Finite Group Databasebeta

← C2×#20254787 #27089164

Subgroups — C2×#20254787 #27089164

Order 12032.

1930 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×#15689660C211yesmaximal, characteristic, complemented
2C2×#15689652C211yesmaximal, characteristic, complemented
3#20254787C2116yesmaximal, direct product factor
4C2×#15689432C211yesmaximal, characteristic, complemented
5C2×#15689430C211yesmaximal, characteristic, complemented
6C2×#15689425C211yesmaximal, characteristic, complemented
7C2×#15689424C211yesmaximal, characteristic, complemented
8C2×#15689378C211yesmaximal, characteristic, complemented
9C2×#15689375C211yesmaximal, characteristic
10C2×#15689372C211yesmaximal, characteristic, complemented
11C2×#15689366C211yesmaximal, characteristic, complemented
12C2×#15689347C211yesmaximal, characteristic, complemented
13C2×#15689340C211yesmaximal, characteristic, complemented
14C2×#15689335C211yesmaximal, characteristic, complemented
15C2×#15689145C211yesmaximal, characteristic, complemented
16C2×C47×#464C211yesmaximal, characteristic, complemented
17C22×#10625336C2211yescharacteristic
18C22×#10625334C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C22×#10625324C2211yescharacteristic
21#15689660—24no—
22#15689660C2218yescomplemented
23#15689652—24no—
24#15689652C2218yescomplemented
25C2×#13094019—21no—
26C2×#13094017—21no—
27C2×#13094016C2211yescharacteristic
28C2×#13094015C2211yescharacteristic
29C2×#13094013C2211yescharacteristic
30C2×#13094009—21no—
31C2×#13094006—21no—
32C2×#13094000C2211yescharacteristic
33C2×#13094000C2211yescharacteristic
34C2×#13093999C2211yescharacteristic
35C2×#13093995C2211yescharacteristic
36C2×Q8×Dic47C2211yescharacteristic
37C2×C4×D188—21no—
38C2×C4×D188C2211yescharacteristic
39C2×D4×Dic47C2211yescharacteristic
40C2×(C22⋊D47)⋊C4—21no—
41C2×#13093981—21no—
42C2×#13093980—21no—
43C2×C42×D47C2211yescharacteristic
44#15689432C2218yescomplemented
45#15689430C2218yescomplemented
46#15689425C2218yescomplemented
47#15689424C2218yescomplemented
48#15689378C2218yescomplemented
49#15689375C2218yes—
50#15689372C2218yescomplemented
51#15689366C2218yescomplemented
52#15689347C2218yescomplemented
53#15689340C2218yescomplemented
54#15689335C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093956C2211yescharacteristic
58C2×#13093955C2211yescharacteristic
59#15689145C2218yescomplemented
60C2×C4⋊(C47⋊C8)C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093948C2211yescharacteristic
65C2×#13093948C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic
68C2×#13093945C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C22×SD16×C47C2211yescharacteristic
71C2×#124×C47C2211yescharacteristic
72C2×C4×Q8×C47C2211yescharacteristic
73C47×#464C2218yescomplemented
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C22×D188—21no—
78C22×D188C2311yescharacteristic
79C22×C22⋊D47—21no—
80C23×Dic47—21no—
81C22×C4×D47—21no—
82C22×C4×D47D411yescharacteristic
83C22×C4×D47D411yescharacteristic
84C22×C4×D47C2311yescharacteristic
85C2×#10625336—42no—
86C2×#10625336C2314yes—
87C2×#10625334—42no—
88C2×#10625334C2314yes—
89C2×#10625324—42no—
90C2×#10625324—42no—
91C2×#10625324C2314yes—
92C2×#10625324C2314yes—
93C22×C47⋊C8C2311yescharacteristic
94C22×C47⋊C8C2311yescharacteristic
95#13094019—28no—
96#13094017—28no—
97#13094016—22no—
