Finite Group Databasebeta

← C2×#20253979 #27086039

Subgroups — C2×#20253979 #27086039

Order 12032.

2266 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689670C211yesmaximal, characteristic, complemented
2C2×#15689660C211yesmaximal, characteristic, complemented
3#20253979C2116yesmaximal, direct product factor
4C2×#15689530C211yesmaximal, characteristic, complemented
5C2×#15689509C211yesmaximal, characteristic, complemented
6C2×#15689486C211yesmaximal, characteristic, complemented
7C2×#15689484C211yesmaximal, characteristic, complemented
8C2×#15689377C211yesmaximal, characteristic, complemented
9C2×#15689375C211yesmaximal, characteristic, complemented
10C2×#15689372C211yesmaximal, characteristic, complemented
11C2×#15689366C211yesmaximal, characteristic, complemented
12C2×C4×#10625336C211yesmaximal, characteristic, complemented
13C2×C4×D376C211yesmaximal, characteristic, complemented
14C2×C4×#10625334C211yesmaximal, characteristic, complemented
15C2×C4×#10625324C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C47C211yesmaximal, characteristic, complemented
17C22×#10625350—21no—
18C22×#10625336C2211yescharacteristic
19C22×D376C2211yescharacteristic
20C22×#10625334C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22C22×#10625324C2211yescharacteristic
23#15689670—24no—
24#15689670C2218yescomplemented
25C2×#13094023C2211yescharacteristic
26C2×#13094020C2211yescharacteristic
27#15689660—24no—
28#15689660C2218yescomplemented
29C2×#13094019—21no—
30C2×#13094015C2211yescharacteristic
31C2×#13094013C2211yescharacteristic
32C2×#13094010—21no—
33C2×#13094009—21no—
34C2×#13094000C2211yescharacteristic
35C2×#13093999C2211yescharacteristic
36C2×#13093999C2211yescharacteristic
37C2×#13093997—21no—
38C2×#13093995C2211yescharacteristic
39C2×C4×D188—21no—
40C2×C4×D188C2211yescharacteristic
41C2×C4×D188C2211yescharacteristic
42C2×C4×C22⋊D47—21no—
43C2×#13093981—21no—
44C2×C42×D47C2211yescharacteristic
45#15689530C2218yescomplemented
46#15689509C2218yescomplemented
47#15689486C2218yescomplemented
48#15689484C2218yescomplemented
49#15689377C2218yescomplemented
50#15689375C2218yescomplemented
51#15689372C2218yescomplemented
52#15689366C2218yescomplemented
53C4×#10625336C2218yescomplemented
54C4×D376C2218yescomplemented
55C4×#10625334C2218yescomplemented
56C2×#13093958C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×#13093955C2211yescharacteristic
59C2×#13093948C2211yescharacteristic
60C2×#13093946C2211yescharacteristic
61C2×#13093946C2211yescharacteristic
62C2×#13093945C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C4×#10625324C2218yescomplemented
66C2×#13093934C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C4×C47⋊C8C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C4×SD16×C47C2218yescomplemented
73C2×#106×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C2×#10625350—28no—
78C2×#10625350—48no—
79C22×Dic94—21no—
80C22×D188—21no—
81C22×D188—21no—
82C22×D188C2311yescharacteristic
