Finite Group Databasebeta

← C2×#21434449 #29457924

Subgroups — C2×#21434449 #29457924

Order 15104.

2262 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838032C211yesmaximal, characteristic, complemented
2C2×#16837970C211yesmaximal, characteristic
3#21434449C2116yesmaximal, direct product factor
4C2×#16837768C211yesmaximal, characteristic, complemented
5C2×#16837765C211yesmaximal, characteristic, complemented
6C2×#16837763C211yesmaximal, characteristic, complemented
7C2×#16837761C211yesmaximal, characteristic, complemented
8C2×#16837758C211yesmaximal, characteristic, complemented
9C2×#16837749C211yesmaximal, characteristic, complemented
10C2×#16837747C211yesmaximal, characteristic, complemented
11C2×#16837402C211yesmaximal, characteristic, complemented
12C2×#16837405C211yesmaximal, characteristic, complemented
13C2×#16837397C211yesmaximal, characteristic, complemented
14C2×#102×D59C211yesmaximal, characteristic, complemented
15C2×#16837356C211yesmaximal, characteristic, complemented
16C2×C59×#488C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C22×D4×D59C2211yescharacteristic
19C22×#11745659C2211yescharacteristic
20C22×C8×D59C2211yescharacteristic
21#16838032—24no—
22#16838032C2218yescomplemented
23#16837970—24no—
24#16837970C2218yes—
25C2×#14273727C2211yescharacteristic, complemented
26C2×#14273726—21no—
27C2×#14273726C2211yescharacteristic, complemented
28C2×#14273724C2211yescharacteristic
29C2×#14273723C2211yescharacteristic
30C2×#14273718C2211yescharacteristic, complemented
31C2×#14273717—21no—
32C2×#14273716C2211yescharacteristic
33C2×#14273707—21no—
34C2×#14273705—21no—
35C2×#14273700—21no—
36C2×#14273700—21no—
37C2×#14273697—21no—
38C2×#14273697—21no—
39C2×#14273685C2211yescharacteristic
40C2×#14273684C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic
42#16837768C2218yescomplemented
43#16837765C2218yescomplemented
44#16837763C2218yescomplemented
45#16837761C2218yescomplemented
46#16837758C2218yescomplemented
47#16837749C2218yescomplemented
48#16837747C2218yescomplemented
49#16837405C2218yescomplemented
50#16837402C2218yescomplemented
51#16837397C2218yescomplemented
52C2×#14273651C2211yescharacteristic, complemented
53C2×#14273651C2211yescharacteristic, complemented
54C2×#14273649C2211yescharacteristic
55C2×#14273649C2211yescharacteristic
56C2×#14273649C2211yescharacteristic, complemented
57C2×#14273649C2211yescharacteristic, complemented
58C2×#14273648C2211yescharacteristic
59C2×#14273648C2211yescharacteristic
60C2×#14273647C2211yescharacteristic
61C2×#14273647C2211yescharacteristic
62C2×#14273647C2211yescharacteristic, complemented
63C2×#14273647C2211yescharacteristic, complemented
64#102×D59C2218yescomplemented
65#16837356C2218yescomplemented
66C2×#14273638C2211yescharacteristic, complemented
67C2×#14273637C2211yescharacteristic, complemented
