Finite Group Databasebeta

← C2×#20254992 #27091379

Subgroups — C2×#20254992 #27091379

Order 12032.

3042 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094051C211yesmaximal, characteristic, complemented
2C22×#13094049C211yesmaximal, characteristic, complemented
3C2×#15689764C211yesmaximal, characteristic, complemented
4C2×#15689761C211yesmaximal, characteristic, complemented
5#20254992C2116yesmaximal, direct product factor
6C2×#15689508C211yesmaximal, characteristic, complemented
7C2×#15689372C211yesmaximal, characteristic, complemented
8C2×#15689371C211yesmaximal, characteristic, complemented
9C2×#15689341C211yesmaximal, characteristic, complemented
10C2×#15689340C211yesmaximal, characteristic, complemented
11C2×#15689284C211yesmaximal, characteristic, complemented
12C2×#15689259C211yesmaximal, characteristic, complemented
13C2×#15689258C211yesmaximal, characteristic, complemented
14C2×#15689203C211yesmaximal, characteristic, complemented
15C2×#15689198C211yesmaximal, characteristic, complemented
16C2×C47×#452C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C23×D188C2211yescharacteristic, complemented
19C22×D4×D47C2211yescharacteristic, complemented
20C2×#13094051—28no—
21C2×#13094051C2218yescomplemented
22C2×#13094049—28no—
23C2×#13094049C2218yescomplemented
24C22×#10625336C2211yescharacteristic, complemented
25C22×#10625336C2211yescharacteristic, complemented
26C22×#10625336C2211yescharacteristic, complemented
27C22×D376C2211yescharacteristic
28C22×D376C2211yescharacteristic
29C22×#10625334C2211yescharacteristic
30C22×#10625334C2211yescharacteristic
31C22×#10625329C2211yescharacteristic, complemented
32C22×#10625324C2211yescharacteristic, complemented
33#15689764—24no—
34#15689764C2218yescomplemented
35#15689761—24no—
36#15689761C2218yescomplemented
37C2×#13094013C2211yescharacteristic, complemented
38C2×#13094013C2211yescharacteristic, complemented
39C2×#13094009—21no—
40C2×#13094007—21no—
41C2×#13094000C2211yescharacteristic, complemented
42C2×#13093999—21no—
43C2×#13093999C2211yescharacteristic
44C2×#13093998C2211yescharacteristic
45C2×#13093996—21no—
46C2×#13093994—21no—
47C2×#13093992—21no—
48C2×D4×Dic47C2211yescharacteristic, complemented
49C2×#13093986C2211yescharacteristic, complemented
50C2×C4×C22⋊D47C2211yescharacteristic
51C22×(C2×D47)⋊C4—21no—
52C2×C22⋊C4×D47—21no—
53#15689508C2218yescomplemented
54#15689372C2218yescomplemented
55#15689371C2218yescomplemented
56#15689341C2218yescomplemented
57#15689340C2218yescomplemented
58#15689284C2218yescomplemented
59#15689259C2218yescomplemented
60#15689258C2218yescomplemented
61#15689203C2218yescomplemented
62#15689198C2218yescomplemented
63C2×#13093957C2211yescharacteristic, complemented
64C2×Dic47⋊C8C2211yescharacteristic, complemented
65C2×#13093948C2211yescharacteristic, complemented
66C2×#13093946C2211yescharacteristic, complemented
67C2×#13093946C2211yescharacteristic, complemented
68C2×#13093944C2211yescharacteristic, complemented