98#13094016C2314yes—
99#13094015—22no—
100#13094015C2314yes—
101#13094013—22no—
102#13094013C2314yes—
103#13094009—28no—
104#13094006—28no—
105#13094000—22no—
106#13094000—22no—
107#13094000C2314yes—
108#13094000C2314yes—
109#13093999—22no—
110#13093999C2314yes—
111#13093995—22no—
112#13093995C2314yes—
113Q8×Dic47—22no—
114Q8×Dic47C2314yes—
115C4×D188—28no—
116C4×D188—22no—
117C4×D188C2314yes—
118D4×Dic47—22no—
119D4×Dic47C2314yes—
120(C22⋊D47)⋊C4—28no—
121#13093981—28no—
122#13093980—28no—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×Dic47⋊C4—21no—
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×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47D411yescharacteristic
143C2×C4×Dic47D411yescharacteristic
144C2×C4×Dic47C2311yescharacteristic
145C42×D47D414yes—
146C42×D47C2314yes—
147#13093958C2314yes—
148#13093957C2314yes—
149#13093956C2314yes—
150#13093955C2314yes—
151C4⋊(C47⋊C8)C2314yes—
152Dic47⋊C8C2314yes—
153Dic47⋊C8C2314yes—
154#13093948C2314yes—
155#13093948C2314yes—
156#13093948C2314yes—
157#13093946C2314yes—
158#13093946C2314yes—
159#13093945C2314yes—
160C22×Q8×C47C2311yescharacteristic
161C22×Q8×C47C2311yescharacteristic
162C22×D4×C47C2311yescharacteristic
163C2×Q16×C47—42no—
164C2×Q16×C47C2314yes—
165C2×SD16×C47—42no—
166C2×SD16×C47C2314yes—
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169#124×C47—22no—
170#124×C47C2314yes—
171C4×Q8×C47—22no—
172C4×Q8×C47C2314yes—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176C2×C22⋊C4×C47—21no—
177C2×C42×C47—21no—
178C2×C42×C47C2311yescharacteristic
179C4⋊C8×C47C2314yes—
180#103×C47C2314yes—
181#102×C47C2314yes—
182C24×C47—21no—
183C23×D47—21no—
184C23×D47C2×D411yescharacteristic
185C2×Q8×C47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—22no—
188C2×Q8×C47—22no—
189C2×Q8×C47—22no—
190C2×Q8×C47—22no—
191C2×Q8×C47C2412yes—
192C2×Q8×C47C2412yes—
193C2×D4×C47—21no—
194C2×D4×C47—22no—
195C2×D4×C47—22no—
196C2×D4×C47C2412yes—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2411yescharacteristic
203C2×C22⋊D47—24no—
204C2×C22⋊D47—44no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—24no—
209C22×Dic47—44no—
210C22×Dic47C2×D411yescharacteristic
211C22×Dic47C2×D411yescharacteristic
212C22×Dic47C2×D411yescharacteristic
213C2×D188—22no—
214C2×D188—22no—
215C2×D188—24no—
216C2×D188—21no—
217C2×D188—44no—
218C2×D188C2412yes—
219C2×C4×D47—22no—
220C2×C4×D47—22no—
221C2×C4×D47—24no—
222C2×C4×D47—42no—
223C2×C4×D47—42no—
224C2×C4×D47—44no—
225C2×C4×D47C2×D412yes—
226C2×C4×D47C2×D414yes—
227C2×C4×D47C2×D414yes—
228C2×C4×D47C2412yes—
229Q16×C47—44no—
230SD16×C47—44no—
231C2×C8×C47—22no—
232C2×C8×C47—22no—
233C2×C8×C47C2412yes—
234C2×C8×C47C2412yes—
235C4⋊C4×C47—24no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47C2412yes—
238C22⋊C4×C47—24no—
239C22⋊C4×C47—24no—
240C42×C47—24no—
241C42×C47C2×D412yes—
242C42×C47C2412yes—
243C22⋊Dic47—24no—
244C22⋊Dic47—24no—
245#10625336—44no—
246#10625334—44no—
247(C2×D47)⋊C4—24no—
248(C2×D47)⋊C4—24no—
249(C2×D47)⋊C4—24no—
250(C2×D47)⋊C4—24no—
251(C2×D47)⋊C4—24no—
252(C2×D47)⋊C4—24no—
253C4⋊Dic47—21no—
254C4⋊Dic47—21no—
255C4⋊Dic47—21no—
256C4⋊Dic47—24no—
257C4⋊Dic47—24no—
258C4⋊Dic47C2412yes—
259C4⋊Dic47C2412yes—
260C4⋊Dic47C2412yes—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4—24no—
266C4×Dic47—24no—
267C4×Dic47C2×D412yes—
