Finite Group Databasebeta

← C2×#20254904 #27091265

Subgroups — C2×#20254904 #27091265

Order 12032.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094053C211yesmaximal, characteristic, complemented
2C22×SD16×D47C211yesmaximal, characteristic, complemented
3C2×#15689788C211yesmaximal, characteristic, complemented
4C2×#15689768C211yesmaximal, characteristic
5#20254904C2116yesmaximal, direct product factor
6C2×#15689515C211yesmaximal, characteristic, complemented
7C2×#15689372C211yesmaximal, characteristic, complemented
8C2×#15689363C211yesmaximal, characteristic, complemented
9C2×#15689346C211yesmaximal, characteristic, complemented
10C2×#15689282C211yesmaximal, characteristic, complemented
11C2×#15689280C211yesmaximal, characteristic, complemented
12C2×#15689263C211yesmaximal, characteristic, complemented
13C2×#15689272C211yesmaximal, characteristic, complemented
14C2×#15689223C211yesmaximal, characteristic, complemented
15C2×#15689193C211yesmaximal, characteristic, complemented
16C2×C47×#461C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C22×Q8×D47C2211yescharacteristic, complemented
20C22×D4×D47C2211yescharacteristic
21C2×#13094053—28no—
22C2×#13094053C2218yescomplemented
23C22×Dic188C2211yescharacteristic, complemented
24C22×#10625337C2211yescharacteristic, complemented
25C22×#10625337C2211yescharacteristic, complemented
26C22×#10625325C2211yescharacteristic
27C22×#10625335C2211yescharacteristic
28C22×#10625336C2211yescharacteristic
29C22×#10625336C2211yescharacteristic
30C2×SD16×D47—28no—
31C2×SD16×D47C2218yescomplemented
32C22×#10625324C2211yescharacteristic, complemented
33C22×C8×D47C2211yescharacteristic
34#15689788—24no—
35#15689788C2218yescomplemented
36#15689768—24no—
37#15689768C2218yes—
38C2×#13094023—21no—
39C2×#13094012C2211yescharacteristic
40C2×#13094008—21no—
41C2×#13094004C2211yescharacteristic
42C2×#13094002—21no—
43C2×#13094002—21no—
44C2×#13094000C2211yescharacteristic
45C2×#13094000C2211yescharacteristic, complemented
46C2×#13093999C2211yescharacteristic
47C2×#13093998—21no—
48C2×#13093994—21no—
49C2×C4×Dic94C2211yescharacteristic, complemented
50C2×C4×D188C2211yescharacteristic
51C2×#13093986—21no—
52C22×(C2×D47)⋊C4—21no—
53#15689515C2218yescomplemented
54#15689372C2218yescomplemented
55#15689363C2218yescomplemented
56#15689346C2218yescomplemented
57#15689282C2218yescomplemented
58#15689280C2218yescomplemented
59#15689272C2218yescomplemented
60#15689263C2218yescomplemented
61#15689223C2218yescomplemented
62#15689193C2218yescomplemented
63C2×#13093957C2211yescharacteristic, complemented
64C2×#13093949C2211yescharacteristic, complemented
65C2×#13093947C2211yescharacteristic, complemented
66C2×#13093946C2211yescharacteristic
