Finite Group Databasebeta

← C2×#20254996 #27091383

Subgroups — C2×#20254996 #27091383

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×#13094052C211yesmaximal, characteristic, complemented
2C22×#13094051C211yesmaximal, characteristic, complemented
3C2×#15689770C211yesmaximal, characteristic, complemented
4C2×#15689764C211yesmaximal, characteristic, complemented
5#20254996C2116yesmaximal, direct product factor
6C2×#15689504C211yesmaximal, characteristic, complemented
7C2×#15689370C211yesmaximal, characteristic, complemented
8C2×#15689341C211yesmaximal, characteristic, complemented
9C2×#15689337C211yesmaximal, characteristic, complemented
10C2×#15689288C211yesmaximal, characteristic, complemented
11C2×#15689283C211yesmaximal, characteristic, complemented
12C2×#15689258C211yesmaximal, characteristic, complemented
13C2×#15689256C211yesmaximal, characteristic, complemented
14C2×#15689205C211yesmaximal, characteristic, complemented
15C2×#15689199C211yesmaximal, characteristic, complemented
16C2×C47×#468C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625350C2211yescharacteristic
19C23×D188C2211yescharacteristic, complemented
20C22×D4×D47C2211yescharacteristic, complemented
21C2×#13094052—28no—
22C2×#13094052C2218yescomplemented
23C2×#13094051—28no—
24C2×#13094051C2218yescomplemented
25C22×#10625337C2211yescharacteristic, complemented
26C22×#10625325C2211yescharacteristic, complemented
27C22×#10625325C2211yescharacteristic, complemented
28C22×#10625336C2211yescharacteristic, complemented
29C22×D376C2211yescharacteristic
30C22×D376C2211yescharacteristic
31C22×#10625334C2211yescharacteristic
32C22×#10625334C2211yescharacteristic
33C22×#10625324C2211yescharacteristic, complemented
34#15689770—24no—
35#15689770C2218yescomplemented
36#15689764—24no—
37#15689764C2218yescomplemented
38C2×#13094013C2211yescharacteristic, complemented
39C2×#13094011C2211yescharacteristic, complemented
40C2×#13094009—21no—
41C2×#13094006—21no—
42C2×#13094004C2211yescharacteristic, complemented
43C2×#13093999—21no—
44C2×#13093999C2211yescharacteristic
45C2×#13093995—21no—
46C2×#13093994—21no—
47C2×#13093992—21no—
48C2×#13093986C2211yescharacteristic, complemented
49C2×#13093986C2211yescharacteristic, complemented
50C2×C4×C22⋊D47C2211yescharacteristic
51C2×C22⋊C4×D47—21no—
52C2×C22⋊C4×D47—21no—
53#15689504C2218yescomplemented
54#15689370C2218yescomplemented
55#15689341C2218yescomplemented
56#15689337C2218yescomplemented
57#15689288C2218yescomplemented
58#15689283C2218yescomplemented
59#15689258C2218yescomplemented
60#15689256C2218yescomplemented
61#15689205C2218yescomplemented
62#15689199C2218yescomplemented
63C2×Dic47⋊C8C2211yescharacteristic, complemented
64C2×#13093947C2211yescharacteristic, complemented
65C2×#13093944C2211yescharacteristic, complemented
66C2×#13093944C2211yescharacteristic, complemented
67C2×#13093944C2211yescharacteristic, complemented
68C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
