Finite Group Databasebeta

← C2×#20253498 #27084459

Subgroups — C2×#20253498 #27084459

Order 12032.

2182 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689659C211yesmaximal, characteristic, complemented
2C2×#41×Dic47C211yesmaximal, characteristic, complemented
3#20253498C2116yesmaximal, direct product factor
4C2×#15689461C211yesmaximal, characteristic, complemented
5C2×#15689448C211yesmaximal, characteristic, complemented
6C2×#15689432C211yesmaximal, characteristic, complemented
7C2×#15689425C211yesmaximal, characteristic, complemented
8C2×#15689347C211yesmaximal, characteristic, complemented
9C2×#15689340C211yesmaximal, characteristic, complemented
10C2×#15689268C211yesmaximal, characteristic
11C2×#15689232C211yesmaximal, characteristic, complemented
12C2×#15689230C211yesmaximal, characteristic, complemented
13C2×#15689226C211yesmaximal, characteristic, complemented
14C2×#15689224C211yesmaximal, characteristic, complemented
15C2×#15689177C211yesmaximal, characteristic, complemented
16C2×C47×#452C211yesmaximal, characteristic, complemented
17C22×#10625336C2211yescharacteristic
18C22×#10625334C2211yescharacteristic
19#15689659—24no—
20#15689659C2218yescomplemented
21C2×#13094019—21no—
22C2×#13094015C2211yescharacteristic
23C2×#13094013C2211yescharacteristic
24C2×#13094008—21no—
25C2×#13093998C2211yescharacteristic
26#41×Dic47—24no—
27#41×Dic47C2218yescomplemented
28C2×Q8×Dic47C2211yescharacteristic
29C2×Q8×Dic47C2211yescharacteristic
30C2×Q8×Dic47C2211yescharacteristic
31C2×D4×Dic47—21no—
32C2×D4×Dic47—21no—
33C2×D4×Dic47C2211yescharacteristic
34C2×D4×Dic47C2211yescharacteristic
35C2×#13093986C2211yescharacteristic
36C2×(C22⋊D47)⋊C4—21no—
37C2×#13093983—21no—
38C2×#13093983C2211yescharacteristic
39C2×#13093982—21no—
40C22×C4×Dic47—21no—
41C22×C4×Dic47C2211yescharacteristic
42#15689461C2218yescomplemented
43#15689448C2218yescomplemented
44#15689432C2218yescomplemented
45#15689425C2218yescomplemented
46#15689347C2218yescomplemented
47#15689340C2218yescomplemented
48#15689268C2218yes—
49#15689232C2218yescomplemented
50#15689230C2218yescomplemented
51#15689226C2218yescomplemented
52#15689224C2218yescomplemented
53#15689177C2218yescomplemented
54C2×#13093958C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C22×#41×C47C2211yescharacteristic
70C22×Q16×C47C2211yescharacteristic
71C22×SD16×C47C2211yescharacteristic
72C2×C22⋊Q8×C47C2211yescharacteristic
73C47×#452C2218yescomplemented
74C2×#103×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C22×D188C2311yescharacteristic
78C22×C22⋊D47—21no—
79C23×Dic47—21no—
80C23×Dic47—21no—
81C23×Dic47D411yescharacteristic
82C23×Dic47D411yescharacteristic
83C22×C4×D47—21no—
84C2×#10625336—24no—
85C2×#10625336C2314yes—
86C2×#10625334—24no—
87C2×#10625334C2314yes—
88C22×C47⋊C8C2311yescharacteristic
89C22×C47⋊C8C2311yescharacteristic
90#13094019—28no—
91#13094015—22no—
