Finite Group Databasebeta

← C2×#20253627 #27084568

Subgroups — C2×#20253627 #27084568

Order 12032.

2338 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689726C211yesmaximal, characteristic, complemented
2C2×#15689597C211yesmaximal, characteristic, complemented
3#20253627C2116yesmaximal, direct product factor
4C2×#15689447C211yesmaximal, characteristic, complemented
5C2×#15689426C211yesmaximal, characteristic, complemented
6C2×#15689422C211yesmaximal, characteristic, complemented
7C2×#15689317C211yesmaximal, characteristic, complemented
8C2×#15689317C211yesmaximal, characteristic, complemented
9C2×#15689259C211yesmaximal, characteristic, complemented
10C2×#15689256C211yesmaximal, characteristic, complemented
11C2×#15689234C211yesmaximal, characteristic, complemented
12C2×#15689232C211yesmaximal, characteristic, complemented
13C2×#15689205C211yesmaximal, characteristic, complemented
14C2×#15689203C211yesmaximal, characteristic, complemented
15C2×#15689181C211yesmaximal, characteristic, complemented
16C2×C47×#482C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C22×D376C2211yescharacteristic
19C22×D376C2211yescharacteristic
20C22×#10625334C2211yescharacteristic
21C22×#10625334C2211yescharacteristic
22#15689726—24no—
23#15689726C2218yescomplemented
24C2×#13094020C2211yescharacteristic, complemented
25C2×#13094015C2211yescharacteristic, complemented
26C2×#13094008—21no—
27C2×#13094006—21no—
28C2×#13093998C2211yescharacteristic
29C2×#13093996—21no—
30C2×#13093995—21no—
31#15689597—24no—
32#15689597C2218yescomplemented
33C2×C4×D188—21no—
34C2×C4×D188—21no—
35C2×D4×Dic47C2211yescharacteristic, complemented
36C2×#13093986C2211yescharacteristic
37C2×#13093986C2211yescharacteristic
38C2×#13093986C2211yescharacteristic
39C2×#13093986C2211yescharacteristic
40C2×#13093986C2211yescharacteristic, complemented
41C2×#13093983C2211yescharacteristic
42C2×C22⋊C4×D47—21no—
43C2×C22⋊C4×D47—21no—
44#15689447C2218yescomplemented
45#15689426C2218yescomplemented
46#15689422C2218yescomplemented
47#15689317C2218yescomplemented
48#15689317C2218yescomplemented
49#15689259C2218yescomplemented
50#15689256C2218yescomplemented
51#15689234C2218yescomplemented
52#15689232C2218yescomplemented
53#15689205C2218yescomplemented
54#15689203C2218yescomplemented
55#15689181C2218yescomplemented
56C2×#13093957C2211yescharacteristic, complemented
57C2×#13093955C2211yescharacteristic, complemented
58C2×Dic47⋊C8C2211yescharacteristic, complemented
59C2×Dic47⋊C8C2211yescharacteristic, complemented
60C2×#13093946C2211yescharacteristic
61C2×#13093946C2211yescharacteristic
62C2×#13093944C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic, complemented
65C2×#13093944C2211yescharacteristic, complemented
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×#13093934C2211yescharacteristic, complemented
