Finite Group Databasebeta

← C2×#20255583 #27093069

Subgroups — C2×#20255583 #27093069

Order 12032.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689769C211yesmaximal, characteristic, complemented
2#20255583C2116yesmaximal, direct product factor
3C2×#15689480C211yesmaximal, characteristic, complemented
4C2×#15689464C211yesmaximal, characteristic, complemented
5C2×#15689436C211yesmaximal, characteristic, complemented
6C2×#15689420C211yesmaximal, characteristic, complemented
7C2×#15689374C211yesmaximal, characteristic, complemented
8C2×#15689367C211yesmaximal, characteristic, complemented
9C2×#15689338C211yesmaximal, characteristic, complemented
10C2×#15689266C211yesmaximal, characteristic, complemented
11C2×#15689256C211yesmaximal, characteristic, complemented
12C2×C4×#10625334C211yesmaximal, characteristic, complemented
13C2×#15689201C211yesmaximal, characteristic, complemented
14C2×#15689122C211yesmaximal, characteristic, complemented
15C2×#15689127C211yesmaximal, characteristic, complemented
16C2×C47×#553C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C22×#10625335C2211yescharacteristic, complemented
20C22×#10625334C2211yescharacteristic
21C22×#10625334C2211yescharacteristic
22C22×#10625329C2211yescharacteristic
23C22×#10625329C2211yescharacteristic, complemented
24#15689769—24no—
25#15689769C2218yescomplemented
26C2×#13094012C2211yescharacteristic
27C2×#13094009—21no—
28C2×#13094003C2211yescharacteristic
29C2×#13093998C2211yescharacteristic
30C2×#13093997—21no—
31C2×#13093992—21no—
32C2×C4×D188C2211yescharacteristic
33C2×C22⋊C4×D47—21no—
34#15689480C2218yescomplemented
35#15689464C2218yescomplemented
36#15689436C2218yescomplemented
37#15689420C2218yescomplemented
38#15689374C2218yescomplemented
39#15689367C2218yescomplemented
40#15689338C2218yescomplemented
41#15689266C2218yescomplemented
42#15689256C2218yescomplemented
43C4×#10625334C2218yescomplemented
44#15689201C2218yescomplemented
45C2×#13093957C2211yescharacteristic, complemented
46C2×#13093957C2211yescharacteristic, complemented
47C2×#13093955C2211yescharacteristic, complemented
48C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
49#15689127C2218yescomplemented
50#15689122C2218yescomplemented
51C2×#13093947C2211yescharacteristic, complemented
52C2×#13093947C2211yescharacteristic, complemented
53C2×#13093947C2211yescharacteristic, complemented
54C2×#13093945C2211yescharacteristic, complemented
55C2×#13093944C2211yescharacteristic
56C2×#13093944C2211yescharacteristic
57C2×#13093944C2211yescharacteristic
58C2×#13093944C2211yescharacteristic
59C2×#13093944C2211yescharacteristic
60C2×#13093944C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
63C2×C4×C47⋊C8C2211yescharacteristic, complemented
64C47×#553—24no—
65C47×#553C2218yescomplemented
66C2×#126×C47—21no—
67C2×#125×C47C2211yescharacteristic, complemented
