Finite Group Databasebeta

← C2×#20254920 #27091282

Subgroups — C2×#20254920 #27091282

Order 12032.

2914 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094052C211yesmaximal, characteristic, complemented
2C22×#13094047C211yesmaximal, characteristic, complemented
3C2×#15689775C211yesmaximal, characteristic, complemented
4C2×#15689764C211yesmaximal, characteristic, complemented
5#20254920C2116yesmaximal, direct product factor
6C2×#15689516C211yesmaximal, characteristic, complemented
7C2×#15689353C211yesmaximal, characteristic, complemented
8C2×#15689341C211yesmaximal, characteristic, complemented
9C2×#15689327C211yesmaximal, characteristic, complemented
10C2×#15689288C211yesmaximal, characteristic, complemented
11C2×#15689283C211yesmaximal, characteristic, complemented
12C2×#15689271C211yesmaximal, characteristic, complemented
13C2×#15689273C211yesmaximal, characteristic, complemented
14C2×#15689234C211yesmaximal, characteristic, complemented
15C2×#15689192C211yesmaximal, characteristic, complemented
16C2×C47×#470C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625354C2211yescharacteristic, complemented
19C22×#10625350C2211yescharacteristic
20C23×D188C2211yescharacteristic
21C2×#13094052—28no—
22C2×#13094052C2218yescomplemented
23C2×#13094047—28no—
24C2×#13094047C2218yescomplemented
25C22×#10625337C2211yescharacteristic, complemented
26C22×#10625325C2211yescharacteristic
27C22×#10625325C2211yescharacteristic
28C22×#10625336C2211yescharacteristic
29C22×#10625336C2211yescharacteristic
30C22×#10625336C2211yescharacteristic, complemented
31C22×D376C2211yescharacteristic
32C22×D376C2211yescharacteristic
33C22×C8×D47C2211yescharacteristic, complemented
34#15689775—24no—
35#15689775C2218yescomplemented
36#15689764—24no—
37#15689764C2218yescomplemented
38C2×#13094022C2211yescharacteristic, complemented
39C2×#13094013C2211yescharacteristic
40C2×#13094009—21no—
41C2×#13094009—21no—
42C2×#13094006—21no—
43C2×#13094004C2211yescharacteristic, complemented
44C2×#13093999—21no—
45C2×#13093999C2211yescharacteristic
46C2×#13093997—21no—
47C2×#13093994—21no—
48C2×#13093986C2211yescharacteristic
49C2×#13093986C2211yescharacteristic, complemented
50C2×C4×C22⋊D47C2211yescharacteristic
51C2×C4⋊C4×D47—21no—
52C2×C22⋊C4×D47—21no—
53#15689516C2218yescomplemented
54#15689353C2218yescomplemented
55#15689341C2218yescomplemented
56#15689327C2218yescomplemented
57#15689288C2218yescomplemented
58#15689283C2218yescomplemented
59#15689273C2218yescomplemented
60#15689271C2218yescomplemented
61#15689234C2218yescomplemented
62#15689192C2218yescomplemented
63C2×Dic47⋊C8C2211yescharacteristic, complemented
64C2×#13093947C2211yescharacteristic, complemented
