Finite Group Databasebeta

← #26225395

Subgroups — #26225395

Order 12032.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689090C211yesmaximal, characteristic, complemented
2#20245980C211yesmaximal, characteristic, complemented
3#20243827C211yesmaximal, characteristic, complemented
4#20243822C211yesmaximal, characteristic, complemented
5#20243817C211yesmaximal, characteristic, complemented
6#20243812C211yesmaximal, characteristic, complemented
7#20243711C211yesmaximal, characteristic, complemented
8#20243706C211yesmaximal, characteristic, complemented
9#20243701C211yesmaximal, characteristic, complemented
10#20243696C211yesmaximal, characteristic, complemented
11#20243478C211yesmaximal, characteristic, complemented
12#20243474C211yesmaximal, characteristic, complemented
13#20243328C211yesmaximal, characteristic, complemented
14#20243328C211yesmaximal, characteristic, complemented
15C2×C47×#537C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20C2×#13093948C2211yescharacteristic
21C2×#13093948C2211yescharacteristic
22C2×#13093948C2211yescharacteristic
23C2×#13093948C2211yescharacteristic
24C2×#13093945C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28#15689090—24no—
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×C22⋊(C47⋊C8)C2211yescharacteristic
31C2×C22⋊(C47⋊C8)C2211yescharacteristic
32C2×C22⋊(C47⋊C8)C2211yescharacteristic
33#15689030—21no—
34#15689026—21no—
35#15689003—21no—
36#15689003—21no—
37#15688983C2211yescharacteristic
38#15688983C2211yescharacteristic
39#15688983C2211yescharacteristic
40#15688983C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49C22×#41×C47C2211yescharacteristic
50C22×#41×C47C2211yescharacteristic
51C47×#537—24no—
52C47×#537C418yescomplemented
53C2×C22⋊Q8×C47—21no—
54C2×C22⋊Q8×C47C2211yescharacteristic
55C2×C22⋊Q8×C47C2211yescharacteristic
56C2×#121×C47—21no—
57C2×#121×C47—21no—
58C2×#121×C47—21no—
59C2×#121×C47C2211yescharacteristic
60C2×#121×C47C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C23×Dic47—21no—
63C2×#10625329—22no—
64C2×#10625329—41no—
65C2×#10625329—41no—
66C22×C47⋊C8—22no—
67C22×C47⋊C8—41no—
68C22×C47⋊C8—41no—
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73#13093983—41no—
74#13093983—41no—
75C2×C4⋊Dic47—21no—
76C2×C4⋊Dic47—41no—
77C2×C4⋊Dic47—41no—
78C2×C4⋊Dic47C2311yescharacteristic
79C2×C4⋊Dic47C2311yescharacteristic
80C2×C4⋊Dic47C2311yescharacteristic
81C2×C4⋊Dic47C2311yescharacteristic
82C2×C22⋊Dic47—21no—
83C2×C22⋊Dic47—21no—
84C2×C22⋊Dic47—21no—
85C2×C22⋊Dic47—21no—
86C2×C22⋊Dic47—21no—
87C2×C4×Dic47—21no—
88#13093948—41no—
89#13093948—41no—
90#13093948—41no—
91#13093948—41no—
92#13093945—41no—
93#13093945—41no—
94#13093945—41no—
95#13093945—41no—
96C22⋊(C47⋊C8)—22no—
97C22⋊(C47⋊C8)—22no—
98C22⋊(C47⋊C8)—22no—
99C22⋊(C47⋊C8)—22no—
100C47⋊#95—21no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C47⋊#95—21no—
104C2×#41×C47—22no—
105C2×#41×C47—41no—
106C2×#41×C47—41no—
107C2×#41×C47—41no—
108C2×#41×C47—41no—
109C2×#41×C47—41no—
110C2×#41×C47—41no—
111C2×#41×C47—41no—
112C2×#41×C47—41no—
113C2×#41×C47C2×C414yes—
114C2×#41×C47C2×C414yescomplemented
115C2×#41×C47D414yes—
116C22×Q8×C47D411yescharacteristic
117C22×Q8×C47C2311yescharacteristic
118C22×D4×C47—21no—
119C22×D4×C47—21no—
120C22×D4×C47—21no—
121C22×D4×C47D411yescharacteristic