68C2×#123×C47—21no—
69C2×#121×C47—21no—
70C2×#121×C47C2211yescharacteristic
71C2×#121×C47C2211yescharacteristic, complemented
72C2×C4×D4×C47—21no—
73C2×C4×D4×C47C2211yescharacteristic
74C2×C4×D4×C47C2211yescharacteristic, complemented
75C2×#117×C47C2211yescharacteristic
76C22×C4⋊C4×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C2×#10625350—22no—
79C2×#10625350—24no—
80C2×#10625350—42no—
81C2×#10625350C2314yes—
82C22×Dic94C2311yescharacteristic
83C22×D188—24no—
84C22×D188—22no—
85C22×D188—21no—
86C22×D188—42no—
87C22×D188C2311yescharacteristic
88C22×D188C2314yes—
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—21no—
91C22×C22⋊D47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C2×#10625335—42no—
95C2×#10625335C2314yescomplemented
96C2×#10625334—24no—
97C2×#10625334—42no—
98C2×#10625334C2314yes—
99C2×#10625334C2314yes—
100C2×#10625329—42no—
101C2×#10625329—42no—
102C2×#10625329C2314yes—
103C2×#10625329C2314yescomplemented
104C22×C47⋊C8C2311yescharacteristic
105C22×C47⋊C8C2311yescharacteristic
106C22×C47⋊C8C2311yescharacteristic
107C22×C47⋊C8C2311yescharacteristic
108#13094012—22no—
109#13094012C2314yes—
110#13094009—28no—
111#13094003—22no—
112#13094003C2314yes—
113#13093998—22no—
114#13093998C2314yes—
115#13093997—28no—
116#13093992—28no—
117C4×D188—22no—
118C4×D188C2314yes—
119C2×C4⋊Dic47C2311yescharacteristic
120C2×Dic47⋊C4—21no—
121C2×C22⋊Dic47—21no—
122C2×(C2×D47)⋊C4—21no—
123C2×(C2×D47)⋊C4—21no—
124C2×(C2×D47)⋊C4—21no—
125C2×(C2×D47)⋊C4—21no—
126C22⋊C4×D47—28no—
127#13093957C2314yescomplemented
128#13093957C2314yescomplemented
129#13093955C2314yescomplemented
130C4⋊(C47⋊C8)C2314yescomplemented
131#13093947C2314yescomplemented
132#13093947C2314yescomplemented
133#13093947C2314yescomplemented
134#13093945C2314yescomplemented
135#13093944C2314yes—
136#13093944C2314yes—
137#13093944C2314yes—
138#13093944C2314yes—
139#13093944C2314yes—
140#13093944C2314yes—
141C22⋊(C47⋊C8)C2314yes—
142C22⋊(C47⋊C8)C2314yescomplemented
143C4×C47⋊C8C2314yescomplemented
144C22×D4×C47—21no—
145C22×D4×C47—21no—
146C22×D4×C47D411yescharacteristic
147C22×D4×C47C2311yescharacteristic
148C23×C4×C47—21no—
149C23×C4×C47—21no—
150C23×C4×C47C2311yescharacteristic
151C23×C4×C47C2311yescharacteristic
152#126×C47—28no—
153#125×C47—22no—
154#125×C47C2314yescomplemented
155#123×C47—28no—
156#121×C47—28no—
157#121×C47—22no—
158#121×C47—22no—
159#121×C47C2314yes—
160#121×C47C2314yescomplemented
161C4×D4×C47—28no—
162C4×D4×C47—22no—
163C4×D4×C47D414yes—
164C4×D4×C47C2314yes—
165C4×D4×C47C2314yescomplemented
166#117×C47—22no—
167#117×C47C2314yes—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47—22no—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47D411yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47C2314yescomplemented
177C2×C22⋊C4×C47—21no—
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47D411yescharacteristic
