Finite Group Databasebeta

← C2×#21436496 #29467159

Subgroups — C2×#21436496 #29467159

Order 15104.

1994 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838104C211yesmaximal, characteristic, complemented
2C2×#16838100C211yesmaximal, characteristic, complemented
3#21436496C2116yesmaximal, direct product factor
4C2×#16837802C211yesmaximal, characteristic, complemented
5C2×#16837721C211yesmaximal, characteristic, complemented
6C2×#16837728C211yesmaximal, characteristic, complemented
7C2×#16837725C211yesmaximal, characteristic, complemented
8C2×#16837704C211yesmaximal, characteristic, complemented
9C2×#16837701C211yesmaximal, characteristic, complemented
10C2×#16837637C211yesmaximal, characteristic, complemented
11C2×#16837636C211yesmaximal, characteristic, complemented
12C2×#16837482C211yesmaximal, characteristic, complemented
13C2×(C22⋊D59)⋊C8C211yesmaximal, characteristic, complemented
14C2×#16837437C211yesmaximal, characteristic, complemented
15C22×#14273660C211yesmaximal, characteristic, complemented
16C2×C59×#481C211yesmaximal, characteristic, complemented
17C22×#11745669C2211yescharacteristic
18C23×C59⋊C8C2211yescharacteristic
19C22×C8×D59C2211yescharacteristic
20#16838104—24no—
21#16838104C2218yescomplemented
22#16838100—24no—
23#16838100C2218yescomplemented
24C2×#14273722—21no—
25C2×#14273720—21no—
26C2×#14273718C2211yescharacteristic
27C2×#14273718C2211yescharacteristic
28C2×#14273712—21no—
29C2×#14273711—21no—
30C2×#14273702C2211yescharacteristic
31C2×#14273701—21no—
32C2×#14273701C2211yescharacteristic
33C2×#14273699—21no—
34C2×#14273698C2211yescharacteristic
35C2×D4×Dic59—21no—
36C2×D4×Dic59C2211yescharacteristic
37C2×#14273689C2211yescharacteristic
38C2×C4×C22⋊D59—21no—
39C2×C4×C22⋊D59C2211yescharacteristic
40C2×#14273685C2211yescharacteristic
41C2×#14273685C2211yescharacteristic
42C22×C4⋊Dic59C2211yescharacteristic
43#16837802C2218yescomplemented
44#16837728C2218yescomplemented
45#16837725C2218yescomplemented
46#16837721C2218yescomplemented
47#16837704C2218yescomplemented
48#16837701C2218yescomplemented
49#16837637C2218yescomplemented
50#16837636C2218yescomplemented
51#16837482C2218yescomplemented
52(C22⋊D59)⋊C8C2218yescomplemented
53#16837437C2218yescomplemented
54C2×#14273660C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58C2×#14273660C2211yescharacteristic
59C2×#14273660C2218yescomplemented
60C2×#14273659C2211yescharacteristic
61C2×#14273659C2211yescharacteristic
62C2×Dic59⋊C8C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×#14273647C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×#121×C59C2211yescharacteristic
70C22×C4⋊C4×C59C2211yescharacteristic
71C59×#481C2218yescomplemented
72C2×#106×C59C2211yescharacteristic
73C2×#106×C59C2211yescharacteristic
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C22×D236—21no—
78C22×D236C2311yescharacteristic
79C22×C22⋊D59—21no—
