Finite Group Databasebeta

← C2×#20254476 #27087627

Subgroups — C2×#20254476 #27087627

Order 12032.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689692C211yesmaximal, characteristic, complemented
2#20254476C2116yesmaximal, direct product factor
3C2×#15689513C211yesmaximal, characteristic, complemented
4C2×#15689505C211yesmaximal, characteristic, complemented
5C2×#15689485C211yesmaximal, characteristic, complemented
6C2×#15689471C211yesmaximal, characteristic, complemented
7C2×#15689345C211yesmaximal, characteristic, complemented
8C2×#15689323C211yesmaximal, characteristic, complemented
9C2×#15689338C211yesmaximal, characteristic, complemented
10C2×#15689318C211yesmaximal, characteristic, complemented
11C2×#15689283C211yesmaximal, characteristic, complemented
12C2×#15689266C211yesmaximal, characteristic, complemented
13C2×#15689273C211yesmaximal, characteristic, complemented
14C2×#15689256C211yesmaximal, characteristic, complemented
15C2×#15689184C211yesmaximal, characteristic, complemented
16C2×C47×#542C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C22×#10625337C2211yescharacteristic, complemented
20C22×#10625335C2211yescharacteristic, complemented
21C22×#10625336C2211yescharacteristic
22C22×#10625336C2211yescharacteristic
23C22×#10625336C2211yescharacteristic, complemented
24C22×#10625334C2211yescharacteristic
25C22×#10625334C2211yescharacteristic
26C22×#10625334C2211yescharacteristic, complemented
27#15689692—24no—
28#15689692C2218yescomplemented
29C2×#13094021C2211yescharacteristic
30C2×#13094021C2211yescharacteristic
31C2×#13094012C2211yescharacteristic
32C2×#13094012C2211yescharacteristic
33C2×#13093999—21no—
34C2×#13093999—21no—
35C2×#13093994—21no—
36C2×#13093994—21no—
37#15689513C2218yescomplemented
38#15689505C2218yescomplemented
39#15689485C2218yescomplemented
40#15689471C2218yescomplemented
41#15689345C2218yescomplemented
42#15689338C2218yescomplemented
43#15689323C2218yescomplemented
44#15689318C2218yescomplemented
45#15689283C2218yescomplemented
46#15689273C2218yescomplemented
47#15689266C2218yescomplemented
48#15689256C2218yescomplemented
49#15689184C2218yescomplemented
50C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
51C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
52C2×#13093947C2211yescharacteristic, complemented
53C2×#13093947C2211yescharacteristic, complemented
54C2×#13093944C2211yescharacteristic
55C2×#13093944C2211yescharacteristic
56C2×#13093944C2211yescharacteristic
57C2×#13093944C2211yescharacteristic
58C2×#13093944C2211yescharacteristic, complemented
59C2×#13093944C2211yescharacteristic, complemented
60C2×C22⋊(C47⋊C8)C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×#13093935C2211yescharacteristic, complemented
63C2×C4×C47⋊C8C2211yescharacteristic, complemented
64C47×#542—24no—
65C47×#542C2218yescomplemented
66C2×C4⋊Q8×C47C2211yescharacteristic, complemented
67C2×#126×C47—21no—
68C2×#124×C47—21no—
69C2×#124×C47C2211yescharacteristic, complemented