83C22×D188C2311yescharacteristic
84C22×C22⋊D47—21no—
85C22×C22⋊D47—21no—
86C22×C22⋊D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47D411yescharacteristic
90C22×C4×D47D411yescharacteristic
91C22×C4×D47C2311yescharacteristic
92C2×#10625336—24no—
93C2×#10625336C2314yes—
94C2×D376—24no—
95C2×D376C2314yes—
96C2×#10625334—24no—
97C2×#10625334C2314yes—
98C2×#10625324—24no—
99C2×#10625324—24no—
100C2×#10625324C2314yes—
101C2×#10625324C2314yes—
102C22×C47⋊C8C2311yescharacteristic
103C22×C47⋊C8C2311yescharacteristic
104#13094023—22no—
105#13094023C2314yes—
106#13094020—22no—
107#13094020C2314yes—
108#13094019—28no—
109#13094015—22no—
110#13094015C2314yes—
111#13094013—22no—
112#13094013C2314yes—
113#13094010—28no—
114#13094009—28no—
115#13094000—22no—
116#13094000C2314yes—
117#13093999—22no—
118#13093999—22no—
119#13093999C2314yes—
120#13093999C2314yes—
121#13093997—28no—
122#13093995—22no—
123#13093995C2314yes—
124C4×D188—28no—
125C4×D188—22no—
126C4×D188—22no—
127C4×D188C2314yes—
128C4×D188C2314yes—
129C4×C22⋊D47—28no—
130#13093981—28no—
131C2×C4⋊Dic47—21no—
132C2×C4⋊Dic47C2311yescharacteristic
133C2×C4⋊Dic47C2311yescharacteristic
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×C22⋊Dic47—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×C4×Dic47D411yescharacteristic
146C2×C4×Dic47D411yescharacteristic
147C2×C4×Dic47C2311yescharacteristic
148C42×D47D414yes—
149C42×D47C2314yes—
150#13093958C2314yes—
151#13093957C2314yes—
152#13093955C2314yes—
153#13093948C2314yes—
154#13093946C2314yes—
155#13093946C2314yes—
156#13093945C2314yes—
157#13093944C2314yes—
158#13093944C2314yes—
159#13093934C2314yes—
160#13093934C2314yes—
161C4×C47⋊C8C2314yes—
162C22×Q8×C47C2311yescharacteristic
163C22×D4×C47C2311yescharacteristic
164C23×C4×C47—21no—
165C2×SD16×C47—24no—
166C2×SD16×C47C2314yes—
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C4×Q8×C47—22no—
170C4×Q8×C47C2314yes—
171C4×D4×C47—22no—
172C4×D4×C47C2314yes—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C22⋊C4×C47—21no—
177C2×C42×C47—21no—
178C2×C42×C47C2311yescharacteristic
179#106×C47C2314yes—
180#103×C47C2314yes—
181#102×C47C2314yes—
182C4×C8×C47C2314yes—
183C24×C47—21no—
184C23×D47—21no—
185C23×D47—21no—
186C23×D47C2×D411yescharacteristic
187C2×Q8×C47—21no—
188C2×Q8×C47—22no—
189C2×Q8×C47—22no—
190C2×Q8×C47C2412yes—
191C2×D4×C47—21no—
192C2×D4×C47—22no—
193C2×D4×C47—22no—
194C2×D4×C47C2412yes—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—24no—
199C22×C4×C47—44no—
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2411yescharacteristic
203C2×C22⋊D47—24no—
204C2×C22⋊D47—24no—
205C2×C22⋊D47—24no—
206C2×C22⋊D47—44no—
207C2×C22⋊D47—44no—
208C2×C22⋊D47—44no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47C2×D411yescharacteristic
212C22×Dic47C2×D411yescharacteristic
213C22×Dic47C2×D411yescharacteristic
214#10625350—432no—
215C2×D188—22no—
216C2×D188—22no—
217C2×D188—22no—
218C2×D188—22no—
219C2×D188—24no—
220C2×D188—24no—
