Finite Group Databasebeta

← C2×#21434286 #29456926

Subgroups — C2×#21434286 #29456926

Order 15104.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838024C211yesmaximal, characteristic, complemented
2C2×#16837874C211yesmaximal, characteristic, complemented
3#21434286C2116yesmaximal, direct product factor
4C2×#16837742C211yesmaximal, characteristic, complemented
5C2×#16837728C211yesmaximal, characteristic, complemented
6C2×#16837691C211yesmaximal, characteristic, complemented
7C2×#16837680C211yesmaximal, characteristic, complemented
8C2×#16837620C211yesmaximal, characteristic, complemented
9C2×#16837619C211yesmaximal, characteristic, complemented
10C2×#16837551C211yesmaximal, characteristic, complemented
11C2×#16837537C211yesmaximal, characteristic
12C2×#16837512C211yesmaximal, characteristic, complemented
13C2×#16837500C211yesmaximal, characteristic, complemented
14C2×C4×D472C211yesmaximal, characteristic, complemented
15C2×#16837461C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C59C211yesmaximal, characteristic, complemented
17C22×D4×D59C2211yescharacteristic
18C22×#11745671C2211yescharacteristic
19C22×D472C2211yescharacteristic
20C22×#11745669C2211yescharacteristic
21#16838024—24no—
22#16838024C2218yescomplemented
23C2×#14273726C2211yescharacteristic, complemented
24C2×#14273721—21no—
25C2×#14273716C2211yescharacteristic, complemented
26C2×#14273715—21no—
27C2×#14273712—21no—
28C2×#14273705—21no—
29C2×#14273703C2211yescharacteristic
30C2×#14273702C2211yescharacteristic
31#16837874—24no—
32#16837874C2218yescomplemented
33C2×C4×D236C2211yescharacteristic
34C2×C4×D236C2211yescharacteristic, complemented
35C2×D4×Dic59C2211yescharacteristic
36C2×#14273689C2211yescharacteristic
37C2×C4×C22⋊D59—21no—
38C2×(C22⋊D59)⋊C4—21no—
39C2×#14273685C2211yescharacteristic
40C2×#14273684C2211yescharacteristic
41C22×(C2×D59)⋊C4—21no—
42C2×C22⋊C4×D59—21no—
43#16837742C2218yescomplemented
44#16837728C2218yescomplemented
45#16837691C2218yescomplemented
46#16837680C2218yescomplemented
47#16837620C2218yescomplemented
48#16837619C2218yescomplemented
49#16837551C2218yescomplemented
50#16837537C2218yes—
51#16837512C2218yescomplemented
52#16837500C2218yescomplemented
53C4×D472C2218yescomplemented
54#16837461C2218yescomplemented
55C2×#14273661C2211yescharacteristic, complemented
56C2×#14273660C2211yescharacteristic, complemented
57C2×#14273658C2211yescharacteristic, complemented
58C2×Dic59⋊C8C2211yescharacteristic, complemented
59C2×Dic59⋊C8C2211yescharacteristic, complemented
60C2×#14273651C2211yescharacteristic, complemented
61C2×#14273649C2211yescharacteristic
62C2×#14273649C2211yescharacteristic, complemented
63C2×#14273648C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic, complemented
