Finite Group Databasebeta

← C2×#21434028 #29456477

Subgroups — C2×#21434028 #29456477

Order 15104.

2346 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837915C211yesmaximal, characteristic
2C2×#117×D59C211yesmaximal, characteristic, complemented
3#21434028C2116yesmaximal, direct product factor
4C2×#16837742C211yesmaximal, characteristic, complemented
5C2×#16837741C211yesmaximal, characteristic, complemented
6C2×#16837740C211yesmaximal, characteristic, complemented
7C2×#16837729C211yesmaximal, characteristic, complemented
8C2×#16837728C211yesmaximal, characteristic, complemented
9C2×#16837727C211yesmaximal, characteristic, complemented
10C2×#16837726C211yesmaximal, characteristic, complemented
11C2×#16837443C211yesmaximal, characteristic, complemented
12C2×#16837441C211yesmaximal, characteristic, complemented
13C2×#16837402C211yesmaximal, characteristic, complemented
14C2×#16837402C211yesmaximal, characteristic, complemented
15C2×#16837364C211yesmaximal, characteristic, complemented
16C2×C59×#485C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C23×C4×D59C2211yescharacteristic
19C22×#11745659C2211yescharacteristic
20C22×#11745659C2211yescharacteristic
21#16837915—24no—
22#16837915C2218yes—
23C2×#14273712—21no—
24C2×#14273703C2211yescharacteristic
25C2×#14273702C2211yescharacteristic
26C2×#14273701C2211yescharacteristic
27C2×#14273697—21no—
28C2×#14273689—21no—
29C2×(C22⋊D59)⋊C4—21no—
30C2×#14273686C2211yescharacteristic
31C2×#14273685C2211yescharacteristic
32C2×#14273685C2211yescharacteristic
33C2×#14273685C2211yescharacteristic
34C2×#14273684—21no—
35C2×#14273683—21no—
36#117×D59—24no—
37#117×D59C2218yescomplemented
38C2×C4⋊C4×D59C2211yescharacteristic
39C2×C4⋊C4×D59C2211yescharacteristic
40C2×C22⋊C4×D59—21no—
41C2×C42×D59—21no—
42#16837742C2218yescomplemented
43#16837741C2218yescomplemented
44#16837740C2218yescomplemented
45#16837729C2218yescomplemented
46#16837728C2218yescomplemented
47#16837727C2218yescomplemented
48#16837726C2218yescomplemented
49#16837443C2218yescomplemented
50#16837441C2218yescomplemented
51C2×#14273661C2211yescharacteristic, complemented
52C2×#14273660C2211yescharacteristic, complemented
53C2×#14273660C2211yescharacteristic, complemented
54C2×#14273659C2211yescharacteristic, complemented
55C2×#14273658C2211yescharacteristic, complemented
56C2×#14273658C2211yescharacteristic, complemented
57#16837402C2218yescomplemented
58#16837402C2218yescomplemented
59C2×#14273651C2211yescharacteristic, complemented
60C2×#14273651C2211yescharacteristic, complemented
61C2×#14273649C2211yescharacteristic, complemented
62C2×#14273649C2211yescharacteristic, complemented
63C2×#14273647C2211yescharacteristic, complemented
64C2×#14273647C2211yescharacteristic, complemented
65#16837364C2218yescomplemented
