Finite Group Databasebeta

← C2×#20255431 #27092955

Subgroups — C2×#20255431 #27092955

Order 12032.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689846C211yesmaximal, characteristic, complemented
2C2×#15689766C211yesmaximal, characteristic
3#20255431C2116yesmaximal, direct product factor
4C2×#15689482C211yesmaximal, characteristic, complemented
5C2×#15689462C211yesmaximal, characteristic, complemented
6C2×#15689446C211yesmaximal, characteristic, complemented
7C2×#15689414C211yesmaximal, characteristic, complemented
8C2×#15689378C211yesmaximal, characteristic, complemented
9C2×#15689349C211yesmaximal, characteristic, complemented
10C2×#15689284C211yesmaximal, characteristic, complemented
11C2×#15689272C211yesmaximal, characteristic, complemented
12C2×#15689221C211yesmaximal, characteristic, complemented
13C2×#15689193C211yesmaximal, characteristic, complemented
14C2×#15689126C211yesmaximal, characteristic, complemented
15C2×#15689118C211yesmaximal, characteristic, complemented
16C2×C47×#464C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×D4×D47C2211yescharacteristic
19C22×#10625336C2211yescharacteristic
20C22×#10625324C2211yescharacteristic
21C22×C8×D47C2211yescharacteristic, complemented
22#15689846—24no—
23#15689846C2218yescomplemented
24#15689766—24no—
25#15689766C2218yes—
26C2×#13094024C2211yescharacteristic, complemented
27C2×#13094019—21no—
28C2×#13094019—21no—
29C2×#13094012—21no—
30C2×#13094006—21no—
31C2×#13094000C2211yescharacteristic
32C2×#13094000C2211yescharacteristic
33C2×#13094000C2211yescharacteristic, complemented
34C2×#13093997—21no—
35C2×#13093995C2211yescharacteristic
36C2×#13093994—21no—
37C2×C4×Dic94—21no—
38C2×C4×D188C2211yescharacteristic
39C2×C4×D188C2211yescharacteristic
40C2×#13093982C2211yescharacteristic
41C2×#13093982C2211yescharacteristic, complemented
42C2×C22⋊C4×D47—21no—
43#15689482C2218yescomplemented
44#15689462C2218yescomplemented
45#15689446C2218yescomplemented
46#15689414C2218yescomplemented
47#15689378C2218yescomplemented
48#15689349C2218yescomplemented
49#15689284C2218yescomplemented
50#15689272C2218yescomplemented
51#15689221C2218yescomplemented
52#15689193C2218yescomplemented
53C2×#13093957C2211yescharacteristic, complemented
54C2×#13093956C2211yescharacteristic, complemented
55C2×#13093956C2211yescharacteristic, complemented
56#15689126C2218yescomplemented
57#15689118C2218yescomplemented
58C2×#13093948C2211yescharacteristic, complemented
59C2×#13093948C2211yescharacteristic, complemented
60C2×#13093948C2211yescharacteristic, complemented
61C2×#13093946C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093945C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
68C2×#13093935C2211yescharacteristic, complemented
69C22×Q16×C47C2211yescharacteristic, complemented
70C22×SD16×C47C2211yescharacteristic
