Finite Group Databasebeta

← C2×#20255909 #27094895

Subgroups — C2×#20255909 #27094895

Order 12032.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689837C211yesmaximal, characteristic
2C2×#15689807C211yesmaximal, characteristic, complemented
3#20255909C2116yesmaximal, direct product factor
4C2×#15689530C211yesmaximal, characteristic, complemented
5C2×#15689440C211yesmaximal, characteristic, complemented
6C2×#15689462C211yesmaximal, characteristic, complemented
7C2×#15689461C211yesmaximal, characteristic, complemented
8C2×#15689444C211yesmaximal, characteristic, complemented
9C2×#15689406C211yesmaximal, characteristic, complemented
10C2×#15689425C211yesmaximal, characteristic, complemented
11C2×#15689366C211yesmaximal, characteristic, complemented
12C2×#15689224C211yesmaximal, characteristic, complemented
13C2×#15689194C211yesmaximal, characteristic, complemented
14C2×#15689162C211yesmaximal, characteristic, complemented
15C2×#15689161C211yesmaximal, characteristic, complemented
16C2×C47×#465C211yesmaximal, characteristic, complemented
17C22×#10625324C2211yescharacteristic
18#15689837—24no—
19#15689837C2218yes—
20#15689807—24no—
21#15689807C2218yescomplemented
22C2×#13094023C2211yescharacteristic
23C2×#13094017—21no—
24C2×#13094015C2211yescharacteristic
25C2×#13094014—21no—
26C2×#13094011—21no—
27C2×#13094010—21no—
28C2×#13094006—21no—
29C2×#13094000C2211yescharacteristic
30C2×#13093996—21no—
31C2×#13093995C2211yescharacteristic
32C2×Q8×Dic47C2211yescharacteristic
33C2×D4×Dic47C2211yescharacteristic
34C2×C4×C22⋊D47C2211yescharacteristic
35C2×#13093983C2211yescharacteristic
36C2×#13093983C2211yescharacteristic
37C2×#13093982—21no—
38C2×#13093982C2211yescharacteristic
39C2×#13093980—21no—
40C2×C4⋊C4×D47C2211yescharacteristic
41#15689530C2218yescomplemented
42#15689462C2218yescomplemented
43#15689461C2218yescomplemented
44#15689444C2218yescomplemented
45#15689440C2218yescomplemented
46#15689425C2218yescomplemented
47#15689406C2218yescomplemented
48#15689366C2218yescomplemented
49#15689224C2218yescomplemented
50#15689194C2218yescomplemented
51#15689162C2218yescomplemented
52#15689161C2218yescomplemented
53C2×#13093958C2211yescharacteristic
54C2×#13093958C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093956C2211yescharacteristic
58C2×#13093956C2211yescharacteristic
59C2×#13093955C2211yescharacteristic
60C2×#13093955C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×#121×C47C2211yescharacteristic
73C47×#465C2218yescomplemented
74C2×#106×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×C22⋊D47—21no—
79C22×C22⋊D47D411yescharacteristic
80C23×Dic47—21no—
81C22×C4×D47—21no—
82C22×C4×D47C2311yescharacteristic
83C2×#10625324—24no—
84C2×#10625324C2314yes—
85C22×C47⋊C8C2311yescharacteristic
86C22×C47⋊C8C2311yescharacteristic
87#13094023—22no—
88#13094023C2314yes—
89#13094017—28no—
90#13094015—22no—
91#13094015C2314yes—
92#13094014—28no—
93#13094011—28no—
94#13094010—28no—
95#13094006—28no—
96#13094000—22no—
97#13094000C2314yes—
98#13093996—28no—
99#13093995—22no—
100#13093995C2314yes—
101Q8×Dic47—22no—
102Q8×Dic47C2314yes—
103D4×Dic47—22no—
104D4×Dic47C2314yes—
105C4×C22⋊D47D414yes—
106C4×C22⋊D47C2314yes—
107#13093983—22no—
108#13093983—22no—
109#13093983C2314yes—