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×(C2×D59)⋊C8C2211yescharacteristic
69C2×C22⋊Q8×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C59×#485C2218yescomplemented
72C2×#107×C59C2211yescharacteristic, complemented
73C2×#106×C59C2211yescharacteristic, complemented
74C2×#103×C59C2211yescharacteristic, complemented
75C2×#103×C59C2211yescharacteristic, complemented
76C2×C22⋊C8×C59C2211yescharacteristic
77C24×D59D411yescharacteristic
78C2×#11745689—22no—
79C2×#11745689—24no—
80C2×#11745689—24no—
81C2×#11745689C2314yes—
82C22×D236—21no—
83C22×D236—21no—
84C22×D236C2311yescharacteristic
85C22×C22⋊D59—21no—
86C23×Dic59D411yescharacteristic
87C22×C4×D59—24no—
88C22×C4×D59—24no—
89C22×C4×D59—21no—
90C22×C4×D59—21no—
91C22×C4×D59—21no—
92C22×C4×D59D411yescharacteristic
93C22×C4×D59D414yes—
94C22×C4×D59D411yescharacteristic
95C22×C4×D59C2311yescharacteristic
96C22×C4×D59C2314yes—
97C22×C4×D59C2311yescharacteristic
98C2×#11745659—24no—
99C2×#11745659—24no—
100C2×#11745659C2314yes—
101C2×#11745659C2314yes—
102C22×C59⋊C8C2311yescharacteristic
103C22×C59⋊C8C2311yescharacteristic
104#14273712—28no—
105#14273703—22no—
106#14273703C2314yes—
107#14273702—22no—
108#14273702C2314yes—
109#14273701—22no—
110#14273701C2314yes—
111#14273697—28no—
112#14273689—28no—
113(C22⋊D59)⋊C4—28no—
114#14273686—22no—
115#14273686C2314yes—
116#14273685—22no—
117#14273685—22no—
118#14273685—22no—
119#14273685C2314yes—
120#14273685C2314yes—
121#14273685C2314yes—
122#14273684—28no—
123#14273683—28no—
124C2×C4⋊Dic59C2311yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C4⋊C4×D59—22no—
131C4⋊C4×D59—22no—
132C4⋊C4×D59C2314yes—
133C4⋊C4×D59C2314yes—
134C2×C22⋊Dic59—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—
141C22⋊C4×D59—28no—
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59—21no—
146C42×D59—28no—
147#14273661C2314yescomplemented
148#14273660C2314yescomplemented
149#14273660C2314yescomplemented
150#14273659C2314yescomplemented
151#14273658C2314yescomplemented
152#14273658C2314yescomplemented
153#14273651C2314yescomplemented
154#14273651C2314yescomplemented
155#14273649C2314yescomplemented
156#14273649C2314yescomplemented
157#14273647C2314yescomplemented
158#14273647C2314yescomplemented
159C22⋊(C59⋊C8)C2314yes—
160(C2×D59)⋊C8C2314yes—
161(C2×D59)⋊C8C2314yes—
162C22×Q8×C59C2311yescharacteristic
163C23×C4×C59C2311yescharacteristic
164C22×C8×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166C22⋊Q8×C59—22no—
167C22⋊Q8×C59C2314yes—
168#117×C59—22no—
169#117×C59C2314yes—
170C2×C4⋊C4×C59—21no—
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×C59C2314yescomplemented
178#106×C59C2314yescomplemented
179#103×C59C2314yescomplemented
180#103×C59C2314yescomplemented
181C22⋊C8×C59C2314yes—
182C24×C59C2×D411yescharacteristic