65C2×#13093944C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×#13093944C2211yescharacteristic, complemented
68C2×C22⋊(C47⋊C8)C2211yescharacteristic
69C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
70C2×#13093934C2211yescharacteristic, complemented
71C22×Q16×C47C2211yescharacteristic, complemented
72C22×M16×C47C2211yescharacteristic
73C2×C22⋊Q8×C47C2211yescharacteristic
74C2×C22⋊Q8×C47C2211yescharacteristic
75C47×#470C2218yescomplemented
76C2×#106×C47C2211yescharacteristic, complemented
77C2×#103×C47C2211yescharacteristic, complemented
78C2×#103×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×#10625350—22no—
89C2×#10625350—24no—
90C2×#10625350—42no—
91C2×#10625350C2314yes—
92C22×Dic94C2311yescharacteristic
93C22×D188—24no—
94C22×D188—21no—
95C22×D188—21no—
96C22×D188—22no—
97C22×D188—21no—
98C22×D188—21no—
99C22×D188—42no—
100C22×D188C2311yescharacteristic
101C22×D188C2314yes—
102C22×D188C2311yescharacteristic
103C22×D188C2311yescharacteristic
104C22×C22⋊D47—21no—
105C22×C22⋊D47D411yescharacteristic
106C22×C4×D47—21no—
107C22×C4×D47—21no—
108C22×C4×D47—21no—
109C22×C4×D47—21no—
110C22×C4×D47—21no—
111C22×C4×D47C2311yescharacteristic
112#13094052—232no—
113#13094047—232no—
114C2×#10625337—42no—
115C2×#10625337C2314yescomplemented
116C2×#10625325—24no—
117C2×#10625325—24no—
118C2×#10625325C2314yes—
119C2×#10625325C2314yes—
120C2×#10625336—24no—
121C2×#10625336—24no—
122C2×#10625336—42no—
123C2×#10625336C2314yes—
124C2×#10625336C2314yes—
125C2×#10625336C2314yescomplemented
126C2×D376—24no—
127C2×D376D418yescomplemented
128C2×D376C2314yes—
129C2×D376C2314yes—
130C22×C47⋊C8C2311yescharacteristic
131C22×C47⋊C8C2311yescharacteristic
132C2×C8×D47—24no—
133C2×C8×D47C2314yescomplemented
134#13094022—22no—
135#13094022C2314yescomplemented
136#13094013—22no—
137#13094013C2314yes—
138#13094009—28no—
139#13094009—28no—
140#13094006—28no—
141#13094004—22no—
142#13094004C2314yescomplemented
143#13093999—22no—
144#13093999—28no—
145#13093999C2314yes—
146#13093997—28no—
147#13093994—28no—
148#13093986—22no—
149#13093986—22no—
150#13093986C2314yes—
151#13093986C2314yescomplemented
152C4×C22⋊D47D414yes—
153C4×C22⋊D47C2314yes—
154C2×C4⋊Dic47—21no—
155C2×Dic47⋊C4—21no—
156C2×Dic47⋊C4—21no—
157C2×Dic47⋊C4D411yescharacteristic
158C4⋊C4×D47—28no—
159C2×C22⋊Dic47D411yescharacteristic
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)⋊C4—21no—
166C2×(C2×D47)⋊C4D411yescharacteristic
167C22⋊C4×D47—28no—
168C2×C4×Dic47C2311yescharacteristic
169Dic47⋊C8C2314yescomplemented
170#13093947C2314yescomplemented
171#13093944C2314yes—
172#13093944C2314yes—
173#13093944C2314yescomplemented
174C22⋊(C47⋊C8)C2314yes—
175(C2×D47)⋊C8C2314yescomplemented