70C2×#123×C47—21no—
71C2×C22⋊Q8×C47—21no—
72C2×C22⋊Q8×C47C2211yescharacteristic
73C2×#121×C47C2211yescharacteristic
74C2×C4×Q8×C47C2211yescharacteristic, complemented
75C2×C4×D4×C47C2211yescharacteristic, complemented
76C2×#117×C47C2211yescharacteristic
77C24×D47—21no—
78C2×#10625350—22no—
79C2×#10625350—42no—
80C2×#10625350—42no—
81C2×#10625350C2314yes—
82C22×Dic94C2311yescharacteristic
83C22×D188—21no—
84C22×D188—22no—
85C22×D188—21no—
86C22×D188—21no—
87C22×D188—21no—
88C22×D188—21no—
89C22×D188—42no—
90C22×D188—42no—
91C22×D188C2311yescharacteristic
92C22×D188C2311yescharacteristic
93C22×D188C2311yescharacteristic
94C22×D188C2314yes—
95C22×C22⋊D47—21no—
96C22×C4×D47—21no—
97C2×#10625337—42no—
98C2×#10625337C2314yescomplemented
99C2×#10625335—42no—
100C2×#10625335C2314yescomplemented
101C2×#10625336—42no—
102C2×#10625336—42no—
103C2×#10625336—42no—
104C2×#10625336C2314yes—
105C2×#10625336C2314yes—
106C2×#10625336C2314yescomplemented
107C2×#10625334—42no—
108C2×#10625334—42no—
109C2×#10625334—42no—
110C2×#10625334C2314yes—
111C2×#10625334C2314yes—
112C2×#10625334C2314yescomplemented
113C22×C47⋊C8C2311yescharacteristic
114C22×C47⋊C8C2311yescharacteristic
115C22×C47⋊C8C2311yescharacteristic
116C22×C47⋊C8C2311yescharacteristic
117#13094021—22no—
118#13094021—22no—
119#13094021C2314yes—
120#13094021C2314yes—
121#13094012—22no—
122#13094012—22no—
123#13094012C2314yes—
124#13094012C2314yes—
125#13093999—28no—
126#13093999—28no—
127#13093994—28no—
128#13093994—28no—
129C2×(C2×D47)⋊C4—21no—
130C2×(C2×D47)⋊C4—21no—
131C2×(C2×D47)⋊C4—21no—
132C2×(C2×D47)⋊C4—21no—
133C4⋊(C47⋊C8)C2314yescomplemented
134C4⋊(C47⋊C8)C2314yescomplemented
135#13093947C2314yescomplemented
136#13093947C2314yescomplemented
137#13093944C2314yes—
138#13093944C2314yes—
139#13093944C2314yes—
140#13093944C2314yes—
141#13093944C2314yescomplemented
142#13093944C2314yescomplemented
143C22⋊(C47⋊C8)C2314yes—
144C22⋊(C47⋊C8)C2314yes—
145#13093935C2314yescomplemented
146C4×C47⋊C8C2314yescomplemented
147C22×Q8×C47—21no—
148C22×Q8×C47C2311yescharacteristic
149C22×D4×C47—21no—
150C22×D4×C47C2311yescharacteristic
151C23×C4×C47—21no—
152C23×C4×C47C2311yescharacteristic
153C4⋊Q8×C47—22no—
154C4⋊Q8×C47C2314yescomplemented
155#126×C47—28no—
156#124×C47—28no—
157#124×C47—22no—
158#124×C47C2314yescomplemented
159#123×C47—28no—
160C22⋊Q8×C47—22no—
161C22⋊Q8×C47—28no—
162C22⋊Q8×C47C2314yes—
163#121×C47—22no—
164#121×C47C2314yes—
165C4×Q8×C47—22no—
166C4×Q8×C47C2314yescomplemented
167C4×D4×C47—22no—
168C4×D4×C47C2314yescomplemented
169#117×C47D414yes—
170#117×C47C2314yes—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47—21no—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47D411yescharacteristic
175C2×C4⋊C4×C47D411yescharacteristic
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182C2×C22⋊C4×C47—21no—
183C2×C22⋊C4×C47D411yescharacteristic
184C2×C22⋊C4×C47D411yescharacteristic
185C2×C42×C47—21no—
