Finite Group Databasebeta

← C2×#20253998 #27086069

Subgroups — C2×#20253998 #27086069

Order 12032.

1970 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689746C211yesmaximal, characteristic, complemented
2C2×#15689740C211yesmaximal, characteristic, complemented
3#20253998C2116yesmaximal, direct product factor
4C2×#15689520C211yesmaximal, characteristic, complemented
5C2×#15689504C211yesmaximal, characteristic, complemented
6C2×#15689484C211yesmaximal, characteristic, complemented
7C2×#15689481C211yesmaximal, characteristic, complemented
8C2×#15689379C211yesmaximal, characteristic, complemented
9C2×#15689374C211yesmaximal, characteristic
10C2×#15689352C211yesmaximal, characteristic, complemented
11C2×#15689232C211yesmaximal, characteristic, complemented
12C2×#15689227C211yesmaximal, characteristic, complemented
13C2×SD16×Dic47C211yesmaximal, characteristic, complemented
14C2×#15689210C211yesmaximal, characteristic, complemented
15C2×#15689078C211yesmaximal, characteristic, complemented
16C2×C47×#465C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625325C2211yescharacteristic
19C22×#10625334C2211yescharacteristic
20C22×#10625329C2211yescharacteristic
21#15689746—24no—
22#15689746C2218yescomplemented
23#15689740—24no—
24#15689740C2218yescomplemented
25C2×#13094023C2211yescharacteristic
26C2×#13094023C2211yescharacteristic
27C2×#13094019—21no—
28C2×#13094017—21no—
29C2×#13094013C2211yescharacteristic
30C2×#13094011—21no—
31C2×#13094011C2211yescharacteristic
32C2×#13094010—21no—
33C2×#13094006—21no—
34C2×#13094005—21no—
35C2×#13094004—21no—
36C2×#13094003C2211yescharacteristic
37C2×#13094001—21no—
38C2×#13093998C2211yescharacteristic
39C2×Q8×Dic47C2211yescharacteristic
40C2×#13093989C2211yescharacteristic
41C2×D4×Dic47C2211yescharacteristic
42C2×#13093986C2211yescharacteristic
43C2×#13093983C2211yescharacteristic
44#15689520C2218yescomplemented
45#15689504C2218yescomplemented
46#15689484C2218yescomplemented
47#15689481C2218yescomplemented
48#15689379C2218yescomplemented
49#15689374C2218yes—
50#15689352C2218yescomplemented
51#15689232C2218yescomplemented
52#15689227C2218yescomplemented
53SD16×Dic47C2218yescomplemented
54#15689210C2218yescomplemented
55C2×#13093956C2211yescharacteristic
56C2×#13093955C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×#13093949C2211yescharacteristic
59C2×#13093948C2211yescharacteristic
60C2×#13093947C2211yescharacteristic
61C2×#13093946C2211yescharacteristic
62C2×#13093945C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64#15689078C2218yescomplemented
65C2×#13093934C2211yescharacteristic
66C2×#13093934C2211yescharacteristic
67C2×C8×Dic47C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
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×Dic94—21no—
79C22×Dic94C2311yescharacteristic
80C22×D188C2311yescharacteristic
81C22×C22⋊D47—21no—
82C23×Dic47—21no—
83C22×C4×D47—21no—
84C2×#10625337—24no—
85C2×#10625337C2314yes—
86C2×#10625325—24no—
87C2×#10625325C2314yes—
88C2×#10625334—24no—
89C2×#10625334C2314yes—
90C2×#10625329—24no—
91C2×#10625329C2314yes—
92C22×C47⋊C8C2311yescharacteristic
93C22×C47⋊C8C2311yescharacteristic
94#13094023—22no—
95#13094023—22no—
96#13094023C2314yes—
97#13094023C2314yes—
98#13094019—28no—
99#13094017—28no—
100#13094013—22no—
101#13094013C2314yes—
102#13094011—28no—
103#13094011—22no—