68C2×C8×Dic47C2211yescharacteristic, complemented
69C2×#121×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic
71C47×#482C2218yescomplemented
72C2×#107×C47C2211yescharacteristic, complemented
73C2×#106×C47C2211yescharacteristic, complemented
74C2×#102×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic, complemented
76C2×C22⋊C8×C47C2211yescharacteristic
77C24×D47—21no—
78C22×D188—21no—
79C22×D188—22no—
80C22×D188—24no—
81C22×D188—24no—
82C22×D188C2314yes—
83C22×D188C2311yescharacteristic
84C22×D188C2311yescharacteristic
85C22×D188C2311yescharacteristic
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C22×C22⋊D47—21no—
89C23×Dic47—21no—
90C22×C4×D47—21no—
91C22×C4×D47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C22×C4×D47—21no—
95C2×D376—24no—
96C2×D376—24no—
97C2×D376C2314yes—
98C2×D376C2314yes—
99C2×#10625334—24no—
100C2×#10625334—24no—
101C2×#10625334C2314yes—
102C2×#10625334C2314yes—
103C22×C47⋊C8C2311yescharacteristic
104C22×C47⋊C8C2311yescharacteristic
105#13094020—22no—
106#13094020C2314yescomplemented
107#13094015—22no—
108#13094015C2314yescomplemented
109#13094008—28no—
110#13094006—28no—
111#13093998—22no—
112#13093998C2314yes—
113#13093996—28no—
114#13093995—28no—
115C4×D188—28no—
116C4×D188—28no—
117D4×Dic47—22no—
118D4×Dic47C2314yescomplemented
119#13093986—22no—
120#13093986—22no—
121#13093986—22no—
122#13093986—22no—
123#13093986—22no—
124#13093986C2314yes—
125#13093986C2314yes—
126#13093986C2314yes—
127#13093986C2314yes—
128#13093986C2314yescomplemented
129#13093983D414yes—
130#13093983C2314yes—
131C2×C4⋊Dic47—21no—
132C2×C4⋊Dic47D411yescharacteristic
133C2×C4⋊Dic47D411yescharacteristic
134C2×C4⋊Dic47C2311yescharacteristic
135C2×Dic47⋊C4—21no—
136C2×C22⋊Dic47—21no—
137C2×C22⋊Dic47D411yescharacteristic
138C2×C22⋊Dic47D411yescharacteristic
139C2×(C2×D47)⋊C4—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—
145C22⋊C4×D47—28no—
146C22⋊C4×D47—28no—
147C2×C4×Dic47C2311yescharacteristic
148C2×C4×Dic47C2311yescharacteristic
149#13093957C2314yescomplemented
150#13093955C2314yescomplemented
151Dic47⋊C8C2314yescomplemented
152Dic47⋊C8C2314yescomplemented
153#13093946C2314yes—
154#13093946C2314yes—
155#13093944C2314yes—
156#13093944C2314yes—
157#13093944C2314yescomplemented
158#13093944C2314yescomplemented
159C22⋊(C47⋊C8)C2314yes—
160#13093934C2314yescomplemented
161C8×Dic47C2314yescomplemented
162C22×D4×C47—21no—
163C22×D4×C47C2311yescharacteristic
164C23×C4×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167#121×C47—22no—
168#121×C47C2314yes—
169#117×C47—22no—
170#117×C47C2314yes—
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176C2×C42×C47—21no—
177#107×C47C2314yescomplemented
178#106×C47C2314yescomplemented
179#102×C47C2314yescomplemented
180#102×C47C2314yescomplemented
