Finite Group Databasebeta

← C2×#20255525 #27092832

Subgroups — C2×#20255525 #27092832

Order 12032.

2642 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689821C211yesmaximal, characteristic, complemented
2C2×D4×C22⋊D47C211yesmaximal, characteristic, complemented
3#20255525C2116yesmaximal, direct product factor
4C2×#15689486C211yesmaximal, characteristic, complemented
5C2×#15689441C211yesmaximal, characteristic, complemented
6C2×#15689445C211yesmaximal, characteristic, complemented
7C2×#15689421C211yesmaximal, characteristic, complemented
8C2×#15689375C211yesmaximal, characteristic, complemented
9C2×#15689359C211yesmaximal, characteristic, complemented
10C2×#15689317C211yesmaximal, characteristic, complemented
11C2×#15689258C211yesmaximal, characteristic, complemented
12C2×#15689257C211yesmaximal, characteristic, complemented
13C2×#15689232C211yesmaximal, characteristic, complemented
14C2×#15689194C211yesmaximal, characteristic, complemented
15C2×#15689126C211yesmaximal, characteristic, complemented
16C22×#102×C47C211yesmaximal, characteristic, complemented
17C23×C22⋊D47—21no—
18C22×D4×D47C2211yescharacteristic
19C22×D376C2211yescharacteristic, complemented
20C22×#10625334C2211yescharacteristic
21C22×#10625334C2211yescharacteristic, complemented
22C22×#10625324C2211yescharacteristic, complemented
23#15689821—24no—
24#15689821C2218yescomplemented
25D4×C22⋊D47—24no—
26D4×C22⋊D47C2218yescomplemented
27C2×#13094020C2211yescharacteristic
28C2×#13094019—21no—
29C2×#13094015C2211yescharacteristic, complemented
30C2×#13094009—21no—
31C2×#13093999C2211yescharacteristic, complemented
32C2×#13093998—21no—
33C2×#13093998C2211yescharacteristic
34C2×#13093998C2211yescharacteristic, complemented
35C2×#13093996—21no—
36C2×#13093995C2211yescharacteristic
37C2×#13093993—21no—
38C2×#13093992—21no—
39C2×D4×Dic47C2211yescharacteristic
40C2×#13093986C2211yescharacteristic, complemented
41C2×C4×C22⋊D47—21no—
42C2×C4×C22⋊D47C2211yescharacteristic
43C2×#13093982C2211yescharacteristic, complemented
44#15689486C2218yescomplemented
45#15689445C2218yescomplemented
46#15689441C2218yescomplemented
47#15689421C2218yescomplemented
48#15689375C2218yescomplemented
49#15689359C2218yescomplemented
50#15689317C2218yescomplemented
51#15689258C2218yescomplemented
52#15689257C2218yescomplemented
53#15689232C2218yescomplemented
54#15689194C2218yescomplemented
55C2×#13093958C2211yescharacteristic, complemented
56C2×#13093955C2211yescharacteristic, complemented
57C2×#13093955C2211yescharacteristic, complemented
58C2×Dic47⋊C8C2211yescharacteristic, complemented
59#15689126C2218yescomplemented
60C2×#13093946C2211yescharacteristic, complemented
61C2×#13093946C2211yescharacteristic, complemented
62C2×#13093945C2211yescharacteristic