176#13093934C2314yescomplemented
177C22×Q8×C47C2311yescharacteristic
178C22×Q8×C47C2311yescharacteristic
179C23×C4×C47C2311yescharacteristic
180C2×Q16×C47—24no—
181C2×Q16×C47C2314yescomplemented
182C2×M16×C47—24no—
183C2×M16×C47C2314yes—
184C22×C8×C47C2311yescharacteristic
185C22×C8×C47C2311yescharacteristic
186C22⋊Q8×C47—22no—
187C22⋊Q8×C47—22no—
188C22⋊Q8×C47C2314yes—
189C22⋊Q8×C47C2314yes—
190C2×C4⋊C4×C47—21no—
191C2×C4⋊C4×C47—21no—
192C2×C4⋊C4×C47C2311yescharacteristic
193C2×C4⋊C4×C47C2311yescharacteristic
194C2×C22⋊C4×C47—21no—
195C2×C22⋊C4×C47—21no—
196#106×C47C2314yescomplemented
197#103×C47C2314yescomplemented
198#103×C47C2314yescomplemented
199C24×C47C2×D411yescharacteristic
200C23×D47—21no—
201C23×D47—21no—
202C23×D47—21no—
203C23×D47—24no—
204C23×D47—44no—
205C23×D47—44no—
206C23×D47—82no—
207C23×D47C2×D411yescharacteristic
208C2×Q8×C47—21no—
209C2×Q8×C47—21no—
210C2×Q8×C47—22no—
211C2×Q8×C47—22no—
212C2×Q8×C47—22no—
213C2×Q8×C47—22no—
214C2×Q8×C47C2412yes—
215C2×Q8×C47C2412yes—
216C22×C4×C47—22no—
217C22×C4×C47—22no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D412yes—
224C22×C4×C47C2412yes—
225C22×C4×C47C2411yescharacteristic
226C2×C22⋊D47—24no—
227C2×C22⋊D47—42no—
228C2×C22⋊D47—44no—
229C2×C22⋊D47C2×D414yes—
230C22×Dic47—21no—
231C22×Dic47C2×D411yescharacteristic
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#10625350—28no—
241#10625350—44no—
242#10625350—48no—
243C2×D188—21no—
244C2×D188—21no—
245C2×D188—22no—
246C2×D188—22no—
247C2×D188—22no—
248C2×D188—22no—
249C2×D188—28no—
250C2×D188—24no—
251C2×D188—24no—
252C2×D188—24no—
253C2×D188—21no—
254C2×D188—24no—
255C2×D188—44no—
256C2×D188—48no—
257C2×D188—44no—
258C2×D188—44no—
259C2×D188—44no—
260C2×D188—82no—
261C2×D188C2×D414yes—
262C2×D188C2×D414yes—
263C2×D188C2412yes—
264C2×D188C2412yes—
265C2×D188C2412yes—
266C2×C4×D47—22no—
267C2×C4×D47—22no—
268C2×C4×D47—24no—
269C2×C4×D47—24no—
270C2×C4×D47—24no—
271C2×C4×D47—24no—
272C2×C4×D47—24no—
273C2×C4×D47—44no—
274C2×C4×D47—44no—
275C2×C4×D47—44no—
276C2×C4×D47—44no—
277C2×C4×D47—82no—
278C2×C4×D47C2×D412yes—
279C2×C4×D47C2412yes—
280C2×Dic94—22no—
281C2×Dic94—22no—
282C2×Dic94—21no—
283C2×Dic94C2412yes—
284Q16×C47—28no—
285M16×C47—28no—
286C2×C8×C47—22no—
287C2×C8×C47C2×D414yes—
288C2×C8×C47C2412yes—
289C2×C8×C47C2412yes—
290C4⋊C4×C47—24no—
291C4⋊C4×C47—24no—
292C4⋊C4×C47—21no—
293C4⋊C4×C47—21no—
294C4⋊C4×C47C2412yes—
295C4⋊C4×C47C2412yes—
296C22⋊C4×C47—24no—
297C22⋊C4×C47—24no—
298C22⋊Dic47C2×D414yes—
299#10625337—44no—
300#10625336—28no—
301#10625336—28no—
302#10625336—44no—
303(C2×D47)⋊C4—24no—
304(C2×D47)⋊C4—24no—
305(C2×D47)⋊C4—24no—
306(C2×D47)⋊C4—24no—
307(C2×D47)⋊C4—24no—
308(C2×D47)⋊C4—24no—
309(C2×D47)⋊C4C2×D414yes—
