Finite Group Databasebeta

← C2×#21434283 #29456923

Subgroups — C2×#21434283 #29456923

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×#16838025C211yesmaximal, characteristic, complemented
2C2×#16837876C211yesmaximal, characteristic, complemented
3#21434283C2116yesmaximal, direct product factor
4C2×#16837726C211yesmaximal, characteristic, complemented
5C2×#16837691C211yesmaximal, characteristic, complemented
6C2×#16837681C211yesmaximal, characteristic, complemented
7C2×#16837620C211yesmaximal, characteristic, complemented
8C2×#16837620C211yesmaximal, characteristic, complemented
9C2×#16837552C211yesmaximal, characteristic, complemented
10C2×#16837538C211yesmaximal, characteristic
11C2×#16837513C211yesmaximal, characteristic, complemented
12C2×#16837505C211yesmaximal, characteristic, complemented
13C2×#16837487C211yesmaximal, characteristic, complemented
14C2×#16837484C211yesmaximal, characteristic, complemented
15C2×#16837460C211yesmaximal, characteristic, complemented
16C2×C59×#485C211yesmaximal, characteristic, complemented
17C23×D236C2211yescharacteristic
18C22×#11745671C2211yescharacteristic
19C22×#11745671C2211yescharacteristic
20C22×D472C2211yescharacteristic
21C22×D472C2211yescharacteristic
22#16838025—24no—
23#16838025C2218yescomplemented
24C2×#14273726C2211yescharacteristic, complemented
25C2×#14273722—21no—
26C2×#14273716C2211yescharacteristic, complemented
27C2×#14273713—21no—
28C2×#14273709—21no—
29C2×#14273707—21no—
30C2×#14273701C2211yescharacteristic
31#16837876—24no—
32#16837876C2218yescomplemented
33C2×Q8×Dic59C2211yescharacteristic, complemented
34C2×C4×D236—21no—
35C2×C4×D236—21no—
36C2×#14273689C2211yescharacteristic
37C2×#14273689C2211yescharacteristic
38C2×#14273689C2211yescharacteristic
39C2×#14273689C2211yescharacteristic
40C2×#14273689C2211yescharacteristic, complemented
41C2×#14273686C2211yescharacteristic
42C2×C22⋊C4×D59—21no—
43C2×C22⋊C4×D59—21no—
44#16837726C2218yescomplemented
45#16837691C2218yescomplemented
46#16837681C2218yescomplemented
47#16837620C2218yescomplemented
48#16837620C2218yescomplemented
49#16837552C2218yescomplemented
50#16837538C2218yes—
51#16837513C2218yescomplemented
52#16837505C2218yescomplemented
53#16837487C2218yescomplemented
54#16837484C2218yescomplemented
55#16837460C2218yescomplemented
56C2×#14273660C2211yescharacteristic, complemented
57C2×#14273658C2211yescharacteristic, complemented
58C2×Dic59⋊C8C2211yescharacteristic, complemented
59C2×Dic59⋊C8C2211yescharacteristic, complemented
60C2×#14273649C2211yescharacteristic
61C2×#14273649C2211yescharacteristic
62C2×#14273647C2211yescharacteristic
63C2×#14273647C2211yescharacteristic
64C2×#14273647C2211yescharacteristic, complemented
65C2×#14273647C2211yescharacteristic, complemented
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×#14273637C2211yescharacteristic, complemented
68C2×C8×Dic59C2211yescharacteristic, complemented
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×D59—21no—
78C22×Dic118—21no—
79C22×D236—21no—
80C22×D236—22no—
81C22×D236—24no—
82C22×D236—24no—
83C22×D236C2311yescharacteristic
84C22×D236C2314yes—
85C22×D236C2311yescharacteristic
86C22×D236C2311yescharacteristic
87C22×C22⋊D59—21no—
88C22×C4×D59—21no—
89C22×C4×D59—21no—
90C22×C4×D59—21no—
91C22×C4×D59—21no—
92C22×C4×D59—21no—
93C2×#11745671—24no—
94C2×#11745671—24no—
95C2×#11745671C2314yes—
96C2×#11745671C2314yes—
97C2×D472—24no—
98C2×D472—24no—