69C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
70C2×C8×Dic47C2211yescharacteristic, complemented
71C22×#41×C47C2211yescharacteristic
72C22×Q16×C47C2211yescharacteristic, complemented
73C22×SD16×C47C2211yescharacteristic, complemented
74C2×C22⋊Q8×C47C2211yescharacteristic, complemented
75C47×#452C2218yescomplemented
76C2×#103×C47C2211yescharacteristic, complemented
77C2×#102×C47C2211yescharacteristic, complemented
78C2×C22⋊C8×C47C2211yescharacteristic, complemented
79C24×D47—21no—
80C24×D47—21no—
81C2×#10625354—22no—
82C2×#10625354—24no—
83C2×#10625354—42no—
84C2×#10625354C2314yes—
85C22×D188—24no—
86C22×D188—21no—
87C22×D188—22no—
88C22×D188—21no—
89C22×D188—21no—
90C22×D188—42no—
91C22×D188C2311yescharacteristic
92C22×D188C2311yescharacteristic
93C22×D188C2311yescharacteristic
94C22×D188C2314yescomplemented
95C22×C22⋊D47—21no—
96C22×C22⋊D47—21no—
97C22×C22⋊D47D411yescharacteristic
98C2×D4×D47—24no—
99C2×D4×D47—22no—
100C2×D4×D47—42no—
101C2×D4×D47C2314yescomplemented
102C23×Dic47—21no—
103C22×C4×D47—21no—
104C22×C4×D47—21no—
105C22×C4×D47C2311yescharacteristic
106#13094051—232no—
107#13094049—232no—
108C2×#10625336—24no—
109C2×#10625336—24no—
110C2×#10625336—24no—
111C2×#10625336C2314yescomplemented
112C2×#10625336C2314yescomplemented
113C2×#10625336C2314yescomplemented
114C2×D376—24no—
115C2×D376—42no—
116C2×D376C2314yes—
117C2×D376C2314yes—
118C2×#10625334—24no—
119C2×#10625334D418yescomplemented
120C2×#10625334C2314yes—
121C2×#10625334C2314yes—
122C2×#10625329—24no—
123C2×#10625329C2314yescomplemented
124C2×#10625324—24no—
125C2×#10625324C2314yescomplemented
126C22×C47⋊C8C2311yescharacteristic
127C22×C47⋊C8C2311yescharacteristic
128#13094013—22no—
129#13094013—22no—
130#13094013C2314yescomplemented
131#13094013C2314yescomplemented
132#13094009—28no—
133#13094007—28no—
134#13094000—22no—
135#13094000C2314yescomplemented
136#13093999—22no—
137#13093999—28no—
138#13093999C2314yes—
139#13093998—22no—
140#13093998C2314yes—
141#13093996—28no—
142#13093994—28no—
143#13093992—28no—
144D4×Dic47—22no—
145D4×Dic47C2314yescomplemented
146#13093986—22no—
147#13093986C2314yescomplemented
148C4×C22⋊D47D414yes—
149C4×C22⋊D47C2314yes—
150C2×C4⋊Dic47C2311yescharacteristic
151C2×Dic47⋊C4—21no—
152C2×Dic47⋊C4D411yescharacteristic
153C2×C22⋊Dic47—21no—
154C2×C22⋊Dic47D411yescharacteristic
155C2×(C2×D47)⋊C4—21no—
156C2×(C2×D47)⋊C4—21no—
157C2×(C2×D47)⋊C4—21no—
158C2×(C2×D47)⋊C4—21no—
159C2×(C2×D47)⋊C4—21no—
160C2×(C2×D47)⋊C4—21no—
161C2×(C2×D47)⋊C4—21no—
162C2×(C2×D47)⋊C4—21no—
163C2×(C2×D47)⋊C4—28no—
164C2×(C2×D47)⋊C4D411yescharacteristic
165C22⋊C4×D47—28no—
166C2×C4×Dic47C2311yescharacteristic
167#13093957C2314yescomplemented
168Dic47⋊C8C2314yescomplemented
169#13093948C2314yescomplemented
170#13093946C2314yescomplemented
171#13093946C2314yescomplemented
172#13093944C2314yescomplemented
173(C2×D47)⋊C8C2314yescomplemented
174C8×Dic47C2314yescomplemented
175C2×#41×C47—22no—
176C2×#41×C47—24no—