110#13093983C2314yes—
111#13093982—22no—
112#13093982—28no—
113#13093982C2314yes—
114#13093980—28no—
115C2×C4⋊Dic47—21no—
116C2×C4⋊Dic47—21no—
117C2×C4⋊Dic47C2311yescharacteristic
118C2×C4⋊Dic47C2311yescharacteristic
119C2×C4⋊Dic47C2311yescharacteristic
120C2×C4⋊Dic47C2311yescharacteristic
121C2×Dic47⋊C4—21no—
122C2×Dic47⋊C4—21no—
123C2×Dic47⋊C4—21no—
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4D411yescharacteristic
126C4⋊C4×D47—22no—
127C4⋊C4×D47C2314yes—
128C2×C22⋊Dic47—21no—
129C2×C22⋊Dic47—21no—
130C2×C22⋊Dic47—21no—
131C2×C22⋊Dic47—21no—
132C2×C22⋊Dic47D411yescharacteristic
133C2×(C2×D47)⋊C4—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4D411yescharacteristic
136C2×C4×Dic47—21no—
137C2×C4×Dic47—21no—
138C2×C4×Dic47—21no—
139C2×C4×Dic47—21no—
140C2×C4×Dic47C2311yescharacteristic
141#13093958C2314yes—
142#13093958C2314yes—
143#13093957C2314yes—
144#13093957C2314yes—
145#13093956C2314yes—
146#13093956C2314yes—
147#13093955C2314yes—
148#13093955C2314yes—
149Dic47⋊C8C2314yes—
150#13093948C2314yes—
151#13093948C2314yes—
152#13093945C2314yes—
153#13093945C2314yes—
154C22⋊(C47⋊C8)C2314yes—
155(C2×D47)⋊C8C2314yes—
156#13093934C2314yes—
157C22×Q8×C47C2311yescharacteristic
158C22×D4×C47—21no—
159C22×D4×C47C2311yescharacteristic
160C23×C4×C47C2311yescharacteristic
161C2×SD16×C47—24no—
162C2×SD16×C47C2314yes—
163C22×C8×C47—24no—
164C22×C8×C47C2314yes—
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C22⋊Q8×C47—22no—
168C22⋊Q8×C47C2314yes—
169#121×C47—22no—
170#121×C47C2314yes—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176#106×C47C2314yes—
177#103×C47C2314yes—
178#102×C47C2314yes—
179C24×C47—21no—
180C24×C47C2×D411yescharacteristic
181C23×D47C2×D411yescharacteristic
182C2×Q8×C47—21no—
183C2×Q8×C47—22no—
184C2×Q8×C47—22no—
185C2×Q8×C47C2412yes—
186C2×D4×C47—24no—
187C2×D4×C47—21no—
188C2×D4×C47—22no—
189C2×D4×C47—22no—
190C2×D4×C47—82no—
191C2×D4×C47C2412yes—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D412yes—
199C22×C4×C47C2412yes—
200C22×C4×C47C2411yescharacteristic
201C2×C22⋊D47—24no—
202C2×C22⋊D47—42no—
203C2×C22⋊D47—82no—
204C2×C22⋊D47C2×D414yes—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—24no—
210C22×Dic47—44no—
211C22×Dic47C2×D411yescharacteristic
212C22×Dic47C2×D411yescharacteristic
213C22×Dic47C2×D411yescharacteristic
214C2×C4×D47—22no—
215C2×C4×D47—22no—
216C2×C4×D47—24no—
217C2×C4×D47—44no—
218C2×C4×D47C2×D412yes—
219C2×C4×D47C2412yes—
220C2×Dic94—24no—
221C2×Dic94—82no—
222SD16×C47—28no—
223C2×C8×C47—22no—
224C2×C8×C47—28no—
225C2×C8×C47#4114yes—
226C2×C8×C47C2412yes—
227C2×C8×C47C2412yes—
228C4⋊C4×C47—24no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47C2412yes—
232C4⋊C4×C47C2412yes—
233C22⋊C4×C47—24no—
234C22⋊C4×C47—24no—
235C22⋊Dic47—24no—
236C22⋊Dic47—24no—
237C22⋊Dic47—24no—
238C22⋊Dic47—24no—
239C22⋊Dic47C2×D414yes—
240(C2×D47)⋊C4—24no—
241(C2×D47)⋊C4—24no—
242(C2×D47)⋊C4C2×D414yes—
243C4⋊Dic47—21no—
244C4⋊Dic47—21no—
245C4⋊Dic47—21no—
246C4⋊Dic47—21no—
247C4⋊Dic47—24no—
248C4⋊Dic47—24no—
249C4⋊Dic47C2412yes—
250C4⋊Dic47C2412yes—
251C4⋊Dic47C2412yes—
252C4⋊Dic47C2412yes—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4C2×D414yes—
258C4×Dic47—24no—
259C4×Dic47—24no—
260C4×Dic47—24no—
261C4×Dic47—24no—
262C4×Dic47C2×D412yes—
