Finite Group Databasebeta

← C2×#20254930 #27091293

Subgroups — C2×#20254930 #27091293

Order 12032.

2966 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094051C211yesmaximal, characteristic, complemented
2C22×#13094045C211yesmaximal, characteristic, complemented
3C2×#15689795C211yesmaximal, characteristic, complemented
4C2×#15689768C211yesmaximal, characteristic, complemented
5#20254930C2116yesmaximal, direct product factor
6C2×#15689512C211yesmaximal, characteristic, complemented
7C2×#15689370C211yesmaximal, characteristic, complemented
8C2×#15689360C211yesmaximal, characteristic, complemented
9C2×#15689345C211yesmaximal, characteristic, complemented
10C2×#15689318C211yesmaximal, characteristic, complemented
11C2×#15689288C211yesmaximal, characteristic, complemented
12C2×#15689271C211yesmaximal, characteristic, complemented
13C2×#15689269C211yesmaximal, characteristic, complemented
14C2×#15689258C211yesmaximal, characteristic, complemented
15C2×#15689196C211yesmaximal, characteristic, complemented
16C2×C47×#440C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625354C2211yescharacteristic, complemented
19C22×#10625352C2211yescharacteristic
20C22×D4×D47C2211yescharacteristic
21C2×#13094051—28no—
22C2×#13094051C2218yescomplemented
23C2×#13094045—28no—
24C2×#13094045C2218yescomplemented
25C22×#10625337C2211yescharacteristic, complemented
26C22×#10625325C2211yescharacteristic, complemented
27C22×#10625325C2211yescharacteristic, complemented
28C22×#10625336C2211yescharacteristic
29C22×D376C2211yescharacteristic
30C22×D376C2211yescharacteristic
31C22×#10625334C2211yescharacteristic
32C22×#10625334C2211yescharacteristic
33C22×#10625324C2211yescharacteristic
34C22×C8×D47C2211yescharacteristic, complemented
35#15689795—24no—
36#15689795C2218yescomplemented
37#15689768—24no—
38#15689768C2218yescomplemented
39C2×#13094021—21no—
40C2×#13094021C2211yescharacteristic, complemented
41C2×#13094012C2211yescharacteristic
42C2×#13094008—21no—
43C2×#13094004C2211yescharacteristic
44C2×#13093999—21no—
45C2×#13093999—21no—
46C2×#13093999C2211yescharacteristic
47C2×#13093999C2211yescharacteristic
48C2×#13093999C2211yescharacteristic, complemented
49C2×#13093998—21no—
50C2×#13093994—21no—
51C2×C4×D188—21no—
52C2×C4×D188C2211yescharacteristic
53C22×(C2×D47)⋊C4—21no—
54#15689512C2218yescomplemented
55#15689370C2218yescomplemented
56#15689360C2218yescomplemented
57#15689345C2218yescomplemented
58#15689318C2218yescomplemented
59#15689288C2218yescomplemented
60#15689271C2218yescomplemented
61#15689269C2218yescomplemented
62#15689258C2218yescomplemented
63#15689196C2218yescomplemented
64C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
65C2×#13093947C2211yescharacteristic, complemented
66C2×#13093944C2211yescharacteristic