182C2×C22⋊C4×C47D411yescharacteristic
183C2×C42×C47—21no—
184C2×C42×C47C2311yescharacteristic
185C24×C47—21no—
186C24×C47C2×D411yescharacteristic
187C24×C47C2×D411yescharacteristic
188C23×D47—21no—
189C23×D47—21no—
190C23×D47—24no—
191C23×D47—44no—
192C23×D47—44no—
193C23×D47—82no—
194C2×D4×C47—24no—
195C2×D4×C47—24no—
196C2×D4×C47—21no—
197C2×D4×C47—22no—
198C2×D4×C47—22no—
199C2×D4×C47—42no—
200C2×D4×C47—44no—
201C2×D4×C47—82no—
202C2×D4×C47C2×D414yes—
203C2×D4×C47C2412yes—
204C22×C4×C47—22no—
205C22×C4×C47—22no—
206C22×C4×C47—22no—
207C22×C4×C47—22no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—24no—
212C22×C4×C47—24no—
213C22×C4×C47—82no—
214C22×C4×C47—82no—
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D412yes—
220C22×C4×C47C2×D412yes—
221C22×C4×C47C2412yes—
222C22×C4×C47C2412yes—
223C22×C4×C47C2411yescharacteristic
224C2×C22⋊D47—24no—
225C2×C22⋊D47—24no—
226C2×C22⋊D47—44no—
227C2×C22⋊D47—82no—
228C22×Dic47—21no—
229C22×Dic47—21no—
230#10625350—28no—
231#10625350—44no—
232#10625350—48no—
233C2×D188—21no—
234C2×D188—22no—
235C2×D188—22no—
236C2×D188—22no—
237C2×D188—28no—
238C2×D188—24no—
239C2×D188—21no—
240C2×D188—44no—
241C2×D188—48no—
242C2×D188—44no—
243C2×D188#4114yes—
244C2×D188C2412yes—
245C2×D188C2412yes—
246C2×C4×D47—24no—
247C2×C4×D47—24no—
248C2×C4×D47—44no—
249C2×C4×D47—82no—
250C2×Dic94—22no—
251C2×Dic94—22no—
252C2×Dic94—21no—
253C2×Dic94C2412yes—
254C4⋊C4×C47—21no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47—24no—
257C4⋊C4×C47—24no—
258C4⋊C4×C47—24no—
259C4⋊C4×C47—21no—
260C4⋊C4×C47C2×D414yes—
261C4⋊C4×C47C2412yes—
262C4⋊C4×C47C2412yes—
263C4⋊C4×C47C2412yes—
264C22⋊C4×C47—24no—
265C22⋊C4×C47—24no—
266C22⋊C4×C47—24no—
267C22⋊C4×C47—24no—
268C22⋊C4×C47C2×D414yes—
269C22⋊C4×C47C2×D414yes—
270C42×C47—24no—
271C42×C47C2×D412yes—
272C42×C47C2412yes—
273C22⋊Dic47—24no—
274#10625335—44no—
275#10625334—28no—
276#10625334—44no—
277(C2×D47)⋊C4—24no—
278(C2×D47)⋊C4—24no—
279(C2×D47)⋊C4—24no—
280(C2×D47)⋊C4—24no—
281C4⋊Dic47—21no—
282C4⋊Dic47C2412yes—
283Dic47⋊C4—24no—
284#10625329—44no—
285#10625329—44no—
286C2×C47⋊C8—22no—
287C2×C47⋊C8—22no—
288C2×C47⋊C8—22no—
289C2×C47⋊C8—22no—
290C2×C47⋊C8C2412yes—
291C2×C47⋊C8C2412yes—
292C2×C47⋊C8C2412yes—
293C2×C47⋊C8C2412yes—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—22no—
300C23×C47—22no—
301C23×C47—42no—
302C23×C47—42no—
303C23×C47—42no—
304C23×C47C22×D412yes—
305C23×C47C22×D412yes—
306C23×C47C22×D411yescharacteristic
307C22×D47—24no—
308C22×D47—22no—
309C22×D47—22no—
310C22×D47—48no—
311C22×D47—42no—
312C22×D47—42no—
313C22×D47—48no—
314C22×D47—42no—
315C22×D47—42no—
316C22×D47—42no—
317C22×D47—84no—
318C22×D47—816no—
319D4×C47—22no—
320D4×C47—22no—
321D4×C47—44no—
322D4×C47—48no—
323D4×C47—42no—
324D4×C47—84no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—24no—