71C2×#124×C47C2211yescharacteristic
72C2×C4×Q8×C47C2211yescharacteristic, complemented
73C47×#464C2218yescomplemented
74C2×C4⋊C8×C47C2211yescharacteristic, complemented
75C2×#103×C47C2211yescharacteristic, complemented
76C2×#102×C47C2211yescharacteristic
77C24×D47—21no—
78C2×#10625354—22no—
79C2×#10625354—24no—
80C2×#10625354—42no—
81C2×#10625354C2314yes—
82C22×Dic94—21no—
83C22×D188—21no—
84C22×D188D411yescharacteristic
85C22×D188C2311yescharacteristic
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C2×D4×D47—24no—
89C2×D4×D47—22no—
90C2×D4×D47—42no—
91C2×D4×D47C2314yes—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C22×C4×D47C2311yescharacteristic
95C22×C4×D47C2311yescharacteristic
96C2×#10625336—24no—
97C2×#10625336C2314yes—
98C2×#10625324—42no—
99C2×#10625324C2314yes—
100C22×C47⋊C8C2311yescharacteristic
101C22×C47⋊C8C2311yescharacteristic
102C2×C8×D47—42no—
103C2×C8×D47C2314yescomplemented
104#13094024—22no—
105#13094024C2314yescomplemented
106#13094019—28no—
107#13094019—28no—
108#13094012—28no—
109#13094006—28no—
110#13094000—22no—
111#13094000—22no—
112#13094000—22no—
113#13094000C2314yes—
114#13094000C2314yes—
115#13094000C2314yescomplemented
116#13093997—28no—
117#13093995—22no—
118#13093995C2314yes—
119#13093994—28no—
120C4×Dic94—28no—
121C4×D188—22no—
122C4×D188D414yes—
123C4×D188C2314yes—
124C4×D188C2314yes—
125#13093982—22no—
126#13093982—22no—
127#13093982C2314yes—
128#13093982C2314yescomplemented
129C2×C4⋊Dic47—21no—
130C2×C4⋊Dic47D411yescharacteristic
131C2×C4⋊Dic47C2311yescharacteristic
132C2×C4⋊Dic47C2311yescharacteristic
133C2×C4⋊Dic47C2311yescharacteristic
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×C22⋊Dic47—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4D411yescharacteristic
145C2×(C2×D47)⋊C4D411yescharacteristic
146C22⋊C4×D47—28no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47—21no—
149#13093957C2314yescomplemented
150#13093956C2314yescomplemented
151#13093956C2314yescomplemented
152#13093948C2314yescomplemented
153#13093948C2314yescomplemented
154#13093948C2314yescomplemented
155#13093946C2314yes—
156#13093946C2314yes—
157#13093945C2314yes—
158#13093945C2314yes—
159#13093944C2314yes—
160(C2×D47)⋊C8C2314yes—
161(C2×D47)⋊C8C2314yescomplemented
162#13093935C2314yescomplemented
163C22×Q8×C47C2311yescharacteristic
164C22×Q8×C47C2311yescharacteristic
165C22×D4×C47C2311yescharacteristic
166C2×Q16×C47—42no—
167C2×Q16×C47C2314yescomplemented
168C2×SD16×C47—42no—
169C2×SD16×C47C2314yes—
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2311yescharacteristic
172#124×C47—22no—
173#124×C47C2314yes—
174C4×Q8×C47—22no—
175C4×Q8×C47C2314yescomplemented
176C2×C4⋊C4×C47—21no—
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180C2×C42×C47—21no—
181C2×C42×C47C2311yescharacteristic
182C4⋊C8×C47C2314yescomplemented
