Finite Group Databasebeta

← C2×#20254912 #27091274

Subgroups — C2×#20254912 #27091274

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×#13094051C211yesmaximal, characteristic, complemented
2C22×#13094047C211yesmaximal, characteristic, complemented
3C2×#15689776C211yesmaximal, characteristic, complemented
4C2×#15689766C211yesmaximal, characteristic, complemented
5#20254912C2116yesmaximal, direct product factor
6C2×#15689378C211yesmaximal, characteristic, complemented
7C2×#15689349C211yesmaximal, characteristic, complemented
8C2×#15689335C211yesmaximal, characteristic, complemented
9C2×#15689325C211yesmaximal, characteristic, complemented
10C2×#15689284C211yesmaximal, characteristic, complemented
11C2×#15689284C211yesmaximal, characteristic, complemented
12C2×#15689267C211yesmaximal, characteristic, complemented
13C2×#15689272C211yesmaximal, characteristic, complemented
14C2×#15689236C211yesmaximal, characteristic, complemented
15C2×#15689196C211yesmaximal, characteristic, complemented
16C2×C47×#497C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625354C2211yescharacteristic
19C22×#10625354C2211yescharacteristic, complemented
20C22×D4×D47C2211yescharacteristic
21C2×#13094051—28no—
22C2×#13094051C2218yescomplemented
23C2×#13094047—28no—
24C2×#13094047C2218yescomplemented
25C22×#10625336C2211yescharacteristic
26C22×#10625336C2211yescharacteristic
27C22×#10625336C2211yescharacteristic, complemented
28C22×D376C2211yescharacteristic
29C22×#10625334C2211yescharacteristic
30C22×#10625324C2211yescharacteristic
31C22×C8×D47C2211yescharacteristic, complemented
32#15689776—24no—
33#15689776C2218yescomplemented
34#15689766—24no—
35#15689766C2218yescomplemented
36C2×#13094009—21no—
37C2×#13094009—21no—
38C2×#13094006—21no—
39C2×#13094000C2211yescharacteristic
40C2×#13094000C2211yescharacteristic
41C2×#13094000C2211yescharacteristic, complemented
42C2×#13093999—21no—
43C2×#13093997—21no—
44C2×#13093995C2211yescharacteristic
45C2×#13093994—21no—
46C2×C4×D188C2211yescharacteristic
47C2×C4×D188C2211yescharacteristic
48C2×C4×D188C2211yescharacteristic, complemented
49C2×C4⋊C4×D47—21no—
50C2×C22⋊C4×D47—21no—
51#15689378C2218yescomplemented
52#15689349C2218yescomplemented
53#15689335C2218yescomplemented
54#15689325C2218yescomplemented
55#15689284C2218yescomplemented
56#15689284C2218yescomplemented
57#15689272C2218yescomplemented
58#15689267C2218yescomplemented
59#15689236C2218yescomplemented
60#15689196C2218yescomplemented
61C2×#13093956C2211yescharacteristic, complemented
62C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
63C2×#13093948C2211yescharacteristic, complemented
64C2×#13093948C2211yescharacteristic, complemented
65C2×#13093948C2211yescharacteristic, complemented
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic, complemented
68C2×#13093945C2211yescharacteristic
69C2×(C2×D47)⋊C8C2211yescharacteristic
70C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
71C22×Q16×C47C2211yescharacteristic, complemented
