Finite Group Databasebeta

← C2×#21436601 #29467289

Subgroups — C2×#21436601 #29467289

Order 15104.

1962 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×#16838117C211yesmaximal, characteristic, complemented
2C2×#16838102C211yesmaximal, characteristic, complemented
3#21436601C2116yesmaximal, direct product factor
4C2×#16837811C211yesmaximal, characteristic, complemented
5C2×#16837725C211yesmaximal, characteristic, complemented
6C2×#16837725C211yesmaximal, characteristic, complemented
7C2×#16837724C211yesmaximal, characteristic, complemented
8C2×#16837714C211yesmaximal, characteristic, complemented
9C2×#16837702C211yesmaximal, characteristic, complemented
10C2×#16837682C211yesmaximal, characteristic, complemented
11C2×#16837652C211yesmaximal, characteristic, complemented
12C2×#16837635C211yesmaximal, characteristic, complemented
13C2×#16837475C211yesmaximal, characteristic, complemented
14C2×#16837441C211yesmaximal, characteristic, complemented
15C2×#16837437C211yesmaximal, characteristic, complemented
16C2×C59×#442C211yesmaximal, characteristic, complemented
17C22×#11745659C2211yescharacteristic
18C22×C8×D59C2211yescharacteristic
19#16838117—24no—
20#16838117C2218yescomplemented
21#16838102—24no—
22#16838102C2218yescomplemented
23C2×#14273727C2211yescharacteristic
24C2×#14273720—21no—
25C2×#14273719C2211yescharacteristic
26C2×#14273713—21no—
27C2×#14273713—21no—
28C2×#14273710—21no—
29C2×#14273701—21no—
30C2×#14273700—21no—
31C2×#14273698C2211yescharacteristic
32C2×#14273698C2211yescharacteristic
33C2×#14273698C2211yescharacteristic
34C2×#14273698C2211yescharacteristic
35C2×C4×D236C2211yescharacteristic
36C2×C4×C22⋊D59—21no—
37C2×#14273686—21no—
38C2×#14273685C2211yescharacteristic
39C2×#14273685C2211yescharacteristic
40C2×#14273685C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic
42#16837811C2218yescomplemented
43#16837725C2218yescomplemented
44#16837725C2218yescomplemented
45#16837724C2218yescomplemented
46#16837714C2218yescomplemented
47#16837702C2218yescomplemented
48#16837682C2218yescomplemented
49#16837652C2218yescomplemented
50#16837635C2218yescomplemented
51#16837475C2218yescomplemented
52#16837441C2218yescomplemented
53#16837437C2218yescomplemented
54C2×#14273661C2211yescharacteristic
55C2×#14273661C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58C2×#14273660C2211yescharacteristic
59C2×#14273659C2211yescharacteristic
60C2×#14273659C2211yescharacteristic
61C2×#14273658C2211yescharacteristic
62C2×C4⋊(C59⋊C8)C2211yescharacteristic
63C2×#14273648C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×#14273648C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×(C2×D59)⋊C8C2211yescharacteristic
69C22×D8×C59C2211yescharacteristic
70C2×C4×D4×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C59×#442C2218yescomplemented