186C2×C42×C47C2311yescharacteristic
187C2×C42×C47C2311yescharacteristic
188C24×C47—21no—
189C24×C47C2×D411yescharacteristic
190C23×D47—21no—
191C23×D47—21no—
192C23×D47—21no—
193C23×D47—24no—
194C23×D47—44no—
195C23×D47—82no—
196C23×D47—82no—
197C2×Q8×C47—21no—
198C2×Q8×C47—24no—
199C2×Q8×C47—22no—
200C2×Q8×C47—22no—
201C2×Q8×C47—82no—
202C2×Q8×C47C2412yes—
203C2×D4×C47—24no—
204C2×D4×C47—21no—
205C2×D4×C47—22no—
206C2×D4×C47—22no—
207C2×D4×C47—82no—
208C2×D4×C47C2412yes—
209C22×C4×C47—22no—
210C22×C4×C47—22no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—24no—
215C22×C4×C47—82no—
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D412yes—
222C22×C4×C47C2412yes—
223C22×C4×C47C2411yescharacteristic
224C2×C22⋊D47—24no—
225C2×C22⋊D47—44no—
226C22×Dic47—21no—
227#10625350—44no—
228#10625350—44no—
229#10625350—48no—
230C2×D188—22no—
231C2×D188—22no—
232C2×D188—22no—
233C2×D188—22no—
234C2×D188—22no—
235C2×D188—22no—
236C2×D188—24no—
237C2×D188—21no—
238C2×D188—21no—
239C2×D188—21no—
240C2×D188—24no—
241C2×D188—24no—
242C2×D188—24no—
243C2×D188—24no—
244C2×D188—44no—
245C2×D188—44no—
246C2×D188—44no—
247C2×D188—48no—
248C2×D188—82no—
249C2×D188—82no—
250C2×D188—82no—
251C2×D188—82no—
252C2×D188C2412yes—
253C2×D188C2412yes—
254C2×D188C2412yes—
255C2×C4×D47—24no—
256C2×C4×D47—44no—
257C2×Dic94—22no—
258C2×Dic94—22no—
259C2×Dic94—21no—
260C2×Dic94C2412yes—
261C4⋊C4×C47—24no—
262C4⋊C4×C47—24no—
263C4⋊C4×C47—24no—
264C4⋊C4×C47—21no—
265C4⋊C4×C47—21no—
266C4⋊C4×C47C2×D414yes—
267C4⋊C4×C47C2×D414yes—
268C4⋊C4×C47C2412yes—
269C4⋊C4×C47C2412yes—
270C22⋊C4×C47—24no—
271C22⋊C4×C47—24no—
272C22⋊C4×C47—24no—
273C22⋊C4×C47—24no—
274C22⋊C4×C47—24no—
275C22⋊C4×C47C2×D414yes—
276C22⋊C4×C47C2×D414yes—
277C42×C47—24no—
278C42×C47C2×D412yes—
279C42×C47C2×D412yes—
280C42×C47C2412yes—
281C42×C47C2412yes—
282#10625337—44no—
283#10625336—44no—
284#10625336—44no—
285#10625336—44no—
286#10625335—44no—
287#10625334—44no—
288#10625334—44no—
289#10625334—44no—
290(C2×D47)⋊C4—24no—
291(C2×D47)⋊C4—24no—
292(C2×D47)⋊C4—24no—
293(C2×D47)⋊C4—24no—
294C2×C47⋊C8—22no—
295C2×C47⋊C8—22no—
296C2×C47⋊C8—22no—
297C2×C47⋊C8—22no—
298C2×C47⋊C8C2412yes—
299C2×C47⋊C8C2412yes—
300C2×C47⋊C8C2412yes—
301C2×C47⋊C8C2412yes—
302C23×C47—22no—
303C23×C47—22no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—42no—
307C23×C47—42no—
308C23×C47—42no—
309C23×C47C22×D412yes—
310C23×C47C22×D411yescharacteristic
311C22×D47—22no—
312C22×D47—22no—
313C22×D47—22no—
314C22×D47—48no—
315C22×D47—42no—
316C22×D47—42no—
317C22×D47—42no—
318C22×D47—42no—
319C22×D47—42no—
320C22×D47—42no—
321C22×D47—42no—
322C22×D47—42no—
323C22×D47—42no—
324C22×D47—84no—
325C22×D47—84no—
326C22×D47—816no—
327Q8×C47—22no—
328Q8×C47—22no—
329Q8×C47—42no—
330Q8×C47—84no—
331D4×C47—22no—
332D4×C47—22no—
333D4×C47—42no—
334D4×C47—84no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—24no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—42no—
347C2×C4×C47—42no—
348C2×C4×C47—42no—
