Finite Group Databasebeta

← C2×#21434051 #29456513

Subgroups — C2×#21434051 #29456513

Order 15104.

2362 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837968C211yesmaximal, characteristic
2C2×#16837882C211yesmaximal, characteristic, complemented
3#21434051C2116yesmaximal, direct product factor
4C2×#16837722C211yesmaximal, characteristic, complemented
5C2×#16837718C211yesmaximal, characteristic, complemented
6C2×#16837729C211yesmaximal, characteristic, complemented
7C2×#16837726C211yesmaximal, characteristic, complemented
8C2×#16837724C211yesmaximal, characteristic, complemented
9C2×#16837716C211yesmaximal, characteristic, complemented
10C2×#16837714C211yesmaximal, characteristic, complemented
11C2×#16837441C211yesmaximal, characteristic, complemented
12C2×#16837439C211yesmaximal, characteristic, complemented
13C2×#16837405C211yesmaximal, characteristic, complemented
14C2×#102×D59C211yesmaximal, characteristic, complemented
15C2×#16837367C211yesmaximal, characteristic, complemented
16C2×C59×#482C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C22×D4×D59C2211yescharacteristic
19C22×#11745659C2211yescharacteristic
20C22×C8×D59C2211yescharacteristic
21#16837968—24no—
22#16837968C2218yes—
23C2×#14273723—21no—
24C2×#14273713—21no—
25C2×#14273702C2211yescharacteristic
26C2×#14273701C2211yescharacteristic
27C2×#14273698C2211yescharacteristic
28C2×#14273697—21no—
29C2×#14273695—21no—
30#16837882—24no—
31#16837882C2218yescomplemented
32C2×C4×Dic118—21no—
33C2×C4×D236—21no—
34C2×(C22⋊D59)⋊C4—21no—
35C2×(C22⋊D59)⋊C4—21no—
36C2×#14273685C2211yescharacteristic
37C2×#14273685C2211yescharacteristic
38C2×#14273685C2211yescharacteristic, complemented
39C22×C4⋊Dic59C2211yescharacteristic, complemented
40C2×C4⋊C4×D59C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic, complemented
42#16837729C2218yescomplemented
43#16837726C2218yescomplemented
44#16837724C2218yescomplemented
45#16837722C2218yescomplemented
46#16837718C2218yescomplemented
47#16837716C2218yescomplemented
48#16837714C2218yescomplemented
49#16837441C2218yescomplemented
50#16837439C2218yescomplemented
51C2×#14273661C2211yescharacteristic, complemented
52C2×#14273661C2211yescharacteristic, complemented
53C2×#14273660C2211yescharacteristic, complemented
54C2×#14273658C2211yescharacteristic, complemented
55C2×#14273658C2211yescharacteristic, complemented
56C2×#14273658C2211yescharacteristic, complemented
57#16837405C2218yescomplemented
58C2×#14273649C2211yescharacteristic
59C2×#14273649C2211yescharacteristic
60C2×#14273648C2211yescharacteristic
61C2×#14273648C2211yescharacteristic
62C2×#14273647C2211yescharacteristic
63C2×#14273647C2211yescharacteristic
64#102×D59C2218yescomplemented
65#16837367C2218yescomplemented
66C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