177C2×#41×C47—42no—
178C2×#41×C47C2314yes—
179C22×Q8×C47C2311yescharacteristic
180C22×Q8×C47C2311yescharacteristic
181C22×D4×C47—21no—
182C22×D4×C47C2311yescharacteristic
183C23×C4×C47—21no—
184C23×C4×C47C2311yescharacteristic
185C2×Q16×C47—42no—
186C2×Q16×C47C2314yescomplemented
187C2×SD16×C47—24no—
188C2×SD16×C47C2314yescomplemented
189C22×C8×C47C2311yescharacteristic
190C22×C8×C47C2311yescharacteristic
191C22⋊Q8×C47—22no—
192C22⋊Q8×C47C2314yescomplemented
193C2×C4⋊C4×C47—21no—
194C2×C4⋊C4×C47C2311yescharacteristic
195C2×C22⋊C4×C47—21no—
196#103×C47C2314yescomplemented
197#102×C47C2314yescomplemented
198C22⋊C8×C47C2314yescomplemented
199C24×C47—21no—
200C24×C47C2×D411yescharacteristic
201C23×D47—21no—
202C23×D47—21no—
203C23×D47—21no—
204C23×D47—24no—
205C23×D47—24no—
206C23×D47—44no—
207C23×D47—44no—
208C23×D47—44no—
209C23×D47—44no—
210C23×D47—82no—
211C23×D47—82no—
212C23×D47C2×D411yescharacteristic
213#41×C47—28no—
214#41×C47—44no—
215#41×C47—48no—
216C2×Q8×C47—21no—
217C2×Q8×C47—21no—
218C2×Q8×C47—22no—
219C2×Q8×C47—22no—
220C2×Q8×C47—22no—
221C2×Q8×C47—22no—
222C2×Q8×C47C2412yes—
223C2×Q8×C47C2412yes—
224C2×D4×C47—24no—
225C2×D4×C47—21no—
226C2×D4×C47—22no—
227C2×D4×C47—44no—
228C2×D4×C47C2×D414yes—
229C2×D4×C47C2412yes—
230C22×C4×C47—22no—
231C22×C4×C47—22no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—24no—
236C22×C4×C47—44no—
237C22×C4×C47C2×D411yescharacteristic
238C22×C4×C47C2×D412yes—
239C22×C4×C47C2412yes—
240C22×C4×C47C2411yescharacteristic
241C2×C22⋊D47—24no—
242C2×C22⋊D47—24no—
243C2×C22⋊D47—42no—
244C2×C22⋊D47—44no—
245C2×C22⋊D47—82no—
246C2×C22⋊D47C2×D414yes—
247C22×Dic47—21no—
248C22×Dic47—24no—
249C22×Dic47—82no—
250C22×Dic47C2×D411yescharacteristic
251C22×Dic47C2×D411yescharacteristic
252C22×Dic47C2×D411yescharacteristic
253#10625354—28no—
254#10625354—44no—
255#10625354—48no—
256D4×D47—28no—
257D4×D47—44no—
258D4×D47—48no—
259C2×D188—21no—
260C2×D188—22no—
261C2×D188—22no—
262C2×D188—22no—
263C2×D188—22no—
264C2×D188—22no—
265C2×D188—28no—
266C2×D188—24no—
267C2×D188—21no—
268C2×D188—24no—
269C2×D188—21no—
270C2×D188—24no—
271C2×D188—44no—
272C2×D188—48no—
273C2×D188—44no—
274C2×D188—44no—
275C2×D188—82no—
276C2×D188C2×D414yes—
277C2×D188C2412yes—
278C2×D188C2412yes—
279C2×D188C2412yes—
280C2×C4×D47—22no—
281C2×C4×D47—22no—
282C2×C4×D47—24no—
283C2×C4×D47—24no—
284C2×C4×D47—44no—
285C2×C4×D47—82no—
286C2×C4×D47C2×D412yes—
287C2×C4×D47C2412yes—
288Q16×C47—44no—
289SD16×C47—28no—
290C2×C8×C47—22no—
291C2×C8×C47—22no—
292C2×C8×C47C2412yes—
293C2×C8×C47C2412yes—
294C4⋊C4×C47—24no—
295C4⋊C4×C47—21no—
296C4⋊C4×C47C2412yes—
297C22⋊C4×C47—24no—
298C22⋊Dic47—24no—
299C22⋊Dic47C2×D414yes—
300#10625336—28no—
301#10625336—28no—
302#10625336—28no—
303#10625334—28no—
304#10625334C2×D4116yescomplemented
305(C2×D47)⋊C4—24no—
306(C2×D47)⋊C4—24no—
307(C2×D47)⋊C4—24no—
308(C2×D47)⋊C4—24no—
309(C2×D47)⋊C4—24no—
310(C2×D47)⋊C4—24no—
311(C2×D47)⋊C4—24no—
312(C2×D47)⋊C4—24no—
313(C2×D47)⋊C4C2×D414yes—