69C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
70C2×C8×Dic47C2211yescharacteristic, complemented
71C22×SD16×C47C2211yescharacteristic, complemented
72C22×M16×C47C2211yescharacteristic, complemented
73C2×C22⋊Q8×C47C2211yescharacteristic, complemented
74C2×#121×C47C2211yescharacteristic
75C47×#468C2218yescomplemented
76C2×#107×C47C2211yescharacteristic, complemented
77C2×#103×C47C2211yescharacteristic, complemented
78C2×#102×C47C2211yescharacteristic, complemented
79C24×D47—21no—
80C24×D47—21no—
81C2×#10625354—22no—
82C2×#10625354—24no—
83C2×#10625354—42no—
84C2×#10625354C2314yes—
85C2×#10625350—22no—
86C2×#10625350—24no—
87C2×#10625350—42no—
88C2×#10625350C2314yes—
89C22×Dic94C2311yescharacteristic
90C22×D188—24no—
91C22×D188—21no—
92C22×D188—22no—
93C22×D188—21no—
94C22×D188—21no—
95C22×D188—42no—
96C22×D188C2311yescharacteristic
97C22×D188C2311yescharacteristic
98C22×D188C2311yescharacteristic
99C22×D188C2314yescomplemented
100C22×C22⋊D47—21no—
101C22×C22⋊D47—21no—
102C22×C22⋊D47D411yescharacteristic
103C2×D4×D47—24no—
104C2×D4×D47—22no—
105C2×D4×D47—42no—
106C2×D4×D47C2314yescomplemented
107C22×C4×D47—21no—
108C22×C4×D47—21no—
109C22×C4×D47—21no—
110C22×C4×D47—21no—
111C22×C4×D47C2311yescharacteristic
112#13094052—232no—
113#13094051—232no—
114C2×#10625337—42no—
115C2×#10625337C2314yescomplemented
116C2×#10625325—24no—
117C2×#10625325—24no—
118C2×#10625325C2314yescomplemented
119C2×#10625325C2314yescomplemented
120C2×#10625336—24no—
121C2×#10625336C2314yescomplemented
122C2×D376—24no—
123C2×D376D418yescomplemented
124C2×D376C2314yes—
125C2×D376C2314yes—
126C2×#10625334—24no—
127C2×#10625334—42no—
128C2×#10625334C2314yes—
129C2×#10625334C2314yes—
130C2×#10625324—24no—
131C2×#10625324C2314yescomplemented
132C22×C47⋊C8C2311yescharacteristic
133C22×C47⋊C8C2311yescharacteristic
134#13094013—22no—
135#13094013C2314yescomplemented
136#13094011—22no—
137#13094011C2314yescomplemented
138#13094009—28no—
139#13094006—28no—
140#13094004—22no—
141#13094004C2314yescomplemented
142#13093999—22no—
143#13093999—28no—
144#13093999C2314yes—
145#13093995—28no—
146#13093994—28no—
147#13093992—28no—
148#13093986—22no—
149#13093986—22no—
150#13093986C2314yescomplemented
151#13093986C2314yescomplemented
152C4×C22⋊D47D414yes—
153C4×C22⋊D47C2314yes—
154C2×C4⋊Dic47—21no—
155C2×Dic47⋊C4D411yescharacteristic
156C2×C22⋊Dic47—21no—
157C2×C22⋊Dic47—21no—
158C2×C22⋊Dic47D411yescharacteristic
159C2×(C2×D47)⋊C4—21no—
160C2×(C2×D47)⋊C4—21no—
161C2×(C2×D47)⋊C4—21no—
162C2×(C2×D47)⋊C4—21no—
163C2×(C2×D47)⋊C4—21no—
164C2×(C2×D47)⋊C4—21no—
165C2×(C2×D47)⋊C4D411yescharacteristic
166C22⋊C4×D47—28no—
167C22⋊C4×D47—28no—
168C2×C4×Dic47C2311yescharacteristic
169Dic47⋊C8C2314yescomplemented
170#13093947C2314yescomplemented
171#13093944C2314yescomplemented
172#13093944C2314yescomplemented
173#13093944C2314yescomplemented
174C22⋊(C47⋊C8)C2314yescomplemented
175(C2×D47)⋊C8C2314yescomplemented