69C2×#121×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic, complemented
71C59×#482C2218yescomplemented
72C2×#107×C59C2211yescharacteristic, complemented
73C2×#106×C59C2211yescharacteristic, complemented
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C2×#11745685—24no—
79C2×#11745685—24no—
80C2×#11745685D414yes—
81C2×#11745685C2314yes—
82C22×Dic118D411yescharacteristic
83C22×D236—21no—
84C22×D236D411yescharacteristic
85C22×D236C2311yescharacteristic
86C22×C22⋊D59—21no—
87C22×C22⋊D59—21no—
88C22×C22⋊D59—21no—
89C22×C22⋊D59D411yescharacteristic
90C22×C22⋊D59D411yescharacteristic
91C2×D4×D59—22no—
92C2×D4×D59—24no—
93C2×D4×D59—24no—
94C2×D4×D59C2314yes—
95C23×Dic59—21no—
96C22×C4×D59—21no—
97C22×C4×D59—21no—
98C22×C4×D59C2311yescharacteristic
99C22×C4×D59C2311yescharacteristic
100C2×#11745659—24no—
101C2×#11745659C2314yes—
102C22×C59⋊C8C2311yescharacteristic
103C22×C59⋊C8C2311yescharacteristic
104C2×C8×D59—24no—
105C2×C8×D59C2314yes—
106#14273723—28no—
107#14273713—28no—
108#14273702—22no—
109#14273702C2314yes—
110#14273701—22no—
111#14273701C2314yes—
112#14273698—22no—
113#14273698C2314yes—
114#14273697—28no—
115#14273695—28no—
116C4×Dic118—28no—
117C4×D236—28no—
118(C22⋊D59)⋊C4—28no—
119(C22⋊D59)⋊C4—28no—
120#14273685—22no—
121#14273685—22no—
122#14273685—22no—
123#14273685C2314yes—
124#14273685C2314yes—
125#14273685C2314yescomplemented
126C2×C4⋊Dic59—21no—
127C2×C4⋊Dic59—22no—
128C2×C4⋊Dic59C2311yescharacteristic
129C2×C4⋊Dic59C2311yescharacteristic
130C2×C4⋊Dic59C2311yescharacteristic
131C2×C4⋊Dic59C2314yescomplemented
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C4⋊C4×D59—22no—
135C4⋊C4×D59—22no—
136C4⋊C4×D59C2314yes—
137C4⋊C4×D59C2314yescomplemented
138C2×C22⋊Dic59—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59—21no—
147#14273661C2314yescomplemented
148#14273661C2314yescomplemented
149#14273660C2314yescomplemented
150#14273658C2314yescomplemented
151#14273658C2314yescomplemented
152#14273658C2314yescomplemented
153#14273649C2314yes—
154#14273649C2314yes—
155#14273648C2314yes—
156#14273648C2314yes—
157#14273647C2314yes—
158#14273647C2314yes—
159C22⋊(C59⋊C8)C2314yescomplemented
160(C2×D59)⋊C8C2314yescomplemented
161(C2×D59)⋊C8C2314yescomplemented
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×C59C2314yescomplemented
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#102×C59C2314yes—
180#102×C59C2314yes—
181C22⋊C8×C59C2314yescomplemented
182C24×C59—21no—
183C24×C59C2×D411yescharacteristic
184C23×D59—21no—
185C23×D59—24no—
186C23×D59—44no—
187C23×D59—82no—
188C23×D59—82no—
189C23×D59C2×D411yescharacteristic
190C23×D59C2×D411yescharacteristic
191C2×D4×C59—24no—
192C2×D4×C59—21no—
193C2×D4×C59—22no—
194C2×D4×C59—22no—
195C2×D4×C59—82no—
196C2×D4×C59C2412yes—
197C22×C4×C59—22no—
198C22×C4×C59—22no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59C2×D411yescharacteristic