73C2×#106×C59C2211yescharacteristic
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×D236D411yescharacteristic
79C22×C22⋊D59—21no—
80C22×C22⋊D59—21no—
81C22×C22⋊D59—21no—
82C22×C22⋊D59—21no—
83C22×C4×D59—21no—
84C22×C4×D59C2311yescharacteristic
85C22×C4×D59C2311yescharacteristic
86C2×#11745659—24no—
87C2×#11745659C2314yes—
88C22×C59⋊C8C2311yescharacteristic
89C22×C59⋊C8C2311yescharacteristic
90C2×C8×D59—24no—
91C2×C8×D59C2314yes—
92#14273727—22no—
93#14273727C2314yes—
94#14273720—28no—
95#14273719—22no—
96#14273719C2314yes—
97#14273713—28no—
98#14273713—28no—
99#14273710—28no—
100#14273701—28no—
101#14273700—28no—
102#14273698—22no—
103#14273698—22no—
104#14273698—22no—
105#14273698—22no—
106#14273698C2314yes—
107#14273698C2314yes—
108#14273698C2314yes—
109#14273698C2314yes—
110C4×D236D414yes—
111C4×D236C2314yes—
112C4×C22⋊D59—28no—
113#14273686—28no—
114#14273685—22no—
115#14273685—22no—
116#14273685—22no—
117#14273685C2314yes—
118#14273685C2314yes—
119#14273685C2314yes—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59D411yescharacteristic
122C2×C4⋊Dic59C2311yescharacteristic
123C2×C4⋊Dic59C2311yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C4⋊C4×D59—22no—
130C4⋊C4×D59C2314yes—
131C2×C22⋊Dic59—21no—
132C2×C22⋊Dic59—21no—
133C2×C22⋊Dic59—21no—
134C2×C22⋊Dic59—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4D411yescharacteristic
139C2×(C2×D59)⋊C4D411yescharacteristic
140C2×C4×Dic59—21no—
141C2×C4×Dic59—21no—
142C2×C4×Dic59—21no—
143#14273661C2314yes—
144#14273661C2314yes—
145#14273660C2314yes—
146#14273660C2314yes—
147#14273660C2314yes—
148#14273659C2314yes—
149#14273659C2314yes—
150#14273658C2314yes—
151C4⋊(C59⋊C8)C2314yes—
152#14273648C2314yes—
153#14273648C2314yes—
154#14273648C2314yes—
155#14273648C2314yes—
156(C2×D59)⋊C8C2314yes—
157(C2×D59)⋊C8C2314yes—
158C22×D4×C59C2311yescharacteristic
159C22×D4×C59C2311yescharacteristic
160C23×C4×C59—21no—
161C23×C4×C59—21no—
162C2×D8×C59—24no—
163C2×D8×C59C2314yes—
164C22×C8×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166C4×D4×C59—22no—
167C4×D4×C59—22no—
168C4×D4×C59C2314yes—
169C4×D4×C59C2314yes—
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C22⋊C4×C59—21no—
173C2×C22⋊C4×C59—21no—
174C2×C42×C59C2311yescharacteristic
175#106×C59C2314yes—
176#102×C59C2314yes—
177#102×C59C2314yes—
178#97×C59C2314yes—
179C24×C59—21no—
180C24×C59—21no—
181C23×D59C2×D411yescharacteristic
182C23×D59C2×D411yescharacteristic
183C2×D4×C59—21no—
184C2×D4×C59—21no—
185C2×D4×C59—22no—
186C2×D4×C59—22no—
187C2×D4×C59—22no—
188C2×D4×C59—22no—
189C2×D4×C59C2412yes—
190C2×D4×C59C2412yes—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—24no—
194C22×C4×C59—24no—
195C22×C4×C59—44no—
196C22×C4×C59—82no—
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2411yescharacteristic
200C2×C22⋊D59—24no—
201C2×C22⋊D59—24no—
202C2×C22⋊D59—24no—
