Finite Group Databasebeta

← C2×#20253586 #27084524

Subgroups — C2×#20253586 #27084524

Order 12032.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689727C211yesmaximal, characteristic, complemented
2C2×#15689605C211yesmaximal, characteristic, complemented
3#20253586C2116yesmaximal, direct product factor
4C2×#15689440C211yesmaximal, characteristic, complemented
5C2×#15689435C211yesmaximal, characteristic, complemented
6C2×#15689430C211yesmaximal, characteristic, complemented
7C2×#15689424C211yesmaximal, characteristic, complemented
8C2×#15689315C211yesmaximal, characteristic, complemented
9C2×#15689267C211yesmaximal, characteristic, complemented
10C2×#15689267C211yesmaximal, characteristic, complemented
11C2×#15689232C211yesmaximal, characteristic, complemented
12C2×#15689224C211yesmaximal, characteristic, complemented
13C2×SD16×Dic47C211yesmaximal, characteristic, complemented
14C2×#15689203C211yesmaximal, characteristic, complemented
15C2×#15689183C211yesmaximal, characteristic, complemented
16C2×C47×#460C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625334C2211yescharacteristic
19C22×#10625334C2211yescharacteristic
20#15689727—24no—
21#15689727C2218yescomplemented
22C2×#13094016C2211yescharacteristic
23C2×#13094005—21no—
24C2×#13094005—21no—
25C2×#13093996—21no—
26C2×#13093996—21no—
27C2×#13093995C2211yescharacteristic
28C2×#13093995C2211yescharacteristic
29#15689605—24no—
30#15689605C2218yescomplemented
31C2×Q8×Dic47C2211yescharacteristic
32C2×C4×D188—21no—
33C2×C4×D188C2211yescharacteristic
34C2×D4×Dic47C2211yescharacteristic
35C2×D4×Dic47C2211yescharacteristic
36C2×#13093986—21no—
37C2×#13093986C2211yescharacteristic
38C2×#13093981—21no—
39C2×#13093981C2211yescharacteristic
40C2×C4⋊C4×D47—21no—
41C2×C4⋊C4×D47C2211yescharacteristic
42#15689440C2218yescomplemented
43#15689435C2218yescomplemented
44#15689430C2218yescomplemented
45#15689424C2218yescomplemented
46#15689315C2218yescomplemented
47#15689267C2218yescomplemented
48#15689267C2218yescomplemented
49#15689232C2218yescomplemented
50#15689224C2218yescomplemented
51SD16×Dic47C2218yescomplemented
52#15689203C2218yescomplemented
53#15689183C2218yescomplemented
54C2×#13093958C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×C4⋊(C47⋊C8)C2211yescharacteristic
59C2×#13093948C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093946C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093945C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C22×SD16×C47C2211yescharacteristic
71C2×#127×C47C2211yescharacteristic
72C2×C4×Q8×C47C2211yescharacteristic
73C47×#460C2218yescomplemented
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C2×#10625354—24no—
78C2×#10625354—24no—
79C2×#10625354—22no—
80C2×#10625354C2314yes—
81C22×D188—21no—
82C22×D188C2311yescharacteristic
83C22×C22⋊D47—21no—
84C22×C22⋊D47—21no—
85C23×Dic47—21no—
86C23×Dic47—21no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47—21no—
