteristic
453C22×D4—21no—
454C22×D4C4×D5911yescharacteristic
455C23×C4—21no—
456C23×C4—1181no—
457C23×C4C22×D5911yescharacteristic
458#137—1188no—
459#137—1188no—
460#137—1188no—
461#137—1188no—
462C2×Q16—598no—
463C2×Q16—1184no—
464C2×Q16—1184no—
465C2×SD16—598no—
466C2×SD16—1184no—
467C2×SD16—1184no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—21no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—592no—
474C2×M16—592no—
475C2×M16—1181no—
476C2×M16—1181no—
477C2×M16—1181no—
478C2×M16—1181no—
479C2×M16C22×D5912yes—
480C22×C8—21no—
481C22×C8—592no—
482C4×Q8—1188no—
483C4×Q8—1188no—
484C4×Q8—1188no—
485C4×Q8—1188no—
486#117—21no—
487#117—21no—
488#117—592no—
489#117—592no—
490#117—592no—
491#117—1188no—
492#117—1188no—
493#117—1181no—
494#117—1181no—
495#117—1181no—
496#117—1181no—
497#117—1181no—
498#117C22⋊D5912yes—
499#117C22×D5912yes—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—1184no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—592no—
506C2×C22⋊C4—1181no—
507C2×C42—1184no—
508C2×C42—1181no—
509C2×C42—1181no—
510C2×C42C22⋊D5912yes—
511#104—28no—
512#103—1188no—
513#99—1188no—
514C24—21no—
515C24D4×D5911yescharacteristic
516#41—22no—
517#41—22no—
518#41—22no—
519#41—22no—
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41—41no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—41no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—594no—
538C2×Q8—594no—
539C2×Q8—594no—
540C2×Q8—594no—
541C2×Q8—594no—
542C2×Q8—594no—
543C2×Q8—594no—
544C2×Q8—1182no—
545C2×Q8—1182no—
546C2×Q8—1182no—
547C2×Q8—1182no—
548C2×Q8—1182no—
549C2×Q8—1182no—
550C2×Q8—1182no—
551C2×Q8—1182no—
552C2×Q8—1182no—
553C2×Q8—1182no—
554C2×Q8—1182no—
555C2×Q8—1182no—
556C2×Q8—1182no—
557C2×Q8—1182no—
558C2×Q8—1182no—
559C2×Q8—1182no—
560C2×Q8—1182no—
561C2×Q8—1182no—
562C2×Q8—1182no—
563C2×Q8—1182no—
564C2×Q8—1182no—
565C2×Q8C2×C4×D5912yes—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4C2×C4×D5912yes—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—1182no—
587C22×C4—1182no—
588C22×C4—1182no—
589C22×C4—1182no—
590C22×C4—1182no—
591C22×C4—1182no—
592C22×C4—1182no—
593C22×C4—1182no—
594C22×C4—2361no—
595C22×C4C2×C4×D5911yescharacteristic
596C22×C4C2×C4×D5911yescharacteristic
597C22×C4#1174568511yescharacteristic
598C22×C4#1174568511yescharacteristic
599C22×C4D4×D5911yescharacteristic
600C22×C4D4×D5911yescharacteristic
601C22×C4D4×D5911yescharacteristic
602C22×C4D4×D5911yescharacteristic
603C22×C4D4×D5911yescharacteristic
604C22×C4#1174568711yescharacteristic
605C22×C4#1174568711yescharacteristic
606C22×C4C2×C22⋊D5911yescharacteristic
607C22×C4C2×C22⋊D5911yescharacteristic
608C22×C4C23×D5911yescharacteristic
609Q16—11816no—
610SD16—11816no—
611M16—22no—
612M16—22no—
613M16—41no—
614M16—41no—
615M16—1182no—
616M16—1182no—
617M16—1182no—
618M16—1182no—
619C2×C8—22no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—594no—
623C2×C8—1182no—
624C2×C8—1182no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—11816no—
628C4⋊C4—1182no—
629C4⋊C4—1182no—
630C4⋊C4—1182no—
631C4⋊C4—2361no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—594no—
635C22⋊C4—1182no—
636C22⋊C4—1182no—
637C22⋊C4—2361no—
638C42—22no—
639C42—11816no—
640C42—1182no—
641C42—1182no—
642C42—1182no—
643C42—2361no—
644C42C2×C22⋊D5914yes—
645C23—22no—
646C23—42no—
647C23—41no—
648C23—41no—
649C23—82no—
650C23(C22⋊D59)⋊C411yescharacteristic
651C23(C22⋊D59)⋊C411yescharacteristic
652C23#1427369511yescharacteristic
653C23#1427369511yescharacteristic