67C2×#13093945C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic
69C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
70C2×#13093935C2211yescharacteristic, complemented
71C22×SD16×C47C2211yescharacteristic
72C22×SD16×C47C2211yescharacteristic
73C2×C4⋊Q8×C47C2211yescharacteristic, complemented
74C2×C4×D4×C47C2211yescharacteristic
75C47×#461C2218yescomplemented
76C2×C4⋊C8×C47C2211yescharacteristic, complemented
77C2×#103×C47C2211yescharacteristic, complemented
78C2×#103×C47C2211yescharacteristic, complemented
79C24×D47—21no—
80C2×#10625352—24no—
81C2×#10625352—22no—
82C2×#10625352—42no—
83C2×#10625352C2314yes—
84C22×Dic94—21no—
85C22×Dic94—21no—
86C22×Dic94C2311yescharacteristic
87C22×Dic94C2311yescharacteristic
88C2×Q8×D47—22no—
89C2×Q8×D47—22no—
90C2×Q8×D47—24no—
91C2×Q8×D47—24no—
92C2×Q8×D47—42no—
93C2×Q8×D47—42no—
94C2×Q8×D47C2314yes—
95C2×Q8×D47C2314yescomplemented
96C22×D188—21no—
97C22×D188D411yescharacteristic
98C22×D188C2311yescharacteristic
99C22×C22⋊D47—21no—
100C22×C22⋊D47—21no—
101C2×D4×D47—24no—
102C2×D4×D47—22no—
103C2×D4×D47—42no—
104C2×D4×D47C2314yes—
105C23×Dic47—21no—
106C22×C4×D47—21no—
107C22×C4×D47—21no—
108C22×C4×D47C2311yescharacteristic
109C22×C4×D47C2311yescharacteristic
110#13094053—232no—
111C2×Dic188—24no—
112C2×Dic188C2314yescomplemented
113C2×#10625337—24no—
114C2×#10625337—42no—
115C2×#10625337C2314yescomplemented
116C2×#10625337C2314yescomplemented
117C2×#10625325—24no—
118C2×#10625325C2314yes—
119C2×#10625335D418yescomplemented
120C2×#10625335C2314yes—
121C2×#10625336—24no—
122C2×#10625336—42no—
123C2×#10625336C2314yes—
124C2×#10625336C2314yes—
125SD16×D47—232no—
126C2×#10625324—24no—
127C2×#10625324C2314yescomplemented
128C22×C47⋊C8C2311yescharacteristic
129C22×C47⋊C8C2311yescharacteristic
130C2×C8×D47—24no—
131C2×C8×D47C2314yes—
132#13094023—28no—
133#13094012—22no—
134#13094012C2314yes—
135#13094008—28no—
136#13094004—22no—
137#13094004C2314yes—
138#13094002—28no—
139#13094002—28no—
140#13094000—22no—
141#13094000—22no—
142#13094000C2314yes—
143#13094000C2314yescomplemented
144#13093999—22no—
145#13093999C2314yes—
146#13093998—28no—
147#13093994—28no—
148C4×Dic94—22no—
149C4×Dic94C2314yescomplemented
150C4×D188D414yes—
151C4×D188C2314yes—
152#13093986—28no—
153C2×C4⋊Dic47—21no—
154C2×C4⋊Dic47D411yescharacteristic
155C2×C4⋊Dic47C2311yescharacteristic
156C2×Dic47⋊C4—21no—
157C2×Dic47⋊C4—21no—
158C2×Dic47⋊C4—21no—
159C2×(C2×D47)⋊C4—21no—
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—28no—
166C2×(C2×D47)⋊C4D411yescharacteristic
167C2×(C2×D47)⋊C4D411yescharacteristic
168C2×C4×Dic47—21no—
169#13093957C2314yescomplemented
170#13093949C2314yescomplemented
171#13093947C2314yescomplemented
172#13093946C2314yes—
173#13093945C2314yes—
