Finite Group Databasebeta

← C2×#20255527 #27092834

Subgroups — C2×#20255527 #27092834

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×#15689757C211yesmaximal, characteristic, complemented
3#20255527C2116yesmaximal, direct product factor
4C2×#15689486C211yesmaximal, characteristic, complemented
5C2×#15689449C211yesmaximal, characteristic, complemented
6C2×#15689422C211yesmaximal, characteristic, complemented
7C2×#15689377C211yesmaximal, characteristic, complemented
8C2×#15689357C211yesmaximal, characteristic, complemented
9C2×#15689317C211yesmaximal, characteristic, complemented
10C2×#15689259C211yesmaximal, characteristic, complemented
11C2×#15689258C211yesmaximal, characteristic, complemented
12C2×#15689234C211yesmaximal, characteristic, complemented
13C2×#15689191C211yesmaximal, characteristic, complemented
14C2×#15689126C211yesmaximal, characteristic, complemented
15C22×#13093944C211yesmaximal, characteristic, complemented
16C2×C47×#481C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C22×D4×D47—21no—
19C22×D4×D47C2211yescharacteristic
20C22×D376C2211yescharacteristic
21C22×D376C2211yescharacteristic, complemented
22C22×#10625334C2211yescharacteristic, complemented
23C22×#10625324C2211yescharacteristic, complemented
24C23×C47⋊C8C2211yescharacteristic, complemented
25#15689821—24no—
26#15689821C2218yescomplemented
27#15689757—24no—
28#15689757C2218yescomplemented
29C2×#13094020C2211yescharacteristic
30C2×#13094019—21no—
31C2×#13094015C2211yescharacteristic, complemented
32C2×#13094009—21no—
33C2×#13093999C2211yescharacteristic
34C2×#13093999C2211yescharacteristic, complemented
35C2×#13093998—21no—
36C2×#13093998C2211yescharacteristic, complemented
37C2×#13093997—21no—
38C2×#13093994—21no—
39C2×#13093992—21no—
40C2×#13093986C2211yescharacteristic
41C2×#13093986C2211yescharacteristic, complemented
42C2×C4×C22⋊D47—21no—
43C2×C4×C22⋊D47C2211yescharacteristic
44C2×#13093982C2211yescharacteristic, complemented
45#15689486C2218yescomplemented
46#15689449C2218yescomplemented
47#15689422C2218yescomplemented
48#15689377C2218yescomplemented
49#15689357C2218yescomplemented
50#15689317C2218yescomplemented
51#15689259C2218yescomplemented
52#15689258C2218yescomplemented
53#15689234C2218yescomplemented
54#15689191C2218yescomplemented
55C2×#13093957C2211yescharacteristic, complemented
56C2×Dic47⋊C8C2211yescharacteristic, complemented
57#15689126C2218yescomplemented
58C2×#13093946C2211yescharacteristic
59C2×#13093946C2211yescharacteristic, complemented
60C2×#13093945C2211yescharacteristic, complemented
61C2×#13093944C2211yescharacteristic
62C2×#13093944C2211yescharacteristic
63C2×#13093944C2211yescharacteristic, complemented
64C2×#13093944C2211yescharacteristic, complemented
65C2×#13093944C2211yescharacteristic, complemented
66C2×#13093944C2218yescomplemented
67C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
68C2×#13093934C2211yescharacteristic, complemented
69C2×#121×C47C2211yescharacteristic
70C22×C4⋊C4×C47C2211yescharacteristic, complemented
71C47×#481C2218yescomplemented
72C2×#106×C47C2211yescharacteristic, complemented
73C2×#106×C47C2211yescharacteristic, complemented