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273638C2211yescharacteristic, complemented
69C22×SD16×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic, complemented
71C2×C4×D4×C59C2211yescharacteristic
72C4×SD16×C59C2218yescomplemented
73C2×#106×C59C2211yescharacteristic, complemented
74C2×#103×C59C2211yescharacteristic, complemented
75C2×#102×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C22×Dic118—21no—
79C22×D236—21no—
80C22×D236C2311yescharacteristic
81C22×D236C2311yescharacteristic
82C22×C22⋊D59—21no—
83C2×D4×D59—24no—
84C2×D4×D59—24no—
85C2×D4×D59—22no—
86C2×D4×D59C2314yes—
87C23×Dic59—21no—
88C22×C4×D59—21no—
89C22×C4×D59—21no—
90C22×C4×D59—21no—
91C22×C4×D59C2311yescharacteristic
92C2×#11745671—24no—
93C2×#11745671C2314yes—
94C2×D472—24no—
95C2×D472C2314yes—
96C2×#11745669—24no—
97C2×#11745669C2314yes—
98C22×C59⋊C8C2311yescharacteristic
99C22×C59⋊C8C2311yescharacteristic
100#14273726—22no—
101#14273726C2314yescomplemented
102#14273721—28no—
103#14273716—22no—
104#14273716C2314yescomplemented
105#14273715—28no—
106#14273712—28no—
107#14273705—28no—
108#14273703—22no—
109#14273703C2314yes—
110#14273702—22no—
111#14273702C2314yes—
112C4×D236—22no—
113C4×D236—22no—
114C4×D236C2314yes—
115C4×D236C2314yescomplemented
116D4×Dic59—22no—
117D4×Dic59C2314yes—
118#14273689—22no—
119#14273689C2314yes—
120C4×C22⋊D59—28no—
121(C22⋊D59)⋊C4—28no—
122#14273685—22no—
123#14273685C2314yes—
124#14273684D414yes—
125#14273684C2314yes—
126C2×C4⋊Dic59C2311yescharacteristic
127C2×C4⋊Dic59C2311yescharacteristic
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4D411yescharacteristic
131C2×Dic59⋊C4D411yescharacteristic
132C2×C22⋊Dic59—21no—
133C2×(C2×D59)⋊C4—21no—
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—28no—
142C2×(C2×D59)⋊C4D411yescharacteristic
143C2×(C2×D59)⋊C4D411yescharacteristic
144C22⋊C4×D59—28no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59C2311yescharacteristic
147#14273661C2314yescomplemented
148#14273660C2314yescomplemented
149#14273658C2314yescomplemented
150Dic59⋊C8C2314yescomplemented
151Dic59⋊C8C2314yescomplemented
152#14273651C2314yescomplemented
153#14273649C2314yes—
154#14273649C2314yescomplemented
155#14273648C2314yes—
156#14273647C2314yes—
157#14273647C2314yescomplemented
158(C2×D59)⋊C8C2314yes—
159(C2×D59)⋊C8C2314yes—
160#14273638C2314yescomplemented
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×C59C2314yescomplemented
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×C59C2314yescomplemented
179#103×C59C2314yescomplemented
180#102×C59C2314yes—
181C4×C8×C59C2314yescomplemented
182C24×C59—21no—
183C23×D59—21no—
184C23×D59—28no—
185C23×D59—24no—
186C23×D59—21no—
187C23×D59—82no—
188C23×D59—82no—
189C23×D59C2×D411yescharacteristic
190C2×Q8×C59—21no—
191C2×Q8×C59—22no—
192C2×Q8×C59—22no—
193C2×Q8×C59C2412yes—