183C23×D59—24no—
184C23×D59—21no—
185C23×D59—42no—
186C23×D59—42no—
187C23×D59C2×D411yescharacteristic
188C23×D59C2×D411yescharacteristic
189C23×D59C2×D414yes—
190C2×Q8×C59—21no—
191C2×Q8×C59—22no—
192C2×Q8×C59—22no—
193C2×Q8×C59C2412yes—
194C22×C4×C59—22no—
195C22×C4×C59—22no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2×D412yes—
202C22×C4×C59C2412yes—
203C22×C4×C59C2411yescharacteristic
204C2×C22⋊D59—24no—
205C2×C22⋊D59—44no—
206C22×Dic59—24no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59C2×D411yescharacteristic
211C22×Dic59C2×D414yes—
212C22×Dic59C2×D411yescharacteristic
213#11745689—28no—
214#11745689—28no—
215#11745689—48no—
216C2×D236—22no—
217C2×D236—22no—
218C2×D236—24no—
219C2×D236—24no—
220C2×D236—21no—
221C2×D236—44no—
222C2×D236—44no—
223C2×D236C2412yes—
224C2×C4×D59—24no—
225C2×C4×D59—22no—
226C2×C4×D59—22no—
227C2×C4×D59—24no—
228C2×C4×D59—216no—
229C2×C4×D59—28no—
230C2×C4×D59—28no—
231C2×C4×D59—24no—
232C2×C4×D59—24no—
233C2×C4×D59—24no—
234C2×C4×D59—44no—
235C2×C4×D59—44no—
236C2×C4×D59—44no—
237C2×C4×D59C2×D414yes—
238C2×C4×D59C2×D414yes—
239C2×C4×D59C2×D412yes—
240C2×C4×D59C2×D412yes—
241C2×C4×D59#4114yes—
242C2×C4×D59#4114yes—
243C2×C4×D59C2412yes—
244C2×C4×D59C2412yes—
245C2×C8×C59—22no—
246C2×C8×C59—22no—
247C2×C8×C59C2412yes—
248C2×C8×C59C2412yes—
249C4⋊C4×C59—24no—
250C4⋊C4×C59—21no—
251C4⋊C4×C59—21no—
252C4⋊C4×C59—21no—
253C4⋊C4×C59C2412yes—
254C4⋊C4×C59C2412yes—
255C4⋊C4×C59C2412yes—
256C22⋊C4×C59—24no—
257C22⋊C4×C59—24no—
258C42×C59—24no—
259C22⋊Dic59—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)⋊C4—24no—
266C4⋊Dic59—21no—
267C4⋊Dic59—21no—
268C4⋊Dic59—21no—
269C4⋊Dic59C2412yes—
270C4⋊Dic59C2412yes—
271C4⋊Dic59C2412yes—
272Dic59⋊C4—24no—
273Dic59⋊C4—24no—
274Dic59⋊C4—24no—
275C4×Dic59—24no—
276C4×Dic59—24no—
277C4×Dic59—24no—
278C4×Dic59—24no—
279C2×C59⋊C8—22no—
280C2×C59⋊C8—22no—
281C2×C59⋊C8C2412yes—
282C2×C59⋊C8C2412yes—
283#11745659—28no—
284#11745659—28no—
285C23×C59—22no—
286C23×C59—22no—
287C23×C59—22no—
288C23×C59C22×D412yes—
289C23×C59C22×D411yescharacteristic
290C22×D59—22no—
291C22×D59—22no—
292C22×D59—22no—
293C22×D59—22no—
294C22×D59—22no—
295C22×D59—28no—
296C22×D59—22no—
297C22×D59—44no—
298C22×D59—44no—
299C22×D59—416no—
300C22×D59—42no—
301C22×D59—42no—
302C22×D59—42no—
303C22×D59#12314yes—
304C22×D59C22×D412yes—
305C22×D59C22×D412yes—
306Q8×C59—22no—
307Q8×C59—22no—
308Q8×C59—42no—
309C2×C4×C59—22no—
310C2×C4×C59—24no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—42no—
318C2×C4×C59—42no—
319C2×C4×C59—42no—
320C2×C4×C59—42no—
321C2×C4×C59C22×D412yes—
322C2×C4×C59C22×D411yescharacteristic
323C2×C4×C59C2×#4112yes—
324C2×C4×C59C2×#4112yes—
325C2×C4×C59C2511yescharacteristic
326C22⋊D59—48no—
327C2×Dic59—22no—
