Finite Group Databasebeta

← C2×#20255309 #27092722

Subgroups — C2×#20255309 #27092722

Order 12032.

2210 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689837C211yesmaximal, characteristic, complemented
2C2×#15689772C211yesmaximal, characteristic, complemented
3#20255309C2116yesmaximal, direct product factor
4C2×#15689472C211yesmaximal, characteristic, complemented
5C2×#15689465C211yesmaximal, characteristic, complemented
6C2×#15689463C211yesmaximal, characteristic, complemented
7C2×#15689411C211yesmaximal, characteristic, complemented
8C2×#15689350C211yesmaximal, characteristic, complemented
9C2×#15689349C211yesmaximal, characteristic, complemented
10C2×#15689326C211yesmaximal, characteristic, complemented
11C2×#15689265C211yesmaximal, characteristic, complemented
12C2×D8×Dic47C211yesmaximal, characteristic, complemented
13C2×(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
14C2×#15689119C211yesmaximal, characteristic, complemented
15C2×#15689116C211yesmaximal, characteristic, complemented
16C2×C47×#449C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×#10625335C2211yescharacteristic
19C23×C47⋊C8C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21#15689837—24no—
22#15689837C2218yescomplemented
23#15689772—24no—
24#15689772C2218yescomplemented
25C2×#13094023C2211yescharacteristic
26C2×#13094022C2211yescharacteristic
27C2×#13094011—21no—
28C2×#13094010—21no—
29C2×#13094007—21no—
30C2×#13094005—21no—
31C2×#13094003C2211yescharacteristic
32C2×#13094000C2211yescharacteristic
33C2×#13093996—21no—
34C2×#13093996—21no—
35C2×#13093995C2211yescharacteristic
36C2×D4×Dic47C2211yescharacteristic
37C2×D4×Dic47C2211yescharacteristic
38C2×C4×C22⋊D47C2211yescharacteristic
39C2×#13093983C2211yescharacteristic
40C2×#13093982C2211yescharacteristic
41C2×#13093980—21no—
42C22×Dic47⋊C4—21no—
43#15689472C2218yescomplemented
44#15689465C2218yescomplemented
45#15689463C2218yescomplemented
46#15689411C2218yescomplemented
47#15689350C2218yescomplemented
48#15689349C2218yescomplemented
49#15689326C2218yescomplemented
50#15689265C2218yescomplemented
51D8×Dic47C2218yescomplemented
52(C22⋊D47)⋊C8C2218yescomplemented
53C2×#13093958C2211yescharacteristic
54C2×#13093956C2211yescharacteristic
55C2×#13093955C2211yescharacteristic
56C2×Dic47⋊C8C2211yescharacteristic
57#15689119C2218yescomplemented
58#15689116C2218yescomplemented
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×#13093945C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×#41×C47C2211yescharacteristic
70C22×SD16×C47C2211yescharacteristic
71C22×D8×C47C2211yescharacteristic
72C2×#121×C47C2211yescharacteristic
73C47×#449C2218yescomplemented
74C2×#103×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C2×#10625352—24no—
78C2×#10625352—22no—
79C2×#10625352—42no—
80C2×#10625352C2314yes—
81C22×Dic94—21no—
82C22×Dic94C2311yescharacteristic
83C22×C22⋊D47—21no—
84C22×C22⋊D47—21no—
85C22×C22⋊D47D411yescharacteristic
86C23×Dic47—21no—
87C23×Dic47—21no—