330C2×C4×C47—24no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—42no—
339C2×C4×C47—42no—
340C2×C4×C47—42no—
341C2×C4×C47—84no—
342C2×C4×C47—84no—
343C2×C4×C47C22×D412yes—
344C2×C4×C47C22×D412yes—
345C2×C4×C47C22×D412yes—
346C2×C4×C47C22×D412yes—
347C2×C4×C47C22×D411yescharacteristic
348C2×C4×C47C2×#4112yes—
349C2×C4×C47H(5,𝔽2)12yes—
350C2×C4×C47C2511yescharacteristic
351C22⋊D47—48no—
352C22⋊D47—84no—
353C2×Dic47—22no—
354C2×Dic47—22no—
355C2×Dic47—42no—
356C2×Dic47—42no—
357D188—24no—
358D188—22no—
359D188—22no—
360D188—22no—
361D188—48no—
362D188—42no—
363D188C2×#4114yes—
364C4×D47—48no—
365C4×D47—84no—
366Dic94—22no—
367Dic94—22no—
368Dic94—42no—
369C47⋊C8—22no—
370C47⋊C8—22no—
371C47⋊C8—22no—
372C47⋊C8—22no—
373C2×#3322—471nomaximal, Sylow
374C22×C47—22no—
375C22×C47—22no—
376C22×C47—22no—
377C22×C47—22no—
378C22×C47—22no—
379C22×C47—22no—
380C22×C47—44no—
381C22×C47—44no—
382C22×C47—42no—
383C22×C47—42no—
384C22×C47—42no—
385C22×C47—84no—
386C22×C47#54612yes—
387C22×C47#57512yes—
388C22×C47#57612yes—
389C22×C47C23×D411yescharacteristic
390C2×D47—24no—
391C2×D47—48no—
392C2×D47—42no—
393C2×D47—42no—
394C2×D47—42no—
395C2×D47—42no—
396C2×D47—42no—
397C2×D47—816no—
398C2×D47—84no—
399C4×C47—22no—
400C4×C47—22no—
401C4×C47—22no—
402C4×C47—22no—
403C4×C47—42no—
404C4×C47—42no—
405C4×C47—42no—
406C4×C47#54612yes—
407C4×C47C22×#4111yescharacteristic
408C4×C47C2×H(5,𝔽2)11yescharacteristic
409Dic47—42no—
410Dic47—42no—
411C2×#553D4711yescharacteristic, complemented
412C2×#546—471no—
413#3322—4716no—
414C2×#488—471no—
415C2×#485—471no—
416C2×#480—471no—
417C2×#478—471no—
418C2×#469—471no—
419C2×#468—471no—
420C2×#463—471no—
421C2×#449—471no—
422C2×#447—471no—
423C2×C4×D8—471no—
424C2×#436—471no—
425C2×#417—471no—
426C2×#418—471no—
427C2×C47—42no—
428C2×C47—42no—
429C2×C47—82no—
430C2×C47#332214yescomplemented
431C2×C47C2×#54611yescharacteristic
432C2×C47C2×#57511yescharacteristic
433C2×C47C2×#57611yescharacteristic
434D47—44no—
435D47—82no—
436C22×#41—471no—
437C23×D4—471no—
438C22×SD16—471no—
439C22×D8—471no—
440C22×D8—471no—
441C22×M16—471no—
442C22×M16—471no—
443#553—24no—
444#553C2×D4718yescomplemented
445#546—478no—
446#546—944no—
447C2×#126—21no—
448C2×#125C2×D4711yescharacteristic, complemented
449C2×#124—471no—
450C2×#123—21no—
451C2×#123—941no—
452C2×C22⋊Q8—471no—
453C2×#121—21no—
454C2×#121—471no—
455C2×#121—941no—
456C2×#121C2×D4711yescharacteristic
457C2×#121C2×D4711yescharacteristic, complemented
458C2×#120—941no—
459C2×C4×D4—21no—
460C2×C4×D4—471no—
461C2×C4×D4C2×D4711yescharacteristic
462C2×C4×D4C2×D4711yescharacteristic, complemented
463C2×#117C2×D4711yescharacteristic
464C22×C4⋊C4C2×D4711yescharacteristic, complemented
465C22×C22⋊C4—941no—
466#488—478no—
467#485—478no—
468#480—478no—
469#478—478no—
470#469—478no—
471#468—478no—
472#463—478no—
473#449—478no—
474#447—478no—
475C4×D8—478no—