174(C2×D47)⋊C8C2314yes—
175(C2×D47)⋊C8C2314yescomplemented
176#13093935C2314yescomplemented
177C22×Q8×C47C2311yescharacteristic
178C22×Q8×C47C2311yescharacteristic
179C22×D4×C47C2311yescharacteristic
180C23×C4×C47—21no—
181C2×SD16×C47—24no—
182C2×SD16×C47—24no—
183C2×SD16×C47C2314yes—
184C2×SD16×C47C2314yes—
185C22×C8×C47C2311yescharacteristic
186C22×C8×C47C2311yescharacteristic
187C4⋊Q8×C47—22no—
188C4⋊Q8×C47C2314yescomplemented
189C4×D4×C47—22no—
190C4×D4×C47C2314yes—
191C2×C4⋊C4×C47—21no—
192C2×C4⋊C4×C47—21no—
193C2×C4⋊C4×C47C2311yescharacteristic
194C2×C22⋊C4×C47—21no—
195C2×C42×C47C2311yescharacteristic
196C4⋊C8×C47C2314yescomplemented
197#103×C47C2314yescomplemented
198#103×C47C2314yescomplemented
199C24×C47—21no—
200C23×D47—21no—
201C23×D47—24no—
202C23×D47—44no—
203C23×D47—44no—
204C23×D47—82no—
205C23×D47C2×D411yescharacteristic
206C23×D47C2×D411yescharacteristic
207C2×Q8×C47—21no—
208C2×Q8×C47—21no—
209C2×Q8×C47—22no—
210C2×Q8×C47—22no—
211C2×Q8×C47—22no—
212C2×Q8×C47—22no—
213C2×Q8×C47C2412yes—
214C2×Q8×C47C2412yes—
215C2×D4×C47—21no—
216C2×D4×C47—22no—
217C2×D4×C47C2×D414yes—
218C2×D4×C47C2412yes—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—24no—
223C22×C4×C47—82no—
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2×D411yescharacteristic
226C22×C4×C47C2411yescharacteristic
227C2×C22⋊D47—24no—
228C2×C22⋊D47—24no—
229C2×C22⋊D47—44no—
230C2×C22⋊D47—44no—
231C22×Dic47—21no—
232C22×Dic47—21no—
233C22×Dic47—21no—
234C22×Dic47—24no—
235C22×Dic47—44no—
236C22×Dic47C2×D411yescharacteristic
237C22×Dic47C2×D411yescharacteristic
238Q8×D47—28no—
239Q8×D47—28no—
240Q8×D47—44no—
241Q8×D47—44no—
242Q8×D47—48no—
243Q8×D47—48no—
244#10625352—28no—
245#10625352—44no—
246#10625352—48no—
247D4×D47—28no—
248D4×D47—44no—
249D4×D47—48no—
250C2×D188—24no—
251C2×D188—22no—
252C2×D188—22no—
253C2×D188—21no—
254C2×D188—24no—
255C2×D188—82no—
256C2×D188C2×D414yes—
257C2×D188C2412yes—
258C2×C4×D47—22no—
259C2×C4×D47—22no—
260C2×C4×D47—22no—
261C2×C4×D47—22no—
262C2×C4×D47—24no—
263C2×C4×D47—24no—
264C2×C4×D47—44no—
265C2×C4×D47—44no—
266C2×C4×D47C2×D412yes—
267C2×C4×D47C2×D412yes—
268C2×C4×D47C2412yes—
269C2×C4×D47C2412yes—
270C2×Dic94—21no—
271C2×Dic94—22no—
272C2×Dic94—22no—
273C2×Dic94—22no—
274C2×Dic94—21no—
275C2×Dic94—24no—
276C2×Dic94—24no—
277C2×Dic94—44no—
278C2×Dic94—44no—
279C2×Dic94C2×D414yes—
280C2×Dic94C2412yes—
281C2×Dic94C2412yes—
282SD16×C47—28no—
283SD16×C47—28no—
284C2×C8×C47—22no—
285C2×C8×C47—22no—
286C2×C8×C47C2412yes—
287C2×C8×C47C2412yes—
288C4⋊C4×C47—24no—
289C4⋊C4×C47—24no—
290C4⋊C4×C47—21no—
291C4⋊C4×C47C2412yes—
292C22⋊C4×C47—24no—
293C42×C47C2×D412yes—
294C42×C47C2412yes—
295#10625337—28no—
296#10625337—44no—
297#10625336—28no—
298#10625336—44no—
