Finite Group Databasebeta

← C2×#20254860 #27089255

Subgroups — C2×#20254860 #27089255

Order 12032.

1882 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×#15689747C211yesmaximal, characteristic, complemented
2C2×#15689738C211yesmaximal, characteristic, complemented
3#20254860C2116yesmaximal, direct product factor
4C2×#15689407C211yesmaximal, characteristic, complemented
5C2×#15689405C211yesmaximal, characteristic, complemented
6C2×#15689412C211yesmaximal, characteristic, complemented
7C2×#15689382C211yesmaximal, characteristic, complemented
8C2×#15689375C211yesmaximal, characteristic
9C2×#15689353C211yesmaximal, characteristic, complemented
10C2×#15689351C211yesmaximal, characteristic, complemented
11C2×#15689346C211yesmaximal, characteristic, complemented
12C2×#15689344C211yesmaximal, characteristic, complemented
13C2×#15689338C211yesmaximal, characteristic, complemented
14C2×#15689337C211yesmaximal, characteristic, complemented
15C2×#15689148C211yesmaximal, characteristic, complemented
16C2×C47×#476C211yesmaximal, characteristic, complemented
17C22×Dic188C2211yescharacteristic
18C22×#10625325C2211yescharacteristic
19C22×#10625335C2211yescharacteristic
20C22×#10625334C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22C22×C8×D47C2211yescharacteristic
23#15689747—24no—
24#15689747C2218yescomplemented
25#15689738—24no—
26#15689738C2218yescomplemented
27C2×#13094023C2211yescharacteristic
28C2×#13094019—21no—
29C2×#13094017—21no—
30C2×#13094013—21no—
31C2×#13094012C2211yescharacteristic
32C2×#13094011C2211yescharacteristic
33C2×#13094010—21no—
34C2×#13094009—21no—
35C2×#13094007—21no—
36C2×#13094004C2211yescharacteristic
37C2×#13094004C2211yescharacteristic
38C2×#13094003—21no—
39C2×#13094000—21no—
40C2×#13093999C2211yescharacteristic
41C2×#13093995C2211yescharacteristic
42C2×C4×Dic94C2211yescharacteristic
43C2×#13093989C2211yescharacteristic
44C2×#13093986C2211yescharacteristic
45C2×#13093981C2211yescharacteristic
46#15689412C2218yescomplemented
47#15689407C2218yescomplemented
48#15689405C2218yescomplemented
49#15689382C2218yescomplemented
50#15689375C2218yes—
51#15689353C2218yescomplemented
52#15689351C2218yescomplemented
53#15689346C2218yescomplemented
54#15689344C2218yescomplemented
55#15689338C2218yescomplemented
56#15689337C2218yescomplemented
57C2×#13093955C2211yescharacteristic
58C2×#13093955C2211yescharacteristic
59#15689148C2218yescomplemented
60C2×C4⋊(C47⋊C8)C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093947C2211yescharacteristic
66C2×#13093947C2211yescharacteristic
67C2×#13093946C2211yescharacteristic
68C2×#13093944C2211yescharacteristic
69C2×C4⋊Q8×C47C2211yescharacteristic
70C2×C4×D4×C47C2211yescharacteristic
71C47×#476C2218yescomplemented
72C2×#106×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×Dic94C2311yescharacteristic
80C22×D188—21no—
81C22×D188C2311yescharacteristic
82C22×C22⋊D47—21no—
83C22×C4×D47—21no—
84C22×C4×D47C2311yescharacteristic
85C2×Dic188—42no—
86C2×Dic188C2314yes—
87C2×#10625325—42no—
88C2×#10625325C2314yes—