88C23×Dic47—21no—
89C22×C4×D47C2311yescharacteristic
90C2×#10625335—42no—
91C2×#10625335C2314yes—
92C22×C47⋊C8—42no—
93C22×C47⋊C8C2311yescharacteristic
94C22×C47⋊C8C2311yescharacteristic
95C22×C47⋊C8C2314yes—
96C2×C8×D47—42no—
97C2×C8×D47C2314yes—
98#13094023—22no—
99#13094023C2314yes—
100#13094022—22no—
101#13094022C2314yes—
102#13094011—28no—
103#13094010—28no—
104#13094007—28no—
105#13094005—28no—
106#13094003—22no—
107#13094003C2314yes—
108#13094000—22no—
109#13094000C2314yes—
110#13093996—28no—
111#13093996—28no—
112#13093995—22no—
113#13093995C2314yes—
114D4×Dic47—22no—
115D4×Dic47—22no—
116D4×Dic47C2314yes—
117D4×Dic47C2314yes—
118C4×C22⋊D47D414yes—
119C4×C22⋊D47C2314yes—
120#13093983—22no—
121#13093983C2314yes—
122#13093982—22no—
123#13093982C2314yes—
124#13093980—28no—
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—28no—
134C2×Dic47⋊C4D411yescharacteristic
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47—21no—
137C2×C22⋊Dic47—21no—
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47—21no—
140C2×C22⋊Dic47D411yescharacteristic
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4D411yescharacteristic
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47C2311yescharacteristic
147#13093958C2314yes—
148#13093956C2314yes—
149#13093955C2314yes—
150Dic47⋊C8C2314yes—
151#13093949C2314yes—
152#13093949C2314yes—
153#13093948C2314yes—
154#13093948C2314yes—
155#13093947C2314yes—
156#13093945C2314yes—
157#13093945C2314yes—
158#13093945C2314yes—
159(C2×D47)⋊C8C2314yes—
160C8×Dic47C2314yes—
161C2×#41×C47—22no—
162C2×#41×C47—24no—
163C2×#41×C47—42no—
164C2×#41×C47C2314yes—
165C22×Q8×C47C2311yescharacteristic
166C22×D4×C47—21no—
167C22×D4×C47—21no—
168C22×D4×C47C2311yescharacteristic
169C22×D4×C47C2311yescharacteristic
170C23×C4×C47—21no—
171C23×C4×C47C2311yescharacteristic
172C2×SD16×C47—42no—
173C2×SD16×C47C2314yes—
174C2×D8×C47—24no—
175C2×D8×C47C2314yes—
176C22×C8×C47C2311yescharacteristic
177C22×C8×C47C2311yescharacteristic
178#121×C47—22no—
179#121×C47C2314yes—
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C22⋊C4×C47—21no—
182#103×C47C2314yes—
183#102×C47C2314yes—
184C22⋊C8×C47C2314yes—
185C24×C47—21no—
186C24×C47—21no—
187C24×C47C2×D411yescharacteristic
188C23×D47C2×D411yescharacteristic
189#41×C47—28no—
190#41×C47—44no—
191#41×C47—48no—
192C2×Q8×C47—21no—
193C2×Q8×C47—22no—
194C2×Q8×C47—22no—
195C2×Q8×C47C2412yes—
196C2×D4×C47—24no—
197C2×D4×C47—24no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—22no—
201C2×D4×C47—22no—
202C2×D4×C47—22no—
203C2×D4×C47—44no—
204C2×D4×C47—82no—
205C2×D4×C47#4114yes—
206C2×D4×C47C2412yes—
207C2×D4×C47C2412yes—
208C22×C4×C47—22no—
209C22×C4×C47—22no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—24no—
213C22×C4×C47—44no—
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D412yes—
216C22×C4×C47C2412yes—
217C22×C4×C47C2411yescharacteristic
218C2×C22⋊D47—24no—
219C2×C22⋊D47—24no—
220C2×C22⋊D47—24no—
221C2×C22⋊D47—44no—
222C2×C22⋊D47—82no—