268C4×Dic47C2×D414yes—
269C4×Dic47C2×D414yes—
270C4×Dic47C2412yes—
271C2×C47⋊C8—22no—
272C2×C47⋊C8—22no—
273C2×C47⋊C8C2412yes—
274C2×C47⋊C8C2412yes—
275#10625324—44no—
276#10625324—44no—
277C23×C47—22no—
278C23×C47—42no—
279C23×C47—42no—
280C23×C47—42no—
281C23×C47C22×D411yescharacteristic
282C22×D47—22no—
283C22×D47—22no—
284C22×D47—22no—
285C22×D47—22no—
286C22×D47—42no—
287C22×D47—42no—
288C22×D47—42no—
289C22×D47C22×D412yes—
290Q8×C47—22no—
291Q8×C47—22no—
292Q8×C47—22no—
293Q8×C47—22no—
294Q8×C47—42no—
295Q8×C47—42no—
296D4×C47—22no—
297D4×C47—22no—
298D4×C47—42no—
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×D412yes—
309C2×C4×C47C22×D411yescharacteristic
310C2×C4×C47H(5,𝔽2)12yes—
311C2×C4×C472−1+412yes—
312C2×C4×C47C2511yescharacteristic
313C22⋊D47—48no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—48no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47C22×D412yes—
325C2×Dic47C22×D412yes—
326C2×Dic47C22×D412yes—
327D188—22no—
328D188—22no—
329D188—48no—
330D188—42no—
331C4×D47—24no—
332C4×D47—22no—
333C4×D47—22no—
334C4×D47—44no—
335C4×D47—44no—
336C4×D47—48no—
337C8×C47—22no—
338C8×C47—22no—
339C47⋊C8—22no—
340C47⋊C8—22no—
341C2×#3256—471nomaximal, Sylow
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—84no—
346C22×C47#53712yes—
347C22×C47#57512yes—
348C22×C47#57512yes—
349C22×C47C23×D411yescharacteristic
350C2×D47—22no—
351C2×D47—22no—
352C2×D47—22no—
353C2×D47—44no—
354C2×D47—42no—
355C2×D47—42no—
356C2×D47—42no—
357C2×D47—84no—
358C4×C47—22no—
359C4×C47—22no—
360C4×C47—42no—
361C4×C47—42no—
362C4×C47—42no—
363C4×C47#53712yes—
364C4×C47C2×H(5,𝔽2)11yescharacteristic
365C4×C47C2×2−1+411yescharacteristic
366Dic47—22no—
367Dic47—22no—
368Dic47—22no—
369Dic47—42no—
370Dic47—42no—
371Dic47—42no—
372C2×#529—471no—
373C2×#529—471no—
374#3256—4716no—
375C2×#479—471no—
376C2×#479—471no—
377C2×#478—471no—
378C2×#478—471no—
379C2×#470—471no—
380C2×#469—471no—
381C2×#468—471no—
382C2×#468—471no—
383C2×#464—471no—
384C2×#464D4711yescharacteristic, complemented
385C2×#463—471no—
386C2×#463—471no—
387C2×#423—471no—
388C2×C47—82no—
389C2×C47#325614yescomplemented
390C2×C47C2×#53711yescharacteristic
391C2×C47C2×#57511yescharacteristic
392C2×C47C2×#57511yescharacteristic
393D47—42no—
394D47—82no—
395C22×Q16C2×D4711yescharacteristic
396C22×SD16—471no—
397C22×SD16C2×D4711yescharacteristic
398C22×D8—471no—
399C22×M16—471no—
400C22×M16—471no—
401#529—478no—
402#529—478no—
403#529—944no—
404#529—944no—
405C2×#126—941no—
406C2×#126—941no—
407C2×#125—471no—
408C2×#125—471no—
409C2×#124—471no—
410C2×#124C2×D4711yescharacteristic
411C2×#123—941no—
412C2×#123—941no—
413C2×C22⋊Q8—471no—
414C2×C22⋊Q8—471no—
415C2×#121—471no—
416C2×#121—471no—
417C2×C4×Q8—471no—
418C2×C4×Q8C2×D4711yescharacteristic
419C2×C4×D4—471no—
420C2×C4×D4—471no—
421C2×C4×D4—941no—
422C2×C4×D4—941no—
423C2×#117—941no—
424C2×#117—941no—
425C22×C42—471no—
426#479—478no—
427#479—478no—
428#478—478no—
429#478—478no—
430#470—478no—
431#469—478no—
432#468—478no—
433#468—478no—
434#464—478no—
435#464C2×D4718yescomplemented
436#463—478no—
437#463—478no—
438C2×#107—471no—
439C2×#107—471no—
440C2×#106—471no—
441C2×#106—471no—
442#423—478no—
443C2×C4⋊C8—471no—
444C2×C4⋊C8—471no—
445C2×C4⋊C8—471no—
446C2×C4⋊C8C2×D4711yescharacteristic
447C2×#103—471no—
448C2×#103—471no—
449C2×#103—471no—
