Finite Group Databasebeta

← C2×#20255348 #27092787

Subgroups — C2×#20255348 #27092787

Order 12032.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689776C211yesmaximal, characteristic, complemented
2C2×#15689766C211yesmaximal, characteristic, complemented
3#20255348C2116yesmaximal, direct product factor
4C2×#15689440C211yesmaximal, characteristic, complemented
5C2×#15689452C211yesmaximal, characteristic, complemented
6C2×#15689410C211yesmaximal, characteristic, complemented
7C2×#15689375C211yesmaximal, characteristic, complemented
8C2×#15689355C211yesmaximal, characteristic, complemented
9C2×#15689335C211yesmaximal, characteristic, complemented
10C2×#15689271C211yesmaximal, characteristic, complemented
11C2×#15689258C211yesmaximal, characteristic, complemented
12C2×#15689236C211yesmaximal, characteristic, complemented
13C2×#15689196C211yesmaximal, characteristic, complemented
14C2×#15689123C211yesmaximal, characteristic, complemented
15C2×#102×D47C211yesmaximal, characteristic, complemented
16C2×C47×#489C211yesmaximal, characteristic, complemented
17C22×#10625354—21no—
18C22×#10625354C2211yescharacteristic
19C22×D4×D47C2211yescharacteristic
20C22×#10625336C2211yescharacteristic, complemented
21C22×D376C2211yescharacteristic
22C22×#10625334C2211yescharacteristic
23C22×#10625324C2211yescharacteristic, complemented
24C22×C8×D47C2211yescharacteristic
25#15689776—24no—
26#15689776C2218yescomplemented
27#15689766—24no—
28#15689766C2218yescomplemented
29C2×#13094009—21no—
30C2×#13094009—21no—
31C2×#13094006—21no—
32C2×#13094000—21no—
33C2×#13094000C2211yescharacteristic
34C2×#13093999C2211yescharacteristic
35C2×#13093999C2211yescharacteristic, complemented
36C2×#13093997—21no—
37C2×#13093995C2211yescharacteristic
38C2×#13093994—21no—
39C2×C4×D188C2211yescharacteristic
40C2×C4×D188C2211yescharacteristic
41C2×C4×D188C2211yescharacteristic, complemented
42C2×C4⋊C4×D47C2211yescharacteristic
43C2×C4⋊C4×D47C2211yescharacteristic, complemented
44C2×C22⋊C4×D47—21no—
45#15689452C2218yescomplemented
46#15689440C2218yescomplemented
47#15689410C2218yescomplemented
48#15689375C2218yescomplemented
49#15689355C2218yescomplemented
50#15689335C2218yescomplemented
51#15689271C2218yescomplemented
52#15689258C2218yescomplemented
53#15689236C2218yescomplemented
54#15689196C2218yescomplemented
55C2×#13093956C2211yescharacteristic, complemented
56C2×#13093955C2211yescharacteristic, complemented
57C2×#13093955C2211yescharacteristic, complemented
58C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
59#15689123C2218yescomplemented
60C2×#13093948C2211yescharacteristic, complemented
61C2×#13093946C2211yescharacteristic
62C2×#13093946C2211yescharacteristic, complemented
63C2×#13093945C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66#102×D47C2218yescomplemented
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
69C2×C4⋊Q8×C47C2211yescharacteristic, complemented
70C2×#124×C47C2211yescharacteristic