183#103×C47C2314yescomplemented
184#102×C47C2314yes—
185C24×C47—21no—
186C23×D47—21no—
187C23×D47—24no—
188C23×D47—44no—
189C23×D47—44no—
190C23×D47—82no—
191C23×D47C2×D411yescharacteristic
192C23×D47C2×D411yescharacteristic
193C2×Q8×C47—21no—
194C2×Q8×C47—21no—
195C2×Q8×C47—22no—
196C2×Q8×C47—22no—
197C2×Q8×C47—22no—
198C2×Q8×C47—22no—
199C2×Q8×C47C2412yes—
200C2×Q8×C47C2412yes—
201C2×D4×C47—21no—
202C2×D4×C47—22no—
203C2×D4×C47—22no—
204C2×D4×C47C2412yes—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2411yescharacteristic
211C2×C22⋊D47—24no—
212C2×C22⋊D47—24no—
213C2×C22⋊D47—44no—
214C2×C22⋊D47—82no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47C2×D411yescharacteristic
219C22×Dic47C2×D411yescharacteristic
220#10625354—28no—
221#10625354—44no—
222#10625354—48no—
223D4×D47—28no—
224D4×D47—44no—
225D4×D47—48no—
226C2×D188—21no—
227C2×D188—22no—
228C2×D188—24no—
229C2×D188—42no—
230C2×D188—44no—
231C2×D188C2×D414yes—
232C2×D188#4114yes—
233C2×D188C2412yes—
234C2×C4×D47—22no—
235C2×C4×D47—22no—
236C2×C4×D47—22no—
237C2×C4×D47—22no—
238C2×C4×D47—24no—
239C2×C4×D47—24no—
240C2×C4×D47—44no—
241C2×C4×D47—82no—
242C2×C4×D47C2×D412yes—
243C2×C4×D47C2×D412yes—
244C2×C4×D47C2412yes—
245C2×C4×D47C2412yes—
246C2×Dic94—24no—
247C2×Dic94—44no—
248Q16×C47—44no—
249SD16×C47—44no—
250C2×C8×C47—22no—
251C2×C8×C47—22no—
252C2×C8×C47C2412yes—
253C2×C8×C47C2412yes—
254C4⋊C4×C47—24no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47C2412yes—
257C22⋊C4×C47—24no—
258C22⋊C4×C47—24no—
259C42×C47—24no—
260C42×C47C2×D412yes—
261C42×C47C2412yes—
262C22⋊Dic47—24no—
263#10625336—28no—
264(C2×D47)⋊C4—24no—
265(C2×D47)⋊C4—24no—
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4—24no—
269(C2×D47)⋊C4—24no—
270(C2×D47)⋊C4C2×D414yes—
271(C2×D47)⋊C4C2×D414yes—
272C4⋊Dic47—24no—
273C4⋊Dic47—21no—
274C4⋊Dic47—21no—
275C4⋊Dic47—21no—
276C4⋊Dic47C2×D414yes—
277C4⋊Dic47C2412yes—
278C4⋊Dic47C2412yes—
279C4⋊Dic47C2412yes—
280Dic47⋊C4—24no—
281Dic47⋊C4—24no—
282Dic47⋊C4—24no—
283C4×Dic47—24no—
284C4×Dic47—24no—
285C2×C47⋊C8—22no—
286C2×C47⋊C8—22no—
287C2×C47⋊C8C2412yes—
288C2×C47⋊C8C2412yes—
289#10625324—44no—
290C8×D47—44no—
291C23×C47—22no—
292C23×C47—42no—
293C23×C47—42no—
294C23×C47—42no—
295C23×C47C22×D411yescharacteristic
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—24no—
299C22×D47—22no—
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—48no—
305C22×D47—48no—
306C22×D47—42no—
307C22×D47—42no—
308C22×D47—84no—
309C22×D47—816no—
310C22×D47C22×D412yes—
311C22×D47C22×D412yes—
312Q8×C47—22no—
313Q8×C47—22no—
314Q8×C47—22no—
315Q8×C47—22no—
316Q8×C47—42no—
317Q8×C47—42no—
318D4×C47—22no—
319D4×C47—22no—
320D4×C47—42no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—42no—
327C2×C4×C47—42no—
328C2×C4×C47—42no—
329C2×C4×C47C22×D412yes—
330C2×C4×C47C22×D412yes—