176C8×Dic47C2314yescomplemented
177C22×Q8×C47C2311yescharacteristic
178C22×D4×C47—21no—
179C22×D4×C47C2311yescharacteristic
180C23×C4×C47C2311yescharacteristic
181C2×SD16×C47—24no—
182C2×SD16×C47C2314yescomplemented
183C2×M16×C47—24no—
184C2×M16×C47C2314yescomplemented
185C22×C8×C47C2311yescharacteristic
186C22×C8×C47C2311yescharacteristic
187C22⋊Q8×C47—22no—
188C22⋊Q8×C47C2314yescomplemented
189#121×C47—22no—
190#121×C47C2314yes—
191C2×C4⋊C4×C47—21no—
192C2×C4⋊C4×C47C2311yescharacteristic
193C2×C4⋊C4×C47C2311yescharacteristic
194C2×C22⋊C4×C47—21no—
195C2×C22⋊C4×C47—21no—
196#107×C47C2314yescomplemented
197#103×C47C2314yescomplemented
198#102×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
213C2×Q8×C47—21no—
214C2×Q8×C47—22no—
215C2×Q8×C47—22no—
216C2×Q8×C47C2412yes—
217C2×D4×C47—24no—
218C2×D4×C47—22no—
219C2×D4×C47—21no—
220C2×D4×C47—22no—
221C2×D4×C47—82no—
222C2×D4×C47C2412yes—
223C22×C4×C47—22no—
224C22×C4×C47—22no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2×D412yes—
230C22×C4×C47C2412yes—
231C22×C4×C47C2411yescharacteristic
232C2×C22⋊D47—24no—
233C2×C22⋊D47—24no—
234C2×C22⋊D47—42no—
235C2×C22⋊D47—44no—
236C2×C22⋊D47—44no—
237C2×C22⋊D47C2×D414yes—
238C22×Dic47—21no—
239C22×Dic47C2×D411yescharacteristic
240C22×Dic47C2×D411yescharacteristic
241C22×Dic47C2×D411yescharacteristic
242#10625354—28no—
243#10625354—44no—
244#10625354—48no—
245D4×D47—28no—
246D4×D47—44no—
247D4×D47—48no—
248#10625350—28no—
249#10625350—44no—
250#10625350—48no—
251C2×D188—21no—
252C2×D188—21no—
253C2×D188—22no—
254C2×D188—22no—
255C2×D188—22no—
256C2×D188—22no—
257C2×D188—28no—
258C2×D188—24no—
259C2×D188—24no—
260C2×D188—21no—
261C2×D188—24no—
262C2×D188—44no—
263C2×D188—48no—
264C2×D188—44no—
265C2×D188—44no—
266C2×D188—82no—
267C2×D188C2×D414yes—
268C2×D188C2×D414yes—
269C2×D188C2412yes—
270C2×D188C2412yes—
271C2×D188C2412yes—
272C2×C4×D47—22no—
273C2×C4×D47—22no—
274C2×C4×D47—24no—
275C2×C4×D47—24no—
276C2×C4×D47—24no—
277C2×C4×D47—24no—
278C2×C4×D47—44no—
279C2×C4×D47—44no—
280C2×C4×D47—82no—
281C2×C4×D47—82no—
282C2×C4×D47C2×D412yes—
283C2×C4×D47C2412yes—
284C2×Dic94—22no—
285C2×Dic94—22no—
286C2×Dic94—21no—
287C2×Dic94C2412yes—
288SD16×C47—28no—
289M16×C47—28no—
290C2×C8×C47—22no—
291C2×C8×C47C2×D414yes—
292C2×C8×C47C2412yes—
293C2×C8×C47C2412yes—
294C4⋊C4×C47—24no—
295C4⋊C4×C47—21no—
296C4⋊C4×C47—21no—
297C4⋊C4×C47C2412yes—
298C4⋊C4×C47C2412yes—
299C22⋊C4×C47—24no—
300C22⋊C4×C47—24no—
301C22⋊Dic47—24no—
302C22⋊Dic47—24no—
303C22⋊Dic47C2×D414yes—
304#10625337—44no—
305#10625336—28no—
306#10625334—28no—
307#10625334—44no—
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)⋊C4—24no—
314(C2×D47)⋊C4C2×D414yes—
315C4⋊Dic47—24no—
316Dic47⋊C4C2×D414yes—
317C4×Dic47C2×D412yes—
318C4×Dic47C2412yes—
319C2×C47⋊C8—22no—
320C2×C47⋊C8—22no—
321C2×C47⋊C8C2412yes—
322C2×C47⋊C8C2412yes—
323D376—28no—
324D376C2×D4116yescomplemented
325#10625325—28no—
326#10625325—28no—
327#10625324—28no—
328C23×C47—22no—