104#13094011C2314yes—
105#13094010—28no—
106#13094006—28no—
107#13094005—28no—
108#13094004—28no—
109#13094003—22no—
110#13094003C2314yes—
111#13094001—28no—
112#13093998—22no—
113#13093998C2314yes—
114Q8×Dic47—22no—
115Q8×Dic47C2314yes—
116#13093989—22no—
117#13093989C2314yes—
118D4×Dic47—22no—
119D4×Dic47C2314yes—
120#13093986—22no—
121#13093986C2314yes—
122#13093983D414yes—
123#13093983C2314yes—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47D411yescharacteristic
126C2×C4⋊Dic47D411yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×C22⋊Dic47—21no—
134C2×C22⋊Dic47—21no—
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47—21no—
137C2×C22⋊Dic47D411yescharacteristic
138C2×C22⋊Dic47D411yescharacteristic
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47—21no—
145C2×C4×Dic47C2311yescharacteristic
146C2×C4×Dic47C2311yescharacteristic
147#13093956C2314yes—
148#13093955C2314yes—
149#13093955C2314yes—
150#13093949C2314yes—
151#13093948C2314yes—
152#13093947C2314yes—
153#13093946C2314yes—
154#13093945C2314yes—
155#13093944C2314yes—
156#13093934C2314yes—
157#13093934C2314yes—
158C8×Dic47C2314yes—
159C8×Dic47C2314yes—
160C22×Q8×C47C2311yescharacteristic
161C22×D4×C47—21no—
162C22×D4×C47C2311yescharacteristic
163C23×C4×C47C2311yescharacteristic
164C2×SD16×C47—24no—
165C2×SD16×C47C2314yes—
166C22×C8×C47—24no—
167C22×C8×C47C2314yes—
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170C22⋊Q8×C47—22no—
171C22⋊Q8×C47C2314yes—
172#121×C47—22no—
173#121×C47C2314yes—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C22⋊C4×C47—21no—
178C2×C22⋊C4×C47—21no—
179#106×C47C2314yes—
180#103×C47C2314yes—
181#102×C47C2314yes—
182C24×C47—21no—
183C24×C47C2×D411yescharacteristic
184C23×D47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—22no—
187C2×Q8×C47—22no—
188C2×Q8×C47C2412yes—
189C2×D4×C47—24no—
190C2×D4×C47—21no—
191C2×D4×C47—22no—
192C2×D4×C47—22no—
193C2×D4×C47—82no—
194C2×D4×C47C2412yes—
195C22×C4×C47—22no—
196C22×C4×C47—22no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D412yes—
202C22×C4×C47C2412yes—
203C22×C4×C47C2411yescharacteristic
204C2×C22⋊D47—24no—
205C2×C22⋊D47—82no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—24no—
210C22×Dic47—82no—
211C22×Dic47C2×D411yescharacteristic
212C22×Dic47C2×D411yescharacteristic
213C22×Dic47C2×D411yescharacteristic
214C22×Dic47C2×D411yescharacteristic
215C2×D188—22no—
216C2×D188—22no—
217C2×D188—21no—
218C2×D188C2412yes—
219C2×C4×D47—24no—
220C2×C4×D47—82no—
221C2×Dic94—22no—
222C2×Dic94—22no—
223C2×Dic94—21no—
224C2×Dic94—24no—
225C2×Dic94—24no—
226C2×Dic94—82no—
227C2×Dic94—82no—
228C2×Dic94C2412yes—
229SD16×C47—28no—
230C2×C8×C47—22no—
231C2×C8×C47—28no—
232C2×C8×C47#4114yes—
233C2×C8×C47C2412yes—
234C2×C8×C47C2412yes—
235C4⋊C4×C47—24no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47C2412yes—
239C4⋊C4×C47C2412yes—
240C22⋊C4×C47—24no—
241C22⋊C4×C47—24no—
242C22⋊Dic47—24no—
243C22⋊Dic47—24no—
244C22⋊Dic47—24no—
245C22⋊Dic47—24no—
246C22⋊Dic47C2×D414yes—
247C22⋊Dic47C2×D414yes—
248#10625337—28no—
249#10625334—28no—
250(C2×D47)⋊C4—24no—
251(C2×D47)⋊C4—24no—
252(C2×D47)⋊C4—24no—
253(C2×D47)⋊C4—24no—
254C4⋊Dic47—21no—
255C4⋊Dic47—21no—
256C4⋊Dic47—24no—
257C4⋊Dic47C2×D414yes—
258C4⋊Dic47C2×D414yes—
259C4⋊Dic47C2412yes—
260C4⋊Dic47C2412yes—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265C4×Dic47—24no—