63C2×#13093945C2211yescharacteristic, complemented
64C2×#13093944C2211yescharacteristic, complemented
65C2×#13093944C2211yescharacteristic, complemented
66C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
68C2×#13093934C2211yescharacteristic, complemented
69C23×D4×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic, complemented
71C22×C4⋊C4×C47C2211yescharacteristic, complemented
72C2×#102×C47C2211yescharacteristic
73C2×#102×C47C2211yescharacteristic
74C2×#102×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic, complemented
76C2×#102×C47C2218yescomplemented
77C24×D47—21no—
78C22×D188—21no—
79C22×D188C2311yescharacteristic
80C22×D188C2311yescharacteristic
81C22×C22⋊D47—21no—
82C22×C22⋊D47—21no—
83C22×C22⋊D47—21no—
84C22×C22⋊D47—28no—
85C22×C22⋊D47—21no—
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C22×C22⋊D47—48no—
89C22×C22⋊D47D411yescharacteristic
90C2×D4×D47—24no—
91C2×D4×D47—22no—
92C2×D4×D47—42no—
93C2×D4×D47C2314yes—
94C23×Dic47—21no—
95C22×C4×D47—21no—
96C22×C4×D47C2311yescharacteristic
97C2×D376—42no—
98C2×D376C2314yescomplemented
99C2×#10625334—24no—
100C2×#10625334—42no—
101C2×#10625334C2314yes—
102C2×#10625334C2314yescomplemented
103C2×#10625324—42no—
104C2×#10625324C2314yescomplemented
105C22×C47⋊C8C2311yescharacteristic
106C22×C47⋊C8C2311yescharacteristic
107#13094020—22no—
108#13094020C2314yes—
109#13094019—28no—
110#13094015—22no—
111#13094015C2314yescomplemented
112#13094009—28no—
113#13093999—22no—
114#13093999C2314yescomplemented
115#13093998—22no—
116#13093998—22no—
117#13093998—28no—
118#13093998C2314yes—
119#13093998C2314yescomplemented
120#13093996—28no—
121#13093995—22no—
122#13093995C2314yes—
123#13093993—28no—
124#13093992—28no—
125D4×Dic47—22no—
126D4×Dic47C2314yes—
127#13093986—22no—
128#13093986C2314yescomplemented
129C4×C22⋊D47—28no—
130C4×C22⋊D47D414yes—
131C4×C22⋊D47C2314yes—
132#13093982—22no—
133#13093982C2314yescomplemented
134C2×C4⋊Dic47—21no—
135C2×C4⋊Dic47C2311yescharacteristic
136C2×C4⋊Dic47C2311yescharacteristic
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4D411yescharacteristic
139C2×C22⋊Dic47—21no—
140C2×C22⋊Dic47—21no—
141C2×C22⋊Dic47D411yescharacteristic
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4D411yescharacteristic
148C2×C4×Dic47—21no—
149C2×C4×Dic47C2311yescharacteristic
150#13093958C2314yescomplemented
151#13093955C2314yescomplemented
152#13093955C2314yescomplemented
153Dic47⋊C8C2314yescomplemented
154#13093946C2314yescomplemented
155#13093946C2314yescomplemented
156#13093945C2314yes—
157#13093945C2314yescomplemented
158#13093944C2314yescomplemented
159#13093944C2314yescomplemented
160C22⋊(C47⋊C8)C2314yescomplemented
161(C2×D47)⋊C8C2314yescomplemented
162#13093934C2314yescomplemented