80C22×C22⋊D59—21no—
81C22×C22⋊D59D411yescharacteristic
82C23×Dic59—21no—
83C23×Dic59—21no—
84C22×C4×D59—21no—
85C22×C4×D59C2311yescharacteristic
86C2×#11745669—24no—
87C2×#11745669C2314yes—
88C22×C59⋊C8—24no—
89C22×C59⋊C8C2314yes—
90C22×C59⋊C8C2311yescharacteristic
91C22×C59⋊C8C2311yescharacteristic
92C2×C8×D59—24no—
93C2×C8×D59C2314yes—
94#14273722—28no—
95#14273720—28no—
96#14273718—22no—
97#14273718—22no—
98#14273718C2314yes—
99#14273718C2314yes—
100#14273712—28no—
101#14273711—28no—
102#14273702—22no—
103#14273702C2314yes—
104#14273701—22no—
105#14273701—28no—
106#14273701C2314yes—
107#14273699—28no—
108#14273698—22no—
109#14273698C2314yes—
110D4×Dic59—28no—
111D4×Dic59—22no—
112D4×Dic59C2314yes—
113#14273689—22no—
114#14273689C2314yes—
115C4×C22⋊D59—28no—
116C4×C22⋊D59D414yes—
117C4×C22⋊D59C2314yes—
118#14273685—22no—
119#14273685—22no—
120#14273685C2314yes—
121#14273685C2314yes—
122C2×C4⋊Dic59—21no—
123C2×C4⋊Dic59—22no—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59—21no—
126C2×C4⋊Dic59C2311yescharacteristic
127C2×C4⋊Dic59C2311yescharacteristic
128C2×C4⋊Dic59C2311yescharacteristic
129C2×C4⋊Dic59C2314yes—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4D411yescharacteristic
133C2×C22⋊Dic59—21no—
134C2×C22⋊Dic59—21no—
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)⋊C4D411yescharacteristic
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59C2311yescharacteristic
145#14273660C2314yes—
146#14273660C2314yes—
147#14273660C2314yes—
148#14273660C2314yes—
149#14273660C2314yes—
150#14273659C2314yes—
151#14273659C2314yes—
152Dic59⋊C8C2314yes—
153#14273649C2314yes—
154#14273649C2314yes—
155#14273648C2314yes—
156#14273647C2314yes—
157(C2×D59)⋊C8C2314yes—
158C8×Dic59C2314yes—
159C22×D4×C59—21no—
160C22×D4×C59C2311yescharacteristic
161C23×C4×C59—21no—
162C23×C4×C59C2311yescharacteristic
163C22×C8×C59C2311yescharacteristic
164C22×C8×C59C2311yescharacteristic
165#121×C59—22no—
166#121×C59C2314yes—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59—22no—
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2314yes—
173C2×C22⋊C4×C59—21no—
174#106×C59C2314yes—
175#106×C59C2314yes—
176#102×C59C2314yes—
177#102×C59C2314yes—
178C22⋊C8×C59C2314yes—
179C24×C59—21no—
180C24×C59C2×D411yescharacteristic
181C23×D59—21no—
182C23×D59C2×D411yescharacteristic
183C2×D4×C59—24no—
184C2×D4×C59—21no—
185C2×D4×C59—22no—
186C2×D4×C59—22no—
187C2×D4×C59—44no—
188C2×D4×C59C2412yes—
189C22×C4×C59—22no—
190C22×C4×C59—22no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—24no—
195C22×C4×C59—82no—
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D412yes—
198C22×C4×C59C2412yes—
199C22×C4×C59C2411yescharacteristic
200C2×C22⋊D59—24no—
201C2×C22⋊D59—24no—
202C2×C22⋊D59—24no—
203C2×C22⋊D59—44no—
204C2×C22⋊D59—82no—
205C2×C22⋊D59C2×D414yes—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—24no—
210C22×Dic59—24no—
211C22×Dic59—82no—