89C2×#10625335—42no—
90C2×#10625335C2314yes—
91C2×#10625334—42no—
92C2×#10625334C2314yes—
93C2×#10625324—42no—
94C2×#10625324C2314yes—
95C22×C47⋊C8C2311yescharacteristic
96C22×C47⋊C8C2311yescharacteristic
97C2×C8×D47—42no—
98C2×C8×D47C2314yes—
99#13094023—22no—
100#13094023C2314yes—
101#13094019—28no—
102#13094017—28no—
103#13094013—28no—
104#13094012—22no—
105#13094012C2314yes—
106#13094011—22no—
107#13094011C2314yes—
108#13094010—28no—
109#13094009—28no—
110#13094007—28no—
111#13094004—22no—
112#13094004—22no—
113#13094004C2314yes—
114#13094004C2314yes—
115#13094003—28no—
116#13094000—28no—
117#13093999—22no—
118#13093999C2314yes—
119#13093995—22no—
120#13093995C2314yes—
121C4×Dic94—22no—
122C4×Dic94C2314yes—
123#13093989—22no—
124#13093989C2314yes—
125#13093986—22no—
126#13093986C2314yes—
127#13093981D414yes—
128#13093981C2314yes—
129C2×C4⋊Dic47—21no—
130C2×C4⋊Dic47—21no—
131C2×C4⋊Dic47C2311yescharacteristic
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4D411yescharacteristic
136C2×Dic47⋊C4D411yescharacteristic
137C2×C22⋊Dic47—21no—
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47—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×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4D411yescharacteristic
147C2×(C2×D47)⋊C4D411yescharacteristic
148C2×C4×Dic47—21no—
149C2×C4×Dic47—21no—
150C2×C4×Dic47C2311yescharacteristic
151#13093955C2314yes—
152#13093955C2314yes—
153C4⋊(C47⋊C8)C2314yes—
154Dic47⋊C8C2314yes—
155Dic47⋊C8C2314yes—
156#13093949C2314yes—
157#13093947C2314yes—
158#13093947C2314yes—
159#13093947C2314yes—
160#13093946C2314yes—
161#13093944C2314yes—
162C22×Q8×C47—21no—
163C22×D4×C47C2311yescharacteristic
164C23×C4×C47—21no—
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C4⋊Q8×C47—22no—
168C4⋊Q8×C47C2314yes—
169C4×D4×C47—22no—
170C4×D4×C47C2314yes—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176C2×C42×C47C2311yescharacteristic
177#106×C47C2314yes—
178#106×C47C2314yes—
179C4⋊C8×C47C2314yes—
180#102×C47C2314yes—
181#102×C47C2314yes—
182C24×C47—21no—
183C23×D47—21no—
184C23×D47C2×D411yescharacteristic
185C2×Q8×C47—24no—
186C2×Q8×C47—82no—
187C2×D4×C47—21no—
188C2×D4×C47—22no—
189C2×D4×C47—22no—
190C2×D4×C47C2412yes—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—24no—
195C22×C4×C47—82no—
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2411yescharacteristic
199C2×C22⋊D47—24no—
200C2×C22⋊D47—82no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47C2×D411yescharacteristic
205C22×Dic47C2×D411yescharacteristic
206C22×Dic47C2×D411yescharacteristic
207C2×D188—22no—
208C2×D188—22no—
209C2×D188—21no—
210C2×D188—24no—
211C2×D188—82no—
212C2×D188C2412yes—
213C2×C4×D47—22no—
214C2×C4×D47—22no—
215C2×C4×D47—24no—
216C2×C4×D47—82no—
217C2×C4×D47C2×D412yes—
218C2×C4×D47C2412yes—
219C2×Dic94—22no—
220C2×Dic94—22no—
221C2×Dic94—22no—
222C2×Dic94—22no—
223C2×Dic94—21no—
224C2×Dic94—21no—
225C2×Dic94—24no—
226C2×Dic94—82no—
227C2×Dic94C2412yes—
228C2×Dic94C2412yes—
229C2×C8×C47—22no—
230C2×C8×C47—22no—
231C2×C8×C47C2412yes—
232C2×C8×C47C2412yes—
