Finite Group Databasebeta

← C2×#21436603 #29467291

Subgroups — C2×#21436603 #29467291

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×#16838118C211yesmaximal, characteristic, complemented
2C2×#16838102C211yesmaximal, characteristic, complemented
3#21436603C2116yesmaximal, direct product factor
4C2×#16837808C211yesmaximal, characteristic, complemented
5C2×#16837729C211yesmaximal, characteristic, complemented
6C2×#16837725C211yesmaximal, characteristic, complemented
7C2×#16837724C211yesmaximal, characteristic, complemented
8C2×#16837717C211yesmaximal, characteristic, complemented
9C2×#16837703C211yesmaximal, characteristic, complemented
10C2×#16837654C211yesmaximal, characteristic, complemented
11C2×#16837637C211yesmaximal, characteristic, complemented
12C2×#16837512C211yesmaximal, characteristic, complemented
13C2×#16837472C211yesmaximal, characteristic, complemented
14C2×#16837443C211yesmaximal, characteristic, complemented
15C2×#16837439C211yesmaximal, characteristic, complemented
16C2×C59×#474C211yesmaximal, characteristic, complemented
17C22×#11745669C2211yescharacteristic
18C22×#11745659C2211yescharacteristic
19C22×C8×D59C2211yescharacteristic
20#16838118—24no—
21#16838118C2218yescomplemented
22#16838102—24no—
23#16838102C2218yescomplemented
24C2×#14273720—21no—
25C2×#14273719C2211yescharacteristic
26C2×#14273716—21no—
27C2×#14273716—21no—
28C2×#14273710—21no—
29C2×#14273702—21no—
30C2×#14273702C2211yescharacteristic
31C2×#14273702C2211yescharacteristic
32C2×#14273700—21no—
33C2×#14273698C2211yescharacteristic
34C2×#14273698C2211yescharacteristic
35C2×C4×D236C2211yescharacteristic
36C2×C4×D236C2211yescharacteristic
37C2×C4×C22⋊D59—21no—
38C2×#14273685—21no—
39C2×#14273685C2211yescharacteristic
40C2×#14273685C2211yescharacteristic
41C2×#14273685C2211yescharacteristic
42C2×C4⋊C4×D59C2211yescharacteristic
43#16837808C2218yescomplemented
44#16837729C2218yescomplemented
45#16837725C2218yescomplemented
46#16837724C2218yescomplemented
47#16837717C2218yescomplemented
48#16837703C2218yescomplemented
49#16837654C2218yescomplemented
50#16837637C2218yescomplemented
51#16837512C2218yescomplemented
52#16837472C2218yescomplemented
53#16837443C2218yescomplemented
54#16837439C2218yescomplemented
55C2×#14273661C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58C2×#14273659C2211yescharacteristic
59C2×#14273658C2211yescharacteristic
60C2×#14273658C2211yescharacteristic
61C2×#14273658C2211yescharacteristic
62C2×#14273649C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273638C2211yescharacteristic
69C2×C4⋊Q8×C59C2211yescharacteristic
70C2×C4×D4×C59C2211yescharacteristic
71C59×#474C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#107×C59C2211yescharacteristic
74C2×C4⋊C8×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C22×D236—21no—
78C22×D236—21no—
79C22×D236D411yescharacteristic
80C22×D236C2311yescharacteristic
81C22×C22⋊D59—21no—
82C22×C22⋊D59—21no—
83C22×C4×D59—21no—
84C22×C4×D59—21no—
85C22×C4×D59C2311yescharacteristic
86C22×C4×D59C2311yescharacteristic
87C2×#11745669—24no—
