Finite Group Databasebeta

← C2×#20243689 #26217451

Subgroups — C2×#20243689 #26217451

Order 12032.

2050 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
1C22×M16×D47C211yesmaximal, characteristic, complemented
2C2×#15689635C211yesmaximal, characteristic
3C22×#13093952C211yesmaximal, characteristic, complemented
4C22×#13093950C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
6#20243689C218yesmaximal, direct product factor
7C2×#15688882C211yesmaximal, characteristic, complemented
8C2×C47×#339C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10C23×C4×D47C2211yescharacteristic
11C22×#10625329C2211yescharacteristic
12C22×#10625324—21no—
13C2×M16×D47—22no—
14C2×M16×D47—24no—
15C2×M16×D47—24no—
16C2×M16×D47C2214yescomplemented
17C22×C8×D47—21no—
18#15689635—22no—
19#15689635—22no—
20#15689635C414yescomplemented
21#15689635C2214yes—
22C2×#13094008—21no—
23C2×#13094004C411yescharacteristic, complemented
24C2×#13094004C411yescharacteristic, complemented
25C2×#13093999C411yescharacteristic, complemented
26C2×#13093999C411yescharacteristic, complemented
27C2×#13093994—21no—
28C2×C4×D188—21no—
29C2×C4×D188—21no—
30C22×(C2×D47)⋊C4—21no—
31C22×C4×Dic47C2211yescharacteristic
32C2×#13093952—24no—
33C2×#13093952C2214yescomplemented
34C2×#13093950—24no—
35C2×#13093950C2214yescomplemented
36C4×(C2×D47)⋊C4—22no—
37C4×(C2×D47)⋊C4C2214yescomplemented
38C2×C47⋊#95—21no—
39#15688882C2214yescomplemented
40C22×M16×C47C2211yescharacteristic
41C2×#117×C47C2211yescharacteristic
42C22×C42×C47C2211yescharacteristic
43C47×#339C2214yescomplemented
44C24×D47D411yescharacteristic
45C2×#10625350—21no—
46C2×#10625350—21no—
47C2×#10625350—22no—
48C2×#10625350—22no—
49C2×#10625350—22no—
50C2×#10625350—22no—
51C2×#10625350C2×C412yes—
52C2×#10625350C2312yes—
53C22×Dic94C2×C411yescharacteristic
54C22×D188—21no—
55C22×D188—21no—
56C22×D188C2×C411yescharacteristic
57C22×C22⋊D47—21no—
58C23×Dic47—21no—
59C23×Dic47D411yescharacteristic
60C22×C4×D47—22no—
61C22×C4×D47—22no—
62C22×C4×D47—22no—
63C22×C4×D47—22no—
64C22×C4×D47—21no—
65C22×C4×D47C2×C411yescharacteristic
66C22×C4×D47C2×C411yescharacteristic
67C22×C4×D47C2×C412yes—
68C22×C4×D47D412yes—
69C22×C4×D47D411yescharacteristic
70C22×C4×D47D411yescharacteristic
71C22×C4×D47D412yes—
72C22×C4×D47C2312yes—
73C2×#10625329—22no—
74C2×#10625329—21no—
75C2×#10625329D414yescomplemented
76C2×#10625329C2312yes—
77C2×#10625324—28no—
78C2×#10625324—24no—
79M16×D47—216no—
80M16×D47—28no—
81M16×D47—28no—
82C22×C47⋊C8—21no—
83C2×C8×D47—28no—
84C2×C8×D47—24no—
85#13094008—24no—
86#13094008—24no—
87#13094004—22no—
88#13094004—22no—
89#13094004C2×C414yescomplemented
90#13094004C2×C414yescomplemented
91#13093999—22no—
92#13093999—22no—
93#13093999C2×C414yescomplemented
94#13093999C2×C414yescomplemented
95#13093994—24no—
96#13093994—24no—
97C4×D188—24no—
98C4×D188—24no—
99C4×D188—24no—
100C4×D188—24no—
101C2×C4⋊Dic47—21no—
102C2×C4⋊Dic47—21no—
103C2×(C2×D47)⋊C4—28no—
104C2×(C2×D47)⋊C4—21no—
105C2×(C2×D47)⋊C4—21no—
106C2×(C2×D47)⋊C4—24no—
107C2×(C2×D47)⋊C4—21no—
108C2×(C2×D47)⋊C4—21no—