654C23#1427370011yescharacteristic
655C23#1427370011yescharacteristic
656C23C2×D4×D5911yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661Q8—598no—
662Q8—1184no—
663Q8—1184no—
664Q8—1184no—
665Q8—1184no—
666Q8—1184no—
667Q8—1184no—
668Q8—1184no—
669D4—22no—
670D4—22no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—41no—
676D4—41no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—44no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—1184no—
687C2×C4—1184no—
688C2×C4—1184no—
689C2×C4—1184no—
690C2×C4—1184no—
691C2×C4—1184no—
692C2×C4—1184no—
693C2×C4—1184no—
694C2×C4—4722no—
695C2×C4—2362no—
696C2×C4—2364no—
697C2×C4C22⋊C4×D5911yescharacteristic
698C2×C4C22⋊C4×D5911yescharacteristic
699C2×C4C22⋊C4×D5911yescharacteristic
700C2×C4C22⋊C4×D5911yescharacteristic
701C2×C4(C22⋊D59)⋊C411yescharacteristic
702C2×C4(C22⋊D59)⋊C411yescharacteristic
703C2×C4C4×C22⋊D5911yescharacteristic
704C2×C4C4×C22⋊D5911yescharacteristic
705C2×C4C4×C22⋊D5911yescharacteristic
706C2×C4C4×C22⋊D5911yescharacteristic
707C2×C4#1427369511yescharacteristic
708C2×C4#1427369511yescharacteristic
709C2×C4#1427369811yescharacteristic
710C2×C4#1427369811yescharacteristic
711C2×C4#1427369811yescharacteristic
712C2×C4#1427369811yescharacteristic
713C2×C4#1427370011yescharacteristic
714C2×C4#1427370011yescharacteristic
715C2×C4#1427370911yescharacteristic
716C2×C4#1427370911yescharacteristic
717C2×C4#1427370911yescharacteristic
718C2×C4#1427370911yescharacteristic
719C2×C4C22×C4×D5911yescharacteristic
720C2×C4C2×D4×D5911yescharacteristic
721C2×C4C2×D4×D5911yescharacteristic
722C2×C4C22×C22⋊D5911yescharacteristic
723C2×C4C2×#1174568711yescharacteristic
724C2×C4C2×#1174568511yescharacteristic
725C8—42no—
726C8—1184no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—42no—
735C22—82no—
736C22—82no—
737C22—82no—
738C22#1683727811yescharacteristic
739C22#1683727811yescharacteristic
740C22#1683727811yescharacteristic
741C22#1683727811yescharacteristic
742C22C2×(C22⋊D59)⋊C411yescharacteristic
743C22C2×#1427369511yescharacteristic
744C22C2×#1427370011yescharacteristic
745C4—44no—
746C4—42no—
747C4—1188no—
748C4—4722no—
749C4—2364no—
750C4#1683727811yescharacteristic
751C4#1683727811yescharacteristic
752C4#1683727811yescharacteristic
753C4#1683727811yescharacteristic
754C4C2×C22⋊C4×D5911yescharacteristic
755C4C2×C4×C22⋊D5911yescharacteristic
756C4C2×#1427369811yescharacteristic
757C4C2×#1427370911yescharacteristic
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—82no—
765C2#2142458712yesdirect product factor
766C2C2×#1683727811yescharacteristic
subgroupG/H
centerC22#16837278
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#421C2
socleC22×C59#386
prime radicalC22×#41×C59C22
cosocleC22×C4×C59C24
hypercenterC2×#421D59
hypocenterC59C2×#1905
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#16837879C2semidirect
3. C2×#16837412C2semidirect
5. #21424587C2direct (N × H)
6. C2×#16837174C2semidirect
7. C2×#16837158C2semidirect
14. C2×#14273757C4semidirect
16. C22×#11745672C4semidirect
17. C22×#11745670C4semidirect
22. #16837879C22semidirect
29. #16837412C22semidirect
34. #16837174C22semidirect
35. #16837158C22semidirect
63. C2×#11745672C2×C4semidirect
66. C2×#11745670C2×C4semidirect
390. C2×C59#1905semidirect
425. C59C2×#1905semidirect
765. C2#21424587direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737572
C2×#168378792
C2×#168374122
C2×#168373762
#214245872
C2×#168371742
C2×#168371582
C2×C59×#4212
C2×#190559