212C22×Dic59—82no—
213C22×Dic59C2×D411yescharacteristic
214C22×Dic59C2×D411yescharacteristic
215C22×Dic59C2×D411yescharacteristic
216C2×D236—22no—
217C2×D236—22no—
218C2×D236—21no—
219C2×D236—24no—
220C2×D236—82no—
221C2×D236C2412yes—
222C2×C4×D59—22no—
223C2×C4×D59—22no—
224C2×C4×D59—24no—
225C2×C4×D59—82no—
226C2×C4×D59C2×D412yes—
227C2×C4×D59C2412yes—
228C2×C8×C59—22no—
229C2×C8×C59—22no—
230C2×C8×C59C2412yes—
231C2×C8×C59C2412yes—
232C4⋊C4×C59—21no—
233C4⋊C4×C59—21no—
234C4⋊C4×C59—24no—
235C4⋊C4×C59—21no—
236C4⋊C4×C59C2412yes—
237C4⋊C4×C59C2412yes—
238C4⋊C4×C59C2412yes—
239C22⋊C4×C59—24no—
240C22⋊Dic59—24no—
241C22⋊Dic59—24no—
242C22⋊Dic59C2×D414yes—
243#11745669—28no—
244(C2×D59)⋊C4—24no—
245(C2×D59)⋊C4—24no—
246(C2×D59)⋊C4—24no—
247(C2×D59)⋊C4—24no—
248(C2×D59)⋊C4—24no—
249(C2×D59)⋊C4C2×D414yes—
250C4⋊Dic59—21no—
251C4⋊Dic59—21no—
252C4⋊Dic59—24no—
253C4⋊Dic59—21no—
254C4⋊Dic59—24no—
255C4⋊Dic59—24no—
256C4⋊Dic59C2412yes—
257C4⋊Dic59C2412yes—
258C4⋊Dic59C2412yes—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4C2×D414yes—
262C4×Dic59—24no—
263C4×Dic59—24no—
264C4×Dic59C2×D412yes—
265C4×Dic59C2412yes—
266C2×C59⋊C8—22no—
267C2×C59⋊C8—28no—
268C2×C59⋊C8#4114yes—
269C2×C59⋊C8C2412yes—
270C2×C59⋊C8C2412yes—
271C8×D59—28no—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59—22no—
275C23×C59—42no—
276C23×C59—42no—
277C23×C59—42no—
278C23×C59#13514yes—
279C23×C59C22×D412yes—
280C23×C59C22×D411yescharacteristic
281C22×D59—22no—
282C22×D59—22no—
283C22×D59—22no—
284C22×D59—22no—
285C22×D59—42no—
286C22×D59—42no—
287C22×D59—42no—
288C22×D59C22×D412yes—
289D4×C59—22no—
290D4×C59—22no—
291D4×C59—48no—
292D4×C59—42no—
293C2×C4×C59—22no—
294C2×C4×C59—24no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—42no—
301C2×C4×C59—42no—
302C2×C4×C59—42no—
303C2×C4×C59—84no—
304C2×C4×C59C22×D412yes—
305C2×C4×C59C22×D411yescharacteristic
306C2×C4×C59C2×#4112yes—
307C2×C4×C592−1+412yes—
308C2×C4×C59C2511yescharacteristic
309C22⋊D59—28no—
310C22⋊D59—48no—
311C22⋊D59—84no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—42no—
319C2×Dic59—42no—
320C2×Dic59—42no—
321C2×Dic59—84no—
322C2×Dic59—84no—
323C2×Dic59C22×D412yes—
324C2×Dic59C22×D412yes—
325C2×Dic59C22×D412yes—
326D236—22no—
327D236—22no—
328D236—42no—
329D236—84no—
330C4×D59—24no—
331C4×D59—22no—
332C4×D59—22no—
333C4×D59—84no—
334C8×C59—22no—
335C8×C59—22no—
336C59⋊C8—22no—
337C59⋊C8C2×#4114yes—
338C2×#3339—591nomaximal, Sylow
339C22×C59—28no—
340C22×C59—22no—
341C22×C59—22no—
342C22×C59—42no—
343C22×C59—42no—
344C22×C59—42no—
345C22×C59—84no—
346C22×C59#54712yes—
347C22×C59C2×#13514yes—
348C22×C59C2×#13512yes—
349C22×C59#57612yes—
350C22×C59C23×D411yescharacteristic
351C2×D59—22no—
352C2×D59—22no—
353C2×D59—22no—
354C2×D59—44no—
355C2×D59—42no—
356C2×D59—42no—
357C2×D59—42no—
358C2×D59—84no—
359C4×C59—22no—
360C4×C59—42no—
361C4×C59—42no—
362C4×C59—42no—