72C22×Q16×C47C2211yescharacteristic, complemented
73C22×SD16×C47C2211yescharacteristic
74C22×SD16×C47C2211yescharacteristic
75C2×C4⋊Q8×C47C2211yescharacteristic, complemented
76C2×#124×C47C2211yescharacteristic
77C47×#497C2218yescomplemented
78C2×#97×C47C2211yescharacteristic, complemented
79C24×D47—21no—
80C2×#10625354—22no—
81C2×#10625354—22no—
82C2×#10625354—22no—
83C2×#10625354—24no—
84C2×#10625354—24no—
85C2×#10625354—24no—
86C2×#10625354—42no—
87C2×#10625354—42no—
88C2×#10625354—42no—
89C2×#10625354C2314yes—
90C2×#10625354C2314yes—
91C2×#10625354C2314yescomplemented
92C22×D188—21no—
93C22×D188—21no—
94C22×D188—21no—
95C22×D188D411yescharacteristic
96C22×D188C2311yescharacteristic
97C22×D188C2311yescharacteristic
98C22×C22⋊D47—21no—
99C22×C22⋊D47—21no—
100C2×D4×D47—24no—
101C2×D4×D47—22no—
102C2×D4×D47—42no—
103C2×D4×D47C2314yes—
104C22×C4×D47—21no—
105C22×C4×D47—21no—
106C22×C4×D47—21no—
107C22×C4×D47—21no—
108C22×C4×D47—21no—
109C22×C4×D47C2311yescharacteristic
110C22×C4×D47C2311yescharacteristic
111#13094051—232no—
112#13094047—232no—
113C2×#10625336—24no—
114C2×#10625336—24no—
115C2×#10625336—24no—
116C2×#10625336C2314yes—
117C2×#10625336C2314yes—
118C2×#10625336C2314yescomplemented
119C2×D376D418yescomplemented
120C2×D376C2314yes—
121C2×#10625334—24no—
122C2×#10625334C2314yes—
123C2×#10625324—24no—
124C2×#10625324C2314yes—
125C22×C47⋊C8C2311yescharacteristic
126C22×C47⋊C8C2311yescharacteristic
127C2×C8×D47—24no—
128C2×C8×D47C2314yescomplemented
129#13094009—28no—
130#13094009—28no—
131#13094006—28no—
132#13094000—22no—
133#13094000—22no—
134#13094000—22no—
135#13094000C2314yes—
136#13094000C2314yes—
137#13094000C2314yescomplemented
138#13093999—28no—
139#13093997—28no—
140#13093995—22no—
141#13093995C2314yes—
142#13093994—28no—
143C4×D188—22no—
144C4×D188—22no—
145C4×D188D414yes—
146C4×D188C2314yes—
147C4×D188C2314yes—
148C4×D188C2314yescomplemented
149C2×C4⋊Dic47D411yescharacteristic
150C2×C4⋊Dic47C2311yescharacteristic
151C2×C4⋊Dic47C2311yescharacteristic
152C2×Dic47⋊C4—21no—
153C2×Dic47⋊C4—21no—
154C2×Dic47⋊C4—21no—
155C4⋊C4×D47—28no—
156C2×C22⋊Dic47—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)⋊C4D411yescharacteristic
163C2×(C2×D47)⋊C4D411yescharacteristic
164C22⋊C4×D47—28no—
165#13093956C2314yescomplemented
166C4⋊(C47⋊C8)C2314yescomplemented
167#13093948C2314yescomplemented
168#13093948C2314yescomplemented
169#13093948C2314yescomplemented
170#13093946C2314yes—
171#13093946C2314yescomplemented
172#13093945C2314yes—
173(C2×D47)⋊C8C2314yes—
174(C2×D47)⋊C8C2314yescomplemented
175C22×Q8×C47C2311yescharacteristic
176C22×Q8×C47C2311yescharacteristic
177C22×Q8×C47C2311yescharacteristic
178C22×D4×C47C2311yescharacteristic
179C2×Q16×C47—24no—
180C2×Q16×C47—42no—
181C2×Q16×C47C2314yescomplemented
182C2×Q16×C47C2314yescomplemented
183C2×SD16×C47—24no—
184C2×SD16×C47—42no—
185C2×SD16×C47C2314yes—
186C2×SD16×C47C2314yes—
187C22×C8×C47C2311yescharacteristic
