Finite Group Databasebeta

← C2×#20253592 #27084530

Subgroups — C2×#20253592 #27084530

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×#15689729C211yesmaximal, characteristic, complemented
2C2×#15689602C211yesmaximal, characteristic, complemented
3#20253592C2116yesmaximal, direct product factor
4C2×#15689443C211yesmaximal, characteristic, complemented
5C2×#15689438C211yesmaximal, characteristic, complemented
6C2×#15689427C211yesmaximal, characteristic, complemented
7C2×#15689324C211yesmaximal, characteristic, complemented
8C2×#15689318C211yesmaximal, characteristic, complemented
9C2×#15689269C211yesmaximal, characteristic, complemented
10C2×#15689269C211yesmaximal, characteristic, complemented
11C2×#15689232C211yesmaximal, characteristic, complemented
12C2×#15689222C211yesmaximal, characteristic, complemented
13C2×#15689210C211yesmaximal, characteristic, complemented
14C2×#15689203C211yesmaximal, characteristic, complemented
15C2×#15689183C211yesmaximal, characteristic, complemented
16C2×C47×#478C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×#10625325C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×#10625334C2211yescharacteristic
21C22×#10625334C2211yescharacteristic
22#15689729—24no—
23#15689729C2218yescomplemented
24C2×#13094021C2211yescharacteristic
25C2×#13094009—21no—
26C2×#13094009—21no—
27C2×#13093999—21no—
28C2×#13093999—21no—
29C2×#13093999C2211yescharacteristic
30C2×#13093999C2211yescharacteristic
31#15689602—24no—
32#15689602C2218yescomplemented
33C2×C4×Dic94C2211yescharacteristic
34C2×#13093989C2211yescharacteristic
35C2×D4×Dic47C2211yescharacteristic
36C2×#13093986C2211yescharacteristic
37C2×#13093986C2211yescharacteristic
38C2×C4×C22⋊D47—21no—
39C2×(C22⋊D47)⋊C4—21no—
40C2×#13093981C2211yescharacteristic
41C2×#13093980—21no—
42C22×Dic47⋊C4—21no—
43C2×C4⋊C4×D47C2211yescharacteristic
44#15689443C2218yescomplemented
45#15689438C2218yescomplemented
46#15689427C2218yescomplemented
47#15689324C2218yescomplemented
48#15689318C2218yescomplemented
49#15689269C2218yescomplemented
50#15689269C2218yescomplemented
51#15689232C2218yescomplemented
52#15689222C2218yescomplemented
53#15689210C2218yescomplemented
54#15689203C2218yescomplemented
55#15689183C2218yescomplemented
56C2×#13093957C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×C4⋊(C47⋊C8)C2211yescharacteristic
59C2×#13093947C2211yescharacteristic
60C2×#13093947C2211yescharacteristic
61C2×#13093946C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×#125×C47C2211yescharacteristic
70C2×C4×D4×C47C2211yescharacteristic
71C47×#478C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C2×#10625352—24no—
78C2×#10625352—22no—
79C2×#10625352—24no—
80C2×#10625352C2314yes—
81C22×Dic94C2311yescharacteristic
82C22×D188—21no—
83C22×D188—21no—
84C22×D188—21no—
85C22×D188—21no—
86C22×D188C2311yescharacteristic
87C22×D188C2311yescharacteristic
88C22×C22⋊D47—21no—
89C23×Dic47—21no—
90C23×Dic47—21no—
91C22×C4×D47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C22×C4×D47C2311yescharacteristic
95C2×#10625325—24no—
96C2×#10625325—24no—
97C2×#10625325C2314yes—
98C2×#10625325C2314yes—
99C2×#10625334—24no—
100C2×#10625334—24no—
101C2×#10625334C2314yes—
102C2×#10625334C2314yes—
103C22×C47⋊C8C2311yescharacteristic