122C22×D4×C47D411yescharacteristic
123C22×D4×C47D411yescharacteristic
124C22×D4×C47C2311yescharacteristic
125C23×C4×C47—21no—
126C23×C4×C47—21no—
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C22⋊Q8×C47—28no—
131C22⋊Q8×C47—22no—
132C22⋊Q8×C47—22no—
133C22⋊Q8×C47C2×C414yes—
134C22⋊Q8×C47C2×C414yescomplemented
135#121×C47—28no—
136#121×C47—28no—
137#121×C47—28no—
138#121×C47—22no—
139#121×C47—22no—
140#121×C47C2×C414yes—
141#121×C47C2×C414yescomplemented
142C2×C4⋊C4×C47—21no—
143C2×C4⋊C4×C47—22no—
144C2×C4⋊C4×C47—21no—
145C2×C4⋊C4×C47—21no—
146C2×C4⋊C4×C47C2×C414yescomplemented
147C2×C4⋊C4×C47C2311yescharacteristic
148C2×C4⋊C4×C47C2311yescharacteristic
149C2×C22⋊C4×C47—21no—
150C2×C22⋊C4×C47—21no—
151C2×C22⋊C4×C47—21no—
152C2×C22⋊C4×C47—21no—
153C24×C47—21no—
154C24×C47C2×D411yescharacteristic
155C24×C47C2×D411yescharacteristic
156C24×C47C2×D411yescharacteristic
157#41×C47—44no—
158#41×C47—44no—
159#41×C47—44no—
160#41×C47—44no—
161#41×C47—44no—
162#41×C47—44no—
163#41×C47—44no—
164#41×C47—44no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×Q8×C47—21no—
169C2×Q8×C47—21no—
170C2×Q8×C47—41no—
171C2×Q8×C47—41no—
172C2×Q8×C47C22⋊C414yes—
173C2×Q8×C47C22×C412yes—
174C2×D4×C47—24no—
175C2×D4×C47—24no—
176C2×D4×C47—24no—
177C2×D4×C47—21no—
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—21no—
182C2×D4×C47—41no—
183C2×D4×C47—41no—
184C2×D4×C47—41no—
185C2×D4×C47—41no—
186C2×D4×C47—41no—
187C2×D4×C47—41no—
188C2×D4×C47—42no—
189C2×D4×C47—42no—
190C2×D4×C47—81no—
191C2×D4×C47—81no—
192C2×D4×C47—81no—
193C2×D4×C47—81no—
194C2×D4×C47C22⋊C414yes—
195C2×D4×C47C22⋊C414yes—
196C2×D4×C47C22⋊C414yes—
197C2×D4×C47C22×C412yes—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—24no—
214C22×C4×C47—24no—
215C22×C4×C47—42no—
216C22×C4×C47—42no—
217C22×C4×C47—81no—
218C22×C4×C47—81no—
219C22×C4×C47C22×C412yes—
220C22×C4×C47C22×C412yes—
221C22×C4×C47C22×C412yes—
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2×D412yes—
226C22×C4×C47C2×D412yes—
227C22×C4×C47C2×D412yes—
228C22×C4×C47C2411yescharacteristic
229C22×Dic47—21no—
230C22×Dic47—21no—
231C22×Dic47—21no—
232C22×Dic47—21no—
233C22×Dic47—42no—
234C22×Dic47—81no—
235C22×Dic47—81no—
236C4⋊C4×C47—24no—
237C4⋊C4×C47—24no—
238C4⋊C4×C47—24no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47C22×C412yes—
242C4⋊C4×C47C22×C412yes—
243C22⋊C4×C47—24no—
244C22⋊C4×C47—24no—
245C22⋊C4×C47—24no—
246C22⋊C4×C47—24no—
247C22⋊Dic47—42no—
248C22⋊Dic47—81no—
249C22⋊Dic47—81no—
250C22⋊Dic47—81no—
251C22⋊Dic47—81no—
252C4⋊Dic47—21no—
253C4⋊Dic47—21no—
254C4⋊Dic47—21no—
255C4⋊Dic47—21no—
256C4⋊Dic47—21no—
257C4⋊Dic47—21no—
258C4⋊Dic47—21no—
259C4⋊Dic47—21no—
260C4⋊Dic47—42no—
261C4×Dic47—42no—
262#10625329—44no—
263C2×C47⋊C8—21no—
264C2×C47⋊C8—21no—
265C2×C47⋊C8—21no—
266C2×C47⋊C8—21no—
267C2×C47⋊C8—21no—
268C2×C47⋊C8—21no—
269C2×C47⋊C8—21no—
270C2×C47⋊C8—21no—
271C2×C47⋊C8—21no—
272C2×C47⋊C8—21no—
273C2×C47⋊C8—21no—
274C2×C47⋊C8—21no—
275C2×C47⋊C8—44no—
276C23×C47—21no—
277C23×C47—21no—
278C23×C47—21no—
279C23×C47—21no—
280C23×C47—21no—
281C23×C47—21no—
282C23×C47—21no—
283C23×C47—21no—
284C23×C47—21no—
285C23×C47—21no—
286C23×C47—21no—
287C23×C47—21no—
288C23×C47—21no—
289C23×C47—21no—
290C23×C47—21no—
291C23×C47—21no—
292C23×C47—21no—
293C23×C47—21no—