74C2×#102×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic, complemented
76C2×C22⋊C8×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C24×D47—21no—
79C22×D188—24no—
80C22×D188—21no—
81C22×D188—22no—
82C22×D188—21no—
83C22×D188—21no—
84C22×D188—42no—
85C22×D188C2311yescharacteristic
86C22×D188C2311yescharacteristic
87C22×D188C2314yes—
88C22×D188C2311yescharacteristic
89C22×C22⋊D47—21no—
90C22×C22⋊D47—21no—
91C22×C22⋊D47—21no—
92C22×C22⋊D47—21no—
93C22×C22⋊D47D411yescharacteristic
94C2×D4×D47—28no—
95C2×D4×D47—24no—
96C2×D4×D47—22no—
97C2×D4×D47—42no—
98C2×D4×D47—48no—
99C2×D4×D47C2314yes—
100C22×C4×D47—21no—
101C22×C4×D47—21no—
102C22×C4×D47C2311yescharacteristic
103C2×D376—24no—
104C2×D376—42no—
105C2×D376C2314yes—
106C2×D376C2314yescomplemented
107C2×#10625334—42no—
108C2×#10625334C2314yescomplemented
109C2×#10625324—42no—
110C2×#10625324C2314yescomplemented
111C22×C47⋊C8—42no—
112C22×C47⋊C8C2311yescharacteristic
113C22×C47⋊C8C2311yescharacteristic
114C22×C47⋊C8C2314yescomplemented
115#13094020—22no—
116#13094020C2314yes—
117#13094019—28no—
118#13094015—22no—
119#13094015C2314yescomplemented
120#13094009—28no—
121#13093999—22no—
122#13093999—22no—
123#13093999C2314yes—
124#13093999C2314yescomplemented
125#13093998—22no—
126#13093998—28no—
127#13093998C2314yescomplemented
128#13093997—28no—
129#13093994—28no—
130#13093992—28no—
131#13093986—22no—
132#13093986—22no—
133#13093986C2314yes—
134#13093986C2314yescomplemented
135C4×C22⋊D47—28no—
136C4×C22⋊D47D414yes—
137C4×C22⋊D47C2314yes—
138#13093982—22no—
139#13093982C2314yescomplemented
140C2×C4⋊Dic47—21no—
141C2×C4⋊Dic47C2311yescharacteristic
142C2×Dic47⋊C4—21no—
143C2×Dic47⋊C4D411yescharacteristic
144C2×C22⋊Dic47D411yescharacteristic
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×(C2×D47)⋊C4—21no—
150C2×(C2×D47)⋊C4—21no—
151C2×(C2×D47)⋊C4D411yescharacteristic
152C2×C4×Dic47—21no—
153C2×C4×Dic47C2311yescharacteristic
154#13093957C2314yescomplemented
155Dic47⋊C8C2314yescomplemented
156#13093946C2314yes—
157#13093946C2314yescomplemented
158#13093945C2314yescomplemented
159#13093944C2314yes—
160#13093944C2314yes—
161#13093944C2314yescomplemented
162#13093944C2314yescomplemented
163#13093944C2314yescomplemented
164(C2×D47)⋊C8C2314yescomplemented
165#13093934C2314yescomplemented
166C22×D4×C47—21no—
167C22×D4×C47C2311yescharacteristic
168C23×C4×C47—21no—
169C23×C4×C47C2311yescharacteristic
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2311yescharacteristic
172#121×C47—22no—
173#121×C47C2314yes—
174C2×C4⋊C4×C47—22no—
175C2×C4⋊C4×C47—21no—
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C4⋊C4×C47C2314yescomplemented
180C2×C22⋊C4×C47—21no—
181#106×C47C2314yescomplemented
182#106×C47C2314yescomplemented
183#102×C47C2314yescomplemented
184#102×C47C2314yescomplemented
185C22⋊C8×C47C2314yescomplemented
186C24×C47—21no—
187C24×C47C2×D411yescharacteristic
188C23×D47—21no—
189C23×D47—21no—
190C23×D47—21no—
191C23×D47—24no—
192C23×D47—24no—
193C23×D47—44no—
194C23×D47—44no—
195C23×D47—44no—
196C23×D47—44no—
197C23×D47—82no—
198C23×D47—82no—
199C23×D47C2×D411yescharacteristic
200C2×D4×C47—24no—