203C22×C4×C59C2×D412yes—
204C22×C4×C59C2412yes—
205C22×C4×C59C2411yescharacteristic
206C2×C22⋊D59—24no—
207C2×C22⋊D59—24no—
208C2×C22⋊D59—24no—
209C2×C22⋊D59—24no—
210C2×C22⋊D59—24no—
211C2×C22⋊D59—44no—
212C2×C22⋊D59—82no—
213C2×C22⋊D59—82no—
214C2×C22⋊D59C2×D414yes—
215C2×C22⋊D59C2×D414yes—
216C22×Dic59—21no—
217C22×Dic59—21no—
218C22×Dic59—21no—
219C22×Dic59—24no—
220C22×Dic59—82no—
221C22×Dic59C2×D411yescharacteristic
222C22×Dic59C2×D411yescharacteristic
223D4×D59—28no—
224D4×D59—28no—
225D4×D59—48no—
226#11745685—216no—
227#11745685—28no—
228#11745685—28no—
229C2×D236—24no—
230C2×D236—22no—
231C2×D236—22no—
232C2×D236—21no—
233C2×D236—24no—
234C2×D236—82no—
235C2×D236C2×D414yes—
236C2×D236C2412yes—
237C2×C4×D59—22no—
238C2×C4×D59—22no—
239C2×C4×D59—24no—
240C2×C4×D59—24no—
241C2×C4×D59—82no—
242C2×C4×D59—82no—
243C2×C4×D59C2×D412yes—
244C2×C4×D59C2×D412yes—
245C2×C4×D59#4114yes—
246C2×C4×D59#4114yes—
247C2×C4×D59C2412yes—
248C2×C4×D59C2412yes—
249C2×Dic118—24no—
250C2×Dic118C2×D414yes—
251C2×C8×C59—22no—
252C2×C8×C59—22no—
253C2×C8×C59C2412yes—
254C2×C8×C59C2412yes—
255C4⋊C4×C59—21no—
256C4⋊C4×C59—21no—
257C4⋊C4×C59—21no—
258C4⋊C4×C59C2412yes—
259C4⋊C4×C59C2412yes—
260C4⋊C4×C59C2412yes—
261C22⋊C4×C59—24no—
262C22⋊C4×C59—24no—
263C42×C59—24no—
264C22⋊Dic59—24no—
265(C2×D59)⋊C4—24no—
266(C2×D59)⋊C4—24no—
267(C2×D59)⋊C4—24no—
268(C2×D59)⋊C4—24no—
269(C2×D59)⋊C4—24no—
270C4⋊Dic59—21no—
271C4⋊Dic59—21no—
272C4⋊Dic59—24no—
273C4⋊Dic59—21no—
274C4⋊Dic59C2412yes—
275C4⋊Dic59C2412yes—
276C4⋊Dic59C2412yes—
277Dic59⋊C4—24no—
278Dic59⋊C4—24no—
279C4×Dic59—24no—
280C4×Dic59—24no—
281C4×Dic59—24no—
282C2×C59⋊C8—22no—
283C2×C59⋊C8—22no—
284C2×C59⋊C8C2412yes—
285C2×C59⋊C8C2412yes—
286#11745659—28no—
287C8×D59—28no—
288C23×C59—22no—
289C23×C59—22no—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59—42no—
293C23×C59—42no—
294C23×C59—42no—
295C23×C59C22×D412yes—
296C23×C59C22×D411yescharacteristic
297C22×D59—22no—
298C22×D59—22no—
299C22×D59—22no—
300C22×D59—22no—
301C22×D59—22no—
302C22×D59—22no—
303C22×D59—42no—
304C22×D59—42no—
305C22×D59—42no—
306C22×D59—48no—
307C22×D59—84no—
308C22×D59—84no—
309C22×D59—816no—
310C22×D59#12314yes—
311C22×D59C22×D412yes—
312C22×D59C22×D412yes—
313D4×C59—22no—
314D4×C59—22no—
315D4×C59—42no—
316D4×C59—84no—
317C2×C4×C59—22no—
318C2×C4×C59—24no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59—22no—
324C2×C4×C59—42no—
325C2×C4×C59—42no—
326C2×C4×C59—42no—
327C2×C4×C59C22×D412yes—
328C2×C4×C59C22×D411yescharacteristic
329C2×C4×C59C2×#4112yes—
330C2×C4×C59C2×#4112yes—
331C2×C4×C59C2511yescharacteristic
332C22⋊D59—28no—
333C22⋊D59—28no—
334C22⋊D59—48no—
335C22⋊D59—84no—
336C22⋊D59—84no—
337C2×Dic59—22no—
338C2×Dic59—22no—
339C2×Dic59—22no—
340C2×Dic59—22no—
341C2×Dic59—42no—
342C2×Dic59—42no—