203C2×C22⋊D59—24no—
204C2×C22⋊D59—44no—
205C2×C22⋊D59—82no—
206C2×C22⋊D59—82no—
207C2×C22⋊D59—82no—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59C2×D411yescharacteristic
213C22×Dic59C2×D411yescharacteristic
214C2×D236—42no—
215C2×D236C2×D414yes—
216C2×C4×D59—22no—
217C2×C4×D59—22no—
218C2×C4×D59—22no—
219C2×C4×D59—22no—
220C2×C4×D59—24no—
221C2×C4×D59—82no—
222C2×C4×D59C2×D412yes—
223C2×C4×D59C2×D412yes—
224C2×C4×D59C2412yes—
225C2×C4×D59C2412yes—
226C2×Dic118—24no—
227C2×Dic118—82no—
228D8×C59—28no—
229C2×C8×C59—22no—
230C2×C8×C59#4114yes—
231C2×C8×C59C2412yes—
232C2×C8×C59C2412yes—
233C4⋊C4×C59—21no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59C2412yes—
236C4⋊C4×C59C2412yes—
237C22⋊C4×C59—24no—
238C22⋊C4×C59—24no—
239C42×C59C2×D412yes—
240C42×C59C2412yes—
241C22⋊Dic59—24no—
242C22⋊Dic59—24no—
243C22⋊Dic59—24no—
244C22⋊Dic59—24no—
245(C2×D59)⋊C4—24no—
246(C2×D59)⋊C4—24no—
247(C2×D59)⋊C4—24no—
248(C2×D59)⋊C4C2×D414yes—
249(C2×D59)⋊C4C2×D414yes—
250C4⋊Dic59—21no—
251C4⋊Dic59—24no—
252C4⋊Dic59—21no—
253C4⋊Dic59—21no—
254C4⋊Dic59—21no—
255C4⋊Dic59C2×D414yes—
256C4⋊Dic59C2412yes—
257C4⋊Dic59C2412yes—
258C4⋊Dic59C2412yes—
259C4⋊Dic59C2412yes—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263C4×Dic59—24no—
264C4×Dic59—24no—
265C4×Dic59—24no—
266C2×C59⋊C8—22no—
267C2×C59⋊C8—22no—
268C2×C59⋊C8C2412yes—
269C2×C59⋊C8C2412yes—
270#11745659—28no—
271C8×D59—28no—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59—42no—
275C23×C59—42no—
276C23×C59—42no—
277C23×C59—42no—
278C23×C59—42no—
279C23×C59—42no—
280C23×C59C22×D411yescharacteristic
281C22×D59—22no—
282C22×D59—22no—
283C22×D59—22no—
284C22×D59—22no—
285C22×D59—22no—
286C22×D59—22no—
287C22×D59C22×D412yes—
288C22×D59C22×D412yes—
289D4×C59—22no—
290D4×C59—22no—
291D4×C59—22no—
292D4×C59—22no—
293D4×C59—42no—
294D4×C59—42no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—48no—
300C2×C4×C59—42no—
301C2×C4×C59—42no—
302C2×C4×C59—84no—
303C2×C4×C59C22×D412yes—
304C2×C4×C59C22×D412yes—
305C2×C4×C59C22×D411yescharacteristic
306C2×C4×C59C2×#4112yes—
307C2×C4×C592−1+412yes—
308C2×C4×C59C2511yescharacteristic
309C22⋊D59—48no—
310C22⋊D59—84no—
311C22⋊D59—84no—
312C22⋊D59—84no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—42no—
320C2×Dic59—42no—
321C2×Dic59—42no—
322C2×Dic59—42no—
323C2×Dic59C22×D412yes—
324C2×Dic59C22×D412yes—
325D236—44no—
326C4×D59—24no—
327C4×D59—24no—
328C4×D59—22no—
329C4×D59—22no—
330C4×D59—22no—
331C4×D59—22no—
332C4×D59—84no—
333Dic118—84no—
334C8×C59—22no—
335C8×C59C2×#4114yes—
336C59⋊C8—22no—
337C59⋊C8—22no—
338C2×#3347—591nomaximal, Sylow
339C22×C59—42no—
340C22×C59—42no—
341C22×C59—42no—
342C22×C59—42no—
343C22×C59—42no—
344C22×C59—42no—
345C22×C59—84no—
346C22×C59—84no—
347C22×C59#54712yes—
348C22×C59#57512yes—
349C22×C59#57612yes—
350C22×C59C23×D411yescharacteristic