328C2×Dic59—28no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—42no—
333C2×Dic59—42no—
334C2×Dic59—42no—
335C2×Dic59#12314yes—
336C2×Dic59C22×D412yes—
337C2×Dic59C22×D412yes—
338D236—22no—
339D236—22no—
340D236—48no—
341D236—48no—
342D236—42no—
343C4×D59—28no—
344C4×D59—24no—
345C4×D59—22no—
346C4×D59—22no—
347C4×D59—28no—
348C4×D59—48no—
349C4×D59—48no—
350C4×D59—48no—
351C4×D59#12318yes—
352C4×D59C2×#4114yes—
353C4×D59C2×#4114yes—
354C8×C59—22no—
355C8×C59—22no—
356C59⋊C8—22no—
357C59⋊C8—22no—
358C2×#3093—591nomaximal, Sylow
359C22×C59—22no—
360C22×C59—22no—
361C22×C59—22no—
362C22×C59—44no—
363C22×C59C2×#12312yes—
364C22×C59#57512yes—
365C22×C59#57512yes—
366C22×C59C23×D411yescharacteristic
367C2×D59—28no—
368C2×D59—22no—
369C2×D59—22no—
370C2×D59—22no—
371C2×D59—22no—
372C2×D59—22no—
373C2×D59—416no—
374C2×D59—44no—
375C2×D59—42no—
376C2×D59—42no—
377C2×D59—42no—
378C2×D59—84no—
379C2×D59C2×#12314yes—
380C4×C59—22no—
381C4×C59—42no—
382C4×C59—42no—
383C4×C59—42no—
384C4×C59—42no—
385C4×C59C2×#12312yes—
386C4×C59C22×#4111yescharacteristic
387C4×C59C22×#4111yescharacteristic
388Dic59—22no—
389Dic59—42no—
390Dic59—42no—
391Dic59—42no—
392Dic59C2×#12314yes—
393C2×#525—591no—
394C22×#117—591no—
395#3093—5916no—
396C2×#485—591no—
397C2×#485—591no—
398C2×#485—591no—
399C2×#485D5911yescharacteristic, complemented
400C2×#482—591no—
401C2×#482—591no—
402C2×#482—591no—
403C2×#482—591no—
404C2×#428—591no—
405C2×#428—591no—
406C2×#417—591no—
407C2×#417—591no—
408C2×#407—591no—
409C2×C59—42no—
410C2×C59#309314yescomplemented
411C2×C59C22×#12311yescharacteristic
412C2×C59C2×#57511yescharacteristic
413C2×C59C2×#57511yescharacteristic
414D59—24no—
415D59—42no—
416D59—82no—
417C22×#41—591no—
418C24×C4—591no—
419C22×M16—591no—
420C22×M16—591no—
421#525—598no—
422#525—1184no—
423C2×#123—1181no—
424C2×C22⋊Q8—591no—
425C2×C22⋊Q8C2×D5911yescharacteristic
426C2×#121—591no—
427C2×#121—591no—
428C2×#120—1181no—
429C2×C4×D4—1181no—
430C2×C4×D4—1181no—
431C2×#117—591no—
432C2×#117—598no—
433C2×#117—591no—
434C2×#117—591no—
435C2×#117—591no—
436C2×#117—1181no—
437C2×#117—1181no—
438C2×#117—1184no—
439C2×#117C2×D5911yescharacteristic
440C22×C4⋊C4—591no—
441C22×C4⋊C4—591no—
442C22×C22⋊C4—1181no—
443C22×C42—1181no—
444#485—598no—
445#485—598no—
446#485—598no—
447#485C2×D5918yescomplemented
448#482—598no—
449#482—598no—
450#482—598no—
451#482—598no—
452#428—598no—
453#428—598no—
454C2×#107—591no—
455C2×#107—591no—
456C2×#107—591no—
457C2×#107C2×D5911yescharacteristic, complemented
458C2×#106—591no—
459C2×#106—591no—
460C2×#106—591no—
461C2×#106C2×D5911yescharacteristic, complemented
462#417—598no—
463#417—598no—
464C2×#103—591no—
465C2×#103—591no—
466C2×#103C2×D5911yescharacteristic, complemented
467C2×#103C2×D5911yescharacteristic, complemented
468C2×#102—591no—