299#10625335C2×D4116yescomplemented
300(C2×D47)⋊C4—24no—
301(C2×D47)⋊C4—24no—
302(C2×D47)⋊C4—24no—
303(C2×D47)⋊C4—24no—
304(C2×D47)⋊C4—24no—
305(C2×D47)⋊C4—24no—
306(C2×D47)⋊C4C2×D414yes—
307(C2×D47)⋊C4C2×D414yes—
308C4⋊Dic47—21no—
309C4⋊Dic47—24no—
310C4⋊Dic47C2×D414yes—
311C4⋊Dic47C2412yes—
312Dic47⋊C4—24no—
313Dic47⋊C4—24no—
314Dic47⋊C4—24no—
315C4×Dic47—24no—
316C2×C47⋊C8—22no—
317C2×C47⋊C8C2×D414yes—
318C2×C47⋊C8C2412yes—
319C2×C47⋊C8C2412yes—
320Dic188—28no—
321#10625325—28no—
322#10625324—28no—
323C8×D47—28no—
324C23×C47—24no—
325C23×C47—22no—
326C23×C47—42no—
327C23×C47—42no—
328C23×C47C22×D411yescharacteristic
329C22×D47—22no—
330C22×D47—22no—
331C22×D47—22no—
332C22×D47—22no—
333C22×D47—22no—
334C22×D47—22no—
335C22×D47—48no—
336C22×D47—42no—
337C22×D47—42no—
338C22×D47—42no—
339C22×D47—48no—
340C22×D47—84no—
341C22×D47—816no—
342C22×D47#13714yescomplemented
343C22×D47C22×D412yes—
344C22×D47C22×D412yes—
345Q8×C47—22no—
346Q8×C47—22no—
347Q8×C47—22no—
348Q8×C47—22no—
349Q8×C47—42no—
350Q8×C47—42no—
351D4×C47—24no—
352D4×C47—22no—
353D4×C47C22×D414yes—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—42no—
360C2×C4×C47—42no—
361C2×C4×C47—42no—
362C2×C4×C47—84no—
363C2×C4×C47C22×D412yes—
364C2×C4×C47C22×D412yes—
365C2×C4×C47C22×D411yescharacteristic
366C2×C4×C47C22×D412yes—
367C2×C4×C47H(5,𝔽2)12yes—
368C2×C4×C47C2511yescharacteristic
369C22⋊D47—48no—
370C22⋊D47—48no—
371C2×Dic47—24no—
372C2×Dic47—22no—
373C2×Dic47—22no—
374C2×Dic47—22no—
375C2×Dic47—22no—
376C2×Dic47—22no—
377C2×Dic47—48no—
378C2×Dic47—42no—
379C2×Dic47—42no—
380C2×Dic47C22×D412yes—
381C2×Dic47C22×D412yes—
382D188—28no—
383D188—22no—
384D188—22no—
385D188—42no—
386D188—84no—
387C4×D47—24no—
388C4×D47—24no—
389C4×D47—22no—
390C4×D47—22no—
391C4×D47—22no—
392C4×D47—22no—
393C4×D47—48no—
394C4×D47—48no—
395Dic94—24no—
396Dic94—22no—
397Dic94—22no—
398Dic94—22no—
399Dic94—48no—
400Dic94—48no—
401Dic94—42no—
402Dic94C22×D414yes—
403C8×C47—22no—
404C8×C47—22no—
405C47⋊C8—22no—
406C47⋊C8C22×D414yes—
407C2×#3266—471nomaximal, Sylow
408C22×C47—24no—
409C22×C47—48no—
410C22×C47—42no—
411C22×C47—42no—
412C22×C47D4212yes—
413C22×C47C2×#13712yes—
414C22×C47#57712yes—
415C22×C47C23×D411yescharacteristic
416C2×D47—22no—
417C2×D47—28no—
418C2×D47—22no—
419C2×D47—22no—
420C2×D47—22no—
421C2×D47—22no—
422C2×D47—44no—
423C2×D47—42no—
424C2×D47—42no—
425C2×D47—42no—
426C2×D47—816no—
427C2×D47—84no—
428C2×D47C2×#13714yescomplemented
429C4×C47—22no—
430C4×C47—22no—
431C4×C47—42no—
432C4×C47—42no—
433C4×C47—42no—
434C4×C47D4212yes—
435C4×C47C23×D411yescharacteristic
436C4×C47C2×H(5,𝔽2)11yescharacteristic
437Dic47—24no—
438Dic47—22no—
439Dic47—22no—
440Dic47—42no—
441Dic47—42no—
442C22×#137—471no—
443C23×SD16—471no—
444C2×D4×Q8—471no—
