Finite Group Databasebeta

← C2×#21434275 #29456915

Subgroups — C2×#21434275 #29456915

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×#16838019C211yesmaximal, characteristic, complemented
2C2×#16837876C211yesmaximal, characteristic, complemented
3#21434275C2116yesmaximal, direct product factor
4C2×#16837743C211yesmaximal, characteristic, complemented
5C2×#16837691C211yesmaximal, characteristic, complemented
6C2×#16837681C211yesmaximal, characteristic, complemented
7C2×#16837616C211yesmaximal, characteristic, complemented
8C2×#16837616C211yesmaximal, characteristic, complemented
9C2×#16837555C211yesmaximal, characteristic, complemented
10C2×#16837535C211yesmaximal, characteristic
11C2×#16837511C211yesmaximal, characteristic, complemented
12C2×#16837501C211yesmaximal, characteristic, complemented
13C2×#16837489C211yesmaximal, characteristic, complemented
14C2×#16837482C211yesmaximal, characteristic, complemented
15C2×#16837460C211yesmaximal, characteristic, complemented
16C2×C59×#482C211yesmaximal, characteristic, complemented
17C23×D236C2211yescharacteristic
18C22×#11745660C2211yescharacteristic
19C22×#11745660C2211yescharacteristic
20C22×#11745669C2211yescharacteristic
21C22×#11745669C2211yescharacteristic
22#16838019—24no—
23#16838019C2218yescomplemented
24C2×#14273726C2211yescharacteristic, complemented
25C2×#14273720—21no—
26C2×#14273714—21no—
27C2×#14273714C2211yescharacteristic, complemented
28C2×#14273708—21no—
29C2×#14273706C2211yescharacteristic
30C2×#14273704—21no—
31#16837876—24no—
32#16837876C2218yescomplemented
33C2×#14273692C2211yescharacteristic, complemented
34C2×C4×D236—21no—
35C2×C4×D236—21no—
36C2×D4×Dic59C2211yescharacteristic, complemented
37C2×#14273689C2211yescharacteristic
38C2×#14273689C2211yescharacteristic
39C2×#14273689C2211yescharacteristic
40C2×#14273689C2211yescharacteristic
41C2×#14273686C2211yescharacteristic
42C2×C22⋊C4×D59—21no—
43C2×C22⋊C4×D59—21no—
44#16837743C2218yescomplemented
45#16837691C2218yescomplemented
46#16837681C2218yescomplemented
47#16837616C2218yescomplemented
48#16837616C2218yescomplemented
49#16837555C2218yescomplemented
50#16837535C2218yes—
51#16837511C2218yescomplemented
52#16837501C2218yescomplemented
53#16837489C2218yescomplemented
54#16837482C2218yescomplemented
55#16837460C2218yescomplemented
56C2×#14273660C2211yescharacteristic, complemented
57C2×#14273658C2211yescharacteristic, complemented
58C2×Dic59⋊C8C2211yescharacteristic, complemented
59C2×Dic59⋊C8C2211yescharacteristic, complemented
60C2×#14273650C2211yescharacteristic, complemented
61C2×#14273650C2211yescharacteristic, complemented
62C2×#14273649C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×#14273637C2211yescharacteristic, complemented
68C2×C8×Dic59C2211yescharacteristic, complemented
69C2×#121×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C59×#482C2218yescomplemented
72C2×#107×C59C2211yescharacteristic, complemented
73C2×#106×C59C2211yescharacteristic, complemented
74C2×#102×C59C2211yescharacteristic, complemented
75C2×#102×C59C2211yescharacteristic, complemented
76C2×C22⋊C8×C59C2211yescharacteristic