68C2×C8×Dic59C2211yescharacteristic, complemented
69C2×#125×C59C2211yescharacteristic, complemented
70C2×#124×C59C2211yescharacteristic
71C59×#488C2218yescomplemented
72C2×#103×C59C2211yescharacteristic, complemented
73C2×#103×C59C2211yescharacteristic, complemented
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C2×#11745689—22no—
79C2×#11745689—24no—
80C2×#11745689—24no—
81C2×#11745689C2314yes—
82C22×Dic118—21no—
83C22×Dic118—21no—
84C22×D236—21no—
85C22×D236—21no—
86C22×D236—21no—
87C22×D236C2311yescharacteristic
88C22×D236C2311yescharacteristic
89C22×C22⋊D59—21no—
90C22×C22⋊D59—21no—
91C22×C22⋊D59—21no—
92C2×D4×D59—22no—
93C2×D4×D59—24no—
94C2×D4×D59—24no—
95C2×D4×D59C2314yes—
96C22×C4×D59—21no—
97C22×C4×D59—21no—
98C22×C4×D59C2311yescharacteristic
99C2×#11745659—24no—
100C2×#11745659C2314yes—
101C22×C59⋊C8C2311yescharacteristic
102C22×C59⋊C8C2311yescharacteristic
103C2×C8×D59—24no—
104C2×C8×D59C2314yes—
105#14273727—22no—
106#14273727C2314yescomplemented
107#14273726—28no—
108#14273726—22no—
109#14273726C2314yescomplemented
110#14273724—22no—
111#14273724C2314yes—
112#14273723—22no—
113#14273723C2314yes—
114#14273718—22no—
115#14273718C2314yescomplemented
116#14273717—28no—
117#14273716—22no—
118#14273716C2314yes—
119#14273707—28no—
120#14273705—28no—
121#14273700—28no—
122#14273700—28no—
123#14273697—28no—
124#14273697—28no—
125#14273685—22no—
126#14273685C2314yes—
127#14273684D414yes—
128#14273684C2314yes—
129C2×C4⋊Dic59—21no—
130C2×C4⋊Dic59—21no—
131C2×C4⋊Dic59C2311yescharacteristic
132C2×C4⋊Dic59C2311yescharacteristic
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4D411yescharacteristic
137C2×Dic59⋊C4D411yescharacteristic
138C4⋊C4×D59—22no—
139C4⋊C4×D59C2314yes—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4D411yescharacteristic
144C2×(C2×D59)⋊C4D411yescharacteristic
145C2×C4×Dic59—21no—
146C2×C4×Dic59C2311yescharacteristic
147#14273651C2314yescomplemented
148#14273651C2314yescomplemented
149#14273649C2314yes—
150#14273649C2314yes—
151#14273649C2314yescomplemented
152#14273649C2314yescomplemented
153#14273648C2314yes—
154#14273648C2314yes—
155#14273647C2314yes—
156#14273647C2314yes—
157#14273647C2314yescomplemented
158#14273647C2314yescomplemented
159#14273638C2314yescomplemented
160#14273637C2314yescomplemented
161C8×Dic59C2314yescomplemented
162C22×Q8×C59C2311yescharacteristic
163C22×D4×C59C2311yescharacteristic
164C22×C8×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166#125×C59—22no—
167#125×C59C2314yescomplemented
168#124×C59—22no—
169#124×C59C2314yes—
170C2×C4⋊C4×C59—21no—
171C2×C4⋊C4×C59—21no—
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59—21no—
176C2×C42×C59C2311yescharacteristic
177#103×C59C2314yescomplemented
178#103×C59C2314yescomplemented
179#102×C59C2314yes—