445C2×#546—471no—
446#3266—4716no—
447C2×#497—471no—
448C2×#468—471no—
449C2×#467—471no—
450C2×#464—471no—
451C2×#461D4711yescharacteristic, complemented
452C2×#452—471no—
453C2×#451—471no—
454C2×#448—471no—
455C2×#450—471no—
456C2×#440—471no—
457C2×#435—471no—
458C2×C47—44no—
459C2×C47#326614yescomplemented
460C2×C47C2×D4211yescharacteristic
461C2×C47C22×#13711yescharacteristic
462C2×C47C2×#57711yescharacteristic
463D47—24no—
464D47—42no—
465D47—82no—
466C22×#41—471no—
467C23×Q8—471no—
468C23×Q8—471no—
469C23×D4—471no—
470C2×#137—478no—
471C2×#137—948no—
472C22×Q16—471no—
473C22×Q16—471no—
474C22×Q16—471no—
475C22×SD16—471no—
476C22×SD16—471no—
477C22×SD16—471no—
478C22×SD16—478no—
479C22×SD16—471no—
480C22×SD16—948no—
481C22×SD16C2×D4711yescharacteristic
482C22×SD16C2×D4711yescharacteristic
483C22×M16—471no—
484C23×C8—471no—
485D4×Q8—478no—
486D4×Q8—944no—
487#546—478no—
488#546—944no—
489C2×C4⋊Q8—941no—
490C2×C4⋊Q8C2×D4711yescharacteristic, complemented
491C2×#124—471no—
492C2×#123—941no—
493C2×C22⋊Q8—471no—
494C2×C22⋊Q8—471no—
495C2×C22⋊Q8—471no—
496C2×C22⋊Q8—941no—
497C2×C22⋊Q8—941no—
498C2×#121—471no—
499C2×#121—941no—
500C2×#120—941no—
501C2×C4×Q8—471no—
502C2×C4×D4—471no—
503C2×C4×D4—941no—
504C2×C4×D4C2×D4711yescharacteristic
505C22×C22⋊C4—941no—
506#497—478no—
507#468—478no—
508#467—478no—
509#464—478no—
510#461C2×D4718yescomplemented
511#452—478no—
512#451—478no—
513#450—478no—
514#448—478no—
515#440—478no—
516#435—478no—
517C2×#107—471no—
518C2×C4⋊C8C2×D4711yescharacteristic, complemented
519C2×#103—471no—
520C2×#103—471no—
521C2×#103C2×D4711yescharacteristic, complemented
522C2×#103C2×D4711yescharacteristic, complemented
523C2×#102—471no—
524C2×#102—471no—
525C2×C22⋊C8—471no—
526C2×C22⋊C8—471no—
527C2×#97—471no—
528C47C2×#326611yescharacteristic, complemented, Sylow
529C25—941no—
530C2×#41—474no—
531C2×#41—942no—
532C2×#41—944no—
533C2×#41—1882no—
534C22×Q8—474no—
535C22×Q8—474no—
536C22×Q8—471no—
537C22×Q8—471no—
538C22×Q8—941no—
539C22×Q8—941no—
540C22×Q8—942no—
541C22×Q8—942no—
542C22×Q8—944no—
543C22×Q8—944no—
544C22×Q8—1882no—
545C22×Q8—1882no—
546C22×Q8C22×D4711yescharacteristic
547C22×Q8C22×D4711yescharacteristic
548C22×D4—474no—
549C22×D4—471no—
550C22×D4—471no—
551C22×D4—941no—
552C22×D4—942no—
553C22×D4—941no—
554C22×D4—944no—
555C22×D4—941no—
556C22×D4—1882no—
557C22×D4C22×D4711yescharacteristic
558C23×C4—21no—
559C23×C4—471no—
560C23×C4—471no—
561C23×C4—941no—
562C23×C4—941no—
563C23×C4—941no—
564#137—9432no—
565C2×Q16—474no—
566C2×Q16—474no—
567C2×Q16—474no—
568C2×Q16—944no—
569C2×Q16—944no—
570C2×Q16—1882no—
571C2×SD16—24no—
572C2×SD16—24no—
573C2×SD16—478no—
574C2×SD16—474no—
575C2×SD16—474no—
576C2×SD16—474no—
577C2×SD16—474no—
578C2×SD16—944no—