104C22×C47⋊C8C2311yescharacteristic
105#13094021—22no—
106#13094021C2314yes—
107#13094009—28no—
108#13094009—28no—
109#13093999—22no—
110#13093999—22no—
111#13093999—28no—
112#13093999—28no—
113#13093999C2314yes—
114#13093999C2314yes—
115C4×Dic94—22no—
116C4×Dic94C2314yes—
117#13093989—22no—
118#13093989C2314yes—
119D4×Dic47—22no—
120D4×Dic47C2314yes—
121#13093986—22no—
122#13093986—22no—
123#13093986C2314yes—
124#13093986C2314yes—
125C4×C22⋊D47—28no—
126(C22⋊D47)⋊C4—28no—
127#13093981D414yes—
128#13093981C2314yes—
129#13093980—28no—
130C2×C4⋊Dic47C2311yescharacteristic
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—28no—
135C2×Dic47⋊C4D411yescharacteristic
136C2×Dic47⋊C4D411yescharacteristic
137C4⋊C4×D47—22no—
138C4⋊C4×D47C2314yes—
139C2×C22⋊Dic47—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4D411yescharacteristic
145C2×(C2×D47)⋊C4D411yescharacteristic
146C2×C4×Dic47—21no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093957C2314yes—
150#13093955C2314yes—
151C4⋊(C47⋊C8)C2314yes—
152#13093947C2314yes—
153#13093947C2314yes—
154#13093946C2314yes—
155#13093946C2314yes—
156#13093944C2314yes—
157#13093944C2314yes—
158(C2×D47)⋊C8C2314yes—
159(C2×D47)⋊C8C2314yes—
160#13093934C2314yes—
161C8×Dic47C2314yes—
162C22×D4×C47C2311yescharacteristic
163C23×C4×C47—21no—
164C22×C8×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166#125×C47—22no—
167#125×C47C2314yes—
168C4×D4×C47—22no—
169C4×D4×C47C2314yes—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176C2×C42×C47C2311yescharacteristic
177#107×C47C2314yes—
178#106×C47C2314yes—
179C4⋊C8×C47C2314yes—
180#102×C47C2314yes—
181#102×C47C2314yes—
182C24×C47—21no—
183C23×D47—21no—
184C23×D47—21no—
185C23×D47C2×D411yescharacteristic
186C2×D4×C47—21no—
187C2×D4×C47—22no—
188C2×D4×C47#4114yes—
189C2×D4×C47C2412yes—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—24no—
194C22×C4×C47—82no—
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2411yescharacteristic
198C2×C22⋊D47—28no—
199C2×C22⋊D47—24no—
200C22×Dic47—28no—
201C22×Dic47—21no—
202C22×Dic47—24no—
203C22×Dic47—21no—
204C22×Dic47—24no—
205C22×Dic47—82no—
206C22×Dic47C2×D411yescharacteristic
207C22×Dic47C2×D411yescharacteristic
208C22×Dic47C2×D411yescharacteristic
209#10625352—216no—
210#10625352—28no—
211#10625352—28no—
212C2×D188—22no—
213C2×D188—22no—
214C2×D188—22no—
215C2×D188—22no—
216C2×D188—21no—
217C2×D188—21no—
218C2×D188—24no—
219C2×D188—24no—
220C2×D188—24no—
221C2×D188—24no—
222C2×D188—82no—
223C2×D188—82no—
224C2×D188—82no—
225C2×D188—82no—
226C2×D188C2412yes—
227C2×D188C2412yes—
228C2×C4×D47—22no—
229C2×C4×D47—22no—
230C2×C4×D47—24no—
231C2×C4×D47—24no—
232C2×C4×D47—24no—
233C2×C4×D47—82no—
234C2×C4×D47—82no—
235C2×C4×D47—82no—
236C2×C4×D47C2×D412yes—
237C2×C4×D47C2412yes—
238C2×Dic94—21no—
239C2×Dic94—22no—
240C2×Dic94#4114yes—
241C2×Dic94C2412yes—
242C2×C8×C47—22no—
243C2×C8×C47—22no—
244C2×C8×C47C2412yes—
245C2×C8×C47C2412yes—
246C4⋊C4×C47—24no—
247C4⋊C4×C47—24no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47C2412yes—
252C4⋊C4×C47C2412yes—
253C4⋊C4×C47C2412yes—
254C22⋊C4×C47—24no—
255C42×C47C2×D412yes—
256C42×C47C2412yes—
257C22⋊Dic47—24no—
258#10625334—28no—
259#10625334—28no—
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4—24no—