310C4⋊Dic47—24no—
311Dic47⋊C4—24no—
312Dic47⋊C4—24no—
313Dic47⋊C4C2×D414yes—
314C4×Dic47C2×D412yes—
315C4×Dic47C2412yes—
316C2×C47⋊C8—22no—
317C2×C47⋊C8—22no—
318C2×C47⋊C8C2412yes—
319C2×C47⋊C8C2412yes—
320D376—28no—
321D376C2×D4116yescomplemented
322#10625325—28no—
323#10625325—28no—
324C8×D47—28no—
325C23×C47—22no—
326C23×C47—22no—
327C23×C47—22no—
328C23×C47C22×D412yes—
329C23×C47C22×D411yescharacteristic
330C22×D47—22no—
331C22×D47—24no—
332C22×D47—24no—
333C22×D47—22no—
334C22×D47—22no—
335C22×D47—22no—
336C22×D47—22no—
337C22×D47—22no—
338C22×D47—48no—
339C22×D47—42no—
340C22×D47—42no—
341C22×D47—42no—
342C22×D47—42no—
343C22×D47—48no—
344C22×D47—42no—
345C22×D47—42no—
346C22×D47—42no—
347C22×D47—84no—
348C22×D47—816no—
349C22×D47C22×D412yes—
350Q8×C47—22no—
351Q8×C47—22no—
352Q8×C47—22no—
353Q8×C47—22no—
354Q8×C47—42no—
355Q8×C47—42no—
356C2×C4×C47—22no—
357C2×C4×C47—24no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—42no—
365C2×C4×C47—42no—
366C2×C4×C47—42no—
367C2×C4×C47—42no—
368C2×C4×C47C22×D412yes—
369C2×C4×C47C22×D411yescharacteristic
370C2×C4×C47C22×D412yes—
371C2×C4×C47H(5,𝔽2)12yes—
372C2×C4×C47C2511yescharacteristic
373C22⋊D47—44no—
374C22⋊D47—48no—
375C2×Dic47—22no—
376C2×Dic47—22no—
377C2×Dic47—22no—
378C2×Dic47—22no—
379C2×Dic47—42no—
380C2×Dic47C22×D412yes—
381C2×Dic47C22×D412yes—
382C2×Dic47C22×D412yes—
383D188—24no—
384D188—24no—
385D188—22no—
386D188—22no—
387D188—22no—
388D188—22no—
389D188—48no—
390D188—48no—
391D188—48no—
392D188—42no—
393D188—84no—
394D188C22×D414yes—
395D188C22×D414yes—
396C4×D47—24no—
397C4×D47—22no—
398C4×D47—22no—
399C4×D47—48no—
400C4×D47—48no—
401C4×D47—48no—
402C4×D47—48no—
403C4×D47—84no—
404Dic94—22no—
405Dic94—22no—
406Dic94—42no—
407C8×C47—22no—
408C8×C47C22×D414yes—
409C47⋊C8—22no—
410C47⋊C8—22no—
411C2×#3267—471nomaximal, Sylow
412C22×C47—22no—
413C22×C47—22no—
414C22×C47—22no—
415C22×C47—44no—
416C22×C47D4212yes—
417C22×C47#57512yes—
418C22×C47#57712yes—
419C22×C47C23×D411yescharacteristic
420C2×D47—22no—
421C2×D47—24no—
422C2×D47—24no—
423C2×D47—22no—
424C2×D47—22no—
425C2×D47—44no—
426C2×D47—48no—
427C2×D47—48no—
428C2×D47—42no—
429C2×D47—42no—
430C2×D47—42no—
431C2×D47—42no—
432C2×D47—42no—
433C2×D47—42no—
434C2×D47—42no—
435C2×D47—816no—
436C2×D47—84no—
437C4×C47—22no—
438C4×C47—42no—
439C4×C47—42no—
440C4×C47—42no—
441C4×C47—42no—
442C4×C47D4212yes—
443C4×C47C23×D411yescharacteristic
444C4×C47C2×H(5,𝔽2)11yescharacteristic
445Dic47—22no—
446Dic47—22no—
447Dic47—22no—
448Dic47—42no—
449C22×AGL(1,ℤ/8)—471no—
450C22×#135—471no—
451C2×#547—471no—
452C2×#546—471no—
453#3267—4716no—
454C2×#497—471no—
455C2×#470D4711yescharacteristic, complemented
456C2×#465—471no—