99C2×D472C2314yes—
100C2×D472C2314yes—
101C22×C59⋊C8C2311yescharacteristic
102C22×C59⋊C8C2311yescharacteristic
103#14273726—22no—
104#14273726C2314yescomplemented
105#14273722—28no—
106#14273716—22no—
107#14273716C2314yescomplemented
108#14273713—28no—
109#14273709—28no—
110#14273707—28no—
111#14273701—22no—
112#14273701C2314yes—
113Q8×Dic59—22no—
114Q8×Dic59C2314yescomplemented
115C4×D236—28no—
116C4×D236—28no—
117#14273689—22no—
118#14273689—22no—
119#14273689—22no—
120#14273689—22no—
121#14273689—22no—
122#14273689C2314yes—
123#14273689C2314yes—
124#14273689C2314yes—
125#14273689C2314yes—
126#14273689C2314yescomplemented
127#14273686D414yes—
128#14273686C2314yes—
129C2×C4⋊Dic59—21no—
130C2×C4⋊Dic59D411yescharacteristic
131C2×C4⋊Dic59D411yescharacteristic
132C2×C4⋊Dic59C2311yescharacteristic
133C2×Dic59⋊C4—21no—
134C2×C22⋊Dic59D411yescharacteristic
135C2×C22⋊Dic59D411yescharacteristic
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—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4—21no—
144C22⋊C4×D59—28no—
145C22⋊C4×D59—28no—
146C2×C4×Dic59—21no—
147C2×C4×Dic59C2311yescharacteristic
148C2×C4×Dic59C2311yescharacteristic
149#14273660C2314yescomplemented
150#14273658C2314yescomplemented
151Dic59⋊C8C2314yescomplemented
152Dic59⋊C8C2314yescomplemented
153#14273649C2314yes—
154#14273649C2314yes—
155#14273647C2314yes—
156#14273647C2314yes—
157#14273647C2314yescomplemented
158#14273647C2314yescomplemented
159C22⋊(C59⋊C8)C2314yes—
160#14273637C2314yescomplemented
161C8×Dic59C2314yescomplemented
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—21no—
184C23×D59—21no—
185C23×D59—28no—
186C23×D59—24no—
187C23×D59—21no—
188C23×D59—82no—
189C23×D59—82no—
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—82no—
206C22×Dic59—21no—
207C22×Dic59C2×D411yescharacteristic
208C22×Dic59C2×D411yescharacteristic
209C22×Dic59C2×D411yescharacteristic
210C22×Dic59C2×D411yescharacteristic
211C2×D236—28no—
212C2×D236—216no—
213C2×D236—21no—
214C2×D236—21no—
215C2×D236—24no—
216C2×D236—22no—
217C2×D236—22no—
218C2×D236—28no—
219C2×D236—28no—
220C2×D236—22no—
221C2×D236—22no—
222C2×D236—21no—
223C2×D236#4114yes—
224C2×D236#4114yes—
225C2×D236C2412yes—
226C2×D236C2412yes—
227C2×D236C2412yes—
228C2×C4×D59—24no—
229C2×C4×D59—24no—
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×D59—82no—
237C2×C4×D59—82no—
238C2×Dic118—24no—
239C2×Dic118—82no—
240C2×C8×C59—22no—
241C2×C8×C59—22no—
242C2×C8×C59C2412yes—
243C2×C8×C59C2412yes—
244C4⋊C4×C59—24no—
245C4⋊C4×C59—21no—
246C4⋊C4×C59—21no—
247C4⋊C4×C59—21no—
248C4⋊C4×C59C2412yes—
249C4⋊C4×C59C2412yes—
250C4⋊C4×C59C2412yes—
251C22⋊C4×C59—24no—
252C22⋊C4×C59—24no—
253C42×C59—24no—
254C22⋊Dic59C2×D414yes—
255C22⋊Dic59C2×D414yes—
256#11745671—28no—
257#11745671—28no—
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)⋊C4—24no—
266C4⋊Dic59—21no—
267C4⋊Dic59—24no—
268C4⋊Dic59C2×D414yes—
269C4⋊Dic59C2×D414yes—
270C4⋊Dic59C2412yes—
271Dic59⋊C4—24no—
272C4×Dic59—24no—
273C4×Dic59C2×D412yes—
274C4×Dic59C2×D412yes—
275C4×Dic59C2412yes—
276C4×Dic59C2412yes—
277C2×C59⋊C8—22no—
278C2×C59⋊C8—22no—
279C2×C59⋊C8C2412yes—
280C2×C59⋊C8C2412yes—
281D472—28no—
282D472—28no—
283C23×C59—22no—
284C23×C59—22no—
285C23×C59—22no—
286C23×C59C22×D412yes—
287C23×C59C22×D411yescharacteristic
288C22×D59—24no—
289C22×D59—24no—
290C22×D59—22no—
291C22×D59—22no—
292C22×D59—216no—
293C22×D59—22no—
294C22×D59—42no—
295C22×D59—42no—