88C2×#11745669C2314yes—
89C2×#11745659—24no—
90C2×#11745659C2314yes—
91C22×C59⋊C8C2311yescharacteristic
92C22×C59⋊C8C2311yescharacteristic
93C2×C8×D59—24no—
94C2×C8×D59C2314yes—
95#14273720—28no—
96#14273719—22no—
97#14273719C2314yes—
98#14273716—28no—
99#14273716—28no—
100#14273710—28no—
101#14273702—28no—
102#14273702—22no—
103#14273702—22no—
104#14273702C2314yes—
105#14273702C2314yes—
106#14273700—28no—
107#14273698—22no—
108#14273698—22no—
109#14273698C2314yes—
110#14273698C2314yes—
111C4×D236—22no—
112C4×D236D414yes—
113C4×D236C2314yes—
114C4×D236C2314yes—
115C4×C22⋊D59—28no—
116#14273685—22no—
117#14273685—22no—
118#14273685—22no—
119#14273685—28no—
120#14273685C2314yes—
121#14273685C2314yes—
122#14273685C2314yes—
123C2×C4⋊Dic59D411yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C4⋊C4×D59—22no—
131C4⋊C4×D59C2314yes—
132C2×C22⋊Dic59—21no—
133C2×C22⋊Dic59—21no—
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4D411yescharacteristic
141C2×(C2×D59)⋊C4D411yescharacteristic
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59—21no—
145#14273661C2314yes—
146#14273660C2314yes—
147#14273660C2314yes—
148#14273659C2314yes—
149#14273658C2314yes—
150#14273658C2314yes—
151#14273658C2314yes—
152#14273649C2314yes—
153#14273649C2314yes—
154#14273648C2314yes—
155#14273647C2314yes—
156(C2×D59)⋊C8C2314yes—
157(C2×D59)⋊C8C2314yes—
158#14273638C2314yes—
159C22×Q8×C59—21no—
160C22×D4×C59C2311yescharacteristic
161C23×C4×C59—21no—
162C22×C8×C59C2311yescharacteristic
163C22×C8×C59C2311yescharacteristic
164C4⋊Q8×C59—22no—
165C4⋊Q8×C59C2314yes—
166C4×D4×C59—22no—
167C4×D4×C59C2314yes—
168C2×C4⋊C4×C59—21no—
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C22⋊C4×C59—21no—
173C2×C42×C59C2311yescharacteristic
174#107×C59C2314yes—
175#107×C59C2314yes—
176C4⋊C8×C59C2314yes—
177#102×C59C2314yes—
178#102×C59C2314yes—
179C24×C59—21no—
180C23×D59—21no—
181C23×D59C2×D411yescharacteristic
182C23×D59C2×D411yescharacteristic
183C2×Q8×C59—24no—
184C2×Q8×C59—82no—
185C2×D4×C59—21no—
186C2×D4×C59—22no—
187C2×D4×C59—22no—
188C2×D4×C59C2412yes—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59—24no—
193C22×C4×C59—82no—
194C22×C4×C59C2×D411yescharacteristic
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2411yescharacteristic
197C2×C22⋊D59—24no—
198C2×C22⋊D59—24no—
199C2×C22⋊D59—44no—
200C2×C22⋊D59—82no—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59C2×D411yescharacteristic
205C22×Dic59C2×D411yescharacteristic
206C2×D236—22no—
207C2×D236—22no—
208C2×D236—21no—
209C2×D236—24no—
210C2×D236—24no—
211C2×D236—42no—
212C2×D236—82no—
213C2×D236—82no—
214C2×D236C2×D414yes—
215C2×D236C2412yes—
216C2×C4×D59—22no—
217C2×C4×D59—22no—
218C2×C4×D59—22no—
219C2×C4×D59—22no—
220C2×C4×D59—24no—
221C2×C4×D59—24no—
222C2×C4×D59—44no—
223C2×C4×D59—82no—
224C2×C4×D59C2×D412yes—
225C2×C4×D59C2×D412yes—
226C2×C4×D59C2412yes—
227C2×C4×D59C2412yes—
228C2×C8×C59—22no—
229C2×C8×C59—22no—
230C2×C8×C59C2412yes—
231C2×C8×C59C2412yes—
232C4⋊C4×C59—24no—
233C4⋊C4×C59—21no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59—21no—