71C47×#489C2218yescomplemented
72C2×#103×C47C2211yescharacteristic, complemented
73C2×#103×C47C2211yescharacteristic, complemented
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C2×#10625354—28no—
79C2×#10625354—22no—
80C2×#10625354—24no—
81C2×#10625354—42no—
82C2×#10625354—48no—
83C2×#10625354C2314yes—
84C22×D188—21no—
85C22×D188—21no—
86C22×D188—21no—
87C22×D188D411yescharacteristic
88C22×D188C2311yescharacteristic
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—21no—
91C22×C22⋊D47—21no—
92C2×D4×D47—24no—
93C2×D4×D47—22no—
94C2×D4×D47—42no—
95C2×D4×D47C2314yes—
96C22×C4×D47—21no—
97C22×C4×D47—21no—
98C22×C4×D47—21no—
99C22×C4×D47—21no—
100C22×C4×D47—21no—
101C22×C4×D47C2311yescharacteristic
102C22×C4×D47C2311yescharacteristic
103C2×#10625336—42no—
104C2×#10625336C2314yescomplemented
105C2×D376—24no—
106C2×D376C2314yes—
107C2×#10625334—42no—
108C2×#10625334C2314yes—
109C2×#10625324—42no—
110C2×#10625324C2314yescomplemented
111C22×C47⋊C8C2311yescharacteristic
112C22×C47⋊C8C2311yescharacteristic
113C2×C8×D47—42no—
114C2×C8×D47C2314yes—
115#13094009—28no—
116#13094009—28no—
117#13094006—28no—
118#13094000—22no—
119#13094000—28no—
120#13094000C2314yes—
121#13093999—22no—
122#13093999—22no—
123#13093999C2314yes—
124#13093999C2314yescomplemented
125#13093997—28no—
126#13093995—22no—
127#13093995C2314yes—
128#13093994—28no—
129C4×D188—22no—
130C4×D188—22no—
131C4×D188D414yes—
132C4×D188C2314yes—
133C4×D188C2314yes—
134C4×D188C2314yescomplemented
135C2×C4⋊Dic47D411yescharacteristic
136C2×C4⋊Dic47C2311yescharacteristic
137C2×C4⋊Dic47C2311yescharacteristic
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—21no—
140C2×Dic47⋊C4—21no—
141C4⋊C4×D47—22no—
142C4⋊C4×D47—22no—
143C4⋊C4×D47C2314yes—
144C4⋊C4×D47C2314yescomplemented
145C2×C22⋊Dic47—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×(C2×D47)⋊C4—21no—
150C2×(C2×D47)⋊C4—21no—
151C2×(C2×D47)⋊C4D411yescharacteristic
152C2×(C2×D47)⋊C4D411yescharacteristic
153C22⋊C4×D47—28no—
154#13093956C2314yescomplemented
155#13093955C2314yescomplemented
156#13093955C2314yescomplemented
157C4⋊(C47⋊C8)C2314yescomplemented
158#13093948C2314yescomplemented
159#13093946C2314yes—
160#13093946C2314yescomplemented
161#13093945C2314yes—
162#13093944C2314yes—
163#13093944C2314yes—
164(C2×D47)⋊C8C2314yes—
165(C2×D47)⋊C8C2314yescomplemented
166C22×Q8×C47—21no—
167C22×Q8×C47C2311yescharacteristic
168C22×D4×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170C22×C8×C47C2311yescharacteristic
171C4⋊Q8×C47—22no—
172C4⋊Q8×C47C2314yescomplemented
173#124×C47—22no—
174#124×C47C2314yes—
175C2×C4⋊C4×C47—21no—
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180C2×C42×C47C2311yescharacteristic
181#103×C47C2314yescomplemented
182#103×C47C2314yescomplemented
183#102×C47C2314yes—
184#102×C47C2314yes—
185#97×C47C2314yescomplemented
186C24×C47—21no—
187C23×D47—21no—
188C23×D47—21no—
189C23×D47—24no—
190C23×D47—44no—
191C23×D47—44no—
192C23×D47—82no—
193C23×D47C2×D411yescharacteristic