90C22×C4×D47—21no—
91C22×C4×D47C2311yescharacteristic
92C2×#10625334—24no—
93C2×#10625334—24no—
94C2×#10625334C2314yes—
95C2×#10625334C2314yes—
96C22×C47⋊C8C2311yescharacteristic
97C22×C47⋊C8C2311yescharacteristic
98#13094016—22no—
99#13094016C2314yes—
100#13094005—28no—
101#13094005—28no—
102#13093996—28no—
103#13093996—28no—
104#13093995—22no—
105#13093995—22no—
106#13093995C2314yes—
107#13093995C2314yes—
108Q8×Dic47—22no—
109Q8×Dic47C2314yes—
110C4×D188—22no—
111C4×D188—28no—
112C4×D188C2314yes—
113D4×Dic47—22no—
114D4×Dic47—22no—
115D4×Dic47C2314yes—
116D4×Dic47C2314yes—
117#13093986—28no—
118#13093986—22no—
119#13093986C2314yes—
120#13093981—28no—
121#13093981D414yes—
122#13093981C2314yes—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4D411yescharacteristic
131C2×Dic47⋊C4D411yescharacteristic
132C4⋊C4×D47—22no—
133C4⋊C4×D47—28no—
134C4⋊C4×D47C2314yes—
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47—21no—
137C2×C22⋊Dic47—21no—
138C2×C22⋊Dic47—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4D411yescharacteristic
142C2×(C2×D47)⋊C4D411yescharacteristic
143C2×C4×Dic47—21no—
144C2×C4×Dic47C2311yescharacteristic
145#13093958C2314yes—
146#13093957C2314yes—
147#13093956C2314yes—
148#13093955C2314yes—
149C4⋊(C47⋊C8)C2314yes—
150#13093948C2314yes—
151#13093948C2314yes—
152#13093946C2314yes—
153#13093946C2314yes—
154#13093945C2314yes—
155#13093945C2314yes—
156(C2×D47)⋊C8C2314yes—
157(C2×D47)⋊C8C2314yes—
158#13093934C2314yes—
159C8×Dic47C2314yes—
160C22×Q8×C47C2311yescharacteristic
161C22×D4×C47—21no—
162C22×D4×C47—21no—
163C22×D4×C47C2311yescharacteristic
164C22×D4×C47C2311yescharacteristic
165C2×SD16×C47—24no—
166C2×SD16×C47—24no—
167C2×SD16×C47C2314yes—
168C2×SD16×C47C2314yes—
169C22×C8×C47C2311yescharacteristic
170C22×C8×C47C2311yescharacteristic
171#127×C47—22no—
172#127×C47C2314yes—
173C4×Q8×C47—22no—
174C4×Q8×C47C2314yes—
175C2×C4⋊C4×C47—21no—
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C42×C47—21no—
178C2×C42×C47C2311yescharacteristic
179C4⋊C8×C47C2314yes—
180#102×C47C2314yes—
181#102×C47C2314yes—
182C24×C47—21no—
183C24×C47—21no—
184C23×D47—21no—
185C23×D47C2×D411yescharacteristic
186C2×Q8×C47—21no—
187C2×Q8×C47—22no—
188C2×Q8×C47#4114yes—
189C2×Q8×C47C2412yes—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—24no—
193C2×D4×C47—24no—
194C2×D4×C47—22no—
195C2×D4×C47—22no—
196C2×D4×C47—22no—
197C2×D4×C47—22no—
198C2×D4×C47—82no—
199C2×D4×C47—82no—
200C2×D4×C47C2412yes—
201C2×D4×C47C2412yes—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2411yescharacteristic
207C2×C22⋊D47—24no—
208C2×C22⋊D47—24no—
209C2×C22⋊D47—82no—
210C2×C22⋊D47—82no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—24no—
215C22×Dic47—24no—
216C22×Dic47—82no—
217C22×Dic47—82no—
218C22×Dic47C2×D411yescharacteristic
219C22×Dic47C2×D411yescharacteristic
220C22×Dic47C2×D411yescharacteristic
221#10625354—216no—
222#10625354—28no—
223#10625354—28no—
224C2×D188—28no—