163C25×C47—21no—
164C22×D4×C47—24no—
165C22×D4×C47—22no—
166C22×D4×C47—21no—
167C22×D4×C47—42no—
168C22×D4×C47C2311yescharacteristic
169C22×D4×C47C2314yes—
170C22×D4×C47C2311yescharacteristic
171C23×C4×C47—21no—
172C23×C4×C47C2311yescharacteristic
173C22×C8×C47—42no—
174C22×C8×C47C2311yescharacteristic
175C22×C8×C47C2311yescharacteristic
176C22×C8×C47C2314yescomplemented
177C2×C4⋊C4×C47—22no—
178C2×C4⋊C4×C47—21no—
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C4⋊C4×C47C2314yescomplemented
182#102×C47C2314yes—
183#102×C47C2314yes—
184#102×C47C2314yescomplemented
185#102×C47C2314yescomplemented
186C24×C47—21no—
187C24×C47—21no—
188C24×C47—24no—
189C24×C47—44no—
190C24×C47—44no—
191C24×C47—82no—
192C24×C47C2×D411yescharacteristic
193C23×D47—21no—
194C23×D47—21no—
195C23×D47—24no—
196C23×D47—44no—
197C23×D47—44no—
198C23×D47—82no—
199C23×D47C2×D411yescharacteristic
200C2×D4×C47—28no—
201C2×D4×C47—21no—
202C2×D4×C47—24no—
203C2×D4×C47—21no—
204C2×D4×C47—22no—
205C2×D4×C47—22no—
206C2×D4×C47—22no—
207C2×D4×C47—44no—
208C2×D4×C47—48no—
209C2×D4×C47—44no—
210C2×D4×C47#4114yes—
211C2×D4×C47C2412yes—
212C2×D4×C47C2412yes—
213C22×C4×C47—22no—
214C22×C4×C47—22no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—24no—
218C22×C4×C47—82no—
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D412yes—
221C22×C4×C47C2412yes—
222C22×C4×C47C2411yescharacteristic
223C2×C22⋊D47—24no—
224C2×C22⋊D47—24no—
225C2×C22⋊D47—24no—
226C2×C22⋊D47—24no—
227C2×C22⋊D47—24no—
228C2×C22⋊D47—24no—
229C2×C22⋊D47—24no—
230C2×C22⋊D47—44no—
231C2×C22⋊D47—44no—
232C2×C22⋊D47—432no—
233C2×C22⋊D47—44no—
234C2×C22⋊D47—44no—
235C2×C22⋊D47—44no—
236C2×C22⋊D47—82no—
237C2×C22⋊D47C2×D414yes—
238C22×Dic47—21no—
239C22×Dic47—21no—
240C22×Dic47—24no—
241C22×Dic47—44no—
242C22×Dic47C2×D411yescharacteristic
243C22×Dic47C2×D411yescharacteristic
244C22×Dic47C2×D411yescharacteristic
245D4×D47—28no—
246D4×D47—44no—
247D4×D47—48no—
248C2×D188—22no—
249C2×D188—22no—
250C2×D188—22no—
251C2×D188—22no—
252C2×D188—21no—
253C2×D188—21no—
254C2×D188—24no—
255C2×D188—82no—
256C2×D188C2412yes—
257C2×D188C2412yes—
258C2×C4×D47—22no—
259C2×C4×D47—22no—
260C2×C4×D47—24no—
261C2×C4×D47—82no—
262C2×C4×D47C2×D412yes—
263C2×C4×D47C2412yes—
264C2×C8×C47—22no—
265C2×C8×C47—22no—
266C2×C8×C47—44no—
267C2×C8×C47C2412yes—
268C2×C8×C47C2412yes—
269C4⋊C4×C47—21no—
270C4⋊C4×C47—21no—
271C4⋊C4×C47—24no—
272C4⋊C4×C47C2412yes—
273C4⋊C4×C47C2412yes—
274C22⋊Dic47—24no—
275C22⋊Dic47—24no—
276C22⋊Dic47C2×D414yes—
277#10625334—28no—
278#10625334—44no—
279(C2×D47)⋊C4—24no—
280(C2×D47)⋊C4—24no—
281(C2×D47)⋊C4—24no—
282(C2×D47)⋊C4—24no—
283(C2×D47)⋊C4—24no—
284(C2×D47)⋊C4C2×D414yes—
285C4⋊Dic47—21no—
286C4⋊Dic47—21no—
287C4⋊Dic47—24no—
288C4⋊Dic47C2412yes—