92#13094015C2314yes—
93#13094013—22no—
94#13094013C2314yes—
95#13094008—28no—
96#13093998—22no—
97#13093998C2314yes—
98Q8×Dic47—22no—
99Q8×Dic47—22no—
100Q8×Dic47—22no—
101Q8×Dic47C2314yes—
102Q8×Dic47C2314yes—
103Q8×Dic47C2314yes—
104D4×Dic47—28no—
105D4×Dic47—28no—
106D4×Dic47—22no—
107D4×Dic47—22no—
108D4×Dic47C2314yes—
109D4×Dic47C2314yes—
110#13093986—22no—
111#13093986C2314yes—
112(C22⋊D47)⋊C4—28no—
113#13093983—22no—
114#13093983—28no—
115#13093983C2314yes—
116#13093982—28no—
117C2×C4⋊Dic47—21no—
118C2×C4⋊Dic47—21no—
119C2×C4⋊Dic47—21no—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47C2311yescharacteristic
122C2×C4⋊Dic47C2311yescharacteristic
123C2×C4⋊Dic47C2311yescharacteristic
124C2×Dic47⋊C4—21no—
125C2×C22⋊Dic47—21no—
126C2×C22⋊Dic47—21no—
127C2×C22⋊Dic47—21no—
128C2×(C2×D47)⋊C4—21no—
129C2×(C2×D47)⋊C4—21no—
130C2×(C2×D47)⋊C4—21no—
131C2×(C2×D47)⋊C4—21no—
132C2×C4×Dic47—21no—
133C2×C4×Dic47—21no—
134C2×C4×Dic47—21no—
135C2×C4×Dic47—21no—
136C2×C4×Dic47—28no—
137C2×C4×Dic47D411yescharacteristic
138C2×C4×Dic47D411yescharacteristic
139C2×C4×Dic47D414yes—
140C2×C4×Dic47C2311yescharacteristic
141C2×C4×Dic47C2311yescharacteristic
142C2×C4×Dic47C2314yes—
143#13093958C2314yes—
144#13093957C2314yes—
145#13093956C2314yes—
146#13093955C2314yes—
147Dic47⋊C8C2314yes—
148Dic47⋊C8C2314yes—
149#13093948C2314yes—
150#13093948C2314yes—
151#13093948C2314yes—
152#13093946C2314yes—
153#13093946C2314yes—
154#13093945C2314yes—
155C22⋊(C47⋊C8)C2314yes—
156#13093934C2314yes—
157#13093934C2314yes—
158C2×#41×C47—24no—
159C2×#41×C47—24no—
160C2×#41×C47—22no—
161C2×#41×C47C2314yes—
162C22×Q8×C47C2311yescharacteristic
163C22×Q8×C47C2311yescharacteristic
164C22×D4×C47—21no—
165C22×D4×C47C2311yescharacteristic
166C23×C4×C47—21no—
167C23×C4×C47C2311yescharacteristic
168C2×Q16×C47—24no—
169C2×Q16×C47C2314yes—
170C2×SD16×C47—24no—
171C2×SD16×C47C2314yes—
172C22×C8×C47C2311yescharacteristic
173C22×C8×C47C2311yescharacteristic
174C22⋊Q8×C47—22no—
175C22⋊Q8×C47C2314yes—
176C2×C4⋊C4×C47—21no—
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C22⋊C4×C47—21no—
179#103×C47C2314yes—
180#102×C47C2314yes—
181C22⋊C8×C47C2314yes—
182C24×C47—21no—
183C24×C47C2×D411yescharacteristic
184C23×D47—21no—
185#41×C47—216no—
186#41×C47—28no—
187#41×C47—28no—
188C2×Q8×C47—21no—
189C2×Q8×C47—21no—
190C2×Q8×C47—22no—
191C2×Q8×C47—22no—
192C2×Q8×C47—22no—
193C2×Q8×C47#4114yes—
194C2×Q8×C47C2412yes—
195C2×Q8×C47C2412yes—
196C2×D4×C47—28no—
197C2×D4×C47—24no—
198C2×D4×C47—21no—
199C2×D4×C47—22no—
200C2×D4×C47#4114yes—
201C2×D4×C47C2412yes—
202C22×C4×C47—28no—
203C22×C4×C47—21no—
204C22×C4×C47—24no—
205C22×C4×C47—22no—
206C22×C4×C47—22no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D412yes—
211C22×C4×C47C2412yes—
212C22×C4×C47C2411yescharacteristic
213C2×C22⋊D47—24no—
214C2×C22⋊D47—44no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—24no—