331C2×C4×C47C22×D411yescharacteristic
332C2×C4×C47C2×#4112yes—
333C2×C4×C47H(5,𝔽2)12yes—
334C2×C4×C47C2511yescharacteristic
335C22⋊D47—48no—
336C22⋊D47—84no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—42no—
343C2×Dic47—42no—
344C2×Dic47—42no—
345C2×Dic47C22×D412yes—
346C2×Dic47C22×D412yes—
347D188—24no—
348D188—22no—
349D188—44no—
350D188—48no—
351D188C2×#4114yes—
352C4×D47—24no—
353C4×D47—24no—
354C4×D47—22no—
355C4×D47—22no—
356C4×D47—22no—
357C4×D47—22no—
358C4×D47—48no—
359C4×D47—84no—
360Dic94—48no—
361C8×C47—22no—
362C8×C47—22no—
363C47⋊C8—22no—
364C47⋊C8—22no—
365C2×#3311—471nomaximal, Sylow
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47—84no—
370C22×C47#54612yes—
371C22×C47#57512yes—
372C22×C47#57712yes—
373C22×C47C23×D411yescharacteristic
374C2×D47—22no—
375C2×D47—22no—
376C2×D47—24no—
377C2×D47—22no—
378C2×D47—22no—
379C2×D47—22no—
380C2×D47—22no—
381C2×D47—44no—
382C2×D47—44no—
383C2×D47—48no—
384C2×D47—42no—
385C2×D47—42no—
386C2×D47—816no—
387C4×C47—22no—
388C4×C47—22no—
389C4×C47—42no—
390C4×C47—42no—
391C4×C47—42no—
392C4×C47#54612yes—
393C4×C47C22×#4111yescharacteristic
394C4×C47C2×H(5,𝔽2)11yescharacteristic
395Dic47—22no—
396Dic47—22no—
397Dic47—42no—
398Dic47—42no—
399Dic47—42no—
400C2×#556—471no—
401C2×#546—471no—
402#3311—4716no—
403C2×#489—471no—
404C2×#485—471no—
405C2×#482—471no—
406C2×#476—471no—
407C2×#470—471no—
408C2×#465—471no—
409C2×#464D4711yescharacteristic, complemented
410C2×#452—471no—
411C2×#450—471no—
412C2×#440—471no—
413C2×#435—471no—
414C2×#418—471no—
415C2×#416—471no—
416C2×C47—82no—
417C2×C47#331114yescomplemented
418C2×C47C2×#54611yescharacteristic
419C2×C47C2×#57511yescharacteristic
420C2×C47C2×#57711yescharacteristic
421D47—42no—
422D47—42no—
423D47—44no—
424C22×#41—471no—
425C23×D4—471no—
426C22×Q16C2×D4711yescharacteristic, complemented
427C22×SD16—471no—
428C22×SD16C2×D4711yescharacteristic
429C22×M16—471no—
430C23×C8—471no—
431#556—478no—
432#556—944no—
433#546—478no—
434#546—944no—
435C2×C4⋊Q8—471no—
436C2×#126—941no—
437C2×#126—941no—
438C2×#124—941no—
439C2×#124C2×D4711yescharacteristic
440C2×#123—941no—
441C2×C22⋊Q8—471no—
442C2×C22⋊Q8—471no—
443C2×C22⋊Q8—471no—
444C2×#121—471no—
445C2×#121—941no—
446C2×#120—941no—
447C2×C4×Q8—941no—
448C2×C4×Q8C2×D4711yescharacteristic, complemented
449C2×C4×D4—471no—
450C2×C4×D4—471no—
451C2×#117—471no—
452C2×#117—471no—
453C22×C22⋊C4—941no—
454#489—478no—
455#485—478no—
456#482—478no—
457#476—478no—
458#470—478no—
459#465—478no—
460#464C2×D4718yescomplemented
461#452—478no—
462#450—478no—
463#440—478no—
464#435—478no—
465C2×#107—471no—
466C2×#106—471no—
467C2×#106—471no—
468C2×C4⋊C8C2×D4711yescharacteristic, complemented
469#418—478no—
470#416—478no—
471C2×#103—471no—
472C2×#103—471no—
473C2×#103—471no—
474C2×#103C2×D4711yescharacteristic, complemented