221C2×D188—21no—
222C2×D188—21no—
223C2×D188—44no—
224C2×D188—44no—
225C2×D188C2412yes—
226C2×D188C2412yes—
227C2×C4×D47—24no—
228C2×C4×D47—22no—
229C2×C4×D47—22no—
230C2×C4×D47—24no—
231C2×C4×D47—24no—
232C2×C4×D47—42no—
233C2×C4×D47—44no—
234C2×C4×D47—44no—
235C2×C4×D47C2×D412yes—
236C2×C4×D47C2×D414yes—
237C2×C4×D47C2×D414yes—
238C2×C4×D47C2412yes—
239C2×Dic94—24no—
240C2×Dic94—44no—
241SD16×C47—28no—
242C2×C8×C47—22no—
243C2×C8×C47#4114yescomplemented
244C2×C8×C47C2412yes—
245C2×C8×C47C2412yes—
246C4⋊C4×C47—24no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47C2412yes—
250C4⋊C4×C47C2412yes—
251C22⋊C4×C47—24no—
252C42×C47—24no—
253C42×C47C2×D412yes—
254C42×C47C2412yes—
255C22⋊Dic47—24no—
256#10625336—28no—
257#10625334—28no—
258(C2×D47)⋊C4—24no—
259(C2×D47)⋊C4—24no—
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4—24no—
264(C2×D47)⋊C4—24no—
265C4⋊Dic47—21no—
266C4⋊Dic47—21no—
267C4⋊Dic47—24no—
268C4⋊Dic47C2412yes—
269C4⋊Dic47C2412yes—
270Dic47⋊C4—24no—
271Dic47⋊C4—24no—
272Dic47⋊C4—24no—
273C4×Dic47C2×D412yes—
274C4×Dic47C2×D414yes—
275C4×Dic47C2×D414yes—
276C4×Dic47C2412yes—
277C2×C47⋊C8—22no—
278C2×C47⋊C8#4114yescomplemented
279C2×C47⋊C8C2412yes—
280C2×C47⋊C8C2412yes—
281D376—28no—
282#10625324—28no—
283#10625324—28no—
284C23×C47—22no—
285C23×C47—42no—
286C23×C47—42no—
287C23×C47—42no—
288C23×C47C22×D411yescharacteristic
289C22×D47—22no—
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—22no—
293C22×D47—22no—
294C22×D47—42no—
295C22×D47—42no—
296C22×D47—42no—
297C22×D47—42no—
298C22×D47—42no—
299C22×D47—42no—
300C22×D47C22×D412yes—
301Q8×C47—22no—
302Q8×C47—22no—
303Q8×C47—42no—
304D4×C47—22no—
305D4×C47—22no—
306D4×C47—42no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
313C2×C4×C47—42no—
314C2×C4×C47—48no—
315C2×C4×C47AGL(1,ℤ/8)14yes—
316C2×C4×C47C22×D412yes—
317C2×C4×C47C22×D411yescharacteristic
318C2×C4×C47C22×D412yes—
319C2×C4×C47C2×#4112yes—
320C2×C4×C47C2×#4112yes—
321C2×C4×C47C2511yescharacteristic
322C22⋊D47—48no—
323C22⋊D47—48no—
324C22⋊D47—48no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47C22×D412yes—
333C2×Dic47C22×D412yes—
334C2×Dic47C22×D412yes—
335D188—22no—
336D188—22no—
337D188—22no—
338D188—22no—
339D188—48no—
340D188—48no—
341D188—42no—
342D188—42no—
343C4×D47—24no—
344C4×D47—28no—
345C4×D47—22no—
346C4×D47—22no—
347C4×D47—44no—
348C4×D47—48no—
349C4×D47—48no—
350Dic94—48no—
351C8×C47—22no—
352C8×C47C2×#4114yescomplemented
353C47⋊C8—22no—
354C47⋊C8C2×#4114yescomplemented
355C2×#3171—471nomaximal, Sylow
356C22×C47—42no—
357C22×C47—42no—
358C22×C47—42no—
359C22×C47—84no—
360C22×C47#53212yes—
361C22×C47C2×AGL(1,ℤ/8)12yes—
362C22×C47#57512yes—
363C22×C47C23×D411yescharacteristic
364C2×D47—22no—
365C2×D47—22no—
366C2×D47—22no—
367C2×D47—44no—
368C2×D47—42no—
369C2×D47—42no—
370C2×D47—42no—
371C2×D47—42no—
372C2×D47—42no—
373C2×D47—42no—
374C2×D47—84no—
375C2×D47—84no—
376C4×C47—22no—
377C4×C47—42no—
378C4×C47—42no—
379C4×C47—42no—
380C4×C47#53212yes—