188C22×C8×C47C2311yescharacteristic
189C4⋊Q8×C47—22no—
190C4⋊Q8×C47C2314yescomplemented
191#124×C47—22no—
192#124×C47C2314yes—
193C2×C4⋊C4×C47—21no—
194C2×C4⋊C4×C47—21no—
195C2×C22⋊C4×C47—21no—
196C2×C22⋊C4×C47—21no—
197C2×C42×C47C2311yescharacteristic
198#97×C47C2314yescomplemented
199C24×C47—21no—
200C23×D47—21no—
201C23×D47—21no—
202C23×D47—24no—
203C23×D47—44no—
204C23×D47—44no—
205C23×D47—82no—
206C23×D47C2×D411yescharacteristic
207C23×D47C2×D411yescharacteristic
208C2×Q8×C47—21no—
209C2×Q8×C47—21no—
210C2×Q8×C47—21no—
211C2×Q8×C47—22no—
212C2×Q8×C47—22no—
213C2×Q8×C47—22no—
214C2×Q8×C47—22no—
215C2×Q8×C47—22no—
216C2×Q8×C47—22no—
217C2×Q8×C47C2412yes—
218C2×Q8×C47C2412yes—
219C2×Q8×C47C2412yes—
220C2×D4×C47—22no—
221C2×D4×C47—21no—
222C2×D4×C47—22no—
223C2×D4×C47C2412yes—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2411yescharacteristic
230C2×C22⋊D47—24no—
231C2×C22⋊D47—24no—
232C2×C22⋊D47—44no—
233C2×C22⋊D47—82no—
234C22×Dic47—21no—
235C22×Dic47—21no—
236C22×Dic47C2×D411yescharacteristic
237C22×Dic47C2×D411yescharacteristic
238#10625354—28no—
239#10625354—28no—
240#10625354—28no—
241#10625354—44no—
242#10625354—44no—
243#10625354—44no—
244#10625354—48no—
245#10625354—48no—
246#10625354—48no—
247D4×D47—28no—
248D4×D47—44no—
249D4×D47—48no—
250C2×D188—21no—
251C2×D188—21no—
252C2×D188—22no—
253C2×D188—22no—
254C2×D188—24no—
255C2×D188—24no—
256C2×D188—24no—
257C2×D188—42no—
258C2×D188—44no—
259C2×D188—44no—
260C2×D188—44no—
261C2×D188C2×D414yes—
262C2×D188C2×D414yes—
263C2×D188C2×D414yes—
264C2×D188C2412yes—
265C2×D188C2412yes—
266C2×C4×D47—22no—
267C2×C4×D47—22no—
268C2×C4×D47—22no—
269C2×C4×D47—22no—
270C2×C4×D47—24no—
271C2×C4×D47—24no—
272C2×C4×D47—24no—
273C2×C4×D47—24no—
274C2×C4×D47—24no—
275C2×C4×D47—44no—
276C2×C4×D47—44no—
277C2×C4×D47—44no—
278C2×C4×D47—44no—
279C2×C4×D47—82no—
280C2×C4×D47C2×D412yes—
281C2×C4×D47C2×D412yes—
282C2×C4×D47C2412yes—
283C2×C4×D47C2412yes—
284Q16×C47—28no—
285Q16×C47—44no—
286SD16×C47—28no—
287SD16×C47—44no—
288C2×C8×C47—22no—
289C2×C8×C47C2×D414yes—
290C2×C8×C47C2412yes—
291C2×C8×C47C2412yes—
292C4⋊C4×C47—24no—
293C4⋊C4×C47—24no—
294C22⋊C4×C47—24no—
295C22⋊C4×C47—24no—
296C42×C47C2×D412yes—
297C42×C47C2412yes—
298C22⋊Dic47—24no—
299#10625336—28no—
300#10625336—28no—
301#10625336—28no—
302#10625334—28no—
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)⋊C4C2×D414yes—
309(C2×D47)⋊C4C2×D414yes—
310C4⋊Dic47—21no—
311C4⋊Dic47—21no—
312C4⋊Dic47C2×D414yes—
313C4⋊Dic47C2412yes—
314C4⋊Dic47C2412yes—
315Dic47⋊C4—24no—
316Dic47⋊C4—24no—
317Dic47⋊C4—24no—
318C2×C47⋊C8—22no—
319C2×C47⋊C8—22no—
320C2×C47⋊C8C2412yes—
321C2×C47⋊C8C2412yes—
322D376C2×D4116yescomplemented
323#10625324—28no—
324C8×D47—28no—
325C23×C47—22no—
326C23×C47—42no—
327C23×C47—42no—
328C23×C47—42no—
329C23×C47C22×D411yescharacteristic
330C22×D47—22no—
331C22×D47—22no—
332C22×D47—24no—
333C22×D47—24no—
334C22×D47—22no—
335C22×D47—22no—
336C22×D47—22no—
337C22×D47—22no—
338C22×D47—22no—