219C22×Dic47—24no—
220C22×Dic47—42no—
221C22×Dic47—42no—
222C22×Dic47—44no—
223C22×Dic47—44no—
224C22×Dic47C2×D411yescharacteristic
225C22×Dic47C2×D411yescharacteristic
226C22×Dic47C2×D411yescharacteristic
227C22×Dic47C2×D411yescharacteristic
228C22×Dic47C2×D414yes—
229C22×Dic47C2×D414yes—
230C2×D188—22no—
231C2×D188—22no—
232C2×D188—21no—
233C2×D188C2412yes—
234C2×C4×D47—24no—
235C2×C4×D47—44no—
236Q16×C47—28no—
237SD16×C47—28no—
238C2×C8×C47—22no—
239C2×C8×C47—22no—
240C2×C8×C47C2412yes—
241C2×C8×C47C2412yes—
242C4⋊C4×C47—24no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47C2412yes—
245C22⋊C4×C47—24no—
246C22⋊Dic47—24no—
247C22⋊Dic47—24no—
248C22⋊Dic47—24no—
249#10625336—28no—
250#10625334—28no—
251(C2×D47)⋊C4—24no—
252(C2×D47)⋊C4—24no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4—24no—
255C4⋊Dic47—21no—
256C4⋊Dic47—21no—
257C4⋊Dic47—21no—
258C4⋊Dic47—24no—
259C4⋊Dic47—24no—
260C4⋊Dic47—24no—
261C4⋊Dic47—24no—
262C4⋊Dic47C2412yes—
263C4⋊Dic47C2412yes—
264C4⋊Dic47C2412yes—
265Dic47⋊C4—24no—
266C4×Dic47—24no—
267C4×Dic47—24no—
268C4×Dic47—24no—
269C4×Dic47—24no—
270C4×Dic47C2×D414yes—
271C4×Dic47C2×D414yes—
272C4×Dic47C2×D412yes—
273C4×Dic47C2×D412yes—
274C4×Dic47C2412yes—
275C4×Dic47C2412yes—
276C2×C47⋊C8—22no—
277C2×C47⋊C8—22no—
278C2×C47⋊C8C2412yes—
279C2×C47⋊C8C2412yes—
280C23×C47—22no—
281C23×C47—24no—
282C23×C47—22no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—42no—
286C23×C47—42no—
287C23×C47C22×D412yes—
288C23×C47C22×D411yescharacteristic
289C22×D47—22no—
290C22×D47—42no—
291C22×D47—42no—
292C22×D47—42no—
293Q8×C47—24no—
294Q8×C47—22no—
295Q8×C47—22no—
296Q8×C47—22no—
297Q8×C47—42no—
298Q8×C47C2×#4114yes—
299D4×C47—216no—
300D4×C47—24no—
301D4×C47—22no—
302D4×C47C2×#4114yes—
303C2×C4×C47—216no—
304C2×C4×C47—22no—
305C2×C4×C47—24no—
306C2×C4×C47—22no—
307C2×C4×C47—24no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—42no—
313C2×C4×C47—42no—
314C2×C4×C47C22×D412yes—
315C2×C4×C47C22×D411yescharacteristic
316C2×C4×C47C2×#4112yes—
317C2×C4×C47C2×#4112yes—
318C2×C4×C47C2511yescharacteristic
319C22⋊D47—48no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—44no—
328C2×Dic47—44no—
329C2×Dic47—48no—
330C2×Dic47—48no—
331C2×Dic47—42no—
332C2×Dic47—42no—
333C2×Dic47—42no—
334C2×Dic47C22×D412yes—
335C2×Dic47C22×D412yes—
336C2×Dic47C22×D412yes—
337C2×Dic47C22×D412yes—
338D188—22no—
339D188—22no—
340D188—42no—
341C4×D47—48no—
342C8×C47—22no—
343C8×C47—22no—
344C47⋊C8—22no—
345C47⋊C8—22no—
346C2×#3111—471nomaximal, Sylow
347C22×C47—22no—
348C22×C47—24no—
349C22×C47—22no—
350C22×C47—22no—
351C22×C47—44no—
352C22×C47—48no—
353C22×C47—42no—
354C22×C47—42no—
355C22×C47#52512yes—
356C22×C47#57512yes—
357C22×C47#57512yes—
358C22×C47C23×D411yescharacteristic
359C2×D47—42no—
360C2×D47—42no—
361C2×D47—42no—
362C2×D47—84no—
363C4×C47—22no—
364C4×C47—24no—
365C4×C47—42no—