289C4⋊Dic47C2412yes—
290Dic47⋊C4—24no—
291Dic47⋊C4C2×D414yes—
292C4×Dic47—24no—
293C4×Dic47C2×D412yes—
294C4×Dic47C2412yes—
295C2×C47⋊C8—22no—
296C2×C47⋊C8—22no—
297C2×C47⋊C8C2412yes—
298C2×C47⋊C8C2412yes—
299D376—44no—
300#10625324—44no—
301C23×C47—22no—
302C23×C47—22no—
303C23×C47—24no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—48no—
307C23×C47—42no—
308C23×C47—42no—
309C23×C47—42no—
310C23×C47—48no—
311C23×C47—42no—
312C23×C47—42no—
313C23×C47—84no—
314C23×C47—816no—
315C23×C47AGL(1,ℤ/8)14yes—
316C23×C47C22×D412yes—
317C23×C47C22×D411yescharacteristic
318C22×D47—22no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—48no—
324C22×D47—48no—
325C22×D47—42no—
326C22×D47—42no—
327C22×D47—42no—
328C22×D47—42no—
329C22×D47—42no—
330C22×D47—42no—
331C22×D47—84no—
332C22×D47—816no—
333C22×D47C22×D412yes—
334D4×C47—24no—
335D4×C47—22no—
336D4×C47—22no—
337D4×C47—22no—
338D4×C47—48no—
339D4×C47—42no—
340D4×C47C2×#4114yes—
341C2×C4×C47—22no—
342C2×C4×C47—24no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—42no—
348C2×C4×C47—42no—
349C2×C4×C47—84no—
350C2×C4×C47C22×D412yes—
351C2×C4×C47C22×D411yescharacteristic
352C2×C4×C47C2×#4112yes—
353C2×C4×C47H(5,𝔽2)12yes—
354C2×C4×C47C2511yescharacteristic
355C22⋊D47—28no—
356C22⋊D47—48no—
357C22⋊D47—48no—
358C22⋊D47—48no—
359C22⋊D47—48no—
360C22⋊D47—48no—
361C22⋊D47—84no—
362C2×Dic47—22no—
363C2×Dic47—22no—
364C2×Dic47—22no—
365C2×Dic47—22no—
366C2×Dic47—22no—
367C2×Dic47—48no—
368C2×Dic47—42no—
369C2×Dic47—42no—
370C2×Dic47C22×D412yes—
371C2×Dic47C22×D412yes—
372C2×Dic47C22×D412yes—
373D188—22no—
374D188—22no—
375D188—22no—
376D188—22no—
377D188—42no—
378D188—42no—
379D188—84no—
380C4×D47—24no—
381C4×D47—22no—
382C4×D47—22no—
383C4×D47—84no—
384C8×C47—22no—
385C8×C47—22no—
386C47⋊C8—22no—
387C47⋊C8—22no—
388C2×#3318—471nomaximal, Sylow
389C22×C47—22no—
390C22×C47—28no—
391C22×C47—22no—
392C22×C47—24no—
393C22×C47—48no—
394C22×C47—42no—
395C22×C47—42no—
396C22×C47—42no—
397C22×C47—42no—
398C22×C47—42no—
399C22×C47—816no—
400C22×C47—84no—
401C22×C47#54612yes—
402C22×C47C2×AGL(1,ℤ/8)14yes—
403C22×C47C2×AGL(1,ℤ/8)12yes—
404C22×C47#57612yes—
405C22×C47C23×D411yescharacteristic
406C2×D47—22no—
407C2×D47—22no—
408C2×D47—22no—
409C2×D47—44no—
410C2×D47—42no—
411C2×D47—42no—
412C2×D47—42no—
413C2×D47—42no—
414C2×D47—42no—
415C2×D47—42no—
416C2×D47—816no—
417C2×D47—84no—
418C2×D47—84no—
419C4×C47—22no—
420C4×C47—42no—
421C4×C47—42no—
422C4×C47#54612yes—
423C4×C47C22×#4111yescharacteristic
424C4×C47C2×H(5,𝔽2)11yescharacteristic
425Dic47—22no—
426Dic47—22no—
427Dic47—22no—
428Dic47—42no—
429Dic47—42no—
430C2×#553—471no—
431C2×D42—471no—
432#3318—4716no—
433C2×#490—471no—
434C2×#481—471no—
435C2×#482—471no—
436C2×#478—471no—
437C2×#469—471no—