475C2×#102—471no—
476C2×#102—471no—
477C2×#102—471no—
478C2×#102—471no—
479C2×#102—471no—
480C2×#102C2×D4711yescharacteristic
481C2×C22⋊C8—471no—
482C2×C22⋊C8—471no—
483C2×#97—471no—
484C47C2×#331111yescharacteristic, complemented, Sylow
485C25—941no—
486C2×#41—474no—
487C2×#41—942no—
488C2×#41—944no—
489C2×#41—1882no—
490C22×Q8—941no—
491C22×Q8C22×D4711yescharacteristic
492C22×Q8C22×D4711yescharacteristic
493C22×D4—474no—
494C22×D4—471no—
495C22×D4—471no—
496C22×D4—941no—
497C22×D4—942no—
498C22×D4—941no—
499C22×D4—944no—
500C22×D4—941no—
501C22×D4—1882no—
502C22×D4C22×D4711yescharacteristic
503C23×C4—471no—
504C23×C4—471no—
505C23×C4—941no—
506C23×C4—941no—
507C2×Q16—42no—
508C2×Q16C22×D4714yescomplemented
509C2×SD16—42no—
510C2×SD16—474no—
511C2×SD16—944no—
512C2×SD16C22×D4714yes—
513C2×M16—474no—
514C2×M16—1882no—
515C22×C8—471no—
516C22×C8—471no—
517C22×C8—474no—
518C22×C8—1882no—
519C22×C8C22×D4711yescharacteristic
520C22×C8C22×D4711yescharacteristic
521C4⋊Q8—474no—
522C4⋊Q8—942no—
523#126—948no—
524#126—948no—
525#124—22no—
526#124—948no—
527#124C22×D4714yes—
528#123—948no—
529C22⋊Q8—474no—
530C22⋊Q8—474no—
531C22⋊Q8—474no—
532C22⋊Q8—942no—
533C22⋊Q8—942no—
534C22⋊Q8—942no—
535#121—474no—
536#121—948no—
537#121—942no—
538#120—948no—
539C4×Q8—22no—
540C4×Q8—948no—
541C4×Q8C22×D4714yescomplemented
542C4×D4—474no—
543C4×D4—474no—
544C4×D4—474no—
545C4×D4—942no—
546#117—474no—
547#117—474no—
548#117—942no—
549#117—942no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—471no—
552C2×C4⋊C4—471no—
553C2×C4⋊C4—471no—
554C2×C4⋊C4—471no—
555C2×C4⋊C4—941no—
556C2×C4⋊C4—941no—
557C2×C4⋊C4—941no—
558C2×C4⋊C4—941no—
559C2×C4⋊C4C22×D4711yescharacteristic
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—471no—
563C2×C22⋊C4—471no—
564C2×C22⋊C4—948no—
565C2×C22⋊C4—941no—
566C2×C22⋊C4—941no—
567C2×C22⋊C4—941no—
568C2×C22⋊C4—941no—
569C2×C22⋊C4—941no—
570C2×C22⋊C4—941no—
571C2×C22⋊C4—941no—
572C2×C42—21no—
573C2×C42—941no—
574C2×C42—941no—
575C2×C42C22×D4711yescharacteristic
576#107—474no—
577#106—474no—
578#106—474no—
579C4⋊C8C22×D4714yescomplemented
580#103—474no—
581#103—474no—
582#103—474no—
583#103C22×D4714yescomplemented
584#102—474no—
585#102—474no—
586#102—474no—
587#102—474no—
588#102—474no—
589#102C22×D4714yes—
590C22⋊C8—474no—
591C22⋊C8—474no—
592#97—474no—
593C24—21no—
594C24—471no—
595C24—471no—
596C24—944no—
597C24—941no—
598C24—3762no—
599C24—1884no—
600C24—1884no—
601#41—948no—
602#41—1884no—
603#41—1888no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—944no—
611C2×Q8—1884no—
612C2×Q8C23×D4712yes—
613C2×Q8C23×D4712yes—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—474no—
618C2×D4—474no—
619C2×D4—472no—
620C2×D4—944no—
621C2×D4—944no—
622C2×D4—948no—
623C2×D4—944no—
624C2×D4—941no—
625C2×D4—942no—
626C2×D4—3762no—
