Finite Group Databasebeta

← C2×#20252916 #27083191

Subgroups — C2×#20252916 #27083191

Order 12032.

2666 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094053C211yesmaximal, characteristic
2C22×Q16×D47C211yesmaximal, characteristic, complemented
3C2×#15689693C211yesmaximal, characteristic
4C2×#15689599C211yesmaximal, characteristic, complemented
5#20252916C2116yesmaximal, direct product factor
6C2×#15689344C211yesmaximal, characteristic, complemented
7C2×#15689343C211yesmaximal, characteristic, complemented
8C2×#15689342C211yesmaximal, characteristic, complemented
9C2×#15689334C211yesmaximal, characteristic, complemented
10C2×#15689333C211yesmaximal, characteristic, complemented
11C2×#15689332C211yesmaximal, characteristic, complemented
12C2×#15689331C211yesmaximal, characteristic, complemented
13C2×#15689148C211yesmaximal, characteristic, complemented
14C2×#15689130C211yesmaximal, characteristic, complemented
15C2×#15689116C211yesmaximal, characteristic
16C2×C47×#464C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C22×Q8×D47C2211yescharacteristic
20C2×#13094053—28no—
21C2×#13094053C2218yes—
22C22×Dic188C2211yescharacteristic
23C22×Dic188C2211yescharacteristic
24C22×#10625337C2211yescharacteristic
25C22×#10625337C2211yescharacteristic
26C22×#10625337C2211yescharacteristic
27C2×Q16×D47—28no—
28C2×Q16×D47C2218yescomplemented
29C22×#10625335C2211yescharacteristic
30C22×#10625324C2211yescharacteristic
31C22×C8×D47C2211yescharacteristic
32#15689693—24no—
33#15689693C2218yes—
34C2×#13094024C2211yescharacteristic
35C2×#13094022C2211yescharacteristic
36C2×#13094011C2211yescharacteristic
37C2×#13094006—21no—
38C2×#13094006—21no—
39C2×#13094001—21no—
40C2×#13094001—21no—
41#15689599—24no—
42#15689599C2218yescomplemented
43C2×Q8×Dic47C2211yescharacteristic
44C2×C4×Dic94—21no—
45C2×C4×Dic94C2211yescharacteristic
46C2×#13093989—21no—
47C2×#13093989C2211yescharacteristic
48C2×#13093982—21no—
49C2×#13093982C2211yescharacteristic
50C2×#13093981—21no—
51C2×#13093981C2211yescharacteristic
52#15689344C2218yescomplemented
53#15689343C2218yescomplemented
54#15689342C2218yescomplemented
55#15689334C2218yescomplemented
56#15689333C2218yescomplemented
57#15689332C2218yescomplemented
58#15689331C2218yescomplemented
59#15689148C2218yescomplemented
60C2×C4⋊(C47⋊C8)C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63#15689130C2218yescomplemented
64#15689116C2218yes—
65C2×#13093949C2211yescharacteristic
66C2×#13093949C2211yescharacteristic
67C2×#13093948C2211yescharacteristic
68C2×#13093947C2211yescharacteristic
69C2×#13093947C2211yescharacteristic
70C2×#13093945C2211yescharacteristic