339C22×D47—22no—
340C22×D47—48no—
341C22×D47—48no—
342C22×D47—42no—
343C22×D47—42no—
344C22×D47—42no—
345C22×D47—42no—
346C22×D47—84no—
347C22×D47—816no—
348C22×D47C22×D412yes—
349C22×D47C22×D412yes—
350Q8×C47—22no—
351Q8×C47—22no—
352Q8×C47—22no—
353Q8×C47—22no—
354Q8×C47—22no—
355Q8×C47—22no—
356Q8×C47—42no—
357Q8×C47—42no—
358Q8×C47—42no—
359D4×C47—22no—
360D4×C47—22no—
361D4×C47—42no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—22no—
365C2×C4×C47—22no—
366C2×C4×C47—22no—
367C2×C4×C47—42no—
368C2×C4×C47—42no—
369C2×C4×C47—42no—
370C2×C4×C47C22×D412yes—
371C2×C4×C47C22×D412yes—
372C2×C4×C47C22×D411yescharacteristic
373C2×C4×C47C22×D412yes—
374C2×C4×C47H(5,𝔽2)12yes—
375C2×C4×C47C2511yescharacteristic
376C22⋊D47—48no—
377C22⋊D47—84no—
378C2×Dic47—22no—
379C2×Dic47—22no—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—42no—
383C2×Dic47—42no—
384C2×Dic47C22×D412yes—
385C2×Dic47C22×D412yes—
386D188—24no—
387D188—24no—
388D188—22no—
389D188—22no—
390D188—44no—
391D188—48no—
392D188—48no—
393D188—48no—
394D188C22×D414yes—
395D188C22×D414yes—
396C4×D47—24no—
397C4×D47—24no—
398C4×D47—22no—
399C4×D47—22no—
400C4×D47—22no—
401C4×D47—22no—
402C4×D47—48no—
403C4×D47—48no—
404C4×D47—48no—
405C4×D47—48no—
406C4×D47—84no—
407C8×C47—22no—
408C8×C47C22×D414yes—
409C47⋊C8—22no—
410C47⋊C8—22no—
411C2×#3267—471nomaximal, Sylow
412C22×C47—42no—
413C22×C47—42no—
414C22×C47—42no—
415C22×C47—84no—
416C22×C47D4212yes—
417C22×C47#57512yes—
418C22×C47#57712yes—
419C22×C47C23×D411yescharacteristic
420C2×D47—22no—
421C2×D47—22no—
422C2×D47—24no—
423C2×D47—24no—
424C2×D47—22no—
425C2×D47—22no—
426C2×D47—22no—
427C2×D47—22no—
428C2×D47—44no—
429C2×D47—44no—
430C2×D47—48no—
431C2×D47—48no—
432C2×D47—42no—
433C2×D47—42no—
434C2×D47—42no—
435C2×D47—42no—
436C2×D47—816no—
437C4×C47—22no—
438C4×C47—22no—
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—42no—
448Dic47—42no—
449C22×AGL(1,ℤ/8)—471no—
450C22×#135—471no—
451C2×#547—471no—
452C2×#546—471no—
453#3267—4716no—
454C2×#497D4711yescharacteristic, complemented
455C2×#470—471no—
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—82no—
466C2×C47#326714yescomplemented
467C2×C47C2×D4211yescharacteristic
468C2×C47C2×#57511yescharacteristic
469C2×C47C2×#57711yescharacteristic
470D47—42no—
471D47—42no—
472D47—44no—
473D47—44no—
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×Q16C2×D4711yescharacteristic, complemented
483C22×Q16C2×D4711yescharacteristic, complemented
484C22×SD16—471no—
485C22×SD16—471no—
486C22×SD16—471no—
487C22×SD16C2×D4711yescharacteristic
488C22×SD16C2×D4711yescharacteristic
489C22×D8—471no—
490C22×D8—471no—
491C22×M16—471no—
492C23×C8—471no—
493#547—478no—
494#547—944no—
495#546—478no—
496#546—944no—
497C2×C4⋊Q8C2×D4711yescharacteristic, complemented
498C2×#124C2×D4711yescharacteristic
499C2×#123—941no—
500C2×#123—941no—
501C2×#123—941no—
502C2×C22⋊Q8—471no—
503C2×C22⋊Q8—471no—
504C2×C22⋊Q8—471no—
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#497C2×D4718yescomplemented