194C23×D47C2×D411yescharacteristic
195C2×Q8×C47—21no—
196C2×Q8×C47—24no—
197C2×Q8×C47—22no—
198C2×Q8×C47—22no—
199C2×Q8×C47—44no—
200C2×Q8×C47C2412yes—
201C2×D4×C47—21no—
202C2×D4×C47—22no—
203C2×D4×C47—22no—
204C2×D4×C47C2412yes—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2411yescharacteristic
211C2×C22⋊D47—24no—
212C2×C22⋊D47—24no—
213C2×C22⋊D47—44no—
214C2×C22⋊D47—82no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47C2×D411yescharacteristic
218C22×Dic47C2×D411yescharacteristic
219#10625354—28no—
220#10625354—44no—
221#10625354—48no—
222#10625354—432no—
223D4×D47—28no—
224D4×D47—44no—
225D4×D47—48no—
226C2×D188—24no—
227C2×D188—21no—
228C2×D188—22no—
229C2×D188—22no—
230C2×D188—22no—
231C2×D188—24no—
232C2×D188—24no—
233C2×D188—24no—
234C2×D188—21no—
235C2×D188—44no—
236C2×D188—44no—
237C2×D188—44no—
238C2×D188C2×D414yes—
239C2×D188#4114yescomplemented
240C2×D188C2412yes—
241C2×D188C2412yes—
242C2×C4×D47—22no—
243C2×C4×D47—22no—
244C2×C4×D47—22no—
245C2×C4×D47—22no—
246C2×C4×D47—24no—
247C2×C4×D47—24no—
248C2×C4×D47—24no—
249C2×C4×D47—24no—
250C2×C4×D47—24no—
251C2×C4×D47—44no—
252C2×C4×D47—44no—
253C2×C4×D47—44no—
254C2×C4×D47—44no—
255C2×C4×D47—82no—
256C2×C4×D47C2×D412yes—
257C2×C4×D47C2×D412yes—
258C2×C4×D47C2412yes—
259C2×C4×D47C2412yes—
260C2×C8×C47—22no—
261C2×C8×C47—22no—
262C2×C8×C47C2412yes—
263C2×C8×C47C2412yes—
264C4⋊C4×C47—24no—
265C4⋊C4×C47—21no—
266C4⋊C4×C47—21no—
267C4⋊C4×C47C2412yes—
268C4⋊C4×C47C2412yes—
269C22⋊C4×C47—24no—
270C22⋊C4×C47—24no—
271C42×C47C2×D412yes—
272C42×C47C2412yes—
273C22⋊Dic47—24no—
274#10625336—44no—
275#10625334—44no—
276(C2×D47)⋊C4—24no—
277(C2×D47)⋊C4—24no—
278(C2×D47)⋊C4—24no—
279(C2×D47)⋊C4—24no—
280(C2×D47)⋊C4—24no—
281(C2×D47)⋊C4C2×D414yes—
282(C2×D47)⋊C4C2×D414yes—
283C4⋊Dic47—21no—
284C4⋊Dic47—21no—
285C4⋊Dic47C2×D414yes—
286C4⋊Dic47C2412yes—
287C4⋊Dic47C2412yes—
288Dic47⋊C4—24no—
289Dic47⋊C4—24no—
290Dic47⋊C4—24no—
291C2×C47⋊C8—22no—
292C2×C47⋊C8—22no—
293C2×C47⋊C8C2412yes—
294C2×C47⋊C8C2412yes—
295D376—28no—
296#10625324—44no—
297C8×D47—44no—
298C23×C47—22no—
299C23×C47—42no—
300C23×C47—42no—
301C23×C47—42no—
302C23×C47C22×D411yescharacteristic
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—24no—
307C22×D47—22no—
308C22×D47—22no—
309C22×D47—22no—
310C22×D47—22no—
311C22×D47—48no—
312C22×D47—42no—
313C22×D47—42no—
314C22×D47—42no—
315C22×D47—42no—
316C22×D47—42no—
317C22×D47—48no—
318C22×D47—84no—
319C22×D47—816no—
320C22×D47AGL(1,ℤ/8)14yes—
321C22×D47C22×D412yes—
322C22×D47C22×D412yes—
323Q8×C47—22no—
324Q8×C47—22no—
325Q8×C47—48no—
326Q8×C47—42no—
327D4×C47—22no—
328D4×C47—22no—
329D4×C47—42no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—42no—
336C2×C4×C47—42no—
337C2×C4×C47—42no—
338C2×C4×C47C22×D412yes—
339C2×C4×C47C22×D412yes—
340C2×C4×C47C22×D411yescharacteristic
341C2×C4×C47C2×#4112yes—
342C2×C4×C47H(5,𝔽2)12yes—
343C2×C4×C47C2511yescharacteristic
344C22⋊D47—48no—
345C22⋊D47—84no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—22no—