381C4×C47C2×AGL(1,ℤ/8)14yes—
382C4×C47C22×#4111yescharacteristic
383C4×C47C22×#4111yescharacteristic
384Dic47—22no—
385Dic47—22no—
386Dic47—22no—
387Dic47—42no—
388Dic47—42no—
389C2×#532—471no—
390C2×#529—471no—
391#3171—4716no—
392C2×#501—471no—
393C2×#496—471no—
394C2×#490—471no—
395C2×#489—471no—
396C2×#469—471no—
397C2×#469—471no—
398C2×#468—471no—
399C2×#468—471no—
400C2×C4×SD16—471no—
401C2×C4×SD16D4711yescharacteristic, complemented
402C2×C4×D8—471no—
403C2×C4×D8—471no—
404C2×C4×M16—471no—
405C2×C47—82no—
406C2×C47#317114yescomplemented
407C2×C47C2×#53211yescharacteristic
408C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
409C2×C47C2×#57511yescharacteristic
410D47—42no—
411D47—82no—
412D47—82no—
413C22×#41—941no—
414C22×SD16—471no—
415C22×SD16C2×D4711yescharacteristic
416C22×D8—471no—
417C22×D8—471no—
418C22×M16—471no—
419C22×M16—471no—
420#532—478no—
421#532—944no—
422C2×C4⋊Q8—471no—
423C2×#127—471no—
424#529—478no—
425#529—944no—
426C2×#126—941no—
427C2×#125—471no—
428C2×#124—471no—
429C2×#124—941no—
430C2×#123—941no—
431C2×C22⋊Q8—471no—
432C2×#121—471no—
433C2×#121—471no—
434C2×#121—471no—
435C2×#121—941no—
436C2×C4×Q8C2×D4711yescharacteristic
437C2×C4×D4—471no—
438C2×C4×D4—471no—
439C2×C4×D4—941no—
440C2×C4×D4—941no—
441C2×C4×D4C2×D4711yescharacteristic
442C2×#117—941no—
443C22×C42—471no—
444#501—478no—
445#496—478no—
446#490—478no—
447#489—478no—
448#469—478no—
449#469—478no—
450#468—478no—
451#468—478no—
452C4×SD16—478no—
453C4×SD16C2×D4718yescomplemented
454C4×D8—478no—
455C4×D8—478no—
456C2×#107—471no—
457C2×#107—471no—
458C2×#106—471no—
459C2×#106C2×D4711yescharacteristic
460C2×#103—471no—
461C2×#103C2×D4711yescharacteristic
462C2×#102—471no—
463C2×#102—471no—
464C2×#102—471no—
465C2×#102—471no—
466C2×#102—471no—
467C2×#102C2×D4711yescharacteristic
468C4×M16—478no—
469C2×#97—471no—
470C2×#97—471no—
471C2×C4×C8—471no—
472C2×C4×C8C2×D4711yescharacteristic
473C47C2×#317111yescharacteristic, complemented, Sylow
474C2×#41—948no—
475C2×#41—1888no—
476C22×Q8—941no—
477C22×Q8C22×D4711yescharacteristic
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—471no—
489C23×C4—471no—
490C23×C4—941no—
491C23×C4—941no—
492C2×SD16—24no—
493C2×SD16—474no—
494C2×SD16—944no—
495C2×SD16C22×D4714yes—
496C2×D8—474no—
497C2×D8—474no—
498C2×D8—944no—
499C2×D8—944no—
500C2×M16—474no—
501C2×M16—474no—
502C2×M16—944no—
503C2×M16—944no—
504C22×C8—471no—
505C22×C8—471no—
506C22×C8C22×D4711yescharacteristic
507C22×C8C22×D4711yescharacteristic
508C4⋊Q8—474no—
509C4⋊Q8—942no—
510#127—474no—
511#127—942no—
512#126—948no—
513#125—474no—
514#125—942no—
515#124—474no—
516#124—948no—
517#124—942no—
518#123—948no—
519C22⋊Q8—474no—
520C22⋊Q8—942no—
521#121—474no—
522#121—474no—
523#121—474no—
524#121—948no—
525#121—942no—
526#121—942no—
527#121—942no—
528C4×Q8—22no—
529C4×Q8C22×D4714yes—
530C4×D4—22no—
531C4×D4—474no—
532C4×D4—474no—
533C4×D4—948no—
534C4×D4—948no—
535C4×D4—942no—
536C4×D4—942no—
537C4×D4C22×D4714yes—