349C2×C4×C47—84no—
350C2×C4×C47C22×D412yes—
351C2×C4×C47C22×D412yes—
352C2×C4×C47C22×D412yes—
353C2×C4×C47C22×D412yes—
354C2×C4×C47C22×D412yes—
355C2×C4×C47C22×D411yescharacteristic
356C2×C4×C47H(5,𝔽2)12yes—
357C2×C4×C47H(5,𝔽2)12yes—
358C2×C4×C47C2511yescharacteristic
359C22⋊D47—48no—
360C2×Dic47—22no—
361C2×Dic47—42no—
362D188—22no—
363D188—22no—
364D188—22no—
365D188—22no—
366D188—22no—
367D188—22no—
368D188—48no—
369D188—42no—
370D188—42no—
371D188—42no—
372D188—84no—
373D188—84no—
374D188—84no—
375D188—84no—
376C4×D47—48no—
377Dic94—22no—
378Dic94—22no—
379Dic94—42no—
380C47⋊C8—22no—
381C47⋊C8—22no—
382C47⋊C8—22no—
383C47⋊C8—22no—
384C2×#3224—471nomaximal, Sylow
385C22×C47—22no—
386C22×C47—22no—
387C22×C47—22no—
388C22×C47—44no—
389C22×C47—42no—
390C22×C47—42no—
391C22×C47—42no—
392C22×C47—84no—
393C22×C47#53512yes—
394C22×C47#57612yes—
395C22×C47#57712yes—
396C22×C47C23×D411yescharacteristic
397C2×D47—42no—
398C2×D47—42no—
399C2×D47—42no—
400C2×D47—42no—
401C2×D47—42no—
402C2×D47—42no—
403C2×D47—42no—
404C2×D47—42no—
405C2×D47—42no—
406C2×D47—816no—
407C2×D47—84no—
408C2×D47—84no—
409C2×D47—84no—
410C4×C47—22no—
411C4×C47—22no—
412C4×C47—22no—
413C4×C47—22no—
414C4×C47—22no—
415C4×C47—42no—
416C4×C47—42no—
417C4×C47—42no—
418C4×C47#53512yes—
419C4×C47C2×H(5,𝔽2)11yescharacteristic
420C4×C47C2×H(5,𝔽2)11yescharacteristic
421Dic47—42no—
422C2×#542D4711yescharacteristic, complemented
423C2×#535—471no—
424#3224—4716no—
425C2×#496—471no—
426C2×#495—471no—
427C2×#489—471no—
428C2×#486—471no—
429C2×#464—471no—
430C2×#460—471no—
431C2×#463—471no—
432C2×#459—471no—
433C2×#452—471no—
434C2×#449—471no—
435C2×#450—471no—
436C2×#447—471no—
437C2×#433—471no—
438C2×C47—42no—
439C2×C47—82no—
440C2×C47#322414yescomplemented
441C2×C47C2×#53511yescharacteristic
442C2×C47C2×#57611yescharacteristic
443C2×C47C2×#57711yescharacteristic
444D47—82no—
445D47—82no—
446D47—82no—
447C22×#41—471no—
448C23×D4—471no—
449C22×Q16—471no—
450C22×SD16—471no—
451C22×SD16—471no—
452C22×SD16—471no—
453C22×SD16—471no—
454C22×D8—471no—
455C22×D8—471no—
456C22×D8—471no—
457#542—24no—
458#542C2×D4718yescomplemented
459#535—478no—
460#535—944no—
461C2×C4⋊Q8C2×D4711yescharacteristic, complemented
462C2×#127—471no—
463C2×#127—471no—
464C2×#126—21no—
465C2×#124—21no—
466C2×#124—471no—
467C2×#124—471no—
468C2×#124C2×D4711yescharacteristic, complemented
469C2×#123—21no—
470C2×C22⋊Q8—21no—
471C2×C22⋊Q8C2×D4711yescharacteristic
472C2×#121—941no—
473C2×#121—941no—
474C2×#121C2×D4711yescharacteristic
475C2×#120—941no—
476C2×#120—941no—
477C2×C4×Q8C2×D4711yescharacteristic, complemented
478C2×C4×D4C2×D4711yescharacteristic, complemented
479C2×#117C2×D4711yescharacteristic
480#496—478no—
481#495—478no—
482#489—478no—
483#486—478no—
484#464—478no—
485#463—478no—
486#460—478no—
487#459—478no—
488#452—478no—
489#450—478no—
490#449—478no—
491#447—478no—
492#433—478no—
493C2×C4⋊C8—471no—
494C2×C4⋊C8—471no—
495C2×#103—471no—
496C2×#103—471no—