450C2×#103C2×D4711yescharacteristic
451C2×#102—471no—
452C2×#102—471no—
453C2×#102—471no—
454C2×#102C2×D4711yescharacteristic
455C47C2×#325611yescharacteristic, complemented, Sylow
456C22×Q8C22×D4711yescharacteristic
457C22×Q8C22×D4711yescharacteristic
458C22×D4—471no—
459C22×D4—941no—
460C22×D4—941no—
461C22×D4C22×D4711yescharacteristic
462C23×C4—471no—
463C23×C4—471no—
464C23×C4—471no—
465C23×C4—941no—
466C23×C4—941no—
467C2×Q16—42no—
468C2×Q16C22×D4714yes—
469C2×SD16—42no—
470C2×SD16—474no—
471C2×SD16—1882no—
472C2×SD16C22×D4714yes—
473C2×D8—474no—
474C2×D8—1882no—
475C2×M16—474no—
476C2×M16—474no—
477C2×M16—1882no—
478C2×M16—1882no—
479C22×C8—471no—
480C22×C8—471no—
481C22×C8C22×D4711yescharacteristic
482C22×C8C22×D4711yescharacteristic
483#126—948no—
484#126—948no—
485#125—474no—
486#125—474no—
487#125—942no—
488#125—942no—
489#124—22no—
490#124—474no—
491#124—942no—
492#124C22×D4714yes—
493#123—948no—
494#123—948no—
495C22⋊Q8—474no—
496C22⋊Q8—474no—
497C22⋊Q8—942no—
498C22⋊Q8—942no—
499#121—474no—
500#121—474no—
501#121—942no—
502#121—942no—
503C4×Q8—22no—
504C4×Q8—474no—
505C4×Q8—942no—
506C4×Q8C22×D4714yes—
507C4×D4—474no—
508C4×D4—474no—
509C4×D4—948no—
510C4×D4—942no—
511C4×D4—948no—
512C4×D4—942no—
513#117—948no—
514#117—948no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—471no—
517C2×C4⋊C4—471no—
518C2×C4⋊C4—471no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4—941no—
521C2×C4⋊C4—941no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4—941no—
526C2×C4⋊C4C22×D4711yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—941no—
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—21no—
538C2×C42—471no—
539C2×C42—471no—
540C2×C42—471no—
541C2×C42—474no—
542C2×C42—474no—
543C2×C42—941no—
544C2×C42C22×D4711yescharacteristic
545#107—474no—
546#107—474no—
547#106—474no—
548#106—474no—
549C4⋊C8—474no—
550C4⋊C8—474no—
551C4⋊C8—474no—
552C4⋊C8C22×D4714yes—
553#103—474no—
554#103—474no—
555#103—474no—
556#103C22×D4714yes—
557#102—474no—
558#102—474no—
559#102—474no—
560#102C22×D4714yes—
561C24—21no—
562C24—471no—
563C24—941no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8C23×D4712yes—
571C2×Q8C23×D4712yes—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—472no—
576C2×D4—944no—
577C2×D4—944no—
578C2×D4—941no—
579C2×D4—942no—
580C2×D4—942no—
581C2×D4—1884no—
582C2×D4—1884no—
583C2×D4C23×D4712yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—471no—
588C22×C4—471no—
589C22×C4—471no—
590C22×C4—472no—
591C22×C4—472no—
592C22×C4—474no—
593C22×C4—474no—
594C22×C4—944no—
595C22×C4—942no—
596C22×C4—942no—
597C22×C4—941no—
598C22×C4—941no—
599C22×C4—941no—
600C22×C4—944no—
601C22×C4—1882no—
602C22×C4—1882no—
603C22×C4—1884no—
604C22×C4—1884no—
605C22×C4D4×D4711yescharacteristic
606C22×C4D4×D4711yescharacteristic
607C22×C4C23×D4711yescharacteristic
608Q16—44no—
609SD16—44no—
610SD16—1884no—
611D8—1884no—
612M16—1884no—
613M16—1884no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—472no—
617C2×C8—472no—
618C2×C8—942no—
619C2×C8—942no—
620C2×C8C23×D4712yes—
621C2×C8C23×D4712yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—472no—
625C4⋊C4—472no—
626C4⋊C4—472no—
627C4⋊C4—944no—
628C4⋊C4—944no—
629C4⋊C4—944no—
630C4⋊C4—944no—
631C4⋊C4—944no—
632C4⋊C4—944no—
633C4⋊C4—944no—
634C4⋊C4—941no—
635C4⋊C4—941no—
636C4⋊C4—941no—