233C4⋊C4×C47—24no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47C2412yes—
238C4⋊C4×C47C2412yes—
239C4⋊C4×C47C2412yes—
240C22⋊C4×C47—24no—
241C42×C47C2×D412yes—
242C42×C47C2412yes—
243C22⋊Dic47—24no—
244C22⋊Dic47—24no—
245C22⋊Dic47—24no—
246#10625335—44no—
247#10625334—44no—
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—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4C2×D414yes—
255(C2×D47)⋊C4C2×D414yes—
256C4⋊Dic47—21no—
257C4⋊Dic47—24no—
258C4⋊Dic47—24no—
259C4⋊Dic47C2412yes—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4C2×D414yes—
264Dic47⋊C4C2×D414yes—
265C4×Dic47—24no—
266C4×Dic47—24no—
267C4×Dic47C2×D412yes—
268C4×Dic47C2412yes—
269C2×C47⋊C8—22no—
270C2×C47⋊C8—22no—
271C2×C47⋊C8C2412yes—
272C2×C47⋊C8C2412yes—
273Dic188—44no—
274#10625325—44no—
275#10625324—44no—
276C8×D47—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—84no—
291D4×C47—22no—
292D4×C47—22no—
293D4×C47—42no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47—84no—
303C2×C4×C47C22×D412yes—
304C2×C4×C47C22×D412yes—
305C2×C4×C47C22×D411yescharacteristic
306C2×C4×C47H(5,𝔽2)12yes—
307C2×C4×C472−1+412yes—
308C2×C4×C47C2511yescharacteristic
309C22⋊D47—84no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—42no—
317C2×Dic47—42no—
318C2×Dic47—42no—
319C2×Dic47C22×D412yes—
320C2×Dic47C22×D412yes—
321C2×Dic47C22×D412yes—
322D188—22no—
323D188—22no—
324D188—42no—
325D188—84no—
326C4×D47—24no—
327C4×D47—22no—
328C4×D47—22no—
329C4×D47—84no—
330Dic94—22no—
331Dic94—22no—
332Dic94—22no—
333Dic94—22no—
334Dic94—42no—
335Dic94—42no—
336Dic94—84no—
337C8×C47—22no—
338C8×C47—22no—
339C47⋊C8—22no—
340C47⋊C8—22no—
341C2×#3263—471nomaximal, Sylow
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—84no—
346C22×C47#53712yes—
347C22×C47#57712yes—
348C22×C47#57712yes—
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×#542—471no—
373C2×#542—471no—
374#3263—4716no—
375C2×#475—471no—
376C2×#475—471no—
377C2×#476—471no—
378C2×#476D4711yescharacteristic, complemented
379C2×#470—471no—
380C2×#469—471no—
381C2×#465—471no—
382C2×#465—471no—
383C2×#464—471no—
384C2×#464—471no—
385C2×#463—471no—
386C2×#463—471no—
387C2×#424—471no—
388C2×C47—82no—
389C2×C47#326314yescomplemented
390C2×C47C2×#53711yescharacteristic
391C2×C47C2×#57711yescharacteristic
392C2×C47C2×#57711yescharacteristic
393D47—42no—
394D47—82no—
395C22×Q16—471no—
396C22×SD16—471no—
397C22×SD16—471no—
398C22×D8—471no—
399C22×M16—471no—
400C23×C8—471no—
401#542—478no—
402#542—478no—
403#542—944no—
404#542—944no—
405C2×C4⋊Q8—471no—
406C2×C4⋊Q8C2×D4711yescharacteristic
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—471no—
417C2×C22⋊Q8—941no—
418C2×C22⋊Q8—941no—
419C2×#121—471no—
420C2×#121—471no—
421C2×C4×Q8—471no—
422C2×C4×Q8—471no—
423C2×C4×D4—471no—
424C2×C4×D4C2×D4711yescharacteristic
425C2×#117—471no—
426#476—478no—
427#476C2×D4718yescomplemented
428#475—478no—
429#475—478no—
430#470—478no—
431#469—478no—
432#465—478no—
433#465—478no—
434#464—478no—
435#464—478no—
436#463—478no—
437#463—478no—
438C2×#106—471no—