351C2×D59—22no—
352C2×D59—22no—
353C2×D59—22no—
354C2×D59—22no—
355C2×D59—22no—
356C2×D59—22no—
357C2×D59—44no—
358C2×D59—44no—
359C4×C59—22no—
360C4×C59—22no—
361C4×C59—42no—
362C4×C59—42no—
363C4×C59#54712yes—
364C4×C59C22×#4111yescharacteristic
365C4×C59C2×2−1+411yescharacteristic
366Dic59—22no—
367Dic59—22no—
368Dic59—42no—
369Dic59—42no—
370Dic59—42no—
371Dic59—42no—
372C2×#555—591no—
373C2×#553—591no—
374#3347—5916no—
375C2×#501—591no—
376C2×#482—591no—
377C2×#482—591no—
378C2×#482—591no—
379C2×#480—591no—
380C2×#478—591no—
381C2×#474—591no—
382C2×#469—591no—
383C2×#466—591no—
384C2×#442D5911yescharacteristic, complemented
385C2×#435—591no—
386C2×#428—591no—
387C2×#427—591no—
388C2×C59—82no—
389C2×C59—82no—
390C2×C59#334714yescomplemented
391C2×C59C2×#54711yescharacteristic
392C2×C59C2×#57511yescharacteristic
393C2×C59C2×#57611yescharacteristic
394D59—42no—
395D59—42no—
396C22×D8C2×D5911yescharacteristic
397C22×M16—591no—
398C23×C8—591no—
399#555—598no—
400#555—1184no—
401#553—598no—
402#553—1184no—
403C2×C4⋊Q8—591no—
404C2×#126—1181no—
405C2×#125—591no—
406C2×#124—1181no—
407C2×#124—1181no—
408C2×#123—1181no—
409C2×#121—591no—
410C2×#121—591no—
411C2×#121—591no—
412C2×#121—591no—
413C2×#121—1181no—
414C2×#121—1181no—
415C2×C4×D4—591no—
416C2×C4×D4—1181no—
417C2×C4×D4C2×D5911yescharacteristic
418C2×C4×D4C2×D5911yescharacteristic
419C2×#117—591no—
420C2×#117—591no—
421C2×#117—591no—
422C2×#117—1181no—
423C22×C4⋊C4—591no—
424#501—598no—
425#482—598no—
426#482—598no—
427#482—598no—
428#480—598no—
429#478—598no—
430#474—598no—
431#469—598no—
432#466—598no—
433#442C2×D5918yescomplemented
434#435—598no—
435#428—598no—
436#427—598no—
437C2×#107—591no—
438C2×#107—591no—
439C2×#107—591no—
440C2×#107—591no—
441C2×#107—591no—
442C2×#106—591no—
443C2×#106—591no—
444C2×#106—591no—
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⋊C8—591no—
455C2×#97C2×D5911yescharacteristic
456C59C2×#334711yescharacteristic, complemented, Sylow
457C22×Q8—1181no—
458C22×D4—591no—
459C22×D4—1181no—
460C22×D4—1181no—
461C22×D4—1181no—
462C22×D4—1181no—
463C22×D4C22×D5911yescharacteristic
464C22×D4C22×D5911yescharacteristic
465C23×C4—21no—
466C23×C4—21no—
467C23×C4—591no—
468C23×C4—591no—
469C23×C4—1181no—
470C2×D8—24no—
471C2×D8C22×D5914yes—
472C2×M16—594no—
473C2×M16—1184no—
474C22×C8—591no—
475C22×C8—591no—
476C22×C8—594no—
477C22×C8—1184no—
478C22×C8C22×D5911yescharacteristic
479C22×C8C22×D5911yescharacteristic
480C4⋊Q8—594no—
481C4⋊Q8—1182no—
482#126—1188no—
483#125—594no—
484#125—1182no—
485#124—1188no—
486#124—1188no—
487#123—1188no—
488#121—594no—
489#121—594no—
490#121—594no—
491#121—594no—
492#121—1188no—
493#121—1188no—
494#121—1182no—
495#121—1182no—
496#121—1182no—
497#121—1182no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—594no—
501C4×D4—594no—