263C4×Dic47C2412yes—
264C2×C47⋊C8—22no—
265C2×C47⋊C8—22no—
266C2×C47⋊C8C2412yes—
267C2×C47⋊C8C2412yes—
268#10625324—28no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—42no—
274C23×C47—42no—
275C23×C47—42no—
276C23×C47C22×D412yes—
277C23×C47C22×D411yescharacteristic
278C22×D47—22no—
279C22×D47—22no—
280C22×D47—22no—
281C22×D47C22×D412yes—
282Q8×C47—22no—
283Q8×C47—22no—
284Q8×C47—42no—
285D4×C47—22no—
286D4×C47—22no—
287D4×C47—42no—
288D4×C47—84no—
289C2×C4×C47—22no—
290C2×C4×C47—24no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47C22×D412yes—
300C2×C4×C47C22×D411yescharacteristic
301C2×C4×C47C2×#4112yes—
302C2×C4×C472−1+412yes—
303C2×C4×C47C2511yescharacteristic
304C22⋊D47—44no—
305C22⋊D47—84no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—48no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47—42no—
318C2×Dic47C22×D412yes—
319C2×Dic47C22×D412yes—
320C2×Dic47C22×D412yes—
321C4×D47—24no—
322C4×D47—22no—
323C4×D47—22no—
324C4×D47—48no—
325Dic94—84no—
326C8×C47—22no—
327C8×C47C2×#4114yes—
328C47⋊C8—22no—
329C47⋊C8—22no—
330C2×#3348—471nomaximal, Sylow
331C22×C47—22no—
332C22×C47—22no—
333C22×C47—22no—
334C22×C47—44no—
335C22×C47—42no—
336C22×C47—42no—
337C22×C47—42no—
338C22×C47—84no—
339C22×C47#54712yes—
340C22×C47#57512yes—
341C22×C47#57712yes—
342C22×C47C23×D411yescharacteristic
343C2×D47—22no—
344C2×D47—22no—
345C2×D47—22no—
346C2×D47—44no—
347C4×C47—22no—
348C4×C47—42no—
349C4×C47—42no—
350C4×C47—42no—
351C4×C47#54712yes—
352C4×C47C22×#4111yescharacteristic
353C4×C47C2×2−1+411yescharacteristic
354Dic47—22no—
355Dic47—22no—
356Dic47—22no—
357Dic47—42no—
358Dic47—42no—
359Dic47—42no—
360Dic47—42no—
361C2×#555—471no—
362C2×#552—471no—
363#3348—4716no—
364C2×#501—471no—
365C2×#481—471no—
366C2×#485—471no—
367C2×#485—471no—
368C2×#482—471no—
369C2×#475—471no—
370C2×#478—471no—
371C2×#468—471no—
372C2×#465D4711yescharacteristic, complemented
373C2×#440—471no—
374C2×#435—471no—
375C2×#428—471no—
376C2×#427—471no—
377C2×C47—42no—
378C2×C47—82no—
379C2×C47#334814yescomplemented
380C2×C47C2×#54711yescharacteristic
381C2×C47C2×#57511yescharacteristic
382C2×C47C2×#57711yescharacteristic
383D47—42no—
384C22×SD16C2×D4711yescharacteristic
385C22×M16—471no—
386C23×C8C2×D4711yescharacteristic
387#555—478no—
388#555—944no—
389#552—478no—
390#552—944no—
391C2×C4⋊Q8—471no—
392C2×#126—941no—
393C2×#125—471no—
394C2×#125—941no—
395C2×#124—941no—
396C2×#124—941no—
397C2×#123—941no—
398C2×C22⋊Q8—471no—
399C2×C22⋊Q8C2×D4711yescharacteristic
400C2×#121—471no—
401C2×#121—941no—
402C2×#121C2×D4711yescharacteristic
403C2×C4×Q8—471no—
404C2×C4×D4—471no—
405C2×C4×D4—471no—
406C2×#117—471no—
407C2×#117—471no—
408C2×#117—471no—
409C2×#117—941no—
410C2×#117—941no—
411C22×C4⋊C4—471no—
412#501—478no—
413#485—478no—
414#485—478no—
415#482—478no—
416#481—478no—
417#478—478no—
418#475—478no—
419#468—478no—
420#465C2×D4718yescomplemented
421#440—478no—
422#435—478no—
423#428—478no—
424#427—478no—
425C2×#107—471no—
426C2×#107—471no—
427C2×#107—471no—
428C2×#107—471no—
429C2×#106—471no—
430C2×#106—471no—
431C2×#106—471no—
432C2×#106—471no—
433C2×#106C2×D4711yescharacteristic
434C2×C4⋊C8—471no—
435C2×#103—471no—
436C2×#103—471no—
437C2×#103C2×D4711yescharacteristic
438C2×#102—471no—
