Finite Group Databasebeta

← #26231803

Subgroups — #26231803

Order 12032.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689195C211yesmaximal, characteristic, complemented
2C2×#15689124C211yesmaximal, characteristic, complemented
3C2×#15689119C211yesmaximal, characteristic, complemented
4#20246317C211yesmaximal, characteristic, complemented
5#20244316C211yesmaximal, characteristic, complemented
6#20244213C211yesmaximal, characteristic, complemented
7#20243827C211yesmaximal, characteristic, complemented
8#20243817C211yesmaximal, characteristic, complemented
9#20243711C211yesmaximal, characteristic, complemented
10#20243706C211yesmaximal, characteristic, complemented
11#20243403C211yesmaximal, characteristic, complemented
12#20243328C211yesmaximal, characteristic, complemented
13#20243328C211yesmaximal, characteristic, complemented
14#20243218C211yesmaximal, characteristic, complemented
15C2×C47×#550C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20#15689195—24no—
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22#15689124—24no—
23#15689119—24no—
24C2×#13093948C2211yescharacteristic
25C2×#13093948C2211yescharacteristic
26C2×#13093948C2211yescharacteristic
27C2×#13093948C2211yescharacteristic
28C2×#13093945C2211yescharacteristic
29C2×#13093945C2211yescharacteristic
30C2×#13093945C2211yescharacteristic
31C2×#13093945C2211yescharacteristic
32C2×#13093945C2211yescharacteristic
33C2×#13093945C2211yescharacteristic
34C2×#13093945C2211yescharacteristic
35C2×#13093945C2211yescharacteristic
36C2×C22⋊(C47⋊C8)C2211yescharacteristic
37C2×C22⋊(C47⋊C8)C2211yescharacteristic
38C2×#13093935C2211yescharacteristic
39#15689016—21no—
40#15689009—21no—
41#15689003—21no—
42#15688989C2211yescharacteristic
43#15688983C2211yescharacteristic
44#15688983C2211yescharacteristic
45C4×C4⋊Dic47C2211yescharacteristic
46C22⋊C4×Dic47—21no—
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51C22×#41×C47C2211yescharacteristic
52C22×#41×C47C2211yescharacteristic
53C47×#550—24no—
54C47×#550C418yescomplemented
55C2×#127×C47—21no—
56C2×#127×C47C2211yescharacteristic
57C2×#121×C47—21no—
58C2×#121×C47—21no—
59C2×#121×C47C2211yescharacteristic
60C2×#121×C47C2211yescharacteristic
61C2×C4×Q8×C47C2211yescharacteristic
62C2×C4×D4×C47—21no—
63C2×C4×D4×C47C2211yescharacteristic
64C23×Dic47—21no—
65C2×#10625329—22no—
66C2×#10625329—22no—
67C2×#10625329—41no—
68C22×C47⋊C8—22no—
69C22×C47⋊C8—22no—
70C22×C47⋊C8—41no—
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75#13093983—22no—
76#13093983—41no—
77C2×C4⋊Dic47—22no—
78C2×C4⋊Dic47—21no—
79C2×C4⋊Dic47—41no—
80C2×C4⋊Dic47C2311yescharacteristic
81C2×C4⋊Dic47C2311yescharacteristic
82C2×C4⋊Dic47C2311yescharacteristic
83C2×C4⋊Dic47C2311yescharacteristic
84C2×C22⋊Dic47—21no—
85C2×C22⋊Dic47—21no—
86C2×C22⋊Dic47—21no—
87C2×C4×Dic47—21no—
88C2×C4×Dic47—21no—
89C4⋊(C47⋊C8)—22no—
90#13093948—22no—
91#13093948—22no—