201C2×D4×C47—21no—
202C2×D4×C47—22no—
203C2×D4×C47—22no—
204C2×D4×C47—44no—
205C2×D4×C47C2412yes—
206C22×C4×C47—22no—
207C22×C4×C47—22no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—24no—
212C22×C4×C47—82no—
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D412yes—
215C22×C4×C47C2412yes—
216C22×C4×C47C2411yescharacteristic
217C2×C22⋊D47—24no—
218C2×C22⋊D47—24no—
219C2×C22⋊D47—24no—
220C2×C22⋊D47—24no—
221C2×C22⋊D47—24no—
222C2×C22⋊D47—44no—
223C2×C22⋊D47—44no—
224C2×C22⋊D47—44no—
225C2×C22⋊D47—82no—
226C2×C22⋊D47C2×D414yes—
227C22×Dic47—21no—
228C22×Dic47C2×D411yescharacteristic
229C22×Dic47C2×D411yescharacteristic
230C22×Dic47C2×D411yescharacteristic
231D4×D47—28no—
232D4×D47—44no—
233D4×D47—48no—
234D4×D47—432no—
235C2×D188—21no—
236C2×D188—22no—
237C2×D188—22no—
238C2×D188—22no—
239C2×D188—22no—
240C2×D188—22no—
241C2×D188—28no—
242C2×D188—24no—
243C2×D188—21no—
244C2×D188—24no—
245C2×D188—21no—
246C2×D188—24no—
247C2×D188—44no—
248C2×D188—48no—
249C2×D188—44no—
250C2×D188—44no—
251C2×D188—82no—
252C2×D188#4114yes—
253C2×D188C2412yes—
254C2×D188C2412yes—
255C2×D188C2412yes—
256C2×C4×D47—22no—
257C2×C4×D47—22no—
258C2×C4×D47—24no—
259C2×C4×D47—24no—
260C2×C4×D47—44no—
261C2×C4×D47—82no—
262C2×C4×D47C2×D412yes—
263C2×C4×D47C2412yes—
264C2×C8×C47—22no—
265C2×C8×C47—22no—
266C2×C8×C47C2412yes—
267C2×C8×C47C2412yes—
268C4⋊C4×C47—21no—
269C4⋊C4×C47—21no—
270C4⋊C4×C47—24no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47C2412yes—
273C4⋊C4×C47C2412yes—
274C4⋊C4×C47C2412yes—
275C22⋊C4×C47—24no—
276C22⋊Dic47C2×D414yes—
277#10625334—44no—
278(C2×D47)⋊C4—24no—
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—24no—
287C4⋊Dic47C2412yes—
288Dic47⋊C4—24no—
289Dic47⋊C4C2×D414yes—
290C4×Dic47—24no—
291C4×Dic47C2×D412yes—
292C4×Dic47C2412yes—
293C2×C47⋊C8—22no—
294C2×C47⋊C8—22no—
295C2×C47⋊C8—44no—
296C2×C47⋊C8C2412yes—
297C2×C47⋊C8C2412yes—
298D376—28no—
299D376—44no—
300#10625324—44no—
301C23×C47—22no—
302C23×C47—22no—
303C23×C47—22no—
304C23×C47—42no—
305C23×C47—42no—
306C23×C47—42no—
307C23×C47AGL(1,ℤ/8)14yes—
308C23×C47C22×D412yes—
309C23×C47C22×D411yescharacteristic
310C22×D47—22no—
311C22×D47—24no—
312C22×D47—22no—
313C22×D47—22no—
314C22×D47—22no—
315C22×D47—22no—
316C22×D47—22no—
317C22×D47—48no—
318C22×D47—48no—
319C22×D47—48no—
320C22×D47—42no—
321C22×D47—42no—
322C22×D47—42no—
323C22×D47—42no—
324C22×D47—42no—
325C22×D47—48no—
326C22×D47—42no—
327C22×D47—42no—
328C22×D47—42no—
329C22×D47—84no—
330C22×D47—84no—
331C22×D47—816no—
332C22×D47—816no—
333C22×D47C22×D412yes—
334D4×C47—22no—
335D4×C47—22no—
336D4×C47—48no—
337D4×C47—42no—
338C2×C4×C47—22no—
339C2×C4×C47—24no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—42no—
346C2×C4×C47—42no—
347C2×C4×C47—42no—
348C2×C4×C47—84no—
349C2×C4×C47C22×D412yes—
350C2×C4×C47C22×D411yescharacteristic
351C2×C4×C47C2×#4112yes—
352C2×C4×C47H(5,𝔽2)12yes—
353C2×C4×C47C2511yescharacteristic
354C22⋊D47—28no—
355C22⋊D47—48no—
356C22⋊D47—48no—
357C22⋊D47—48no—
358C22⋊D47—84no—
359C2×Dic47—22no—
360C2×Dic47—22no—
361C2×Dic47—22no—
362C2×Dic47—22no—
363C2×Dic47—42no—
364C2×Dic47C22×D412yes—
365C2×Dic47C22×D412yes—
366C2×Dic47C22×D412yes—