579C2×SD16—944no—
580C2×SD16—9432no—
581C2×SD16—1882no—
582C2×SD16C22×D4714yes—
583C2×SD16C22×D4714yes—
584C2×M16—474no—
585C2×M16—944no—
586C22×C8—471no—
587C22×C8—471no—
588C22×C8—474no—
589C22×C8—944no—
590C22×C8C22×D4711yescharacteristic
591C22×C8C22×D4711yescharacteristic
592C4⋊Q8—22no—
593C4⋊Q8—948no—
594C4⋊Q8C22×D4714yescomplemented
595#124—474no—
596#124—942no—
597#123—948no—
598C22⋊Q8—474no—
599C22⋊Q8—474no—
600C22⋊Q8—474no—
601C22⋊Q8—948no—
602C22⋊Q8—948no—
603C22⋊Q8—942no—
604C22⋊Q8—942no—
605C22⋊Q8—942no—
606#121—474no—
607#121—948no—
608#121—942no—
609#120—948no—
610C4×Q8—474no—
611C4×Q8—942no—
612C4×D4—22no—
613C4×D4—474no—
614C4×D4—474no—
615C4×D4—948no—
616C4×D4C22×D4714yes—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—471no—
620C2×C4⋊C4—471no—
621C2×C4⋊C4—941no—
622C2×C4⋊C4—941no—
623C2×C4⋊C4—941no—
624C2×C4⋊C4—941no—
625C2×C4⋊C4C22×D4711yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—471no—
628C2×C22⋊C4—471no—
629C2×C22⋊C4—948no—
630C2×C22⋊C4—941no—
631C2×C22⋊C4—941no—
632C2×C22⋊C4—941no—
633C2×C22⋊C4—941no—
634C2×C22⋊C4—941no—
635C2×C22⋊C4—941no—
636C2×C42—941no—
637C2×C42C22×D4711yescharacteristic
638#107—474no—
639C4⋊C8C22×D4714yescomplemented
640#103—474no—
641#103—474no—
642#103C22×D4714yescomplemented
643#103C22×D4714yescomplemented
644#102—474no—
645#102—474no—
646C22⋊C8—474no—
647C22⋊C8—474no—
648#97—474no—
649C24—21no—
650C24—471no—
651C24—471no—
652C24—944no—
653C24—941no—
654C24—3762no—
655C24—1884no—
656C24—1884no—
657#41—948no—
658#41—1884no—
659#41—1888no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—22no—
663C2×Q8—22no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—474no—
667C2×Q8—472no—
668C2×Q8—472no—
669C2×Q8—944no—
670C2×Q8—944no—
671C2×Q8—941no—
672C2×Q8—941no—
673C2×Q8—942no—
674C2×Q8—948no—
675C2×Q8—948no—
676C2×Q8—942no—
677C2×Q8—942no—
678C2×Q8—1884no—
679C2×Q8—1884no—
680C2×Q8—1884no—
681C2×Q8—1884no—
682C2×Q8—1888no—
683C2×Q8—1888no—
684C2×Q8C23×D4712yes—
685C2×Q8C23×D4712yes—
686C2×D4—21no—
687C2×D4—22no—
688C2×D4—474no—
689C2×D4—472no—
690C2×D4—944no—
691C2×D4—944no—
692C2×D4—944no—
693C2×D4—948no—
694C2×D4—944no—
695C2×D4—942no—
696C2×D4—941no—
697C2×D4—942no—
698C2×D4—3762no—
699C2×D4—1884no—
700C2×D4—1888no—
701C2×D4—1884no—
702C2×D4—1884no—
703C2×D4D4×D4714yes—
704C2×D4C23×D4712yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—24no—
709C22×C4—82no—
710C22×C4—471no—
711C22×C4—471no—
712C22×C4—472no—
713C22×C4—472no—
714C22×C4—472no—
715C22×C4—472no—
716C22×C4—944no—
717C22×C4—944no—
718C22×C4—944no—
719C22×C4—941no—
720C22×C4—942no—
721C22×C4—942no—
722C22×C4—942no—
723C22×C4—942no—
724C22×C4—941no—
725C22×C4—941no—
726C22×C4—1884no—
727C22×C4—1884no—
728C22×C4—1884no—