109C2×C4×Dic47—22no—
110C2×C4×Dic47—22no—
111C2×C4×Dic47—21no—
112C2×C4×Dic47C2312yes—
113#13093952—28no—
114#13093950—28no—
115C47⋊#95—24no—
116C23×C4×C47—21no—
117C23×C4×C47C2311yescharacteristic
118C2×M16×C47—22no—
119C2×M16×C47—21no—
120C2×M16×C47D414yescomplemented
121C2×M16×C47C2312yes—
122C22×C8×C47—21no—
123#117×C47—21no—
124#117×C47—21no—
125#117×C47C2×C412yes—
126#117×C47C2312yes—
127C2×C4⋊C4×C47C2×C411yescharacteristic
128C2×C4⋊C4×C47C2×C411yescharacteristic
129C2×C22⋊C4×C47—21no—
130C2×C42×C47—21no—
131C2×C42×C47—22no—
132C2×C42×C47—22no—
133C2×C42×C47—21no—
134C2×C42×C47C2312yes—
135C24×C47C2×D411yescharacteristic
136C23×D47—22no—
137C23×D47—22no—
138C23×D47—24no—
139C23×D47—21no—
140C23×D47—42no—
141C23×D47C22⋊C411yescharacteristic
142C23×D47C22⋊C412yes—
143C23×D47C22⋊C411yescharacteristic
144C23×D47C2×D412yes—
145C22×C4×C47—24no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—22no—
149C22×C4×C47—42no—
150C22×C4×C47—42no—
151C22×C4×C47C22×C411yescharacteristic
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2×D411yescharacteristic
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47C2×D412yes—
157C22×C4×C47C2×D412yes—
158C22×C4×C47#4112yes—
159C22×C4×C47#4112yes—
160C22×C4×C47C2411yescharacteristic
161C2×C22⋊D47—22no—
162C2×C22⋊D47—22no—
163C2×C22⋊D47—42no—
164C2×C22⋊D47—42no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—24no—
168C22×Dic47—21no—
169C22×Dic47—22no—
170C22×Dic47—42no—
171C22×Dic47—42no—
172C22×Dic47C22⋊C411yescharacteristic
173C22×Dic47C22⋊C411yescharacteristic
174C22×Dic47C22⋊C412yes—
175C22×Dic47C2×D412yes—
176#10625350—24no—
177#10625350—24no—
178#10625350—22no—
179#10625350—22no—
180#10625350—22no—
181#10625350—22no—
182#10625350—42no—
183#10625350—42no—
184#10625350—42no—
185#10625350—42no—
186C2×D188—22no—
187C2×D188—22no—
188C2×D188—24no—
189C2×D188—24no—
190C2×D188—21no—
191C2×D188—44no—
192C2×D188—44no—
193C2×D188C22×C412yes—
194C2×C4×D47—22no—
195C2×C4×D47—22no—
196C2×C4×D47—24no—
197C2×C4×D47—22no—
198C2×C4×D47—22no—
199C2×C4×D47—24no—
200C2×C4×D47—22no—
201C2×C4×D47—24no—
202C2×C4×D47—22no—
203C2×C4×D47—24no—
204C2×C4×D47—24no—
205C2×C4×D47—22no—
206C2×C4×D47—22no—
207C2×C4×D47—24no—
208C2×C4×D47—22no—
209C2×C4×D47—22no—
210C2×C4×D47—22no—
211C2×C4×D47—22no—
212C2×C4×D47—22no—
213C2×C4×D47—22no—
214C2×C4×D47—42no—
215C2×C4×D47—42no—
216C2×C4×D47C22⋊C412yes—
217C2×C4×D47C22⋊C412yes—
218C2×C4×D47C22⋊C412yes—
219C2×C4×D47C22⋊C412yes—
220C2×C4×D47C22×C412yes—
221C2×C4×D47C22×C412yes—
222C2×C4×D47C2×D412yes—
223C2×C4×D47C2×D412yes—
224C2×Dic94—22no—
225C2×Dic94—22no—
226C2×Dic94—21no—
227C2×Dic94C22×C412yes—
228M16×C47—24no—
229M16×C47—22no—
230M16×C47C2×D414yescomplemented
231C2×C8×C47—24no—
232C2×C8×C47—22no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47C22×C412yes—
236C4⋊C4×C47C22×C412yes—
237C22⋊C4×C47—22no—
238C22⋊C4×C47—22no—
239C42×C47—22no—
240C42×C47—22no—
241C42×C47—22no—
242C42×C47—22no—
243C42×C47—42no—
244(C2×D47)⋊C4—216no—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4—24no—