264(C2×D47)⋊C4C2×D414yes—
265(C2×D47)⋊C4C2×D414yes—
266C4⋊Dic47—21no—
267C4⋊Dic47C2412yes—
268Dic47⋊C4—24no—
269Dic47⋊C4—24no—
270Dic47⋊C4—24no—
271Dic47⋊C4C2×D414yes—
272Dic47⋊C4C2×D414yes—
273C4×Dic47—24no—
274C4×Dic47—24no—
275C4×Dic47C2×D412yes—
276C4×Dic47C2412yes—
277C2×C47⋊C8—22no—
278C2×C47⋊C8—22no—
279C2×C47⋊C8C2412yes—
280C2×C47⋊C8C2412yes—
281#10625325—28no—
282#10625325—28no—
283C23×C47—24no—
284C23×C47—22no—
285C23×C47—42no—
286C23×C47—42no—
287C23×C47C22×D411yescharacteristic
288C22×D47—22no—
289C22×D47—22no—
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—22no—
293C22×D47—42no—
294C22×D47—42no—
295C22×D47—42no—
296C22×D47—42no—
297C22×D47—42no—
298C22×D47—42no—
299C22×D47C22×D412yes—
300D4×C47—24no—
301D4×C47—22no—
302D4×C47C2×#4114yes—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—42no—
309C2×C4×C47—42no—
310C2×C4×C47—42no—
311C2×C4×C47—84no—
312C2×C4×C47C22×D412yes—
313C2×C4×C47C22×D412yes—
314C2×C4×C47C22×D411yescharacteristic
315C2×C4×C47C2×#4112yes—
316C2×C4×C47C2×#4112yes—
317C2×C4×C47C2511yescharacteristic
318C22⋊D47—216no—
319C2×Dic47—216no—
320C2×Dic47—24no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—42no—
327C2×Dic47—84no—
328C2×Dic47C22×D412yes—
329C2×Dic47C22×D412yes—
330C2×Dic47C22×D412yes—
331D188—22no—
332D188—22no—
333D188—22no—
334D188—22no—
335D188—42no—
336D188—42no—
337D188—84no—
338D188—84no—
339D188—84no—
340D188—84no—
341C4×D47—24no—
342C4×D47—22no—
343C4×D47—22no—
344C4×D47—84no—
345C4×D47—84no—
346C4×D47—84no—
347Dic94—24no—
348Dic94—22no—
349Dic94C2×#4114yes—
350C8×C47—22no—
351C8×C47—22no—
352C47⋊C8—22no—
353C47⋊C8—22no—
354C2×#3119—471nomaximal, Sylow
355C22×C47—24no—
356C22×C47—48no—
357C22×C47—42no—
358C22×C47—42no—
359C22×C47#52512yes—
360C22×C47#57612yes—
361C22×C47#57712yes—
362C22×C47C23×D411yescharacteristic
363C2×D47—22no—
364C2×D47—22no—
365C2×D47—22no—
366C2×D47—44no—
367C2×D47—42no—
368C2×D47—42no—
369C2×D47—42no—
370C2×D47—42no—
371C2×D47—42no—
372C2×D47—42no—
373C2×D47—84no—
374C2×D47—84no—
375C4×C47—22no—
376C4×C47—22no—
377C4×C47—42no—
378C4×C47—42no—
379C4×C47—42no—
380C4×C47#52512yes—
381C4×C47C22×#4111yescharacteristic
382C4×C47C22×#4111yescharacteristic
383Dic47—24no—
384Dic47—22no—
385Dic47—22no—
386Dic47—22no—
387Dic47—42no—
388C2×#540—471no—
389C2×#520—471no—
390#3119—4716no—
391C2×#481—471no—
392C2×#480—471no—
393C2×#479—471no—
394C2×#478D4711yescharacteristic, complemented
395C2×#460—471no—
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—44no—
405C2×C47#311914yescomplemented
406C2×C47C2×#52511yescharacteristic
407C2×C47C2×#57611yescharacteristic
408C2×C47C2×#57711yescharacteristic
409D47—42no—
410D47—82no—
411D47—82no—
412C22×#41—471no—
413C22×SD16—471no—
414C22×SD16—471no—
415C22×D8—471no—
416C22×D8—471no—
417#540—478no—
418#540—944no—
419C2×#127—471no—
420C2×#125C2×D4711yescharacteristic
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×Q8—471no—
431C2×C4×D4—471no—
432C2×C4×D4—471no—
433C2×C4×D4—471no—
434C2×C4×D4—941no—
435C2×C4×D4—941no—
436C2×C4×D4C2×D4711yescharacteristic
437C2×#117—471no—
438C2×#117—941no—
439C22×C4⋊C4—471no—
440C22×C4⋊C4—941no—
441#481—478no—
442#480—478no—
443#479—478no—
444#478C2×D4718yescomplemented
445#460—478no—