71C22×Q16×C47C2211yescharacteristic
72C22×SD16×C47C2211yescharacteristic
73C2×#124×C47C2211yescharacteristic
74C2×C4×Q8×C47C2211yescharacteristic
75C47×#464C2218yescomplemented
76C2×C4⋊C8×C47C2211yescharacteristic
77C2×#103×C47C2211yescharacteristic
78C2×#102×C47C2211yescharacteristic
79C2×#10625352—24no—
80C2×#10625352—22no—
81C2×#10625352—24no—
82C2×#10625352C2314yes—
83C22×Dic94—21no—
84C22×Dic94—21no—
85C22×Dic94C2311yescharacteristic
86C22×Dic94C2311yescharacteristic
87C22×Dic94C2311yescharacteristic
88C2×Q8×D47—22no—
89C2×Q8×D47—22no—
90C2×Q8×D47—24no—
91C2×Q8×D47—24no—
92C2×Q8×D47—24no—
93C2×Q8×D47D418yes—
94C2×Q8×D47C2314yes—
95C2×Q8×D47C2314yes—
96C22×C22⋊D47—21no—
97C23×Dic47—21no—
98C22×C4×D47—21no—
99C22×C4×D47—21no—
100C22×C4×D47C2311yescharacteristic
101#13094053—232no—
102C2×Dic188—24no—
103C2×Dic188—24no—
104C2×Dic188C2314yes—
105C2×Dic188C2314yes—
106C2×#10625337—24no—
107C2×#10625337—24no—
108C2×#10625337—24no—
109C2×#10625337C2314yes—
110C2×#10625337C2314yes—
111C2×#10625337C2314yes—
112Q16×D47—232no—
113C2×#10625335—24no—
114C2×#10625335C2314yes—
115C2×#10625324—24no—
116C2×#10625324C2314yes—
117C22×C47⋊C8C2311yescharacteristic
118C22×C47⋊C8C2311yescharacteristic
119C2×C8×D47—24no—
120C2×C8×D47C2314yes—
121#13094024—22no—
122#13094024C2314yes—
123#13094022—22no—
124#13094022C2314yes—
125#13094011—22no—
126#13094011C2314yes—
127#13094006—28no—
128#13094006—28no—
129#13094001—28no—
130#13094001—28no—
131Q8×Dic47—22no—
132Q8×Dic47C2314yes—
133C4×Dic94—22no—
134C4×Dic94—28no—
135C4×Dic94C2314yes—
136#13093989—28no—
137#13093989—22no—
138#13093989C2314yes—
139#13093982—22no—
140#13093982—28no—
141#13093982C2314yes—
142#13093981—28no—
143#13093981D414yes—
144#13093981C2314yes—
145C2×C4⋊Dic47—21no—
146C2×C4⋊Dic47—21no—
147C2×C4⋊Dic47—21no—
148C2×C4⋊Dic47C2311yescharacteristic
149C2×Dic47⋊C4—21no—
150C2×Dic47⋊C4—21no—
151C2×Dic47⋊C4—21no—
152C2×Dic47⋊C4—21no—
153C2×Dic47⋊C4D411yescharacteristic
154C2×Dic47⋊C4D411yescharacteristic
155C2×C22⋊Dic47—21no—
156C2×C22⋊Dic47—21no—
157C2×(C2×D47)⋊C4—21no—
158C2×(C2×D47)⋊C4D411yescharacteristic
159C2×(C2×D47)⋊C4D411yescharacteristic
160C2×C4×Dic47—21no—
161C2×C4×Dic47—21no—
162C2×C4×Dic47—21no—
163C2×C4×Dic47—21no—
164C2×C4×Dic47C2311yescharacteristic
165C4⋊(C47⋊C8)C2314yes—
166Dic47⋊C8C2314yes—
167Dic47⋊C8C2314yes—
168#13093949C2314yes—
169#13093949C2314yes—
170#13093948C2314yes—
171#13093947C2314yes—
172#13093947C2314yes—
173#13093945C2314yes—
174C22×Q8×C47C2311yescharacteristic
175C22×Q8×C47C2311yescharacteristic
176C22×D4×C47C2311yescharacteristic
177C2×Q16×C47—24no—
178C2×Q16×C47C2314yes—
179C2×SD16×C47—24no—