225C2×D188—24no—
226C2×D188—21no—
227C2×D188—22no—
228C2×D188#4114yes—
229C2×D188C2412yes—
230C2×C4×D47—28no—
231C2×C4×D47—22no—
232C2×C4×D47—22no—
233C2×C4×D47—24no—
234C2×C4×D47—24no—
235C2×C4×D47—24no—
236C2×C4×D47—24no—
237C2×C4×D47—82no—
238C2×C4×D47—82no—
239C2×C4×D47—82no—
240C2×C4×D47C2×D412yes—
241C2×C4×D47C2412yes—
242SD16×C47—28no—
243SD16×C47—28no—
244C2×C8×C47—22no—
245C2×C8×C47—22no—
246C2×C8×C47C2412yes—
247C2×C8×C47C2412yes—
248C4⋊C4×C47—24no—
249C4⋊C4×C47—21no—
250C4⋊C4×C47C2412yes—
251C42×C47—24no—
252C42×C47C2×D412yes—
253C42×C47C2412yes—
254C22⋊Dic47—24no—
255C22⋊Dic47—24no—
256C22⋊Dic47—24no—
257C22⋊Dic47—24no—
258#10625334—28no—
259#10625334—28no—
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4C2×D414yes—
263(C2×D47)⋊C4C2×D414yes—
264C4⋊Dic47—21no—
265C4⋊Dic47—21no—
266C4⋊Dic47—21no—
267C4⋊Dic47—24no—
268C4⋊Dic47C2412yes—
269C4⋊Dic47C2412yes—
270C4⋊Dic47C2412yes—
271Dic47⋊C4—24no—
272Dic47⋊C4—24no—
273Dic47⋊C4—24no—
274Dic47⋊C4C2×D414yes—
275Dic47⋊C4C2×D414yes—
276C4×Dic47—24no—
277C4×Dic47C2×D412yes—
278C4×Dic47C2412yes—
279C2×C47⋊C8—22no—
280C2×C47⋊C8—22no—
281C2×C47⋊C8C2412yes—
282C2×C47⋊C8C2412yes—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—42no—
286C23×C47—42no—
287C23×C47—42no—
288C23×C47—42no—
289C23×C47—42no—
290C23×C47—42no—
291C23×C47C22×D411yescharacteristic
292C22×D47—22no—
293C22×D47—24no—
294C22×D47—22no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—42no—
298C22×D47—42no—
299C22×D47C22×D412yes—
300Q8×C47—24no—
301Q8×C47—22no—
302Q8×C47C2×#4114yes—
303D4×C47—22no—
304D4×C47—22no—
305D4×C47—22no—
306D4×C47—22no—
307D4×C47—42no—
308D4×C47—42no—
309D4×C47—84no—
310D4×C47—84no—
311C2×C4×C47—24no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—42no—
317C2×C4×C47C22×D412yes—
318C2×C4×C47C22×D412yes—
319C2×C4×C47C22×D411yescharacteristic
320C2×C4×C47C2×#4112yes—
321C2×C4×C47C2×#4112yes—
322C2×C4×C47C2511yescharacteristic
323C22⋊D47—84no—
324C22⋊D47—84no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—42no—
332C2×Dic47—42no—
333C2×Dic47—42no—
334C2×Dic47—84no—
335C2×Dic47—84no—
336C2×Dic47C22×D412yes—
337C2×Dic47C22×D412yes—
338C2×Dic47C22×D412yes—
339D188—216no—
340D188—24no—
341D188—22no—
342D188C2×#4114yes—
343C4×D47—216no—
344C4×D47—24no—
345C4×D47—22no—
346C4×D47—22no—
347C4×D47—84no—
348C4×D47—84no—
349C4×D47—84no—
350C8×C47—22no—
351C8×C47—22no—
352C47⋊C8—22no—
353C47⋊C8—22no—
354C2×#3119—471nomaximal, Sylow
355C22×C47—42no—
356C22×C47—42no—
357C22×C47—42no—
358C22×C47—42no—
359C22×C47—42no—
360C22×C47—42no—
361C22×C47—84no—
362C22×C47—84no—
363C22×C47#52512yes—
364C22×C47#57612yes—
365C22×C47#57712yes—
366C22×C47C23×D411yescharacteristic
367C2×D47—22no—
368C2×D47—24no—
369C2×D47—22no—
370C2×D47—22no—
371C2×D47—44no—
372C2×D47—48no—
373C2×D47—42no—
374C2×D47—42no—
375C4×C47—24no—
376C4×C47—22no—
377C4×C47—22no—
378C4×C47—42no—
379C4×C47#52512yes—
380C4×C47C22×#4111yescharacteristic