194C2×D4×C59—21no—
195C2×D4×C59—22no—
196C2×D4×C59#4114yes—
197C2×D4×C59C2412yes—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—24no—
202C22×C4×C59—82no—
203C22×C4×C59C2×D411yescharacteristic
204C22×C4×C59C2×D411yescharacteristic
205C22×C4×C59C2411yescharacteristic
206C2×C22⋊D59—28no—
207C2×C22⋊D59—24no—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59—24no—
211C22×Dic59—82no—
212C22×Dic59C2×D411yescharacteristic
213C22×Dic59C2×D411yescharacteristic
214C22×Dic59C2×D411yescharacteristic
215D4×D59—216no—
216D4×D59—28no—
217D4×D59—28no—
218C2×D236—21no—
219C2×D236—22no—
220C2×D236—22no—
221C2×D236—22no—
222C2×D236—21no—
223C2×D236—24no—
224C2×D236—82no—
225C2×D236#4114yes—
226C2×D236C2412yes—
227C2×D236C2412yes—
228C2×C4×D59—22no—
229C2×C4×D59—22no—
230C2×C4×D59—24no—
231C2×C4×D59—24no—
232C2×C4×D59—24no—
233C2×C4×D59—82no—
234C2×C4×D59—82no—
235C2×C4×D59—82no—
236C2×C4×D59C2×D412yes—
237C2×C4×D59C2412yes—
238C2×Dic118—24no—
239C2×Dic118—82no—
240SD16×C59—28no—
241C2×C8×C59—22no—
242C2×C8×C59—22no—
243C2×C8×C59C2412yes—
244C2×C8×C59C2412yes—
245C4⋊C4×C59—24no—
246C4⋊C4×C59—21no—
247C4⋊C4×C59—21no—
248C4⋊C4×C59C2412yes—
249C4⋊C4×C59C2412yes—
250C22⋊C4×C59—24no—
251C42×C59—24no—
252C42×C59C2×D412yes—
253C42×C59C2412yes—
254C22⋊Dic59—24no—
255#11745671—28no—
256#11745669—28no—
257(C2×D59)⋊C4—24no—
258(C2×D59)⋊C4—24no—
259(C2×D59)⋊C4—24no—
260(C2×D59)⋊C4—24no—
261(C2×D59)⋊C4—24no—
262(C2×D59)⋊C4—24no—
263(C2×D59)⋊C4—24no—
264(C2×D59)⋊C4—24no—
265(C2×D59)⋊C4C2×D414yes—
266(C2×D59)⋊C4C2×D414yes—
267C4⋊Dic59—21no—
268C4⋊Dic59—21no—
269C4⋊Dic59C2412yes—
270C4⋊Dic59C2412yes—
271Dic59⋊C4—24no—
272Dic59⋊C4—24no—
273Dic59⋊C4C2×D414yes—
274Dic59⋊C4C2×D414yes—
275C4×Dic59—24no—
276C4×Dic59C2×D412yes—
277C4×Dic59C2412yes—
278C2×C59⋊C8—22no—
279C2×C59⋊C8—22no—
280C2×C59⋊C8C2412yes—
281C2×C59⋊C8C2412yes—
282D472—28no—
283C23×C59—24no—
284C23×C59—22no—
285C23×C59—42no—
286C23×C59—42no—
287C23×C59C22×D411yescharacteristic
288C22×D59—22no—
289C22×D59—24no—
290C22×D59—22no—
291C22×D59—22no—
292C22×D59—22no—
293C22×D59—216no—
294C22×D59—22no—
295C22×D59—42no—
296C22×D59—42no—
297C22×D59—42no—
298C22×D59—42no—
299C22×D59—42no—
300C22×D59—84no—
301C22×D59—84no—
302C22×D59—816no—
303C22×D59C22×D412yes—
304Q8×C59—22no—
305Q8×C59—22no—
306Q8×C59—42no—
307D4×C59—24no—
308D4×C59—22no—
309D4×C59C2×#4114yes—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—42no—
316C2×C4×C59—42no—
317C2×C4×C59—42no—
318C2×C4×C59—84no—
319C2×C4×C59C22×D412yes—
320C2×C4×C59C22×D412yes—
321C2×C4×C59C22×D411yescharacteristic
322C2×C4×C59C2×#4112yes—
323C2×C4×C59C2×#4112yes—
324C2×C4×C59C2511yescharacteristic
325C22⋊D59—216no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—42no—
332C2×Dic59—42no—
333C2×Dic59—84no—
334C2×Dic59C22×D412yes—
335C2×Dic59C22×D412yes—