67C2×#13093944C2211yescharacteristic, complemented
68C2×#13093944C2211yescharacteristic, complemented
69C2×(C2×D47)⋊C8C2211yescharacteristic
70C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
71C22×SD16×C47C2211yescharacteristic
72C2×C4×Q8×C47C2211yescharacteristic, complemented
73C2×C4×D4×C47C2211yescharacteristic
74C47×#440C2218yescomplemented
75C2×#107×C47C2211yescharacteristic, complemented
76C2×#103×C47C2211yescharacteristic, complemented
77C2×#102×C47C2211yescharacteristic
78C2×#97×C47C2211yescharacteristic, complemented
79C24×D47—21no—
80C2×#10625354—22no—
81C2×#10625354—22no—
82C2×#10625354—24no—
83C2×#10625354—24no—
84C2×#10625354—42no—
85C2×#10625354—42no—
86C2×#10625354C2314yes—
87C2×#10625354C2314yescomplemented
88C2×#10625352—24no—
89C2×#10625352—22no—
90C2×#10625352—42no—
91C2×#10625352C2314yes—
92C22×Dic94C2311yescharacteristic
93C22×D188—21no—
94C22×D188—21no—
95C22×D188—21no—
96C22×D188—21no—
97C22×D188—21no—
98C22×D188—21no—
99C22×D188—21no—
100C22×D188D411yescharacteristic
101C22×D188C2311yescharacteristic
102C22×D188C2311yescharacteristic
103C22×D188C2311yescharacteristic
104C22×C22⋊D47—21no—
105C22×C22⋊D47—21no—
106C2×D4×D47—24no—
107C2×D4×D47—22no—
108C2×D4×D47—42no—
109C2×D4×D47C2314yes—
110C23×Dic47—21no—
111C22×C4×D47—21no—
112C22×C4×D47—21no—
113C22×C4×D47C2311yescharacteristic
114C22×C4×D47C2311yescharacteristic
115#13094051—232no—
116#13094045—232no—
117C2×#10625337—24no—
118C2×#10625337C2314yescomplemented
119C2×#10625325—24no—
120C2×#10625325—42no—
121C2×#10625325C2314yescomplemented
122C2×#10625325C2314yescomplemented
123C2×#10625336—24no—
124C2×#10625336C2314yes—
125C2×D376—24no—
126C2×D376—42no—
127C2×D376C2314yes—
128C2×D376C2314yes—
129C2×#10625334—24no—
130C2×#10625334—24no—
131C2×#10625334C2314yes—
132C2×#10625334C2314yes—
133C2×#10625324—24no—
134C2×#10625324C2314yes—
135C22×C47⋊C8C2311yescharacteristic
136C22×C47⋊C8C2311yescharacteristic
137C2×C8×D47—24no—
138C2×C8×D47C2314yescomplemented
139#13094021—28no—
140#13094021—22no—
141#13094021C2314yescomplemented
142#13094012—22no—
143#13094012C2314yes—
144#13094008—28no—
145#13094004—22no—
146#13094004C2314yes—
147#13093999—22no—
148#13093999—22no—
149#13093999—22no—
150#13093999—28no—
151#13093999—28no—
152#13093999C2314yes—
153#13093999C2314yes—
154#13093999C2314yescomplemented
155#13093998—28no—
156#13093994—28no—
157C4×D188—28no—
158C4×D188D414yes—
159C4×D188C2314yes—
160C2×C4⋊Dic47—21no—
161C2×C4⋊Dic47D411yescharacteristic
162C2×(C2×D47)⋊C4—21no—
163C2×(C2×D47)⋊C4—21no—
164C2×(C2×D47)⋊C4—21no—
165C2×(C2×D47)⋊C4—21no—
166C2×(C2×D47)⋊C4—21no—
167C2×(C2×D47)⋊C4—21no—
168C2×(C2×D47)⋊C4—28no—
169C2×(C2×D47)⋊C4D411yescharacteristic
170C2×(C2×D47)⋊C4D411yescharacteristic
171C4⋊(C47⋊C8)C2314yescomplemented
172#13093947C2314yescomplemented