439C2×#106—471no—
440C2×#106C2×D4711yescharacteristic
441C2×#106C2×D4711yescharacteristic
442#424—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×#103—471no—
451C2×#102—471no—
452C2×#102—471no—
453C2×#102C2×D4711yescharacteristic
454C2×#102C2×D4711yescharacteristic
455C47C2×#326311yescharacteristic, complemented, Sylow
456C22×Q8—21no—
457C22×Q8—471no—
458C22×Q8—471no—
459C22×Q8—941no—
460C22×D4—471no—
461C22×D4—941no—
462C22×D4—941no—
463C22×D4C22×D4711yescharacteristic
464C23×C4—21no—
465C23×C4—471no—
466C23×C4—941no—
467C2×Q16—474no—
468C2×Q16—1882no—
469C2×SD16—474no—
470C2×SD16—474no—
471C2×SD16—1882no—
472C2×SD16—1882no—
473C2×D8—474no—
474C2×D8—1882no—
475C2×M16—474no—
476C2×M16—1882no—
477C22×C8—471no—
478C22×C8—471no—
479C22×C8—474no—
480C22×C8—1882no—
481C22×C8C22×D4711yescharacteristic
482C22×C8C22×D4711yescharacteristic
483C4⋊Q8—22no—
484C4⋊Q8—474no—
485C4⋊Q8—942no—
486C4⋊Q8C22×D4714yes—
487#126—948no—
488#126—948no—
489#124—474no—
490#124—474no—
491#124—942no—
492#124—948no—
493#124—948no—
494#124—942no—
495#123—948no—
496#123—948no—
497C22⋊Q8—474no—
498C22⋊Q8—474no—
499C22⋊Q8—942no—
500C22⋊Q8—942no—
501C22⋊Q8—948no—
502C22⋊Q8—948no—
503#121—474no—
504#121—474no—
505#121—942no—
506#121—942no—
507C4×Q8—474no—
508C4×Q8—474no—
509C4×Q8—942no—
510C4×Q8—942no—
511C4×D4—22no—
512C4×D4—474no—
513C4×D4—942no—
514C4×D4C22×D4714yes—
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—941no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4—941no—
526C2×C4⋊C4C22×D4711yescharacteristic
527C2×C4⋊C4C22×D4711yescharacteristic
528C2×C4⋊C4C22×D4711yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—471no—
531C2×C22⋊C4—471no—
532C2×C22⋊C4—941no—
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—941no—
543C2×C42—941no—
544C2×C42C22×D4711yescharacteristic
545#106—474no—
546#106—474no—
547#106C22×D4714yes—
548#106C22×D4714yes—
549C4⋊C8—474no—
550C4⋊C8—474no—
551C4⋊C8—474no—
552C4⋊C8C22×D4714yes—
553#103—474no—
554#103—474no—
555#103—474no—
556#103—474no—
557#102—474no—
558#102—474no—
559#102C22×D4714yes—
560#102C22×D4714yes—
561C24—21no—
562C24—471no—
563C24—941no—
564C2×Q8—24no—
565C2×Q8—82no—
566C2×Q8—472no—
567C2×Q8—472no—
568C2×Q8—944no—
569C2×Q8—941no—
570C2×Q8—941no—
571C2×Q8—942no—
572C2×Q8—942no—
573C2×Q8—942no—
574C2×Q8—942no—
575C2×Q8—3762no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—472no—
580C2×D4—944no—
581C2×D4—944no—
582C2×D4—941no—
583C2×D4—942no—
584C2×D4—942no—
585C2×D4—3762no—
586C2×D4—3762no—
587C2×D4C23×D4712yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—82no—
593C22×C4—471no—
594C22×C4—471no—
595C22×C4—471no—
596C22×C4—472no—
597C22×C4—472no—
598C22×C4—944no—
599C22×C4—942no—
600C22×C4—942no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—941no—
604C22×C4—3762no—
605C22×C4D4×D4711yescharacteristic
606C22×C4D4×D4711yescharacteristic
607C22×C4C23×D4711yescharacteristic
608Q16—1884no—
609SD16—1884no—
610SD16—1884no—
611D8—1884no—
612M16—1884no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—472no—
616C2×C8—472no—