223C2×C22⋊D47C2×D414yes—
224C22×Dic47—21no—
225C22×Dic47—21no—
226C22×Dic47—21no—
227C22×Dic47—21no—
228C22×Dic47—24no—
229C22×Dic47—24no—
230C22×Dic47—24no—
231C22×Dic47—44no—
232C22×Dic47—44no—
233C22×Dic47—44no—
234C22×Dic47C2×D411yescharacteristic
235C22×Dic47C2×D411yescharacteristic
236C22×Dic47C2×D411yescharacteristic
237#10625352—28no—
238#10625352—44no—
239#10625352—48no—
240C2×C4×D47—22no—
241C2×C4×D47—22no—
242C2×C4×D47C2×D412yes—
243C2×C4×D47C2412yes—
244C2×Dic94—22no—
245C2×Dic94—22no—
246C2×Dic94—21no—
247C2×Dic94—24no—
248C2×Dic94—82no—
249C2×Dic94C2412yes—
250SD16×C47—44no—
251D8×C47—28no—
252C2×C8×C47—22no—
253C2×C8×C47—22no—
254C2×C8×C47C2412yes—
255C2×C8×C47C2412yes—
256C4⋊C4×C47—21no—
257C4⋊C4×C47C2412yes—
258C22⋊C4×C47—24no—
259C22⋊Dic47—24no—
260C22⋊Dic47—24no—
261C22⋊Dic47—24no—
262C22⋊Dic47—24no—
263C22⋊Dic47—24no—
264C22⋊Dic47C2×D414yes—
265#10625335—44no—
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4C2×D414yes—
269C4⋊Dic47—21no—
270C4⋊Dic47—21no—
271C4⋊Dic47—21no—
272C4⋊Dic47C2412yes—
273C4⋊Dic47C2412yes—
274C4⋊Dic47C2412yes—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277Dic47⋊C4—24no—
278Dic47⋊C4—24no—
279Dic47⋊C4—24no—
280Dic47⋊C4C2×D414yes—
281C4×Dic47—24no—
282C4×Dic47—24no—
283C4×Dic47C2×D412yes—
284C4×Dic47C2412yes—
285C2×C47⋊C8—22no—
286C2×C47⋊C8—22no—
287C2×C47⋊C8—44no—
288C2×C47⋊C8C2412yes—
289C2×C47⋊C8C2412yes—
290C8×D47—44no—
291C23×C47—24no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—42no—
298C23×C47—42no—
299C23×C47—42no—
300C23×C47—42no—
301C23×C47—42no—
302C23×C47C22×D412yes—
303C23×C47C22×D411yescharacteristic
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47C22×D412yes—
308Q8×C47—22no—
309Q8×C47—22no—
310Q8×C47—42no—
311D4×C47—24no—
312D4×C47—22no—
313D4×C47—22no—
314D4×C47—22no—
315D4×C47—48no—
316D4×C47—42no—
317D4×C47—84no—
318D4×C47C2×#4114yes—
319C2×C4×C47—22no—
320C2×C4×C47—24no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—48no—
326C2×C4×C47—42no—
327C2×C4×C47—42no—
328C2×C4×C47C22×D412yes—
329C2×C4×C47C22×D411yescharacteristic
330C2×C4×C47C2×#4112yes—
331C2×C4×C47H(5,𝔽2)12yes—
332C2×C4×C47C2511yescharacteristic
333C22⋊D47—28no—
334C22⋊D47—48no—
335C22⋊D47—84no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—48no—
343C2×Dic47—42no—
344C2×Dic47—42no—
345C2×Dic47—42no—
346C2×Dic47—42no—
347C2×Dic47—48no—
348C2×Dic47—48no—
349C2×Dic47#13514yes—
350C2×Dic47C22×D412yes—
351C2×Dic47C22×D412yes—
352C2×Dic47C22×D412yes—
353C4×D47—24no—
354C4×D47—22no—
355C4×D47—22no—
356Dic94—22no—
357Dic94—22no—
358Dic94—42no—
359Dic94—84no—
360C8×C47—22no—
361C8×C47—22no—
362C47⋊C8—22no—
363C47⋊C8—22no—
364C2×#3303—471nomaximal, Sylow
365C22×C47—24no—
366C22×C47—22no—
367C22×C47—22no—
368C22×C47—22no—
369C22×C47—44no—
370C22×C47—48no—
371C22×C47—42no—
372C22×C47—42no—
373C22×C47—42no—
374C22×C47—42no—
375C22×C47—42no—
376C22×C47—84no—
377C22×C47#54612yes—
378C22×C47C2×#13512yes—
379C22×C47#57712yes—
380C22×C47C23×D411yescharacteristic