329C23×C47—22no—
330C23×C47—22no—
331C23×C47—22no—
332C23×C47—42no—
333C23×C47—42no—
334C23×C47—42no—
335C23×C47C22×D412yes—
336C23×C47C22×D411yescharacteristic
337C22×D47—22no—
338C22×D47—24no—
339C22×D47—24no—
340C22×D47—22no—
341C22×D47—22no—
342C22×D47—22no—
343C22×D47—22no—
344C22×D47—22no—
345C22×D47—48no—
346C22×D47—48no—
347C22×D47—48no—
348C22×D47—42no—
349C22×D47—42no—
350C22×D47—42no—
351C22×D47—42no—
352C22×D47—48no—
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—42no—
364D4×C47—22no—
365D4×C47—22no—
366D4×C47—42no—
367D4×C47—84no—
368C2×C4×C47—22no—
369C2×C4×C47—24no—
370C2×C4×C47—22no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—42no—
376C2×C4×C47—42no—
377C2×C4×C47—42no—
378C2×C4×C47C22×D412yes—
379C2×C4×C47C22×D411yescharacteristic
380C2×C4×C47C22×D412yes—
381C2×C4×C47H(5,𝔽2)12yes—
382C2×C4×C47C2511yescharacteristic
383C22⋊D47—44no—
384C22⋊D47—48no—
385C22⋊D47—48no—
386C2×Dic47—22no—
387C2×Dic47—22no—
388C2×Dic47—22no—
389C2×Dic47—22no—
390C2×Dic47—42no—
391C2×Dic47C22×D412yes—
392C2×Dic47C22×D412yes—
393C2×Dic47C22×D412yes—
394D188—24no—
395D188—24no—
396D188—22no—
397D188—22no—
398D188—22no—
399D188—22no—
400D188—48no—
401D188—48no—
402D188—42no—
403D188—84no—
404D188C22×D414yes—
405D188C22×D414yes—
406C4×D47—24no—
407C4×D47—22no—
408C4×D47—22no—
409C4×D47—48no—
410C4×D47—48no—
411C4×D47—84no—
412C4×D47—84no—
413Dic94—22no—
414Dic94—22no—
415Dic94—42no—
416C8×C47—22no—
417C8×C47C22×D414yes—
418C47⋊C8—22no—
419C47⋊C8—22no—
420C2×#3273—471nomaximal, Sylow
421C22×C47—22no—
422C22×C47—22no—
423C22×C47—22no—
424C22×C47—44no—
425C22×C47—42no—
426C22×C47—42no—
427C22×C47—42no—
428C22×C47—84no—
429C22×C47D4212yes—
430C22×C47#57512yes—
431C22×C47#57612yes—
432C22×C47C23×D411yescharacteristic
433C2×D47—22no—
434C2×D47—24no—
435C2×D47—24no—
436C2×D47—22no—
437C2×D47—22no—
438C2×D47—44no—
439C2×D47—48no—
440C2×D47—48no—
441C2×D47—42no—
442C2×D47—42no—
443C2×D47—42no—
444C2×D47—42no—
445C2×D47—42no—
446C2×D47—42no—
447C2×D47—42no—
448C2×D47—816no—
449C2×D47—816no—
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×#468D4711yescharacteristic, complemented
470C2×#463—471no—
471C2×#463—471no—
472C2×#452—471no—
473C2×#452—471no—
474C2×#447—471no—
475C2×#447—471no—
476C2×C4×D8—471no—
477C2×#436—471no—
478C2×C47—42no—
479C2×C47—82no—
480C2×C47#327314yescomplemented
481C2×C47C2×D4211yescharacteristic
482C2×C47C2×#57511yescharacteristic
483C2×C47C2×#57611yescharacteristic
484D47—42no—
485D47—44no—
486D47—44no—
487D47—82no—
488C22×#41—471no—
489C22×#41—471no—
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×Q16—471no—
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×M16C2×D4711yescharacteristic, complemented
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—941no—
519C2×#121—941no—
520C2×#121C2×D4711yescharacteristic
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#468C2×D4718yescomplemented
531#463—478no—
532#463—478no—
533#452—478no—