77C24×D59—21no—
78C22×Dic118—21no—
79C22×Dic118C2311yescharacteristic
80C22×D236—21no—
81C22×D236—22no—
82C22×D236—24no—
83C22×D236—24no—
84C22×D236C2314yes—
85C22×D236C2311yescharacteristic
86C22×D236C2311yescharacteristic
87C23×Dic59—21no—
88C22×C4×D59—21no—
89C22×C4×D59—21no—
90C22×C4×D59—21no—
91C22×C4×D59—21no—
92C2×#11745660—24no—
93C2×#11745660—24no—
94C2×#11745660C2314yes—
95C2×#11745660C2314yes—
96C2×#11745669—24no—
97C2×#11745669—24no—
98C2×#11745669C2314yes—
99C2×#11745669C2314yes—
100C22×C59⋊C8C2311yescharacteristic
101C22×C59⋊C8C2311yescharacteristic
102#14273726—22no—
103#14273726C2314yescomplemented
104#14273720—28no—
105#14273714—28no—
106#14273714—22no—
107#14273714C2314yescomplemented
108#14273708—28no—
109#14273706—22no—
110#14273706C2314yes—
111#14273704—28no—
112#14273692—22no—
113#14273692C2314yescomplemented
114C4×D236—28no—
115C4×D236—28no—
116D4×Dic59—22no—
117D4×Dic59C2314yescomplemented
118#14273689—22no—
119#14273689—22no—
120#14273689—22no—
121#14273689—22no—
122#14273689C2314yes—
123#14273689C2314yes—
124#14273689C2314yes—
125#14273689C2314yes—
126#14273686D414yes—
127#14273686C2314yes—
128C2×C4⋊Dic59D411yescharacteristic
129C2×C4⋊Dic59D411yescharacteristic
130C2×C4⋊Dic59C2311yescharacteristic
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×C22⋊Dic59—21no—
135C2×C22⋊Dic59—21no—
136C2×C22⋊Dic59—21no—
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59D411yescharacteristic
139C2×C22⋊Dic59D411yescharacteristic
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#14273650C2314yescomplemented
154#14273650C2314yescomplemented
155#14273649C2314yes—
156#14273649C2314yes—
157#14273647C2314yes—
158#14273647C2314yes—
159C22⋊(C59⋊C8)C2314yes—
160#14273637C2314yescomplemented
161C8×Dic59C2314yescomplemented
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×C59C2314yes—
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×C59C2314yescomplemented
180#102×C59C2314yescomplemented
181C22⋊C8×C59C2314yes—
182C24×C59—21no—
183C24×C59C2×D411yescharacteristic
184C23×D59—21no—
185C23×D59—21no—
186C23×D59—28no—
187C23×D59—24no—
188C23×D59—82no—
189C23×D59—82no—
190C2×D4×C59—24no—
191C2×D4×C59—21no—
192C2×D4×C59—22no—
193C2×D4×C59—22no—
194C2×D4×C59—82no—
195C2×D4×C59C2412yes—
196C22×C4×C59—22no—
197C22×C4×C59—22no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×D412yes—
203C22×C4×C59C2412yes—
204C22×C4×C59C2411yescharacteristic
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—24no—
208C22×Dic59—82no—
209C22×Dic59C2×D411yescharacteristic
210C22×Dic59C2×D411yescharacteristic
211C22×Dic59C2×D411yescharacteristic
212C22×Dic59C2×D411yescharacteristic
213C2×D236—28no—
214C2×D236—216no—
215C2×D236—21no—
216C2×D236—21no—
217C2×D236—24no—
218C2×D236—22no—
219C2×D236—22no—
220C2×D236—28no—
221C2×D236—28no—
222C2×D236#4114yes—
223C2×D236#4114yes—
224C2×D236C2412yes—
225C2×D236C2412yes—
226C2×C4×D59—24no—
227C2×C4×D59—24no—
228C2×C4×D59—24no—
229C2×C4×D59—24no—
230C2×C4×D59—82no—
231C2×C4×D59—82no—
232C2×C4×D59—82no—
233C2×C4×D59—82no—
234C2×Dic118—22no—
235C2×Dic118—22no—
236C2×Dic118—21no—