538#117—948no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—471no—
541C2×C4⋊C4—471no—
542C2×C4⋊C4—941no—
543C2×C4⋊C4—941no—
544C2×C4⋊C4—941no—
545C2×C4⋊C4—941no—
546C2×C4⋊C4C22×D4711yescharacteristic
547C2×C4⋊C4C22×D4711yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—941no—
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×C22⋊C4—941no—
557C2×C42—21no—
558C2×C42—471no—
559C2×C42—471no—
560C2×C42—471no—
561C2×C42—474no—
562C2×C42—474no—
563C2×C42C22×D4711yescharacteristic
564#107—474no—
565#107—474no—
566#106—474no—
567#106C22×D4714yes—
568#103—474no—
569#103C22×D4714yes—
570#102—474no—
571#102—474no—
572#102—474no—
573#102—474no—
574#102—474no—
575#102C22×D4714yes—
576#97—474no—
577#97—474no—
578C4×C8—474no—
579C4×C8C22×D4714yes—
580C24—21no—
581C24—471no—
582C24—941no—
583C24—941no—
584#41—18832no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—944no—
589C2×Q8—1884no—
590C2×Q8C23×D4712yes—
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—472no—
595C2×D4—472no—
596C2×D4—944no—
597C2×D4—944no—
598C2×D4—944no—
599C2×D4—944no—
600C2×D4—944no—
601C2×D4—941no—
602C2×D4—941no—
603C2×D4—942no—
604C2×D4—942no—
605C2×D4—942no—
606C2×D4—942no—
607C2×D4—1884no—
608C2×D4—1884no—
609C2×D4—1884no—
610C2×D4—1884no—
611C2×D4—1884no—
612C2×D4C23×D4712yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—24no—
617C22×C4—44no—
618C22×C4—471no—
619C22×C4—471no—
620C22×C4—471no—
621C22×C4—474no—
622C22×C4—472no—
623C22×C4—472no—
624C22×C4—474no—
625C22×C4—944no—
626C22×C4—942no—
627C22×C4—942no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—944no—
631C22×C4—944no—
632C22×C4—1882no—
633C22×C4—1884no—
634C22×C4—1884no—
635C22×C4D4×D4711yescharacteristic
636C22×C4D4×D4711yescharacteristic
637C22×C4C23×D4711yescharacteristic
638SD16—28no—
639SD16—948no—
640D8—948no—
641D8—948no—
642M16—948no—
643M16—948no—
644C2×C8—22no—
645C2×C8—474no—
646C2×C8—472no—
647C2×C8—472no—
648C2×C8—942no—
649C2×C8#1062535014yescomplemented
650C2×C8C23×D4712yes—
651C2×C8C23×D4712yes—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
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⋊C4C23×D4712yes—
664C4⋊C4C23×D4712yes—
665C22⋊C4—24no—
666C22⋊C4—944no—
667C22⋊C4—944no—
668C22⋊C4—944no—
669C22⋊C4—944no—
670C22⋊C4—944no—
671C22⋊C4—944no—
672C22⋊C4—944no—
673C22⋊C4—944no—
674C42—24no—
675C42—474no—
676C42—474no—
677C42—472no—
678C42—472no—
679C42D4×D4712yes—
680C42C23×D4712yes—
681C23—22no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—472no—
686C23—942no—
687C23—942no—
688C23—942no—
689C23—942no—
690C23—942no—
691C23—1882no—
692C23—1882no—
693C23—1882no—
694C23—1882no—
695C23—1882no—
696C23—1882no—
697C23C2×D4×D4711yescharacteristic
698Q8—22no—
699Q8—22no—
700Q8—42no—
701Q8—1888no—
702D4—22no—
703D4—22no—
704D4—42no—
705D4—942no—
706D4—942no—
707D4—942no—
708D4—942no—
709D4—1888no—
710D4—1888no—
711D4—1888no—
712D4—1888no—
713D4—1888no—
714D4—1882no—
715D4—1882no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—48no—