180C2×SD16×C47C2314yes—
181C22×C8×C47C2311yescharacteristic
182C22×C8×C47C2311yescharacteristic
183#124×C47—22no—
184#124×C47C2314yes—
185C4×Q8×C47—22no—
186C4×Q8×C47C2314yes—
187C2×C4⋊C4×C47—21no—
188C2×C4⋊C4×C47C2311yescharacteristic
189C2×C22⋊C4×C47—21no—
190C2×C22⋊C4×C47—21no—
191C2×C42×C47—21no—
192C2×C42×C47C2311yescharacteristic
193C4⋊C8×C47C2314yes—
194#103×C47C2314yes—
195#102×C47C2314yes—
196C24×C47—21no—
197C23×D47C2×D411yescharacteristic
198C2×Q8×C47—21no—
199C2×Q8×C47—21no—
200C2×Q8×C47—22no—
201C2×Q8×C47—22no—
202C2×Q8×C47—22no—
203C2×Q8×C47C2×D414yes—
204C2×Q8×C47C2412yes—
205C2×Q8×C47C2412yes—
206C2×D4×C47—22no—
207C2×D4×C47—21no—
208C2×D4×C47—22no—
209C2×D4×C47C2412yes—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2411yescharacteristic
216C2×C22⋊D47—24no—
217C2×C22⋊D47—44no—
218C22×Dic47—21no—
219C22×Dic47—21no—
220C22×Dic47—21no—
221C22×Dic47—21no—
222C22×Dic47—24no—
223C22×Dic47—44no—
224C22×Dic47C2×D411yescharacteristic
225C22×Dic47C2×D411yescharacteristic
226C22×Dic47C2×D411yescharacteristic
227Q8×D47—216no—
228Q8×D47—28no—
229Q8×D47—28no—
230Q8×D47—28no—
231Q8×D47—48no—
232Q8×D47C2×D4116yes—
233#10625352—28no—
234#10625352—28no—
235#10625352—48no—
236C2×C4×D47—28no—
237C2×C4×D47—24no—
238C2×C4×D47—24no—
239C2×C4×D47—44no—
240C2×C4×D47C2×D412yes—
241C2×C4×D47C2×D414yes—
242C2×C4×D47#4114yes—
243C2×C4×D47C2412yes—
244C2×Dic94—21no—
245C2×Dic94—22no—
246C2×Dic94—28no—
247C2×Dic94—24no—
248C2×Dic94—22no—
249C2×Dic94—22no—
250C2×Dic94—22no—
251C2×Dic94—22no—
252C2×Dic94—21no—
253C2×Dic94—21no—
254C2×Dic94—24no—
255C2×Dic94—44no—
256C2×Dic94C2×D414yes—
257C2×Dic94C2412yes—
258C2×Dic94C2412yes—
259C2×Dic94C2412yes—
260Q16×C47—28no—
261SD16×C47—28no—
262C2×C8×C47—22no—
263C2×C8×C47—22no—
264C2×C8×C47C2412yes—
265C2×C8×C47C2412yes—
266C4⋊C4×C47—24no—
267C4⋊C4×C47—21no—
268C4⋊C4×C47C2412yes—
269C22⋊C4×C47—24no—
270C22⋊C4×C47—24no—
271C42×C47—24no—
272C42×C47C2×D412yes—
273C42×C47C2412yes—
274C22⋊Dic47—24no—
275C22⋊Dic47—24no—
276#10625337—28no—
277#10625337—28no—
278#10625337—28no—
279#10625335—28no—
280(C2×D47)⋊C4—24no—
281(C2×D47)⋊C4C2×D414yes—
282(C2×D47)⋊C4C2×D414yes—
283C4⋊Dic47—24no—
284C4⋊Dic47—24no—
285C4⋊Dic47—21no—
286C4⋊Dic47—24no—
287C4⋊Dic47C2412yes—
288Dic47⋊C4—24no—
289Dic47⋊C4—24no—
290Dic47⋊C4—24no—
291Dic47⋊C4—24no—
292Dic47⋊C4C2×D414yes—
293Dic47⋊C4C2×D414yes—
294C4×Dic47—24no—
295C4×Dic47—24no—
296C4×Dic47—24no—
297C4×Dic47—24no—
298C4×Dic47C2×D412yes—
299C4×Dic47C2412yes—
300C2×C47⋊C8—22no—
301C2×C47⋊C8—22no—
302C2×C47⋊C8C2412yes—
303C2×C47⋊C8C2412yes—
304Dic188—28no—
305Dic188—28no—
306#10625324—28no—
307C8×D47—28no—
308C23×C47—22no—