181C22⋊C8×C47C2314yes—
182C24×C47—21no—
183C24×C47C2×D411yescharacteristic
184C23×D47—21no—
185C23×D47—21no—
186C23×D47—28no—
187C23×D47—24no—
188C23×D47—21no—
189C23×D47—82no—
190C23×D47—82no—
191C2×D4×C47—24no—
192C2×D4×C47—21no—
193C2×D4×C47—22no—
194C2×D4×C47—22no—
195C2×D4×C47—82no—
196C2×D4×C47C2412yes—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D412yes—
204C22×C4×C47C2412yes—
205C22×C4×C47C2411yescharacteristic
206C2×C22⋊D47—24no—
207C2×C22⋊D47—24no—
208C2×C22⋊D47—24no—
209C2×C22⋊D47—82no—
210C2×C22⋊D47—82no—
211C2×C22⋊D47—82no—
212C22×Dic47—21no—
213C22×Dic47—24no—
214C22×Dic47—82no—
215C22×Dic47C2×D411yescharacteristic
216C22×Dic47C2×D411yescharacteristic
217C22×Dic47C2×D411yescharacteristic
218C22×Dic47C2×D411yescharacteristic
219C2×D188—28no—
220C2×D188—216no—
221C2×D188—21no—
222C2×D188—21no—
223C2×D188—24no—
224C2×D188—22no—
225C2×D188—22no—
226C2×D188—28no—
227C2×D188—28no—
228C2×D188—22no—
229C2×D188—22no—
230C2×D188—21no—
231C2×D188#4114yes—
232C2×D188#4114yes—
233C2×D188C2412yes—
234C2×D188C2412yes—
235C2×D188C2412yes—
236C2×C4×D47—24no—
237C2×C4×D47—24no—
238C2×C4×D47—24no—
239C2×C4×D47—24no—
240C2×C4×D47—24no—
241C2×C4×D47—82no—
242C2×C4×D47—82no—
243C2×C4×D47—82no—
244C2×C4×D47—82no—
245C2×C4×D47—82no—
246C2×C8×C47—22no—
247C2×C8×C47—22no—
248C2×C8×C47C2412yes—
249C2×C8×C47C2412yes—
250C4⋊C4×C47—21no—
251C4⋊C4×C47—21no—
252C4⋊C4×C47—21no—
253C4⋊C4×C47C2412yes—
254C4⋊C4×C47C2412yes—
255C4⋊C4×C47C2412yes—
256C22⋊C4×C47—24no—
257C22⋊C4×C47—24no—
258C42×C47—24no—
259C22⋊Dic47—24no—
260C22⋊Dic47C2×D414yes—
261C22⋊Dic47C2×D414yes—
262#10625334—28no—
263#10625334—28no—
264(C2×D47)⋊C4—24no—
265(C2×D47)⋊C4—24no—
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4—24no—
269(C2×D47)⋊C4—24no—
270C4⋊Dic47—21no—
271C4⋊Dic47—24no—
272C4⋊Dic47C2×D414yes—
273C4⋊Dic47C2×D414yes—
274C4⋊Dic47C2412yes—
275Dic47⋊C4—24no—
276C4×Dic47C2×D412yes—
277C4×Dic47C2×D412yes—
278C4×Dic47C2412yes—
279C4×Dic47C2412yes—
280C2×C47⋊C8—22no—
281C2×C47⋊C8—22no—
282C2×C47⋊C8C2412yes—
283C2×C47⋊C8C2412yes—
284D376—28no—
285D376—28no—
286C23×C47—22no—
287C23×C47—22no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—42no—
291C23×C47—42no—
292C23×C47—42no—
293C23×C47C22×D412yes—
294C23×C47C22×D411yescharacteristic
295C22×D47—24no—
296C22×D47—24no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—216no—
300C22×D47—22no—
301C22×D47—42no—
302C22×D47—42no—
303C22×D47—42no—
304C22×D47—42no—
305C22×D47—42no—
306C22×D47—42no—
307C22×D47—42no—
308C22×D47—84no—
309C22×D47—84no—
310C22×D47—816no—
311D4×C47—22no—
312D4×C47—22no—
313D4×C47—42no—
314D4×C47—84no—
315C2×C4×C47—22no—
316C2×C4×C47—24no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—42no—
323C2×C4×C47—42no—
324C2×C4×C47—42no—
325C2×C4×C47C22×D412yes—
326C2×C4×C47C22×D411yescharacteristic