336C2×Dic59C22×D412yes—
337D236—24no—
338D236—22no—
339D236—22no—
340D236—22no—
341D236—42no—
342D236—84no—
343D236C2×#4114yes—
344C4×D59—24no—
345C4×D59—22no—
346C4×D59—22no—
347C4×D59—84no—
348C4×D59—84no—
349C4×D59—84no—
350Dic118—84no—
351C8×C59—22no—
352C8×C59—22no—
353C59⋊C8—22no—
354C59⋊C8—22no—
355C2×#3118—591nomaximal, Sylow
356C22×C59—24no—
357C22×C59—48no—
358C22×C59—42no—
359C22×C59—42no—
360C22×C59#52512yes—
361C22×C59#57612yes—
362C22×C59#57712yes—
363C22×C59C23×D411yescharacteristic
364C2×D59—22no—
365C2×D59—24no—
366C2×D59—22no—
367C2×D59—22no—
368C2×D59—44no—
369C2×D59—48no—
370C2×D59—42no—
371C2×D59—42no—
372C2×D59—42no—
373C2×D59—42no—
374C2×D59—42no—
375C2×D59—816no—
376C2×D59—84no—
377C4×C59—22no—
378C4×C59—22no—
379C4×C59—42no—
380C4×C59—42no—
381C4×C59—42no—
382C4×C59#52512yes—
383C4×C59C22×#4111yescharacteristic
384C4×C59C22×#4111yescharacteristic
385Dic59—22no—
386Dic59—22no—
387Dic59—22no—
388Dic59—42no—
389Dic59—42no—
390C2×#542—591no—
391C2×#518—591no—
392#3118—5916no—
393C2×#485—591no—
394C2×#482—591no—
395C2×#476—591no—
396C2×#474—591no—
397C2×#463—591no—
398C2×#463—591no—
399C2×#450—591no—
400C2×#447—591no—
401C2×#442—591no—
402C2×#440—591no—
403C2×C4×SD16D5911yescharacteristic, complemented
404C2×C4×D8—591no—
405C2×#433—591no—
406C2×C59—44no—
407C2×C59#311814yescomplemented
408C2×C59C2×#52511yescharacteristic
409C2×C59C2×#57611yescharacteristic
410C2×C59C2×#57711yescharacteristic
411D59—42no—
412D59—44no—
413D59—82no—
414C23×D4—591no—
415C22×SD16—591no—
416C22×SD16C2×D5911yescharacteristic
417C22×D8—591no—
418C22×D8—591no—
419#542—598no—
420#542—1184no—
421C2×C4⋊Q8—591no—
422C2×#126—1181no—
423C2×#124—591no—
424C2×#124—1181no—
425C2×#123—1181no—
426C2×C22⋊Q8—591no—
427C2×C22⋊Q8—1181no—
428C2×#121—591no—
429#518—598no—
430#518—1184no—
431C2×C4×Q8C2×D5911yescharacteristic, complemented
432C2×C4×D4—591no—
433C2×C4×D4—591no—
434C2×C4×D4—591no—
435C2×C4×D4—591no—
436C2×C4×D4—1181no—
437C2×C4×D4—1181no—
438C2×C4×D4C2×D5911yescharacteristic
439C2×#117—591no—
440C2×#117—591no—
441C22×C22⋊C4—1181no—
442C22×C22⋊C4—1181no—
443#485—598no—
444#482—598no—
445#476—598no—
446#474—598no—
447#463—598no—
448#463—598no—
449#450—598no—
450#447—598no—
451#442—598no—
452#440—598no—
453C4×SD16C2×D5918yescomplemented
454C4×D8—598no—
455#433—598no—
456C2×#107—591no—
457C2×#107—591no—
458C2×#106—591no—
459C2×#106C2×D5911yescharacteristic, complemented
460C2×C4⋊C8—591no—
461C2×C4⋊C8—591no—
462C2×#103—591no—
463C2×#103C2×D5911yescharacteristic, complemented
464C2×#102—591no—
465C2×#102—591no—
466C2×#102—591no—
467C2×#102—591no—
468C2×#102—591no—
469C2×#102C2×D5911yescharacteristic
470C2×C22⋊C8—591no—
471C2×C22⋊C8—591no—
472C2×#97—591no—
473C2×C4×C8C2×D5911yescharacteristic, complemented
474C59C2×#311811yescharacteristic, complemented, Sylow