294C23×C47—22no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—41no—
298C23×C47—41no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47C2×C22⋊C412yes—
302C23×C47C2×C22⋊C412yes—
303C23×C47C2×C22⋊C412yes—
304C23×C47C22×D411yescharacteristic
305Q8×C47—22no—
306Q8×C47—22no—
307Q8×C47—44no—
308Q8×C47—41no—
309Q8×C47—41no—
310D4×C47—22no—
311D4×C47—22no—
312D4×C47—44no—
313D4×C47—44no—
314D4×C47—44no—
315D4×C47—48no—
316D4×C47—41no—
317D4×C47—41no—
318D4×C47—84no—
319D4×C47—84no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
324C2×C4×C47—21no—
325C2×C4×C47—21no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—48no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—84no—
349C2×C4×C47C2×C22⋊C412yes—
350C2×C4×C47C2×C22⋊C412yes—
351C2×C4×C47C2×C22⋊C412yes—
352C2×C4×C47C23×C411yescharacteristic
353C2×C4×C47C22×D411yescharacteristic
354C2×C4×C47H(5,𝔽2)11yescharacteristic
355C2×C4×C47H(5,𝔽2)11yescharacteristic
356C2×C4×C47H(5,𝔽2)11yescharacteristic
357C2×C4×C47H(5,𝔽2)11yescharacteristic
358C2×Dic47—41no—
359C2×Dic47—41no—
360C2×Dic47—41no—
361C2×Dic47—41no—
362C2×Dic47—41no—
363C2×Dic47—41no—
364C2×Dic47—41no—
365C2×Dic47—41no—
366C2×Dic47—41no—
367C2×Dic47—41no—
368C2×Dic47—41no—
369C2×Dic47—41no—
370C2×Dic47—84no—
371C47⋊C8—41no—
372C47⋊C8—41no—
373C47⋊C8—41no—
374C47⋊C8—41no—
375#21772—471nomaximal, Sylow
376C22×C47—22no—
377C22×C47—22no—
378C22×C47—22no—
379C22×C47—22no—
380C22×C47—22no—
381C22×C47—22no—
382C22×C47—22no—
383C22×C47—22no—
384C22×C47—22no—
385C22×C47—41no—
386C22×C47—41no—
387C22×C47—41no—
388C22×C47—41no—
389C22×C47—41no—
390C22×C47—41no—
391C22×C47—41no—
392C22×C47—41no—
393C22×C47—41no—
394C22×C47—41no—
395C22×C47—41no—
396C22×C47—41no—
397C22×C47—42no—
398C22×C47—42no—
399C22×C47—42no—
400C22×C47—81no—
401C22×C47—81no—
402C22×C47—81no—
403C22×C47—81no—
404C22×C47C22×C22⋊C411yescharacteristic
405C22×C47#53411yescharacteristic
406C22×C47#53411yescharacteristic
407C22×C47#57611yescharacteristic
408C22×C47#57711yescharacteristic
409C22×C47#57711yescharacteristic
410C22×C47#57811yescharacteristic
411C4×C47—22no—
412C4×C47—22no—
413C4×C47—22no—
414C4×C47—42no—
415C4×C47—42no—
416C4×C47—42no—
417C4×C47#51811yescharacteristic
418C4×C47#51811yescharacteristic
419C4×C47#53411yescharacteristic
420C4×C47#53411yescharacteristic
421Dic47—81no—
422Dic47—81no—
423Dic47—81no—
424Dic47—81no—
425C2×#537D4711yescharacteristic
426C2×#408—471no—
427#2311—471no—
428#1895—471no—
429#1894—471no—
430#1893—471no—
431#1892—471no—
432#1875—471no—
433#1874—471no—
434#1873—471no—
435#1872—471no—
436#1824—471no—
437#1823—471no—
438#1788—471no—
439#1788—471no—
440C2×C47—42no—
441C2×C47—42no—
442C2×C47—42no—
443C2×C47—82no—
444C2×C47#230811yescharacteristic
445C2×C47#289711yescharacteristic
446C2×C47#289811yescharacteristic
447C2×C47#319811yescharacteristic
448C2×C47#320111yescharacteristic
449C2×C47#320311yescharacteristic
450C2×C47#320411yescharacteristic
451C22×#41C2×D4711yescharacteristic
452C22×#41C2×D4711yescharacteristic
453C22×M16—471no—
454C23×C8—471no—
455#537—24no—
456#537Dic4718yescomplemented
457C2×C22⋊Q8—21no—
458C2×C22⋊Q8C2×D4711yescharacteristic
459C2×C22⋊Q8C2×D4711yescharacteristic
460C2×#121—21no—
461C2×#121—21no—
462C2×#121—21no—
463C2×#121C2×D4711yescharacteristic
464C2×#121C2×D4711yescharacteristic