309C23×C47—42no—
310C23×C47—42no—
311C23×C47—42no—
312C23×C47C22×D411yescharacteristic
313C22×D47—22no—
314C22×D47—22no—
315C22×D47#12114yes—
316C22×D47C22×D412yes—
317Q8×C47—24no—
318Q8×C47—22no—
319Q8×C47—22no—
320Q8×C47—22no—
321Q8×C47—42no—
322Q8×C47C22×D414yes—
323D4×C47—22no—
324D4×C47—22no—
325D4×C47—42no—
326C2×C4×C47—24no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—42no—
333C2×C4×C47—42no—
334C2×C4×C47C22×D412yes—
335C2×C4×C47C22×D412yes—
336C2×C4×C47C22×D411yescharacteristic
337C2×C4×C47C22×D412yes—
338C2×C4×C47C2×#4112yes—
339C2×C4×C47C2511yescharacteristic
340C22⋊D47—48no—
341C2×Dic47—24no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—42no—
349C2×Dic47—42no—
350C2×Dic47—42no—
351C2×Dic47—48no—
352C2×Dic47#12114yes—
353C2×Dic47C22×D412yes—
354C2×Dic47C22×D412yes—
355C2×Dic47C22×D412yes—
356C4×D47—216no—
357C4×D47—48no—
358C4×D47#12118yes—
359C4×D47C22×D414yes—
360C4×D47C2×#4114yes—
361Dic94—24no—
362Dic94—22no—
363Dic94—216no—
364Dic94—22no—
365Dic94—22no—
366Dic94—22no—
367Dic94—22no—
368Dic94—42no—
369Dic94—42no—
370Dic94—48no—
371Dic94C22×D414yes—
372C8×C47—22no—
373C8×C47—22no—
374C47⋊C8—22no—
375C47⋊C8—22no—
376C2×#3044—471nomaximal, Sylow
377C22×C47—42no—
378C22×C47—42no—
379C22×C47—42no—
380C22×C47—84no—
381C22×C47C2×#12112yes—
382C22×C47#57812yes—
383C22×C47#57812yes—
384C22×C47C23×D411yescharacteristic
385C2×D47—28no—
386C2×D47—22no—
387C2×D47—22no—
388C2×D47C2×#12114yes—
389C4×C47—24no—
390C4×C47—22no—
391C4×C47—22no—
392C4×C47—42no—
393C4×C47—42no—
394C4×C47C2×#12112yes—
395C4×C47C23×D411yescharacteristic
396C4×C47C22×#4111yescharacteristic
397Dic47—24no—
398Dic47—22no—
399Dic47—22no—
400Dic47—42no—
401Dic47—42no—
402Dic47—42no—
403Dic47C2×#12114yes—
404C22×#137—471no—
405C23×Q16—471no—
406C2×#536—471no—
407C2×#519—471no—
408#3044—4716no—
409C2×#464—471no—
410C2×#464—471no—
411C2×#464—471no—
412C2×#464D4711yescharacteristic, complemented
413C2×#462—471no—
414C2×#462—471no—
415C2×#462—471no—
416C2×#462—471no—
417C2×#424—471no—
418C2×#419—471no—
419C2×#416—471no—
420C2×C47—82no—
421C2×C47#304414yescomplemented
422C2×C47C22×#12111yescharacteristic
423C2×C47C2×#57811yescharacteristic
424C2×C47C2×#57811yescharacteristic
425D47—24no—
426C22×#41—471no—
427C23×Q8—471no—
428C23×Q8—471no—
429C2×#137—478no—
430C2×#137—948no—
431C22×Q16—471no—
432C22×Q16—471no—
433C22×Q16—471no—
434C22×Q16—478no—
435C22×Q16—471no—
436C22×Q16—471no—
437C22×Q16—948no—
438C22×Q16C2×D4711yescharacteristic
439C22×SD16—471no—
440C22×SD16C2×D4711yescharacteristic
441C22×M16—471no—
442C23×C8—471no—
443#536—478no—
444#536—944no—
445C2×C4⋊Q8—471no—
446C2×C4⋊Q8—471no—