327C2×C4×C47C2×#4112yes—
328C2×C4×C47C2×#4112yes—
329C2×C4×C47C2511yescharacteristic
330C22⋊D47—84no—
331C22⋊D47—84no—
332C22⋊D47—84no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—42no—
339C2×Dic47—84no—
340C2×Dic47C22×D412yes—
341C2×Dic47C22×D412yes—
342C2×Dic47C22×D412yes—
343C2×Dic47C22×D412yes—
344D188—216no—
345D188—24no—
346D188—24no—
347D188—22no—
348D188—22no—
349D188—22no—
350D188—22no—
351D188—42no—
352D188C2×#4114yes—
353D188C2×#4114yes—
354C4×D47—84no—
355C4×D47—84no—
356C4×D47—84no—
357C4×D47—84no—
358C4×D47—84no—
359C8×C47—22no—
360C8×C47—22no—
361C47⋊C8—22no—
362C47⋊C8—22no—
363C2×#3122—471nomaximal, Sylow
364C22×C47—22no—
365C22×C47—22no—
366C22×C47—22no—
367C22×C47—44no—
368C22×C47—42no—
369C22×C47—42no—
370C22×C47—42no—
371C22×C47—84no—
372C22×C47#52512yes—
373C22×C47#57612yes—
374C22×C47#57612yes—
375C22×C47C23×D411yescharacteristic
376C2×D47—24no—
377C2×D47—24no—
378C2×D47—48no—
379C2×D47—48no—
380C2×D47—42no—
381C2×D47—42no—
382C2×D47—42no—
383C2×D47—42no—
384C2×D47—42no—
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—816no—
388C2×D47—84no—
389C4×C47—22no—
390C4×C47—42no—
391C4×C47—42no—
392C4×C47—42no—
393C4×C47#52512yes—
394C4×C47C22×#4111yescharacteristic
395C4×C47C22×#4111yescharacteristic
396Dic47—22no—
397Dic47—22no—
398Dic47—22no—
399Dic47—22no—
400Dic47—42no—
401C2×#540—471no—
402C2×#518—471no—
403#3122—4716no—
404C2×#482—471no—
405C2×#482D4711yescharacteristic, complemented
406C2×#478—471no—
407C2×#478—471no—
408C2×#459—471no—
409C2×#459—471no—
410C2×#447—471no—
411C2×#447—471no—
412C2×#442—471no—
413C2×#442—471no—
414C2×C4×D8—471no—
415C2×C4×D8—471no—
416C2×#433—471no—
417C2×C47—42no—
418C2×C47—82no—
419C2×C47#312214yescomplemented
420C2×C47C2×#52511yescharacteristic
421C2×C47C2×#57611yescharacteristic
422C2×C47C2×#57611yescharacteristic
423D47—44no—
424D47—44no—
425D47—82no—
426C23×D4—471no—
427C22×D8—471no—
428C22×D8—471no—
429C22×D8—471no—
430C22×D8—471no—
431#540—478no—
432#540—944no—
433C2×#127—471no—
434C2×#125—471no—
435C2×#123—941no—
436C2×#123—941no—
437C2×#121—471no—
438C2×#121—941no—
439C2×#121—941no—
440C2×#121C2×D4711yescharacteristic
441#518—478no—
442#518—944no—
443C2×C4×D4—471no—
444C2×C4×D4—471no—
445C2×C4×D4—471no—
446C2×C4×D4—471no—
447C2×C4×D4—471no—
448C2×C4×D4—471no—
449C2×C4×D4—941no—
450C2×C4×D4—941no—
451C2×#117—471no—
452C2×#117C2×D4711yescharacteristic
453C22×C22⋊C4—941no—
454C22×C22⋊C4—941no—
455#482—478no—
456#482C2×D4718yescomplemented
457#478—478no—
458#478—478no—
459#459—478no—
460#459—478no—
461#447—478no—
462#447—478no—
463#442—478no—
464#442—478no—
465C4×D8—478no—
466C4×D8—478no—
467#433—478no—
468C2×#107—471no—
469C2×#107C2×D4711yescharacteristic, complemented
470C2×#106—471no—
471C2×#106C2×D4711yescharacteristic, complemented
472C2×C4⋊C8—471no—
473C2×C4⋊C8—471no—