465C2×#117—471no—
466C22×C4⋊C4—471no—
467C22×C4⋊C4C2×D4711yescharacteristic
468C2×#103—471no—
469C2×#103—471no—
470C2×#103—471no—
471C2×#103—471no—
472C2×#102—471no—
473C2×#102—471no—
474C2×#102—471no—
475C2×#102—471no—
476#408—944no—
477C2×C22⋊C8—471no—
478C2×C22⋊C8—471no—
479C2×C22⋊C8—471no—
480C2×C22⋊C8—471no—
481#391—941no—
482#390—941no—
483#386—941no—
484#386—941no—
485#380—471no—
486#380—471no—
487#380—471no—
488#380—471no—
489#340—471no—
490#340—471no—
491#340—471no—
492#340—471no—
493#340—471no—
494#340—471no—
495#340—471no—
496#340—471no—
497C47#2177211yescharacteristic, complemented, Sylow
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41C2×Dic4714yes—
508C2×#41C2×Dic4714yescomplemented
509C2×#41C22⋊D4714yes—
510C22×Q8C22⋊D4711yescharacteristic
511C22×Q8C22×D4711yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4C22⋊D4711yescharacteristic
516C22×D4C22⋊D4711yescharacteristic
517C22×D4C22⋊D4711yescharacteristic
518C22×D4C22×D4711yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—941no—
522C23×C4C22×D4711yescharacteristic
523C23×C4C22×D4711yescharacteristic
524C23×C4C22×D4711yescharacteristic
525C2×M16—942no—
526C2×M16—1881no—
527C2×M16—1881no—
528C22×C8—471no—
529C22×C8—471no—
530C22×C8—471no—
531C22×C8—471no—
532C22×C8—942no—
533C22×C8—1881no—
534C22×C8—1881no—
535C22⋊Q8—28no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8C2×Dic4714yes—
539C22⋊Q8C2×Dic4714yescomplemented
540#121—28no—
541#121—28no—
542#121—28no—
543#121—22no—
544#121—22no—
545#121C2×Dic4714yes—
546#121C2×Dic4714yescomplemented
547#117—1881no—
548#117—1881no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—471no—
554C2×C4⋊C4—471no—
555C2×C4⋊C4—471no—
556C2×C4⋊C4—471no—
557C2×C4⋊C4—941no—
558C2×C4⋊C4—1881no—
559C2×C4⋊C4—1881no—
560C2×C4⋊C4C2×Dic4714yescomplemented
561C2×C4⋊C4C22×D4711yescharacteristic
562C2×C4⋊C4C22×D4711yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—941no—
568C2×C22⋊C4—941no—
569C2×C22⋊C4—941no—
570C2×C22⋊C4—941no—
571C2×C22⋊C4—941no—
572C2×C42—941no—
573#103—1881no—
574#103—1881no—
575#103—1881no—
576#103—1881no—
577#102—1881no—
578#102—1881no—
579#102—1881no—
580#102—1881no—
581C22⋊C8—942no—
582C22⋊C8—942no—
583C22⋊C8—942no—
584C22⋊C8—942no—
585#95—941no—
586#95—941no—
587#95—941no—
588#95—941no—
589C24—21no—
590C24C2×C22⋊D4711yescharacteristic
591C24C2×C22⋊D4711yescharacteristic
592C24C2×C22⋊D4711yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—41no—
607C2×Q8—41no—
608C2×Q8C22⋊Dic4714yes—
609C2×Q8C22×Dic4712yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4C22⋊Dic4714yes—
631C2×D4C22⋊Dic4714yes—
632C2×D4C22⋊Dic4714yes—
633C2×D4C22×Dic4712yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—81no—
654C22×C4—81no—
655C22×C4—941no—
656C22×C4—941no—
657C22×C4—941no—
658C22×C4—941no—
659C22×C4—3761no—
660C22×C4—3761no—
661C22×C4—1882no—
662C22×C4C22×Dic4712yes—
663C22×C4C22×Dic4712yes—
664C22×C4C22×Dic4712yes—
665C22×C4C2×C22⋊D4711yescharacteristic
666C22×C4C2×C22⋊D4711yescharacteristic
667C22×C4C2×C22⋊D4711yescharacteristic
668C22×C4C2×C22⋊D4712yes—
669C22×C4C2×C22⋊D4712yes—
670C22×C4C2×C22⋊D4712yes—
671C22×C4C23×D4711yescharacteristic
672M16—1884no—
673C2×C8—941no—
674C2×C8—941no—
675C2×C8—941no—
676C2×C8—941no—
677C2×C8—941no—
678C2×C8—941no—
679C2×C8—941no—