349C2×Dic47—22no—
350C2×Dic47—42no—
351C2×Dic47—42no—
352C2×Dic47C22×D412yes—
353C2×Dic47C22×D412yes—
354D188—28no—
355D188—24no—
356D188—22no—
357D188—22no—
358D188—22no—
359D188—48no—
360D188—48no—
361D188—48no—
362D188—42no—
363D188C2×#4114yescomplemented
364C4×D47—24no—
365C4×D47—24no—
366C4×D47—22no—
367C4×D47—22no—
368C4×D47—22no—
369C4×D47—22no—
370C4×D47—48no—
371C4×D47—48no—
372C4×D47—48no—
373C4×D47—48no—
374C4×D47—84no—
375C8×C47—22no—
376C8×C47—22no—
377C47⋊C8—22no—
378C47⋊C8—22no—
379C2×#3306—471nomaximal, Sylow
380C22×C47—42no—
381C22×C47—42no—
382C22×C47—42no—
383C22×C47—84no—
384C22×C47#54612yes—
385C22×C47C2×AGL(1,ℤ/8)12yes—
386C22×C47#57712yes—
387C22×C47C23×D411yescharacteristic
388C2×D47—22no—
389C2×D47—28no—
390C2×D47—22no—
391C2×D47—22no—
392C2×D47—24no—
393C2×D47—22no—
394C2×D47—22no—
395C2×D47—44no—
396C2×D47—48no—
397C2×D47—42no—
398C2×D47—42no—
399C2×D47—42no—
400C2×D47—42no—
401C2×D47—42no—
402C2×D47—816no—
403C2×D47—84no—
404C2×D47C2×AGL(1,ℤ/8)14yes—
405C4×C47—22no—
406C4×C47—22no—
407C4×C47—42no—
408C4×C47—42no—
409C4×C47—42no—
410C4×C47#54612yes—
411C4×C47C22×#4111yescharacteristic
412C4×C47C2×H(5,𝔽2)11yescharacteristic
413Dic47—22no—
414Dic47—22no—
415Dic47—42no—
416Dic47—42no—
417C2×#547—471no—
418C2×#546—471no—
419#3306—4716no—
420C2×#489D4711yescharacteristic, complemented
421C2×#481—471no—
422C2×#483—471no—
423C2×#476—471no—
424C2×#469—471no—
425C2×#465—471no—
426C2×#463—471no—
427C2×#449—471no—
428C2×#447—471no—
429C2×#442—471no—
430C2×#435—471no—
431C2×#417—471no—
432C22×#102—471no—
433C2×C47—82no—
434C2×C47#330614yescomplemented
435C2×C47C2×#54611yescharacteristic
436C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
437C2×C47C2×#57711yescharacteristic
438D47—24no—
439D47—42no—
440D47—44no—
441D47—82no—
442C22×#41—471no—
443C22×#41—941no—
444C23×D4—471no—
445C22×SD16—471no—
446C22×D8—471no—
447C22×D8—471no—
448C22×M16—471no—
449C23×C8—471no—
450#547—478no—
451#547—944no—
452#546—478no—
453#546—944no—
454C2×C4⋊Q8C2×D4711yescharacteristic, complemented
455C2×#124C2×D4711yescharacteristic
456C2×#123—941no—
457C2×#123—941no—
458C2×#123—941no—
459C2×C22⋊Q8—471no—
460C2×C22⋊Q8—941no—
461C2×#121—471no—
462C2×#121—471no—
463C2×#121—471no—
464C2×#121—941no—
465C2×#120—941no—
466C2×C4×D4—471no—
467C2×C4×D4—471no—
468C2×C4×D4—471no—
469C22×C4⋊C4—471no—
470C22×C4⋊C4—471no—
471C22×C22⋊C4—941no—
472#489C2×D4718yescomplemented
473#483—478no—
474#481—478no—
475#476—478no—
476#469—478no—
477#465—478no—
478#463—478no—
479#449—478no—
480#447—478no—
481#442—478no—
482#435—478no—
483C2×#106—471no—
484C2×#106—471no—
485C2×#106—471no—
486C2×C4⋊C8—471no—
487#417—478no—
488C2×#103—471no—
489C2×#103C2×D4711yescharacteristic, complemented
490C2×#103C2×D4711yescharacteristic, complemented
491C2×#102—471no—
492C2×#102—471no—
493C2×#102—471no—
494C2×#102—471no—
495C2×#102—471no—
496C2×#102—478no—
497C2×#102C2×D4711yescharacteristic
498C2×#102C2×D4711yescharacteristic