497C2×#102—471no—
498C2×#102—471no—
499C2×#102—471no—
500C2×#102—471no—
501C2×#102—471no—
502C2×#102—471no—
503C2×C22⋊C8—471no—
504C2×C22⋊C8—471no—
505C2×#97—471no—
506C2×C4×C8—471no—
507C47C2×#322411yescharacteristic, complemented, Sylow
508C25—941no—
509C2×#41—474no—
510C2×#41—942no—
511C2×#41—1882no—
512C2×#41—1882no—
513C22×Q8—21no—
514C22×Q8—471no—
515C22×Q8C22×D4711yescharacteristic
516C22×D4—21no—
517C22×D4—471no—
518C22×D4—471no—
519C22×D4—471no—
520C22×D4—474no—
521C22×D4—941no—
522C22×D4—941no—
523C22×D4—941no—
524C22×D4—941no—
525C22×D4—941no—
526C22×D4—941no—
527C22×D4—942no—
528C22×D4—1882no—
529C22×D4—1882no—
530C22×D4C22×D4711yescharacteristic
531C23×C4—21no—
532C23×C4—941no—
533C23×C4C22×D4711yescharacteristic
534C2×Q16—474no—
535C2×Q16—1882no—
536C2×SD16—474no—
537C2×SD16—474no—
538C2×SD16—474no—
539C2×SD16—474no—
540C2×SD16—1882no—
541C2×SD16—1882no—
542C2×SD16—1882no—
543C2×SD16—1882no—
544C2×D8—474no—
545C2×D8—474no—
546C2×D8—474no—
547C2×D8—1882no—
548C2×D8—1882no—
549C2×D8—1882no—
550C22×C8—471no—
551C22×C8—471no—
552C22×C8—471no—
553C22×C8—471no—
554C4⋊Q8—22no—
555C4⋊Q8C22×D4714yescomplemented
556#127—474no—
557#127—474no—
558#127—942no—
559#127—942no—
560#126—28no—
561#124—28no—
562#124—22no—
563#124—474no—
564#124—474no—
565#124—942no—
566#124—942no—
567#124C22×D4714yescomplemented
568#123—28no—
569C22⋊Q8—22no—
570C22⋊Q8—28no—
571C22⋊Q8C22×D4714yes—
572#121—22no—
573#121—948no—
574#121—948no—
575#121C22×D4714yes—
576#120—948no—
577#120—948no—
578C4×Q8—22no—
579C4×Q8C22×D4714yescomplemented
580C4×D4—22no—
581C4×D4C22×D4714yescomplemented
582#117C22⋊D4714yes—
583#117C22×D4714yes—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4C22⋊D4711yescharacteristic
588C2×C4⋊C4C22⋊D4711yescharacteristic
589C2×C4⋊C4C22×D4711yescharacteristic
590C2×C4⋊C4C22×D4711yescharacteristic
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—941no—
597C2×C22⋊C4—941no—
598C2×C22⋊C4—941no—
599C2×C22⋊C4—941no—
600C2×C22⋊C4C22⋊D4711yescharacteristic
601C2×C22⋊C4C22⋊D4711yescharacteristic
602C2×C42—21no—
603C2×C42C22×D4711yescharacteristic
604C2×C42C22×D4711yescharacteristic
605C4⋊C8—474no—
606C4⋊C8—474no—
607#103—474no—
608#103—474no—
609#102—474no—
610#102—474no—
611#102—474no—
612#102—474no—
613#102—474no—
614#102—474no—
615C22⋊C8—474no—
616C22⋊C8—474no—
617#97—474no—
618C4×C8—474no—
619C24—21no—
620C24—944no—
621C24—941no—
622C24—941no—
623C24—941no—
624C24—3762no—
625C24—3762no—
626C24—1884no—
627C24C2×C22⋊D4711yescharacteristic
628#41—1884no—
629#41—1884no—
630#41—1888no—
631C2×Q8—21no—
632C2×Q8—24no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—82no—
636C2×Q8—472no—
637C2×Q8—941no—
638C2×Q8—942no—
639C2×Q8—942no—
640C2×Q8C23×D4712yes—
641C2×D4—24no—
642C2×D4—21no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—82no—
646C2×D4—472no—
647C2×D4—472no—
648C2×D4—472no—
649C2×D4—944no—
650C2×D4—944no—
651C2×D4—944no—
652C2×D4—944no—
653C2×D4—944no—
654C2×D4—944no—
655C2×D4—941no—