680C2×C8—941no—
681C2×C8—941no—
682C2×C8—941no—
683C2×C8—941no—
684C2×C8—941no—
685C2×C8—1884no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—941no—
692C4⋊C4—941no—
693C4⋊C4—941no—
694C4⋊C4—941no—
695C4⋊C4—941no—
696C4⋊C4—941no—
697C4⋊C4—941no—
698C4⋊C4—941no—
699C4⋊C4—1882no—
700C4⋊C4C22×Dic4712yes—
701C4⋊C4C22×Dic4712yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—3761no—
707C22⋊C4—3761no—
708C22⋊C4—3761no—
709C22⋊C4—3761no—
710C22⋊C4—1882no—
711C42—1882no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×C22⋊Dic4712yes—
738C23C2×C22⋊Dic4712yes—
739C23C2×C22⋊Dic4712yes—
740C23C22×C22⋊D4711yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—44no—
744Q8—41no—
745Q8—41no—
746D4—22no—
747D4—22no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—48no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—84no—
785C2×C4—3764no—
786C2×C4—1881no—
787C2×C4—1881no—
788C2×C4—1881no—
789C2×C4—1881no—
790C2×C4—1881no—
791C2×C4—1881no—
792C2×C4—1881no—
793C2×C4—1881no—
794C2×C4—1881no—
795C2×C4—1881no—
796C2×C4—1881no—
797C2×C4—1881no—
798C2×C4C2×C22⋊Dic4712yes—
799C2×C4C2×C22⋊Dic4712yes—
800C2×C4C2×C22⋊Dic4712yes—
801C2×C4C23×Dic4711yescharacteristic
802C2×C4C22×C22⋊D4711yescharacteristic
803C2×C4#1309406911yescharacteristic
804C2×C4#1309406911yescharacteristic
805C2×C4#1309406911yescharacteristic
806C2×C4#1309406911yescharacteristic
807C8—1881no—
808C8—1881no—
809C8—1881no—
810C8—1881no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C22×C22⋊Dic4711yescharacteristic
840C22#1568968211yescharacteristic
841C22#1568968211yescharacteristic
842C22#1568992611yescharacteristic
843C22#1568993111yescharacteristic
844C22#1568993411yescharacteristic
845C22#1568993811yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—3761no—
853C4—3761no—
854C4—3761no—
855C4—3761no—
856C4#1568959811yescharacteristic
857C4#1568959811yescharacteristic
858C4#1568968211yescharacteristic
859C4#1568968211yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—82no—
864C2#2024596611yescharacteristic
865C2#2025191411yescharacteristic
866C2#2025192111yescharacteristic
867C2#2025423411yescharacteristic
868C2#2025426411yescharacteristic
869C2#2025428511yescharacteristic
870C2#2025429411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×C47×#537C2
socleC23×C47C22×D4
cosocleC22×C4×C47C24
hypercenterC2×#537D47
hypocenterC47#21772
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#15689090C2semidirect
2. #20245980C2semidirect
3. #20243827C2semidirect
4. #20243822C2semidirect
5. #20243817C2semidirect
6. #20243812C2semidirect
7. #20243711C2semidirect
8. #20243706C2semidirect
9. #20243701C2semidirect
10. #20243696C2semidirect
11. #20243478C2semidirect
12. #20243474C2semidirect
13. #20243328C2semidirect
14. #20243328C2semidirect
52. C47×#537C4semidirect
114. C2×#41×C47C2×C4semidirect
134. C22⋊Q8×C47C2×C4semidirect
141. #121×C47C2×C4semidirect
146. C2×C4⋊C4×C47C2×C4semidirect
456. #537Dic47semidirect
497. C47#21772semidirect
508. C2×#41C2×Dic47semidirect
539. C22⋊Q8C2×Dic47semidirect
546. #121C2×Dic47semidirect
560. C2×C4⋊C4C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156890902
#202459802
#202438272
#202438222
#202438172
#202438122
#202437112
#202437062
#202437012
#202436962
#202434782
#202434742
#202433282
C2×C47×#5372
#2177247