515#470—478no—
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×#106—471no—
526C2×C4⋊C8—471no—
527C2×#103—471no—
528C2×#103—471no—
529C2×#103—471no—
530C2×#102—471no—
531C2×#102—471no—
532C2×#102—471no—
533C2×C22⋊C8—471no—
534C2×C22⋊C8—471no—
535C2×#97C2×D4711yescharacteristic, complemented
536C47C2×#326711yescharacteristic, complemented, Sylow
537C25—941no—
538C2×#41—474no—
539C2×#41—474no—
540C2×#41—474no—
541C2×#41—942no—
542C2×#41—942no—
543C2×#41—942no—
544C2×#41—944no—
545C2×#41—944no—
546C2×#41—944no—
547C2×#41—1882no—
548C2×#41—1882no—
549C2×#41—1882no—
550C22×Q8C22×D4711yescharacteristic
551C22×Q8C22×D4711yescharacteristic
552C22×Q8C22×D4711yescharacteristic
553C22×D4—474no—
554C22×D4—471no—
555C22×D4—471no—
556C22×D4—471no—
557C22×D4—941no—
558C22×D4—941no—
559C22×D4—941no—
560C22×D4—942no—
561C22×D4—941no—
562C22×D4—944no—
563C22×D4—941no—
564C22×D4—1882no—
565C22×D4C22×D4711yescharacteristic
566C23×C4—471no—
567C23×C4—471no—
568C23×C4—941no—
569C23×C4—941no—
570C23×C4—941no—
571C23×C4—941no—
572C23×C4—941no—
573AGL(1,ℤ/8)—9432no—
574#135—9432no—
575C2×Q16—24no—
576C2×Q16—42no—
577C2×Q16C22×D4714yescomplemented
578C2×Q16C22×D4714yescomplemented
579C2×SD16—24no—
580C2×SD16—42no—
581C2×SD16—474no—
582C2×SD16—474no—
583C2×SD16—474no—
584C2×SD16—944no—
585C2×SD16—944no—
586C2×SD16—944no—
587C2×SD16C22×D4714yes—
588C2×SD16C22×D4714yes—
589C2×D8—474no—
590C2×D8—478no—
591C2×D8—474no—
592C2×D8—944no—
593C2×M16—474no—
594C2×M16—944no—
595C22×C8—471no—
596C22×C8—471no—
597C22×C8—474no—
598C22×C8—944no—
599C22×C8C22×D4711yescharacteristic
600C22×C8C22×D4711yescharacteristic
601C4⋊Q8—22no—
602C4⋊Q8C22×D4714yescomplemented
603#124—22no—
604#124C22×D4714yes—
605#123—948no—
606#123—948no—
607#123—948no—
608C22⋊Q8—474no—
609C22⋊Q8—474no—
610C22⋊Q8—474no—
611C22⋊Q8—942no—
612C22⋊Q8—942no—
613C22⋊Q8—942no—
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—471no—
629C2×C4⋊C4—471no—
630C2×C4⋊C4—948no—
631C2×C4⋊C4—941no—
632C2×C4⋊C4—941no—
633C2×C4⋊C4—941no—
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×C42C22×D4711yescharacteristic
646#106—474no—
647C4⋊C8—474no—
648#103—474no—
649#103—474no—
650#103—474no—
651#102—474no—
652#102—474no—
653#102—474no—
654C22⋊C8—474no—
655C22⋊C8—474no—
656#97C22×D4714yescomplemented
657C24—21no—
658C24—471no—
659C24—471no—
660C24—944no—
661C24—941no—
662C24—941no—
663C24—3762no—
664C24—1884no—
665C24—1884no—
666#41—948no—
667#41—948no—
668#41—948no—
669#41—1884no—
670#41—1884no—
671#41—1884no—
672#41—1888no—
673#41—1888no—
674#41—1888no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—22no—
679C2×Q8—22no—
680C2×Q8—22no—
681C2×Q8—22no—
682C2×Q8—22no—
683C2×Q8—22no—
684C2×Q8C23×D4712yes—
685C2×Q8C23×D4712yes—
686C2×Q8C23×D4712yes—
687C2×D4—22no—
688C2×D4—21no—
689C2×D4—22no—
690C2×D4—474no—
691C2×D4—474no—
692C2×D4—474no—
693C2×D4—472no—
694C2×D4—472no—
695C2×D4—944no—
696C2×D4—944no—
697C2×D4—944no—
698C2×D4—944no—