457C2×#463—471no—
458C2×#461—471no—
459C2×#452—471no—
460C2×#452—471no—
461C2×#449—471no—
462C2×#450—471no—
463C2×#442—471no—
464C2×#435—471no—
465C2×C47—42no—
466C2×C47#326714yescomplemented
467C2×C47C2×D4211yescharacteristic
468C2×C47C2×#57511yescharacteristic
469C2×C47C2×#57711yescharacteristic
470D47—42no—
471D47—44no—
472D47—44no—
473D47—82no—
474C22×#41—471no—
475C22×#41—471no—
476C22×#41—471no—
477C23×D4—471no—
478C2×AGL(1,ℤ/8)—478no—
479C2×AGL(1,ℤ/8)—948no—
480C2×#135—478no—
481C2×#135—948no—
482C22×Q16—471no—
483C22×Q16C2×D4711yescharacteristic, complemented
484C22×SD16—471no—
485C22×SD16—471no—
486C22×SD16—471no—
487C22×SD16—471no—
488C22×SD16—471no—
489C22×D8—471no—
490C22×D8—471no—
491C22×M16C2×D4711yescharacteristic
492C23×C8—471no—
493#547—478no—
494#547—944no—
495#546—478no—
496#546—944no—
497C2×C4⋊Q8—471no—
498C2×#124—471no—
499C2×#123—941no—
500C2×#123—941no—
501C2×#123—941no—
502C2×C22⋊Q8—471no—
503C2×C22⋊Q8C2×D4711yescharacteristic
504C2×C22⋊Q8C2×D4711yescharacteristic
505C2×#121—471no—
506C2×#121—941no—
507C2×#121—941no—
508C2×#120—941no—
509C2×C4×D4—471no—
510C2×C4×D4—471no—
511C2×C4×D4—471no—
512C22×C4⋊C4—941no—
513C22×C22⋊C4—941no—
514#497—478no—
515#470C2×D4718yescomplemented
516#465—478no—
517#463—478no—
518#461—478no—
519#452—478no—
520#452—478no—
521#450—478no—
522#449—478no—
523#442—478no—
524#435—478no—
525C2×#106C2×D4711yescharacteristic, complemented
526C2×C4⋊C8—471no—
527C2×#103—471no—
528C2×#103C2×D4711yescharacteristic, complemented
529C2×#103C2×D4711yescharacteristic, complemented
530C2×#102—471no—
531C2×#102—471no—
532C2×#102—471no—
533C2×C22⋊C8—471no—
534C2×C22⋊C8—471no—
535C2×#97—471no—
536C47C2×#326711yescharacteristic, complemented, Sylow
537C25—941no—
538C2×#41—474no—
539C2×#41—474no—
540C2×#41—474no—
541C2×#41—944no—
542C2×#41—942no—
543C2×#41—942no—
544C2×#41—942no—
545C2×#41—944no—
546C2×#41—944no—
547C2×#41—1882no—
548C2×#41—1882no—
549C2×#41—1882no—
550C22×Q8—471no—
551C22×Q8C22×D4711yescharacteristic
552C22×Q8C22×D4711yescharacteristic
553C22×D4—471no—
554C22×D4—471no—
555C22×D4—471no—
556C22×D4—471no—
557C22×D4—474no—
558C22×D4—944no—
559C22×D4—941no—
560C22×D4—941no—
561C22×D4—941no—
562C22×D4—941no—
563C22×D4—941no—
564C22×D4—942no—
565C22×D4—1882no—
566C23×C4—471no—
567C23×C4—941no—
568C23×C4—941no—
569C23×C4—941no—
570C23×C4—941no—
571C23×C4—941no—
572C23×C4C22×D4711yescharacteristic
573AGL(1,ℤ/8)—9432no—
574#135—9432no—
575C2×Q16—24no—
576C2×Q16—474no—
577C2×Q16—1882no—
578C2×Q16C22×D4714yescomplemented
579C2×SD16—474no—
580C2×SD16—474no—
581C2×SD16—474no—
582C2×SD16—474no—
583C2×SD16—474no—
584C2×SD16—944no—
585C2×SD16—944no—
586C2×SD16—944no—
587C2×SD16—944no—
588C2×SD16—1882no—
589C2×D8—478no—