499C2×C22⋊C8—471no—
500C2×C22⋊C8—471no—
501C2×#97C2×D4711yescharacteristic, complemented
502C47C2×#330611yescharacteristic, complemented, Sylow
503C25—941no—
504C2×#41—474no—
505C2×#41—942no—
506C2×#41—948no—
507C2×#41—944no—
508C2×#41—1882no—
509C2×#41—1888no—
510C22×Q8—21no—
511C22×Q8C22×D4711yescharacteristic
512C22×D4—474no—
513C22×D4—471no—
514C22×D4—471no—
515C22×D4—471no—
516C22×D4—941no—
517C22×D4—941no—
518C22×D4—941no—
519C22×D4—942no—
520C22×D4—941no—
521C22×D4—944no—
522C22×D4—941no—
523C22×D4—1882no—
524C22×D4C22×D4711yescharacteristic
525C23×C4—471no—
526C23×C4—471no—
527C23×C4—941no—
528C23×C4—941no—
529C23×C4—941no—
530C23×C4—941no—
531C23×C4—941no—
532C2×SD16—474no—
533C2×SD16—1882no—
534C2×D8—474no—
535C2×D8—474no—
536C2×D8—944no—
537C2×D8—1882no—
538C2×M16—474no—
539C2×M16—1882no—
540C22×C8—471no—
541C22×C8—471no—
542C22×C8—474no—
543C22×C8—1882no—
544C22×C8C22×D4711yescharacteristic
545C22×C8C22×D4711yescharacteristic
546C4⋊Q8—22no—
547C4⋊Q8C22×D4714yescomplemented
548#124—22no—
549#124C22×D4714yes—
550#123—948no—
551#123—948no—
552#123—948no—
553C22⋊Q8—474no—
554C22⋊Q8—948no—
555C22⋊Q8—942no—
556#121—474no—
557#121—474no—
558#121—474no—
559#121—948no—
560#121—942no—
561#121—942no—
562#121—942no—
563#120—948no—
564C4×D4—474no—
565C4×D4—474no—
566C4×D4—474no—
567C4×D4—474no—
568C4×D4—942no—
569C4×D4—942no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—471no—
572C2×C4⋊C4—471no—
573C2×C4⋊C4—471no—
574C2×C4⋊C4—474no—
575C2×C4⋊C4—474no—
576C2×C4⋊C4—942no—
577C2×C4⋊C4—942no—
578C2×C4⋊C4—941no—
579C2×C4⋊C4—941no—
580C2×C4⋊C4—941no—
581C2×C4⋊C4C22×D4711yescharacteristic
582C2×C4⋊C4C22×D4711yescharacteristic
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—471no—
586C2×C22⋊C4—471no—
587C2×C22⋊C4—948no—
588C2×C22⋊C4—941no—
589C2×C22⋊C4—941no—
590C2×C22⋊C4—941no—
591C2×C22⋊C4—941no—
592C2×C22⋊C4—941no—
593C2×C22⋊C4—941no—
594C2×C42C22×D4711yescharacteristic
595#106—474no—
596#106—474no—
597#106—474no—
598C4⋊C8—474no—
599#103—474no—
600#103C22×D4714yescomplemented
601#103C22×D4714yescomplemented
602#102—474no—
603#102—474no—
604#102—474no—
605#102—474no—
606#102—474no—
607#102C22×D4714yes—
608#102C22×D4714yes—
609C22⋊C8—474no—
610C22⋊C8—474no—
611#97C22×D4714yescomplemented
612C24—21no—
613C24—471no—
614C24—471no—
615C24—944no—
616C24—941no—
617C24—941no—
618C24—3762no—
619C24—1884no—
620C24—1884no—
621#41—948no—
622#41—1884no—
623#41—1888no—
624#41—18832no—
625C2×Q8—21no—
626C2×Q8—24no—
627C2×Q8—22no—
628C2×Q8—22no—
629C2×Q8—44no—
630C2×Q8C23×D4712yes—
631C2×D4—21no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—474no—
635C2×D4—474no—
636C2×D4—472no—
637C2×D4—472no—
638C2×D4—944no—
639C2×D4—944no—
640C2×D4—944no—
641C2×D4—944no—
642C2×D4—944no—
643C2×D4—948no—
644C2×D4—944no—
645C2×D4—941no—
646C2×D4—941no—
647C2×D4—942no—
648C2×D4—942no—
649C2×D4—942no—
650C2×D4—3762no—
651C2×D4—1884no—
652C2×D4—1884no—
653C2×D4—1884no—
654C2×D4—1884no—
655C2×D4—1888no—