617C2×C8—942no—
618C2×C8—942no—
619C2×C8—1884no—
620C2×C8C23×D4712yes—
621C2×C8C23×D4712yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—474no—
627C4⋊C4—474no—
628C4⋊C4—472no—
629C4⋊C4—944no—
630C4⋊C4—944no—
631C4⋊C4—944no—
632C4⋊C4—944no—
633C4⋊C4—944no—
634C4⋊C4—941no—
635C4⋊C4C23×D4712yes—
636C4⋊C4C23×D4712yes—
637C4⋊C4C23×D4712yes—
638C22⋊C4—24no—
639C22⋊C4—474no—
640C22⋊C4—474no—
641C22⋊C4—944no—
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—944no—
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—84no—
670Q8—942no—
671Q8—942no—
672Q8—942no—
673Q8—942no—
674Q8—3764no—
675Q8—1882no—
676Q8—1882no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—942no—
681D4—942no—
682D4—3764no—
683D4—3764no—
684D4—1882no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—84no—
694C2×C4—472no—
695C2×C4—472no—
696C2×C4—472no—
697C2×C4—942no—
698C2×C4—942no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—944no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—942no—
706C2×C4—3764no—
707C2×C4—1882no—
708C2×C4—1882no—
709C2×C4—1882no—
710C2×C4C2×D4×D4712yes—
711C2×C4C2×D4×D4712yes—
712C2×C4C2×D4×D4711yescharacteristic
713C2×C4#1309407012yes—
714C2×C4#1309407212yes—
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#1568970312yes—
733C22#1568992912yes—
734C22#1568993312yes—
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#1568970312yes—
748C4C2×#1309407011yescharacteristic
749C4C2×#1309407211yescharacteristic
750C2—82no—
751C2—3762no—
752C2—1882no—
753C2#2025486014yesdirect product factor
754C2C2×#1568970311yescharacteristic
755C2C2×#1568992911yescharacteristic
756C2C2×#1568993311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#476C2
socleC23×C47C22×D4
prime radicalC2×#15689375C2
hypercenterC2×#476D47
hypocenterC47C2×#3263
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#15689747C2semidirect
2. C2×#15689738C2semidirect
3. #20254860C2direct (N × H)
4. C2×#15689407C2semidirect
5. C2×#15689405C2semidirect
6. C2×#15689412C2semidirect
7. C2×#15689382C2semidirect
9. C2×#15689353C2semidirect
10. C2×#15689351C2semidirect
11. C2×#15689346C2semidirect
12. C2×#15689344C2semidirect
13. C2×#15689338C2semidirect
14. C2×#15689337C2semidirect
15. C2×#15689148C2semidirect
16. C2×C47×#476C2semidirect
24. #15689747C22semidirect
26. #15689738C22semidirect
46. #15689412C22semidirect
47. #15689407C22semidirect
48. #15689405C22semidirect
49. #15689382C22semidirect
51. #15689353C22semidirect
52. #15689351C22semidirect
53. #15689346C22semidirect
54. #15689344C22semidirect
55. #15689338C22semidirect
56. #15689337C22semidirect
59. #15689148C22semidirect
71. C47×#476C22semidirect
378. C2×#476D47semidirect
389. C2×C47#3263semidirect
427. #476C2×D47semidirect
455. C47C2×#3263semidirect
753. C2#20254860direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897472
C2×#156897382
#202548602
C2×#156894072
C2×#156894052
C2×#156894122
C2×#156893822
C2×#156893752
C2×#156893532
C2×#156893512
C2×#156893462
C2×#156893442
C2×#156893382
C2×#156893372
C2×#156891482
C2×C47×#4762
C2×#326347