656C2×D4—941no—
657C2×D4—941no—
658C2×D4—942no—
659C2×D4—942no—
660C2×D4—942no—
661C2×D4—942no—
662C2×D4—942no—
663C2×D4—942no—
664C2×D4—3762no—
665C2×D4—3762no—
666C2×D4—3762no—
667C2×D4—3762no—
668C2×D4—1884no—
669C2×D4—1884no—
670C2×D4—1884no—
671C2×D4—1888no—
672C2×D4—1884no—
673C2×D4C23×D4712yes—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—24no—
680C22×C4—82no—
681C22×C4—941no—
682C22×C4—944no—
683C22×C4—1884no—
684C22×C4C2×C22⋊D4712yes—
685C22×C4C2×C22⋊D4711yescharacteristic
686C22×C4C2×C22⋊D4711yescharacteristic
687C22×C4C2×C22⋊D4711yescharacteristic
688C22×C4C2×C22⋊D4711yescharacteristic
689C22×C4C2×C22⋊D4711yescharacteristic
690C22×C4C23×D4712yes—
691C22×C4C23×D4711yescharacteristic
692Q16—1884no—
693SD16—1884no—
694SD16—1884no—
695SD16—1884no—
696SD16—1884no—
697D8—1884no—
698D8—1884no—
699D8—1884no—
700C2×C8—472no—
701C2×C8—472no—
702C2×C8—472no—
703C2×C8—472no—
704C2×C8—942no—
705C2×C8—942no—
706C2×C8—942no—
707C2×C8—942no—
708C4⋊C4—24no—
709C4⋊C4—24no—
710C4⋊C4—24no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4C2×C22⋊D4714yes—
714C4⋊C4C2×C22⋊D4714yes—
715C4⋊C4C23×D4712yes—
716C4⋊C4C23×D4712yes—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—24no—
722C22⋊C4—944no—
723C22⋊C4—944no—
724C22⋊C4—944no—
725C22⋊C4—944no—
726C22⋊C4C2×C22⋊D4714yes—
727C22⋊C4C2×C22⋊D4714yes—
728C42—24no—
729C42C2×C22⋊D4712yes—
730C42C2×C22⋊D4712yes—
731C42C23×D4712yes—
732C42C23×D4712yes—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—942no—
741C23—942no—
742C23—942no—
743C23—3764no—
744C23—3764no—
745C23—37616no—
746C23—1888no—
747C23—1882no—
748C23—1882no—
749C23—1882no—
750C23—1882no—
751C23—1882no—
752C23—1882no—
753C23—1882no—
754C23—1882no—
755C23—1882no—
756C23C22×C22⋊D4712yes—
757C23C22×C22⋊D4711yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—42no—
761Q8—84no—
762Q8—942no—
763Q8—942no—
764Q8—1882no—
765D4—22no—
766D4—22no—
767D4—42no—
768D4—84no—
769D4—942no—
770D4—942no—
771D4—942no—
772D4—942no—
773D4—942no—
774D4—942no—
775D4—3764no—
776D4—3764no—
777D4—3764no—
778D4—3764no—
779D4—1888no—
780D4—1888no—
781D4—1882no—
782D4—1882no—
783D4—1882no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—84no—
799C2×C4—942no—
800C2×C4—1888no—
801C2×C4—1882no—
802C2×C4C22×C22⋊D4712yes—
803C2×C4C22×C22⋊D4712yes—
804C2×C4C22×C22⋊D4712yes—
805C2×C4C22×C22⋊D4712yes—
806C2×C4C22×C22⋊D4712yes—
807C2×C4C22×C22⋊D4711yescharacteristic
808C2×C4#1309407012yes—
809C2×C4#1309407012yes—
810C2×C4C24×D4711yescharacteristic
811C8—942no—
812C8—942no—
813C8—942no—
814C8—942no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—44no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—84no—
823C22—37616no—
824C22—3764no—
825C22—3764no—
826C22—3764no—
827C22—1882no—
828C22—1882no—
829C22—1882no—
830C22—1882no—
831C22—1882no—
832C22—1882no—
833C22—1882no—
834C22—1882no—
835C22—1882no—
836C22#1568968712yes—
837C22#1568992612yes—
838C22#1568993112yes—
839C22C23×C22⋊D4711yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—1882no—