590C2×D8—474no—
591C2×D8—474no—
592C2×D8—944no—
593C2×M16—24no—
594C2×M16C22×D4714yes—
595C22×C8—471no—
596C22×C8—471no—
597C22×C8—474no—
598C22×C8—944no—
599C22×C8C22×D4711yescharacteristic
600C22×C8C22×D4711yescharacteristic
601C4⋊Q8—474no—
602C4⋊Q8—942no—
603#124—474no—
604#124—942no—
605#123—948no—
606#123—948no—
607#123—948no—
608C22⋊Q8—22no—
609C22⋊Q8—22no—
610C22⋊Q8—474no—
611C22⋊Q8—942no—
612C22⋊Q8C22×D4714yes—
613C22⋊Q8C22×D4714yes—
614#121—474no—
615#121—948no—
616#121—948no—
617#121—942no—
618#120—948no—
619C4×D4—474no—
620C4×D4—474no—
621C4×D4—474no—
622C4×D4—474no—
623C4×D4—942no—
624C4×D4—942no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—471no—
628C2×C4⋊C4—948no—
629C2×C4⋊C4—941no—
630C2×C4⋊C4—941no—
631C2×C4⋊C4—941no—
632C2×C4⋊C4C22×D4711yescharacteristic
633C2×C4⋊C4C22×D4711yescharacteristic
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—471no—
637C2×C22⋊C4—471no—
638C2×C22⋊C4—948no—
639C2×C22⋊C4—941no—
640C2×C22⋊C4—941no—
641C2×C22⋊C4—941no—
642C2×C22⋊C4—941no—
643C2×C22⋊C4—941no—
644C2×C22⋊C4—941no—
645C2×C42—471no—
646#106C22×D4714yescomplemented
647C4⋊C8—474no—
648#103—474no—
649#103C22×D4714yescomplemented
650#103C22×D4714yescomplemented
651#102—474no—
652#102—474no—
653#102—474no—
654C22⋊C8—474no—
655C22⋊C8—474no—
656#97—474no—
657C24—471no—
658C24—941no—
659C24—941no—
660C24—944no—
661C24—941no—
662C24—3762no—
663C24—1884no—
664C24—1884no—
665C24D4×D4711yescharacteristic
666#41—948no—
667#41—948no—
668#41—948no—
669#41—1884no—
670#41—1888no—
671#41—1884no—
672#41—1884no—
673#41—1888no—
674#41—1888no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—22no—
678C2×Q8—22no—
679C2×Q8—22no—
680C2×Q8—22no—
681C2×Q8—472no—
682C2×Q8—941no—
683C2×Q8—942no—
684C2×Q8—942no—
685C2×Q8C23×D4712yes—
686C2×Q8C23×D4712yes—
687C2×D4—474no—
688C2×D4—474no—
689C2×D4—474no—
690C2×D4—472no—
691C2×D4—472no—
692C2×D4—472no—
693C2×D4—948no—
694C2×D4—944no—
695C2×D4—944no—
696C2×D4—944no—
697C2×D4—944no—
698C2×D4—941no—
699C2×D4—941no—
700C2×D4—942no—
701C2×D4—944no—
702C2×D4—941no—
703C2×D4—942no—
704C2×D4—942no—
705C2×D4—942no—
706C2×D4—3762no—
707C2×D4—1884no—
708C2×D4—1888no—
709C2×D4—1884no—
710C2×D4—1884no—
711C2×D4—1884no—
712C2×D4—1882no—
713C2×D4—1884no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—471no—
721C22×C4—471no—
722C22×C4—471no—
723C22×C4—472no—
724C22×C4—472no—
725C22×C4—944no—
726C22×C4—944no—
727C22×C4—944no—
728C22×C4—944no—
729C22×C4—942no—
730C22×C4—942no—
731C22×C4—941no—
732C22×C4—944no—
733C22×C4—3762no—
734C22×C4—1884no—
735C22×C4—1884no—
736C22×C4—1884no—
737C22×C4—1884no—
738C22×C4D4×D4712yes—
739C22×C4D4×D4711yescharacteristic
740C22×C4C23×D4712yes—
741C22×C4C23×D4711yescharacteristic