180#102×C59C2314yes—
181C4×C8×C59C2314yescomplemented
182C24×C59—21no—
183C23×D59—21no—
184C23×D59—21no—
185C23×D59—24no—
186C23×D59—44no—
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—22no—
197C2×D4×C59C2412yes—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×D411yescharacteristic
203C22×C4×C59C2411yescharacteristic
204C2×C22⋊D59—24no—
205C2×C22⋊D59—24no—
206C2×C22⋊D59—24no—
207C2×C22⋊D59—44no—
208C2×C22⋊D59—82no—
209C2×C22⋊D59—82no—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59C2×D411yescharacteristic
213C22×Dic59C2×D411yescharacteristic
214C22×Dic59C2×D411yescharacteristic
215#11745689—28no—
216#11745689—28no—
217#11745689—48no—
218D4×D59—28no—
219D4×D59—28no—
220D4×D59—48no—
221C2×D236—22no—
222C2×D236—22no—
223C2×D236—22no—
224C2×D236—22no—
225C2×D236—24no—
226C2×D236—21no—
227C2×D236—21no—
228C2×D236—24no—
229C2×D236—24no—
230C2×D236—44no—
231C2×D236—82no—
232C2×D236—82no—
233C2×D236C2412yes—
234C2×D236C2412yes—
235C2×C4×D59—24no—
236C2×C4×D59—24no—
237C2×C4×D59—44no—
238C2×C4×D59—82no—
239C2×C4×D59C2×D412yes—
240C2×C4×D59#4114yes—
241C2×C4×D59#4114yes—
242C2×C4×D59C2412yes—
243C2×Dic118—24no—
244C2×Dic118—24no—
245C2×Dic118—82no—
246C2×Dic118—82no—
247C2×C8×C59—22no—
248C2×C8×C59—22no—
249C2×C8×C59C2412yes—
250C2×C8×C59C2412yes—
251C4⋊C4×C59—24no—
252C4⋊C4×C59—24no—
253C4⋊C4×C59—21no—
254C4⋊C4×C59—21no—
255C4⋊C4×C59C2412yes—
256C4⋊C4×C59C2412yes—
257C22⋊C4×C59—24no—
258C22⋊C4×C59—24no—
259C42×C59C2×D412yes—
260C42×C59C2412yes—
261(C2×D59)⋊C4—24no—
262(C2×D59)⋊C4—24no—
263(C2×D59)⋊C4—24no—
264(C2×D59)⋊C4C2×D414yes—
265(C2×D59)⋊C4C2×D414yes—
266C4⋊Dic59—21no—
267C4⋊Dic59—24no—
268C4⋊Dic59—21no—
269C4⋊Dic59—24no—
270C4⋊Dic59C2412yes—
271C4⋊Dic59C2412yes—
272Dic59⋊C4—24no—
273Dic59⋊C4—24no—
274Dic59⋊C4—24no—
275Dic59⋊C4C2×D414yes—
276Dic59⋊C4C2×D414yes—
277C4×Dic59—24no—
278C4×Dic59C2×D412yes—
279C4×Dic59C2412yes—
280C2×C59⋊C8—22no—
281C2×C59⋊C8—22no—
282C2×C59⋊C8C2412yes—
283C2×C59⋊C8C2412yes—
284#11745659—28no—
285C8×D59—28no—
286C23×C59—22no—
287C23×C59—42no—
288C23×C59—42no—
289C23×C59—42no—
290C23×C59C22×D411yescharacteristic
291C22×D59—22no—
292C22×D59—22no—
293C22×D59—22no—
294C22×D59—22no—
295C22×D59—42no—
296C22×D59—42no—
297C22×D59—42no—
298C22×D59—42no—
299C22×D59—42no—
300C22×D59—42no—
301C22×D59—48no—
302C22×D59—84no—
303C22×D59—84no—
304C22×D59—816no—
305C22×D59#12414yes—
306C22×D59C22×D412yes—
307Q8×C59—22no—
308Q8×C59—22no—
309Q8×C59—42no—
310D4×C59—22no—
311D4×C59—22no—
312D4×C59—42no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—42no—
319C2×C4×C59—42no—
320C2×C4×C59—42no—
321C2×C4×C59C22×D412yes—
322C2×C4×C59C22×D412yes—
323C2×C4×C59C22×D411yescharacteristic
324C2×C4×C59C2×#4112yes—
325C2×C4×C59C2×#4112yes—
326C2×C4×C59C2511yescharacteristic
327C22⋊D59—48no—
328C22⋊D59—84no—