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×#107C2×D4711yescharacteristic
456C2×#106—471no—
457C2×#106C2×D4711yescharacteristic
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×Q8—471no—
478C22×D4—471no—
479C22×D4—471no—
480C22×D4—941no—
481C22×D4—941no—
482C22×D4—941no—
483C22×D4—941no—
484C22×D4—941no—
485C22×D4C22×D4711yescharacteristic
486C23×C4—21no—
487C23×C4—471no—
488C23×C4—941no—
489C23×C4—941no—
490C23×C4—941no—
491C23×C4—941no—
492C23×C4—941no—
493C2×SD16—474no—
494C2×SD16—474no—
495C2×SD16—944no—
496C2×SD16—944no—
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—474no—
506#127—942no—
507#125—22no—
508#125C22×D4714yes—
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—474no—
518C4×Q8—474no—
519C4×Q8—942no—
520C4×Q8—942no—
521C4×D4—22no—
522C4×D4—474no—
523C4×D4—474no—
524C4×D4—474no—
525C4×D4—942no—
526C4×D4—942no—
527C4×D4—942no—
528C4×D4—948no—
529C4×D4—948no—
530C4×D4C22×D4714yes—
531#117—474no—
532#117—474no—
533#117—948no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—471no—
538C2×C4⋊C4—471no—
539C2×C4⋊C4—474no—
540C2×C4⋊C4—942no—
541C2×C4⋊C4—948no—
542C2×C4⋊C4—941no—
543C2×C4⋊C4—941no—
544C2×C4⋊C4—941no—
545C2×C4⋊C4C22×D4711yescharacteristic
546C2×C4⋊C4C22×D4711yescharacteristic
547C2×C4⋊C4C22×D4711yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—471no—
550C2×C22⋊C4—471no—
551C2×C22⋊C4—941no—
552C2×C22⋊C4—941no—
553C2×C22⋊C4—941no—
554C2×C22⋊C4—941no—
555C2×C22⋊C4—941no—
556C2×C42—471no—
557C2×C42—941no—
558C2×C42—941no—
559C2×C42C22×D4711yescharacteristic
560#107—474no—
561#107C22×D4714yes—
562#106—474no—
563#106C22×D4714yes—
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—471no—
580C24—941no—
581C24—941no—
582#41—948no—
583#41—9416no—
584#41—948no—
585C2×Q8—474no—
586C2×Q8—472no—
587C2×Q8—941no—
588C2×Q8—942no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—472no—
592C2×D4—472no—
593C2×D4—944no—
594C2×D4—944no—
595C2×D4—944no—
596C2×D4—948no—
597C2×D4—944no—
598C2×D4—944no—
599C2×D4—941no—
600C2×D4—941no—
601C2×D4—942no—
602C2×D4—942no—
603C2×D4—942no—
604C2×D4—942no—
605C2×D4—3762no—
606C2×D4—3762no—
607C2×D4—3762no—
608C2×D4—3762no—
609C2×D4#1062535414yes—
610C2×D4C23×D4712yes—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—24no—
615C22×C4—82no—
616C22×C4—471no—
617C22×C4—471no—
618C22×C4—471no—
619C22×C4—472no—
620C22×C4—472no—
621C22×C4—944no—
622C22×C4—944no—
623C22×C4—944no—
624C22×C4—944no—
625C22×C4—944no—
626C22×C4—948no—
627C22×C4—941no—
628C22×C4—942no—
629C22×C4—942no—
630C22×C4—941no—
631C22×C4—3762no—
632C22×C4—3762no—
633C22×C4—3762no—
634C22×C4—3762no—
635C22×C4D4×D4711yescharacteristic
636C22×C4D4×D4711yescharacteristic
637C22×C4C23×D4711yescharacteristic
638SD16—948no—
639SD16—948no—
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—24no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—474no—
656C4⋊C4—474no—
657C4⋊C4—472no—
658C4⋊C4—944no—
659C4⋊C4—944no—
660C4⋊C4—944no—
661C4⋊C4—941no—
662C4⋊C4C23×D4712yes—
663C4⋊C4C23×D4712yes—
664C4⋊C4C23×D4712yes—
665C22⋊C4—24no—
666C22⋊C4—474no—
667C22⋊C4—474no—
668C22⋊C4—944no—
669C22⋊C4—944no—
670C22⋊C4—944no—
671C22⋊C4—944no—
672C22⋊C4—944no—
673C42—472no—
674C42—472no—
675C42—944no—
676C42—944no—
677C42D4×D4712yes—
678C42C23×D4712yes—