314C4⋊Dic47—21no—
315C4⋊Dic47C2412yes—
316Dic47⋊C4—24no—
317Dic47⋊C4C2×D414yes—
318C4×Dic47C2×D412yes—
319C4×Dic47C2412yes—
320#10625329—28no—
321C2×C47⋊C8—22no—
322C2×C47⋊C8C2×D414yes—
323C2×C47⋊C8C2412yes—
324C2×C47⋊C8C2412yes—
325D376—28no—
326D376—44no—
327#10625324—28no—
328C23×C47—24no—
329C23×C47—22no—
330C23×C47—22no—
331C23×C47—22no—
332C23×C47—22no—
333C23×C47—42no—
334C23×C47—42no—
335C23×C47C22×D412yes—
336C23×C47C22×D411yescharacteristic
337C22×D47—22no—
338C22×D47—24no—
339C22×D47—22no—
340C22×D47—22no—
341C22×D47—22no—
342C22×D47—22no—
343C22×D47—22no—
344C22×D47—48no—
345C22×D47—48no—
346C22×D47—48no—
347C22×D47—42no—
348C22×D47—42no—
349C22×D47—48no—
350C22×D47—42no—
351C22×D47—42no—
352C22×D47—42no—
353C22×D47—42no—
354C22×D47—42no—
355C22×D47—42no—
356C22×D47—84no—
357C22×D47—84no—
358C22×D47—816no—
359C22×D47—816no—
360C22×D47C22×D412yes—
361Q8×C47—22no—
362Q8×C47—22no—
363Q8×C47—22no—
364Q8×C47—22no—
365Q8×C47—42no—
366Q8×C47—42no—
367D4×C47—24no—
368D4×C47—22no—
369D4×C47—48no—
370D4×C47C22×D414yes—
371C2×C4×C47—22no—
372C2×C4×C47—24no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—22no—
376C2×C4×C47—22no—
377C2×C4×C47—22no—
378C2×C4×C47—48no—
379C2×C4×C47—42no—
380C2×C4×C47—42no—
381C2×C4×C47—42no—
382C2×C4×C47C22×D412yes—
383C2×C4×C47C22×D411yescharacteristic
384C2×C4×C47C22×D412yes—
385C2×C4×C47H(5,𝔽2)12yes—
386C2×C4×C47C2511yescharacteristic
387C22⋊D47—44no—
388C22⋊D47—48no—
389C22⋊D47—84no—
390C2×Dic47—22no—
391C2×Dic47—22no—
392C2×Dic47—22no—
393C2×Dic47—22no—
394C2×Dic47—42no—
395C2×Dic47—84no—
396C2×Dic47C22×D412yes—
397C2×Dic47C22×D412yes—
398C2×Dic47C22×D412yes—
399D188—24no—
400D188—22no—
401D188—22no—
402D188—22no—
403D188—22no—
404D188—22no—
405D188—48no—
406D188—48no—
407D188—42no—
408D188—42no—
409D188—84no—
410D188C22×D414yes—
411C4×D47—24no—
412C4×D47—22no—
413C4×D47—22no—
414C4×D47—48no—
415C4×D47—84no—
416C8×C47—22no—
417C8×C47—22no—
418C47⋊C8—22no—
419C47⋊C8C22×D414yes—
420C2×#3273—471nomaximal, Sylow
421C22×C47—24no—
422C22×C47—22no—
423C22×C47—22no—
424C22×C47—22no—
425C22×C47—44no—
426C22×C47—48no—
427C22×C47—42no—
428C22×C47—42no—
429C22×C47D4212yes—
430C22×C47#57512yes—
431C22×C47#57612yes—
432C22×C47C23×D411yescharacteristic
433C2×D47—22no—
434C2×D47—24no—
435C2×D47—22no—
436C2×D47—22no—
437C2×D47—44no—
438C2×D47—48no—
439C2×D47—42no—
440C2×D47—42no—
441C2×D47—42no—
442C2×D47—42no—
443C2×D47—42no—
444C2×D47—42no—
445C2×D47—42no—
446C2×D47—42no—
447C2×D47—816no—
448C2×D47—816no—
449C2×D47—84no—
450C2×D47—84no—
451C4×C47—22no—
452C4×C47—42no—
453C4×C47—42no—
454C4×C47—42no—
455C4×C47D4212yes—
456C4×C47C23×D411yescharacteristic
457C4×C47C2×H(5,𝔽2)11yescharacteristic
458Dic47—22no—
459Dic47—22no—
460Dic47—22no—
461Dic47—42no—
462C22×AGL(1,ℤ/8)—471no—
463C22×AGL(1,ℤ/8)—471no—
464C2×#546—471no—
465C2×#546—471no—
466#3273—4716no—
467C2×#495—471no—
468C2×#468—471no—
469C2×#468—471no—
470C2×#463—471no—
471C2×#463—471no—
472C2×#452—471no—