366C4×C47—42no—
367C4×C47#52512yes—
368C4×C47C22×#4111yescharacteristic
369C4×C47C22×#4111yescharacteristic
370Dic47—22no—
371Dic47—22no—
372Dic47—22no—
373Dic47—22no—
374Dic47—42no—
375Dic47—42no—
376Dic47—42no—
377C2×#529—471no—
378C2×C4×#41—471no—
379#3111—4716no—
380C2×#485—471no—
381C2×#482—471no—
382C2×#479—471no—
383C2×#478—471no—
384C2×#464—471no—
385C2×#463—471no—
386C2×#452D4711yescharacteristic, complemented
387C2×#449—471no—
388C2×#442—471no—
389C2×#441—471no—
390C2×#440—471no—
391C2×#440—471no—
392C2×#432—471no—
393C2×C47—42no—
394C2×C47—44no—
395C2×C47#311114yescomplemented
396C2×C47C2×#52511yescharacteristic
397C2×C47C2×#57511yescharacteristic
398C2×C47C2×#57511yescharacteristic
399D47—82no—
400C22×#41C2×D4711yescharacteristic
401C22×Q16C2×D4711yescharacteristic
402C22×SD16—471no—
403C22×SD16C2×D4711yescharacteristic
404C22×D8—471no—
405#529—478no—
406#529—944no—
407C2×#126—941no—
408C2×#125—471no—
409C2×#124—471no—
410C2×#123—941no—
411C2×C22⋊Q8C2×D4711yescharacteristic
412C2×#121—471no—
413C4×#41—478no—
414C4×#41—944no—
415C2×C4×Q8—471no—
416C2×C4×Q8—471no—
417C2×C4×Q8—471no—
418C2×C4×D4—471no—
419C2×C4×D4—471no—
420C2×C4×D4—471no—
421C2×C4×D4—941no—
422C2×C4×D4—941no—
423C2×C4×D4—941no—
424C2×#117—471no—
425C2×#117—941no—
426C2×#117—941no—
427C22×C42—471no—
428C22×C42—941no—
429#485—478no—
430#482—478no—
431#479—478no—
432#478—478no—
433#464—478no—
434#463—478no—
435#452C2×D4718yescomplemented
436#449—478no—
437#442—478no—
438#441—478no—
439#440—478no—
440#440—478no—
441#432—478no—
442C2×#107—471no—
443C2×#107—471no—
444C2×#106—471no—
445C2×#106—471no—
446C2×C4⋊C8—471no—
447C2×C4⋊C8—471no—
448C2×#103—471no—
449C2×#103—471no—
450C2×#103—471no—
451C2×#103C2×D4711yescharacteristic
452C2×#102—471no—
453C2×#102—471no—
454C2×#102—471no—
455C2×#102C2×D4711yescharacteristic
456C2×C22⋊C8—471no—
457C2×C22⋊C8C2×D4711yescharacteristic
458C2×#97—471no—
459C2×#97—471no—
460C47C2×#311111yescharacteristic, complemented, Sylow
461C2×#41—24no—
462C2×#41—24no—
463C2×#41—22no—
464C2×#41C22×D4714yes—
465C22×Q8C22×D4711yescharacteristic
466C22×Q8C22×D4711yescharacteristic
467C22×D4—21no—
468C22×D4—471no—
469C22×D4—941no—
470C22×D4C22×D4711yescharacteristic
471C23×C4—21no—
472C23×C4—471no—
473C23×C4—471no—
474C23×C4—941no—
475C23×C4—941no—
476C23×C4—941no—
477C23×C4C22×D4711yescharacteristic
478C2×Q16—24no—
479C2×Q16C22×D4714yes—
480C2×SD16—24no—
481C2×SD16—474no—
482C2×SD16—944no—
483C2×SD16C22×D4714yes—
484C2×D8—474no—
485C2×D8—944no—
486C22×C8—471no—
487C22×C8—471no—
488C22×C8C22×D4711yescharacteristic
489C22×C8C22×D4711yescharacteristic
490#126—948no—
491#125—474no—
492#125—942no—
493#124—474no—
494#124—942no—
495#123—948no—
496C22⋊Q8—22no—
497C22⋊Q8C22×D4714yes—
498#121—474no—
499#121—942no—
500C4×Q8—474no—
501C4×Q8—474no—
502C4×Q8—474no—
503C4×Q8—942no—
504C4×Q8—942no—
505C4×Q8—942no—
506C4×D4—474no—