475C25—1181no—
476C22×Q8—1181no—
477C22×Q8C22×D5911yescharacteristic
478C22×D4—594no—
479C22×D4—591no—
480C22×D4—591no—
481C22×D4—1181no—
482C22×D4—1182no—
483C22×D4—1181no—
484C22×D4—1184no—
485C22×D4—1184no—
486C22×D4C22×D5911yescharacteristic
487C23×C4—21no—
488C23×C4—591no—
489C23×C4—1181no—
490C23×C4—1181no—
491C23×C4—1181no—
492C23×C4—1181no—
493C2×SD16—24no—
494C2×SD16—594no—
495C2×SD16—1184no—
496C2×SD16C22×D5914yes—
497C2×D8—594no—
498C2×D8—594no—
499C2×D8—1184no—
500C2×D8—1184no—
501C22×C8—591no—
502C22×C8—591no—
503C22×C8C22×D5911yescharacteristic
504C22×C8C22×D5911yescharacteristic
505C4⋊Q8—594no—
506C4⋊Q8—1182no—
507#126—1188no—
508#124—594no—
509#124—1188no—
510#124—1182no—
511#123—1188no—
512C22⋊Q8—594no—
513C22⋊Q8—1188no—
514C22⋊Q8—1182no—
515#121—594no—
516#121—1182no—
517C4×Q8—22no—
518C4×Q8C22×D5914yescomplemented
519C4×D4—22no—
520C4×D4—594no—
521C4×D4—594no—
522C4×D4—594no—
523C4×D4—594no—
524C4×D4—1182no—
525C4×D4—1182no—
526C4×D4—1188no—
527C4×D4—1188no—
528C4×D4—1182no—
529C4×D4—1182no—
530C4×D4C22×D5914yes—
531#117—594no—
532#117—594no—
533#117—594no—
534#117—1182no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—591no—
537C2×C4⋊C4—591no—
538C2×C4⋊C4—591no—
539C2×C4⋊C4—591no—
540C2×C4⋊C4—1181no—
541C2×C4⋊C4—1181no—
542C2×C4⋊C4C22×D5911yescharacteristic
543C2×C4⋊C4C22×D5911yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—591no—
546C2×C22⋊C4—591no—
547C2×C22⋊C4—1188no—
548C2×C22⋊C4—1188no—
549C2×C22⋊C4—1181no—
550C2×C22⋊C4—1181no—
551C2×C22⋊C4—1181no—
552C2×C22⋊C4—1181no—
553C2×C22⋊C4—1181no—
554C2×C22⋊C4—1181no—
555C2×C22⋊C4—1181no—
556C2×C22⋊C4—1181no—
557C2×C22⋊C4—1181no—
558C2×C42—21no—
559C2×C42—591no—
560C2×C42—1181no—
561C2×C42C22×D5911yescharacteristic
562#107—594no—
563#107—594no—
564#106—594no—
565#106C22×D5914yescomplemented
566C4⋊C8—594no—
567C4⋊C8—594no—
568#103—594no—
569#103C22×D5914yescomplemented
570#102—594no—
571#102—594no—
572#102—594no—
573#102—594no—
574#102—594no—
575#102C22×D5914yes—
576C22⋊C8—594no—
577C22⋊C8—594no—
578#97—594no—
579C4×C8C22×D5914yescomplemented
580C24—21no—
581C24—591no—
582C24—1184no—
583C24—1188no—
584C24—1181no—
585C24—1181no—
586C24—4722no—
587C24—4722no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—1184no—
592C2×Q8—4722no—
593C2×Q8C23×D5912yes—
594C2×D4—21no—
595C2×D4—22no—
596C2×D4—594no—
597C2×D4—592no—
598C2×D4—592no—
599C2×D4—1184no—
600C2×D4—1184no—
601C2×D4—1188no—
602C2×D4—11816no—
603C2×D4—1188no—
604C2×D4—1188no—
605C2×D4—1181no—
606C2×D4—1181no—
607C2×D4—1182no—
608C2×D4—1182no—
609C2×D4—1182no—
610C2×D4—4722no—
611C2×D4#1174568514yes—
612C2×D4C23×D5912yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—24no—
617C22×C4—82no—
618C22×C4—591no—
619C22×C4—591no—
620C22×C4—591no—
621C22×C4—592no—