266C4×Dic47—24no—
267C4×Dic47C2×D412yes—
268C4×Dic47C2×D412yes—
269C4×Dic47C2412yes—
270C4×Dic47C2412yes—
271#10625329—28no—
272C2×C47⋊C8—22no—
273C2×C47⋊C8#4114yes—
274C2×C47⋊C8C2412yes—
275C2×C47⋊C8C2412yes—
276#10625325—28no—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47—22no—
281C23×C47—42no—
282C23×C47—42no—
283C23×C47—42no—
284C23×C47C22×D412yes—
285C23×C47C22×D411yescharacteristic
286C22×D47—22no—
287C22×D47—42no—
288C22×D47—42no—
289C22×D47—42no—
290Q8×C47—22no—
291Q8×C47—22no—
292Q8×C47—42no—
293D4×C47—22no—
294D4×C47—22no—
295D4×C47—42no—
296D4×C47—84no—
297C2×C4×C47—22no—
298C2×C4×C47—24no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—42no—
305C2×C4×C47—42no—
306C2×C4×C47—42no—
307C2×C4×C47C22×D412yes—
308C2×C4×C47C22×D411yescharacteristic
309C2×C4×C47C2×#4112yes—
310C2×C4×C47C2×#4112yes—
311C2×C4×C47C2511yescharacteristic
312C22⋊D47—84no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—42no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47—84no—
324C2×Dic47C22×D412yes—
325C2×Dic47C22×D412yes—
326C2×Dic47C22×D412yes—
327C2×Dic47C22×D412yes—
328D188—22no—
329D188—22no—
330D188—42no—
331C4×D47—84no—
332Dic94—22no—
333Dic94—22no—
334Dic94—42no—
335Dic94—84no—
336Dic94—84no—
337C8×C47—22no—
338C8×C47C2×#4114yes—
339C47⋊C8—22no—
340C47⋊C8C2×#4114yes—
341C2×#3173—471nomaximal, Sylow
342C22×C47—22no—
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—44no—
346C22×C47—42no—
347C22×C47—42no—
348C22×C47—42no—
349C22×C47—84no—
350C22×C47#53212yes—
351C22×C47#57712yes—
352C22×C47#57712yes—
353C22×C47C23×D411yescharacteristic
354C2×D47—42no—
355C2×D47—42no—
356C2×D47—42no—
357C2×D47—84no—
358C4×C47—22no—
359C4×C47—42no—
360C4×C47—42no—
361C4×C47—42no—
362C4×C47#53212yes—
363C4×C47C22×#4111yescharacteristic
364C4×C47C22×#4111yescharacteristic
365Dic47—22no—
366Dic47—22no—
367Dic47—22no—
368Dic47—22no—
369Dic47—42no—
370Dic47—42no—
371Dic47—42no—
372C2×#542—471no—
373C2×#542—471no—
374#3173—4716no—
375C2×#498—471no—
376C2×#495—471no—
377C2×#489—471no—
378C2×#489—471no—
379C2×#470—471no—
380C2×#469—471no—
381C2×#465—471no—
382C2×#465D4711yescharacteristic, complemented
383C2×#442—471no—
384C2×#441—471no—
385C2×C4×SD16—471no—
386C2×C4×SD16—471no—
387C2×#405—471no—
388C2×C47—42no—
389C2×C47—82no—
390C2×C47#317314yescomplemented
391C2×C47C2×#53211yescharacteristic
392C2×C47C2×#57711yescharacteristic
393C2×C47C2×#57711yescharacteristic
394D47—82no—
395C22×Q16—471no—
396C22×SD16—471no—
397C22×SD16C2×D4711yescharacteristic
398C22×D8—471no—
399C22×M16—471no—
400C23×C8C2×D4711yescharacteristic
401#542—478no—
402#542—478no—
403#542—944no—
404#542—944no—
405C2×C4⋊Q8—471no—
406C2×C4⋊Q8—471no—
407C2×#126—941no—
408C2×#126—941no—
409C2×#124—471no—
410C2×#124—471no—
411C2×#124—941no—
412C2×#124—941no—
413C2×#123—941no—
414C2×#123—941no—
415C2×C22⋊Q8—471no—
416C2×C22⋊Q8—941no—
417C2×C22⋊Q8—941no—
418C2×C22⋊Q8C2×D4711yescharacteristic
419C2×#121—471no—
420C2×#121C2×D4711yescharacteristic
421C2×C4×Q8—471no—
422C2×C4×Q8—471no—
423C2×C4×D4—471no—
424C2×C4×D4—471no—
425C2×#117—471no—
426#498—478no—
427#495—478no—
428#489—478no—
429#489—478no—
430#470—478no—
431#469—478no—
432#465—478no—
433#465C2×D4718yescomplemented
434#442—478no—
435#441—478no—
436C4×SD16—478no—
437C4×SD16—478no—
438C2×#106—471no—
439C2×#106—471no—
440C2×#106—471no—
441C2×#106C2×D4711yescharacteristic