367D188—24no—
368D188—22no—
369D188—22no—
370D188—22no—
371D188—22no—
372D188—22no—
373D188—48no—
374D188—48no—
375D188—42no—
376D188—42no—
377D188—84no—
378D188C2×#4114yes—
379C4×D47—24no—
380C4×D47—22no—
381C4×D47—22no—
382C4×D47—48no—
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—42no—
393C22×C47—42no—
394C22×C47—42no—
395C22×C47—84no—
396C22×C47#54612yes—
397C22×C47C2×AGL(1,ℤ/8)14yes—
398C22×C47C2×AGL(1,ℤ/8)12yes—
399C22×C47#57612yes—
400C22×C47C23×D411yescharacteristic
401C2×D47—22no—
402C2×D47—24no—
403C2×D47—22no—
404C2×D47—22no—
405C2×D47—44no—
406C2×D47—48no—
407C2×D47—42no—
408C2×D47—42no—
409C2×D47—42no—
410C2×D47—42no—
411C2×D47—42no—
412C2×D47—42no—
413C2×D47—42no—
414C2×D47—42no—
415C2×D47—816no—
416C2×D47—816no—
417C2×D47—84no—
418C2×D47—84no—
419C4×C47—22no—
420C4×C47—42no—
421C4×C47—42no—
422C4×C47—42no—
423C4×C47#54612yes—
424C4×C47C22×#4111yescharacteristic
425C4×C47C2×H(5,𝔽2)11yescharacteristic
426Dic47—22no—
427Dic47—22no—
428Dic47—22no—
429Dic47—42no—
430C2×#553—471no—
431C2×D42—471no—
432#3318—4716no—
433C2×#490—471no—
434C2×#481D4711yescharacteristic, complemented
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×#102—471no—
446C2×C47—24no—
447C2×C47—82no—
448C2×C47#331814yescomplemented
449C2×C47C2×#54611yescharacteristic
450C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
451C2×C47C2×#57611yescharacteristic
452D47—42no—
453D47—44no—
454D47—82no—
455D47—82no—
456C23×D4—471no—
457C23×D4—471no—
458C23×D4—941no—
459C22×D8—471no—
460C22×D8—471no—
461C22×D8—471no—
462C22×M16—471no—
463C23×C8—471no—
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—941no—
476C2×#121—941no—
477C2×#121C2×D4711yescharacteristic
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#481C2×D4718yescomplemented
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×#106C2×D4711yescharacteristic, complemented
499C2×#106C2×D4711yescharacteristic, complemented
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×#102—471no—
509C2×#102—471no—
510C2×#102—478no—
511C2×#102C2×D4711yescharacteristic, complemented
512C2×#102C2×D4711yescharacteristic, complemented
513C2×C22⋊C8—471no—
514C2×C22⋊C8C2×D4711yescharacteristic, complemented
515C2×#97—471no—
516C47C2×#331811yescharacteristic, complemented, Sylow
517C25—941no—
518C25—941no—
519C22×D4—21no—
520C22×D4—471no—
521C22×D4—474no—
522C22×D4—471no—
523C22×D4—471no—
524C22×D4—471no—
525C22×D4—474no—
526C22×D4—944no—
527C22×D4—941no—
528C22×D4—941no—
529C22×D4—942no—
530C22×D4—941no—
531C22×D4—941no—
532C22×D4—941no—
533C22×D4—944no—
534C22×D4—948no—
535C22×D4—941no—
536C22×D4—941no—
537C22×D4—942no—
538C22×D4—1882no—
539C22×D4—1882no—
540C22×D4—1888no—
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—471no—
556C22×C8—471no—
557C22×C8—474no—
558C22×C8—1882no—
559C22×C8C22×D4711yescharacteristic
560C22×C8C22×D4711yescharacteristic
561#127—474no—
562#127—942no—
563#126—948no—
564#125—474no—
565#125—942no—
566#123—948no—
567#121—22no—
568#121—474no—
569#121—474no—
570#121—474no—
571#121—948no—
572#121—942no—
573#121—942no—
574#121—948no—
575#121—942no—
576#121C22×D4714yes—
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—941no—