534#452—478no—
535#447—478no—
536#447—478no—
537C4×D8—478no—
538#436—478no—
539C2×#107C2×D4711yescharacteristic, complemented
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⋊C8—471no—
549C2×C4×C8—471no—
550C47C2×#327311yescharacteristic, complemented, Sylow
551C25—941no—
552C25—941no—
553C2×#41—474no—
554C2×#41—474no—
555C2×#41—944no—
556C2×#41—942no—
557C2×#41—942no—
558C2×#41—944no—
559C2×#41—1882no—
560C2×#41—1882no—
561C22×Q8—471no—
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—471no—
583C23×C4—941no—
584C23×C4—941no—
585C23×C4—941no—
586C23×C4—941no—
587C23×C4C22×D4711yescharacteristic
588AGL(1,ℤ/8)—9432no—
589AGL(1,ℤ/8)—9432no—
590C2×Q16—474no—
591C2×Q16—1882no—
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—474no—
601C2×D8—474no—
602C2×D8—478no—
603C2×D8—474no—
604C2×D8—474no—
605C2×D8—944no—
606C2×D8—944no—
607C2×D8—1882no—
608C2×M16—24no—
609C2×M16—474no—
610C2×M16—944no—
611C2×M16C22×D4714yescomplemented
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—22no—
627#121—474no—
628#121—948no—
629#121—948no—
630#121—942no—
631#121C22×D4714yes—
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—941no—
643C2×C4⋊C4C22×D4711yescharacteristic
644C2×C4⋊C4C22×D4711yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—471no—
648C2×C22⋊C4—471no—
649C2×C22⋊C4—948no—
650C2×C22⋊C4—948no—
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#107C22×D4714yescomplemented
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⋊C8—474no—
670C4×C8—474no—
671C24—21no—
672C24—471no—
673C24—944no—
674C24—941no—
675C24—941no—
676C24—944no—
677C24—941no—
678C24—3762no—
679C24—3762no—
680C24—1884no—
681C24—1884no—
682C24—1884no—
683C24—1884no—
684C24D4×D4711yescharacteristic
685#41—948no—
686#41—948no—
687#41—1884no—
688#41—1888no—
689#41—1884no—
690#41—1888no—
691C2×Q8—21no—
692C2×Q8—22no—
693C2×Q8—22no—
694C2×Q8—472no—
695C2×Q8—941no—
696C2×Q8—942no—
697C2×Q8—942no—
698C2×Q8C23×D4712yes—
699C2×D4—24no—
700C2×D4—22no—
701C2×D4—21no—
702C2×D4—22no—
703C2×D4—82no—
704C2×D4—474no—
705C2×D4—474no—
706C2×D4—474no—
707C2×D4—472no—
708C2×D4—472no—
709C2×D4—472no—
710C2×D4—948no—
711C2×D4—944no—
712C2×D4—944no—
713C2×D4—944no—
714C2×D4—948no—
715C2×D4—944no—
716C2×D4—941no—
717C2×D4—941no—
718C2×D4—942no—
719C2×D4—944no—
720C2×D4—941no—
721C2×D4—942no—
722C2×D4—942no—
723C2×D4—942no—
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×D4—1884no—
734C2×D4C23×D4712yes—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—471no—
741C22×C4—471no—
742C22×C4—471no—
743C22×C4—472no—
744C22×C4—472no—
745C22×C4—944no—
746C22×C4—944no—
747C22×C4—944no—
748C22×C4—942no—
749C22×C4—942no—
750C22×C4—941no—
751C22×C4—944no—
752C22×C4—3762no—
753C22×C4—3762no—
754C22×C4—1884no—
755C22×C4—1884no—
756C22×C4D4×D4712yes—
757C22×C4D4×D4711yescharacteristic
758C22×C4C23×D4712yes—
759C22×C4C23×D4711yescharacteristic
760Q16—1884no—
761SD16—28no—
762SD16—948no—
763SD16—948no—
764SD16—948no—
765D8—4716no—