473C2×#452D4711yescharacteristic, complemented
474C2×#447—471no—
475C2×#447—471no—
476C2×C4×D8—471no—
477C2×#436—471no—
478C2×C47—42no—
479C2×C47—44no—
480C2×C47#327314yescomplemented
481C2×C47C2×D4211yescharacteristic
482C2×C47C2×#57511yescharacteristic
483C2×C47C2×#57611yescharacteristic
484D47—42no—
485D47—44no—
486D47—82no—
487D47—82no—
488C22×#41—471no—
489C22×#41C2×D4711yescharacteristic
490C23×D4—471no—
491C23×D4—471no—
492C2×AGL(1,ℤ/8)—478no—
493C2×AGL(1,ℤ/8)—478no—
494C2×AGL(1,ℤ/8)—948no—
495C2×AGL(1,ℤ/8)—948no—
496C22×Q16C2×D4711yescharacteristic, complemented
497C22×SD16—471no—
498C22×SD16—471no—
499C22×SD16—471no—
500C22×SD16C2×D4711yescharacteristic, complemented
501C22×D8—471no—
502C22×D8—471no—
503C22×D8—471no—
504C22×D8—471no—
505C22×M16—471no—
506C22×M16—471no—
507#546—478no—
508#546—478no—
509#546—944no—
510#546—944no—
511C2×#124—471no—
512C2×#124—471no—
513C2×#123—941no—
514C2×#123—941no—
515C2×C22⋊Q8—471no—
516C2×C22⋊Q8C2×D4711yescharacteristic, complemented
517C2×#121—471no—
518C2×#121—471no—
519C2×#121—941no—
520C2×#121—941no—
521C2×#120—941no—
522C2×#120—941no—
523C2×C4×D4—471no—
524C2×C4×D4—471no—
525C2×C4×D4—471no—
526C22×C22⋊C4—941no—
527C22×C22⋊C4—941no—
528#495—478no—
529#468—478no—
530#468—478no—
531#463—478no—
532#463—478no—
533#452—478no—
534#452C2×D4718yescomplemented
535#447—478no—
536#447—478no—
537C4×D8—478no—
538#436—478no—
539C2×#107—471no—
540C2×C4⋊C8—471no—
541C2×#103—471no—
542C2×#103C2×D4711yescharacteristic, complemented
543C2×#102—471no—
544C2×#102—471no—
545C2×#102—471no—
546C2×#102C2×D4711yescharacteristic, complemented
547C2×C22⋊C8—471no—
548C2×C22⋊C8C2×D4711yescharacteristic, complemented
549C2×C4×C8—471no—
550C47C2×#327311yescharacteristic, complemented, Sylow
551C25—941no—
552C25—941no—
553C2×#41—22no—
554C2×#41—24no—
555C2×#41—42no—
556C2×#41—474no—
557C2×#41—942no—
558C2×#41—944no—
559C2×#41—1882no—
560C2×#41C22×D4714yes—
561C22×Q8C22×D4711yescharacteristic
562C22×Q8C22×D4711yescharacteristic
563C22×D4—21no—
564C22×D4—471no—
565C22×D4—474no—
566C22×D4—471no—
567C22×D4—471no—
568C22×D4—471no—
569C22×D4—474no—
570C22×D4—944no—
571C22×D4—941no—
572C22×D4—941no—
573C22×D4—942no—
574C22×D4—941no—
575C22×D4—944no—
576C22×D4—941no—
577C22×D4—941no—
578C22×D4—942no—
579C22×D4—1882no—
580C22×D4—1882no—
581C22×D4C22×D4711yescharacteristic
582C23×C4—21no—
583C23×C4—471no—
584C23×C4—941no—
585C23×C4—941no—
586C23×C4—941no—
587C23×C4C22×D4711yescharacteristic
588AGL(1,ℤ/8)—9432no—
589AGL(1,ℤ/8)—9432no—
590C2×Q16—42no—
591C2×Q16C22×D4714yescomplemented
592C2×SD16—24no—
593C2×SD16—474no—
594C2×SD16—474no—
595C2×SD16—474no—
596C2×SD16—944no—
597C2×SD16—944no—
598C2×SD16—944no—
599C2×SD16C22×D4714yescomplemented
600C2×D8—478no—
601C2×D8—474no—
602C2×D8—474no—
603C2×D8—474no—
604C2×D8—474no—
605C2×D8—944no—
606C2×D8—944no—
607C2×D8—1882no—
608C2×M16—474no—
609C2×M16—474no—
610C2×M16—944no—
611C2×M16—944no—
612C22×C8—471no—
613C22×C8—471no—
614C22×C8C22×D4711yescharacteristic