329C22⋊D59—84no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—22no—
333C2×Dic59—22no—
334C2×Dic59—42no—
335C2×Dic59—42no—
336C2×Dic59#12414yes—
337C2×Dic59C22×D412yes—
338C2×Dic59C22×D412yes—
339C2×Dic59C22×D412yes—
340D236—22no—
341D236—22no—
342D236—22no—
343D236—22no—
344D236—48no—
345D236—42no—
346D236—42no—
347D236—84no—
348D236—84no—
349C4×D59—48no—
350C4×D59—84no—
351C4×D59#12418yes—
352C4×D59C2×#4114yes—
353C4×D59C2×#4114yes—
354Dic118—84no—
355Dic118—84no—
356C8×C59—22no—
357C8×C59—22no—
358C59⋊C8—22no—
359C59⋊C8—22no—
360C2×#3136—591nomaximal, Sylow
361C22×C59—42no—
362C22×C59—42no—
363C22×C59—42no—
364C22×C59—84no—
365C22×C59C2×#12412yes—
366C22×C59#57612yes—
367C22×C59#57712yes—
368C22×C59C23×D411yescharacteristic
369C2×D59—28no—
370C2×D59—22no—
371C2×D59—22no—
372C2×D59—42no—
373C2×D59—42no—
374C2×D59—42no—
375C2×D59—42no—
376C2×D59—42no—
377C2×D59—42no—
378C2×D59—816no—
379C2×D59—84no—
380C2×D59—84no—
381C2×D59C2×#12414yes—
382C4×C59—22no—
383C4×C59—22no—
384C4×C59—42no—
385C4×C59—42no—
386C4×C59—42no—
387C4×C59C2×#12412yes—
388C4×C59C22×#4111yescharacteristic
389C4×C59C22×#4111yescharacteristic
390Dic59—22no—
391Dic59—22no—
392Dic59—42no—
393Dic59—42no—
394Dic59C2×#12414yes—
395C2×#544—591no—
396C2×#535—591no—
397#3136—5916no—
398C2×#490—591no—
399C2×#490—591no—
400C2×#489—591no—
401C2×#489—591no—
402C2×#488—591no—
403C2×#488D5911yescharacteristic, complemented
404C2×#486—591no—
405C2×#486—591no—
406C2×#417—591no—
407C2×#418—591no—
408C2×#416—591no—
409C22×#102—591no—
410C2×#405—591no—
411C2×C59—82no—
412C2×C59#313614yescomplemented
413C2×C59C22×#12411yescharacteristic
414C2×C59C2×#57611yescharacteristic
415C2×C59C2×#57711yescharacteristic
416D59—24no—
417D59—82no—
418D59—82no—
419C22×#41—591no—
420C23×D4—591no—
421C22×M16—591no—
422C23×C8—591no—
423#544—598no—
424#544—1184no—
425#535—598no—
426#535—1184no—
427C2×C4⋊Q8—591no—
428C2×C4⋊Q8—591no—
429C2×C4⋊Q8—1181no—
430C2×#127—591no—
431C2×#127—591no—
432C2×#125—591no—
433C2×#125—1181no—
434C2×#125C2×D5911yescharacteristic, complemented
435C2×#124—591no—
436C2×#124C2×D5911yescharacteristic
437C2×C22⋊Q8—1181no—
438C2×C22⋊Q8—1181no—
439C2×#121—1181no—
440C2×#121—1181no—
441C2×#120—1181no—
442C2×#120—1181no—
443C2×#117—591no—
444C2×#117—591no—
445C22×C4⋊C4—591no—
446#490—598no—
447#490—598no—
448#489—598no—
449#489—598no—
450#488—598no—
451#488C2×D5918yescomplemented
452#486—598no—
453#486—598no—
454#418—598no—
455#417—598no—
456#416—598no—
457C2×#103—591no—
458C2×#103—591no—
459C2×#103C2×D5911yescharacteristic, complemented
460C2×#103C2×D5911yescharacteristic, complemented
461C2×#102—591no—
462C2×#102—591no—
463C2×#102—591no—
464C2×#102—591no—
465C2×#102—591no—
466C2×#102—591no—
467C2×#102—591no—
468C2×#102—591no—
469C2×#102—591no—
470C2×#102—591no—
471C2×#102—598no—
472C2×#102C2×D5911yescharacteristic