742Q16—28no—
743Q16—1884no—
744SD16—948no—
745SD16—948no—
746SD16—948no—
747SD16—948no—
748SD16—1884no—
749D8—4716no—
750D8—948no—
751M16—28no—
752C2×C8—22no—
753C2×C8—472no—
754C2×C8—472no—
755C2×C8—942no—
756C2×C8—942no—
757C2×C8—948no—
758C2×C8D4×D4714yes—
759C2×C8C23×D4712yes—
760C2×C8C23×D4712yes—
761C4⋊C4—24no—
762C4⋊C4—24no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—474no—
766C4⋊C4—944no—
767C4⋊C4—944no—
768C4⋊C4—944no—
769C4⋊C4C23×D4712yes—
770C4⋊C4C23×D4712yes—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—474no—
774C22⋊C4—474no—
775C22⋊C4—944no—
776C22⋊C4—944no—
777C22⋊C4—944no—
778C22⋊C4—944no—
779C22⋊C4—944no—
780C22⋊C4—944no—
781C42—472no—
782C42—472no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—472no—
787C23—942no—
788C23—944no—
789C23—944no—
790C23—942no—
791C23—942no—
792C23—942no—
793C23—942no—
794C23—942no—
795C23—3764no—
796C23—37616no—
797C23—1888no—
798C23—1888no—
799C23—1882no—
800C23—1882no—
801C23—1882no—
802C23—1882no—
803C23—1882no—
804C23—1882no—
805C23—1882no—
806C23C2×D4×D4712yes—
807C23C2×D4×D4711yescharacteristic
808Q8—22no—
809Q8—22no—
810Q8—22no—
811Q8—22no—
812Q8—42no—
813Q8—42no—
814Q8—942no—
815Q8—942no—
816Q8—1882no—
817D4—474no—
818D4—474no—
819D4—944no—
820D4—944no—
821D4—942no—
822D4—942no—
823D4—942no—
824D4—942no—
825D4—3764no—
826D4—1888no—
827D4—1888no—
828D4—1888no—
829D4—1884no—
830D4—1888no—
831D4—1882no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—472no—
845C2×C4—472no—
846C2×C4—472no—
847C2×C4—942no—
848C2×C4—942no—
849C2×C4—942no—
850C2×C4—944no—
851C2×C4—942no—
852C2×C4—942no—
853C2×C4—942no—
854C2×C4—3764no—
855C2×C4—1888no—
856C2×C4—1888no—
857C2×C4—1888no—
858C2×C4—1888no—
859C2×C4—1882no—
860C2×C4C2×D4×D4712yes—
861C2×C4C2×D4×D4711yescharacteristic
862C2×C4C2×D4×D4712yes—
863C2×C4#1309407012yes—
864C2×C4C24×D4711yescharacteristic
865C8—22no—
866C8—942no—
867C8—942no—
868C8C2×D4×D4714yes—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—44no—
873C22—942no—
874C22—944no—
875C22—944no—
876C22—942no—
877C22—942no—
878C22—37616no—
879C22—3764no—
880C22—1882no—
881C22—1882no—
882C22—1882no—
883C22—1882no—
884C22—1882no—
885C22—1882no—
886C22—1882no—
887C22—1884no—
888C22—1888no—
889C22—1888no—
890C22#1568975712yes—
891C22#1568992212yes—
892C22#1568993212yes—
893C22C22×D4×D4711yescharacteristic
894C4—22no—
895C4—42no—
896C4—42no—
897C4—42no—
898C4—42no—
899C4—942no—
900C4—942no—
901C4—942no—
902C4—1882no—
903C4#1568975712yes—
904C4C22×D4×D4711yescharacteristic
905C4C2×#1309407011yescharacteristic
906C2—42no—
907C2—3762no—
908C2—1882no—
909C2—1884no—
910C2—1884no—
911C2#2025492014yesdirect product factor
912C2C2×#1568975711yescharacteristic