593C2×C4⋊C4—941no—
594C2×C4⋊C4C22×D4711yescharacteristic
595C2×C4⋊C4C22×D4711yescharacteristic
596C2×C4⋊C4C22×D4711yescharacteristic
597C2×C4⋊C4C22×D4714yescomplemented
598C2×C22⋊C4—21no—
599C2×C22⋊C4—471no—
600C2×C22⋊C4—471no—
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#106C22×D4714yescomplemented
611#106C22×D4714yescomplemented
612C4⋊C8—474no—
613#102—474no—
614#102—474no—
615#102—474no—
616#102—474no—
617#102—474no—
618#102—474no—
619#102—474no—
620#102—474no—
621#102C22×D4714yescomplemented
622#102C22×D4714yescomplemented
623C22⋊C8—474no—
624C22⋊C8C22×D4714yescomplemented
625#97—474no—
626C24—21no—
627C24—471no—
628C24—944no—
629C24—941no—
630C24—944no—
631C24—941no—
632C24—941no—
633C24—3762no—
634C24—3762no—
635C24—1884no—
636C24—1884no—
637C24—1884no—
638C24—1884no—
639C24D4×D4711yescharacteristic
640C2×D4—24no—
641C2×D4—21no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—44no—
645C2×D4—474no—
646C2×D4—474no—
647C2×D4—472no—
648C2×D4—472no—
649C2×D4—472no—
650C2×D4—948no—
651C2×D4—944no—
652C2×D4—944no—
653C2×D4—944no—
654C2×D4—944no—
655C2×D4—944no—
656C2×D4—948no—
657C2×D4—944no—
658C2×D4—944no—
659C2×D4—941no—
660C2×D4—941no—
661C2×D4—944no—
662C2×D4—941no—
663C2×D4—942no—
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—1884no—
675C2×D4—1888no—
676C2×D4—1884no—
677C2×D4—1884no—
678C2×D4—18832no—
679C2×D4—1884no—
680C2×D4C23×D4712yes—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—24no—
687C22×C4—82no—
688C22×C4—471no—
689C22×C4—471no—
690C22×C4—471no—
691C22×C4—472no—
692C22×C4—472no—
693C22×C4—944no—
694C22×C4—944no—
695C22×C4—942no—
696C22×C4—942no—
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—472no—
711C2×C8—472no—
712C2×C8—942no—
713C2×C8—942no—
714C2×C8—1884no—
715C2×C8C23×D4712yes—
716C2×C8C23×D4712yes—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—24no—
720C4⋊C4—21no—
721C4⋊C4—474no—
722C4⋊C4—472no—
723C4⋊C4—944no—
724C4⋊C4—944no—
725C4⋊C4—941no—
726C4⋊C4C23×D4712yes—
727C4⋊C4C23×D4712yes—
728C4⋊C4C23×D4712yes—
729C22⋊C4—24no—
730C22⋊C4—474no—
731C22⋊C4—474no—
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—22no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—472no—
748C23—942no—
749C23—944no—
750C23—942no—
751C23—942no—
752C23—942no—
753C23—942no—
754C23—942no—
755C23—37616no—
756C23—3764no—
757C23—3764no—
758C23—37616no—
759C23—1888no—
760C23—1888no—
761C23—1888no—
762C23—1882no—
763C23—1882no—
764C23—1888no—
765C23—1882no—
766C23—1882no—
767C23—1882no—
768C23—1882no—
769C23—1882no—
770C23—1882no—
771C23#1309405114yes—
772C23C2×D4×D4712yes—
773C23C2×D4×D4711yescharacteristic
774D4—22no—
775D4—22no—
776D4—48no—
777D4—42no—
778D4—474no—
779D4—948no—
780D4—944no—
781D4—942no—
782D4—942no—
783D4—942no—
784D4—942no—
785D4—942no—
786D4—3764no—
787D4—3764no—
788D4—1888no—
789D4—1888no—
790D4—1888no—
791D4—1888no—
792D4—1888no—
793D4—1882no—
794D4—1882no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—84no—
806C2×C4—472no—
807C2×C4—472no—
808C2×C4—472no—
809C2×C4—942no—
810C2×C4—942no—
811C2×C4—942no—
812C2×C4—944no—
813C2×C4—942no—
814C2×C4—942no—
815C2×C4—942no—