656C2×D4—1884no—
657C2×D4C23×D4712yes—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—471no—
662C22×C4—471no—
663C22×C4—472no—
664C22×C4—472no—
665C22×C4—472no—
666C22×C4—472no—
667C22×C4—944no—
668C22×C4—944no—
669C22×C4—944no—
670C22×C4—942no—
671C22×C4—942no—
672C22×C4—942no—
673C22×C4—942no—
674C22×C4—941no—
675C22×C4—941no—
676C22×C4—944no—
677C22×C4—944no—
678C22×C4—3762no—
679C22×C4—1884no—
680C22×C4—1884no—
681C22×C4—1884no—
682C22×C4—1884no—
683C22×C4D4×D4711yescharacteristic
684C22×C4D4×D4711yescharacteristic
685C22×C4C23×D4711yescharacteristic
686SD16—1884no—
687D8—948no—
688D8—1884no—
689M16—1884no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—472no—
693C2×C8—472no—
694C2×C8—942no—
695C2×C8—942no—
696C2×C8—1884no—
697C2×C8C23×D4712yes—
698C2×C8C23×D4712yes—
699C4⋊C4—24no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—474no—
703C4⋊C4—472no—
704C4⋊C4—472no—
705C4⋊C4—944no—
706C4⋊C4—944no—
707C4⋊C4—944no—
708C4⋊C4—941no—
709C4⋊C4—941no—
710C4⋊C4C23×D4712yes—
711C4⋊C4C23×D4712yes—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—474no—
715C22⋊C4—474no—
716C22⋊C4—944no—
717C22⋊C4—944no—
718C22⋊C4—944no—
719C22⋊C4—944no—
720C22⋊C4—944no—
721C22⋊C4—944no—
722C42D4×D4712yes—
723C42C23×D4712yes—
724C23—22no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—474no—
729C23—472no—
730C23—472no—
731C23—942no—
732C23—942no—
733C23—942no—
734C23—944no—
735C23—942no—
736C23—942no—
737C23—942no—
738C23—942no—
739C23—3764no—
740C23—37616no—
741C23—1888no—
742C23—1888no—
743C23—1882no—
744C23—1882no—
745C23—1882no—
746C23—1882no—
747C23—1882no—
748C23C2×D4×D4711yescharacteristic
749Q8—22no—
750Q8—22no—
751Q8—48no—
752Q8—42no—
753D4—22no—
754D4—22no—
755D4—42no—
756D4—474no—
757D4—948no—
758D4—944no—
759D4—942no—
760D4—942no—
761D4—942no—
762D4—3764no—
763D4—1888no—
764D4—1888no—
765D4—1888no—
766D4—1888no—
767D4—1882no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—472no—
777C2×C4—472no—
778C2×C4—942no—
779C2×C4—942no—
780C2×C4—944no—
781C2×C4—944no—
782C2×C4—942no—
783C2×C4—942no—
784C2×C4—942no—
785C2×C4—942no—
786C2×C4—942no—
787C2×C4—942no—
788C2×C4—3764no—
789C2×C4—1888no—
790C2×C4—1888no—
791C2×C4—1888no—
792C2×C4—1888no—
793C2×C4—1882no—
794C2×C4—1882no—
795C2×C4C2×D4×D4712yes—
796C2×C4C2×D4×D4712yes—
797C2×C4C2×D4×D4711yescharacteristic
798C2×C4#41×D4712yes—
799C2×C4#1309407012yes—
800C2×C4C24×D4711yescharacteristic
801C8—22no—
802C8—22no—
803C8—942no—
804C8—942no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—84no—
809C22—474no—
810C22—942no—
811C22—942no—
812C22—948no—
813C22—942no—
814C22—944no—
815C22—942no—
816C22—942no—
817C22—37616no—
818C22—3764no—
819C22—1882no—
820C22—1882no—
821C22—1882no—
822C22—1882no—
823C22—1882no—
824C22—1884no—
825C22—1888no—
826C22#1568976612yes—
827C22AGL(1,ℤ/8)×D4712yes—
828C22#1568993212yes—
829C22C22×D4×D4711yescharacteristic
830C4—22no—
831C4—22no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—942no—
836C4—942no—