236C4⋊C4×C59C2412yes—
237C4⋊C4×C59C2412yes—
238C4⋊C4×C59C2412yes—
239C22⋊C4×C59—24no—
240C42×C59C2×D412yes—
241C42×C59C2412yes—
242C22⋊Dic59—24no—
243C22⋊Dic59—24no—
244#11745669—28no—
245(C2×D59)⋊C4—24no—
246(C2×D59)⋊C4—24no—
247(C2×D59)⋊C4—24no—
248(C2×D59)⋊C4—24no—
249(C2×D59)⋊C4—24no—
250(C2×D59)⋊C4—24no—
251(C2×D59)⋊C4C2×D414yes—
252(C2×D59)⋊C4C2×D414yes—
253C4⋊Dic59—21no—
254C4⋊Dic59—21no—
255C4⋊Dic59—21no—
256C4⋊Dic59C2×D414yes—
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#4114yes—
268C2×C59⋊C8C2412yes—
269C2×C59⋊C8C2412yes—
270#11745659—28no—
271C8×D59—28no—
272C23×C59—22no—
273C23×C59—42no—
274C23×C59—42no—
275C23×C59—42no—
276C23×C59C22×D411yescharacteristic
277C22×D59—22no—
278C22×D59—22no—
279C22×D59—22no—
280C22×D59—22no—
281C22×D59—22no—
282C22×D59—22no—
283C22×D59—22no—
284C22×D59—42no—
285C22×D59—42no—
286C22×D59—42no—
287C22×D59C22×D412yes—
288C22×D59C22×D412yes—
289Q8×C59—84no—
290D4×C59—22no—
291D4×C59—22no—
292D4×C59—42no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—42no—
299C2×C4×C59—42no—
300C2×C4×C59—42no—
301C2×C4×C59—84no—
302C2×C4×C59C22×D412yes—
303C2×C4×C59C22×D412yes—
304C2×C4×C59C22×D411yescharacteristic
305C2×C4×C59C2×#4112yes—
306C2×C4×C592−1+412yes—
307C2×C4×C59C2511yescharacteristic
308C22⋊D59—48no—
309C22⋊D59—84no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—42no—
316C2×Dic59—42no—
317C2×Dic59—42no—
318C2×Dic59C22×D412yes—
319C2×Dic59C22×D412yes—
320D236—22no—
321D236—22no—
322D236—44no—
323D236—42no—
324D236—84no—
325D236—84no—
326C4×D59—24no—
327C4×D59—24no—
328C4×D59—22no—
329C4×D59—22no—
330C4×D59—22no—
331C4×D59—22no—
332C4×D59—48no—
333C4×D59—84no—
334C8×C59—22no—
335C8×C59—22no—
336C59⋊C8—22no—
337C59⋊C8C2×#4114yes—
338C2×#3347—591nomaximal, Sylow
339C22×C59—42no—
340C22×C59—42no—
341C22×C59—42no—
342C22×C59—84no—
343C22×C59#54712yes—
344C22×C59#57512yes—
345C22×C59#57612yes—
346C22×C59C23×D411yescharacteristic
347C2×D59—22no—
348C2×D59—22no—
349C2×D59—22no—
350C2×D59—22no—
351C2×D59—22no—
352C2×D59—22no—
353C2×D59—44no—
354C2×D59—44no—
355C2×D59—42no—
356C2×D59—42no—
357C2×D59—42no—
358C2×D59—84no—
359C4×C59—22no—
360C4×C59—22no—
361C4×C59—42no—
362C4×C59—42no—
363C4×C59—42no—
364C4×C59#54712yes—
365C4×C59C22×#4111yescharacteristic
366C4×C59C2×2−1+411yescharacteristic
367Dic59—22no—
368Dic59—22no—
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×#474D5911yescharacteristic, complemented
382C2×#469—591no—
383C2×#466—591no—
384C2×#442—591no—
385C2×#435—591no—
386C2×#428—591no—
387C2×#427—591no—
388C2×C59—82no—
389C2×C59#334714yescomplemented
390C2×C59C2×#54711yescharacteristic
391C2×C59C2×#57511yescharacteristic
392C2×C59C2×#57611yescharacteristic
393D59—42no—
394D59—42no—
395D59—82no—
396C22×D8—591no—
397C22×M16—591no—
398C23×C8—591no—
399#555—598no—
400#555—1184no—
401#553—598no—
402#553—1184no—
403C2×C4⋊Q8C2×D5911yescharacteristic
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—591no—
417C2×C4×D4—1181no—
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#474C2×D5918yescomplemented
431#469—598no—
432#466—598no—