729C22×C4D4×D4711yescharacteristic
730C22×C4D4×D4711yescharacteristic
731C22×C4C23×D4711yescharacteristic
732Q16—948no—
733Q16—948no—
734Q16—1884no—
735SD16—28no—
736SD16—28no—
737SD16—4716no—
738SD16—948no—
739SD16—948no—
740SD16—1884no—
741M16—948no—
742C2×C8—22no—
743C2×C8—22no—
744C2×C8—474no—
745C2×C8—472no—
746C2×C8—472no—
747C2×C8—948no—
748C2×C8—942no—
749C2×C8C23×D4712yes—
750C2×C8C23×D4712yes—
751C4⋊C4—24no—
752C4⋊C4—24no—
753C4⋊C4—21no—
754C4⋊C4—474no—
755C4⋊C4—472no—
756C4⋊C4—944no—
757C4⋊C4—944no—
758C4⋊C4—944no—
759C4⋊C4—944no—
760C4⋊C4—941no—
761C4⋊C4C23×D4712yes—
762C22⋊C4—24no—
763C22⋊C4—474no—
764C22⋊C4—474no—
765C22⋊C4—944no—
766C22⋊C4—944no—
767C22⋊C4—944no—
768C22⋊C4—944no—
769C22⋊C4—944no—
770C22⋊C4—944no—
771C42—944no—
772C42D4×D4712yes—
773C42C23×D4712yes—
774C23—24no—
775C23—22no—
776C23—42no—
777C23—42no—
778C23—474no—
779C23—472no—
780C23—472no—
781C23—942no—
782C23—942no—
783C23—942no—
784C23—942no—
785C23—942no—
786C23—942no—
787C23—37616no—
788C23—3764no—
789C23—1888no—
790C23—1888no—
791C23—1882no—
792C23—1882no—
793C23—1882no—
794C23C2×D4×D4711yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—22no—
798Q8—22no—
799Q8—42no—
800Q8—42no—
801Q8—474no—
802Q8—944no—
803Q8—942no—
804Q8—942no—
805Q8—942no—
806Q8—1888no—
807Q8—1888no—
808Q8—1882no—
809D4—24no—
810D4—22no—
811D4—948no—
812D4—942no—
813D4—942no—
814D4—3764no—
815D4—1888no—
816D4—1888no—
817D4—1882no—
818D4C2×D4×D4714yes—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—84no—
828C2×C4—472no—
829C2×C4—472no—
830C2×C4—942no—
831C2×C4—942no—
832C2×C4—944no—
833C2×C4—942no—
834C2×C4—944no—
835C2×C4—944no—
836C2×C4—942no—
837C2×C4—942no—
838C2×C4—942no—
839C2×C4—942no—
840C2×C4—942no—
841C2×C4—942no—
842C2×C4—1888no—
843C2×C4—1888no—
844C2×C4—1888no—
845C2×C4—1882no—
846C2×C4—1882no—
847C2×C4C2×D4×D4712yes—
848C2×C4C2×D4×D4712yes—
849C2×C4C2×D4×D4711yescharacteristic
850C2×C4C2×D4×D4712yes—
851C2×C4#1309407012yes—
852C2×C4C24×D4711yescharacteristic
853C8—22no—
854C8—22no—
855C8—474no—
856C8—942no—
857C22—24no—
858C22—42no—
859C22—42no—
860C22—48no—
861C22—474no—
862C22—942no—
863C22—942no—
864C22—948no—
865C22—942no—
866C22—942no—
867C22—942no—
868C22—37616no—
869C22—3764no—
870C22—1882no—
871C22—1882no—
872C22—1882no—
873C22—1884no—
874C22#1568975712yes—
875C22#137×D4712yes—
876C22#1568992912yes—
877C22C22×D4×D4711yescharacteristic
878C4—22no—
879C4—22no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—942no—
884C4—942no—
885C4—944no—
886C4—1882no—
887C4—1882no—
888C4#1568975712yes—
889C4C22×D4×D4711yescharacteristic
890C4C2×#1309407011yescharacteristic
891C2—44no—
892C2—944no—
893C2—3762no—
894C2—1882no—
895C2#2025490414yesdirect product factor
896C2C2×#1568975711yescharacteristic