447C2×#124—471no—
448C2×#124C2×D4711yescharacteristic
449C2×#123—941no—
450C2×#123—941no—
451C2×C22⋊Q8—941no—
452C2×C22⋊Q8—941no—
453#519—478no—
454#519—944no—
455C2×C4×Q8—471no—
456C2×C4×Q8—471no—
457C2×C4×Q8—471no—
458C2×C4×Q8—941no—
459C2×C4×Q8—941no—
460C2×C4×Q8C2×D4711yescharacteristic
461C2×#117—471no—
462C2×#117—471no—
463C2×#117—941no—
464C2×#117—941no—
465#464—478no—
466#464—478no—
467#464—478no—
468#464C2×D4718yescomplemented
469#462—478no—
470#462—478no—
471#462—478no—
472#462—478no—
473#424—478no—
474C2×C4⋊C8—471no—
475C2×C4⋊C8—471no—
476C2×C4⋊C8—471no—
477C2×C4⋊C8C2×D4711yescharacteristic
478#419—478no—
479#416—478no—
480C2×#103—471no—
481C2×#103—471no—
482C2×#103—471no—
483C2×#103—471no—
484C2×#103—471no—
485C2×#103C2×D4711yescharacteristic
486C2×#102—471no—
487C2×#102C2×D4711yescharacteristic
488C47C2×#304411yescharacteristic, complemented, Sylow
489C2×#41—474no—
490C2×#41—942no—
491C2×#41—944no—
492C2×#41—944no—
493C22×Q8—478no—
494C22×Q8—474no—
495C22×Q8—474no—
496C22×Q8—471no—
497C22×Q8—471no—
498C22×Q8—471no—
499C22×Q8—941no—
500C22×Q8—941no—
501C22×Q8—942no—
502C22×Q8—944no—
503C22×Q8—942no—
504C22×Q8—944no—
505C22×Q8—944no—
506C22×Q8C22×D4711yescharacteristic
507C22×Q8C22×D4711yescharacteristic
508C22×D4—941no—
509C22×D4C22×D4711yescharacteristic
510C23×C4—471no—
511C23×C4—941no—
512C23×C4—941no—
513C23×C4—941no—
514#137—9432no—
515C2×Q16—24no—
516C2×Q16—474no—
517C2×Q16—474no—
518C2×Q16—474no—
519C2×Q16—474no—
520C2×Q16—474no—
521C2×Q16—944no—
522C2×Q16—944no—
523C2×Q16—9432no—
524C2×Q16—944no—
525C2×Q16—944no—
526C2×Q16—944no—
527C2×Q16C22×D4714yes—
528C2×SD16—24no—
529C2×SD16—474no—
530C2×SD16—944no—
531C2×SD16C22×D4714yes—
532C2×M16—474no—
533C2×M16—944no—
534C22×C8—471no—
535C22×C8—471no—
536C22×C8—474no—
537C22×C8—944no—
538C22×C8C22×D4711yescharacteristic
539C22×C8C22×D4711yescharacteristic
540C4⋊Q8—474no—
541C4⋊Q8—474no—
542C4⋊Q8—942no—
543C4⋊Q8—942no—
544#124—22no—
545#124—474no—
546#124—942no—
547#124C22×D4714yes—
548#123—948no—
549#123—948no—
550C22⋊Q8—948no—
551C22⋊Q8—948no—
552C4×Q8—22no—
553C4×Q8—474no—
554C4×Q8—474no—
555C4×Q8—474no—
556C4×Q8—948no—
557C4×Q8—942no—
558C4×Q8—942no—
559C4×Q8—948no—
560C4×Q8—942no—
561C4×Q8C22×D4714yes—
562#117—474no—
563#117—474no—
564#117—474no—
565#117—948no—
566#117—948no—
567#117—942no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—471no—
570C2×C4⋊C4—471no—
571C2×C4⋊C4—471no—
572C2×C4⋊C4—941no—
573C2×C4⋊C4—941no—
574C2×C4⋊C4—941no—
575C2×C4⋊C4—941no—
576C2×C4⋊C4—941no—
577C2×C4⋊C4—941no—
578C2×C4⋊C4—941no—
579C2×C4⋊C4C22×D4711yescharacteristic
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—471no—