173#13093944C2314yes—
174#13093944C2314yescomplemented
175#13093944C2314yescomplemented
176(C2×D47)⋊C8C2314yes—
177(C2×D47)⋊C8C2314yescomplemented
178C22×Q8×C47C2311yescharacteristic
179C22×D4×C47C2311yescharacteristic
180C23×C4×C47—21no—
181C2×SD16×C47D418yescomplemented
182C2×SD16×C47C2314yes—
183C22×C8×C47C2311yescharacteristic
184C22×C8×C47C2311yescharacteristic
185C4×Q8×C47—22no—
186C4×Q8×C47C2314yescomplemented
187C4×D4×C47—22no—
188C4×D4×C47C2314yes—
189C2×C4⋊C4×C47—21no—
190C2×C4⋊C4×C47C2311yescharacteristic
191C2×C4⋊C4×C47C2311yescharacteristic
192C2×C22⋊C4×C47—21no—
193C2×C42×C47—21no—
194C2×C42×C47C2311yescharacteristic
195#107×C47C2314yescomplemented
196#103×C47C2314yescomplemented
197#102×C47C2314yes—
198#97×C47C2314yescomplemented
199C24×C47—21no—
200C23×D47—21no—
201C23×D47—21no—
202C23×D47—21no—
203C23×D47—24no—
204C23×D47—44no—
205C23×D47—44no—
206C23×D47—82no—
207C23×D47C2×D411yescharacteristic
208C23×D47C2×D411yescharacteristic
209C2×Q8×C47—21no—
210C2×Q8×C47—22no—
211C2×Q8×C47C2×D414yes—
212C2×Q8×C47C2412yes—
213C2×D4×C47—21no—
214C2×D4×C47—22no—
215C2×D4×C47C2×D414yes—
216C2×D4×C47C2412yes—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—24no—
221C22×C4×C47—82no—
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2411yescharacteristic
225C2×C22⋊D47—24no—
226C2×C22⋊D47—24no—
227C2×C22⋊D47—44no—
228C2×C22⋊D47—44no—
229C22×Dic47—21no—
230C22×Dic47—24no—
231C22×Dic47—44no—
232C22×Dic47C2×D411yescharacteristic
233C22×Dic47C2×D411yescharacteristic
234#10625354—28no—
235#10625354—28no—
236#10625354—44no—
237#10625354—44no—
238#10625354—48no—
239#10625354—48no—
240#10625352—28no—
241#10625352—44no—
242#10625352—48no—
243D4×D47—28no—
244D4×D47—44no—
245D4×D47—48no—
246C2×D188—22no—
247C2×D188—22no—
248C2×D188—22no—
249C2×D188—22no—
250C2×D188—22no—
251C2×D188—22no—
252C2×D188—24no—
253C2×D188—24no—
254C2×D188—24no—
255C2×D188—21no—
256C2×D188—21no—
257C2×D188—21no—
258C2×D188—24no—
259C2×D188—24no—
260C2×D188—24no—
261C2×D188—24no—
262C2×D188—42no—
263C2×D188—44no—
264C2×D188—44no—
265C2×D188—44no—
266C2×D188—82no—
267C2×D188—82no—
268C2×D188—82no—
269C2×D188—82no—
270C2×D188C2×D414yes—
271C2×D188C2412yes—
272C2×D188C2412yes—
273C2×D188C2412yes—
274C2×C4×D47—22no—
275C2×C4×D47—22no—
276C2×C4×D47—22no—
277C2×C4×D47—22no—
278C2×C4×D47—24no—
279C2×C4×D47—24no—
280C2×C4×D47—44no—
281C2×C4×D47—44no—
282C2×C4×D47C2×D412yes—
283C2×C4×D47C2×D412yes—
284C2×C4×D47C2412yes—
285C2×C4×D47C2412yes—
286C2×Dic94—22no—
287C2×Dic94—22no—
288C2×Dic94—21no—
289C2×Dic94C2412yes—
290SD16×C47C2×D4116yescomplemented
291C2×C8×C47—22no—
292C2×C8×C47C2×D414yes—
293C2×C8×C47C2412yes—
294C2×C8×C47C2412yes—
295C4⋊C4×C47—24no—
296C4⋊C4×C47—21no—
297C4⋊C4×C47—21no—
298C4⋊C4×C47C2412yes—
299C4⋊C4×C47C2412yes—
300C22⋊C4×C47—24no—
301C42×C47—24no—