507C4×D4—474no—
508C4×D4—474no—
509C4×D4—942no—
510C4×D4—942no—
511C4×D4—942no—
512C4×D4—948no—
513C4×D4—948no—
514C4×D4—948no—
515#117—474no—
516#117—948no—
517#117—948no—
518#117—942no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—471no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4—941no—
526C2×C4⋊C4—941no—
527C2×C4⋊C4—941no—
528C2×C4⋊C4C22×D4711yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—941no—
531C2×C22⋊C4—941no—
532C2×C22⋊C4—941no—
533C2×C22⋊C4—941no—
534C2×C22⋊C4—941no—
535C2×C22⋊C4—941no—
536C2×C22⋊C4—941no—
537C2×C42—471no—
538C2×C42—474no—
539C2×C42—471no—
540C2×C42—471no—
541C2×C42—471no—
542C2×C42—474no—
543C2×C42—948no—
544C2×C42—941no—
545C2×C42—941no—
546C2×C42—941no—
547C2×C42—941no—
548#107—474no—
549#107—474no—
550#106—474no—
551#106—474no—
552C4⋊C8—474no—
553C4⋊C8—474no—
554#103—474no—
555#103—474no—
556#103—474no—
557#103C22×D4714yes—
558#102—474no—
559#102—474no—
560#102—474no—
561#102C22×D4714yes—
562C22⋊C8—474no—
563C22⋊C8C22×D4714yes—
564#97—474no—
565#97—474no—
566C24—21no—
567C24—941no—
568C24D4×D4711yescharacteristic
569#41—216no—
570#41—28no—
571#41—28no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8#1062535214yes—
578C2×Q8C23×D4712yes—
579C2×Q8C23×D4712yes—
580C2×D4—28no—
581C2×D4—24no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—472no—
585C2×D4—944no—
586C2×D4—941no—
587C2×D4—942no—
588C2×D4—942no—
589C2×D4—1884no—
590C2×D4#1062535214yes—
591C2×D4C23×D4712yes—
592C22×C4—28no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—471no—
600C22×C4—471no—
601C22×C4—471no—
602C22×C4—471no—
603C22×C4—474no—
604C22×C4—474no—
605C22×C4—944no—
606C22×C4—944no—
607C22×C4—944no—
608C22×C4—941no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—1884no—
612C22×C4—1882no—
613C22×C4—1882no—
614C22×C4—1884no—
615C22×C4—1884no—
616C22×C4D4×D4712yes—
617C22×C4D4×D4711yescharacteristic
618C22×C4C23×D4712yes—
619C22×C4C23×D4711yescharacteristic
620Q16—28no—
621SD16—28no—
622SD16—948no—
623D8—948no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—472no—
627C2×C8—472no—
628C2×C8—942no—
629C2×C8—942no—
630C2×C8C23×D4712yes—
631C2×C8C23×D4712yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—472no—
635C4⋊C4—472no—
636C4⋊C4—472no—
637C4⋊C4—944no—
638C4⋊C4—944no—
639C4⋊C4—944no—
640C4⋊C4—944no—
641C4⋊C4—944no—
642C4⋊C4—941no—
643C4⋊C4—941no—
644C4⋊C4—941no—
645C4⋊C4C23×D4712yes—
646C22⋊C4—24no—
647C22⋊C4—944no—
648C22⋊C4—944no—
649C22⋊C4—944no—
650C22⋊C4—944no—
651C22⋊C4—944no—
652C22⋊C4—944no—
653C22⋊C4—944no—
654C42—474no—
655C42—474no—
656C42—472no—
657C42—472no—
658C42—472no—
659C42—472no—
660C42—944no—
661C42—944no—
662C42—944no—
663C42—944no—
664C23—22no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—42no—
670C23—42no—
671C23—942no—
672C23—1882no—
673C23—1882no—
674C23—1882no—
675C23C2×D4×D4712yes—
676C23C2×D4×D4711yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—22no—