438C2×#466—471no—
439C2×#459—471no—
440C2×#447—471no—
441C2×#447—471no—
442C2×#442—471no—
443C2×#435—471no—
444C2×#418—471no—
445C22×#102D4711yescharacteristic, complemented
446C2×C47—24no—
447C2×C47—44no—
448C2×C47—82no—
449C2×C47#331814yescomplemented
450C2×C47C2×#54611yescharacteristic
451C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
452C2×C47C2×#57611yescharacteristic
453D47—42no—
454D47—82no—
455D47—82no—
456C23×D4—471no—
457C23×D4—941no—
458C23×D4C2×D4711yescharacteristic
459C22×D8—471no—
460C22×D8—471no—
461C22×D8—471no—
462C22×M16—471no—
463C23×C8C2×D4711yescharacteristic, complemented
464#553—478no—
465#553—944no—
466D42—478no—
467D42—944no—
468C2×#127—471no—
469C2×#126—941no—
470C2×#125—471no—
471C2×#123—941no—
472C2×#121—471no—
473C2×#121—471no—
474C2×#121—471no—
475C2×#121—471no—
476C2×#121—941no—
477C2×#121—941no—
478C2×#120—941no—
479C2×#120—941no—
480C2×C4×D4—471no—
481C2×C4×D4—471no—
482C2×C4×D4—471no—
483C2×C4×D4—941no—
484C2×#117—471no—
485C22×C4⋊C4C2×D4711yescharacteristic, complemented
486#490—478no—
487#482—478no—
488#481—478no—
489#478—478no—
490#469—478no—
491#466—478no—
492#459—478no—
493#447—478no—
494#447—478no—
495#442—478no—
496#435—478no—
497C2×#107—471no—
498C2×#106—471no—
499C2×#106—471no—
500C2×C4⋊C8—471no—
501#418—478no—
502C2×#102—471no—
503C2×#102—471no—
504C2×#102—471no—
505C2×#102—471no—
506C2×#102—471no—
507C2×#102—471no—
508C2×#102C2×D4711yescharacteristic
509C2×#102C2×D4711yescharacteristic
510C2×#102C2×D4718yescomplemented
511C2×#102C2×D4711yescharacteristic, complemented
512C2×#102C2×D4711yescharacteristic, complemented
513C2×C22⋊C8—471no—
514C2×C22⋊C8—471no—
515C2×#97—471no—
516C47C2×#331811yescharacteristic, complemented, Sylow
517C25—21no—
518C25—941no—
519C22×D4—24no—
520C22×D4—21no—
521C22×D4—22no—
522C22×D4—42no—
523C22×D4—471no—
524C22×D4—474no—
525C22×D4—471no—
526C22×D4—471no—
527C22×D4—941no—
528C22×D4—942no—
529C22×D4—941no—
530C22×D4—941no—
531C22×D4—941no—
532C22×D4—948no—
533C22×D4—944no—
534C22×D4—941no—
535C22×D4—941no—
536C22×D4—941no—
537C22×D4—1882no—
538C22×D4—1888no—
539C22×D4C22×D4711yescharacteristic
540C22×D4C22×D4714yes—
541C22×D4C22×D4711yescharacteristic
542C23×C4—21no—
543C23×C4—471no—
544C23×C4—941no—
545C23×C4—941no—
546C23×C4C22×D4711yescharacteristic
547C2×D8—474no—
548C2×D8—474no—
549C2×D8—474no—
550C2×D8—944no—
551C2×D8—1882no—
552C2×D8—1882no—
553C2×M16—474no—
554C2×M16—1882no—
555C22×C8—42no—
556C22×C8—471no—
557C22×C8—471no—
558C22×C8C22×D4711yescharacteristic
559C22×C8C22×D4711yescharacteristic
560C22×C8C22×D4714yescomplemented
561#127—474no—
562#127—942no—
563#126—948no—
564#125—474no—
565#125—942no—
566#123—948no—
567#121—474no—
568#121—474no—
569#121—474no—
570#121—474no—
571#121—942no—