302C42×C47C2×D412yes—
303C42×C47C2412yes—
304#10625337—28no—
305#10625336—28no—
306#10625334—28no—
307#10625334—28no—
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—
315(C2×D47)⋊C4C2×D414yes—
316C4⋊Dic47—24no—
317C4⋊Dic47C2×D414yes—
318C2×C47⋊C8—22no—
319C2×C47⋊C8—22no—
320C2×C47⋊C8C2412yes—
321C2×C47⋊C8C2412yes—
322D376—28no—
323D376—44no—
324#10625325—28no—
325#10625325—44no—
326#10625324—28no—
327C8×D47—28no—
328C23×C47—24no—
329C23×C47—22no—
330C23×C47—42no—
331C23×C47—42no—
332C23×C47C22×D411yescharacteristic
333C22×D47—22no—
334C22×D47—22no—
335C22×D47—22no—
336C22×D47—22no—
337C22×D47—22no—
338C22×D47—22no—
339C22×D47—22no—
340C22×D47—22no—
341C22×D47—22no—
342C22×D47—48no—
343C22×D47—48no—
344C22×D47—42no—
345C22×D47—42no—
346C22×D47—42no—
347C22×D47—42no—
348C22×D47—42no—
349C22×D47—42no—
350C22×D47—42no—
351C22×D47—42no—
352C22×D47—42no—
353C22×D47—84no—
354C22×D47—816no—
355C22×D47C22×D412yes—
356C22×D47C22×D412yes—
357Q8×C47—24no—
358Q8×C47—22no—
359Q8×C47C22×D414yes—
360D4×C47—24no—
361D4×C47—22no—
362D4×C47C22×D414yes—
363C2×C4×C47—24no—
364C2×C4×C47—22no—
365C2×C4×C47—22no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—42no—
370C2×C4×C47—42no—
371C2×C4×C47—84no—
372C2×C4×C47C22×D412yes—
373C2×C4×C47C22×D412yes—
374C2×C4×C47C22×D411yescharacteristic
375C2×C4×C47C22×D412yes—
376C2×C4×C47H(5,𝔽2)12yes—
377C2×C4×C47C2511yescharacteristic
378C22⋊D47—48no—
379C22⋊D47—48no—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—22no—
383C2×Dic47—48no—
384C2×Dic47—42no—
385C2×Dic47C22×D412yes—
386C2×Dic47C22×D412yes—
387D188—22no—
388D188—22no—
389D188—22no—
390D188—22no—
391D188—22no—
392D188—22no—
393D188—44no—
394D188—48no—
395D188—48no—
396D188—48no—
397D188—42no—
398D188—42no—
399D188—42no—
400D188—84no—
401D188—84no—
402D188—84no—
403D188—84no—
404C4×D47—24no—
405C4×D47—24no—
406C4×D47—22no—
407C4×D47—22no—
408C4×D47—22no—
409C4×D47—22no—
410C4×D47—48no—
411C4×D47—48no—
412Dic94—22no—
413Dic94—22no—
414Dic94—42no—
415C8×C47—22no—
416C8×C47C22×D414yes—
417C47⋊C8—22no—
418C47⋊C8—22no—
419C2×#3268—471nomaximal, Sylow
420C22×C47—24no—
421C22×C47—48no—
422C22×C47—42no—
423C22×C47—42no—
424C22×C47D4212yes—
425C22×C47#57512yes—
426C22×C47#57612yes—
427C22×C47C23×D411yescharacteristic
428C2×D47—22no—
429C2×D47—22no—
430C2×D47—22no—
431C2×D47—22no—
432C2×D47—22no—
433C2×D47—22no—
434C2×D47—44no—
435C2×D47—44no—
436C2×D47—42no—
437C2×D47—42no—
438C2×D47—42no—
439C2×D47—42no—
440C2×D47—42no—
441C2×D47—42no—
442C2×D47—42no—
443C2×D47—42no—
444C2×D47—42no—
445C2×D47—816no—
446C2×D47—84no—
447C2×D47—84no—
448C2×D47—84no—
449C4×C47—24no—
450C4×C47—22no—
451C4×C47—22no—
452C4×C47—42no—
453C4×C47—42no—
454C4×C47D4212yes—
455C4×C47C23×D411yescharacteristic
456C4×C47C2×H(5,𝔽2)11yescharacteristic
457Dic47—22no—