473C2×#102C2×D5911yescharacteristic
474#405—598no—
475C2×#97—591no—
476C2×#97—591no—
477C2×C4×C8—591no—
478C2×C4×C8C2×D5911yescharacteristic, complemented
479C59C2×#313611yescharacteristic, complemented, Sylow
480C25—1181no—
481C2×#41—594no—
482C2×#41—1182no—
483C2×#41—1184no—
484C2×#41—1184no—
485C22×Q8—1181no—
486C22×Q8—1181no—
487C22×Q8C22×D5911yescharacteristic
488C22×D4—594no—
489C22×D4—591no—
490C22×D4—591no—
491C22×D4—1181no—
492C22×D4—1184no—
493C22×D4—1184no—
494C22×D4—1182no—
495C22×D4—1181no—
496C22×D4—1181no—
497C22×D4—1181no—
498C22×D4—1181no—
499C22×D4—1181no—
500C22×D4C22×D5911yescharacteristic
501C23×C4—591no—
502C23×C4—1181no—
503C23×C4—1181no—
504C2×M16—594no—
505C2×M16—1184no—
506C22×C8—591no—
507C22×C8—591no—
508C22×C8—594no—
509C22×C8—1184no—
510C22×C8C22×D5911yescharacteristic
511C22×C8C22×D5911yescharacteristic
512C4⋊Q8—594no—
513C4⋊Q8—594no—
514C4⋊Q8—1182no—
515C4⋊Q8—1188no—
516C4⋊Q8—1182no—
517#127—594no—
518#127—594no—
519#127—1182no—
520#127—1182no—
521#125—22no—
522#125—594no—
523#125—1182no—
524#125—1188no—
525#125C22×D5914yescomplemented
526#124—22no—
527#124—594no—
528#124—1182no—
529#124C22×D5914yes—
530C22⋊Q8—1188no—
531C22⋊Q8—1188no—
532#121—1188no—
533#121—1188no—
534#120—1188no—
535#120—1188no—
536#117—594no—
537#117—594no—
538#117—594no—
539#117—1182no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—591no—
543C2×C4⋊C4—591no—
544C2×C4⋊C4—591no—
545C2×C4⋊C4—591no—
546C2×C4⋊C4—594no—
547C2×C4⋊C4—1182no—
548C2×C4⋊C4—1181no—
549C2×C4⋊C4—1181no—
550C2×C4⋊C4—1181no—
551C2×C4⋊C4—1181no—
552C2×C4⋊C4—1181no—
553C2×C4⋊C4C22×D5911yescharacteristic
554C2×C4⋊C4C22×D5911yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—591no—
558C2×C22⋊C4—591no—
559C2×C22⋊C4—1181no—
560C2×C22⋊C4—1181no—
561C2×C22⋊C4—1181no—
562C2×C42—591no—
563C2×C42—1181no—
564C2×C42C22×D5911yescharacteristic
565#103—594no—
566#103—594no—
567#103C22×D5914yescomplemented
568#103C22×D5914yescomplemented
569#102—594no—
570#102—594no—
571#102—594no—
572#102—594no—
573#102—594no—
574#102—594no—
575#102—594no—
576#102—594no—
577#102—594no—
578#102—594no—
579#102C22×D5914yes—
580#102C22×D5914yes—
581#97—594no—
582#97—594no—
583C4×C8—594no—
584C4×C8C22×D5914yescomplemented
585C24—21no—
586C24—591no—
587C24—1184no—
588C24—1181no—
589C24—1181no—
590C24—4722no—
591C24—4722no—
592C24—2364no—
593#41—1188no—
594#41—1188no—
595#41—2368no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—22no—
599C2×Q8—1184no—
600C2×Q8—1184no—
601C2×Q8—4722no—
602C2×Q8—4722no—
603C2×Q8C23×D5912yes—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—592no—
608C2×D4—592no—
609C2×D4—1184no—
610C2×D4—1188no—
611C2×D4—1188no—
612C2×D4—1184no—
613C2×D4—1184no—
614C2×D4—1184no—
615C2×D4—1184no—
616C2×D4—1184no—
617C2×D4—1181no—
618C2×D4—1181no—
619C2×D4—1182no—
620C2×D4—1182no—
621C2×D4—1182no—