680Q8—22no—
681Q8—42no—
682Q8C2×#1062535214yes—
683D4—216no—
684D4—24no—
685D4—22no—
686D4—942no—
687D4—942no—
688D4—1888no—
689D4—1882no—
690D4C2×#1062535214yes—
691C2×C4—216no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—472no—
703C2×C4—472no—
704C2×C4—472no—
705C2×C4—472no—
706C2×C4—942no—
707C2×C4—942no—
708C2×C4—942no—
709C2×C4—942no—
710C2×C4—942no—
711C2×C4—942no—
712C2×C4—942no—
713C2×C4—1888no—
714C2×C4—1884no—
715C2×C4—1884no—
716C2×C4—1888no—
717C2×C4—1888no—
718C2×C4—1882no—
719C2×C4—1882no—
720C2×C4—1882no—
721C2×C4C2×D4×D4712yes—
722C2×C4C2×D4×D4711yescharacteristic
723C2×C4C2×#1062535212yes—
724C2×C4C2×#1062535212yes—
725C2×C4C24×D4711yescharacteristic
726C8—22no—
727C8—22no—
728C8—942no—
729C8—942no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—24no—
734C22—44no—
735C22—48no—
736C22—42no—
737C22—42no—
738C22—3764no—
739C22—1882no—
740C22—1882no—
741C22—1882no—
742C22#1568962912yes—
743C22#1568992012yes—
744C22#1568992212yes—
745C22C22×D4×D4711yescharacteristic
746C4—22no—
747C4—24no—
748C4—42no—
749C4—42no—
750C4—942no—
751C4—942no—
752C4—942no—
753C4—942no—
754C4—1882no—
755C4—1882no—
756C4—1882no—
757C4#1568962912yes—
758C4C22×#1062535211yescharacteristic
759C4C22×#1062535211yescharacteristic
760C2—42no—
761C2—44no—
762C2—3762no—
763C2#2025349814yesdirect product factor
764C2C2×#1568962911yescharacteristic
765C2C2×#1568992011yescharacteristic
766C2C2×#1568992211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#452C2
socleC23×C47C22×D4
prime radicalC2×#15689268C2
hypercenterC2×#452D47
hypocenterC47C2×#3111
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#15689659C2semidirect
2. C2×#41×Dic47C2semidirect
3. #20253498C2direct (N × H)
4. C2×#15689461C2semidirect
5. C2×#15689448C2semidirect
6. C2×#15689432C2semidirect
7. C2×#15689425C2semidirect
8. C2×#15689347C2semidirect
9. C2×#15689340C2semidirect
11. C2×#15689232C2semidirect
12. C2×#15689230C2semidirect
13. C2×#15689226C2semidirect
14. C2×#15689224C2semidirect
15. C2×#15689177C2semidirect
16. C2×C47×#452C2semidirect
20. #15689659C22semidirect
27. #41×Dic47C22semidirect
42. #15689461C22semidirect
43. #15689448C22semidirect
44. #15689432C22semidirect
45. #15689425C22semidirect
46. #15689347C22semidirect
47. #15689340C22semidirect
49. #15689232C22semidirect
50. #15689230C22semidirect
51. #15689226C22semidirect
52. #15689224C22semidirect
53. #15689177C22semidirect
73. C47×#452C22semidirect
386. C2×#452D47semidirect
395. C2×C47#3111semidirect
435. #452C2×D47semidirect
460. C47C2×#3111semidirect
763. C2#20253498direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896592
C2×#41×Dic472
#202534982
C2×#156894612
C2×#156894482
C2×#156894322
C2×#156894252
C2×#156893472
C2×#156893402
C2×#156892682
C2×#156892322
C2×#156892302
C2×#156892262
C2×#156892242
C2×#156891772
C2×C47×#4522
C2×#311147