458Dic47—22no—
459Dic47—42no—
460C22×AGL(1,ℤ/8)—471no—
461C22×#135—471no—
462C2×#550—471no—
463C2×#546—471no—
464#3268—4716no—
465C2×#496—471no—
466C2×#468—471no—
467C2×#466—471no—
468C2×#464—471no—
469C2×#459—471no—
470C2×#452—471no—
471C2×#449—471no—
472C2×#449—471no—
473C2×#447—471no—
474C2×#440D4711yescharacteristic, complemented
475C2×#435—471no—
476C2×C47—44no—
477C2×C47#326814yescomplemented
478C2×C47C2×D4211yescharacteristic
479C2×C47C2×#57511yescharacteristic
480C2×C47C2×#57611yescharacteristic
481D47—42no—
482D47—42no—
483D47—82no—
484D47—82no—
485D47—82no—
486C22×#41—471no—
487C22×#41—471no—
488C22×#41—471no—
489C23×D4—471no—
490C2×AGL(1,ℤ/8)—478no—
491C2×AGL(1,ℤ/8)—948no—
492C2×#135—478no—
493C2×#135—948no—
494C22×Q16—471no—
495C22×SD16—471no—
496C22×SD16—471no—
497C22×SD16—471no—
498C22×SD16C2×D4711yescharacteristic
499C22×D8—471no—
500C22×D8—471no—
501C22×D8—471no—
502C22×D8—471no—
503C22×M16—471no—
504C23×C8—471no—
505#550—478no—
506#550—944no—
507#546—478no—
508#546—944no—
509C2×#127—471no—
510C2×#127—941no—
511C2×#124—471no—
512C2×#123—941no—
513C2×C22⋊Q8—471no—
514C2×#121—471no—
515C2×#121—471no—
516C2×#121—471no—
517C2×#121—941no—
518C2×#121—941no—
519C2×#121—941no—
520C2×#120—941no—
521C2×C4×Q8C2×D4711yescharacteristic, complemented
522C2×C4×D4—471no—
523C2×C4×D4—941no—
524C2×C4×D4C2×D4711yescharacteristic
525C22×C22⋊C4—941no—
526#496—478no—
527#468—478no—
528#466—478no—
529#464—478no—
530#459—478no—
531#452—478no—
532#449—478no—
533#449—478no—
534#447—478no—
535#440C2×D4718yescomplemented
536#435—478no—
537C2×#107C2×D4711yescharacteristic, complemented
538C2×C4⋊C8—471no—
539C2×#103—471no—
540C2×#103C2×D4711yescharacteristic, complemented
541C2×#102—471no—
542C2×#102—471no—
543C2×#102—471no—
544C2×#102C2×D4711yescharacteristic
545C2×C22⋊C8—471no—
546C2×C22⋊C8—471no—
547C2×#97C2×D4711yescharacteristic, complemented
548C47C2×#326811yescharacteristic, complemented, Sylow
549C25—941no—
550C2×#41—474no—
551C2×#41—474no—
552C2×#41—474no—
553C2×#41—942no—
554C2×#41—942no—
555C2×#41—942no—
556C2×#41—944no—
557C2×#41—944no—
558C2×#41—944no—
559C2×#41—1882no—
560C2×#41—1882no—
561C2×#41—1882no—
562C22×Q8—471no—
563C22×Q8C22×D4711yescharacteristic
564C22×D4—474no—
565C22×D4—471no—
566C22×D4—471no—
567C22×D4—471no—
568C22×D4—471no—
569C22×D4—941no—
570C22×D4—941no—
571C22×D4—941no—
572C22×D4—941no—
573C22×D4—941no—
574C22×D4—942no—
575C22×D4—941no—
576C22×D4—944no—
577C22×D4—941no—
578C22×D4—941no—
579C22×D4—941no—
580C22×D4—1882no—
581C22×D4C22×D4711yescharacteristic
582C23×C4—21no—
583C23×C4—471no—
584C23×C4—471no—
585C23×C4—941no—
586C23×C4—941no—
587C23×C4—941no—
588AGL(1,ℤ/8)—9432no—
589#135—9432no—
590C2×Q16—474no—
591C2×Q16—944no—
592C2×SD16—474no—
593C2×SD16—474no—
594C2×SD16—474no—
595C2×SD16—944no—
596C2×SD16—944no—