433#442—598no—
434#435—598no—
435#428—598no—
436#427—598no—
437C2×#107—591no—
438C2×#107—591no—
439C2×#107—591no—
440C2×#107C2×D5911yescharacteristic
441C2×#107C2×D5911yescharacteristic
442C2×#106—591no—
443C2×#106—591no—
444C2×#106—591no—
445C2×#106—591no—
446C2×C4⋊C8C2×D5911yescharacteristic
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×#97—591no—
456C59C2×#334711yescharacteristic, complemented, Sylow
457C22×Q8—21no—
458C22×D4—591no—
459C22×D4—591no—
460C22×D4—1181no—
461C22×D4—1181no—
462C22×D4—1181no—
463C22×D4—1181no—
464C22×D4C22×D5911yescharacteristic
465C23×C4—21no—
466C23×C4—591no—
467C23×C4—591no—
468C23×C4—1181no—
469C23×C4—1181no—
470C2×D8—594no—
471C2×D8—1184no—
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—22no—
481C4⋊Q8C22×D5914yes—
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—1182no—
494#121—1182no—
495#121—1188no—
496#121—1182no—
497#121—1182no—
498C4×D4—22no—
499C4×D4—594no—
500C4×D4—594no—
501C4×D4—594no—
502C4×D4—1188no—
503C4×D4—1182no—
504C4×D4C22×D5914yes—
505#117—594no—
506#117—594no—
507#117—594no—
508#117—1188no—
509#117—1182no—
510#117—1182no—
511#117—1182no—
512C2×C4⋊C4—21no—
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⋊C4C22×D5911yescharacteristic
523C2×C4⋊C4C22×D5911yescharacteristic
524C2×C4⋊C4C22×D5911yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—591no—
527C2×C22⋊C4—591no—
528C2×C22⋊C4—1181no—
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#107C22×D5914yes—
544#107C22×D5914yes—
545#106—594no—
546#106—594no—
547#106—594no—
548#106—594no—
549C4⋊C8C22×D5914yes—
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#97—594no—
559C24—21no—
560C24—591no—
561C24—591no—
562C24—1181no—
563C2×Q8—24no—
564C2×Q8—82no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
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—4722no—
580C2×D4—2362no—
581C2×D4—2364no—
582C2×D4C23×D5912yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—82no—
588C22×C4—591no—
589C22×C4—591no—
590C22×C4—592no—
591C22×C4—592no—
592C22×C4—592no—
593C22×C4—592no—
594C22×C4—1184no—
595C22×C4—1182no—
596C22×C4—1182no—
597C22×C4—1182no—
598C22×C4—1182no—
599C22×C4—1181no—
600C22×C4—1181no—
601C22×C4—1181no—
602C22×C4—1184no—
603C22×C4—4722no—
604C22×C4—2364no—
605C22×C4D4×D5911yescharacteristic
606C22×C4D4×D5911yescharacteristic
607C22×C4C23×D5911yescharacteristic
608D8—1188no—
609M16—1188no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—594no—
613C2×C8—592no—
614C2×C8—592no—
615C2×C8—1188no—
616C2×C8—1182no—
617C2×C8C23×D5912yes—
618C2×C8C23×D5912yes—
619C4⋊C4—24no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—594no—
624C4⋊C4—592no—
625C4⋊C4—592no—
626C4⋊C4—592no—
627C4⋊C4—1184no—
628C4⋊C4—1181no—
629C4⋊C4—1181no—
630C4⋊C4—1181no—
631C4⋊C4—1184no—
632C4⋊C4—1184no—
633C4⋊C4C23×D5912yes—
634C4⋊C4C23×D5912yes—
635C4⋊C4C23×D5912yes—
636C22⋊C4—24no—
637C22⋊C4—594no—
638C22⋊C4—594no—
639C22⋊C4—1184no—
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—42no—
654C23—42no—
655C23—42no—
656C23—592no—
657C23—592no—
658C23—1182no—
659C23—1182no—