476#436—478no—
477C2×#107—471no—
478C2×#107—471no—
479C2×#106—471no—
480C2×C4⋊C8—471no—
481#418—478no—
482#417—478no—
483C2×#103—471no—
484C2×#103—471no—
485C2×#103—471no—
486C2×#102—471no—
487C2×#102—471no—
488C2×#102—471no—
489C2×#102—471no—
490C2×#102—471no—
491C2×#102—471no—
492C2×#102—471no—
493C2×C22⋊C8—471no—
494C2×C22⋊C8—471no—
495C2×C4×C8—471no—
496C47C2×#332211yescharacteristic, complemented, Sylow
497C25—941no—
498C2×#41—474no—
499C2×#41—944no—
500C2×#41—942no—
501C2×#41—1882no—
502C22×Q8—471no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—471no—
506C22×D4—471no—
507C22×D4—474no—
508C22×D4—944no—
509C22×D4—941no—
510C22×D4—941no—
511C22×D4—941no—
512C22×D4—942no—
513C22×D4—1882no—
514C22×D4C22⋊D4711yescharacteristic
515C22×D4C22×D4711yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—941no—
519C23×C4—941no—
520C23×C4C22×D4711yescharacteristic
521C23×C4C22×D4711yescharacteristic
522C2×SD16—474no—
523C2×SD16—1882no—
524C2×D8—474no—
525C2×D8—474no—
526C2×D8—944no—
527C2×D8—1882no—
528C2×M16—474no—
529C2×M16—474no—
530C2×M16—1882no—
531C2×M16—1882no—
532C22×C8—471no—
533C22×C8—471no—
534C22×C8—471no—
535C22×C8—471no—
536#126—28no—
537#125—22no—
538#125C22×D4714yescomplemented
539#124—474no—
540#124—942no—
541#123—28no—
542#123—948no—
543C22⋊Q8—474no—
544C22⋊Q8—942no—
545#121—28no—
546#121—22no—
547#121—22no—
548#121—474no—
549#121—942no—
550#121—948no—
551#121C22×D4714yes—
552#121C22×D4714yescomplemented
553#120—948no—
554C4×D4—28no—
555C4×D4—22no—
556C4×D4—474no—
557C4×D4—942no—
558C4×D4C22⋊D4714yes—
559C4×D4C22×D4714yes—
560C4×D4C22×D4714yescomplemented
561#117—22no—
562#117C22×D4714yes—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—471no—
568C2×C4⋊C4—941no—
569C2×C4⋊C4C22⋊D4711yescharacteristic
570C2×C4⋊C4C22×D4711yescharacteristic
571C2×C4⋊C4C22×D4711yescharacteristic
572C2×C4⋊C4C22×D4711yescharacteristic
573C2×C4⋊C4C22×D4714yescomplemented
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—941no—
579C2×C22⋊C4—941no—
580C2×C22⋊C4—941no—
581C2×C22⋊C4—941no—
582C2×C22⋊C4—941no—
583C2×C22⋊C4—948no—
584C2×C22⋊C4C22⋊D4711yescharacteristic
585C2×C22⋊C4C22⋊D4711yescharacteristic
586C2×C42—21no—
587C2×C42C22×D4711yescharacteristic
588#107—474no—
589#107—474no—
590#106—474no—
591C4⋊C8—474no—
592#103—474no—
593#103—474no—
594#103—474no—
595#102—474no—
596#102—474no—
597#102—474no—
598#102—474no—
599#102—474no—
600#102—474no—
601#102—474no—
602C22⋊C8—474no—
603C22⋊C8—474no—
604C4×C8—474no—
605C24—21no—
606C24—941no—
607C24—944no—
608C24—941no—
609C24—3762no—
610C24—1884no—
611C24—1884no—
612C24C2×C22⋊D4711yescharacteristic
613C24C2×C22⋊D4711yescharacteristic
614#41—948no—
615#41—1884no—
616#41—1888no—
617C2×Q8—472no—
618C2×Q8—941no—
619C2×Q8—942no—
620C2×Q8—942no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—42no—
627C2×D4—44no—
628C2×D4—82no—
629C2×D4—474no—