502C4×D4—1188no—
503C4×D4C22×D5914yes—
504C4×D4C22×D5914yes—
505#117—594no—
506#117—594no—
507#117—594no—
508#117—1182no—
509#117—1182no—
510#117—1182no—
511#117—1188no—
512C2×C4⋊C4—591no—
513C2×C4⋊C4—591no—
514C2×C4⋊C4—591no—
515C2×C4⋊C4—591no—
516C2×C4⋊C4—591no—
517C2×C4⋊C4—594no—
518C2×C4⋊C4—1182no—
519C2×C4⋊C4—1181no—
520C2×C4⋊C4—1181no—
521C2×C4⋊C4—1181no—
522C2×C4⋊C4—1181no—
523C2×C4⋊C4C22×D5911yescharacteristic
524C2×C4⋊C4C22×D5911yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—591no—
528C2×C22⋊C4—591no—
529C2×C22⋊C4—1181no—
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×C42—1181no—
537C2×C42—1181no—
538C2×C42—1181no—
539C2×C42C22×D5911yescharacteristic
540#107—594no—
541#107—594no—
542#107—594no—
543#107—594no—
544#107—594no—
545#106—594no—
546#106—594no—
547#106—594no—
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⋊C8—594no—
558#97C22×D5914yes—
559C24—21no—
560C24—21no—
561C24—591no—
562C24—591no—
563C2×Q8—1184no—
564C2×Q8—4722no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—594no—
572C2×D4—1184no—
573C2×D4—1184no—
574C2×D4—1184no—
575C2×D4—1184no—
576C2×D4—4722no—
577C2×D4—4722no—
578C2×D4—4722no—
579C2×D4—2362no—
580C2×D4—2364no—
581C2×D4C23×D5912yes—
582C2×D4C23×D5912yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—44no—
588C22×C4—82no—
589C22×C4—591no—
590C22×C4—591no—
591C22×C4—592no—
592C22×C4—592no—
593C22×C4—592no—
594C22×C4—592no—
595C22×C4—1184no—
596C22×C4—1182no—
597C22×C4—1182no—
598C22×C4—1182no—
599C22×C4—1182no—
600C22×C4—1181no—
601C22×C4—1181no—
602C22×C4—1181no—
603C22×C4—1181no—
604C22×C4—4722no—
605C22×C4D4×D5911yescharacteristic
606C22×C4D4×D5911yescharacteristic
607C22×C4C23×D5911yescharacteristic
608D8—28no—
609M16—1188no—
610C2×C8—22no—
611C2×C8—592no—
612C2×C8—592no—
613C2×C8—1182no—
614C2×C8—1182no—
615C2×C8—1188no—
616C2×C8#1174568514yes—
617C2×C8C23×D5912yes—
618C2×C8C23×D5912yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—594no—
622C4⋊C4—592no—
623C4⋊C4—592no—
624C4⋊C4—592no—
625C4⋊C4—592no—
626C4⋊C4—1184no—
627C4⋊C4—1181no—
628C4⋊C4—1181no—
629C4⋊C4—1181no—
630C4⋊C4—1181no—
631C4⋊C4—1184no—
632C4⋊C4—1184no—
633C4⋊C4—1184no—
634C4⋊C4C23×D5912yes—
635C4⋊C4C23×D5912yes—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—594no—
639C22⋊C4—594no—
640C22⋊C4—1184no—
641C22⋊C4—1184no—
642C22⋊C4—1184no—
643C22⋊C4—1184no—
644C22⋊C4—1184no—
645C22⋊C4—1184no—
646C22⋊C4—1184no—
647C42—1184no—
648C42—1184no—
649C42—1184no—
650C42D4×D5912yes—
651C42C23×D5912yes—
652C23—22no—
653C23—22no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—592no—
661C23—592no—
662C23—1182no—
663C23—1182no—
664C23—1182no—
665C23—1182no—
666C23—1182no—
667C23—1182no—
668C23C2×D4×D5911yescharacteristic
669Q8—4724no—
670D4—22no—
671D4—22no—
672D4—22no—
673D4—22no—
674D4—42no—
675D4—42no—
676D4—4724no—
677D4—4724no—
678D4—4724no—