597C2×SD16—1882no—
598C2×SD16D18818yescomplemented
599C2×SD16C22×D4714yes—
600C2×D8—474no—
601C2×D8—474no—
602C2×D8—474no—
603C2×D8—474no—
604C2×D8—944no—
605C2×D8—944no—
606C2×D8—944no—
607C2×D8—1882no—
608C2×M16—474no—
609C2×M16—944no—
610C22×C8—471no—
611C22×C8—471no—
612C22×C8—474no—
613C22×C8—944no—
614C22×C8C22×D4711yescharacteristic
615C22×C8C22×D4711yescharacteristic
616#127—474no—
617#127—948no—
618#127—942no—
619#124—474no—
620#124—942no—
621#123—948no—
622C22⋊Q8—474no—
623C22⋊Q8—942no—
624#121—474no—
625#121—474no—
626#121—474no—
627#121—948no—
628#121—948no—
629#121—948no—
630#121—942no—
631#121—942no—
632#121—942no—
633#120—948no—
634C4×Q8—22no—
635C4×Q8C22×D4714yescomplemented
636C4×D4—22no—
637C4×D4—474no—
638C4×D4—474no—
639C4×D4—948no—
640C4×D4C22×D4714yes—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—471no—
643C2×C4⋊C4—941no—
644C2×C4⋊C4C22×D4711yescharacteristic
645C2×C4⋊C4C22×D4711yescharacteristic
646C2×C22⋊C4—21no—
647C2×C22⋊C4—471no—
648C2×C22⋊C4—471no—
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×C42—21no—
657C2×C42C22×D4711yescharacteristic
658#107C22×D4714yescomplemented
659C4⋊C8—474no—
660#103—474no—
661#103C22×D4714yescomplemented
662#102—474no—
663#102—474no—
664#102—474no—
665#102C22×D4714yes—
666C22⋊C8—474no—
667C22⋊C8—474no—
668#97C22×D4714yescomplemented
669C24—21no—
670C24—471no—
671C24—471no—
672C24—944no—
673C24—941no—
674C24—941no—
675C24—941no—
676C24—3762no—
677C24—1884no—
678C24—1884no—
679#41—948no—
680#41—948no—
681#41—948no—
682#41—1884no—
683#41—1888no—
684#41—1884no—
685#41—1884no—
686#41—1888no—
687#41—1888no—
688C2×Q8—21no—
689C2×Q8—22no—
690C2×Q8—472no—
691C2×Q8—941no—
692C2×Q8—942no—
693C2×Q8—942no—
694C2×Q8C2×D18814yes—
695C2×Q8C23×D4712yes—
696C2×D4—21no—
697C2×D4—22no—
698C2×D4—474no—
699C2×D4—472no—
700C2×D4—472no—
701C2×D4—472no—
702C2×D4—944no—
703C2×D4—944no—
704C2×D4—944no—
705C2×D4—944no—
706C2×D4—944no—
707C2×D4—944no—
708C2×D4—948no—
709C2×D4—944no—
710C2×D4—944no—
711C2×D4—944no—
712C2×D4—941no—
713C2×D4—941no—
714C2×D4—941no—
715C2×D4—942no—
716C2×D4—942no—
717C2×D4—942no—
718C2×D4—942no—
719C2×D4—942no—
720C2×D4—942no—
721C2×D4—3762no—
722C2×D4—3762no—
723C2×D4—3762no—
724C2×D4—3762no—
725C2×D4—1882no—
726C2×D4—1884no—
727C2×D4—1884no—
728C2×D4—1884no—
729C2×D4—1884no—
730C2×D4—1888no—
731C2×D4—1884no—
732C2×D4—1884no—
733C2×D4C2×D18814yes—
734C2×D4C23×D4712yes—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—24no—
739C22×C4—82no—
740C22×C4—471no—
741C22×C4—471no—
742C22×C4—472no—
743C22×C4—472no—
744C22×C4—472no—
745C22×C4—472no—
746C22×C4—944no—
747C22×C4—944no—
748C22×C4—944no—
749C22×C4—942no—
750C22×C4—942no—
751C22×C4—942no—
752C22×C4—942no—
753C22×C4—941no—
754C22×C4—1884no—
755C22×C4—1884no—
756C22×C4—1884no—