583C2×C22⋊C4—471no—
584C2×C22⋊C4—941no—
585C2×C22⋊C4—941no—
586C2×C22⋊C4—941no—
587C2×C42—21no—
588C2×C42—471no—
589C2×C42—941no—
590C2×C42—941no—
591C2×C42—941no—
592C2×C42—941no—
593C2×C42C22×D4711yescharacteristic
594C4⋊C8—474no—
595C4⋊C8—474no—
596C4⋊C8—474no—
597C4⋊C8C22×D4714yes—
598#103—474no—
599#103—474no—
600#103—474no—
601#103—474no—
602#103—474no—
603#103C22×D4714yes—
604#102—474no—
605#102C22×D4714yes—
606C24—21no—
607C24—471no—
608#41—948no—
609#41—948no—
610#41—1888no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—22no—
614C2×Q8—22no—
615C2×Q8—22no—
616C2×Q8—4716no—
617C2×Q8—474no—
618C2×Q8—472no—
619C2×Q8—472no—
620C2×Q8—472no—
621C2×Q8—944no—
622C2×Q8—948no—
623C2×Q8—944no—
624C2×Q8—9416no—
625C2×Q8—948no—
626C2×Q8—948no—
627C2×Q8—948no—
628C2×Q8—941no—
629C2×Q8—941no—
630C2×Q8—941no—
631C2×Q8—942no—
632C2×Q8—942no—
633C2×Q8—942no—
634C2×Q8—942no—
635C2×Q8—942no—
636C2×Q8—1884no—
637C2×Q8—1888no—
638C2×Q8D4×D4714yes—
639C2×Q8C23×D4712yes—
640C2×Q8C23×D4712yes—
641C2×D4—22no—
642C2×D4—21no—
643C2×D4—22no—
644C2×D4—944no—
645C2×D4—1884no—
646C2×D4C23×D4712yes—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—471no—
651C22×C4—472no—
652C22×C4—474no—
653C22×C4—474no—
654C22×C4—472no—
655C22×C4—471no—
656C22×C4—471no—
657C22×C4—944no—
658C22×C4—948no—
659C22×C4—944no—
660C22×C4—944no—
661C22×C4—941no—
662C22×C4—941no—
663C22×C4—941no—
664C22×C4—941no—
665C22×C4—1884no—
666C22×C4—1884no—
667C22×C4D4×D4711yescharacteristic
668C22×C4D4×D4711yescharacteristic
669C22×C4C23×D4711yescharacteristic
670Q16—28no—
671Q16—948no—
672Q16—948no—
673Q16—948no—
674Q16—948no—
675Q16—948no—
676SD16—28no—
677SD16—948no—
678M16—948no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—472no—
682C2×C8—472no—
683C2×C8—948no—
684C2×C8—942no—
685C2×C8—942no—
686C2×C8C23×D4712yes—
687C2×C8C23×D4712yes—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—474no—
691C4⋊C4—474no—
692C4⋊C4—472no—
693C4⋊C4—944no—
694C4⋊C4—944no—
695C4⋊C4—944no—
696C4⋊C4—944no—
697C4⋊C4—944no—
698C4⋊C4—941no—
699C4⋊C4—944no—
700C4⋊C4—944no—
701C4⋊C4C23×D4712yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—474no—
705C22⋊C4—474no—
706C22⋊C4—944no—
707C22⋊C4—944no—
708C22⋊C4—944no—
709C42—24no—
710C42—472no—
711C42—472no—
712C42—944no—
713C42—944no—
714C42—944no—
715C42—944no—
716C42D4×D4712yes—
717C42C23×D4712yes—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—474no—
723C23—472no—
724C23—942no—
725C23—942no—
726C23C2×D4×D4711yescharacteristic
727Q8—24no—
728Q8—22no—
729Q8—22no—
730Q8—22no—
731Q8—42no—
732Q8—474no—
733Q8—9416no—
734Q8—944no—
735Q8—942no—
736Q8—942no—
737Q8—942no—