296C22×D59—42no—
297C22×D59—42no—
298C22×D59—42no—
299C22×D59—42no—
300C22×D59—42no—
301C22×D59—84no—
302C22×D59—84no—
303C22×D59—816no—
304Q8×C59—22no—
305Q8×C59—22no—
306Q8×C59—42no—
307C2×C4×C59—22no—
308C2×C4×C59—24no—
309C2×C4×C59—22no—
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—42no—
319C2×C4×C59C22×D412yes—
320C2×C4×C59C22×D411yescharacteristic
321C2×C4×C59C2×#4112yes—
322C2×C4×C59C2×#4112yes—
323C2×C4×C59C2511yescharacteristic
324C22⋊D59—84no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—42no—
331C2×Dic59C22×D412yes—
332C2×Dic59C22×D412yes—
333C2×Dic59C22×D412yes—
334C2×Dic59C22×D412yes—
335D236—216no—
336D236—24no—
337D236—24no—
338D236—22no—
339D236—22no—
340D236—22no—
341D236—22no—
342D236—42no—
343D236C2×#4114yes—
344D236C2×#4114yes—
345C4×D59—84no—
346C4×D59—84no—
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—22no—
357C22×C59—22no—
358C22×C59—22no—
359C22×C59—44no—
360C22×C59#52512yes—
361C22×C59#57612yes—
362C22×C59#57712yes—
363C22×C59C23×D411yescharacteristic
364C2×D59—24no—
365C2×D59—24no—
366C2×D59—48no—
367C2×D59—48no—
368C2×D59—42no—
369C2×D59—42no—
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—42no—
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—22no—
389Dic59—42no—
390C2×#542—591no—
391C2×#518—591no—
392#3118—5916no—
393C2×#485D5911yescharacteristic, complemented
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×SD16—591no—
404C2×C4×D8—591no—
405C2×#433—591no—
406C2×C59—42no—
407C2×C59#311814yescomplemented
408C2×C59C2×#52511yescharacteristic
409C2×C59C2×#57611yescharacteristic
410C2×C59C2×#57711yescharacteristic
411D59—44no—
412D59—44no—
413D59—82no—
414C23×D4—591no—
415C22×SD16—591no—
416C22×SD16—591no—
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—1181no—
427C2×C22⋊Q8C2×D5911yescharacteristic
428C2×#121—591no—
429#518—598no—
430#518—1184no—
431C2×C4×Q8—591no—
432C2×C4×D4—591no—
433C2×C4×D4—591no—
434C2×C4×D4—591no—
435C2×C4×D4—591no—
436C2×C4×D4—591no—
437C2×C4×D4—1181no—
438C2×C4×D4—1181no—
439C2×#117—591no—
440C2×#117C2×D5911yescharacteristic
441C22×C22⋊C4—1181no—
442C22×C22⋊C4—1181no—
443#485C2×D5918yescomplemented
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×SD16—598no—
454C4×D8—598no—
455#433—598no—
456C2×#107—591no—
457C2×#107C2×D5911yescharacteristic, complemented
458C2×#106—591no—
459C2×#106C2×D5911yescharacteristic, complemented
460C2×C4⋊C8—591no—
461C2×C4⋊C8—591no—
462C2×#103C2×D5911yescharacteristic, complemented
463C2×#103C2×D5911yescharacteristic, complemented
464C2×#102—591no—
465C2×#102—591no—
466C2×#102—591no—
467C2×#102—591no—
468C2×#102—591no—
469C2×#102—591no—
470C2×C22⋊C8—591no—
471C2×C22⋊C8C2×D5911yescharacteristic
472C2×#97—591no—
473C2×C4×C8—591no—
474C59C2×#311811yescharacteristic, complemented, Sylow
475C25—1181no—
476C22×Q8—1181no—
477C22×Q8C22×D5911yescharacteristic
478C22×D4—591no—
479C22×D4—591no—
480C22×D4—591no—
481C22×D4—594no—
482C22×D4—1184no—
483C22×D4—1184no—
484C22×D4—1181no—
485C22×D4—1181no—
486C22×D4—1182no—
487C23×C4—1181no—
488C23×C4—1181no—
489C23×C4—1181no—
490C23×C4—1181no—
491C23×C4—1181no—
492C23×C4C22×D5911yescharacteristic
493C2×SD16—594no—
494C2×SD16—594no—
495C2×SD16—1184no—
496C2×SD16—1184no—
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—1182no—
510#124—1188no—
511#123—1188no—
512C22⋊Q8—22no—
513C22⋊Q8—1188no—
514C22⋊Q8C22×D5914yes—
515#121—594no—
516#121—1182no—
517C4×Q8—594no—