622C2×D4—1182no—
623C2×D4—4722no—
624C2×D4—4722no—
625C2×D4—4722no—
626C2×D4—4722no—
627C2×D4—2364no—
628C2×D4—2368no—
629C2×D4—2364no—
630C2×D4C23×D5912yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—591no—
635C22×C4—592no—
636C22×C4—594no—
637C22×C4—594no—
638C22×C4—592no—
639C22×C4—591no—
640C22×C4—591no—
641C22×C4—1184no—
642C22×C4—1184no—
643C22×C4—1181no—
644C22×C4—1181no—
645C22×C4—4722no—
646C22×C4—2364no—
647C22×C4D4×D5911yescharacteristic
648C22×C4D4×D5911yescharacteristic
649C22×C4C23×D5911yescharacteristic
650M16—1188no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—592no—
654C2×C8—592no—
655C2×C8—1188no—
656C2×C8—1182no—
657C2×C8—1182no—
658C2×C8C23×D5912yes—
659C2×C8C23×D5912yes—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—594no—
665C4⋊C4—594no—
666C4⋊C4—592no—
667C4⋊C4—592no—
668C4⋊C4—1184no—
669C4⋊C4—1184no—
670C4⋊C4—1184no—
671C4⋊C4—1184no—
672C4⋊C4—1181no—
673C4⋊C4—1181no—
674C4⋊C4—1184no—
675C4⋊C4C23×D5912yes—
676C4⋊C4C23×D5912yes—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—594no—
680C22⋊C4—594no—
681C22⋊C4—1184no—
682C22⋊C4—1184no—
683C22⋊C4—1184no—
684C42—592no—
685C42—592no—
686C42—1184no—
687C42D4×D5912yes—
688C42C23×D5912yes—
689C23—22no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—594no—
694C23—592no—
695C23—1182no—
696C23—1182no—
697C23—1182no—
698C23—1182no—
699C23—4724no—
700C23—4724no—
701C23—47216no—
702C23—2368no—
703C23—2362no—
704C23—2362no—
705C23—2362no—
706C23—2362no—
707C23—2362no—
708C23—2362no—
709C23C2×D4×D5911yescharacteristic
710Q8—22no—
711Q8—22no—
712Q8—42no—
713Q8—4724no—
714Q8—4724no—
715D4—22no—
716D4—22no—
717D4—42no—
718D4—1182no—
719D4—1182no—
720D4—1182no—
721D4—1182no—
722D4—4724no—
723D4—4724no—
724D4—4724no—
725D4—4724no—
726D4—2368no—
727D4—2368no—
728D4—2362no—
729D4—2362no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—594no—
739C2×C4—592no—
740C2×C4—598no—
741C2×C4—594no—
742C2×C4—594no—
743C2×C4—592no—
744C2×C4—592no—
745C2×C4—1182no—
746C2×C4—1182no—
747C2×C4—1182no—
748C2×C4—1182no—
749C2×C4—4724no—
750C2×C4—2368no—
751C2×C4—2362no—
752C2×C4—2362no—
753C2×C4C2×D4×D5912yes—
754C2×C4C2×D4×D5912yes—
755C2×C4C2×D4×D5911yescharacteristic
756C2×C4#41×D5912yes—
757C2×C4#41×D5912yes—
758C2×C4C24×D5911yescharacteristic
759C8—22no—
760C8—22no—
761C8—1182no—
762C8—1182no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—84no—
767C22—594no—
768C22—1188no—
769C22—1182no—
770C22—1182no—
771C22—47216no—
772C22—4724no—
773C22—4724no—
774C22—2362no—
775C22—2362no—
776C22—2362no—
777C22—2362no—
778C22—2362no—
779C22—2362no—
780C22#124×D5912yes—
781C22#1683820412yes—
782C22#1683820912yes—
783C22C22×D4×D5911yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—594no—
790C4—1182no—
791C4—1182no—
792C4—2362no—
793C4—2362no—
794C4#124×D5912yes—