442C2×#103—471no—
443C2×#103—471no—
444C2×#103—471no—
445C2×#103C2×D4711yescharacteristic
446C2×#102—471no—
447C2×#102—471no—
448C2×#102—471no—
449C2×#102C2×D4711yescharacteristic
450#405—478no—
451C2×#97—471no—
452C2×#97—471no—
453C2×C4×C8—471no—
454C2×C4×C8—471no—
455C47C2×#317311yescharacteristic, complemented, Sylow
456C22×Q8—471no—
457C22×Q8—941no—
458C22×Q8—941no—
459C22×Q8C22×D4711yescharacteristic
460C22×D4—21no—
461C22×D4—471no—
462C22×D4—941no—
463C22×D4C22×D4711yescharacteristic
464C23×C4—941no—
465C23×C4—941no—
466C23×C4C22×D4711yescharacteristic
467C2×Q16—474no—
468C2×Q16—944no—
469C2×SD16—24no—
470C2×SD16—474no—
471C2×SD16—944no—
472C2×SD16C22×D4714yes—
473C2×D8—474no—
474C2×D8—944no—
475C2×M16—474no—
476C2×M16—944no—
477C22×C8—24no—
478C22×C8—471no—
479C22×C8—471no—
480C22×C8C22×D4711yescharacteristic
481C22×C8C22×D4714yes—
482C22×C8C22×D4711yescharacteristic
483C4⋊Q8—474no—
484C4⋊Q8—474no—
485C4⋊Q8—942no—
486C4⋊Q8—942no—
487#126—948no—
488#126—948no—
489#124—474no—
490#124—474no—
491#124—942no—
492#124—942no—
493#124—948no—
494#124—948no—
495#123—948no—
496#123—948no—
497C22⋊Q8—22no—
498C22⋊Q8—474no—
499C22⋊Q8—948no—
500C22⋊Q8—948no—
501C22⋊Q8—942no—
502C22⋊Q8C22×D4714yes—
503#121—22no—
504#121—474no—
505#121—942no—
506#121C22×D4714yes—
507C4×Q8—474no—
508C4×Q8—474no—
509C4×Q8—942no—
510C4×Q8—942no—
511C4×D4—474no—
512C4×D4—474no—
513C4×D4—942no—
514C4×D4—942no—
515#117—474no—
516#117—474no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—471no—
519C2×C4⋊C4—471no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4—941no—
526C2×C4⋊C4—941no—
527C2×C4⋊C4C22×D4711yescharacteristic
528C2×C4⋊C4C22×D4711yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—471no—
532C2×C22⋊C4—471no—
533C2×C22⋊C4—941no—
534C2×C22⋊C4—941no—
535C2×C22⋊C4—941no—
536C2×C22⋊C4—941no—
537C2×C22⋊C4—941no—
538C2×C22⋊C4—941no—
539C2×C22⋊C4—941no—
540C2×C22⋊C4—941no—
541C2×C42—471no—
542C2×C42—471no—
543C2×C42—941no—
544C2×C42—941no—
545#106—474no—
546#106—474no—
547#106—474no—
548#106C22×D4714yes—
549#103—474no—
550#103—474no—
551#103—474no—
552#103C22×D4714yes—
553#102—474no—
554#102—474no—
555#102—474no—
556#102C22×D4714yes—
557#97—474no—
558#97—474no—
559C4×C8—474no—
560C4×C8—474no—
561C24—21no—
562C24—941no—
563C24D4×D4711yescharacteristic
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—472no—
568C2×Q8—944no—
569C2×Q8—944no—
570C2×Q8—941no—
571C2×Q8—942no—
572C2×Q8—942no—
573C2×Q8—3762no—
574C2×Q8—3762no—
575C2×Q8C23×D4712yes—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—82no—
581C2×D4—472no—
582C2×D4—944no—
583C2×D4—941no—
584C2×D4—942no—
585C2×D4—942no—
586C2×D4—3762no—
587C2×D4C23×D4712yes—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—471no—
594C22×C4—471no—
595C22×C4—471no—
596C22×C4—471no—
597C22×C4—944no—
598C22×C4—944no—
599C22×C4—941no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—3762no—
603C22×C4—3762no—
604C22×C4D4×D4712yes—
605C22×C4D4×D4711yescharacteristic
606C22×C4C23×D4712yes—
607C22×C4C23×D4711yescharacteristic
608Q16—948no—
609SD16—28no—
610SD16—948no—
611D8—948no—
612M16—948no—
613C2×C8—22no—
614C2×C8—28no—
615C2×C8—474no—
616C2×C8—472no—
617C2×C8—472no—
618C2×C8—942no—
619C2×C8#1062535214yes—
620C2×C8C23×D4712yes—
621C2×C8C23×D4712yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—474no—
626C4⋊C4—474no—
627C4⋊C4—472no—