849C4#1568968712yes—
850C4C2×#1309407011yescharacteristic
851C4C2×#1309407011yescharacteristic
852C2—42no—
853C2—82no—
854C2—3762no—
855C2—3762no—
856C2—3762no—
857C2#2025447614yesdirect product factor
858C2C2×#1568968711yescharacteristic
859C2C2×#1568992611yescharacteristic
860C2C2×#1568993111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#542C2
socleC23×C47C22×D4
hypercenterC2×#542D47
hypocenterC47C2×#3224
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#15689692C2semidirect
2. #20254476C2direct (N × H)
3. C2×#15689513C2semidirect
4. C2×#15689505C2semidirect
5. C2×#15689485C2semidirect
6. C2×#15689471C2semidirect
7. C2×#15689345C2semidirect
8. C2×#15689323C2semidirect
9. C2×#15689338C2semidirect
10. C2×#15689318C2semidirect
11. C2×#15689283C2semidirect
12. C2×#15689266C2semidirect
13. C2×#15689273C2semidirect
14. C2×#15689256C2semidirect
15. C2×#15689184C2semidirect
16. C2×C47×#542C2semidirect
19. C22×#10625337C22semidirect
20. C22×#10625335C22semidirect
23. C22×#10625336C22semidirect
26. C22×#10625334C22semidirect
28. #15689692C22semidirect
37. #15689513C22semidirect
38. #15689505C22semidirect
39. #15689485C22semidirect
40. #15689471C22semidirect
41. #15689345C22semidirect
42. #15689338C22semidirect
43. #15689323C22semidirect
44. #15689318C22semidirect
45. #15689283C22semidirect
46. #15689273C22semidirect
47. #15689266C22semidirect
48. #15689256C22semidirect
49. #15689184C22semidirect
50. C2×C4⋊(C47⋊C8)C22semidirect
51. C2×C4⋊(C47⋊C8)C22semidirect
52. C2×#13093947C22semidirect
53. C2×#13093947C22semidirect
58. C2×#13093944C22semidirect
59. C2×#13093944C22semidirect
62. C2×#13093935C22semidirect
63. C2×C4×C47⋊C8C22semidirect
65. C47×#542C22semidirect
66. C2×C4⋊Q8×C47C22semidirect
69. C2×#124×C47C22semidirect
74. C2×C4×Q8×C47C22semidirect
75. C2×C4×D4×C47C22semidirect
98. C2×#10625337C23semidirect
100. C2×#10625335C23semidirect
106. C2×#10625336C23semidirect
112. C2×#10625334C23semidirect
133. C4⋊(C47⋊C8)C23semidirect
134. C4⋊(C47⋊C8)C23semidirect
135. #13093947C23semidirect
136. #13093947C23semidirect
141. #13093944C23semidirect
142. #13093944C23semidirect
145. #13093935C23semidirect
146. C4×C47⋊C8C23semidirect
154. C4⋊Q8×C47C23semidirect
158. #124×C47C23semidirect
166. C4×Q8×C47C23semidirect
168. C4×D4×C47C23semidirect
422. C2×#542D47semidirect
440. C2×C47#3224semidirect
458. #542C2×D47semidirect
461. C2×C4⋊Q8C2×D47semidirect
468. C2×#124C2×D47semidirect
477. C2×C4×Q8C2×D47semidirect
478. C2×C4×D4C2×D47semidirect
507. C47C2×#3224semidirect
555. C4⋊Q8C22×D47semidirect
567. #124C22×D47semidirect
579. C4×Q8C22×D47semidirect
581. C4×D4C22×D47semidirect
857. C2#20254476direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896922
#202544762
C2×#156895132
C2×#156895052
C2×#156894852
C2×#156894712
C2×#156893452
C2×#156893232
C2×#156893382
C2×#156893182
C2×#156892832
C2×#156892662
C2×#156892732
C2×#156892562
C2×#156891842
C2×C47×#5422
C2×#322447