795C4C2×#41×D5911yescharacteristic
796C4C2×#41×D5911yescharacteristic
797C2—82no—
798C2—1184no—
799C2—4722no—
800C2—4722no—
801C2#2143444914yesdirect product factor
802C2C2×#124×D5911yescharacteristic
803C2C2×#1683820411yescharacteristic
804C2C2×#1683820911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#488C2
socleC23×C59C22×D4
prime radicalC2×#16837970C2
hypercenterC2×#488D59
hypocenterC59C2×#3136
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#16838032C2semidirect
3. #21434449C2direct (N × H)
4. C2×#16837768C2semidirect
5. C2×#16837765C2semidirect
6. C2×#16837763C2semidirect
7. C2×#16837761C2semidirect
8. C2×#16837758C2semidirect
9. C2×#16837749C2semidirect
10. C2×#16837747C2semidirect
11. C2×#16837402C2semidirect
12. C2×#16837405C2semidirect
13. C2×#16837397C2semidirect
14. C2×#102×D59C2semidirect
15. C2×#16837356C2semidirect
16. C2×C59×#488C2semidirect
22. #16838032C22semidirect
25. C2×#14273727C22semidirect
27. C2×#14273726C22semidirect
30. C2×#14273718C22semidirect
42. #16837768C22semidirect
43. #16837765C22semidirect
44. #16837763C22semidirect
45. #16837761C22semidirect
46. #16837758C22semidirect
47. #16837749C22semidirect
48. #16837747C22semidirect
49. #16837405C22semidirect
50. #16837402C22semidirect
51. #16837397C22semidirect
52. C2×#14273651C22semidirect
53. C2×#14273651C22semidirect
56. C2×#14273649C22semidirect
57. C2×#14273649C22semidirect
62. C2×#14273647C22semidirect
63. C2×#14273647C22semidirect
64. #102×D59C22semidirect
65. #16837356C22semidirect
66. C2×#14273638C22semidirect
67. C2×#14273637C22semidirect
68. C2×C8×Dic59C22semidirect
69. C2×#125×C59C22semidirect
71. C59×#488C22semidirect
72. C2×#103×C59C22semidirect
73. C2×#103×C59C22semidirect
76. C2×C4×C8×C59C22semidirect
106. #14273727C23semidirect
109. #14273726C23semidirect
115. #14273718C23semidirect
147. #14273651C23semidirect
148. #14273651C23semidirect
151. #14273649C23semidirect
152. #14273649C23semidirect
157. #14273647C23semidirect
158. #14273647C23semidirect
159. #14273638C23semidirect
160. #14273637C23semidirect
161. C8×Dic59C23semidirect
167. #125×C59C23semidirect
177. #103×C59C23semidirect
178. #103×C59C23semidirect
181. C4×C8×C59C23semidirect
403. C2×#488D59semidirect
412. C2×C59#3136semidirect
434. C2×#125C2×D59semidirect
451. #488C2×D59semidirect
459. C2×#103C2×D59semidirect
460. C2×#103C2×D59semidirect
478. C2×C4×C8C2×D59semidirect
479. C59C2×#3136semidirect
525. #125C22×D59semidirect
567. #103C22×D59semidirect
568. #103C22×D59semidirect
584. C4×C8C22×D59semidirect
801. C2#21434449direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380322
C2×#168379702
#214344492
C2×#168377682
C2×#168377652
C2×#168377632
C2×#168377612
C2×#168377582
C2×#168377492
C2×#168377472
C2×#168374022
C2×#168374052
C2×#168373972
C2×#102×D592
C2×#168373562
C2×C59×#4882
C2×#313659