572#121—948no—
573#121—948no—
574#121—942no—
575#121—942no—
576#121—942no—
577#120—948no—
578#120—948no—
579C4×D4—474no—
580C4×D4—474no—
581C4×D4—474no—
582C4×D4—474no—
583C4×D4—942no—
584C4×D4—942no—
585C4×D4—948no—
586#117—474no—
587#117—942no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—471no—
591C2×C4⋊C4—471no—
592C2×C4⋊C4—471no—
593C2×C4⋊C4—941no—
594C2×C4⋊C4—941no—
595C2×C4⋊C4C22×D4711yescharacteristic
596C2×C4⋊C4C22×D4711yescharacteristic
597C2×C4⋊C4C22×D4714yescomplemented
598C2×C22⋊C4—471no—
599C2×C22⋊C4—471no—
600C2×C22⋊C4—941no—
601C2×C22⋊C4—941no—
602C2×C22⋊C4—941no—
603C2×C22⋊C4—941no—
604C2×C22⋊C4—941no—
605C2×C22⋊C4—941no—
606C2×C22⋊C4—941no—
607C2×C42—471no—
608C2×C42—941no—
609#107—474no—
610#106—474no—
611#106—474no—
612C4⋊C8—474no—
613#102—474no—
614#102—474no—
615#102—474no—
616#102—474no—
617#102—474no—
618#102—474no—
619#102C22×D4714yes—
620#102C22×D4714yes—
621#102C22×D4714yescomplemented
622#102C22×D4714yescomplemented
623C22⋊C8—474no—
624C22⋊C8—474no—
625#97—474no—
626C24—21no—
627C24—21no—
628C24—24no—
629C24—44no—
630C24—44no—
631C24—82no—
632C24—471no—
633C24—944no—
634C24—941no—
635C24—941no—
636C24—3762no—
637C24—1884no—
638C24—1884no—
639C24D4×D4711yescharacteristic
640C2×D4—28no—
641C2×D4—21no—
642C2×D4—24no—
643C2×D4—21no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—44no—
648C2×D4—48no—
649C2×D4—44no—
650C2×D4—474no—
651C2×D4—472no—
652C2×D4—472no—
653C2×D4—944no—
654C2×D4—944no—
655C2×D4—944no—
656C2×D4—944no—
657C2×D4—944no—
658C2×D4—948no—
659C2×D4—944no—
660C2×D4—944no—
661C2×D4—944no—
662C2×D4—941no—
663C2×D4—941no—
664C2×D4—942no—
665C2×D4—942no—
666C2×D4—942no—
667C2×D4—942no—
668C2×D4—3762no—
669C2×D4—3762no—
670C2×D4—1884no—
671C2×D4—1888no—
672C2×D4—1884no—
673C2×D4—1884no—
674C2×D4—18832no—
675C2×D4—1884no—
676C2×D4—1884no—
677C2×D4—1884no—
678C2×D4#1062535014yes—
679C2×D4C23×D4712yes—
680C2×D4C23×D4712yes—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—24no—
686C22×C4—82no—
687C22×C4—471no—
688C22×C4—471no—
689C22×C4—471no—
690C22×C4—472no—
691C22×C4—472no—
692C22×C4—944no—
693C22×C4—944no—
694C22×C4—942no—
695C22×C4—942no—
696C22×C4—941no—
697C22×C4—941no—
698C22×C4—3762no—
699C22×C4—1884no—
700C22×C4D4×D4712yes—
701C22×C4D4×D4711yescharacteristic
702C22×C4C23×D4712yes—
703C22×C4C23×D4711yescharacteristic
704D8—948no—
705D8—1884no—
706D8—1884no—
707M16—1884no—
708C2×C8—22no—
709C2×C8—22no—
710C2×C8—44no—
711C2×C8—472no—
712C2×C8—472no—
713C2×C8—942no—
714C2×C8—942no—
715C2×C8C23×D4712yes—
716C2×C8C23×D4712yes—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—24no—
720C4⋊C4—474no—
721C4⋊C4—472no—
722C4⋊C4—472no—
723C4⋊C4—944no—
724C4⋊C4—944no—
725C4⋊C4—941no—
726C4⋊C4—941no—
727C4⋊C4C23×D4712yes—
728C4⋊C4C23×D4712yes—