628C4⋊C4—472no—
629C4⋊C4—944no—
630C4⋊C4—944no—
631C4⋊C4—944no—
632C4⋊C4—944no—
633C4⋊C4—944no—
634C4⋊C4—941no—
635C4⋊C4—941no—
636C4⋊C4C23×D4712yes—
637C4⋊C4C23×D4712yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—474no—
641C22⋊C4—474no—
642C22⋊C4—944no—
643C22⋊C4—944no—
644C22⋊C4—944no—
645C22⋊C4—944no—
646C22⋊C4—944no—
647C22⋊C4—944no—
648C22⋊C4—944no—
649C22⋊C4—944no—
650C42—472no—
651C42—472no—
652C42—472no—
653C42—472no—
654C42—944no—
655C42—944no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—942no—
664C23—1882no—
665C23—1882no—
666C23—1882no—
667C23C2×D4×D4712yes—
668C23C2×D4×D4711yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—942no—
673Q8—942no—
674Q8—3764no—
675Q8—3764no—
676Q8—1882no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—84no—
681D4—942no—
682D4—942no—
683D4—3764no—
684D4—1882no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—472no—
696C2×C4—472no—
697C2×C4—472no—
698C2×C4—472no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—942no—
706C2×C4—3764no—
707C2×C4—3764no—
708C2×C4—1882no—
709C2×C4—1882no—
710C2×C4—1882no—
711C2×C4C2×D4×D4712yes—
712C2×C4C2×D4×D4711yescharacteristic
713C2×C4#41×D4712yes—
714C2×C4C2×#1062535212yes—
715C2×C4C24×D4711yescharacteristic
716C8—22no—
717C8—474no—
718C8—942no—
719C8C2×#1062535214yes—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—3764no—
729C22—1882no—
730C22—1882no—
731C22—1882no—
732C22#1568966812yes—
733C22#1568992912yes—
734C22#1568993012yes—
735C22C22×D4×D4711yescharacteristic
736C4—22no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—942no—
741C4—942no—
742C4—942no—
743C4—942no—
744C4—1882no—
745C4—1882no—
746C4—1882no—
747C4#1568966812yes—
748C4C2×#41×D4711yescharacteristic
749C4C22×#1062535211yescharacteristic
750C2—42no—
751C2—82no—
752C2—3762no—
753C2#2025399814yesdirect product factor
754C2C2×#1568966811yescharacteristic
755C2C2×#1568992911yescharacteristic
756C2C2×#1568993011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#465C2
socleC23×C47C22×D4
prime radicalC2×#15689374C2
hypercenterC2×#465D47
hypocenterC47C2×#3173
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
1. C2×#15689746C2semidirect
2. C2×#15689740C2semidirect
3. #20253998C2direct (N × H)
4. C2×#15689520C2semidirect
5. C2×#15689504C2semidirect
6. C2×#15689484C2semidirect
7. C2×#15689481C2semidirect
8. C2×#15689379C2semidirect
10. C2×#15689352C2semidirect
11. C2×#15689232C2semidirect
12. C2×#15689227C2semidirect
13. C2×SD16×Dic47C2semidirect
14. C2×#15689210C2semidirect
15. C2×#15689078C2semidirect
16. C2×C47×#465C2semidirect
22. #15689746C22semidirect
24. #15689740C22semidirect
44. #15689520C22semidirect
45. #15689504C22semidirect
46. #15689484C22semidirect
47. #15689481C22semidirect
48. #15689379C22semidirect
50. #15689352C22semidirect
51. #15689232C22semidirect
52. #15689227C22semidirect
53. SD16×Dic47C22semidirect
54. #15689210C22semidirect
64. #15689078C22semidirect
73. C47×#465C22semidirect
382. C2×#465D47semidirect
390. C2×C47#3173semidirect
433. #465C2×D47semidirect
455. C47C2×#3173semidirect
753. C2#20253998direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897462
C2×#156897402
#202539982
C2×#156895202
C2×#156895042
C2×#156894842
C2×#156894812
C2×#156893792
C2×#156893742
C2×#156893522
C2×#156892322
C2×#156892272
C2×SD16×Dic472
C2×#156892102
C2×#156890782
C2×C47×#4652
C2×#317347