757C22×C4D4×D4711yescharacteristic
758C22×C4D4×D4711yescharacteristic
759C22×C4C23×D4711yescharacteristic
760Q16—948no—
761SD16—948no—
762SD16—948no—
763SD16—1884no—
764SD16C2×D188116yescomplemented
765D8—948no—
766D8—948no—
767D8—948no—
768D8—1884no—
769M16—948no—
770C2×C8—22no—
771C2×C8—472no—
772C2×C8—472no—
773C2×C8—942no—
774C2×C8—942no—
775C2×C8—948no—
776C2×C8C2×D18814yes—
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—474no—
788C22⋊C4—474no—
789C22⋊C4—944no—
790C22⋊C4—944no—
791C22⋊C4—944no—
792C22⋊C4—944no—
793C22⋊C4—944no—
794C22⋊C4—944no—
795C42—24no—
796C42D4×D4712yes—
797C42C23×D4712yes—
798C23—24no—
799C23—22no—
800C23—42no—
801C23—42no—
802C23—472no—
803C23—472no—
804C23—942no—
805C23—942no—
806C23—942no—
807C23—942no—
808C23—942no—
809C23—942no—
810C23—942no—
811C23—942no—
812C23—942no—
813C23—3764no—
814C23—37616no—
815C23—1888no—
816C23—1888no—
817C23—1882no—
818C23—1882no—
819C23—1882no—
820C23—1882no—
821C23—1882no—
822C23—1882no—
823C23—1882no—
824C23—1882no—
825C23—1882no—
826C23C2×D4×D4711yescharacteristic
827Q8—24no—
828Q8—22no—
829Q8—942no—
830Q8—942no—
831Q8—1882no—
832Q8C22×D18814yes—
833D4—24no—
834D4—22no—
835D4—942no—
836D4—942no—
837D4—942no—
838D4—942no—
839D4—942no—
840D4—942no—
841D4—3764no—
842D4—3764no—
843D4—3764no—
844D4—3764no—
845D4—1884no—
846D4—1888no—
847D4—1888no—
848D4—1888no—
849D4—1888no—
850D4—1888no—
851D4—1882no—
852D4—1882no—
853D4—1882no—
854D4C22×D18814yes—
855C2×C4—24no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—84no—
864C2×C4—472no—
865C2×C4—472no—
866C2×C4—942no—
867C2×C4—942no—
868C2×C4—944no—
869C2×C4—944no—
870C2×C4—942no—
871C2×C4—942no—
872C2×C4—942no—
873C2×C4—942no—
874C2×C4—942no—
875C2×C4—1888no—
876C2×C4—1888no—
877C2×C4—1888no—
878C2×C4—1882no—
879C2×C4C2×D4×D4712yes—
880C2×C4C2×D4×D4712yes—
881C2×C4C2×D4×D4711yescharacteristic
882C2×C4C22×D18812yes—
883C2×C4#1309407012yes—
884C2×C4C24×D4711yescharacteristic
885C8—22no—
886C8—942no—
887C8—942no—
888C8C22×D18814yes—
889C22—24no—
890C22—42no—
891C22—42no—
892C22—48no—
893C22—942no—
894C22—942no—
895C22—942no—
896C22—942no—
897C22—942no—
898C22—942no—
899C22—37616no—
900C22—3764no—
901C22—3764no—
902C22—3764no—
903C22—1882no—
904C22—1882no—
905C22—1882no—
906C22—1882no—
907C22—1882no—
908C22—1882no—
909C22—1882no—
910C22—1882no—
911C22—1882no—
912C22—1884no—
913C22—1884no—
914C22D4×D18812yes—
915C22#1568992212yes—
916C22#1568992712yes—
917C22C22×D4×D4711yescharacteristic
918C4—24no—
919C4—22no—
920C4—22no—
921C4—42no—
922C4—42no—
923C4—942no—
924C4—942no—
925C4—1882no—
926C4D4×D18812yes—
927C4C23×D18811yescharacteristic
928C4C2×#1309407011yescharacteristic
929C2—44no—
930C2—3762no—
931C2—3762no—
932C2—3762no—
933C2—1882no—
934C2—1882no—
935C2#2025493014yesdirect product factor
936C2C2×D4×D18811yescharacteristic