343C2×Dic59—42no—
344C2×Dic59—84no—
345C2×Dic59#12314yes—
346C2×Dic59C22×D412yes—
347C2×Dic59C22×D412yes—
348D236—28no—
349D236—22no—
350D236—22no—
351D236—42no—
352D236—84no—
353C4×D59—24no—
354C4×D59—22no—
355C4×D59—22no—
356C4×D59—84no—
357C4×D59—84no—
358C4×D59#12318yes—
359C4×D59C2×#4114yes—
360C4×D59C2×#4114yes—
361Dic118—28no—
362C8×C59—22no—
363C8×C59—22no—
364C59⋊C8—22no—
365C59⋊C8—22no—
366C2×#3096—591nomaximal, Sylow
367C22×C59—22no—
368C22×C59—22no—
369C22×C59—22no—
370C22×C59—44no—
371C22×C59—42no—
372C22×C59—42no—
373C22×C59—42no—
374C22×C59—84no—
375C22×C59C2×#12312yes—
376C22×C59#57612yes—
377C22×C59#57712yes—
378C22×C59C23×D411yescharacteristic
379C2×D59—28no—
380C2×D59—22no—
381C2×D59—22no—
382C2×D59—22no—
383C2×D59—22no—
384C2×D59—22no—
385C2×D59—44no—
386C2×D59—42no—
387C2×D59—42no—
388C2×D59—42no—
389C2×D59—816no—
390C2×D59—84no—
391C2×D59C2×#12314yes—
392C4×C59—22no—
393C4×C59—42no—
394C4×C59—42no—
395C4×C59—42no—
396C4×C59C2×#12312yes—
397C4×C59C22×#4111yescharacteristic
398C4×C59C22×#4111yescharacteristic
399Dic59—22no—
400Dic59—42no—
401Dic59—42no—
402Dic59—42no—
403Dic59C2×#12314yes—
404C2×#535—591no—
405C2×#520—591no—
406#3096—5916no—
407C2×#481—591no—
408C2×#481—591no—
409C2×#482—591no—
410C2×#482—591no—
411C2×#482—591no—
412C2×#482D5911yescharacteristic, complemented
413C2×#480—591no—
414C2×#480—591no—
415C2×#428—591no—
416C2×#427—591no—
417C2×#418—591no—
418C22×#102—591no—
419C2×#408—591no—
420C2×C59—42no—
421C2×C59—82no—
422C2×C59#309614yescomplemented
423C2×C59C22×#12311yescharacteristic
424C2×C59C2×#57611yescharacteristic
425C2×C59C2×#57711yescharacteristic
426D59—24no—
427D59—42no—
428D59—82no—
429C22×#41—591no—
430C23×D4—591no—
431C22×M16—591no—
432C23×C8—591no—
433#535—598no—
434#535—1184no—
435C2×#127—1181no—
436C2×#124—1181no—
437C2×#121—591no—
438C2×#121—591no—
439C2×#121—591no—
440C2×#121C2×D5911yescharacteristic
441C2×#120—1181no—
442C2×#120—1181no—
443#520—598no—
444#520—1184no—
445C2×C4×Q8—1181no—
446C2×C4×D4—1181no—
447C2×C4×D4—1181no—
448C2×C4×D4—1181no—
449C2×#117—591no—
450C2×#117—591no—
451C2×#117—591no—
452C2×#117C2×D5911yescharacteristic, complemented
453C22×C4⋊C4—591no—
454C22×C4⋊C4—591no—
455C22×C4⋊C4—591no—
456#482—598no—
457#482—598no—
458#482—598no—
459#482C2×D5918yescomplemented
460#481—598no—
461#481—598no—
462#480—598no—
463#480—598no—
464#428—598no—
465#427—598no—
466C2×#107—591no—
467C2×#107—591no—
468C2×#107—591no—
469C2×#107C2×D5911yescharacteristic, complemented
470C2×#106—591no—
471C2×#106—591no—
472C2×#106—591no—
473C2×#106C2×D5911yescharacteristic, complemented
474#418—598no—
475C2×#102—591no—
476C2×#102—591no—
477C2×#102—591no—
478C2×#102—591no—
479C2×#102—591no—
480C2×#102—591no—
481C2×#102—598no—
482C2×#102C2×D5911yescharacteristic
483C2×#102C2×D5911yescharacteristic
484#408—598no—