630C2×D4—472no—
631C2×D4—472no—
632C2×D4—948no—
633C2×D4—944no—
634C2×D4—944no—
635C2×D4—941no—
636C2×D4—944no—
637C2×D4—941no—
638C2×D4—942no—
639C2×D4—942no—
640C2×D4—942no—
641C2×D4—3762no—
642C2×D4—1884no—
643C2×D4—1888no—
644C2×D4—1884no—
645C2×D4—1884no—
646C2×D4C2×C22⋊D4714yes—
647C2×D4C23×D4712yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—82no—
658C22×C4—82no—
659C22×C4—941no—
660C22×C4—941no—
661C22×C4—944no—
662C22×C4—944no—
663C22×C4—3762no—
664C22×C4—1884no—
665C22×C4C2×C22⋊D4712yes—
666C22×C4C2×C22⋊D4712yes—
667C22×C4C2×C22⋊D4711yescharacteristic
668C22×C4C2×C22⋊D4711yescharacteristic
669C22×C4C2×C22⋊D4711yescharacteristic
670C22×C4C2×C22⋊D4711yescharacteristic
671C22×C4C23×D4712yes—
672C22×C4C23×D4712yes—
673C22×C4C23×D4711yescharacteristic
674SD16—1884no—
675D8—948no—
676D8—1884no—
677M16—1884no—
678M16—1884no—
679C2×C8—472no—
680C2×C8—472no—
681C2×C8—472no—
682C2×C8—472no—
683C2×C8—942no—
684C2×C8—942no—
685C2×C8—942no—
686C2×C8—942no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—21no—
693C4⋊C4—472no—
694C4⋊C4—944no—
695C4⋊C4—941no—
696C4⋊C4C2×C22⋊D4714yes—
697C4⋊C4C23×D4712yes—
698C4⋊C4C23×D4712yes—
699C4⋊C4C23×D4712yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—944no—
705C22⋊C4—944no—
706C22⋊C4—944no—
707C22⋊C4—944no—
708C22⋊C4—944no—
709C22⋊C4C2×C22⋊D4714yes—
710C22⋊C4C2×C22⋊D4714yes—
711C42—24no—
712C42C2×C22⋊D4712yes—
713C42C23×D4712yes—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—944no—
725C23—942no—
726C23—942no—
727C23—3764no—
728C23—37616no—
729C23—1888no—
730C23—1888no—
731C23—1882no—
732C23—1882no—
733C23—1882no—
734C23—1882no—
735C23—1882no—
736C23C22×C22⋊D4712yes—
737C23C22×C22⋊D4712yes—
738C23C22×C22⋊D4711yescharacteristic
739Q8—942no—
740Q8—942no—
741Q8—1882no—
742D4—22no—
743D4—22no—
744D4—44no—
745D4—48no—
746D4—42no—
747D4—84no—
748D4—474no—
749D4—944no—
750D4—942no—
751D4—942no—
752D4—942no—
753D4—3764no—
754D4—1888no—
755D4—1888no—
756D4—1882no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4—942no—
776C2×C4—942no—
777C2×C4—3764no—
778C2×C4—1888no—
779C2×C4—1882no—
780C2×C4—1882no—
781C2×C4C22×C22⋊D4712yes—
782C2×C4C22×C22⋊D4712yes—
783C2×C4C22×C22⋊D4712yes—
784C2×C4C22×C22⋊D4712yes—
785C2×C4C22×C22⋊D4711yescharacteristic
786C2×C4#41×D4712yes—
787C2×C4#1309407012yes—
788C2×C4C24×D4711yescharacteristic
789C8—942no—
790C8—942no—
791C8—942no—
792C8—942no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—44no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—84no—
805C22—944no—
806C22—37616no—
807C22—3764no—
808C22—1882no—
809C22—1882no—
810C22—1882no—
811C22—1882no—
812C22—1882no—
813C22—1888no—
814C22#1568976112yes—
815C22#1568992112yes—
816C22#1568992612yes—
817C22C23×C22⋊D4711yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—1882no—
826C4—1882no—
827C4#1568976112yes—
828C4C2×#41×D4711yescharacteristic