699C2×D4—948no—
700C2×D4—944no—
701C2×D4—941no—
702C2×D4—941no—
703C2×D4—942no—
704C2×D4—942no—
705C2×D4—3762no—
706C2×D4—1882no—
707C2×D4—1884no—
708C2×D4—1884no—
709C2×D4—1884no—
710C2×D4—1884no—
711C2×D4—1888no—
712C2×D4—1884no—
713C2×D4C23×D4712yes—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—471no—
718C22×C4—471no—
719C22×C4—472no—
720C22×C4—472no—
721C22×C4—472no—
722C22×C4—472no—
723C22×C4—944no—
724C22×C4—944no—
725C22×C4—944no—
726C22×C4—942no—
727C22×C4—942no—
728C22×C4—942no—
729C22×C4—942no—
730C22×C4—941no—
731C22×C4—941no—
732C22×C4—944no—
733C22×C4—944no—
734C22×C4—3762no—
735C22×C4—1884no—
736C22×C4—1884no—
737C22×C4—1884no—
738C22×C4—1884no—
739C22×C4D4×D4711yescharacteristic
740C22×C4D4×D4711yescharacteristic
741C22×C4C23×D4711yescharacteristic
742Q16—28no—
743Q16—44no—
744SD16—28no—
745SD16—44no—
746SD16—948no—
747SD16—948no—
748SD16—948no—
749D8—4716no—
750D8—948no—
751M16—948no—
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—474no—
764C4⋊C4—472no—
765C4⋊C4—472no—
766C4⋊C4—944no—
767C4⋊C4—944no—
768C4⋊C4—944no—
769C4⋊C4—941no—
770C4⋊C4—941no—
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—
781C42D4×D4712yes—
782C42C23×D4712yes—
783C23—22no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—472no—
788C23—472no—
789C23—942no—
790C23—942no—
791C23—944no—
792C23—944no—
793C23—942no—
794C23—942no—
795C23—942no—
796C23—942no—
797C23—942no—
798C23—942no—
799C23—3764no—
800C23—37616no—
801C23—1888no—
802C23—1888no—
803C23—1882no—
804C23—1882no—
805C23—1882no—
806C23—1882no—
807C23C2×D4×D4711yescharacteristic
808Q8—22no—
809Q8—22no—
810Q8—22no—
811Q8—22no—
812Q8—22no—
813Q8—22no—
814Q8—42no—
815Q8—42no—
816Q8—42no—
817D4—22no—
818D4—22no—
819D4—42no—
820D4—474no—
821D4—474no—
822D4—944no—
823D4—944no—
824D4—942no—
825D4—942no—
826D4—3764no—
827D4—1884no—
828D4—1888no—
829D4—1888no—
830D4—1888no—
831D4—1888no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—472no—
841C2×C4—472no—
842C2×C4—942no—
843C2×C4—942no—
844C2×C4—944no—
845C2×C4—944no—
846C2×C4—942no—
847C2×C4—942no—
848C2×C4—942no—
849C2×C4—942no—
850C2×C4—942no—
851C2×C4—942no—
852C2×C4—3764no—
853C2×C4—1888no—
854C2×C4—1888no—
855C2×C4—1888no—
856C2×C4—1888no—
857C2×C4—1882no—
858C2×C4—1882no—
859C2×C4C2×D4×D4712yes—
860C2×C4C2×D4×D4712yes—
861C2×C4C2×D4×D4711yescharacteristic
862C2×C4C2×D4×D4712yes—
863C2×C4#1309406912yes—
864C2×C4C24×D4711yescharacteristic
865C8—22no—
866C8—942no—
867C8—942no—
868C8C2×D4×D4714yes—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—84no—
873C22—942no—
874C22—942no—
875C22—944no—
876C22—944no—
877C22—942no—
878C22—942no—
879C22—942no—
880C22—942no—
881C22—37616no—
882C22—1882no—
883C22—1882no—
884C22—1882no—
885C22—1882no—
886C22—1884no—
887C22—1884no—
888C22—1888no—
889C22—1888no—
890C22#1568975812yes—
891C22#1568992212yes—
892C22#1568993212yes—
893C22C22×D4×D4711yescharacteristic
894C4—22no—
895C4—22no—
896C4—42no—
897C4—42no—
898C4—42no—
899C4—942no—