679C23—24no—
680C23—22no—
681C23—42no—
682C23—42no—
683C23—472no—
684C23—942no—
685C23—942no—
686C23—942no—
687C23—942no—
688C23—942no—
689C23—1882no—
690C23—1882no—
691C23—1882no—
692C23—1882no—
693C23—1882no—
694C23—1882no—
695C23C2×D4×D4711yescharacteristic
696Q8—474no—
697Q8—944no—
698Q8—942no—
699D4—24no—
700D4—22no—
701D4—9416no—
702D4—942no—
703D4—942no—
704D4—942no—
705D4—942no—
706D4—3764no—
707D4—3764no—
708D4—3764no—
709D4—3764no—
710D4—1882no—
711D4—1882no—
712D4C2×#1062535414yes—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—84no—
722C2×C4—472no—
723C2×C4—472no—
724C2×C4—472no—
725C2×C4—9416no—
726C2×C4—942no—
727C2×C4—944no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—944no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—3764no—
736C2×C4—3764no—
737C2×C4—3764no—
738C2×C4—3764no—
739C2×C4—1882no—
740C2×C4C2×D4×D4712yes—
741C2×C4C2×D4×D4712yes—
742C2×C4C2×D4×D4711yescharacteristic
743C2×C4#41×D4712yes—
744C2×C4C2×#1062535412yes—
745C2×C4C24×D4711yescharacteristic
746C8—22no—
747C8—22no—
748C8—942no—
749C8—942no—
750C22—24no—
751C22—42no—
752C22—42no—
753C22—48no—
754C22—942no—
755C22—942no—
756C22—942no—
757C22—3764no—
758C22—3764no—
759C22—1882no—
760C22—1882no—
761C22—1882no—
762C22—1882no—
763C22—1882no—
764C22—1882no—
765C22—1884no—
766C22#1568963612yes—
767C22#1568992712yes—
768C22#1568993012yes—
769C22C22×D4×D4711yescharacteristic
770C4—22no—
771C4—22no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—942no—
776C4—942no—
777C4—942no—
778C4—944no—
779C4—1882no—
780C4#1568963612yes—
781C4C2×#41×D4711yescharacteristic
782C4C22×#1062535411yescharacteristic
783C2—44no—
784C2—3762no—
785C2—3762no—
786C2—1882no—
787C2#2025359214yesdirect product factor
788C2C2×#1568963611yescharacteristic
789C2C2×#1568992711yescharacteristic
790C2C2×#1568993011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#478C2
socleC23×C47C22×D4
hypercenterC2×#478D47
hypocenterC47C2×#3119
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#15689729C2semidirect
2. C2×#15689602C2semidirect
3. #20253592C2direct (N × H)
4. C2×#15689443C2semidirect
5. C2×#15689438C2semidirect
6. C2×#15689427C2semidirect
7. C2×#15689324C2semidirect
8. C2×#15689318C2semidirect
9. C2×#15689269C2semidirect
10. C2×#15689269C2semidirect
11. C2×#15689232C2semidirect
12. C2×#15689222C2semidirect
13. C2×#15689210C2semidirect
14. C2×#15689203C2semidirect
15. C2×#15689183C2semidirect
16. C2×C47×#478C2semidirect
23. #15689729C22semidirect
32. #15689602C22semidirect
44. #15689443C22semidirect
45. #15689438C22semidirect
46. #15689427C22semidirect
47. #15689324C22semidirect
48. #15689318C22semidirect
49. #15689269C22semidirect
50. #15689269C22semidirect
51. #15689232C22semidirect
52. #15689222C22semidirect
53. #15689210C22semidirect
54. #15689203C22semidirect
55. #15689183C22semidirect
71. C47×#478C22semidirect
394. C2×#478D47semidirect
405. C2×C47#3119semidirect
444. #478C2×D47semidirect
472. C47C2×#3119semidirect
787. C2#20253592direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897292
C2×#156896022
#202535922
C2×#156894432
C2×#156894382
C2×#156894272
C2×#156893242
C2×#156893182
C2×#156892692
C2×#156892322
C2×#156892222
C2×#156892102
C2×#156892032
C2×#156891832
C2×C47×#4782
C2×#311947