469C2×#102—591no—
470C2×#102—591no—
471C2×#102—591no—
472#407—598no—
473C2×C22⋊C8—591no—
474C2×C22⋊C8—591no—
475C2×C22⋊C8—591no—
476C2×C22⋊C8C2×D5911yescharacteristic
477C59C2×#309311yescharacteristic, complemented, Sylow
478C25—591no—
479C2×#41—594no—
480C2×#41—1182no—
481C2×#41—1184no—
482C2×#41—1184no—
483C22×Q8C22×D5911yescharacteristic
484C22×D4—591no—
485C22×D4—1181no—
486C22×D4—1181no—
487C22×D4—1181no—
488C23×C4—591no—
489C23×C4—591no—
490C23×C4—591no—
491C23×C4—594no—
492C23×C4—591no—
493C23×C4—591no—
494C23×C4—594no—
495C23×C4—1184no—
496C23×C4—1184no—
497C23×C4—1181no—
498C23×C4—1181no—
499C23×C4—1181no—
500C23×C4C22×D5911yescharacteristic
501C2×M16—594no—
502C2×M16—594no—
503C2×M16—1184no—
504C2×M16—1184no—
505C22×C8—591no—
506C22×C8—591no—
507C22×C8C22×D5911yescharacteristic
508C22×C8C22×D5911yescharacteristic
509#123—1188no—
510C22⋊Q8—22no—
511C22⋊Q8—594no—
512C22⋊Q8—1182no—
513C22⋊Q8C22×D5914yes—
514#121—594no—
515#121—594no—
516#121—1182no—
517#121—1182no—
518#120—1188no—
519C4×D4—1188no—
520C4×D4—1188no—
521#117—22no—
522#117—594no—
523#117—594no—
524#117—594no—
525#117—594no—
526#117—1188no—
527#117—1188no—
528#117—1182no—
529#117—1182no—
530#117—1182no—
531#117—1182no—
532#117C22×D5914yes—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—591no—
535C2×C4⋊C4—591no—
536C2×C4⋊C4—591no—
537C2×C4⋊C4—594no—
538C2×C4⋊C4—594no—
539C2×C4⋊C4—1182no—
540C2×C4⋊C4—1182no—
541C2×C4⋊C4—1181no—
542C2×C4⋊C4—1181no—
543C2×C4⋊C4—1181no—
544C2×C4⋊C4C22×D5911yescharacteristic
545C2×C4⋊C4C22×D5911yescharacteristic
546C2×C4⋊C4C22×D5911yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1188no—
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×C42—21no—
558C2×C42—1188no—
559C2×C42—1181no—
560C2×C42—1181no—
561C2×C42—1181no—
562C2×C42—1181no—
563#107—594no—
564#107—594no—
565#107—594no—
566#107C22×D5914yescomplemented
567#106—594no—
568#106—594no—
569#106—594no—
570#106C22×D5914yescomplemented
571#103—594no—
572#103—594no—
573#103C22×D5914yescomplemented
574#103C22×D5914yescomplemented
575#102—594no—
576#102—594no—
577#102—594no—
578#102—594no—
579C22⋊C8—594no—
580C22⋊C8—594no—
581C22⋊C8—594no—
582C22⋊C8C22×D5914yes—
583C24—591no—
584C24—591no—
585C24—594no—
586C24—1184no—
587C24—1181no—
588C24—2362no—
589C24—2362no—
590C24D4×D5911yescharacteristic
591#41—1188no—
592#41—1188no—
593#41—2368no—
594C2×Q8—21no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8C23×D5912yes—
598C2×D4—592no—
599C2×D4—1184no—
600C2×D4—1184no—
601C2×D4—1184no—
602C2×D4—1181no—
603C2×D4—1182no—
604C2×D4—1182no—
605C2×D4—2364no—
606C2×D4—2364no—
607C2×D4—2364no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—591no—
615C22×C4—592no—
616C22×C4—594no—
617C22×C4—594no—
618C22×C4—592no—
619C22×C4—594no—
620C22×C4—591no—
621C22×C4—594no—