92#13093948—22no—
93#13093948D414yescomplemented
94#13093945—22no—
95#13093945—22no—
96#13093945—22no—
97#13093945—22no—
98#13093945—41no—
99#13093945—41no—
100#13093945—41no—
101#13093945—41no—
102C22⋊(C47⋊C8)—22no—
103C22⋊(C47⋊C8)—22no—
104#13093935—22no—
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C2×#41×C47—22no—
111C2×#41×C47—22no—
112C2×#41×C47—22no—
113C2×#41×C47—22no—
114C2×#41×C47—22no—
115C2×#41×C47—22no—
116C2×#41×C47—41no—
117C2×#41×C47—41no—
118C2×#41×C47—41no—
119C2×#41×C47—41no—
120C2×#41×C47C2×C414yes—
121C2×#41×C47C2×C414yescomplemented
122C22×Q8×C47C2311yescharacteristic
123C22×D4×C47—21no—
124C22×D4×C47—21no—
125C22×D4×C47—21no—
126C22×D4×C47—21no—
127C22×D4×C47—21no—
128C22×D4×C47—21no—
129C22×D4×C47D411yescharacteristic
130C22×D4×C47C2311yescharacteristic
131C22×D4×C47C2311yescharacteristic
132C23×C4×C47—21no—
133C23×C4×C47—21no—
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136#127×C47—28no—
137#127×C47—22no—
138#127×C47C2×C414yescomplemented
139#121×C47—22no—
140#121×C47—22no—
141#121×C47—28no—
142#121×C47—28no—
143#121×C47C2×C414yes—
144#121×C47C2×C414yescomplemented
145C4×Q8×C47—22no—
146C4×Q8×C47C2×C414yescomplemented
147C4×D4×C47—28no—
148C4×D4×C47C2×C414yes—
149C4×D4×C47D414yes—
150C2×C4⋊C4×C47—21no—
151C2×C4⋊C4×C47D411yescharacteristic
152C2×C4⋊C4×C47C2311yescharacteristic
153C2×C22⋊C4×C47—21no—
154C2×C22⋊C4×C47—21no—
155C2×C22⋊C4×C47D411yescharacteristic
156C2×C22⋊C4×C47D411yescharacteristic
157C2×C42×C47—21no—
158C2×C42×C47C2311yescharacteristic
159C24×C47—21no—
160C24×C47—21no—
161C24×C47C2×D411yescharacteristic
162C24×C47C2×D411yescharacteristic
163#41×C47—28no—
164#41×C47—28no—
165#41×C47—44no—
166#41×C47—44no—
167#41×C47—44no—
168#41×C47—44no—
169#41×C47—44no—
170#41×C47—44no—
171C2×Q8×C47—21no—
172C2×Q8×C47—21no—
173C2×Q8×C47—21no—
174C2×Q8×C47C22×C412yes—
175C2×Q8×C47C2×D412yes—
176C2×Q8×C47#4112yes—
177C2×D4×C47—24no—
178C2×D4×C47—24no—
179C2×D4×C47—24no—
180C2×D4×C47—24no—
181C2×D4×C47—24no—
182C2×D4×C47—24no—
183C2×D4×C47—21no—
184C2×D4×C47—21no—
185C2×D4×C47—21no—
186C2×D4×C47—21no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—21no—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—21no—
193C2×D4×C47—41no—
194C2×D4×C47—41no—
195C2×D4×C47—42no—
196C2×D4×C47—42no—
197C2×D4×C47—42no—
198C2×D4×C47—42no—
199C2×D4×C47—42no—
200C2×D4×C47—42no—
201C2×D4×C47—81no—
202C2×D4×C47—81no—
203C2×D4×C47—81no—
204C2×D4×C47—81no—
205C2×D4×C47—81no—
206C2×D4×C47—81no—
207C2×D4×C47C22⋊C414yes—
208C2×D4×C47C22×C412yes—
209C2×D4×C47C22×C412yes—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—24no—
221C22×C4×C47—24no—
222C22×C4×C47—42no—
223C22×C4×C47—42no—
224C22×C4×C47—42no—
225C22×C4×C47—42no—
226C22×C4×C47C22×C412yes—
227C22×C4×C47C22×C412yes—
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2×D411yescharacteristic
230C22×C4×C47C2×D411yescharacteristic