615C22×C8C22×D4711yescharacteristic
616#124—474no—
617#124—474no—
618#124—942no—
619#124—942no—
620#123—948no—
621#123—948no—
622C22⋊Q8—22no—
623C22⋊Q8—474no—
624C22⋊Q8—942no—
625C22⋊Q8C22×D4714yescomplemented
626#121—474no—
627#121—474no—
628#121—948no—
629#121—948no—
630#121—942no—
631#121—942no—
632#120—948no—
633#120—948no—
634C4×D4—474no—
635C4×D4—474no—
636C4×D4—474no—
637C4×D4—474no—
638C4×D4—942no—
639C4×D4—942no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—471no—
642C2×C4⋊C4—471no—
643C2×C4⋊C4—941no—
644C2×C4⋊C4C22×D4711yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—471no—
647C2×C22⋊C4—471no—
648C2×C22⋊C4—948no—
649C2×C22⋊C4—948no—
650C2×C22⋊C4—941no—
651C2×C22⋊C4—941no—
652C2×C22⋊C4—941no—
653C2×C22⋊C4—941no—
654C2×C22⋊C4—941no—
655C2×C22⋊C4—941no—
656C2×C22⋊C4—941no—
657C2×C22⋊C4—941no—
658C2×C22⋊C4—941no—
659C2×C42—471no—
660#107—474no—
661C4⋊C8—474no—
662#103—474no—
663#103C22×D4714yescomplemented
664#102—474no—
665#102—474no—
666#102—474no—
667#102C22×D4714yescomplemented
668C22⋊C8—474no—
669C22⋊C8C22×D4714yescomplemented
670C4×C8—474no—
671C24—21no—
672C24—471no—
673C24—944no—
674C24—941no—
675C24—944no—
676C24—941no—
677C24—941no—
678C24—3762no—
679C24—3762no—
680C24—1884no—
681C24—1884no—
682C24—1884no—
683C24—1884no—
684C24D4×D4711yescharacteristic
685#41—28no—
686#41—44no—
687#41—48no—
688#41—948no—
689#41—1884no—
690#41—1888no—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—22no—
694C2×Q8—22no—
695C2×Q8—22no—
696C2×Q8—22no—
697C2×Q8C23×D4712yes—
698C2×Q8C23×D4712yes—
699C2×D4—24no—
700C2×D4—21no—
701C2×D4—22no—
702C2×D4—44no—
703C2×D4—474no—
704C2×D4—474no—
705C2×D4—472no—
706C2×D4—472no—
707C2×D4—472no—
708C2×D4—948no—
709C2×D4—944no—
710C2×D4—944no—
711C2×D4—944no—
712C2×D4—948no—
713C2×D4—944no—
714C2×D4—941no—
715C2×D4—942no—
716C2×D4—942no—
717C2×D4—944no—
718C2×D4—941no—
719C2×D4—941no—
720C2×D4—942no—
721C2×D4—942no—
722C2×D4—942no—
723C2×D4—3762no—
724C2×D4—3762no—
725C2×D4—1884no—
726C2×D4—1888no—
727C2×D4—1884no—
728C2×D4—1884no—
729C2×D4—1884no—
730C2×D4—1888no—
731C2×D4—1882no—
732C2×D4—1884no—
733C2×D4D4×D4714yes—
734C2×D4C23×D4712yes—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—24no—
741C22×C4—44no—
742C22×C4—471no—
743C22×C4—471no—
744C22×C4—471no—
745C22×C4—472no—
746C22×C4—472no—
747C22×C4—944no—
748C22×C4—944no—
749C22×C4—944no—
750C22×C4—942no—
751C22×C4—942no—
752C22×C4—941no—
753C22×C4—3762no—
754C22×C4—3762no—
755C22×C4—1884no—
756C22×C4D4×D4712yes—
757C22×C4D4×D4711yescharacteristic
758C22×C4C23×D4712yes—
759C22×C4C23×D4711yescharacteristic
760Q16—44no—
761SD16—28no—
762SD16—948no—
763SD16—948no—
764SD16—948no—
765D8—4716no—
766D8—948no—
767D8—948no—
768D8—1884no—
769M16—948no—
770M16—948no—
771C2×C8—22no—
772C2×C8—22no—
773C2×C8—474no—
774C2×C8—472no—
775C2×C8—472no—
776C2×C8—942no—
777C2×C8C23×D4712yes—
778C2×C8C23×D4712yes—
779C4⋊C4—24no—
780C4⋊C4—21no—
781C4⋊C4—474no—
782C4⋊C4—472no—
783C4⋊C4—944no—
784C4⋊C4—941no—