829C4C2×#1309407011yescharacteristic
830C2—42no—
831C2—42no—
832C2—82no—
833C2—3762no—
834C2—1884no—
835C2#2025558314yesdirect product factor
836C2C2×#1568976111yescharacteristic
837C2C2×#1568992111yescharacteristic
838C2C2×#1568992611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#553C2
socleC23×C47C22×D4
hypercenterC2×#553D47
hypocenterC47C2×#3322
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#15689769C2semidirect
2. #20255583C2direct (N × H)
3. C2×#15689480C2semidirect
4. C2×#15689464C2semidirect
5. C2×#15689436C2semidirect
6. C2×#15689420C2semidirect
7. C2×#15689374C2semidirect
8. C2×#15689367C2semidirect
9. C2×#15689338C2semidirect
10. C2×#15689266C2semidirect
11. C2×#15689256C2semidirect
12. C2×C4×#10625334C2semidirect
13. C2×#15689201C2semidirect
14. C2×#15689122C2semidirect
15. C2×#15689127C2semidirect
16. C2×C47×#553C2semidirect
19. C22×#10625335C22semidirect
23. C22×#10625329C22semidirect
25. #15689769C22semidirect
34. #15689480C22semidirect
35. #15689464C22semidirect
36. #15689436C22semidirect
37. #15689420C22semidirect
38. #15689374C22semidirect
39. #15689367C22semidirect
40. #15689338C22semidirect
41. #15689266C22semidirect
42. #15689256C22semidirect
43. C4×#10625334C22semidirect
44. #15689201C22semidirect
45. C2×#13093957C22semidirect
46. C2×#13093957C22semidirect
47. C2×#13093955C22semidirect
48. C2×C4⋊(C47⋊C8)C22semidirect
49. #15689127C22semidirect
50. #15689122C22semidirect
51. C2×#13093947C22semidirect
52. C2×#13093947C22semidirect
53. C2×#13093947C22semidirect
54. C2×#13093945C22semidirect
62. C2×C22⋊(C47⋊C8)C22semidirect
63. C2×C4×C47⋊C8C22semidirect
65. C47×#553C22semidirect
67. C2×#125×C47C22semidirect
71. C2×#121×C47C22semidirect
74. C2×C4×D4×C47C22semidirect
76. C22×C4⋊C4×C47C22semidirect
95. C2×#10625335C23semidirect
103. C2×#10625329C23semidirect
127. #13093957C23semidirect
128. #13093957C23semidirect
129. #13093955C23semidirect
130. C4⋊(C47⋊C8)C23semidirect
131. #13093947C23semidirect
132. #13093947C23semidirect
133. #13093947C23semidirect
134. #13093945C23semidirect
142. C22⋊(C47⋊C8)C23semidirect
143. C4×C47⋊C8C23semidirect
154. #125×C47C23semidirect
160. #121×C47C23semidirect
165. C4×D4×C47C23semidirect
176. C2×C4⋊C4×C47C23semidirect
411. C2×#553D47semidirect
430. C2×C47#3322semidirect
444. #553C2×D47semidirect
448. C2×#125C2×D47semidirect
457. C2×#121C2×D47semidirect
462. C2×C4×D4C2×D47semidirect
464. C22×C4⋊C4C2×D47semidirect
496. C47C2×#3322semidirect
538. #125C22×D47semidirect
552. #121C22×D47semidirect
560. C4×D4C22×D47semidirect
573. C2×C4⋊C4C22×D47semidirect
835. C2#20255583direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897692
#202555832
C2×#156894802
C2×#156894642
C2×#156894362
C2×#156894202
C2×#156893742
C2×#156893672
C2×#156893382
C2×#156892662
C2×#156892562
C2×C4×#106253342
C2×#156892012
C2×#156891222
C2×#156891272
C2×C47×#5532
C2×#332247