237C2×Dic118—24no—
238C2×Dic118—82no—
239C2×Dic118C2412yes—
240C2×C8×C59—22no—
241C2×C8×C59—22no—
242C2×C8×C59C2412yes—
243C2×C8×C59C2412yes—
244C4⋊C4×C59—21no—
245C4⋊C4×C59—21no—
246C4⋊C4×C59—21no—
247C4⋊C4×C59C2412yes—
248C4⋊C4×C59C2412yes—
249C4⋊C4×C59C2412yes—
250C22⋊C4×C59—24no—
251C22⋊C4×C59—24no—
252C42×C59—24no—
253C22⋊Dic59—24no—
254C22⋊Dic59—24no—
255C22⋊Dic59—24no—
256C22⋊Dic59—24no—
257C22⋊Dic59C2×D414yes—
258C22⋊Dic59C2×D414yes—
259#11745669—28no—
260#11745669—28no—
261(C2×D59)⋊C4—24no—
262(C2×D59)⋊C4—24no—
263(C2×D59)⋊C4—24no—
264(C2×D59)⋊C4—24no—
265C4⋊Dic59—21no—
266C4⋊Dic59C2×D414yes—
267C4⋊Dic59C2×D414yes—
268C4⋊Dic59C2412yes—
269Dic59⋊C4—24no—
270Dic59⋊C4—24no—
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—
281#11745660—28no—
282#11745660—28no—
283C23×C59—22no—
284C23×C59—22no—
285C23×C59—22no—
286C23×C59—22no—
287C23×C59—42no—
288C23×C59—42no—
289C23×C59—42no—
290C23×C59C22×D412yes—
291C23×C59C22×D411yescharacteristic
292C22×D59—24no—
293C22×D59—24no—
294C22×D59—22no—
295C22×D59—22no—
296C22×D59—216no—
297C22×D59—42no—
298C22×D59—42no—
299C22×D59—42no—
300C22×D59—42no—
301C22×D59—84no—
302C22×D59—84no—
303C22×D59—816no—
304D4×C59—22no—
305D4×C59—22no—
306D4×C59—42no—
307D4×C59—84no—
308C2×C4×C59—22no—
309C2×C4×C59—24no—
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×C59C22×D412yes—
319C2×C4×C59C22×D411yescharacteristic
320C2×C4×C59C2×#4112yes—
321C2×C4×C59C2×#4112yes—
322C2×C4×C59C2511yescharacteristic
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—42no—
330C2×Dic59—42no—
331C2×Dic59—84no—
332C2×Dic59C22×D412yes—
333C2×Dic59C22×D412yes—
334C2×Dic59C22×D412yes—
335C2×Dic59C22×D412yes—
336D236—216no—
337D236—24no—
338D236—24no—
339D236—22no—
340D236—22no—
341D236C2×#4114yes—
342D236C2×#4114yes—
343C4×D59—84no—
344C4×D59—84no—
345C4×D59—84no—
346C4×D59—84no—
347Dic118—22no—
348Dic118—22no—
349Dic118—42no—
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—42no—
361C22×C59—42no—
362C22×C59—42no—
363C22×C59—84no—
364C22×C59#52512yes—
365C22×C59#57612yes—
366C22×C59#57712yes—
367C22×C59C23×D411yescharacteristic
368C2×D59—24no—
369C2×D59—24no—
370C2×D59—48no—
371C2×D59—48no—
372C2×D59—42no—
373C2×D59—42no—
374C2×D59—42no—
375C2×D59—42no—
376C2×D59—816no—
377C4×C59—22no—
378C4×C59—42no—
379C4×C59—42no—
380C4×C59—42no—
381C4×C59#52512yes—
382C4×C59C22×#4111yescharacteristic
383C4×C59C22×#4111yescharacteristic
384Dic59—22no—
385Dic59—22no—
386Dic59—22no—
387Dic59—22no—
388Dic59—42no—
389Dic59—42no—
390C2×#542—591no—
391C2×#518—591no—
392#3118—5916no—
393C2×#485—591no—
394C2×#482D5911yescharacteristic, complemented
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—82no—
408C2×C59#311814yescomplemented
409C2×C59C2×#52511yescharacteristic
410C2×C59C2×#57611yescharacteristic
411C2×C59C2×#57711yescharacteristic
412D59—44no—
413D59—44no—
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—591no—
427C2×C22⋊Q8—1181no—
428C2×#121C2×D5911yescharacteristic
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#485—598no—
444#482C2×D5918yescomplemented
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×#103—591no—