363C4×C59#54712yes—
364C4×C59C22×#4111yescharacteristic
365C4×C59C2×2−1+411yescharacteristic
366Dic59—22no—
367Dic59—22no—
368Dic59—22no—
369Dic59—42no—
370Dic59—42no—
371Dic59—42no—
372C2×#553—591no—
373C2×#553—591no—
374#3339—5916no—
375C2×#499—591no—
376C2×#481—591no—
377C2×#481D5911yescharacteristic, complemented
378C2×#482—591no—
379C2×#482—591no—
380C2×#478—591no—
381C2×#478—591no—
382C2×#466—591no—
383C2×#466—591no—
384C2×C4×D8—591no—
385C2×C8×D4—591no—
386C2×#427—591no—
387C22×#107—591no—
388C2×C59—24no—
389C2×C59—82no—
390C2×C59#333914yescomplemented
391C2×C59C2×#54711yescharacteristic
392C2×C59C22×#13511yescharacteristic
393C2×C59C2×#57611yescharacteristic
394D59—42no—
395D59—82no—
396C22×D8—591no—
397C23×C8—591no—
398C23×C8—591no—
399#553—598no—
400#553—598no—
401#553—1184no—
402#553—1184no—
403C2×#126—1181no—
404C2×#126—1181no—
405C2×#125—591no—
406C2×#125—591no—
407C2×#123—1181no—
408C2×#123—1181no—
409C2×#121—591no—
410C2×#121—591no—
411C2×#121—591no—
412C2×#121—1181no—
413C2×#121—1181no—
414C2×#121C2×D5911yescharacteristic
415C2×C4×D4—591no—
416C2×C4×D4—591no—
417C2×C4×D4—591no—
418C2×C4×D4—1181no—
419C2×C4×D4—1181no—
420C2×#117—591no—
421C2×#117—591no—
422C22×C4⋊C4—591no—
423C22×C4⋊C4C2×D5911yescharacteristic
424#499—598no—
425#482—598no—
426#482—598no—
427#481—598no—
428#481C2×D5918yescomplemented
429#478—598no—
430#478—598no—
431#466—598no—
432#466—598no—
433C4×D8—598no—
434C8×D4—598no—
435#427—598no—
436C2×#107—591no—
437C2×#107—591no—
438C2×#107—598no—
439C2×#107—591no—
440C2×#107—591no—
441C2×#107—591no—
442C2×#106—591no—
443C2×#106—591no—
444C2×#106C2×D5911yescharacteristic
445C2×#106C2×D5911yescharacteristic
446C2×C4⋊C8—591no—
447C2×#102—591no—
448C2×#102—591no—
449C2×#102—591no—
450C2×#102—591no—
451C2×#102C2×D5911yescharacteristic
452C2×#102C2×D5911yescharacteristic
453C2×C22⋊C8—591no—
454C2×C22⋊C8C2×D5911yescharacteristic
455C2×C4×C8—591no—
456C59C2×#333911yescharacteristic, complemented, Sylow
457C22×D4—21no—
458C22×D4—591no—
459C22×D4—591no—
460C22×D4—1181no—
461C22×D4—1181no—
462C22×D4—1181no—
463C22×D4C22×D5911yescharacteristic
464C23×C4—21no—
465C23×C4—591no—
466C23×C4—1181no—
467C23×C4—1181no—
468C23×C4—1181no—
469C23×C4C22×D5911yescharacteristic
470C2×D8—594no—
471C2×D8—1184no—
472C22×C8—591no—
473C22×C8—591no—
474C22×C8—594no—
475C22×C8—594no—
476C22×C8—1184no—
477C22×C8—1184no—
478C22×C8C22×D5911yescharacteristic
479C22×C8C22×D5911yescharacteristic
480#126—1188no—
481#126—1188no—
482#125—594no—
483#125—594no—
484#125—1182no—
485#125—1182no—
486#123—1188no—
487#123—1188no—
488#121—22no—
489#121—594no—
490#121—594no—
491#121—594no—
492#121—1182no—
493#121—1188no—
494#121—1182no—
495#121—1188no—
496#121—1182no—
497#121C22×D5914yes—
498C4×D4—594no—
499C4×D4—594no—
500C4×D4—594no—
501C4×D4—594no—
502C4×D4—1182no—
503C4×D4—1182no—
504C4×D4—1188no—
505C4×D4—1188no—
506#117—594no—
507#117—594no—