622C22×C4—594no—
623C22×C4—592no—
624C22×C4—592no—
625C22×C4—1184no—
626C22×C4—11816no—
627C22×C4—1188no—
628C22×C4—1188no—
629C22×C4—1184no—
630C22×C4—1184no—
631C22×C4—1184no—
632C22×C4—1184no—
633C22×C4—1184no—
634C22×C4—1182no—
635C22×C4—1182no—
636C22×C4—1181no—
637C22×C4—1181no—
638C22×C4—1181no—
639C22×C4—2364no—
640C22×C4—2364no—
641C22×C4—2364no—
642C22×C4D4×D5912yes—
643C22×C4D4×D5911yescharacteristic
644C22×C4C23×D5912yes—
645C22×C4C23×D5911yescharacteristic
646M16—1188no—
647M16—1188no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—592no—
651C2×C8—592no—
652C2×C8—1182no—
653C2×C8—1182no—
654C2×C8C23×D5912yes—
655C2×C8C23×D5912yes—
656C4⋊C4—24no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—592no—
661C4⋊C4—592no—
662C4⋊C4—592no—
663C4⋊C4—1184no—
664C4⋊C4—1184no—
665C4⋊C4—1184no—
666C4⋊C4—1181no—
667C4⋊C4—1181no—
668C4⋊C4—1181no—
669C4⋊C4C23×D5912yes—
670C4⋊C4C23×D5912yes—
671C4⋊C4C23×D5912yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—1184no—
675C22⋊C4—1184no—
676C22⋊C4—1184no—
677C22⋊C4—1184no—
678C22⋊C4—1184no—
679C22⋊C4—1184no—
680C22⋊C4—1184no—
681C42—24no—
682C42—1184no—
683C42—1184no—
684C42—1184no—
685C42—1184no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—594no—
690C23—592no—
691C23—592no—
692C23—1188no—
693C23—1182no—
694C23—1182no—
695C23—1182no—
696C23—1182no—
697C23—1182no—
698C23—1182no—
699C23—2364no—
700C23—2364no—
701C23—23616no—
702C23—2362no—
703C23—2362no—
704C23—2362no—
705C23C2×D4×D5912yes—
706C23C2×D4×D5911yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—42no—
710D4—1182no—
711D4—1182no—
712D4—2368no—
713D4—2368no—
714D4—2368no—
715D4—2362no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—594no—
729C2×C4—592no—
730C2×C4—598no—
731C2×C4—594no—
732C2×C4—594no—
733C2×C4—592no—
734C2×C4—1188no—
735C2×C4—1188no—
736C2×C4—1188no—
737C2×C4—1182no—
738C2×C4—1184no—
739C2×C4—1182no—
740C2×C4—1182no—
741C2×C4—1182no—
742C2×C4—1182no—
743C2×C4—1182no—
744C2×C4—2368no—
745C2×C4—2368no—
746C2×C4—2368no—
747C2×C4—2362no—
748C2×C4—2362no—
749C2×C4—2362no—
750C2×C4C2×D4×D5912yes—
751C2×C4C2×D4×D5911yescharacteristic
752C2×C4#41×D5912yes—
753C2×C4#41×D5912yes—
754C2×C4C24×D5911yescharacteristic
755C8—22no—
756C8—22no—
757C8—1182no—
758C8—1182no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—44no—
763C22—594no—
764C22—1182no—
765C22—1182no—
766C22—1188no—
767C22—1182no—
768C22—1182no—
769C22—1182no—
770C22—4724no—
771C22—23616no—
772C22—2362no—
773C22—2362no—
774C22—2362no—
775C22—2364no—
776C22#123×D5912yes—
777C22#1683819912yes—
778C22#1683820112yes—
779C22C22×D4×D5911yescharacteristic
780C4—22no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—594no—
786C4—1182no—
787C4—2362no—
788C4—2362no—
789C4—2362no—
790C4#123×D5912yes—
791C4C2×#41×D5911yescharacteristic