247(C2×D47)⋊C4—24no—
248(C2×D47)⋊C4—24no—
249C4⋊Dic47—24no—
250C4⋊Dic47—24no—
251C4×Dic47—22no—
252C4×Dic47—22no—
253C4×Dic47—42no—
254#10625329—24no—
255#10625329—22no—
256#10625329C2×D414yescomplemented
257C2×C47⋊C8—24no—
258C2×C47⋊C8—22no—
259#10625324—216no—
260C8×D47—216no—
261C23×C47—22no—
262C23×C47—22no—
263C23×C47C2×C22⋊C411yescharacteristic
264C23×C47C2×C22⋊C411yescharacteristic
265C23×C47#12112yes—
266C23×C47#12112yes—
267C23×C47C22×D411yescharacteristic
268C22×D47—22no—
269C22×D47—22no—
270C22×D47—22no—
271C22×D47—22no—
272C22×D47—24no—
273C22×D47—22no—
274C22×D47—22no—
275C22×D47—22no—
276C22×D47—24no—
277C22×D47—24no—
278C22×D47—22no—
279C22×D47—42no—
280C22×D47—42no—
281C22×D47—48no—
282C22×D47—48no—
283C22×D47—42no—
284C22×D47—42no—
285C22×D47—42no—
286C22×D47#10414yescomplemented
287C22×D47C2×C22⋊C412yes—
288C22×D47C2×C22⋊C412yes—
289C2×C4×C47—24no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—48no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47C2×C22⋊C411yescharacteristic
298C2×C4×C47C2×C22⋊C411yescharacteristic
299C2×C4×C47C4×D412yes—
300C2×C4×C47C4×D412yes—
301C2×C4×C47C4×D412yes—
302C2×C4×C47C4×D412yes—
303C2×C4×C47#12012yes—
304C2×C4×C47#12012yes—
305C2×C4×C47#12112yes—
306C2×C4×C47#12112yes—
307C2×C4×C47#12312yes—
308C2×C4×C47#12312yes—
309C2×C4×C47C23×C411yescharacteristic
310C2×C4×C47C22×D411yescharacteristic
311C2×C4×C47C22×D411yescharacteristic
312C2×C4×C47C22×D411yescharacteristic
313C2×C4×C47C2×#4111yescharacteristic
314C2×C4×C47C2×#4111yescharacteristic
315C22⋊D47—42no—
316C22⋊D47—42no—
317C22⋊D47—44no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—24no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—24no—
324C2×Dic47—22no—
325C2×Dic47—48no—
326C2×Dic47—42no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47C2×C22⋊C412yes—
330C2×Dic47C2×C22⋊C412yes—
331D188—22no—
332D188—22no—
333D188—48no—
334D188—48no—
335D188—42no—
336C4×D47—22no—
337C4×D47—22no—
338C4×D47—22no—
339C4×D47—22no—
340C4×D47—22no—
341C4×D47—22no—
342C4×D47—22no—
343C4×D47—22no—
344C4×D47—24no—
345C4×D47—24no—
346C4×D47—24no—
347C4×D47—24no—
348C4×D47—42no—
349C4×D47—42no—
350C4×D47—44no—
351Dic94—22no—
352Dic94—22no—
353Dic94—42no—
354C8×C47—24no—
355C47⋊C8—24no—
356C2×#1871—471nomaximal, Sylow
357C22×C47—24no—
358C22×C47—24no—
359C22×C47—21no—
360C22×C47—21no—
361C22×C47—21no—
362C22×C47—21no—
363C22×C47#38612yes—
364C22×C47#38612yes—
365C22×C47C2×#10412yes—
366C22×C47#42112yes—
367C22×C47C22×C22⋊C411yescharacteristic
368C22×C47C2×#12111yescharacteristic
369C22×C47C2×#12111yescharacteristic
370C2×D47—28no—
371C2×D47—22no—
372C2×D47—22no—
373C2×D47—22no—
374C2×D47—22no—
375C2×D47—22no—
376C2×D47—44no—
377C2×D47—44no—
378C2×D47—48no—
379C2×D47—44no—
380C2×D47—42no—
381C2×D47—42no—
382C2×D47—42no—
383C2×D47—84no—
384C2×D47C2×#10414yescomplemented
385C4×C47—44no—
386C4×C47—42no—
387C4×C47—42no—
388C4×C47#38612yes—
389C4×C47#38612yes—
390C4×C47C2×C4×D411yescharacteristic
391C4×C47C2×C4×D411yescharacteristic
392C4×C47C2×#12011yescharacteristic
393C4×C47C2×#12311yescharacteristic