913C2C2×#1568992211yescharacteristic
914C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#470C2
socleC23×C47C22×D4
hypercenterC2×#470D47
hypocenterC47C2×#3267
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
1. C22×#13094052C2semidirect
2. C22×#13094047C2semidirect
3. C2×#15689775C2semidirect
4. C2×#15689764C2semidirect
5. #20254920C2direct (N × H)
6. C2×#15689516C2semidirect
7. C2×#15689353C2semidirect
8. C2×#15689341C2semidirect
9. C2×#15689327C2semidirect
10. C2×#15689288C2semidirect
11. C2×#15689283C2semidirect
12. C2×#15689271C2semidirect
13. C2×#15689273C2semidirect
14. C2×#15689234C2semidirect
15. C2×#15689192C2semidirect
16. C2×C47×#470C2semidirect
18. C22×#10625354C22semidirect
22. C2×#13094052C22semidirect
24. C2×#13094047C22semidirect
25. C22×#10625337C22semidirect
30. C22×#10625336C22semidirect
33. C22×C8×D47C22semidirect
35. #15689775C22semidirect
37. #15689764C22semidirect
38. C2×#13094022C22semidirect
43. C2×#13094004C22semidirect
49. C2×#13093986C22semidirect
53. #15689516C22semidirect
54. #15689353C22semidirect
55. #15689341C22semidirect
56. #15689327C22semidirect
57. #15689288C22semidirect
58. #15689283C22semidirect
59. #15689273C22semidirect
60. #15689271C22semidirect
61. #15689234C22semidirect
62. #15689192C22semidirect
63. C2×Dic47⋊C8C22semidirect
64. C2×#13093947C22semidirect
67. C2×#13093944C22semidirect
69. C2×(C2×D47)⋊C8C22semidirect
70. C2×#13093934C22semidirect
71. C22×Q16×C47C22semidirect
75. C47×#470C22semidirect
76. C2×#106×C47C22semidirect
77. C2×#103×C47C22semidirect
78. C2×#103×C47C22semidirect
87. C2×#10625354C23semidirect
115. C2×#10625337C23semidirect
125. C2×#10625336C23semidirect
127. C2×D376D4semidirect
133. C2×C8×D47C23semidirect
135. #13094022C23semidirect
142. #13094004C23semidirect
151. #13093986C23semidirect
169. Dic47⋊C8C23semidirect
170. #13093947C23semidirect
173. #13093944C23semidirect
175. (C2×D47)⋊C8C23semidirect
176. #13093934C23semidirect
181. C2×Q16×C47C23semidirect
196. #106×C47C23semidirect
197. #103×C47C23semidirect
198. #103×C47C23semidirect
321. D376C2×D4semidirect
455. C2×#470D47semidirect
466. C2×C47#3267semidirect
483. C22×Q16C2×D47semidirect
515. #470C2×D47semidirect
525. C2×#106C2×D47semidirect
528. C2×#103C2×D47semidirect
529. C2×#103C2×D47semidirect
536. C47C2×#3267semidirect
578. C2×Q16C22×D47semidirect
646. #106C22×D47semidirect
649. #103C22×D47semidirect
650. #103C22×D47semidirect
911. C2#20254920direct (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×#130940472
C2×#156897752
C2×#156897642
#202549202
C2×#156895162
C2×#156893532
C2×#156893412
C2×#156893272
C2×#156892882
C2×#156892832
C2×#156892712
C2×#156892732
C2×#156892342
C2×#156891922
C2×C47×#4702
C2×#326747