231C22×C4×C47C2×D411yescharacteristic
232C22×C4×C47C2×D412yes—
233C22×C4×C47C2×D412yes—
234C22×C4×C47C2411yescharacteristic
235C22×Dic47—21no—
236C22×Dic47—21no—
237C22×Dic47—21no—
238C22×Dic47—21no—
239C22×Dic47—42no—
240C22×Dic47—42no—
241C22×Dic47—81no—
242C4⋊C4×C47—24no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47C22⋊C414yes—
245C4⋊C4×C47C22×C412yes—
246C22⋊C4×C47—24no—
247C22⋊C4×C47—24no—
248C22⋊C4×C47C22⋊C414yes—
249C22⋊C4×C47C22⋊C414yes—
250C42×C47—24no—
251C42×C47C22×C412yes—
252C42×C47C2×D412yes—
253C22⋊Dic47—42no—
254C22⋊Dic47—42no—
255C22⋊Dic47—81no—
256C4⋊Dic47—21no—
257C4⋊Dic47—21no—
258C4⋊Dic47—21no—
259C4⋊Dic47—21no—
260C4⋊Dic47—21no—
261C4⋊Dic47—21no—
262C4⋊Dic47—21no—
263C4⋊Dic47—42no—
264C4⋊Dic47C2×D412yes—
265C4×Dic47—42no—
266C4×Dic47—81no—
267#10625329—44no—
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—21no—
276C2×C47⋊C8—21no—
277C2×C47⋊C8—21no—
278C2×C47⋊C8—21no—
279C2×C47⋊C8—44no—
280C2×C47⋊C8C2×D412yes—
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—22no—
294C23×C47—22no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—41no—
298C23×C47—41no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47C2×C22⋊C412yes—
308C23×C47C2×C22⋊C412yes—
309C23×C47C22×D411yescharacteristic
310Q8×C47—22no—
311Q8×C47—22no—
312Q8×C47—22no—
313Q8×C47C4×D414yes—
314D4×C47—22no—
315D4×C47—22no—
316D4×C47—22no—
317D4×C47—22no—
318D4×C47—44no—
319D4×C47—48no—
320D4×C47—48no—
321D4×C47—48no—
322D4×C47—41no—
323D4×C47—41no—
324D4×C47—41no—
325D4×C47—41no—
326D4×C47—84no—
327D4×C47—84no—
328D4×C47—84no—
329C2×C4×C47—22no—
330C2×C4×C47—21no—
331C2×C4×C47—21no—
332C2×C4×C47—22no—
333C2×C4×C47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—22no—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—21no—
339C2×C4×C47—21no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—48no—
350C2×C4×C47—48no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47C2×C22⋊C412yes—
354C2×C4×C47C2×C22⋊C412yes—
355C2×C4×C47C2×C22⋊C412yes—
356C2×C4×C47C2×C22⋊C412yes—
357C2×C4×C47C23×C411yescharacteristic
358C2×C4×C47C22×D411yescharacteristic
359C2×C4×C47C22×D411yescharacteristic
360C2×C4×C47C2×#4111yescharacteristic
361C2×C4×C47H(5,𝔽2)11yescharacteristic
362C2×C4×C47H(5,𝔽2)11yescharacteristic
363C2×Dic47—22no—
364C2×Dic47—41no—
365C2×Dic47—41no—
366C2×Dic47—41no—
367C2×Dic47—41no—
368C2×Dic47—41no—
369C2×Dic47—41no—
370C2×Dic47—41no—
371C2×Dic47—41no—
372C2×Dic47—41no—
373C2×Dic47—41no—
374C2×Dic47—41no—
375C2×Dic47—84no—
376C47⋊C8—22no—
377C47⋊C8—41no—
378C47⋊C8—41no—
379C47⋊C8—41no—
380#22422—471nomaximal, Sylow
381C22×C47—22no—
382C22×C47—22no—
383C22×C47—22no—
384C22×C47—22no—
385C22×C47—22no—
386C22×C47—22no—
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—42no—
396C22×C47—42no—
397C22×C47—42no—
398C22×C47—42no—
399C22×C47—42no—
400C22×C47—42no—
401C22×C47—81no—
402C22×C47—81no—
403C22×C47—81no—
404C22×C47—81no—