627C2×D4—1882no—
628C2×D4—1884no—
629C2×D4—1884no—
630C2×D4—1888no—
631C2×D4—1884no—
632C2×D4C23×D4712yes—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—471no—
637C22×C4—471no—
638C22×C4—472no—
639C22×C4—472no—
640C22×C4—472no—
641C22×C4—472no—
642C22×C4—944no—
643C22×C4—942no—
644C22×C4—942no—
645C22×C4—942no—
646C22×C4—942no—
647C22×C4—941no—
648C22×C4—941no—
649C22×C4—941no—
650C22×C4—944no—
651C22×C4—3762no—
652C22×C4—1884no—
653C22×C4D4×D4711yescharacteristic
654C22×C4D4×D4711yescharacteristic
655C22×C4C23×D4711yescharacteristic
656Q16—44no—
657SD16—44no—
658SD16—948no—
659M16—1884no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—472no—
663C2×C8—472no—
664C2×C8—942no—
665C2×C8—942no—
666C2×C8—1884no—
667C2×C8C23×D4712yes—
668C2×C8C23×D4712yes—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—474no—
672C4⋊C4—472no—
673C4⋊C4—472no—
674C4⋊C4—472no—
675C4⋊C4—944no—
676C4⋊C4—944no—
677C4⋊C4—944no—
678C4⋊C4—941no—
679C4⋊C4—941no—
680C4⋊C4—941no—
681C4⋊C4—944no—
682C4⋊C4C23×D4712yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—474no—
686C22⋊C4—474no—
687C22⋊C4—944no—
688C22⋊C4—944no—
689C22⋊C4—944no—
690C22⋊C4—944no—
691C22⋊C4—944no—
692C22⋊C4—944no—
693C22⋊C4—944no—
694C42—24no—
695C42—944no—
696C42—944no—
697C42D4×D4712yes—
698C42C23×D4712yes—
699C23—22no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—472no—
704C23—472no—
705C23—942no—
706C23—942no—
707C23—944no—
708C23—942no—
709C23—942no—
710C23—942no—
711C23—942no—
712C23—942no—
713C23—3764no—
714C23—37616no—
715C23—1888no—
716C23—1888no—
717C23—1882no—
718C23—1882no—
719C23C2×D4×D4711yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—42no—
725Q8—42no—
726Q8—1888no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—474no—
731D4—944no—
732D4—942no—
733D4—3764no—
734D4—1884no—
735D4—1888no—
736D4—1888no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—472no—
746C2×C4—472no—
747C2×C4—942no—
748C2×C4—942no—
749C2×C4—944no—
750C2×C4—944no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—942no—
758C2×C4—3764no—
759C2×C4—1888no—
760C2×C4—1882no—
761C2×C4—1882no—
762C2×C4—1882no—
763C2×C4C2×D4×D4712yes—
764C2×C4C2×D4×D4712yes—
765C2×C4C2×D4×D4711yescharacteristic
766C2×C4#41×D4712yes—
767C2×C4#1309406912yes—
768C2×C4C24×D4711yescharacteristic
769C8—22no—
770C8—22no—
771C8—942no—
772C8—942no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—84no—
777C22—942no—
778C22—942no—
779C22—944no—
780C22—942no—
781C22—942no—
782C22—942no—
783C22—942no—
784C22—37616no—
785C22—1882no—
786C22—1882no—
787C22—1884no—
788C22—1884no—
789C22—1888no—
790C22#1568977012yes—
791C22#1568992212yes—
792C22#1568993012yes—
793C22C22×D4×D4711yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—942no—
800C4—942no—
801C4—1882no—
802C4—1882no—
803C4—1882no—
804C4#1568977012yes—
805C4C2×#41×D4711yescharacteristic