508#117—1182no—
509#117—1182no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—591no—
513C2×C4⋊C4—591no—
514C2×C4⋊C4—591no—
515C2×C4⋊C4—594no—
516C2×C4⋊C4—591no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4—1181no—
519C2×C4⋊C4—1181no—
520C2×C4⋊C4—1181no—
521C2×C4⋊C4—1181no—
522C2×C4⋊C4—1182no—
523C2×C4⋊C4C22×D5911yescharacteristic
524C2×C4⋊C4C22×D5911yescharacteristic
525C2×C4⋊C4C22×D5914yes—
526C2×C4⋊C4C22×D5911yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—591no—
529C2×C22⋊C4—591no—
530C2×C22⋊C4—1181no—
531C2×C22⋊C4—1181no—
532C2×C22⋊C4—1181no—
533C2×C22⋊C4—1181no—
534C2×C22⋊C4—1181no—
535C2×C22⋊C4—1181no—
536C2×C22⋊C4—1181no—
537C2×C42—591no—
538C2×C42—1181no—
539C2×C42—1181no—
540#107—594no—
541#107—594no—
542#107—594no—
543#107—594no—
544#107—594no—
545#106—594no—
546#106—594no—
547#106C22×D5914yes—
548#106C22×D5914yes—
549C4⋊C8—594no—
550#102—594no—
551#102—594no—
552#102—594no—
553#102—594no—
554#102C22×D5914yes—
555#102C22×D5914yes—
556C22⋊C8—594no—
557C22⋊C8C22×D5914yes—
558C4×C8—594no—
559C24—21no—
560C24—591no—
561C24—1181no—
562C24D4×D5911yescharacteristic
563C2×D4—24no—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—44no—
568C2×D4—594no—
569C2×D4—592no—
570C2×D4—1184no—
571C2×D4—1184no—
572C2×D4—1184no—
573C2×D4—1184no—
574C2×D4—1181no—
575C2×D4—1182no—
576C2×D4—1182no—
577C2×D4—4722no—
578C2×D4—4722no—
579C2×D4—2364no—
580C2×D4C23×D5912yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—82no—
588C22×C4—591no—
589C22×C4—591no—
590C22×C4—591no—
591C22×C4—592no—
592C22×C4—592no—
593C22×C4—1184no—
594C22×C4—1184no—
595C22×C4—1182no—
596C22×C4—1182no—
597C22×C4—1184no—
598C22×C4—1181no—
599C22×C4—1181no—
600C22×C4—1181no—
601C22×C4—4722no—
602C22×C4—4722no—
603C22×C4—4722no—
604C22×C4D4×D5912yes—
605C22×C4D4×D5911yescharacteristic
606C22×C4C23×D5912yes—
607C22×C4C23×D5911yescharacteristic
608D8—1188no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—594no—
612C2×C8—592no—
613C2×C8—592no—
614C2×C8—1188no—
615C2×C8—1188no—
616C2×C8—1182no—
617C2×C8C23×D5912yes—
618C2×C8C23×D5912yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—594no—
624C4⋊C4—592no—
625C4⋊C4—592no—
626C4⋊C4—592no—
627C4⋊C4—1184no—
628C4⋊C4—1184no—
629C4⋊C4—1184no—
630C4⋊C4—1184no—
631C4⋊C4—1181no—
632C4⋊C4—1181no—
633C4⋊C4—1184no—
634C4⋊C4—1181no—
635C4⋊C4C23×D5912yes—
636C4⋊C4C23×D5912yes—
637C4⋊C4C23×D5912yes—
638C22⋊C4—24no—
639C22⋊C4—594no—
640C22⋊C4—594no—
641C22⋊C4—1184no—
642C22⋊C4—1184no—
643C22⋊C4—1184no—
644C22⋊C4—1184no—
645C22⋊C4—1184no—
646C22⋊C4—1184no—
647C22⋊C4—1184no—
648C42—592no—
649C42—592no—
650C42—1184no—
651C42—1184no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—592no—
659C23—1182no—
660C23—1182no—
661C23—1182no—
662C23—1182no—
663C23—2362no—
664C23—2362no—
665C23—2362no—
666C23#1427374814yes—
667C23C2×D4×D5912yes—
668C23C2×D4×D5911yescharacteristic
669D4—22no—
670D4—22no—