405C22×C47—81no—
406C22×C47—81no—
407C22×C47—81no—
408C22×C47—81no—
409C22×C47C22×C22⋊C411yescharacteristic
410C22×C47D4211yescharacteristic
411C22×C47#54611yescharacteristic
412C22×C47#57511yescharacteristic
413C22×C47#57511yescharacteristic
414C22×C47#57611yescharacteristic
415C22×C47#57711yescharacteristic
416C4×C47—22no—
417C4×C47—22no—
418C4×C47—24no—
419C4×C47—22no—
420C4×C47—22no—
421C4×C47—42no—
422C4×C47C2×C4×D411yescharacteristic
423C4×C47#51811yescharacteristic
424C4×C47D4211yescharacteristic
425C4×C47#54611yescharacteristic
426Dic47—42no—
427Dic47—81no—
428Dic47—81no—
429Dic47—81no—
430C2×#550D4711yescharacteristic
431C2×#435—471no—
432C2×#417—471no—
433C2×#416—471no—
434#2352—471no—
435#1982—471no—
436#1961—471no—
437#1895—471no—
438#1893—471no—
439#1875—471no—
440#1874—471no—
441#1805—471no—
442#1788—471no—
443#1788—471no—
444#1763—471no—
445C2×C47—42no—
446C2×C47—42no—
447C2×C47—82no—
448C2×C47—82no—
449C2×C47D4×C22⋊C411yescharacteristic
450C2×C47#289611yescharacteristic
451C2×C47#289711yescharacteristic
452C2×C47#326811yescharacteristic
453C2×C47#327111yescharacteristic
454C2×C47#330911yescharacteristic
455C2×C47#331711yescharacteristic
456C22×#41C2×D4711yescharacteristic
457C22×#41C2×D4711yescharacteristic
458C22×M16—471no—
459C23×C8—471no—
460#550—24no—
461#550Dic4718yescomplemented
462C2×#127—21no—
463C2×#127C2×D4711yescharacteristic
464C2×#121—21no—
465C2×#121—21no—
466C2×#121C2×D4711yescharacteristic
467C2×#121C2×D4711yescharacteristic
468C2×C4×Q8C2×D4711yescharacteristic
469C2×C4×D4—21no—
470C2×C4×D4C2×D4711yescharacteristic
471C2×#117—471no—
472C22×C4⋊C4—471no—
473#435—944no—
474C2×C4⋊C8—471no—
475#417—944no—
476#416—944no—
477C2×#103—471no—
478C2×#103—471no—
479C2×#103—471no—
480C2×#103—471no—
481C2×#102—471no—
482C2×#102—471no—
483C2×#102—471no—
484C2×#102—471no—
485C2×#102—471no—
486C2×#102—471no—
487C2×#102—471no—
488C2×#102—471no—
489C2×C22⋊C8—471no—
490C2×C22⋊C8—471no—
491C2×#97—471no—
492#388—941no—
493#387—941no—
494#386—941no—
495#382—471no—
496#380—471no—
497#380—471no—
498C4×C4⋊C4—471no—
499C4×C22⋊C4—941no—
500#340—471no—
501#340—471no—
502#340—471no—
503#340—471no—
504C47#2242211yescharacteristic, complemented, Sylow
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×Dic4714yes—
516C2×#41C2×Dic4714yescomplemented
517C22×Q8C22×D4711yescharacteristic
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4C22⋊D4711yescharacteristic
525C22×D4C22×D4711yescharacteristic
526C22×D4C22×D4711yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—941no—
530C23×C4C22×D4711yescharacteristic
531C23×C4C22×D4711yescharacteristic
532C2×M16—942no—
533C2×M16—942no—
534C2×M16—1881no—
535C22×C8—471no—
536C22×C8—471no—
537C22×C8—471no—
538C22×C8—471no—
539C22×C8—942no—
540C22×C8—942no—
541C22×C8—1881no—
542#127—28no—
543#127—22no—
544#127C2×Dic4714yescomplemented
545#121—22no—
546#121—22no—
547#121—28no—