394Dic47—22no—
395Dic47—22no—
396Dic47—44no—
397Dic47—42no—
398C23×M16—471no—
399C2×#525—471no—
400C22×#104—471no—
401C22×#104—471no—
402C2×C4×C22⋊C4—471no—
403#1871—478no—
404C2×#339—471no—
405C2×#339D4711yescharacteristic, complemented
406C2×C47—21no—
407C2×C47—21no—
408C2×C47—22no—
409C2×C47#187114yescomplemented
410C2×C47C2×#38611yescharacteristic
411C2×C47C22×#10411yescharacteristic
412C2×C47C2×#42111yescharacteristic
413D47—24no—
414D47—42no—
415D47—82no—
416C22×#41—471no—
417C24×C4—471no—
418C22×M16—471no—
419C22×M16—474no—
420C22×M16—941no—
421C22×M16—944no—
422C22×M16—942no—
423C22×M16—944no—
424C22×M16C2×D4711yescharacteristic
425C23×C8—941no—
426#525—474no—
427#525—474no—
428#525—942no—
429#525—942no—
430C2×#123—941no—
431C2×C22⋊Q8—471no—
432C2×C22⋊Q8—471no—
433C2×#121—471no—
434C2×#121—471no—
435C2×#120—941no—
436C2×C4×D4—941no—
437C2×C4×D4—941no—
438C2×#117C2×D4711yescharacteristic
439C22×C22⋊C4—941no—
440C22×C42—471no—
441C22×C42C2×D4711yescharacteristic
442C2×#104—474no—
443C2×#104—474no—
444C2×#104—944no—
445C2×#104—944no—
446C4×C22⋊C4—474no—
447C4×C22⋊C4—942no—
448C2×#95—941no—
449#339—474no—
450#339C2×D4714yescomplemented
451C47C2×#187111yescharacteristic, complemented, Sylow
452C25—471no—
453C2×#41—472no—
454C2×#41—472no—
455C2×#41—941no—
456C2×#41—941no—
457C2×#41—942no—
458C2×#41—942no—
459C2×#41—942no—
460C2×#41—942no—
461C22×Q8—471no—
462C22×D4—471no—
463C22×D4—941no—
464C22×D4—941no—
465C22×D4—941no—
466C23×C4—21no—
467C23×C4—471no—
468C23×C4—471no—
469C23×C4—471no—
470C23×C4—472no—
471C23×C4—472no—
472C23×C4—472no—
473C23×C4—471no—
474C23×C4—471no—
475C23×C4—472no—
476C23×C4—942no—
477C23×C4—942no—
478C23×C4—942no—
479C23×C4—942no—
480C23×C4—941no—
481C23×C4—941no—
482C23×C4C22×D4711yescharacteristic
483C2×M16—22no—
484C2×M16—21no—
485C2×M16—474no—
486C2×M16—472no—
487C2×M16—944no—
488C2×M16—948no—
489C2×M16—948no—
490C2×M16—9416no—
491C2×M16—942no—
492C2×M16—941no—
493C2×M16—948no—
494C2×M16D18814yescomplemented
495C2×M16C22×D4712yes—
496C22×C8—21no—
497C22×C8—944no—
498C22×C8—948no—
499C22×C8—941no—
500#123—944no—
501#123—944no—
502C22⋊Q8—474no—
503C22⋊Q8—474no—
504C22⋊Q8—942no—
505C22⋊Q8—942no—
506#121—474no—
507#121—474no—
508#121—942no—
509#121—942no—
510#120—944no—
511#120—944no—
512C4×D4—944no—
513C4×D4—944no—
514C4×D4—944no—
515C4×D4—944no—
516#117—21no—
517#117—21no—
518#117C4×D4712yes—
519#117C22×D4712yes—
520C2×C4⋊C4—941no—
521C2×C4⋊C4—941no—
522C2×C4⋊C4C4×D4711yescharacteristic
523C2×C4⋊C4C4×D4711yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—944no—
528C2×C22⋊C4—941no—
529C2×C22⋊C4—941no—
530C2×C22⋊C4—948no—
531C2×C42—21no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—21no—
535C2×C42—472no—
536C2×C42—942no—
537C2×C42—942no—
538C2×C42—941no—
539C2×C42C22×D4712yes—
540#104—948no—
541#104—948no—
542#95—944no—
543C24—471no—
544C24—471no—
545C24—472no—
546C24—472no—
547C24—944no—
548C24—942no—
549C24—942no—
550C24—941no—
551C24—1882no—
552C24D4×D4711yescharacteristic
553#41—944no—
554#41—944no—
555#41—942no—
556#41—942no—