729C22⋊C4—474no—
730C22⋊C4—474no—
731C22⋊C4—944no—
732C22⋊C4—944no—
733C22⋊C4—944no—
734C22⋊C4—944no—
735C22⋊C4—944no—
736C22⋊C4—944no—
737C22⋊C4—944no—
738C42—472no—
739C42—472no—
740C42—944no—
741C23—22no—
742C23—22no—
743C23—24no—
744C23—22no—
745C23—22no—
746C23—48no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—48no—
751C23—42no—
752C23—42no—
753C23—84no—
754C23—816no—
755C23—472no—
756C23—942no—
757C23—942no—
758C23—942no—
759C23—942no—
760C23—942no—
761C23—3764no—
762C23—37616no—
763C23—1888no—
764C23—1888no—
765C23—1882no—
766C23—1882no—
767C23—1882no—
768C23—1882no—
769C23—1882no—
770C23—1882no—
771C23#1309405114yes—
772C23C2×D4×D4712yes—
773C23C2×D4×D4711yescharacteristic
774D4—24no—
775D4—22no—
776D4—22no—
777D4—22no—
778D4—48no—
779D4—42no—
780D4—948no—
781D4—942no—
782D4—942no—
783D4—942no—
784D4—942no—
785D4—3764no—
786D4—3764no—
787D4—1888no—
788D4—1888no—
789D4—1888no—
790D4—1888no—
791D4—1888no—
792D4—1882no—
793D4—1882no—
794D4C2×#1062535014yes—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—84no—
804C2×C4—472no—
805C2×C4—472no—
806C2×C4—472no—
807C2×C4—942no—
808C2×C4—942no—
809C2×C4—942no—
810C2×C4—944no—
811C2×C4—942no—
812C2×C4—942no—
813C2×C4—942no—
814C2×C4—942no—
815C2×C4—3764no—
816C2×C4—1888no—
817C2×C4—1882no—
818C2×C4—1882no—
819C2×C4C2×D4×D4712yes—
820C2×C4C2×D4×D4711yescharacteristic
821C2×C4C2×#1062535012yes—
822C2×C4#1309406912yes—
823C2×C4C24×D4711yescharacteristic
824C8—22no—
825C8—22no—
826C8—942no—
827C8—942no—
828C22—28no—
829C22—22no—
830C22—22no—
831C22—24no—
832C22—48no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—816no—
839C22—84no—
840C22—942no—
841C22—942no—
842C22—942no—
843C22—37616no—
844C22—3764no—
845C22—3764no—
846C22—1882no—
847C22—1882no—
848C22—1882no—
849C22—1882no—
850C22—1882no—
851C22—1882no—
852C22—1884no—
853C22#1568976312yes—
854C22C2×#1309405114yes—
855C22C2×#1309405112yes—
856C22#1568992412yes—
857C22C22×D4×D4711yescharacteristic
858C4—22no—
859C4—42no—
860C4—42no—
861C4—942no—
862C4—942no—
863C4—942no—
864C4—1882no—
865C4—1882no—
866C4#1568976312yes—
867C4C22×#1062535011yescharacteristic
868C4C2×#1309406911yescharacteristic
869C2—24no—
870C2—44no—
871C2—82no—
872C2—3762no—
873C2—3762no—
874C2—1882no—
875C2#2025552514yesdirect product factor
876C2C2×#1568976311yescharacteristic
877C2C22×#1309405111yescharacteristic
878C2C2×#1568992411yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC22×#102×C47C2
socleC23×C47C22×D4
hypercenterC22×#102D47
hypocenterC47C2×#3318
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. C2×#15689821C2semidirect
2. C2×D4×C22⋊D47C2semidirect
3. #20255525C2direct (N × H)
4. C2×#15689486C2semidirect
5. C2×#15689441C2semidirect
6. C2×#15689445C2semidirect