463C2×#103—591no—
464C2×#102—591no—
465C2×#102—591no—
466C2×#102—591no—
467C2×#102—591no—
468C2×#102C2×D5911yescharacteristic, complemented
469C2×#102C2×D5911yescharacteristic, complemented
470C2×C22⋊C8—591no—
471C2×C22⋊C8C2×D5911yescharacteristic
472C2×#97—591no—
473C2×C4×C8—591no—
474C59C2×#311811yescharacteristic, complemented, Sylow
475C25—1181no—
476C22×Q8—591no—
477C22×Q8—1181no—
478C22×D4—21no—
479C22×D4—591no—
480C22×D4—591no—
481C22×D4—594no—
482C22×D4—1184no—
483C22×D4—1184no—
484C22×D4—1181no—
485C22×D4—1182no—
486C22×D4C22×D5911yescharacteristic
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—594no—
513C22⋊Q8—1188no—
514C22⋊Q8—1182no—
515#121—22no—
516#121C22×D5914yes—
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—591no—
536C2×C4⋊C4—591no—
537C2×C4⋊C4—591no—
538C2×C4⋊C4—1181no—
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#103—594no—
569#103—594no—
570#102—594no—
571#102—594no—
572#102—594no—
573#102—594no—
574#102C22×D5914yescomplemented
575#102C22×D5914yescomplemented
576C22⋊C8—594no—
577C22⋊C8C22×D5914yes—
578#97—594no—
579C4×C8—594no—
580C24—21no—
581C24—1188no—
582C24—1184no—
583C24—1181no—
584C24—1181no—
585C24—4722no—
586C24—4722no—
587C24D4×D5911yescharacteristic
588C2×Q8—592no—
589C2×Q8—1184no—
590C2×Q8—1181no—
591C2×Q8—1182no—
592C2×Q8—1182no—
593C2×Q8—4722no—
594C2×D4—24no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—82no—
599C2×D4—594no—
600C2×D4—594no—
601C2×D4—592no—
602C2×D4—592no—
603C2×D4—1188no—
604C2×D4—1188no—
605C2×D4—1188no—
606C2×D4—11816no—
607C2×D4—1184no—
608C2×D4—1181no—
609C2×D4—1181no—
610C2×D4—1182no—
611C2×D4—1182no—
612C2×D4C23×D5912yes—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—591no—
619C22×C4—591no—
620C22×C4—591no—
621C22×C4—591no—
622C22×C4—1184no—
623C22×C4—1184no—
624C22×C4—1184no—
625C22×C4—1184no—
626C22×C4—1184no—
627C22×C4—1181no—
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—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—594no—
654C4⋊C4—594no—
655C4⋊C4—592no—
656C4⋊C4—1184no—
657C4⋊C4—1184no—
658C4⋊C4—1181no—
659C4⋊C4—1184no—
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—22no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—11816no—
689C23—1184no—
690C23—1184no—
691C23—1182no—
692C23—1182no—
693C23—4724no—
694C23—4724no—
695C23—47216no—
696C23—2362no—
697C23—2362no—
698C23—2362no—
699C23—2362no—
700C23C2×D4×D5912yes—
701C23C2×D4×D5911yescharacteristic
702Q8—1182no—
703Q8—1182no—
704Q8—4724no—
705Q8—2362no—
706D4—22no—
707D4—22no—
708D4—42no—
709D4—84no—
710D4—594no—
711D4—594no—
712D4—11816no—
713D4—1184no—
714D4—1184no—
715D4—1182no—
716D4—1182no—
717C2×C4—22no—
718C2×C4—24no—
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—592no—
728C2×C4—592no—
729C2×C4—592no—
730C2×C4—592no—
731C2×C4—1182no—
732C2×C4—1182no—
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—4724no—
742C2×C4—2362no—
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—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22—1184no—
762C22—1184no—
763C22—47216no—
764C22—2362no—
765C22—2362no—