485C2×C22⋊C8—591no—
486C2×C22⋊C8—591no—
487C2×C22⋊C8—591no—
488C2×C22⋊C8C2×D5911yescharacteristic, complemented
489C59C2×#309611yescharacteristic, complemented, Sylow
490C25—1181no—
491C2×#41—594no—
492C2×#41—594no—
493C2×#41—1184no—
494C2×#41—1184no—
495C22×Q8—591no—
496C22×D4—21no—
497C22×D4—591no—
498C22×D4—591no—
499C22×D4—594no—
500C22×D4—591no—
501C22×D4—591no—
502C22×D4—1181no—
503C22×D4—1184no—
504C22×D4—1184no—
505C22×D4—1182no—
506C22×D4—1181no—
507C22×D4—1181no—
508C22×D4—1181no—
509C22×D4C22×D5911yescharacteristic
510C23×C4—591no—
511C23×C4—591no—
512C23×C4—1181no—
513C23×C4—1181no—
514C23×C4—1181no—
515C23×C4C22×D5911yescharacteristic
516C2×M16—594no—
517C2×M16—1184no—
518C22×C8—591no—
519C22×C8—591no—
520C22×C8—594no—
521C22×C8—1184no—
522C22×C8C22×D5911yescharacteristic
523C22×C8C22×D5911yescharacteristic
524#127—1188no—
525#124—1188no—
526#121—22no—
527#121—594no—
528#121—594no—
529#121—594no—
530#121—1182no—
531#121—1182no—
532#121—1182no—
533#121C22×D5914yes—
534#120—1188no—
535#120—1188no—
536C4×Q8—1188no—
537C4×D4—1188no—
538C4×D4—1188no—
539C4×D4—1188no—
540#117—22no—
541#117—594no—
542#117—594no—
543#117—594no—
544#117—1182no—
545#117—1182no—
546#117—1182no—
547#117C22×D5914yescomplemented
548C2×C4⋊C4—591no—
549C2×C4⋊C4—591no—
550C2×C4⋊C4—594no—
551C2×C4⋊C4—591no—
552C2×C4⋊C4—594no—
553C2×C4⋊C4—594no—
554C2×C4⋊C4—1182no—
555C2×C4⋊C4—1182no—
556C2×C4⋊C4—1181no—
557C2×C4⋊C4—1181no—
558C2×C4⋊C4—1181no—
559C2×C4⋊C4—1182no—
560C2×C4⋊C4C22×D5911yescharacteristic
561C2×C4⋊C4C22×D5911yescharacteristic
562C2×C4⋊C4C22×D5911yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—1181no—
566C2×C22⋊C4—1181no—
567C2×C22⋊C4—1181no—
568C2×C22⋊C4—1181no—
569C2×C22⋊C4—1181no—
570C2×C22⋊C4—1181no—
571C2×C42—21no—
572C2×C42—1181no—
573C2×C42—1181no—
574C2×C42—1181no—
575#107—594no—
576#107—594no—
577#107—594no—
578#107C22×D5914yescomplemented
579#106—594no—
580#106—594no—
581#106—594no—
582#106C22×D5914yescomplemented
583#102—594no—
584#102—594no—
585#102—594no—
586#102—594no—
587#102—594no—
588#102—594no—
589#102C22×D5914yes—
590#102C22×D5914yes—
591C22⋊C8—594no—
592C22⋊C8—594no—
593C22⋊C8—594no—
594C22⋊C8C22×D5914yescomplemented
595C24—21no—
596C24—591no—
597C24—591no—
598C24—1184no—
599C24—1181no—
600C24—4722no—
601C24—4722no—
602C24—2364no—
603C24D4×D5911yescharacteristic
604#41—11816no—
605#41—1188no—
606#41—1188no—
607C2×Q8—594no—
608C2×Q8—1184no—
609C2×D4—24no—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—82no—
614C2×D4—594no—
615C2×D4—594no—
616C2×D4—594no—
617C2×D4—592no—
618C2×D4—1184no—
619C2×D4—1184no—
620C2×D4—1188no—
621C2×D4—1188no—
622C2×D4—1184no—
623C2×D4—1184no—
624C2×D4—1184no—
625C2×D4—1184no—
626C2×D4—1184no—
627C2×D4—1181no—
628C2×D4—1182no—
629C2×D4—1182no—
630C2×D4—4722no—
631C2×D4—4722no—
632C2×D4—4722no—
633C2×D4—2368no—