381C2×D47—22no—
382C2×D47—22no—
383C2×D47—22no—
384C2×D47—44no—
385C4×C47—22no—
386C4×C47—42no—
387C4×C47—42no—
388C4×C47#54612yes—
389C4×C47C22×#4111yescharacteristic
390C4×C47C2×H(5,𝔽2)11yescharacteristic
391Dic47—22no—
392Dic47—22no—
393Dic47—42no—
394Dic47—42no—
395Dic47—42no—
396Dic47—42no—
397Dic47C2×#13514yes—
398C2×#555—471no—
399C2×#547—471no—
400#3303—4716no—
401C2×#487—471no—
402C2×#485—471no—
403C2×#485—471no—
404C2×#476—471no—
405C2×#465—471no—
406C2×#465—471no—
407C2×#461—471no—
408C2×#449—471no—
409C2×#449D4711yescharacteristic, complemented
410C2×C4×D8—471no—
411C2×C8×D4—471no—
412C2×#416—471no—
413C2×#416—471no—
414C2×C47—42no—
415C2×C47—44no—
416C2×C47—82no—
417C2×C47#330314yescomplemented
418C2×C47C2×#54611yescharacteristic
419C2×C47C22×#13511yescharacteristic
420C2×C47C2×#57711yescharacteristic
421D47—42no—
422C22×#41—471no—
423C22×#41C2×D4711yescharacteristic
424C22×SD16—471no—
425C22×SD16C2×D4711yescharacteristic
426C22×D8C2×D4711yescharacteristic
427C23×C8—471no—
428C23×C8—471no—
429#555—478no—
430#555—944no—
431#547—478no—
432#547—944no—
433C2×C4⋊Q8—471no—
434C2×C4⋊Q8—471no—
435C2×#124—941no—
436C2×#124—941no—
437C2×#123—941no—
438C2×#123—941no—
439C2×C22⋊Q8—471no—
440C2×C22⋊Q8—471no—
441C2×#121—471no—
442C2×#121—941no—
443C2×#121—941no—
444C2×#121C2×D4711yescharacteristic
445C2×C4×D4—471no—
446C2×C4×D4—471no—
447C2×C4×D4—471no—
448C2×#117—471no—
449C2×#117—471no—
450C2×#117—941no—
451C22×C4⋊C4—941no—
452#487—478no—
453#485—478no—
454#485—478no—
455#476—478no—
456#465—478no—
457#465—478no—
458#461—478no—
459#449—478no—
460#449C2×D4718yescomplemented
461C4×D8—478no—
462C8×D4—478no—
463C2×#107—471no—
464C2×#106—471no—
465C2×#106—471no—
466C2×C4⋊C8—471no—
467#416—478no—
468#416—478no—
469C2×#103—471no—
470C2×#103—471no—
471C2×#103—471no—
472C2×#103—471no—
473C2×#103—471no—
474C2×#103C2×D4711yescharacteristic
475C2×#102—471no—
476C2×#102—471no—
477C2×#102—471no—
478C2×#102C2×D4711yescharacteristic
479C2×C22⋊C8—471no—
480C2×C22⋊C8C2×D4711yescharacteristic
481C2×C4×C8—471no—
482C47C2×#330311yescharacteristic, complemented, Sylow
483C2×#41—22no—
484C2×#41—24no—
485C2×#41—42no—
486C2×#41—474no—
487C2×#41—942no—
488C2×#41—944no—
489C2×#41—1882no—
490C2×#41C22×D4714yes—
491C22×Q8—471no—
492C22×Q8—941no—
493C22×Q8C22×D4711yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—471no—
497C22×D4—941no—
498C22×D4—941no—
499C22×D4C22×D4711yescharacteristic
500C22×D4C22×D4711yescharacteristic
501C23×C4—21no—
502C23×C4—471no—
503C23×C4—941no—
504C23×C4—941no—
505C23×C4—941no—
506C23×C4C22×D4711yescharacteristic
507C2×SD16—42no—
508C2×SD16—474no—
509C2×SD16—1882no—
510C2×SD16C22×D4714yes—
511C2×D8—24no—
512C2×D8C22×D4714yes—
513C22×C8—471no—
514C22×C8—471no—
515C22×C8—474no—
516C22×C8—474no—
517C22×C8—1882no—
518C22×C8—1882no—
519C22×C8C22×D4711yescharacteristic
520C22×C8C22×D4711yescharacteristic
521C4⋊Q8—474no—
522C4⋊Q8—474no—
523C4⋊Q8—942no—
524C4⋊Q8—942no—
525#124—948no—
526#124—948no—
527#123—948no—