724C2×C4—472no—
725C2×C4—472no—
726C2×C4—472no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—948no—
731C2×C4—944no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—1884no—
737C2×C4—1882no—
738C2×C4—1882no—
739C2×C4—1888no—
740C2×C4—1888no—
741C2×C4#1309405114yes—
742C2×C4C2×D4×D4712yes—
743C2×C4C2×D4×D4712yes—
744C2×C4C2×D4×D4711yescharacteristic
745C2×C4#41×D4712yes—
746C2×C4C2×#1062535012yes—
747C2×C4C24×D4711yescharacteristic
748C8—22no—
749C8—474no—
750C8—942no—
751C8C2×#1062535014yescomplemented
752C22—42no—
753C22—42no—
754C22—42no—
755C22—84no—
756C22—942no—
757C22—942no—
758C22—942no—
759C22—3764no—
760C22—3764no—
761C22—1882no—
762C22—1882no—
763C22—1882no—
764C22—1882no—
765C22—1882no—
766C22—1882no—
767C22—1884no—
768C22#1568967012yes—
769C22C2×#1309405112yes—
770C22#1568992012yes—
771C22C22×D4×D4711yescharacteristic
772C4—22no—
773C4—42no—
774C4—42no—
775C4—42no—
776C4—942no—
777C4—942no—
778C4—942no—
779C4—1882no—
780C4—1882no—
781C4#1568967012yes—
782C4C2×#1309405114yes—
783C4C2×#41×D4711yescharacteristic
784C4C22×#1062535011yescharacteristic
785C2—82no—
786C2—3762no—
787C2—3762no—
788C2—1882no—
789C2#2025397914yesdirect product factor
790C2C2×#1568967011yescharacteristic
791C2C22×#1309405111yescharacteristic
792C2C2×#1568992011yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C4×SD16×C47C2
socleC23×C47C22×D4
hypercenterC2×C4×SD16D47
hypocenterC47C2×#3171
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#15689670C2semidirect
2. C2×#15689660C2semidirect
3. #20253979C2direct (N × H)
4. C2×#15689530C2semidirect
5. C2×#15689509C2semidirect
6. C2×#15689486C2semidirect
7. C2×#15689484C2semidirect
8. C2×#15689377C2semidirect
9. C2×#15689375C2semidirect
10. C2×#15689372C2semidirect
11. C2×#15689366C2semidirect
12. C2×C4×#10625336C2semidirect
13. C2×C4×D376C2semidirect
14. C2×C4×#10625334C2semidirect
15. C2×C4×#10625324C2semidirect
16. C2×C4×SD16×C47C2semidirect
24. #15689670C22semidirect
28. #15689660C22semidirect
45. #15689530C22semidirect
46. #15689509C22semidirect
47. #15689486C22semidirect
48. #15689484C22semidirect
49. #15689377C22semidirect
50. #15689375C22semidirect
51. #15689372C22semidirect
52. #15689366C22semidirect
53. C4×#10625336C22semidirect
54. C4×D376C22semidirect
55. C4×#10625334C22semidirect
65. C4×#10625324C22semidirect
72. C4×SD16×C47C22semidirect
243. C2×C8×C47#41semidirect
278. C2×C47⋊C8#41semidirect
352. C8×C47C2×#41semidirect
354. C47⋊C8C2×#41semidirect
401. C2×C4×SD16D47semidirect
406. C2×C47#3171semidirect
453. C4×SD16C2×D47semidirect
473. C47C2×#3171semidirect
649. C2×C8#10625350semidirect
751. C8C2×#10625350semidirect
789. C2#20253979direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896702
C2×#156896602
#202539792
C2×#156895302
C2×#156895092
C2×#156894862
C2×#156894842
C2×#156893772
C2×#156893752
C2×#156893722
C2×#156893662
C2×C4×#106253362
C2×C4×D3762
C2×C4×#106253342
C2×C4×#106253242
C2×C4×SD16×C472
C2×#317147