897C2C2×#137×D4711yescharacteristic
898C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#461C2
socleC23×C47C22×D4
prime radicalC2×#15689768C2
hypercenterC2×#461D47
hypocenterC47C2×#3266
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C22×#13094053C2semidirect
2. C22×SD16×D47C2semidirect
3. C2×#15689788C2semidirect
5. #20254904C2direct (N × H)
6. C2×#15689515C2semidirect
7. C2×#15689372C2semidirect
8. C2×#15689363C2semidirect
9. C2×#15689346C2semidirect
10. C2×#15689282C2semidirect
11. C2×#15689280C2semidirect
12. C2×#15689263C2semidirect
13. C2×#15689272C2semidirect
14. C2×#15689223C2semidirect
15. C2×#15689193C2semidirect
16. C2×C47×#461C2semidirect
19. C22×Q8×D47C22semidirect
22. C2×#13094053C22semidirect
23. C22×Dic188C22semidirect
24. C22×#10625337C22semidirect
25. C22×#10625337C22semidirect
31. C2×SD16×D47C22semidirect
32. C22×#10625324C22semidirect
35. #15689788C22semidirect
45. C2×#13094000C22semidirect
49. C2×C4×Dic94C22semidirect
53. #15689515C22semidirect
54. #15689372C22semidirect
55. #15689363C22semidirect
56. #15689346C22semidirect
57. #15689282C22semidirect
58. #15689280C22semidirect
59. #15689272C22semidirect
60. #15689263C22semidirect
61. #15689223C22semidirect
62. #15689193C22semidirect
63. C2×#13093957C22semidirect
64. C2×#13093949C22semidirect
65. C2×#13093947C22semidirect
69. C2×(C2×D47)⋊C8C22semidirect
70. C2×#13093935C22semidirect
73. C2×C4⋊Q8×C47C22semidirect
75. C47×#461C22semidirect
76. C2×C4⋊C8×C47C22semidirect
77. C2×#103×C47C22semidirect
78. C2×#103×C47C22semidirect
95. C2×Q8×D47C23semidirect
112. C2×Dic188C23semidirect
115. C2×#10625337C23semidirect
116. C2×#10625337C23semidirect
119. C2×#10625335D4semidirect
127. C2×#10625324C23semidirect
143. #13094000C23semidirect
149. C4×Dic94C23semidirect
169. #13093957C23semidirect
170. #13093949C23semidirect
171. #13093947C23semidirect
175. (C2×D47)⋊C8C23semidirect
176. #13093935C23semidirect
188. C4⋊Q8×C47C23semidirect
196. C4⋊C8×C47C23semidirect
197. #103×C47C23semidirect
198. #103×C47C23semidirect
299. #10625335C2×D4semidirect
342. C22×D47#137semidirect
428. C2×D47C2×#137semidirect
451. C2×#461D47semidirect
459. C2×C47#3266semidirect
490. C2×C4⋊Q8C2×D47semidirect
510. #461C2×D47semidirect
518. C2×C4⋊C8C2×D47semidirect
521. C2×#103C2×D47semidirect
522. C2×#103C2×D47semidirect
528. C47C2×#3266semidirect
594. C4⋊Q8C22×D47semidirect
639. C4⋊C8C22×D47semidirect
642. #103C22×D47semidirect
643. #103C22×D47semidirect
895. C2#20254904direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940532
C22×SD16×D472
C2×#156897882
C2×#156897682
#202549042
C2×#156895152
C2×#156893722
C2×#156893632
C2×#156893462
C2×#156892822
C2×#156892802
C2×#156892632
C2×#156892722
C2×#156892232
C2×#156891932
C2×C47×#4612
C2×#326647