622C22×C4—592no—
623C22×C4—1184no—
624C22×C4—1184no—
625C22×C4—1182no—
626C22×C4—1182no—
627C22×C4—1181no—
628C22×C4—1181no—
629C22×C4—1184no—
630C22×C4—1184no—
631C22×C4—4722no—
632C22×C4—4722no—
633C22×C4—4722no—
634C22×C4—4722no—
635C22×C4D4×D5911yescharacteristic
636C22×C4D4×D5911yescharacteristic
637C22×C4C23×D5911yescharacteristic
638SD16—28no—
639SD16—1188no—
640D8—1188no—
641D8—1188no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—592no—
645C2×C8—592no—
646C2×C8—1182no—
647C2×C8—1182no—
648C2×C8C23×D5912yes—
649C2×C8C23×D5912yes—
650C4⋊C4—24no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—594no—
654C4⋊C4—594no—
655C4⋊C4—592no—
656C4⋊C4—592no—
657C4⋊C4—1184no—
658C4⋊C4—1184no—
659C4⋊C4—1181no—
660C4⋊C4—1181no—
661C4⋊C4C23×D5912yes—
662C4⋊C4C23×D5912yes—
663C22⋊C4—24no—
664C22⋊C4—594no—
665C22⋊C4—594no—
666C22⋊C4—1184no—
667C22⋊C4—1184no—
668C22⋊C4—1184no—
669C22⋊C4—1184no—
670C22⋊C4—1184no—
671C22⋊C4—1184no—
672C22⋊C4—1184no—
673C22⋊C4—1184no—
674C22⋊C4—1184no—
675C42—24no—
676C42—592no—
677C42—592no—
678C42—1184no—
679C42D4×D5912yes—
680C42C23×D5912yes—
681C23—24no—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—592no—
686C23—11816no—
687C23—1182no—
688C23—1184no—
689C23—1182no—
690C23—1182no—
691C23—1182no—
692C23—1182no—
693C23—4724no—
694C23—4724no—
695C23—47216no—
696C23—2362no—
697C23—2362no—
698C23—2362no—
699C23—2362no—
700C23—2362no—
701C23C2×D4×D5911yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—42no—
705Q8—4724no—
706D4—24no—
707D4—22no—
708D4—594no—
709D4—11816no—
710D4—1184no—
711D4—1182no—
712D4—1182no—
713D4—1182no—
714D4—4724no—
715D4—2362no—
716D4C2×#1174568514yes—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—84no—
726C2×C4—592no—
727C2×C4—592no—
728C2×C4—592no—
729C2×C4—1182no—
730C2×C4—1182no—
731C2×C4—1182no—
732C2×C4—1184no—
733C2×C4—1182no—
734C2×C4—1182no—
735C2×C4—1182no—
736C2×C4—1182no—
737C2×C4—4724no—
738C2×C4—4724no—
739C2×C4—4724no—
740C2×C4—4724no—
741C2×C4—2362no—
742C2×C4—2362no—
743C2×C4C2×D4×D5912yes—
744C2×C4C2×D4×D5912yes—
745C2×C4C2×D4×D5911yescharacteristic
746C2×C4#41×D5912yes—
747C2×C4C2×#1174568512yes—
748C2×C4C24×D5911yescharacteristic
749C8—22no—
750C8—22no—
751C8—1182no—
752C8—1182no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—48no—
757C22—1182no—
758C22—1182no—
759C22—1182no—
760C22—1184no—
761C22—47216no—
762C22—4724no—
763C22—2362no—
764C22—2362no—
765C22—2362no—
766C22—2362no—
767C22—2362no—
768C22—2364no—
769C22—2368no—
770C22#1683791112yes—
771C22#1683820412yes—
772C22#1683820812yes—
773C22C22×D4×D5911yescharacteristic
774C4—22no—
775C4—22no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—1182no—
780C4—1182no—
781C4—1182no—
782C4—2362no—
783C4—2362no—
784C4#1683791112yes—
785C4C2×#41×D5911yescharacteristic
786C4C22×#1174568511yescharacteristic