474C2×#102—471no—
475C2×#102—471no—
476C2×#102—471no—
477C2×#102—471no—
478C2×#102—471no—
479C2×#102—471no—
480C2×#102C2×D4711yescharacteristic, complemented
481C2×#102C2×D4711yescharacteristic, complemented
482C2×C22⋊C8—471no—
483C2×C22⋊C8C2×D4711yescharacteristic
484C2×#97—471no—
485C2×C4×C8—471no—
486C47C2×#312211yescharacteristic, complemented, Sylow
487C25—941no—
488C22×D4—21no—
489C22×D4—471no—
490C22×D4—471no—
491C22×D4—471no—
492C22×D4—474no—
493C22×D4—944no—
494C22×D4—944no—
495C22×D4—941no—
496C22×D4—941no—
497C22×D4—941no—
498C22×D4—941no—
499C22×D4—942no—
500C22×D4C22×D4711yescharacteristic
501C23×C4—941no—
502C23×C4—941no—
503C23×C4—941no—
504C23×C4—941no—
505C23×C4—941no—
506C23×C4—941no—
507C23×C4C22×D4711yescharacteristic
508C2×D8—474no—
509C2×D8—474no—
510C2×D8—474no—
511C2×D8—474no—
512C2×D8—944no—
513C2×D8—944no—
514C2×D8—944no—
515C2×D8—944no—
516C22×C8—471no—
517C22×C8—471no—
518C22×C8C22×D4711yescharacteristic
519C22×C8C22×D4711yescharacteristic
520#127—474no—
521#127—942no—
522#125—474no—
523#125—942no—
524#123—948no—
525#123—948no—
526#121—22no—
527#121—474no—
528#121—948no—
529#121—948no—
530#121—942no—
531#121C22×D4714yes—
532C4×D4—474no—
533C4×D4—474no—
534C4×D4—474no—
535C4×D4—474no—
536C4×D4—474no—
537C4×D4—474no—
538C4×D4—948no—
539C4×D4—948no—
540C4×D4—942no—
541C4×D4—942no—
542C4×D4—942no—
543C4×D4—942no—
544C4×D4—942no—
545C4×D4—942no—
546#117—22no—
547#117—474no—
548#117—474no—
549#117C22×D4714yes—
550C2×C4⋊C4—471no—
551C2×C4⋊C4—471no—
552C2×C4⋊C4—471no—
553C2×C4⋊C4—941no—
554C2×C4⋊C4—941no—
555C2×C4⋊C4C22×D4711yescharacteristic
556C2×C4⋊C4C22×D4711yescharacteristic
557C2×C4⋊C4C22×D4711yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—471no—
561C2×C22⋊C4—471no—
562C2×C22⋊C4—948no—
563C2×C22⋊C4—948no—
564C2×C22⋊C4—941no—
565C2×C22⋊C4—941no—
566C2×C22⋊C4—941no—
567C2×C22⋊C4—941no—
568C2×C22⋊C4—941no—
569C2×C22⋊C4—941no—
570C2×C22⋊C4—941no—
571C2×C42—21no—
572C2×C42—471no—
573C2×C42—471no—
574#107—474no—
575#107C22×D4714yescomplemented
576#106—474no—
577#106C22×D4714yescomplemented
578C4⋊C8—474no—
579C4⋊C8—474no—
580#102—474no—
581#102—474no—
582#102—474no—
583#102—474no—
584#102—474no—
585#102—474no—
586#102C22×D4714yescomplemented
587#102C22×D4714yescomplemented
588C22⋊C8—474no—
589C22⋊C8C22×D4714yes—
590#97—474no—
591C4×C8—474no—
592C24—21no—
593C24—948no—
594C24—944no—
595C24—941no—
596C24—941no—
597C24—941no—
598C24—3762no—
599C24—3762no—
600C24D4×D4711yescharacteristic
601C2×D4—24no—
602C2×D4—21no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—82no—
606C2×D4—474no—
607C2×D4—474no—
608C2×D4—472no—
609C2×D4—472no—
610C2×D4—472no—
611C2×D4—948no—
612C2×D4—948no—
613C2×D4—948no—
614C2×D4—9416no—
615C2×D4—944no—
616C2×D4—944no—
617C2×D4—944no—
618C2×D4—944no—
619C2×D4—941no—
620C2×D4—941no—
621C2×D4—941no—