557#41—942no—
558#41—942no—
559#41—1882no—
560#41—1882no—
561#41—1882no—
562#41—1882no—
563C2×Q8—472no—
564C2×Q8—941no—
565C2×Q8—942no—
566C2×Q8—942no—
567C2×D4—472no—
568C2×D4—944no—
569C2×D4—944no—
570C2×D4—942no—
571C2×D4—942no—
572C2×D4—941no—
573C2×D4—942no—
574C2×D4—942no—
575C2×D4—1884no—
576C2×D4—1884no—
577C2×D4—1882no—
578C2×D4—1882no—
579C22×C4—24no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—471no—
586C22×C4—471no—
587C22×C4—472no—
588C22×C4—472no—
589C22×C4—472no—
590C22×C4—472no—
591C22×C4—472no—
592C22×C4—472no—
593C22×C4—472no—
594C22×C4—472no—
595C22×C4—472no—
596C22×C4—472no—
597C22×C4—942no—
598C22×C4—942no—
599C22×C4—942no—
600C22×C4—942no—
601C22×C4—944no—
602C22×C4—942no—
603C22×C4—942no—
604C22×C4—944no—
605C22×C4—942no—
606C22×C4—944no—
607C22×C4—942no—
608C22×C4—944no—
609C22×C4—944no—
610C22×C4—942no—
611C22×C4—942no—
612C22×C4—944no—
613C22×C4—942no—
614C22×C4—942no—
615C22×C4—942no—
616C22×C4—942no—
617C22×C4—944no—
618C22×C4—941no—
619C22×C4—942no—
620C22×C4—942no—
621C22×C4—942no—
622C22×C4—1882no—
623C22×C4—1882no—
624C22×C4—1882no—
625C22×C4—1882no—
626C22×C4C2×C4×D4711yescharacteristic
627C22×C4C2×C4×D4711yescharacteristic
628C22×C4C2×D18812yes—
629C22×C4#1062535012yes—
630C22×C4D4×D4711yescharacteristic
631C22×C4D4×D4711yescharacteristic
632C22×C4D4×D4712yes—
633C22×C4D4×D4711yescharacteristic
634C22×C4#1062535412yes—
635C22×C4C23×D4711yescharacteristic
636M16—24no—
637M16—22no—
638M16—474no—
639M16—9416no—
640M16—944no—
641M16—942no—
642M16C2×D18814yescomplemented
643C2×C8—24no—
644C2×C8—22no—
645C2×C8—9416no—
646C2×C8—944no—
647C2×C8—942no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—944no—
651C4⋊C4—944no—
652C4⋊C4C2×C4×D4712yes—
653C4⋊C4C2×C4×D4712yes—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—944no—
657C22⋊C4—944no—
658C22⋊C4—944no—
659C22⋊C4—944no—
660C22⋊C4—9416no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—22no—
665C42—42no—
666C42—942no—
667C42—942no—
668C42—1882no—
669C23—22no—
670C23—22no—
671C23—472no—
672C23—474no—
673C23—472no—
674C23—944no—
675C23—944no—
676C23—942no—
677C23—942no—
678C23—944no—
679C23—942no—
680C23—942no—
681C23—942no—
682C23—942no—
683C23—942no—
684C23—942no—
685C23—1882no—
686C23—1882no—
687C23—1888no—
688C23—1888no—
689C23—1882no—
690C23—1882no—
691C23—1882no—
692C23C22⋊C4×D4711yescharacteristic
693C23C22⋊C4×D4711yescharacteristic
694C23#1309399712yes—
695C23#1309399912yes—
696C23C2×D4×D4711yescharacteristic
697Q8—942no—
698Q8—942no—
699Q8—1882no—
700D4—942no—
701D4—942no—
702D4—1888no—
703D4—1888no—
704D4—1884no—
705D4—1882no—
706D4—1882no—
707D4—1882no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—42no—
712C2×C4—48no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—472no—
717C2×C4—472no—
718C2×C4—944no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—944no—
724C2×C4—944no—
725C2×C4—944no—
726C2×C4—944no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—944no—
736C2×C4—942no—
737C2×C4—1882no—
738C2×C4—1888no—
739C2×C4—1882no—
740C2×C4—1882no—
741C2×C4—1884no—