634C2×D4—2364no—
635C2×D4C23×D5912yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—591no—
642C22×C4—592no—
643C22×C4—594no—
644C22×C4—594no—
645C22×C4—592no—
646C22×C4—591no—
647C22×C4—592no—
648C22×C4—592no—
649C22×C4—1184no—
650C22×C4—1184no—
651C22×C4—1182no—
652C22×C4—1182no—
653C22×C4—1184no—
654C22×C4—1181no—
655C22×C4—1181no—
656C22×C4—1181no—
657C22×C4—4722no—
658C22×C4—4722no—
659C22×C4—4722no—
660C22×C4D4×D5912yes—
661C22×C4D4×D5911yescharacteristic
662C22×C4C23×D5912yes—
663C22×C4C23×D5911yescharacteristic
664M16—1188no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—592no—
668C2×C8—592no—
669C2×C8—1188no—
670C2×C8—1182no—
671C2×C8—1182no—
672C2×C8C23×D5912yes—
673C2×C8C23×D5912yes—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—592no—
678C4⋊C4—592no—
679C4⋊C4—592no—
680C4⋊C4—1184no—
681C4⋊C4—1184no—
682C4⋊C4—1181no—
683C4⋊C4—1181no—
684C4⋊C4—1184no—
685C4⋊C4—1181no—
686C4⋊C4C23×D5912yes—
687C4⋊C4C23×D5912yes—
688C4⋊C4C23×D5912yes—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—1184no—
692C22⋊C4—1184no—
693C22⋊C4—1184no—
694C22⋊C4—1184no—
695C22⋊C4—1184no—
696C22⋊C4—1184no—
697C42—24no—
698C42—1184no—
699C42—1184no—
700C42—1184no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—594no—
709C23—592no—
710C23—592no—
711C23—1182no—
712C23—1182no—
713C23—1182no—
714C23—1182no—
715C23—1182no—
716C23—1182no—
717C23—4724no—
718C23—4724no—
719C23—47216no—
720C23—2368no—
721C23—2362no—
722C23—2362no—
723C23—2362no—
724C23C2×D4×D5912yes—
725C23C2×D4×D5911yescharacteristic
726Q8—1188no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—1188no—
732D4—1188no—
733D4—1188no—
734D4—1182no—
735D4—1182no—
736D4—4724no—
737D4—4724no—
738D4—4724no—
739D4—2368no—
740D4—2362no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—594no—
752C2×C4—592no—
753C2×C4—598no—
754C2×C4—594no—
755C2×C4—594no—
756C2×C4—592no—
757C2×C4—1182no—
758C2×C4—1184no—
759C2×C4—1182no—
760C2×C4—1182no—
761C2×C4—1182no—
762C2×C4—1182no—
763C2×C4—1182no—
764C2×C4—4724no—
765C2×C4—4724no—
766C2×C4—4724no—
767C2×C4—2362no—
768C2×C4—2362no—
769C2×C4—2362no—
770C2×C4C2×D4×D5912yes—
771C2×C4C2×D4×D5911yescharacteristic
772C2×C4#41×D5912yes—
773C2×C4#41×D5912yes—
774C2×C4C24×D5911yescharacteristic
775C8—22no—
776C8—22no—
777C8—1182no—
778C8—1182no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—84no—
787C22—594no—
788C22—1182no—
789C22—1182no—
790C22—1188no—
791C22—1182no—
792C22—1182no—
793C22—1182no—
794C22—47216no—
795C22—4724no—
796C22—2362no—
797C22—2362no—
798C22—2362no—
799C22—2364no—
800C22#123×D5912yes—
801C22#1683820412yes—
802C22#1683821212yes—
803C22C22×D4×D5911yescharacteristic
804C4—22no—
805C4—42no—
806C4—42no—
807C4—42no—
808C4—594no—
809C4—1182no—
810C4—2362no—
811C4—2362no—
812C4—2362no—
813C4#123×D5912yes—
814C4C2×#41×D5911yescharacteristic