787C2—44no—
788C2—4722no—
789C2—2362no—
790C2—2364no—
791C2#2143428614yesdirect product factor
792C2C2×#1683791111yescharacteristic
793C2C2×#1683820411yescharacteristic
794C2C2×#1683820811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C4×SD16×C59C2
socleC23×C59C22×D4
prime radicalC2×#16837537C2
hypercenterC2×C4×SD16D59
hypocenterC59C2×#3118
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×#16838024C2semidirect
2. C2×#16837874C2semidirect
3. #21434286C2direct (N × H)
4. C2×#16837742C2semidirect
5. C2×#16837728C2semidirect
6. C2×#16837691C2semidirect
7. C2×#16837680C2semidirect
8. C2×#16837620C2semidirect
9. C2×#16837619C2semidirect
10. C2×#16837551C2semidirect
12. C2×#16837512C2semidirect
13. C2×#16837500C2semidirect
14. C2×C4×D472C2semidirect
15. C2×#16837461C2semidirect
16. C2×C4×SD16×C59C2semidirect
22. #16838024C22semidirect
23. C2×#14273726C22semidirect
25. C2×#14273716C22semidirect
32. #16837874C22semidirect
34. C2×C4×D236C22semidirect
43. #16837742C22semidirect
44. #16837728C22semidirect
45. #16837691C22semidirect
46. #16837680C22semidirect
47. #16837620C22semidirect
48. #16837619C22semidirect
49. #16837551C22semidirect
51. #16837512C22semidirect
52. #16837500C22semidirect
53. C4×D472C22semidirect
54. #16837461C22semidirect
55. C2×#14273661C22semidirect
56. C2×#14273660C22semidirect
57. C2×#14273658C22semidirect
58. C2×Dic59⋊C8C22semidirect
59. C2×Dic59⋊C8C22semidirect
60. C2×#14273651C22semidirect
62. C2×#14273649C22semidirect
65. C2×#14273647C22semidirect
68. C2×#14273638C22semidirect
70. C2×C4×Q8×C59C22semidirect
72. C4×SD16×C59C22semidirect
73. C2×#106×C59C22semidirect
74. C2×#103×C59C22semidirect
76. C2×C4×C8×C59C22semidirect
101. #14273726C23semidirect
104. #14273716C23semidirect
115. C4×D236C23semidirect
147. #14273661C23semidirect
148. #14273660C23semidirect
149. #14273658C23semidirect
150. Dic59⋊C8C23semidirect
151. Dic59⋊C8C23semidirect
152. #14273651C23semidirect
154. #14273649C23semidirect
157. #14273647C23semidirect
160. #14273638C23semidirect
169. C4×Q8×C59C23semidirect
178. #106×C59C23semidirect
179. #103×C59C23semidirect
181. C4×C8×C59C23semidirect
403. C2×C4×SD16D59semidirect
407. C2×C59#3118semidirect
431. C2×C4×Q8C2×D59semidirect
453. C4×SD16C2×D59semidirect
459. C2×#106C2×D59semidirect
463. C2×#103C2×D59semidirect
473. C2×C4×C8C2×D59semidirect
474. C59C2×#3118semidirect
518. C4×Q8C22×D59semidirect
565. #106C22×D59semidirect
569. #103C22×D59semidirect
579. C4×C8C22×D59semidirect
791. C2#21434286direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380242
C2×#168378742
#214342862
C2×#168377422
C2×#168377282
C2×#168376912
C2×#168376802
C2×#168376202
C2×#168376192
C2×#168375512
C2×#168375372
C2×#168375122
C2×#168375002
C2×C4×D4722
C2×#168374612
C2×C4×SD16×C592
C2×#311859