738Q8—942no—
739Q8—942no—
740Q8—1888no—
741Q8—1882no—
742Q8—1882no—
743Q8C2×D4×D4714yes—
744D4—22no—
745D4—22no—
746D4—42no—
747D4—1888no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—474no—
757C2×C4—472no—
758C2×C4—478no—
759C2×C4—474no—
760C2×C4—474no—
761C2×C4—472no—
762C2×C4—472no—
763C2×C4—9416no—
764C2×C4—944no—
765C2×C4—942no—
766C2×C4—942no—
767C2×C4—942no—
768C2×C4—942no—
769C2×C4—942no—
770C2×C4—942no—
771C2×C4—1888no—
772C2×C4—1888no—
773C2×C4—1882no—
774C2×C4—1882no—
775C2×C4—1882no—
776C2×C4C2×D4×D4712yes—
777C2×C4C2×D4×D4712yes—
778C2×C4C2×D4×D4711yescharacteristic
779C2×C4C2×D4×D4712yes—
780C2×C4#41×D4712yes—
781C2×C4C24×D4711yescharacteristic
782C8—22no—
783C8—22no—
784C8—942no—
785C8—942no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—84no—
790C22—474no—
791C22—942no—
792C22—942no—
793C22—948no—
794C22#121×D4712yes—
795C22#1568993712yes—
796C22#1568993912yes—
797C22C22×D4×D4711yescharacteristic
798C4—24no—
799C4—22no—
800C4—22no—
801C4—42no—
802C4—42no—
803C4—474no—
804C4—944no—
805C4—942no—
806C4—942no—
807C4—1882no—
808C4—1882no—
809C4—1882no—
810C4#121×D4712yes—
811C4C22×D4×D4711yescharacteristic
812C4C2×#41×D4711yescharacteristic
813C2—82no—
814C2—944no—
815C2#2025291614yesdirect product factor
816C2C2×#121×D4711yescharacteristic
817C2C2×#1568993711yescharacteristic
818C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#464C2
socleC23×C47C22×D4
prime radicalC22×#10625352C22
hypercenterC2×#464D47
hypocenterC47C2×#3044
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
2. C22×Q16×D47C2semidirect
4. C2×#15689599C2semidirect
5. #20252916C2direct (N × H)
6. C2×#15689344C2semidirect
7. C2×#15689343C2semidirect
8. C2×#15689342C2semidirect
9. C2×#15689334C2semidirect
10. C2×#15689333C2semidirect
11. C2×#15689332C2semidirect
12. C2×#15689331C2semidirect
13. C2×#15689148C2semidirect
14. C2×#15689130C2semidirect
16. C2×C47×#464C2semidirect
28. C2×Q16×D47C22semidirect
42. #15689599C22semidirect
52. #15689344C22semidirect
53. #15689343C22semidirect
54. #15689342C22semidirect
55. #15689334C22semidirect
56. #15689333C22semidirect
57. #15689332C22semidirect
58. #15689331C22semidirect
59. #15689148C22semidirect
63. #15689130C22semidirect
75. C47×#464C22semidirect
412. C2×#464D47semidirect
421. C2×C47#3044semidirect
468. #464C2×D47semidirect
488. C47C2×#3044semidirect
815. C2#20252916direct (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×Q16×D472
C2×#156896932
C2×#156895992
#202529162
C2×#156893442
C2×#156893432
C2×#156893422
C2×#156893342
C2×#156893332
C2×#156893322
C2×#156893312
C2×#156891482
C2×#156891302
C2×#156891162
C2×C47×#4642
C2×#304447