528#123—948no—
529C22⋊Q8—474no—
530C22⋊Q8—474no—
531C22⋊Q8—942no—
532C22⋊Q8—942no—
533#121—22no—
534#121—474no—
535#121—942no—
536#121—948no—
537#121—948no—
538#121C22×D4714yes—
539C4×D4—474no—
540C4×D4—474no—
541C4×D4—474no—
542C4×D4—474no—
543C4×D4—942no—
544C4×D4—942no—
545#117—474no—
546#117—474no—
547#117—948no—
548#117—942no—
549#117—942no—
550C2×C4⋊C4—471no—
551C2×C4⋊C4—471no—
552C2×C4⋊C4—471no—
553C2×C4⋊C4—471no—
554C2×C4⋊C4—948no—
555C2×C4⋊C4—941no—
556C2×C4⋊C4—941no—
557C2×C4⋊C4—941no—
558C2×C4⋊C4—941no—
559C2×C4⋊C4—941no—
560C2×C4⋊C4C22×D4711yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—471no—
563C2×C22⋊C4—471no—
564C2×C22⋊C4—941no—
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×C42—471no—
572C2×C42—941no—
573C2×C42—941no—
574#107—474no—
575#106—474no—
576#106—474no—
577C4⋊C8—474no—
578#103—474no—
579#103—474no—
580#103—474no—
581#103—474no—
582#103—474no—
583#103C22×D4714yes—
584#102—474no—
585#102—474no—
586#102—474no—
587#102C22×D4714yes—
588C22⋊C8—474no—
589C22⋊C8C22×D4714yes—
590C4×C8—474no—
591C24—21no—
592C24—21no—
593C24—471no—
594C24D4×D4711yescharacteristic
595#41—28no—
596#41—44no—
597#41—48no—
598#41—948no—
599#41—1884no—
600#41—1888no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—472no—
605C2×Q8—944no—
606C2×Q8—941no—
607C2×Q8—942no—
608C2×Q8—942no—
609C2×Q8—3762no—
610C2×Q8C23×D4712yes—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—44no—
619C2×D4—82no—
620C2×D4—474no—
621C2×D4—944no—
622C2×D4—944no—
623C2×D4—944no—
624C2×D4—3762no—
625C2×D4—1884no—
626C2×D4#1062535214yes—
627C2×D4C23×D4712yes—
628C2×D4C23×D4712yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—24no—
634C22×C4—44no—
635C22×C4—471no—
636C22×C4—471no—
637C22×C4—471no—
638C22×C4—472no—
639C22×C4—472no—
640C22×C4—944no—
641C22×C4—944no—
642C22×C4—944no—
643C22×C4—942no—
644C22×C4—942no—
645C22×C4—941no—
646C22×C4—941no—
647C22×C4—941no—
648C22×C4—941no—
649C22×C4—1884no—
650C22×C4—1884no—
651C22×C4—1884no—
652C22×C4D4×D4712yes—
653C22×C4D4×D4711yescharacteristic
654C22×C4C23×D4712yes—
655C22×C4C23×D4711yescharacteristic
656SD16—44no—
657SD16—1884no—
658D8—28no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—472no—
662C2×C8—472no—
663C2×C8—942no—
664C2×C8—942no—
665C2×C8—1884no—
666C2×C8—1884no—
667C2×C8C23×D4712yes—
668C2×C8C23×D4712yes—
669C4⋊C4—21no—
670C4⋊C4—474no—
671C4⋊C4—472no—
672C4⋊C4—472no—
673C4⋊C4—472no—
674C4⋊C4—944no—
675C4⋊C4—944no—
676C4⋊C4—944no—
677C4⋊C4—944no—
678C4⋊C4—944no—
679C4⋊C4—941no—
680C4⋊C4—941no—
681C4⋊C4—941no—
682C4⋊C4C23×D4712yes—
683C22⋊C4—24no—
684C22⋊C4—474no—
685C22⋊C4—474no—
686C22⋊C4—944no—
687C22⋊C4—944no—
688C22⋊C4—944no—
689C22⋊C4—944no—
690C22⋊C4—944no—
691C22⋊C4—944no—
692C22⋊C4—944no—
693C42—472no—
694C42—472no—
695C42—944no—
696C42—944no—
697C23—22no—
698C23—24no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—472no—
709C23—942no—
710C23—942no—
711C23—942no—
712C23C2×D4×D4712yes—
713C23C2×D4×D4711yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—942no—