766C22—2362no—
767C22—2362no—
768C22—2368no—
769C22—2368no—
770C22#1683791012yes—
771C22#1683820612yes—
772C22#1683820912yes—
773C22C22×D4×D5911yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—1182no—
779C4—1182no—
780C4—1182no—
781C4—1182no—
782C4—2362no—
783C4—2362no—
784C4#1683791012yes—
785C4C2×#41×D5911yescharacteristic
786C4C2×#41×D5911yescharacteristic
787C2—42no—
788C2—82no—
789C2—2364no—
790C2—2364no—
791C2#2143427514yesdirect product factor
792C2C2×#1683791011yescharacteristic
793C2C2×#1683820611yescharacteristic
794C2C2×#1683820911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#482C2
socleC23×C59C22×D4
prime radicalC2×#16837535C2
hypercenterC2×#482D59
hypocenterC59C2×#3118
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
1. C2×#16838019C2semidirect
2. C2×#16837876C2semidirect
3. #21434275C2direct (N × H)
4. C2×#16837743C2semidirect
5. C2×#16837691C2semidirect
6. C2×#16837681C2semidirect
7. C2×#16837616C2semidirect
8. C2×#16837616C2semidirect
9. C2×#16837555C2semidirect
11. C2×#16837511C2semidirect
12. C2×#16837501C2semidirect
13. C2×#16837489C2semidirect
14. C2×#16837482C2semidirect
15. C2×#16837460C2semidirect
16. C2×C59×#482C2semidirect
23. #16838019C22semidirect
24. C2×#14273726C22semidirect
27. C2×#14273714C22semidirect
32. #16837876C22semidirect
33. C2×#14273692C22semidirect
36. C2×D4×Dic59C22semidirect
44. #16837743C22semidirect
45. #16837691C22semidirect
46. #16837681C22semidirect
47. #16837616C22semidirect
48. #16837616C22semidirect
49. #16837555C22semidirect
51. #16837511C22semidirect
52. #16837501C22semidirect
53. #16837489C22semidirect
54. #16837482C22semidirect
55. #16837460C22semidirect
56. C2×#14273660C22semidirect
57. C2×#14273658C22semidirect
58. C2×Dic59⋊C8C22semidirect
59. C2×Dic59⋊C8C22semidirect
60. C2×#14273650C22semidirect
61. C2×#14273650C22semidirect
67. C2×#14273637C22semidirect
68. C2×C8×Dic59C22semidirect
71. C59×#482C22semidirect
72. C2×#107×C59C22semidirect
73. C2×#106×C59C22semidirect
74. C2×#102×C59C22semidirect
75. C2×#102×C59C22semidirect
103. #14273726C23semidirect
107. #14273714C23semidirect
113. #14273692C23semidirect
117. D4×Dic59C23semidirect
149. #14273660C23semidirect
150. #14273658C23semidirect
151. Dic59⋊C8C23semidirect
152. Dic59⋊C8C23semidirect
153. #14273650C23semidirect
154. #14273650C23semidirect
160. #14273637C23semidirect
161. C8×Dic59C23semidirect
177. #107×C59C23semidirect
178. #106×C59C23semidirect
179. #102×C59C23semidirect
180. #102×C59C23semidirect
394. C2×#482D59semidirect
408. C2×C59#3118semidirect
444. #482C2×D59semidirect
457. C2×#107C2×D59semidirect
459. C2×#106C2×D59semidirect
468. C2×#102C2×D59semidirect
469. C2×#102C2×D59semidirect
474. C59C2×#3118semidirect
563. #107C22×D59semidirect
565. #106C22×D59semidirect
574. #102C22×D59semidirect
575. #102C22×D59semidirect
791. C2#21434275direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380192
C2×#168378762
#214342752
C2×#168377432
C2×#168376912
C2×#168376812
C2×#168376162
C2×#168375552
C2×#168375352
C2×#168375112
C2×#168375012
C2×#168374892
C2×#168374822
C2×#168374602
C2×C59×#4822
C2×#311859