766D8—948no—
767D8—948no—
768D8—1884no—
769M16—28no—
770M16—948no—
771C2×C8—22no—
772C2×C8—472no—
773C2×C8—472no—
774C2×C8—942no—
775C2×C8—942no—
776C2×C8D4×D4714yes—
777C2×C8C23×D4712yes—
778C2×C8C23×D4712yes—
779C4⋊C4—24no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—474no—
783C4⋊C4—944no—
784C4⋊C4C23×D4712yes—
785C4⋊C4C23×D4712yes—
786C22⋊C4—24no—
787C22⋊C4—24no—
788C22⋊C4—474no—
789C22⋊C4—474no—
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—22no—
802C23—22no—
803C23—22no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—472no—
808C23—942no—
809C23—944no—
810C23—944no—
811C23—942no—
812C23—942no—
813C23—942no—
814C23—942no—
815C23—942no—
816C23—3764no—
817C23—3764no—
818C23—37616no—
819C23—37616no—
820C23—1888no—
821C23—1888no—
822C23—1888no—
823C23—1888no—
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—42no—
836Q8—942no—
837Q8—942no—
838Q8—1882no—
839D4—22no—
840D4—22no—
841D4—42no—
842D4—84no—
843D4—474no—
844D4—474no—
845D4—944no—
846D4—944no—
847D4—942no—
848D4—942no—
849D4—942no—
850D4—942no—
851D4—3764no—
852D4—1888no—
853D4—1888no—
854D4—1884no—
855D4—1888no—
856D4—1888no—
857D4—1882no—
858C2×C4—22no—
859C2×C4—24no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—472no—
869C2×C4—472no—
870C2×C4—472no—
871C2×C4—942no—
872C2×C4—942no—
873C2×C4—942no—
874C2×C4—944no—
875C2×C4—942no—
876C2×C4—942no—
877C2×C4—942no—
878C2×C4—3764no—
879C2×C4—3764no—
880C2×C4—1888no—
881C2×C4—1888no—
882C2×C4—1882no—
883C2×C4C2×D4×D4712yes—
884C2×C4C2×D4×D4711yescharacteristic
885C2×C4C2×D4×D4712yes—
886C2×C4#1309407012yes—
887C2×C4C24×D4711yescharacteristic
888C8—22no—
889C8—942no—
890C8—942no—
891C8C2×D4×D4714yes—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—84no—
900C22—942no—
901C22—944no—
902C22—944no—
903C22—942no—
904C22—942no—
905C22—37616no—
906C22—37616no—
907C22—3764no—
908C22—1882no—
909C22—1882no—
910C22—1882no—
911C22—1884no—
912C22—1888no—
913C22—1888no—
914C22—1882no—
915C22—1882no—
916C22—1882no—
917C22—1882no—
918C22#1568975712yes—
919C22#1568992212yes—
920C22#1568992712yes—
921C22C22×D4×D4711yescharacteristic
922C4—22no—
923C4—42no—
924C4—42no—
925C4—42no—
926C4—942no—
927C4—942no—
928C4—942no—
929C4—1882no—
930C4#1568975712yes—
931C4C22×D4×D4711yescharacteristic
932C4C2×#1309407011yescharacteristic
933C2—42no—
934C2—82no—
935C2—3762no—
936C2—1882no—
937C2—1884no—
938C2—1884no—
939C2#2025499614yesdirect product factor
940C2C2×#1568975711yescharacteristic
941C2C2×#1568992211yescharacteristic
942C2C2×#1568992711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#468C2
socleC23×C47C22×D4
hypercenterC2×#468D47
hypocenterC47C2×#3273
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C22×#13094052C2semidirect
2. C22×#13094051C2semidirect
3. C2×#15689770C2semidirect
4. C2×#15689764C2semidirect
5. #20254996C2direct (N × H)
6. C2×#15689504C2semidirect
7. C2×#15689370C2semidirect
8. C2×#15689341C2semidirect
9. C2×#15689337C2semidirect