381C4×C47C22×#4111yescharacteristic
382Dic47—22no—
383Dic47—22no—
384Dic47—22no—
385Dic47—42no—
386Dic47—42no—
387Dic47—42no—
388C2×#540—471no—
389C2×#520—471no—
390#3119—4716no—
391C2×#481—471no—
392C2×#480—471no—
393C2×#479—471no—
394C2×#478—471no—
395C2×#460D4711yescharacteristic, complemented
396C2×#459—471no—
397C2×#449—471no—
398C2×#449—471no—
399C2×#442—471no—
400C2×#440—471no—
401C2×C4×SD16—471no—
402C2×C4×D8—471no—
403C2×#433—471no—
404C2×C47—82no—
405C2×C47—82no—
406C2×C47#311914yescomplemented
407C2×C47C2×#52511yescharacteristic
408C2×C47C2×#57611yescharacteristic
409C2×C47C2×#57711yescharacteristic
410D47—42no—
411D47—44no—
412C22×#41—471no—
413C22×SD16C2×D4711yescharacteristic
414C22×SD16C2×D4711yescharacteristic
415C22×D8—471no—
416C22×D8—471no—
417#540—478no—
418#540—944no—
419C2×#127C2×D4711yescharacteristic
420C2×#125—471no—
421C2×#123—941no—
422C2×#123—941no—
423C2×#121—471no—
424C2×#121—471no—
425C2×#121—941no—
426C2×#121—941no—
427#520—478no—
428#520—944no—
429C2×C4×Q8—471no—
430C2×C4×Q8C2×D4711yescharacteristic
431C2×C4×D4—471no—
432C2×C4×D4—471no—
433C2×C4×D4—471no—
434C2×C4×D4—471no—
435C2×C4×D4—941no—
436C2×C4×D4—941no—
437C2×#117—471no—
438C2×#117—941no—
439C22×C4⋊C4—471no—
440C22×C4⋊C4—941no—
441#481—478no—
442#480—478no—
443#479—478no—
444#478—478no—
445#460C2×D4718yescomplemented
446#459—478no—
447#449—478no—
448#449—478no—
449#442—478no—
450#440—478no—
451C4×SD16—478no—
452C4×D8—478no—
453#433—478no—
454C2×#107—471no—
455C2×#107—471no—
456C2×#106—471no—
457C2×#106—471no—
458C2×C4⋊C8—471no—
459C2×C4⋊C8C2×D4711yescharacteristic
460C2×#103—471no—
461C2×#103—471no—
462C2×#102—471no—
463C2×#102—471no—
464C2×#102—471no—
465C2×#102—471no—
466C2×#102C2×D4711yescharacteristic
467C2×#102C2×D4711yescharacteristic
468C2×C22⋊C8—471no—
469C2×C22⋊C8—471no—
470C2×#97—471no—
471C2×C4×C8—471no—
472C47C2×#311911yescharacteristic, complemented, Sylow
473C2×#41—474no—
474C2×#41—942no—
475C2×#41—944no—
476C2×#41—944no—
477C22×Q8C22×D4711yescharacteristic
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—471no—
481C22×D4—941no—
482C22×D4—941no—
483C22×D4—941no—
484C22×D4C22×D4711yescharacteristic
485C22×D4C22×D4711yescharacteristic
486C23×C4—471no—
487C23×C4—941no—
488C23×C4—941no—
489C23×C4—941no—
490C23×C4—941no—
491C23×C4—941no—
492C23×C4—941no—
493C2×SD16—24no—
494C2×SD16—24no—
495C2×SD16C22×D4714yes—
496C2×SD16C22×D4714yes—
497C2×D8—474no—
498C2×D8—474no—
499C2×D8—944no—
500C2×D8—944no—
501C22×C8—471no—
502C22×C8—471no—
503C22×C8C22×D4711yescharacteristic
504C22×C8C22×D4711yescharacteristic
505#127—22no—
506#127C22×D4714yes—
507#125—474no—
508#125—942no—
509#123—948no—
510#123—948no—
511#121—474no—
512#121—474no—
513#121—948no—
514#121—948no—
515#121—942no—
516#121—942no—
517C4×Q8—22no—
518C4×Q8—474no—
519C4×Q8—942no—
520C4×Q8C22×D4714yes—
521C4×D4—474no—
522C4×D4—474no—
523C4×D4—474no—
524C4×D4—474no—
525C4×D4—948no—
526C4×D4—942no—
527C4×D4—942no—
528C4×D4—942no—