548#121—28no—
549#121C2×Dic4714yes—
550#121C2×Dic4714yescomplemented
551C4×Q8—22no—
552C4×Q8C2×Dic4714yescomplemented
553C4×D4—28no—
554C4×D4C2×Dic4714yes—
555C4×D4C22⋊D4714yes—
556#117—942no—
557#117—1881no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—471no—
560C2×C4⋊C4—471no—
561C2×C4⋊C4—471no—
562C2×C4⋊C4—471no—
563C2×C4⋊C4—942no—
564C2×C4⋊C4—941no—
565C2×C4⋊C4—1881no—
566C2×C4⋊C4C22⋊D4711yescharacteristic
567C2×C4⋊C4C22×D4711yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—941no—
571C2×C22⋊C4—941no—
572C2×C22⋊C4—941no—
573C2×C22⋊C4C22⋊D4711yescharacteristic
574C2×C22⋊C4C22⋊D4711yescharacteristic
575C2×C42—21no—
576C2×C42—941no—
577C2×C42—941no—
578C2×C42C22×D4711yescharacteristic
579C4⋊C8—942no—
580#103—474no—
581#103—942no—
582#103—942no—
583#103—942no—
584#102—942no—
585#102—942no—
586#102—942no—
587#102—942no—
588#102—1881no—
589#102—1881no—
590#102—1881no—
591#102—1881no—
592C22⋊C8—942no—
593C22⋊C8—942no—
594#97—942no—
595#95—941no—
596#95—941no—
597#95—941no—
598#95—941no—
599#95—941no—
600C24—21no—
601C24—21no—
602C24C2×C22⋊D4711yescharacteristic
603C24C2×C22⋊D4711yescharacteristic
604#41—28no—
605#41—28no—
606#41—44no—
607#41—44no—
608#41—44no—
609#41—44no—
610#41—44no—
611#41—44no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8D4×D4712yes—
616C2×Q8#1062535212yes—
617C2×Q8C22×Dic4712yes—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊Dic4714yes—
649C2×D4C22×Dic4712yes—
650C2×D4C22×Dic4712yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—24no—
662C22×C4—24no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—941no—
668C22×C4—941no—
669C22×C4—941no—
670C22×C4—941no—
671C22×C4—3761no—
672C22×C4—1882no—
673C22×C4—1882no—
674C22×C4C22×Dic4712yes—
675C22×C4C22×Dic4712yes—
676C22×C4C2×C22⋊D4711yescharacteristic
677C22×C4C2×C22⋊D4711yescharacteristic
678C22×C4C2×C22⋊D4711yescharacteristic
679C22×C4C2×C22⋊D4711yescharacteristic
680C22×C4C2×C22⋊D4712yes—
681C22×C4C2×C22⋊D4712yes—
682C22×C4C23×D4711yescharacteristic
683M16—1884no—
684C2×C8—472no—
685C2×C8—941no—
686C2×C8—941no—
687C2×C8—941no—
688C2×C8—941no—
689C2×C8—941no—
690C2×C8—941no—
691C2×C8—941no—
692C2×C8—941no—
693C2×C8—941no—
694C2×C8—941no—
695C2×C8—941no—
696C2×C8—1884no—
697C4⋊C4—24no—
698C4⋊C4—21no—
699C4⋊C4—472no—
700C4⋊C4—941no—
701C4⋊C4—941no—
702C4⋊C4—941no—
703C4⋊C4—941no—
704C4⋊C4—941no—
705C4⋊C4—941no—
706C4⋊C4—941no—
707C4⋊C4—1882no—
708C4⋊C4C22⋊Dic4714yes—
709C4⋊C4C22×Dic4712yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—3761no—
713C22⋊C4—1882no—
714C22⋊C4—1882no—
715C22⋊C4C22⋊Dic4714yes—
716C22⋊C4C22⋊Dic4714yes—
717C42—24no—
718C42—3761no—
719C42—1882no—
720C42C22×Dic4712yes—
721C42C2×C22⋊D4712yes—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—22no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23C2×C22⋊Dic4712yes—
749C23C2×C22⋊Dic4712yes—