900C4—942no—
901C4—1882no—
902C4—1882no—
903C4#1568975812yes—
904C4C22×D4×D4711yescharacteristic
905C4C2×#1309406911yescharacteristic
906C2—82no—
907C2—1882no—
908C2—1882no—
909C2—1884no—
910C2—1884no—
911C2#2025491214yesdirect product factor
912C2C2×#1568975811yescharacteristic
913C2C2×#1568992211yescharacteristic
914C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#497C2
socleC23×C47C22×D4
hypercenterC2×#497D47
hypocenterC47C2×#3267
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C22×#13094051C2semidirect
2. C22×#13094047C2semidirect
3. C2×#15689776C2semidirect
4. C2×#15689766C2semidirect
5. #20254912C2direct (N × H)
6. C2×#15689378C2semidirect
7. C2×#15689349C2semidirect
8. C2×#15689335C2semidirect
9. C2×#15689325C2semidirect
10. C2×#15689284C2semidirect
11. C2×#15689284C2semidirect
12. C2×#15689267C2semidirect
13. C2×#15689272C2semidirect
14. C2×#15689236C2semidirect
15. C2×#15689196C2semidirect
16. C2×C47×#497C2semidirect
19. C22×#10625354C22semidirect
22. C2×#13094051C22semidirect
24. C2×#13094047C22semidirect
27. C22×#10625336C22semidirect
31. C22×C8×D47C22semidirect
33. #15689776C22semidirect
35. #15689766C22semidirect
41. C2×#13094000C22semidirect
48. C2×C4×D188C22semidirect
51. #15689378C22semidirect
52. #15689349C22semidirect
53. #15689335C22semidirect
54. #15689325C22semidirect
55. #15689284C22semidirect
56. #15689284C22semidirect
57. #15689272C22semidirect
58. #15689267C22semidirect
59. #15689236C22semidirect
60. #15689196C22semidirect
61. C2×#13093956C22semidirect
62. C2×C4⋊(C47⋊C8)C22semidirect
63. C2×#13093948C22semidirect
64. C2×#13093948C22semidirect
65. C2×#13093948C22semidirect
67. C2×#13093946C22semidirect
70. C2×(C2×D47)⋊C8C22semidirect
71. C22×Q16×C47C22semidirect
72. C22×Q16×C47C22semidirect
75. C2×C4⋊Q8×C47C22semidirect
77. C47×#497C22semidirect
78. C2×#97×C47C22semidirect
91. C2×#10625354C23semidirect
118. C2×#10625336C23semidirect
119. C2×D376D4semidirect
128. C2×C8×D47C23semidirect
137. #13094000C23semidirect
148. C4×D188C23semidirect
165. #13093956C23semidirect
166. C4⋊(C47⋊C8)C23semidirect
167. #13093948C23semidirect
168. #13093948C23semidirect
169. #13093948C23semidirect
171. #13093946C23semidirect
174. (C2×D47)⋊C8C23semidirect
181. C2×Q16×C47C23semidirect
182. C2×Q16×C47C23semidirect
190. C4⋊Q8×C47C23semidirect
198. #97×C47C23semidirect
322. D376C2×D4semidirect
454. C2×#497D47semidirect
466. C2×C47#3267semidirect
482. C22×Q16C2×D47semidirect
483. C22×Q16C2×D47semidirect
497. C2×C4⋊Q8C2×D47semidirect
514. #497C2×D47semidirect
535. C2×#97C2×D47semidirect
536. C47C2×#3267semidirect
577. C2×Q16C22×D47semidirect
578. C2×Q16C22×D47semidirect
602. C4⋊Q8C22×D47semidirect
656. #97C22×D47semidirect
911. C2#20254912direct (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×#130940472
C2×#156897762
C2×#156897662
#202549122
C2×#156893782
C2×#156893492
C2×#156893352
C2×#156893252
C2×#156892842
C2×#156892672
C2×#156892722
C2×#156892362
C2×#156891962
C2×C47×#4972
C2×#326747