806C4C2×#1309406911yescharacteristic
807C2—82no—
808C2—1882no—
809C2—1882no—
810C2—1884no—
811C2#2025543114yesdirect product factor
812C2C2×#1568977011yescharacteristic
813C2C2×#1568992211yescharacteristic
814C2C2×#1568993011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#464C2
socleC23×C47C22×D4
prime radicalC2×#15689766C2
hypercenterC2×#464D47
hypocenterC47C2×#3311
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#15689846C2semidirect
3. #20255431C2direct (N × H)
4. C2×#15689482C2semidirect
5. C2×#15689462C2semidirect
6. C2×#15689446C2semidirect
7. C2×#15689414C2semidirect
8. C2×#15689378C2semidirect
9. C2×#15689349C2semidirect
10. C2×#15689284C2semidirect
11. C2×#15689272C2semidirect
12. C2×#15689221C2semidirect
13. C2×#15689193C2semidirect
14. C2×#15689126C2semidirect
15. C2×#15689118C2semidirect
16. C2×C47×#464C2semidirect
21. C22×C8×D47C22semidirect
23. #15689846C22semidirect
26. C2×#13094024C22semidirect
33. C2×#13094000C22semidirect
41. C2×#13093982C22semidirect
43. #15689482C22semidirect
44. #15689462C22semidirect
45. #15689446C22semidirect
46. #15689414C22semidirect
47. #15689378C22semidirect
48. #15689349C22semidirect
49. #15689284C22semidirect
50. #15689272C22semidirect
51. #15689221C22semidirect
52. #15689193C22semidirect
53. C2×#13093957C22semidirect
54. C2×#13093956C22semidirect
55. C2×#13093956C22semidirect
56. #15689126C22semidirect
57. #15689118C22semidirect
58. C2×#13093948C22semidirect
59. C2×#13093948C22semidirect
60. C2×#13093948C22semidirect
67. C2×(C2×D47)⋊C8C22semidirect
68. C2×#13093935C22semidirect
69. C22×Q16×C47C22semidirect
72. C2×C4×Q8×C47C22semidirect
73. C47×#464C22semidirect
74. C2×C4⋊C8×C47C22semidirect
75. C2×#103×C47C22semidirect
103. C2×C8×D47C23semidirect
105. #13094024C23semidirect
115. #13094000C23semidirect
128. #13093982C23semidirect
149. #13093957C23semidirect
150. #13093956C23semidirect
151. #13093956C23semidirect
152. #13093948C23semidirect
153. #13093948C23semidirect
154. #13093948C23semidirect
161. (C2×D47)⋊C8C23semidirect
162. #13093935C23semidirect
167. C2×Q16×C47C23semidirect
175. C4×Q8×C47C23semidirect
182. C4⋊C8×C47C23semidirect
183. #103×C47C23semidirect
409. C2×#464D47semidirect
417. C2×C47#3311semidirect
426. C22×Q16C2×D47semidirect
448. C2×C4×Q8C2×D47semidirect
460. #464C2×D47semidirect
468. C2×C4⋊C8C2×D47semidirect
474. C2×#103C2×D47semidirect
484. C47C2×#3311semidirect
508. C2×Q16C22×D47semidirect
541. C4×Q8C22×D47semidirect
579. C4⋊C8C22×D47semidirect
583. #103C22×D47semidirect
811. C2#20255431direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898462
C2×#156897662
#202554312
C2×#156894822
C2×#156894622
C2×#156894462
C2×#156894142
C2×#156893782
C2×#156893492
C2×#156892842
C2×#156892722
C2×#156892212
C2×#156891932
C2×#156891262
C2×#156891182
C2×C47×#4642
C2×#331147