529C4×D4—948no—
530C4×D4—942no—
531#117—474no—
532#117—474no—
533#117—948no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—471no—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—471no—
538C2×C4⋊C4—471no—
539C2×C4⋊C4—471no—
540C2×C4⋊C4—474no—
541C2×C4⋊C4—948no—
542C2×C4⋊C4—942no—
543C2×C4⋊C4—941no—
544C2×C4⋊C4—941no—
545C2×C4⋊C4—941no—
546C2×C4⋊C4—941no—
547C2×C4⋊C4C22×D4711yescharacteristic
548C2×C22⋊C4—471no—
549C2×C22⋊C4—471no—
550C2×C22⋊C4—941no—
551C2×C22⋊C4—941no—
552C2×C22⋊C4—941no—
553C2×C22⋊C4—941no—
554C2×C22⋊C4—941no—
555C2×C22⋊C4—941no—
556C2×C42—21no—
557C2×C42—471no—
558C2×C42—941no—
559C2×C42C22×D4711yescharacteristic
560#107—474no—
561#107—474no—
562#106—474no—
563#106—474no—
564C4⋊C8—474no—
565C4⋊C8C22×D4714yes—
566#103—474no—
567#103—474no—
568#102—474no—
569#102—474no—
570#102—474no—
571#102—474no—
572#102C22×D4714yes—
573#102C22×D4714yes—
574C22⋊C8—474no—
575C22⋊C8—474no—
576#97—474no—
577C4×C8—474no—
578C24—21no—
579C24—21no—
580C24—471no—
581C24—941no—
582#41—948no—
583#41—9416no—
584#41—948no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8#1062535214yes—
588C2×Q8C23×D4712yes—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—24no—
592C2×D4—24no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—82no—
598C2×D4—82no—
599C2×D4—474no—
600C2×D4—472no—
601C2×D4—944no—
602C2×D4—948no—
603C2×D4—944no—
604C2×D4—944no—
605C2×D4—941no—
606C2×D4—942no—
607C2×D4—3762no—
608C2×D4—3762no—
609C2×D4C23×D4712yes—
610C2×D4C23×D4712yes—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—471no—
614C22×C4—471no—
615C22×C4—471no—
616C22×C4—472no—
617C22×C4—472no—
618C22×C4—944no—
619C22×C4—944no—
620C22×C4—948no—
621C22×C4—944no—
622C22×C4—944no—
623C22×C4—944no—
624C22×C4—942no—
625C22×C4—942no—
626C22×C4—941no—
627C22×C4—941no—
628C22×C4—941no—
629C22×C4—944no—
630C22×C4—3762no—
631C22×C4—3762no—
632C22×C4—3762no—
633C22×C4—3762no—
634C22×C4—3762no—
635C22×C4D4×D4711yescharacteristic
636C22×C4D4×D4711yescharacteristic
637C22×C4C23×D4711yescharacteristic
638SD16—28no—
639SD16—28no—
640D8—948no—
641D8—948no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—472no—
645C2×C8—472no—
646C2×C8—942no—
647C2×C8—942no—
648C2×C8C23×D4712yes—
649C2×C8C23×D4712yes—
650C4⋊C4—24no—
651C4⋊C4—21no—
652C4⋊C4—474no—
653C4⋊C4—474no—
654C4⋊C4—472no—
655C4⋊C4—472no—
656C4⋊C4—472no—
657C4⋊C4—944no—
658C4⋊C4—944no—
659C4⋊C4—944no—
660C4⋊C4—944no—
661C4⋊C4—941no—
662C4⋊C4—941no—
663C4⋊C4—941no—
664C4⋊C4C23×D4712yes—
665C22⋊C4—474no—
666C22⋊C4—474no—
667C22⋊C4—944no—
668C22⋊C4—944no—
669C22⋊C4—944no—
670C22⋊C4—944no—
671C22⋊C4—944no—
672C22⋊C4—944no—
673C42—24no—
674C42—472no—
675C42—472no—
676C42—944no—
677C42D4×D4712yes—
678C42C23×D4712yes—
679C23—22no—
680C23—22no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—472no—
688C23—944no—
689C23—942no—
690C23—942no—
691C23—942no—
692C23—942no—
693C23—1882no—
694C23—1882no—
695C23C2×D4×D4711yescharacteristic