439C2×#102—471no—
440C2×#102C2×D4711yescharacteristic
441C2×C22⋊C8—471no—
442C2×C22⋊C8—471no—
443C2×#97—471no—
444C47C2×#334811yescharacteristic, complemented, Sylow
445C22×Q8—941no—
446C22×Q8C22×D4711yescharacteristic
447C22×D4—21no—
448C22×D4—471no—
449C22×D4—941no—
450C22×D4C22×D4711yescharacteristic
451C23×C4—471no—
452C23×C4—941no—
453C23×C4—941no—
454C23×C4C22×D4711yescharacteristic
455C2×SD16—24no—
456C2×SD16C22×D4714yes—
457C2×M16—474no—
458C2×M16—944no—
459C22×C8—24no—
460C22×C8—471no—
461C22×C8—471no—
462C22×C8C22×D4711yescharacteristic
463C22×C8C22×D4714yes—
464C22×C8C22×D4711yescharacteristic
465C4⋊Q8—474no—
466C4⋊Q8—942no—
467#126—948no—
468#125—474no—
469#125—942no—
470#125—948no—
471#124—948no—
472#124—948no—
473#123—948no—
474C22⋊Q8—22no—
475C22⋊Q8—474no—
476C22⋊Q8—942no—
477C22⋊Q8C22×D4714yes—
478#121—22no—
479#121—474no—
480#121—942no—
481#121—948no—
482#121C22×D4714yes—
483C4×Q8—474no—
484C4×Q8—942no—
485C4×D4—474no—
486C4×D4—474no—
487C4×D4—474no—
488C4×D4—942no—
489#117—474no—
490#117—474no—
491#117—474no—
492#117—948no—
493#117—948no—
494#117—942no—
495#117—942no—
496#117—942no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—471no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—471no—
502C2×C4⋊C4—471no—
503C2×C4⋊C4—474no—
504C2×C4⋊C4—942no—
505C2×C4⋊C4—941no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4—941no—
508C2×C4⋊C4—941no—
509C2×C4⋊C4—941no—
510C2×C4⋊C4—941no—
511C2×C4⋊C4C22×D4711yescharacteristic
512C2×C4⋊C4C22×D4711yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—471no—
516C2×C22⋊C4—471no—
517C2×C22⋊C4—941no—
518C2×C22⋊C4—941no—
519C2×C22⋊C4—941no—
520C2×C22⋊C4—941no—
521C2×C22⋊C4—941no—
522C2×C22⋊C4—941no—
523C2×C42—471no—
524C2×C42—941no—
525C2×C42—941no—
526C2×C42—941no—
527C2×C42—941no—
528#107—474no—
529#107—474no—
530#107—474no—
531#107—474no—
532#106—474no—
533#106—474no—
534#106—474no—
535#106—474no—
536#106C22×D4714yes—
537C4⋊C8—474no—
538#103—474no—
539#103—474no—
540#103C22×D4714yes—
541#102—474no—
542#102—474no—
543#102C22×D4714yes—
544C22⋊C8—474no—
545C22⋊C8—474no—
546#97—474no—
547C24—21no—
548C24—471no—
549C24D4×D4711yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—944no—
554C2×Q8—3762no—
555C2×Q8C23×D4712yes—
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—82no—
561C2×D4—474no—
562C2×D4—944no—
563C2×D4—3762no—
564C2×D4—1882no—
565C2×D4C23×D4712yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—471no—
572C22×C4—471no—
573C22×C4—471no—
574C22×C4—472no—
575C22×C4—472no—
576C22×C4—944no—
577C22×C4—944no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—941no—
581C22×C4—941no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—1884no—
585C22×C4—1884no—
586C22×C4D4×D4712yes—
587C22×C4D4×D4711yescharacteristic
588C22×C4C23×D4712yes—
589C22×C4C23×D4711yescharacteristic
590SD16—28no—
591M16—948no—
592C2×C8—22no—
593C2×C8—28no—
594C2×C8—472no—
595C2×C8—472no—
596C2×C8—942no—
597C2×C8—942no—
598C2×C8#1062535214yes—
599C2×C8C23×D4712yes—
600C2×C8C23×D4712yes—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—474no—
605C4⋊C4—472no—
606C4⋊C4—472no—
607C4⋊C4—472no—
608C4⋊C4—472no—
609C4⋊C4—944no—
610C4⋊C4—944no—
611C4⋊C4—944no—
612C4⋊C4—944no—
613C4⋊C4—944no—
614C4⋊C4—944no—
615C4⋊C4—941no—
616C4⋊C4—941no—