785C4⋊C4C23×D4712yes—
786C22⋊C4—24no—
787C22⋊C4—474no—
788C22⋊C4—474no—
789C22⋊C4—944no—
790C22⋊C4—944no—
791C22⋊C4—944no—
792C22⋊C4—944no—
793C22⋊C4—944no—
794C22⋊C4—944no—
795C22⋊C4—944no—
796C22⋊C4—944no—
797C22⋊C4—944no—
798C42—472no—
799C42—472no—
800C23—22no—
801C23—24no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—42no—
806C23—42no—
807C23—472no—
808C23—942no—
809C23—944no—
810C23—942no—
811C23—942no—
812C23—942no—
813C23—942no—
814C23—942no—
815C23—3764no—
816C23—3764no—
817C23—37616no—
818C23—37616no—
819C23—1888no—
820C23—1888no—
821C23—1888no—
822C23—1888no—
823C23—1882no—
824C23—1882no—
825C23—1882no—
826C23—1882no—
827C23—1882no—
828C23—1882no—
829C23—1882no—
830C23—1882no—
831C23C2×D4×D4712yes—
832C23C2×D4×D4711yescharacteristic
833Q8—22no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—42no—
838Q8—42no—
839D4—24no—
840D4—22no—
841D4—48no—
842D4—474no—
843D4—944no—
844D4—942no—
845D4—942no—
846D4—942no—
847D4—942no—
848D4—942no—
849D4—3764no—
850D4—3764no—
851D4—1888no—
852D4—1888no—
853D4—1884no—
854D4—1888no—
855D4—1882no—
856D4—1882no—
857D4C2×D4×D4714yes—
858C2×C4—22no—
859C2×C4—24no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—48no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—472no—
870C2×C4—472no—
871C2×C4—472no—
872C2×C4—942no—
873C2×C4—942no—
874C2×C4—942no—
875C2×C4—944no—
876C2×C4—942no—
877C2×C4—942no—
878C2×C4—942no—
879C2×C4—3764no—
880C2×C4—3764no—
881C2×C4—1888no—
882C2×C4—1882no—
883C2×C4C2×D4×D4712yes—
884C2×C4C2×D4×D4711yescharacteristic
885C2×C4C2×D4×D4712yes—
886C2×C4#1309406912yes—
887C2×C4C24×D4711yescharacteristic
888C8—22no—
889C8—22no—
890C8—474no—
891C8—942no—
892C22—22no—
893C22—24no—
894C22—22no—
895C22—22no—
896C22—44no—
897C22—48no—
898C22—42no—
899C22—42no—
900C22—942no—
901C22—944no—
902C22—942no—
903C22—942no—
904C22—37616no—
905C22—37616no—
906C22—3764no—
907C22—3764no—
908C22—1882no—
909C22—1882no—
910C22—1882no—
911C22—1882no—
912C22—1882no—
913C22—1882no—
914C22—1884no—
915C22—1888no—
916C22—1882no—
917C22—1882no—
918C22#1568975512yes—
919C22#1568992212yes—
920C22#1568992512yes—
921C22C22×D4×D4711yescharacteristic
922C4—22no—
923C4—42no—
924C4—42no—
925C4—42no—
926C4—942no—
927C4—942no—
928C4—942no—
929C4—1882no—
930C4#1568975512yes—
931C4C22×D4×D4711yescharacteristic
932C4C2×#1309406911yescharacteristic
933C2—42no—
934C2—44no—
935C2—3762no—
936C2—3762no—
937C2—1882no—
938C2—1884no—
939C2#2025499214yesdirect product factor
940C2C2×#1568975511yescharacteristic
941C2C2×#1568992211yescharacteristic
942C2C2×#1568992511yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#452C2
socleC23×C47C22×D4
hypercenterC2×#452D47
hypocenterC47C2×#3273
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C22×#13094051C2semidirect
2. C22×#13094049C2semidirect
3. C2×#15689764C2semidirect
4. C2×#15689761C2semidirect
5. #20254992C2direct (N × H)
6. C2×#15689508C2semidirect
7. C2×#15689372C2semidirect
8. C2×#15689371C2semidirect
9. C2×#15689341C2semidirect