671D4—48no—
672D4—42no—
673D4—1188no—
674D4—1182no—
675D4—1182no—
676D4—4724no—
677D4—4724no—
678D4—2368no—
679D4—2362no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—84no—
691C2×C4—592no—
692C2×C4—592no—
693C2×C4—592no—
694C2×C4—1182no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—1182no—
698C2×C4—1182no—
699C2×C4—1184no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—4724no—
704C2×C4—4724no—
705C2×C4—4724no—
706C2×C4—2362no—
707C2×C4—2362no—
708C2×C4—2362no—
709C2×C4C2×D4×D5912yes—
710C2×C4C2×D4×D5911yescharacteristic
711C2×C4#41×D5912yes—
712C2×C4#1427377412yes—
713C2×C4C24×D5911yescharacteristic
714C8—22no—
715C8—22no—
716C8—594no—
717C8—1182no—
718C22—28no—
719C22—22no—
720C22—22no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—84no—
725C22—1182no—
726C22—1182no—
727C22—1182no—
728C22—4724no—
729C22—2362no—
730C22—2362no—
731C22—2362no—
732C22—2364no—
733C22#1683805012yes—
734C22C2×#1427374814yes—
735C22C2×#1427374812yes—
736C22#1683820612yes—
737C22C22×D4×D5911yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—1182no—
743C4—1182no—
744C4—1182no—
745C4—2362no—
746C4—2362no—
747C4—2362no—
748C4#1683805012yes—
749C4C2×#41×D5911yescharacteristic
750C4C2×#1427377411yescharacteristic
751C2—24no—
752C2—82no—
753C2—4722no—
754C2—2362no—
755C2#2143649614yesdirect product factor
756C2C2×#1683805011yescharacteristic
757C2C22×#1427374811yescharacteristic
758C2C2×#1683820611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#481C2
socleC23×C59C22×D4
hypercenterC2×#481D59
hypocenterC59C2×#3339
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#16838104C2semidirect
2. C2×#16838100C2semidirect
3. #21436496C2direct (N × H)
4. C2×#16837802C2semidirect
5. C2×#16837721C2semidirect
6. C2×#16837728C2semidirect
7. C2×#16837725C2semidirect
8. C2×#16837704C2semidirect
9. C2×#16837701C2semidirect
10. C2×#16837637C2semidirect
11. C2×#16837636C2semidirect
12. C2×#16837482C2semidirect
13. C2×(C22⋊D59)⋊C8C2semidirect
14. C2×#16837437C2semidirect
15. C22×#14273660C2semidirect
16. C2×C59×#481C2semidirect
21. #16838104C22semidirect
23. #16838100C22semidirect
43. #16837802C22semidirect
44. #16837728C22semidirect
45. #16837725C22semidirect
46. #16837721C22semidirect
47. #16837704C22semidirect
48. #16837701C22semidirect
49. #16837637C22semidirect
50. #16837636C22semidirect
51. #16837482C22semidirect
52. (C22⋊D59)⋊C8C22semidirect
53. #16837437C22semidirect
59. C2×#14273660C22semidirect
71. C59×#481C22semidirect
377. C2×#481D59semidirect
390. C2×C59#3339semidirect
428. #481C2×D59semidirect
456. C59C2×#3339semidirect
755. C2#21436496direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381042
C2×#168381002
#214364962
C2×#168378022
C2×#168377212
C2×#168377282
C2×#168377252
C2×#168377042
C2×#168377012
C2×#168376372
C2×#168376362
C2×#168374822
C2×(C22⋊D59)⋊C82
C2×#168374372
C22×#142736602
C2×C59×#4812
C2×#333959