660C23—1182no—
661C23—1182no—
662C23—1182no—
663C23—1182no—
664C23—1182no—
665C23—2362no—
666C23—2362no—
667C23—2362no—
668C23C2×D4×D5911yescharacteristic
669Q8—84no—
670D4—22no—
671D4—22no—
672D4—42no—
673D4—1182no—
674D4—1182no—
675D4—4724no—
676D4—4724no—
677D4—4724no—
678D4—2364no—
679D4—2368no—
680D4—2362no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—84no—
690C2×C4—592no—
691C2×C4—592no—
692C2×C4—1182no—
693C2×C4—1182no—
694C2×C4—1182no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—1182no—
698C2×C4—1184no—
699C2×C4—1184no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—4724no—
704C2×C4—2368no—
705C2×C4—2362no—
706C2×C4—2362no—
707C2×C4—2362no—
708C2×C4C2×D4×D5912yes—
709C2×C4C2×D4×D5912yes—
710C2×C4C2×D4×D5911yescharacteristic
711C2×C4#41×D5912yes—
712C2×C4#1427377512yes—
713C2×C4C24×D5911yescharacteristic
714C8—22no—
715C8—22no—
716C8—594no—
717C8—1182no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—84no—
722C22—1182no—
723C22—1182no—
724C22—1182no—
725C22—1182no—
726C22—1182no—
727C22—1182no—
728C22—4724no—
729C22—2362no—
730C22—2362no—
731C22—2362no—
732C22—2364no—
733C22—2364no—
734C22#1683805412yes—
735C22#1683820112yes—
736C22#1683820312yes—
737C22C22×D4×D5911yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—1182no—
744C4—1182no—
745C4—2362no—
746C4—2362no—
747C4—2362no—
748C4#1683805412yes—
749C4C2×#41×D5911yescharacteristic
750C4C2×#1427377511yescharacteristic
751C2—82no—
752C2—4722no—
753C2—2362no—
754C2—2362no—
755C2#2143660314yesdirect product factor
756C2C2×#1683805411yescharacteristic
757C2C2×#1683820111yescharacteristic
758C2C2×#1683820311yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#474C2
socleC23×C59C22×D4
hypercenterC2×#474D59
hypocenterC59C2×#3347
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#16838118C2semidirect
2. C2×#16838102C2semidirect
3. #21436603C2direct (N × H)
4. C2×#16837808C2semidirect
5. C2×#16837729C2semidirect
6. C2×#16837725C2semidirect
7. C2×#16837724C2semidirect
8. C2×#16837717C2semidirect
9. C2×#16837703C2semidirect
10. C2×#16837654C2semidirect
11. C2×#16837637C2semidirect
12. C2×#16837512C2semidirect
13. C2×#16837472C2semidirect
14. C2×#16837443C2semidirect
15. C2×#16837439C2semidirect
16. C2×C59×#474C2semidirect
21. #16838118C22semidirect
23. #16838102C22semidirect
43. #16837808C22semidirect
44. #16837729C22semidirect
45. #16837725C22semidirect
46. #16837724C22semidirect
47. #16837717C22semidirect
48. #16837703C22semidirect
49. #16837654C22semidirect
50. #16837637C22semidirect
51. #16837512C22semidirect
52. #16837472C22semidirect
53. #16837443C22semidirect
54. #16837439C22semidirect
71. C59×#474C22semidirect
381. C2×#474D59semidirect
389. C2×C59#3347semidirect
430. #474C2×D59semidirect
456. C59C2×#3347semidirect
755. C2#21436603direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381182
C2×#168381022
#214366032
C2×#168378082
C2×#168377292
C2×#168377252
C2×#168377242
C2×#168377172
C2×#168377032
C2×#168376542
C2×#168376372
C2×#168375122
C2×#168374722
C2×#168374432
C2×#168374392
C2×C59×#4742
C2×#334759