10. C2×#15689340C2semidirect
11. C2×#15689284C2semidirect
12. C2×#15689259C2semidirect
13. C2×#15689258C2semidirect
14. C2×#15689203C2semidirect
15. C2×#15689198C2semidirect
16. C2×C47×#452C2semidirect
18. C23×D188C22semidirect
19. C22×D4×D47C22semidirect
21. C2×#13094051C22semidirect
23. C2×#13094049C22semidirect
24. C22×#10625336C22semidirect
25. C22×#10625336C22semidirect
26. C22×#10625336C22semidirect
31. C22×#10625329C22semidirect
32. C22×#10625324C22semidirect
34. #15689764C22semidirect
36. #15689761C22semidirect
37. C2×#13094013C22semidirect
38. C2×#13094013C22semidirect
41. C2×#13094000C22semidirect
48. C2×D4×Dic47C22semidirect
49. C2×#13093986C22semidirect
53. #15689508C22semidirect
54. #15689372C22semidirect
55. #15689371C22semidirect
56. #15689341C22semidirect
57. #15689340C22semidirect
58. #15689284C22semidirect
59. #15689259C22semidirect
60. #15689258C22semidirect
61. #15689203C22semidirect
62. #15689198C22semidirect
63. C2×#13093957C22semidirect
64. C2×Dic47⋊C8C22semidirect
65. C2×#13093948C22semidirect
66. C2×#13093946C22semidirect
67. C2×#13093946C22semidirect
68. C2×#13093944C22semidirect
69. C2×(C2×D47)⋊C8C22semidirect
70. C2×C8×Dic47C22semidirect
72. C22×Q16×C47C22semidirect
73. C22×SD16×C47C22semidirect
74. C2×C22⋊Q8×C47C22semidirect
75. C47×#452C22semidirect
76. C2×#103×C47C22semidirect
77. C2×#102×C47C22semidirect
78. C2×C22⋊C8×C47C22semidirect
94. C22×D188C23semidirect
101. C2×D4×D47C23semidirect
111. C2×#10625336C23semidirect
112. C2×#10625336C23semidirect
113. C2×#10625336C23semidirect
119. C2×#10625334D4semidirect
123. C2×#10625329C23semidirect
125. C2×#10625324C23semidirect
130. #13094013C23semidirect
131. #13094013C23semidirect
135. #13094000C23semidirect
145. D4×Dic47C23semidirect
147. #13093986C23semidirect
167. #13093957C23semidirect
168. Dic47⋊C8C23semidirect
169. #13093948C23semidirect
170. #13093946C23semidirect
171. #13093946C23semidirect
172. #13093944C23semidirect
173. (C2×D47)⋊C8C23semidirect
174. C8×Dic47C23semidirect
186. C2×Q16×C47C23semidirect
188. C2×SD16×C47C23semidirect
192. C22⋊Q8×C47C23semidirect
196. #103×C47C23semidirect
197. #102×C47C23semidirect
198. C22⋊C8×C47C23semidirect
304. #10625334C2×D4semidirect
473. C2×#452D47semidirect
480. C2×C47#3273semidirect
496. C22×Q16C2×D47semidirect
500. C22×SD16C2×D47semidirect
516. C2×C22⋊Q8C2×D47semidirect
534. #452C2×D47semidirect
542. C2×#103C2×D47semidirect
546. C2×#102C2×D47semidirect
548. C2×C22⋊C8C2×D47semidirect
550. C47C2×#3273semidirect
591. C2×Q16C22×D47semidirect
599. C2×SD16C22×D47semidirect
625. C22⋊Q8C22×D47semidirect
663. #103C22×D47semidirect
667. #102C22×D47semidirect
669. C22⋊C8C22×D47semidirect
939. C2#20254992direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940512
C22×#130940492
C2×#156897642
C2×#156897612
#202549922
C2×#156895082
C2×#156893722
C2×#156893712
C2×#156893412
C2×#156893402
C2×#156892842
C2×#156892592
C2×#156892582
C2×#156892032
C2×#156891982
C2×C47×#4522
C2×#327347