750C23C22×C22⋊D4711yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8D4×Dic4714yes—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—44no—
760D4—48no—
761D4—48no—
762D4—48no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—84no—
768D4—84no—
769D4—84no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—48no—
791C2×C4—48no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—942no—
795C2×C4—3764no—
796C2×C4—1881no—
797C2×C4—1881no—
798C2×C4—1881no—
799C2×C4—1881no—
800C2×C4—1881no—
801C2×C4—1881no—
802C2×C4—1881no—
803C2×C4—1881no—
804C2×C4—1881no—
805C2×C4—1881no—
806C2×C4—1881no—
807C2×C4C2×C22⋊Dic4712yes—
808C2×C4C2×C22⋊Dic4712yes—
809C2×C4C2×C22⋊Dic4712yes—
810C2×C4C2×C22⋊Dic4712yes—
811C2×C4C23×Dic4711yescharacteristic
812C2×C4C2×D4×D4711yescharacteristic
813C2×C4C22×C22⋊D4711yescharacteristic
814C2×C4C2×#1062535211yescharacteristic
815C2×C4#1309406911yescharacteristic
816C2×C4#1309406911yescharacteristic
817C8—942no—
818C8—1881no—
819C8—1881no—
820C8—1881no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22C22×C22⋊Dic4711yescharacteristic
850C22D4×C22⋊D4711yescharacteristic
851C22#1568976711yescharacteristic
852C22#1568992111yescharacteristic
853C22#1568992111yescharacteristic
854C22#1568992611yescharacteristic
855C22#1568993411yescharacteristic
856C4—22no—
857C4—22no—
858C4—22no—
859C4—22no—
860C4—24no—
861C4—42no—
862C4—3761no—
863C4—3761no—
864C4—3761no—
865C4—1882no—
866C4C2×D4×Dic4711yescharacteristic
867C4#1568959811yescharacteristic
868C4D4×C22⋊D4711yescharacteristic
869C4#1568976711yescharacteristic
870C2—42no—
871C2—42no—
872C2—82no—
873C2—82no—
874C2D4×C22⋊Dic4711yescharacteristic
875C2#2025190711yescharacteristic
876C2#2025191411yescharacteristic
877C2#2025492911yescharacteristic
878C2#2025496911yescharacteristic
879C2#2025539411yescharacteristic
880C2#2025551411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×C47×#550C2
socleC23×C47C22×D4
cosocleC22×C4×C47C24
hypercenterC2×#550D47
hypocenterC47#22422
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#15689195C2semidirect
2. C2×#15689124C2semidirect
3. C2×#15689119C2semidirect
4. #20246317C2semidirect
5. #20244316C2semidirect
6. #20244213C2semidirect
7. #20243827C2semidirect
8. #20243817C2semidirect
9. #20243711C2semidirect
10. #20243706C2semidirect
11. #20243403C2semidirect
12. #20243328C2semidirect
13. #20243328C2semidirect
14. #20243218C2semidirect
54. C47×#550C4semidirect
93. #13093948D4semidirect
121. C2×#41×C47C2×C4semidirect
138. #127×C47C2×C4semidirect
144. #121×C47C2×C4semidirect
146. C4×Q8×C47C2×C4semidirect
461. #550Dic47semidirect
504. C47#22422semidirect
516. C2×#41C2×Dic47semidirect
544. #127C2×Dic47semidirect
550. #121C2×Dic47semidirect
552. C4×Q8C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156891952
C2×#156891242
C2×#156891192
#202463172
#202443162
#202442132
#202438272
#202438172
#202437112
#202437062
#202434032
#202433282
#202432182
C2×C47×#5502
#2242247