718Q8—942no—
719Q8—3764no—
720Q8—1882no—
721D4—24no—
722D4—22no—
723D4—22no—
724D4—22no—
725D4—48no—
726D4—42no—
727D4—84no—
728D4—948no—
729D4—3764no—
730D4—1888no—
731D4C2×#1062535214yes—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—48no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—474no—
742C2×C4—472no—
743C2×C4—472no—
744C2×C4—472no—
745C2×C4—942no—
746C2×C4—942no—
747C2×C4—944no—
748C2×C4—942no—
749C2×C4—942no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—1888no—
755C2×C4—1888no—
756C2×C4—1888no—
757C2×C4—1882no—
758C2×C4—1882no—
759C2×C4—1882no—
760C2×C4—1882no—
761C2×C4C2×D4×D4712yes—
762C2×C4C2×D4×D4711yescharacteristic
763C2×C4C2×#1062535212yes—
764C2×C4#1309406912yes—
765C2×C4C24×D4711yescharacteristic
766C8—22no—
767C8—22no—
768C8—942no—
769C8—942no—
770C22—22no—
771C22—24no—
772C22—22no—
773C22—22no—
774C22—42no—
775C22—44no—
776C22—48no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—942no—
783C22—942no—
784C22—942no—
785C22—1884no—
786C22#1568976012yes—
787C22#135×D4712yes—
788C22#1568993312yes—
789C22C22×D4×D4711yescharacteristic
790C4—22no—
791C4—42no—
792C4—42no—
793C4—474no—
794C4—942no—
795C4—942no—
796C4—1882no—
797C4—1882no—
798C4—1882no—
799C4—1882no—
800C4#1568976012yes—
801C4C22×#1062535211yescharacteristic
802C4C2×#1309406911yescharacteristic
803C2—42no—
804C2—44no—
805C2—82no—
806C2—1882no—
807C2#2025530914yesdirect product factor
808C2C2×#1568976011yescharacteristic
809C2C2×#135×D4711yescharacteristic
810C2C2×#1568993311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#449C2
socleC23×C47C22×D4
hypercenterC2×#449D47
hypocenterC47C2×#3303
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#15689837C2semidirect
2. C2×#15689772C2semidirect
3. #20255309C2direct (N × H)
4. C2×#15689472C2semidirect
5. C2×#15689465C2semidirect
6. C2×#15689463C2semidirect
7. C2×#15689411C2semidirect
8. C2×#15689350C2semidirect
9. C2×#15689349C2semidirect
10. C2×#15689326C2semidirect
11. C2×#15689265C2semidirect
12. C2×D8×Dic47C2semidirect
13. C2×(C22⋊D47)⋊C8C2semidirect
14. C2×#15689119C2semidirect
15. C2×#15689116C2semidirect
16. C2×C47×#449C2semidirect
22. #15689837C22semidirect
24. #15689772C22semidirect
43. #15689472C22semidirect
44. #15689465C22semidirect
45. #15689463C22semidirect
46. #15689411C22semidirect
47. #15689350C22semidirect
48. #15689349C22semidirect
49. #15689326C22semidirect
50. #15689265C22semidirect
51. D8×Dic47C22semidirect
52. (C22⋊D47)⋊C8C22semidirect
57. #15689119C22semidirect
58. #15689116C22semidirect
73. C47×#449C22semidirect
409. C2×#449D47semidirect
417. C2×C47#3303semidirect
460. #449C2×D47semidirect
482. C47C2×#3303semidirect
807. C2#20255309direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898372
C2×#156897722
#202553092
C2×#156894722
C2×#156894652
C2×#156894632
C2×#156894112
C2×#156893502
C2×#156893492
C2×#156893262
C2×#156892652
C2×D8×Dic472
C2×(C22⋊D47)⋊C82
C2×#156891192
C2×#156891162
C2×C47×#4492
C2×#330347