637C4⋊C4C23×D4712yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—944no—
641C22⋊C4—944no—
642C22⋊C4—944no—
643C22⋊C4—944no—
644C22⋊C4—944no—
645C22⋊C4—944no—
646C22⋊C4—944no—
647C22⋊C4—944no—
648C42—24no—
649C42—474no—
650C42—472no—
651C42—474no—
652C42—472no—
653C42—944no—
654C42D4×D4712yes—
655C42C23×D4712yes—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—472no—
661C23—942no—
662C23—942no—
663C23—942no—
664C23—942no—
665C23—1882no—
666C23—1882no—
667C23—1882no—
668C23C2×D4×D4711yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—42no—
674Q8—42no—
675D4—22no—
676D4—22no—
677D4—42no—
678D4—942no—
679D4—942no—
680D4—1888no—
681D4—1888no—
682D4—1882no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—472no—
692C2×C4—472no—
693C2×C4—472no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—942no—
698C2×C4—942no—
699C2×C4—944no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—1884no—
704C2×C4—1884no—
705C2×C4—1888no—
706C2×C4—1888no—
707C2×C4—1882no—
708C2×C4—1882no—
709C2×C4—1882no—
710C2×C4C2×D4×D4712yes—
711C2×C4C2×D4×D4712yes—
712C2×C4C2×D4×D4711yescharacteristic
713C2×C4#1309406912yes—
714C2×C4#1309407112yes—
715C2×C4C24×D4711yescharacteristic
716C8—22no—
717C8—22no—
718C8—942no—
719C8—942no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—84no—
724C22—942no—
725C22—942no—
726C22—942no—
727C22—3764no—
728C22—1882no—
729C22—1882no—
730C22—1882no—
731C22—1884no—
732C22#1568970212yes—
733C22#1568992012yes—
734C22#1568992212yes—
735C22C22×D4×D4711yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—942no—
742C4—942no—
743C4—942no—
744C4—1882no—
745C4—1882no—
746C4—1882no—
747C4#1568970212yes—
748C4C2×#1309406911yescharacteristic
749C4C2×#1309407111yescharacteristic
750C2—82no—
751C2—3762no—
752C2—1882no—
753C2#2025478714yesdirect product factor
754C2C2×#1568970211yescharacteristic
755C2C2×#1568992011yescharacteristic
756C2C2×#1568992211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#464C2
socleC23×C47C22×D4
prime radicalC2×#15689375C2
hypercenterC2×#464D47
hypocenterC47C2×#3256
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#15689660C2semidirect
2. C2×#15689652C2semidirect
3. #20254787C2direct (N × H)
4. C2×#15689432C2semidirect
5. C2×#15689430C2semidirect
6. C2×#15689425C2semidirect
7. C2×#15689424C2semidirect
8. C2×#15689378C2semidirect
10. C2×#15689372C2semidirect
11. C2×#15689366C2semidirect
12. C2×#15689347C2semidirect
13. C2×#15689340C2semidirect
14. C2×#15689335C2semidirect
15. C2×#15689145C2semidirect
16. C2×C47×#464C2semidirect
22. #15689660C22semidirect
24. #15689652C22semidirect
44. #15689432C22semidirect
45. #15689430C22semidirect
46. #15689425C22semidirect
47. #15689424C22semidirect
48. #15689378C22semidirect
50. #15689372C22semidirect
51. #15689366C22semidirect
52. #15689347C22semidirect
53. #15689340C22semidirect
54. #15689335C22semidirect
59. #15689145C22semidirect
73. C47×#464C22semidirect
384. C2×#464D47semidirect
389. C2×C47#3256semidirect
435. #464C2×D47semidirect
455. C47C2×#3256semidirect
753. C2#20254787direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896602
C2×#156896522
#202547872
C2×#156894322
C2×#156894302
C2×#156894252
C2×#156894242
C2×#156893782
C2×#156893752
C2×#156893722
C2×#156893662
C2×#156893472
C2×#156893402
C2×#156893352
C2×#156891452
C2×C47×#4642
C2×#325647