622C2×D4—942no—
623C2×D4—942no—
624C2×D4—942no—
625C2×D4—942no—
626C2×D4—3762no—
627C2×D4—3762no—
628C2×D4—3762no—
629C2×D4C23×D4712yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—471no—
636C22×C4—471no—
637C22×C4—471no—
638C22×C4—471no—
639C22×C4—944no—
640C22×C4—944no—
641C22×C4—944no—
642C22×C4—944no—
643C22×C4—944no—
644C22×C4—944no—
645C22×C4—941no—
646C22×C4—3762no—
647C22×C4—3762no—
648C22×C4—3762no—
649C22×C4—3762no—
650C22×C4—3762no—
651C22×C4—3762no—
652C22×C4D4×D4712yes—
653C22×C4D4×D4711yescharacteristic
654C22×C4C23×D4712yes—
655C22×C4C23×D4711yescharacteristic
656D8—948no—
657D8—948no—
658D8—948no—
659D8—948no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—472no—
663C2×C8—472no—
664C2×C8—942no—
665C2×C8—942no—
666C2×C8C23×D4712yes—
667C2×C8C23×D4712yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—474no—
672C4⋊C4—474no—
673C4⋊C4—472no—
674C4⋊C4—944no—
675C4⋊C4—944no—
676C4⋊C4—941no—
677C4⋊C4C23×D4712yes—
678C4⋊C4C23×D4712yes—
679C4⋊C4C23×D4712yes—
680C22⋊C4—24no—
681C22⋊C4—24no—
682C22⋊C4—474no—
683C22⋊C4—474no—
684C22⋊C4—944no—
685C22⋊C4—944no—
686C22⋊C4—944no—
687C22⋊C4—944no—
688C22⋊C4—944no—
689C22⋊C4—944no—
690C22⋊C4—944no—
691C42—24no—
692C42—472no—
693C42—472no—
694C42—472no—
695C42—472no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—9416no—
704C23—944no—
705C23—944no—
706C23—942no—
707C23—942no—
708C23—942no—
709C23—3764no—
710C23—3764no—
711C23—37616no—
712C23—1882no—
713C23—1882no—
714C23—1882no—
715C23—1882no—
716C23—1882no—
717C23—1882no—
718C23—1882no—
719C23C2×D4×D4712yes—
720C23C2×D4×D4711yescharacteristic
721D4—22no—
722D4—22no—
723D4—42no—
724D4—84no—
725D4—474no—
726D4—474no—
727D4—9416no—
728D4—944no—
729D4—944no—
730D4—942no—
731D4—942no—
732D4—942no—
733D4—942no—
734D4—3764no—
735D4—3764no—
736D4—3764no—
737D4—1882no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—472no—
749C2×C4—472no—
750C2×C4—472no—
751C2×C4—472no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—3764no—
758C2×C4—3764no—
759C2×C4—3764no—
760C2×C4—3764no—
761C2×C4—3764no—
762C2×C4—3764no—
763C2×C4—1882no—
764C2×C4C2×D4×D4712yes—
765C2×C4C2×D4×D4711yescharacteristic
766C2×C4#41×D4712yes—
767C2×C4#41×D4712yes—
768C2×C4C24×D4711yescharacteristic
769C8—22no—
770C8—22no—
771C8—942no—
772C8—942no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—944no—
782C22—944no—
783C22—37616no—
784C22—3764no—
785C22—1882no—
786C22—1882no—
787C22—1882no—
788C22—1882no—
789C22—1882no—
790C22—1882no—
791C22—1882no—
792C22—1888no—
793C22—1888no—
794C22#1568963112yes—
795C22#1568992512yes—
796C22#1568992712yes—
797C22C22×D4×D4711yescharacteristic
798C4—22no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—942no—
803C4—942no—
804C4—942no—
805C4—942no—
806C4—1882no—
807C4#1568963112yes—
808C4C2×#41×D4711yescharacteristic