696Q8—24no—
697Q8—22no—
698Q8C2×#1062535214yes—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—22no—
703D4—42no—
704D4—42no—
705D4—84no—
706D4—84no—
707D4—474no—
708D4—9416no—
709D4—944no—
710D4—942no—
711D4—3764no—
712D4—3764no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—42no—
719C2×C4—472no—
720C2×C4—472no—
721C2×C4—472no—
722C2×C4—9416no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—944no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—3764no—
733C2×C4—3764no—
734C2×C4—3764no—
735C2×C4—3764no—
736C2×C4—3764no—
737C2×C4—1882no—
738C2×C4—1882no—
739C2×C4—1882no—
740C2×C4C2×D4×D4712yes—
741C2×C4C2×D4×D4712yes—
742C2×C4C2×D4×D4711yescharacteristic
743C2×C4#41×D4712yes—
744C2×C4C2×#1062535212yes—
745C2×C4C24×D4711yescharacteristic
746C8—22no—
747C8—22no—
748C8—942no—
749C8—942no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—84no—
757C22—84no—
758C22—942no—
759C22—942no—
760C22—944no—
761C22—942no—
762C22—1882no—
763C22—1882no—
764C22—1884no—
765C22—1888no—
766C22#1568963312yes—
767C22#1568992712yes—
768C22#1568992912yes—
769C22C22×D4×D4711yescharacteristic
770C4—22no—
771C4—22no—
772C4—24no—
773C4—42no—
774C4—942no—
775C4—942no—
776C4—942no—
777C4—1882no—
778C4—1882no—
779C4—1882no—
780C4#1568963312yes—
781C4C2×#41×D4711yescharacteristic
782C4C22×#1062535211yescharacteristic
783C2—82no—
784C2—82no—
785C2—1882no—
786C2—1884no—
787C2#2025358614yesdirect product factor
788C2C2×#1568963311yescharacteristic
789C2C2×#1568992711yescharacteristic
790C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#460C2
socleC23×C47C22×D4
hypercenterC2×#460D47
hypocenterC47C2×#3119
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#15689727C2semidirect
2. C2×#15689605C2semidirect
3. #20253586C2direct (N × H)
4. C2×#15689440C2semidirect
5. C2×#15689435C2semidirect
6. C2×#15689430C2semidirect
7. C2×#15689424C2semidirect
8. C2×#15689315C2semidirect
9. C2×#15689267C2semidirect
10. C2×#15689267C2semidirect
11. C2×#15689232C2semidirect
12. C2×#15689224C2semidirect
13. C2×SD16×Dic47C2semidirect
14. C2×#15689203C2semidirect
15. C2×#15689183C2semidirect
16. C2×C47×#460C2semidirect
21. #15689727C22semidirect
30. #15689605C22semidirect
42. #15689440C22semidirect
43. #15689435C22semidirect
44. #15689430C22semidirect
45. #15689424C22semidirect
46. #15689315C22semidirect
47. #15689267C22semidirect
48. #15689267C22semidirect
49. #15689232C22semidirect
50. #15689224C22semidirect
51. SD16×Dic47C22semidirect
52. #15689203C22semidirect
53. #15689183C22semidirect
73. C47×#460C22semidirect
395. C2×#460D47semidirect
406. C2×C47#3119semidirect
445. #460C2×D47semidirect
472. C47C2×#3119semidirect
787. C2#20253586direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897272
C2×#156896052
#202535862
C2×#156894402
C2×#156894352
C2×#156894302
C2×#156894242
C2×#156893152
C2×#156892672
C2×#156892322
C2×#156892242
C2×SD16×Dic472
C2×#156892032
C2×#156891832
C2×C47×#4602
C2×#311947