10. C2×#15689288C2semidirect
11. C2×#15689283C2semidirect
12. C2×#15689258C2semidirect
13. C2×#15689256C2semidirect
14. C2×#15689205C2semidirect
15. C2×#15689199C2semidirect
16. C2×C47×#468C2semidirect
19. C23×D188C22semidirect
20. C22×D4×D47C22semidirect
22. C2×#13094052C22semidirect
24. C2×#13094051C22semidirect
25. C22×#10625337C22semidirect
26. C22×#10625325C22semidirect
27. C22×#10625325C22semidirect
28. C22×#10625336C22semidirect
33. C22×#10625324C22semidirect
35. #15689770C22semidirect
37. #15689764C22semidirect
38. C2×#13094013C22semidirect
39. C2×#13094011C22semidirect
42. C2×#13094004C22semidirect
48. C2×#13093986C22semidirect
49. C2×#13093986C22semidirect
53. #15689504C22semidirect
54. #15689370C22semidirect
55. #15689341C22semidirect
56. #15689337C22semidirect
57. #15689288C22semidirect
58. #15689283C22semidirect
59. #15689258C22semidirect
60. #15689256C22semidirect
61. #15689205C22semidirect
62. #15689199C22semidirect
63. C2×Dic47⋊C8C22semidirect
64. C2×#13093947C22semidirect
65. C2×#13093944C22semidirect
66. C2×#13093944C22semidirect
67. C2×#13093944C22semidirect
68. C2×C22⋊(C47⋊C8)C22semidirect
69. C2×(C2×D47)⋊C8C22semidirect
70. C2×C8×Dic47C22semidirect
71. C22×SD16×C47C22semidirect
72. C22×M16×C47C22semidirect
73. C2×C22⋊Q8×C47C22semidirect
75. C47×#468C22semidirect
76. C2×#107×C47C22semidirect
77. C2×#103×C47C22semidirect
78. C2×#102×C47C22semidirect
99. C22×D188C23semidirect
106. C2×D4×D47C23semidirect
115. C2×#10625337C23semidirect
118. C2×#10625325C23semidirect
119. C2×#10625325C23semidirect
121. C2×#10625336C23semidirect
123. C2×D376D4semidirect
131. C2×#10625324C23semidirect
135. #13094013C23semidirect
137. #13094011C23semidirect
141. #13094004C23semidirect
150. #13093986C23semidirect
151. #13093986C23semidirect
169. Dic47⋊C8C23semidirect
170. #13093947C23semidirect
171. #13093944C23semidirect
172. #13093944C23semidirect
173. #13093944C23semidirect
174. C22⋊(C47⋊C8)C23semidirect
175. (C2×D47)⋊C8C23semidirect
176. C8×Dic47C23semidirect
182. C2×SD16×C47C23semidirect
184. C2×M16×C47C23semidirect
188. C22⋊Q8×C47C23semidirect
196. #107×C47C23semidirect
197. #103×C47C23semidirect
198. #102×C47C23semidirect
324. D376C2×D4semidirect
469. C2×#468D47semidirect
480. C2×C47#3273semidirect
500. C22×SD16C2×D47semidirect
506. C22×M16C2×D47semidirect
516. C2×C22⋊Q8C2×D47semidirect
530. #468C2×D47semidirect
539. C2×#107C2×D47semidirect
542. C2×#103C2×D47semidirect
546. C2×#102C2×D47semidirect
550. C47C2×#3273semidirect
599. C2×SD16C22×D47semidirect
611. C2×M16C22×D47semidirect
625. C22⋊Q8C22×D47semidirect
660. #107C22×D47semidirect
663. #103C22×D47semidirect
667. #102C22×D47semidirect
939. C2#20254996direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940522
C22×#130940512
C2×#156897702
C2×#156897642
#202549962
C2×#156895042
C2×#156893702
C2×#156893412
C2×#156893372
C2×#156892882
C2×#156892832
C2×#156892582
C2×#156892562
C2×#156892052
C2×#156891992
C2×C47×#4682
C2×#327347