792C4C2×#41×D5911yescharacteristic
793C2—42no—
794C2—1184no—
795C2—4722no—
796C2—2362no—
797C2#2143402814yesdirect product factor
798C2C2×#123×D5911yescharacteristic
799C2C2×#1683819911yescharacteristic
800C2C2×#1683820111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#485C2
socleC23×C59C22×D4
prime radicalC2×#16837915C2
hypercenterC2×#485D59
hypocenterC59C2×#3093
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
2. C2×#117×D59C2semidirect
3. #21434028C2direct (N × H)
4. C2×#16837742C2semidirect
5. C2×#16837741C2semidirect
6. C2×#16837740C2semidirect
7. C2×#16837729C2semidirect
8. C2×#16837728C2semidirect
9. C2×#16837727C2semidirect
10. C2×#16837726C2semidirect
11. C2×#16837443C2semidirect
12. C2×#16837441C2semidirect
13. C2×#16837402C2semidirect
14. C2×#16837402C2semidirect
15. C2×#16837364C2semidirect
16. C2×C59×#485C2semidirect
37. #117×D59C22semidirect
42. #16837742C22semidirect
43. #16837741C22semidirect
44. #16837740C22semidirect
45. #16837729C22semidirect
46. #16837728C22semidirect
47. #16837727C22semidirect
48. #16837726C22semidirect
49. #16837443C22semidirect
50. #16837441C22semidirect
51. C2×#14273661C22semidirect
52. C2×#14273660C22semidirect
53. C2×#14273660C22semidirect
54. C2×#14273659C22semidirect
55. C2×#14273658C22semidirect
56. C2×#14273658C22semidirect
57. #16837402C22semidirect
58. #16837402C22semidirect
59. C2×#14273651C22semidirect
60. C2×#14273651C22semidirect
61. C2×#14273649C22semidirect
62. C2×#14273649C22semidirect
63. C2×#14273647C22semidirect
64. C2×#14273647C22semidirect
65. #16837364C22semidirect
71. C59×#485C22semidirect
72. C2×#107×C59C22semidirect
73. C2×#106×C59C22semidirect
74. C2×#103×C59C22semidirect
75. C2×#103×C59C22semidirect
147. #14273661C23semidirect
148. #14273660C23semidirect
149. #14273660C23semidirect
150. #14273659C23semidirect
151. #14273658C23semidirect
152. #14273658C23semidirect
153. #14273651C23semidirect
154. #14273651C23semidirect
155. #14273649C23semidirect
156. #14273649C23semidirect
157. #14273647C23semidirect
158. #14273647C23semidirect
177. #107×C59C23semidirect
178. #106×C59C23semidirect
179. #103×C59C23semidirect
180. #103×C59C23semidirect
399. C2×#485D59semidirect
410. C2×C59#3093semidirect
447. #485C2×D59semidirect
457. C2×#107C2×D59semidirect
461. C2×#106C2×D59semidirect
466. C2×#103C2×D59semidirect
467. C2×#103C2×D59semidirect
477. C59C2×#3093semidirect
566. #107C22×D59semidirect
570. #106C22×D59semidirect
573. #103C22×D59semidirect
574. #103C22×D59semidirect
797. C2#21434028direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379152
C2×#117×D592
#214340282
C2×#168377422
C2×#168377412
C2×#168377402
C2×#168377292
C2×#168377282
C2×#168377272
C2×#168377262
C2×#168374432
C2×#168374412
C2×#168374022
C2×#168373642
C2×C59×#4852
C2×#309359