837C4—1882no—
838C4—1882no—
839C4#1568976612yes—
840C4C2×#41×D4711yescharacteristic
841C4C2×#1309407011yescharacteristic
842C2—82no—
843C2—944no—
844C2—3762no—
845C2—1882no—
846C2—1884no—
847C2#2025534814yesdirect product factor
848C2C2×#1568976611yescharacteristic
849C2C2×AGL(1,ℤ/8)×D4711yescharacteristic
850C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#489C2
socleC23×C47C22×D4
hypercenterC2×#489D47
hypocenterC47C2×#3306
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#15689776C2semidirect
2. C2×#15689766C2semidirect
3. #20255348C2direct (N × H)
4. C2×#15689440C2semidirect
5. C2×#15689452C2semidirect
6. C2×#15689410C2semidirect
7. C2×#15689375C2semidirect
8. C2×#15689355C2semidirect
9. C2×#15689335C2semidirect
10. C2×#15689271C2semidirect
11. C2×#15689258C2semidirect
12. C2×#15689236C2semidirect
13. C2×#15689196C2semidirect
14. C2×#15689123C2semidirect
15. C2×#102×D47C2semidirect
16. C2×C47×#489C2semidirect
20. C22×#10625336C22semidirect
23. C22×#10625324C22semidirect
26. #15689776C22semidirect
28. #15689766C22semidirect
35. C2×#13093999C22semidirect
41. C2×C4×D188C22semidirect
43. C2×C4⋊C4×D47C22semidirect
45. #15689452C22semidirect
46. #15689440C22semidirect
47. #15689410C22semidirect
48. #15689375C22semidirect
49. #15689355C22semidirect
50. #15689335C22semidirect
51. #15689271C22semidirect
52. #15689258C22semidirect
53. #15689236C22semidirect
54. #15689196C22semidirect
55. C2×#13093956C22semidirect
56. C2×#13093955C22semidirect
57. C2×#13093955C22semidirect
58. C2×C4⋊(C47⋊C8)C22semidirect
59. #15689123C22semidirect
60. C2×#13093948C22semidirect
62. C2×#13093946C22semidirect
66. #102×D47C22semidirect
68. C2×(C2×D47)⋊C8C22semidirect
69. C2×C4⋊Q8×C47C22semidirect
71. C47×#489C22semidirect
72. C2×#103×C47C22semidirect
73. C2×#103×C47C22semidirect
76. C2×#97×C47C22semidirect
104. C2×#10625336C23semidirect
110. C2×#10625324C23semidirect
124. #13093999C23semidirect
134. C4×D188C23semidirect
144. C4⋊C4×D47C23semidirect
154. #13093956C23semidirect
155. #13093955C23semidirect
156. #13093955C23semidirect
157. C4⋊(C47⋊C8)C23semidirect
158. #13093948C23semidirect
160. #13093946C23semidirect
165. (C2×D47)⋊C8C23semidirect
172. C4⋊Q8×C47C23semidirect
181. #103×C47C23semidirect
182. #103×C47C23semidirect
185. #97×C47C23semidirect
239. C2×D188#41semidirect
363. D188C2×#41semidirect
420. C2×#489D47semidirect
434. C2×C47#3306semidirect
454. C2×C4⋊Q8C2×D47semidirect
472. #489C2×D47semidirect
489. C2×#103C2×D47semidirect
490. C2×#103C2×D47semidirect
501. C2×#97C2×D47semidirect
502. C47C2×#3306semidirect
547. C4⋊Q8C22×D47semidirect
600. #103C22×D47semidirect
601. #103C22×D47semidirect
611. #97C22×D47semidirect
847. C2#20255348direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897762
C2×#156897662
#202553482
C2×#156894402
C2×#156894522
C2×#156894102
C2×#156893752
C2×#156893552
C2×#156893352
C2×#156892712
C2×#156892582
C2×#156892362
C2×#156891962
C2×#156891232
C2×#102×D472
C2×C47×#4892
C2×#330647