518C4×Q8—1182no—
519C4×D4—594no—
520C4×D4—594no—
521C4×D4—594no—
522C4×D4—594no—
523C4×D4—594no—
524C4×D4—1188no—
525C4×D4—1188no—
526C4×D4—1182no—
527C4×D4—1182no—
528C4×D4—1182no—
529C4×D4—1182no—
530C4×D4—1182no—
531#117—22no—
532#117—594no—
533#117—594no—
534#117C22×D5914yes—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—591no—
537C2×C4⋊C4—591no—
538C2×C4⋊C4—591no—
539C2×C4⋊C4—1181no—
540C2×C4⋊C4—1181no—
541C2×C4⋊C4C22×D5911yescharacteristic
542C2×C4⋊C4C22×D5911yescharacteristic
543C2×C4⋊C4C22×D5911yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—591no—
547C2×C22⋊C4—591no—
548C2×C22⋊C4—1188no—
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×C22⋊C4—1181no—
558C2×C42—21no—
559C2×C42—591no—
560C2×C42—591no—
561C2×C42—1181no—
562#107—594no—
563#107C22×D5914yescomplemented
564#106—594no—
565#106C22×D5914yescomplemented
566C4⋊C8—594no—
567C4⋊C8—594no—
568#103C22×D5914yescomplemented
569#103C22×D5914yescomplemented
570#102—594no—
571#102—594no—
572#102—594no—
573#102—594no—
574#102—594no—
575#102—594no—
576C22⋊C8—594no—
577C22⋊C8C22×D5914yes—
578#97—594no—
579C4×C8—594no—
580C24—1188no—
581C24—1184no—
582C24—1181no—
583C24—1181no—
584C24—1181no—
585C24—4722no—
586C24—4722no—
587C24D4×D5911yescharacteristic
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—1184no—
592C2×Q8—4722no—
593C2×Q8C23×D5912yes—
594C2×D4—594no—
595C2×D4—594no—
596C2×D4—592no—
597C2×D4—592no—
598C2×D4—592no—
599C2×D4—1188no—
600C2×D4—1188no—
601C2×D4—1188no—
602C2×D4—11816no—
603C2×D4—1184no—
604C2×D4—1184no—
605C2×D4—1181no—
606C2×D4—1181no—
607C2×D4—1181no—
608C2×D4—1182no—
609C2×D4—1182no—
610C2×D4—1182no—
611C2×D4—1182no—
612C2×D4—4722no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—591no—
620C22×C4—591no—
621C22×C4—591no—
622C22×C4—591no—
623C22×C4—1184no—
624C22×C4—1184no—
625C22×C4—1184no—
626C22×C4—1184no—
627C22×C4—1184no—
628C22×C4—1181no—
629C22×C4—4722no—
630C22×C4—4722no—
631C22×C4—4722no—
632C22×C4—4722no—
633C22×C4—4722no—
634C22×C4D4×D5912yes—
635C22×C4D4×D5911yescharacteristic
636C22×C4C23×D5912yes—
637C22×C4C23×D5911yescharacteristic
638SD16—1188no—
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—21no—
654C4⋊C4—594no—
655C4⋊C4—594no—
656C4⋊C4—592no—
657C4⋊C4—1184no—
658C4⋊C4—1184no—
659C4⋊C4—1181no—
660C4⋊C4C23×D5912yes—
661C4⋊C4C23×D5912yes—
662C4⋊C4C23×D5912yes—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—594no—
666C22⋊C4—594no—
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—592no—
679C42—592no—
680C42—1184no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—11816no—
685C23—1184no—
686C23—1184no—
687C23—1182no—
688C23—1182no—
689C23—1182no—
690C23—4724no—
691C23—4724no—
692C23—47216no—
693C23—2362no—
694C23—2362no—
695C23—2362no—
696C23—2362no—
697C23—2362no—
698C23—2362no—
699C23—2362no—
700C23C2×D4×D5912yes—
701C23C2×D4×D5911yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—42no—
705Q8—4724no—
706D4—594no—
707D4—594no—
708D4—11816no—
709D4—1184no—
710D4—1184no—
711D4—1182no—
712D4—1182no—
713D4—1182no—
714D4—1182no—
715D4—4724no—
716D4—2362no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—592no—
730C2×C4—592no—
731C2×C4—592no—
732C2×C4—592no—
733C2×C4—1182no—
734C2×C4—1182no—
735C2×C4—1182no—
736C2×C4—1182no—
737C2×C4—1182no—
738C2×C4—4724no—
739C2×C4—4724no—
740C2×C4—4724no—
741C2×C4—4724no—
742C2×C4—4724no—
743C2×C4—2362no—
744C2×C4C2×D4×D5912yes—
745C2×C4C2×D4×D5911yescharacteristic