742C2×C4—1882no—
743C2×C4—1882no—
744C2×C4C22⋊C4×D4711yescharacteristic
745C2×C4C22⋊C4×D4711yescharacteristic
746C2×C4#1309398612yes—
747C2×C4#1309398612yes—
748C2×C4C4×D18812yes—
749C2×C4C4×D18812yes—
750C2×C4#1309399412yes—
751C2×C4#1309399412yes—
752C2×C4#1309399712yes—
753C2×C4#1309399912yes—
754C2×C4#1309400912yes—
755C2×C4#1309400912yes—
756C2×C4C22×C4×D4711yescharacteristic
757C2×C4C2×D4×D4711yescharacteristic
758C2×C4C2×D4×D4711yescharacteristic
759C2×C4C22×D18811yescharacteristic
760C2×C4C2×#1062535011yescharacteristic
761C2×C4C2×#1062535411yescharacteristic
762C8—24no—
763C8—944no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—24no—
769C22—24no—
770C22—474no—
771C22—942no—
772C22—942no—
773C22—948no—
774C22—942no—
775C22—942no—
776C22—942no—
777C22—3764no—
778C22—1884no—
779C22—1884no—
780C22—1888no—
781C22—1882no—
782C22—1882no—
783C22—1882no—
784C22—1884no—
785C22#1568900112yes—
786C22#1568900112yes—
787C22#104×D4712yes—
788C22#1568913812yes—
789C22C2×C22⋊C4×D4711yescharacteristic
790C22C2×#1309399711yescharacteristic
791C22C2×#1309399911yescharacteristic
792C4—44no—
793C4—42no—
794C4—42no—
795C4—942no—
796C4—942no—
797C4—1884no—
798C4—1882no—
799C4#1568900112yes—
800C4#1568900112yes—
801C4C2×#1309398611yescharacteristic
802C4C2×C4×D18811yescharacteristic
803C4C2×#1309399411yescharacteristic
804C4C2×#1309400911yescharacteristic
805C2—21no—
806C2—21no—
807C2—22no—
808C2—944no—
809C2—3762no—
810C2—1882no—
811C2#2024368914yesdirect product factor
812C2C2×#1568900111yescharacteristic
813C2C2×#104×D4711yescharacteristic
814C2C2×#1568913811yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#339C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#15689635C2
cosocleC22×C4×C47C24
hypercenterC2×#339D47
hypocenterC47C2×#1871
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
1. C22×M16×D47C2semidirect
3. C22×#13093952C2semidirect
4. C22×#13093950C2semidirect
5. C2×C4×(C2×D47)⋊C4C2semidirect
6. #20243689C2direct (N × H)
7. C2×#15688882C2semidirect
8. C2×C47×#339C2semidirect
16. C2×M16×D47C22semidirect
20. #15689635C4semidirect
23. C2×#13094004C4semidirect
24. C2×#13094004C4semidirect
25. C2×#13093999C4semidirect
26. C2×#13093999C4semidirect
33. C2×#13093952C22semidirect
35. C2×#13093950C22semidirect
37. C4×(C2×D47)⋊C4C22semidirect
39. #15688882C22semidirect
43. C47×#339C22semidirect
75. C2×#10625329D4semidirect
89. #13094004C2×C4semidirect
90. #13094004C2×C4semidirect
93. #13093999C2×C4semidirect
94. #13093999C2×C4semidirect
120. C2×M16×C47D4semidirect
230. M16×C47C2×D4semidirect
256. #10625329C2×D4semidirect
286. C22×D47#104semidirect
384. C2×D47C2×#104semidirect
405. C2×#339D47semidirect
409. C2×C47#1871semidirect
450. #339C2×D47semidirect
451. C47C2×#1871semidirect
494. C2×M16D188semidirect
642. M16C2×D188semidirect
811. C2#20243689direct (N × H)

Maximal subgroups

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

subgroupindex
C22×M16×D472
C2×#156896352
C22×#130939522
C22×#130939502
C2×C4×(C2×D47)⋊C42
#202436892
C2×#156888822
C2×C47×#3392
C2×#187147