937C2C2×#1568992211yescharacteristic
938C2C2×#1568992711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#440C2
socleC23×C47C22×D4
hypercenterC2×#440D47
hypocenterC47C2×#3268
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C22×#13094051C2semidirect
2. C22×#13094045C2semidirect
3. C2×#15689795C2semidirect
4. C2×#15689768C2semidirect
5. #20254930C2direct (N × H)
6. C2×#15689512C2semidirect
7. C2×#15689370C2semidirect
8. C2×#15689360C2semidirect
9. C2×#15689345C2semidirect
10. C2×#15689318C2semidirect
11. C2×#15689288C2semidirect
12. C2×#15689271C2semidirect
13. C2×#15689269C2semidirect
14. C2×#15689258C2semidirect
15. C2×#15689196C2semidirect
16. C2×C47×#440C2semidirect
18. C22×#10625354C22semidirect
22. C2×#13094051C22semidirect
24. C2×#13094045C22semidirect
25. C22×#10625337C22semidirect
26. C22×#10625325C22semidirect
27. C22×#10625325C22semidirect
34. C22×C8×D47C22semidirect
36. #15689795C22semidirect
38. #15689768C22semidirect
40. C2×#13094021C22semidirect
48. C2×#13093999C22semidirect
54. #15689512C22semidirect
55. #15689370C22semidirect
56. #15689360C22semidirect
57. #15689345C22semidirect
58. #15689318C22semidirect
59. #15689288C22semidirect
60. #15689271C22semidirect
61. #15689269C22semidirect
62. #15689258C22semidirect
63. #15689196C22semidirect
64. C2×C4⋊(C47⋊C8)C22semidirect
65. C2×#13093947C22semidirect
67. C2×#13093944C22semidirect
68. C2×#13093944C22semidirect
70. C2×(C2×D47)⋊C8C22semidirect
72. C2×C4×Q8×C47C22semidirect
74. C47×#440C22semidirect
75. C2×#107×C47C22semidirect
76. C2×#103×C47C22semidirect
78. C2×#97×C47C22semidirect
87. C2×#10625354C23semidirect
118. C2×#10625337C23semidirect
121. C2×#10625325C23semidirect
122. C2×#10625325C23semidirect
138. C2×C8×D47C23semidirect
141. #13094021C23semidirect
154. #13093999C23semidirect
171. C4⋊(C47⋊C8)C23semidirect
172. #13093947C23semidirect
174. #13093944C23semidirect
175. #13093944C23semidirect
177. (C2×D47)⋊C8C23semidirect
181. C2×SD16×C47D4semidirect
186. C4×Q8×C47C23semidirect
195. #107×C47C23semidirect
196. #103×C47C23semidirect
198. #97×C47C23semidirect
290. SD16×C47C2×D4semidirect
474. C2×#440D47semidirect
477. C2×C47#3268semidirect
521. C2×C4×Q8C2×D47semidirect
535. #440C2×D47semidirect
537. C2×#107C2×D47semidirect
540. C2×#103C2×D47semidirect
547. C2×#97C2×D47semidirect
548. C47C2×#3268semidirect
598. C2×SD16D188semidirect
635. C4×Q8C22×D47semidirect
658. #107C22×D47semidirect
661. #103C22×D47semidirect
668. #97C22×D47semidirect
764. SD16C2×D188semidirect
935. C2#20254930direct (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×#130940452
C2×#156897952
C2×#156897682
#202549302
C2×#156895122
C2×#156893702
C2×#156893602
C2×#156893452
C2×#156893182
C2×#156892882
C2×#156892712
C2×#156892692
C2×#156892582
C2×#156891962
C2×C47×#4402
C2×#326847