746C2×C4#41×D5912yes—
747C2×C4#41×D5912yes—
748C2×C4C24×D5911yescharacteristic
749C8—22no—
750C8—22no—
751C8—1182no—
752C8—1182no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—1184no—
758C22—1184no—
759C22—47216no—
760C22—4724no—
761C22—2362no—
762C22—2362no—
763C22—2362no—
764C22—2362no—
765C22—2362no—
766C22—2362no—
767C22—2362no—
768C22—2368no—
769C22—2368no—
770C22#1683791012yes—
771C22#1683820412yes—
772C22#1683821112yes—
773C22C22×D4×D5911yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—1182no—
780C4—1182no—
781C4—1182no—
782C4—1182no—
783C4—2362no—
784C4#1683791012yes—
785C4C2×#41×D5911yescharacteristic
786C4C2×#41×D5911yescharacteristic
787C2—42no—
788C2—4722no—
789C2—2364no—
790C2—2364no—
791C2#2143428314yesdirect product factor
792C2C2×#1683791011yescharacteristic
793C2C2×#1683820411yescharacteristic
794C2C2×#1683821111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#485C2
socleC23×C59C22×D4
prime radicalC2×#16837538C2
hypercenterC2×#485D59
hypocenterC59C2×#3118
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
1. C2×#16838025C2semidirect
2. C2×#16837876C2semidirect
3. #21434283C2direct (N × H)
4. C2×#16837726C2semidirect
5. C2×#16837691C2semidirect
6. C2×#16837681C2semidirect
7. C2×#16837620C2semidirect
8. C2×#16837620C2semidirect
9. C2×#16837552C2semidirect
11. C2×#16837513C2semidirect
12. C2×#16837505C2semidirect
13. C2×#16837487C2semidirect
14. C2×#16837484C2semidirect
15. C2×#16837460C2semidirect
16. C2×C59×#485C2semidirect
23. #16838025C22semidirect
24. C2×#14273726C22semidirect
26. C2×#14273716C22semidirect
32. #16837876C22semidirect
33. C2×Q8×Dic59C22semidirect
40. C2×#14273689C22semidirect
44. #16837726C22semidirect
45. #16837691C22semidirect
46. #16837681C22semidirect
47. #16837620C22semidirect
48. #16837620C22semidirect
49. #16837552C22semidirect
51. #16837513C22semidirect
52. #16837505C22semidirect
53. #16837487C22semidirect
54. #16837484C22semidirect
55. #16837460C22semidirect
56. C2×#14273660C22semidirect
57. C2×#14273658C22semidirect
58. C2×Dic59⋊C8C22semidirect
59. C2×Dic59⋊C8C22semidirect
64. C2×#14273647C22semidirect
65. C2×#14273647C22semidirect
67. C2×#14273637C22semidirect
68. C2×C8×Dic59C22semidirect
71. C59×#485C22semidirect
72. C2×#107×C59C22semidirect
73. C2×#106×C59C22semidirect
74. C2×#103×C59C22semidirect
75. C2×#103×C59C22semidirect
104. #14273726C23semidirect
107. #14273716C23semidirect
114. Q8×Dic59C23semidirect
126. #14273689C23semidirect
149. #14273660C23semidirect
150. #14273658C23semidirect
151. Dic59⋊C8C23semidirect
152. Dic59⋊C8C23semidirect
157. #14273647C23semidirect
158. #14273647C23semidirect
160. #14273637C23semidirect
161. C8×Dic59C23semidirect
177. #107×C59C23semidirect
178. #106×C59C23semidirect
179. #103×C59C23semidirect
180. #103×C59C23semidirect
393. C2×#485D59semidirect
407. C2×C59#3118semidirect
443. #485C2×D59semidirect
457. C2×#107C2×D59semidirect
459. C2×#106C2×D59semidirect
462. C2×#103C2×D59semidirect
463. C2×#103C2×D59semidirect
474. C59C2×#3118semidirect
563. #107C22×D59semidirect
565. #106C22×D59semidirect
568. #103C22×D59semidirect
569. #103C22×D59semidirect
791. C2#21434283direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380252
C2×#168378762
#214342832
C2×#168377262
C2×#168376912
C2×#168376812
C2×#168376202
C2×#168375522
C2×#168375382
C2×#168375132
C2×#168375052
C2×#168374872
C2×#168374842
C2×#168374602
C2×C59×#4852
C2×#311859