617C4⋊C4—941no—
618C4⋊C4—941no—
619C4⋊C4C23×D4712yes—
620C4⋊C4C23×D4712yes—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—474no—
624C22⋊C4—474no—
625C22⋊C4—944no—
626C22⋊C4—944no—
627C22⋊C4—944no—
628C22⋊C4—944no—
629C22⋊C4—944no—
630C22⋊C4—944no—
631C42—472no—
632C42—472no—
633C42—944no—
634C42—944no—
635C42—944no—
636C42—944no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—472no—
645C23—942no—
646C23—942no—
647C23—942no—
648C23C2×D4×D4712yes—
649C23C2×D4×D4711yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—3764no—
654D4—22no—
655D4—22no—
656D4—42no—
657D4—84no—
658D4—3764no—
659D4—1884no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—472no—
671C2×C4—472no—
672C2×C4—472no—
673C2×C4—942no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—944no—
677C2×C4—942no—
678C2×C4—942no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—1888no—
684C2×C4—1888no—
685C2×C4—1882no—
686C2×C4—1882no—
687C2×C4—1882no—
688C2×C4—1882no—
689C2×C4C2×D4×D4712yes—
690C2×C4C2×D4×D4711yescharacteristic
691C2×C4C2×#1062535212yes—
692C2×C4#1309407112yes—
693C2×C4C24×D4711yescharacteristic
694C8—22no—
695C8—942no—
696C8—942no—
697C8C2×#1062535214yes—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—44no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—84no—
706C22—942no—
707C22—942no—
708C22—942no—
709C22—1884no—
710C22#1568977312yes—
711C22#1568992012yes—
712C22#1568992912yes—
713C22C22×D4×D4711yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—942no—
719C4—942no—
720C4—942no—
721C4—1882no—
722C4—1882no—
723C4—1882no—
724C4—1882no—
725C4#1568977312yes—
726C4C22×#1062535211yescharacteristic
727C4C2×#1309407111yescharacteristic
728C2—42no—
729C2—82no—
730C2—1882no—
731C2#2025590914yesdirect product factor
732C2C2×#1568977311yescharacteristic
733C2C2×#1568992011yescharacteristic
734C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#465C2
socleC23×C47C22×D4
prime radicalC2×#15689837C2
hypercenterC2×#465D47
hypocenterC47C2×#3348
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
2. C2×#15689807C2semidirect
3. #20255909C2direct (N × H)
4. C2×#15689530C2semidirect
5. C2×#15689440C2semidirect
6. C2×#15689462C2semidirect
7. C2×#15689461C2semidirect
8. C2×#15689444C2semidirect
9. C2×#15689406C2semidirect
10. C2×#15689425C2semidirect
11. C2×#15689366C2semidirect
12. C2×#15689224C2semidirect
13. C2×#15689194C2semidirect
14. C2×#15689162C2semidirect
15. C2×#15689161C2semidirect
16. C2×C47×#465C2semidirect
21. #15689807C22semidirect
41. #15689530C22semidirect
42. #15689462C22semidirect
43. #15689461C22semidirect
44. #15689444C22semidirect
45. #15689440C22semidirect
46. #15689425C22semidirect
47. #15689406C22semidirect
48. #15689366C22semidirect
49. #15689224C22semidirect
50. #15689194C22semidirect
51. #15689162C22semidirect
52. #15689161C22semidirect
73. C47×#465C22semidirect
372. C2×#465D47semidirect
379. C2×C47#3348semidirect
420. #465C2×D47semidirect
444. C47C2×#3348semidirect
731. C2#20255909direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898372
C2×#156898072
#202559092
C2×#156895302
C2×#156894402
C2×#156894622
C2×#156894612
C2×#156894442
C2×#156894062
C2×#156894252
C2×#156893662
C2×#156892242
C2×#156891942
C2×#156891622
C2×#156891612
C2×C47×#4652
C2×#334847