679D4—2364no—
680D4—2368no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—48no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—84no—
689C2×C4—592no—
690C2×C4—592no—
691C2×C4—1182no—
692C2×C4—1182no—
693C2×C4—1182no—
694C2×C4—1182no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—1184no—
698C2×C4—1184no—
699C2×C4—1182no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—4724no—
704C2×C4—2362no—
705C2×C4—2362no—
706C2×C4—2362no—
707C2×C4—2362no—
708C2×C4C2×D4×D5912yes—
709C2×C4C2×D4×D5912yes—
710C2×C4C2×D4×D5911yescharacteristic
711C2×C4C2×#1174568512yes—
712C2×C4#1427377412yes—
713C2×C4C24×D5911yescharacteristic
714C8—22no—
715C8—1182no—
716C8—1182no—
717C8C2×#1174568514yes—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—84no—
725C22—84no—
726C22—1182no—
727C22—1182no—
728C22—1182no—
729C22—1182no—
730C22—1182no—
731C22—1182no—
732C22—2364no—
733C22—2364no—
734C22#1683805712yes—
735C22#1683819812yes—
736C22#1683820612yes—
737C22C22×D4×D5911yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—1182no—
743C4—1182no—
744C4—2362no—
745C4—2362no—
746C4—2362no—
747C4—2362no—
748C4#1683805712yes—
749C4C22×#1174568511yescharacteristic
750C4C2×#1427377411yescharacteristic
751C2—82no—
752C2—82no—
753C2—2362no—
754C2—2362no—
755C2#2143660114yesdirect product factor
756C2C2×#1683805711yescharacteristic
757C2C2×#1683819811yescharacteristic
758C2C2×#1683820611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#442C2
socleC23×C59C22×D4
hypercenterC2×#442D59
hypocenterC59C2×#3347
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#16838117C2semidirect
2. C2×#16838102C2semidirect
3. #21436601C2direct (N × H)
4. C2×#16837811C2semidirect
5. C2×#16837725C2semidirect
6. C2×#16837725C2semidirect
7. C2×#16837724C2semidirect
8. C2×#16837714C2semidirect
9. C2×#16837702C2semidirect
10. C2×#16837682C2semidirect
11. C2×#16837652C2semidirect
12. C2×#16837635C2semidirect
13. C2×#16837475C2semidirect
14. C2×#16837441C2semidirect
15. C2×#16837437C2semidirect
16. C2×C59×#442C2semidirect
20. #16838117C22semidirect
22. #16838102C22semidirect
42. #16837811C22semidirect
43. #16837725C22semidirect
44. #16837725C22semidirect
45. #16837724C22semidirect
46. #16837714C22semidirect
47. #16837702C22semidirect
48. #16837682C22semidirect
49. #16837652C22semidirect
50. #16837635C22semidirect
51. #16837475C22semidirect
52. #16837441C22semidirect
53. #16837437C22semidirect
72. C59×#442C22semidirect
384. C2×#442D59semidirect
390. C2×C59#3347semidirect
433. #442C2×D59semidirect
456. C59C2×#3347semidirect
755. C2#21436601direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381172
C2×#168381022
#214366012
C2×#168378112
C2×#168377252
C2×#168377242
C2×#168377142
C2×#168377022
C2×#168376822
C2×#168376522
C2×#168376352
C2×#168374752
C2×#168374412
C2×#168374372
C2×C59×#4422
C2×#334759