7. C2×#15689421C2semidirect
8. C2×#15689375C2semidirect
9. C2×#15689359C2semidirect
10. C2×#15689317C2semidirect
11. C2×#15689258C2semidirect
12. C2×#15689257C2semidirect
13. C2×#15689232C2semidirect
14. C2×#15689194C2semidirect
15. C2×#15689126C2semidirect
16. C22×#102×C47C2semidirect
19. C22×D376C22semidirect
21. C22×#10625334C22semidirect
22. C22×#10625324C22semidirect
24. #15689821C22semidirect
26. D4×C22⋊D47C22semidirect
29. C2×#13094015C22semidirect
31. C2×#13093999C22semidirect
34. C2×#13093998C22semidirect
40. C2×#13093986C22semidirect
43. C2×#13093982C22semidirect
44. #15689486C22semidirect
45. #15689445C22semidirect
46. #15689441C22semidirect
47. #15689421C22semidirect
48. #15689375C22semidirect
49. #15689359C22semidirect
50. #15689317C22semidirect
51. #15689258C22semidirect
52. #15689257C22semidirect
53. #15689232C22semidirect
54. #15689194C22semidirect
55. C2×#13093958C22semidirect
56. C2×#13093955C22semidirect
57. C2×#13093955C22semidirect
58. C2×Dic47⋊C8C22semidirect
59. #15689126C22semidirect
60. C2×#13093946C22semidirect
61. C2×#13093946C22semidirect
63. C2×#13093945C22semidirect
64. C2×#13093944C22semidirect
65. C2×#13093944C22semidirect
66. C2×C22⋊(C47⋊C8)C22semidirect
67. C2×(C2×D47)⋊C8C22semidirect
68. C2×#13093934C22semidirect
70. C23×C8×C47C22semidirect
71. C22×C4⋊C4×C47C22semidirect
74. C2×#102×C47C22semidirect
75. C2×#102×C47C22semidirect
76. C2×#102×C47C22semidirect
98. C2×D376C23semidirect
102. C2×#10625334C23semidirect
104. C2×#10625324C23semidirect
111. #13094015C23semidirect
114. #13093999C23semidirect
119. #13093998C23semidirect
128. #13093986C23semidirect
133. #13093982C23semidirect
150. #13093958C23semidirect
151. #13093955C23semidirect
152. #13093955C23semidirect
153. Dic47⋊C8C23semidirect
154. #13093946C23semidirect
155. #13093946C23semidirect
157. #13093945C23semidirect
158. #13093944C23semidirect
159. #13093944C23semidirect
160. C22⋊(C47⋊C8)C23semidirect
161. (C2×D47)⋊C8C23semidirect
162. #13093934C23semidirect
176. C22×C8×C47C23semidirect
181. C2×C4⋊C4×C47C23semidirect
184. #102×C47C23semidirect
185. #102×C47C23semidirect
445. C22×#102D47semidirect
449. C2×C47#3318semidirect
463. C23×C8C2×D47semidirect
485. C22×C4⋊C4C2×D47semidirect
510. C2×#102C2×D47semidirect
511. C2×#102C2×D47semidirect
512. C2×#102C2×D47semidirect
516. C47C2×#3318semidirect
560. C22×C8C22×D47semidirect
597. C2×C4⋊C4C22×D47semidirect
621. #102C22×D47semidirect
622. #102C22×D47semidirect
875. C2#20255525direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898212
C2×D4×C22⋊D472
#202555252
C2×#156894862
C2×#156894412
C2×#156894452
C2×#156894212
C2×#156893752
C2×#156893592
C2×#156893172
C2×#156892582
C2×#156892572
C2×#156892322
C2×#156891942
C2×#156891262
C22×#102×C472
C2×#331847