809C4C2×#41×D4711yescharacteristic
810C2—42no—
811C2—82no—
812C2—3762no—
813C2—1884no—
814C2—1884no—
815C2#2025362714yesdirect product factor
816C2C2×#1568963111yescharacteristic
817C2C2×#1568992511yescharacteristic
818C2C2×#1568992711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#482C2
socleC23×C47C22×D4
hypercenterC2×#482D47
hypocenterC47C2×#3122
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#15689726C2semidirect
2. C2×#15689597C2semidirect
3. #20253627C2direct (N × H)
4. C2×#15689447C2semidirect
5. C2×#15689426C2semidirect
6. C2×#15689422C2semidirect
7. C2×#15689317C2semidirect
8. C2×#15689317C2semidirect
9. C2×#15689259C2semidirect
10. C2×#15689256C2semidirect
11. C2×#15689234C2semidirect
12. C2×#15689232C2semidirect
13. C2×#15689205C2semidirect
14. C2×#15689203C2semidirect
15. C2×#15689181C2semidirect
16. C2×C47×#482C2semidirect
23. #15689726C22semidirect
24. C2×#13094020C22semidirect
25. C2×#13094015C22semidirect
32. #15689597C22semidirect
35. C2×D4×Dic47C22semidirect
40. C2×#13093986C22semidirect
44. #15689447C22semidirect
45. #15689426C22semidirect
46. #15689422C22semidirect
47. #15689317C22semidirect
48. #15689317C22semidirect
49. #15689259C22semidirect
50. #15689256C22semidirect
51. #15689234C22semidirect
52. #15689232C22semidirect
53. #15689205C22semidirect
54. #15689203C22semidirect
55. #15689181C22semidirect
56. C2×#13093957C22semidirect
57. C2×#13093955C22semidirect
58. C2×Dic47⋊C8C22semidirect
59. C2×Dic47⋊C8C22semidirect
64. C2×#13093944C22semidirect
65. C2×#13093944C22semidirect
67. C2×#13093934C22semidirect
68. C2×C8×Dic47C22semidirect
71. C47×#482C22semidirect
72. C2×#107×C47C22semidirect
73. C2×#106×C47C22semidirect
74. C2×#102×C47C22semidirect
75. C2×#102×C47C22semidirect
106. #13094020C23semidirect
108. #13094015C23semidirect
118. D4×Dic47C23semidirect
128. #13093986C23semidirect
149. #13093957C23semidirect
150. #13093955C23semidirect
151. Dic47⋊C8C23semidirect
152. Dic47⋊C8C23semidirect
157. #13093944C23semidirect
158. #13093944C23semidirect
160. #13093934C23semidirect
161. C8×Dic47C23semidirect
177. #107×C47C23semidirect
178. #106×C47C23semidirect
179. #102×C47C23semidirect
180. #102×C47C23semidirect
405. C2×#482D47semidirect
419. C2×C47#3122semidirect
456. #482C2×D47semidirect
469. C2×#107C2×D47semidirect
471. C2×#106C2×D47semidirect
480. C2×#102C2×D47semidirect
481. C2×#102C2×D47semidirect
486. C47C2×#3122semidirect
575. #107C22×D47semidirect
577. #106C22×D47semidirect
586. #102C22×D47semidirect
587. #102C22×D47semidirect
815. C2#20253627direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897262
C2×#156895972
#202536272
C2×#156894472
C2×#156894262
C2×#156894222
C2×#156893172
C2×#156892592
C2×#156892562
C2×#156892342
C2×#156892322
C2×#156892052
C2×#156892032
C2×#156891812
C2×C47×#4822
C2×#312247