815C4C2×#41×D5911yescharacteristic
816C2—42no—
817C2—82no—
818C2—1184no—
819C2—4722no—
820C2—2362no—
821C2#2143405114yesdirect product factor
822C2C2×#123×D5911yescharacteristic
823C2C2×#1683820411yescharacteristic
824C2C2×#1683821211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#482C2
socleC23×C59C22×D4
prime radicalC2×#16837968C2
hypercenterC2×#482D59
hypocenterC59C2×#3096
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×#16837882C2semidirect
3. #21434051C2direct (N × H)
4. C2×#16837722C2semidirect
5. C2×#16837718C2semidirect
6. C2×#16837729C2semidirect
7. C2×#16837726C2semidirect
8. C2×#16837724C2semidirect
9. C2×#16837716C2semidirect
10. C2×#16837714C2semidirect
11. C2×#16837441C2semidirect
12. C2×#16837439C2semidirect
13. C2×#16837405C2semidirect
14. C2×#102×D59C2semidirect
15. C2×#16837367C2semidirect
16. C2×C59×#482C2semidirect
31. #16837882C22semidirect
38. C2×#14273685C22semidirect
39. C22×C4⋊Dic59C22semidirect
41. C2×C4⋊C4×D59C22semidirect
42. #16837729C22semidirect
43. #16837726C22semidirect
44. #16837724C22semidirect
45. #16837722C22semidirect
46. #16837718C22semidirect
47. #16837716C22semidirect
48. #16837714C22semidirect
49. #16837441C22semidirect
50. #16837439C22semidirect
51. C2×#14273661C22semidirect
52. C2×#14273661C22semidirect
53. C2×#14273660C22semidirect
54. C2×#14273658C22semidirect
55. C2×#14273658C22semidirect
56. C2×#14273658C22semidirect
57. #16837405C22semidirect
64. #102×D59C22semidirect
65. #16837367C22semidirect
66. C2×C22⋊(C59⋊C8)C22semidirect
67. C2×(C2×D59)⋊C8C22semidirect
68. C2×(C2×D59)⋊C8C22semidirect
70. C2×#117×C59C22semidirect
71. C59×#482C22semidirect
72. C2×#107×C59C22semidirect
73. C2×#106×C59C22semidirect
76. C2×C22⋊C8×C59C22semidirect
125. #14273685C23semidirect
131. C2×C4⋊Dic59C23semidirect
137. C4⋊C4×D59C23semidirect
147. #14273661C23semidirect
148. #14273661C23semidirect
149. #14273660C23semidirect
150. #14273658C23semidirect
151. #14273658C23semidirect
152. #14273658C23semidirect
159. C22⋊(C59⋊C8)C23semidirect
160. (C2×D59)⋊C8C23semidirect
161. (C2×D59)⋊C8C23semidirect
170. #117×C59C23semidirect
177. #107×C59C23semidirect
178. #106×C59C23semidirect
181. C22⋊C8×C59C23semidirect
412. C2×#482D59semidirect
422. C2×C59#3096semidirect
452. C2×#117C2×D59semidirect
459. #482C2×D59semidirect
469. C2×#107C2×D59semidirect
473. C2×#106C2×D59semidirect
488. C2×C22⋊C8C2×D59semidirect
489. C59C2×#3096semidirect
547. #117C22×D59semidirect
578. #107C22×D59semidirect
582. #106C22×D59semidirect
594. C22⋊C8C22×D59semidirect
821. C2#21434051direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379682
C2×#168378822
#214340512
C2×#168377222
C2×#168377182
C2×#168377292
C2×#168377262
C2×#168377242
C2×#168377162
C2×#168377142
C2×#168374412
C2×#168374392
C2×#168374052
C2×#102×D592
C2×#168373672
C2×C59×#4822
C2×#309659