816C2×C4—3764no—
817C2×C4—1888no—
818C2×C4—1882no—
819C2×C4C2×D4×D4712yes—
820C2×C4C2×D4×D4711yescharacteristic
821C2×C4#41×D4712yes—
822C2×C4#1309407012yes—
823C2×C4C24×D4711yescharacteristic
824C8—22no—
825C8—22no—
826C8—942no—
827C8—942no—
828C22—28no—
829C22—22no—
830C22—22no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—84no—
835C22—942no—
836C22—944no—
837C22—942no—
838C22—942no—
839C22—37616no—
840C22—37616no—
841C22—3764no—
842C22—3764no—
843C22—1882no—
844C22—1882no—
845C22—1882no—
846C22—1882no—
847C22—1882no—
848C22—1882no—
849C22—1884no—
850C22—1888no—
851C22—1882no—
852C22—1882no—
853C22#1568976512yes—
854C22C2×#1309405114yes—
855C22C2×#1309405112yes—
856C22#1568992712yes—
857C22C22×D4×D4711yescharacteristic
858C4—22no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—942no—
863C4—942no—
864C4—942no—
865C4—1882no—
866C4#1568976512yes—
867C4C2×#41×D4711yescharacteristic
868C4C2×#1309407011yescharacteristic
869C2—24no—
870C2—82no—
871C2—3762no—
872C2—3762no—
873C2—1882no—
874C2—1884no—
875C2#2025552714yesdirect product factor
876C2C2×#1568976511yescharacteristic
877C2C22×#1309405111yescharacteristic
878C2C2×#1568992711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#481C2
socleC23×C47C22×D4
hypercenterC2×#481D47
hypocenterC47C2×#3318
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#15689821C2semidirect
2. C2×#15689757C2semidirect
3. #20255527C2direct (N × H)
4. C2×#15689486C2semidirect
5. C2×#15689449C2semidirect
6. C2×#15689422C2semidirect
7. C2×#15689377C2semidirect
8. C2×#15689357C2semidirect
9. C2×#15689317C2semidirect
10. C2×#15689259C2semidirect
11. C2×#15689258C2semidirect
12. C2×#15689234C2semidirect
13. C2×#15689191C2semidirect
14. C2×#15689126C2semidirect
15. C22×#13093944C2semidirect
16. C2×C47×#481C2semidirect
21. C22×D376C22semidirect
22. C22×#10625334C22semidirect
23. C22×#10625324C22semidirect
24. C23×C47⋊C8C22semidirect
26. #15689821C22semidirect
28. #15689757C22semidirect
31. C2×#13094015C22semidirect
34. C2×#13093999C22semidirect
36. C2×#13093998C22semidirect
41. C2×#13093986C22semidirect
44. C2×#13093982C22semidirect
45. #15689486C22semidirect
46. #15689449C22semidirect
47. #15689422C22semidirect
48. #15689377C22semidirect
49. #15689357C22semidirect
50. #15689317C22semidirect
51. #15689259C22semidirect
52. #15689258C22semidirect
53. #15689234C22semidirect
54. #15689191C22semidirect
55. C2×#13093957C22semidirect
56. C2×Dic47⋊C8C22semidirect
57. #15689126C22semidirect
59. C2×#13093946C22semidirect
60. C2×#13093945C22semidirect
63. C2×#13093944C22semidirect
64. C2×#13093944C22semidirect
65. C2×#13093944C22semidirect
66. C2×#13093944C22semidirect
67. C2×(C2×D47)⋊C8C22semidirect
68. C2×#13093934C22semidirect
70. C22×C4⋊C4×C47C22semidirect
71. C47×#481C22semidirect
72. C2×#106×C47C22semidirect
73. C2×#106×C47C22semidirect
74. C2×#102×C47C22semidirect
75. C2×#102×C47C22semidirect
76. C2×C22⋊C8×C47C22semidirect
106. C2×D376C23semidirect
108. C2×#10625334C23semidirect
110. C2×#10625324C23semidirect
114. C22×C47⋊C8C23semidirect
119. #13094015C23semidirect
124. #13093999C23semidirect
127. #13093998C23semidirect
134. #13093986C23semidirect
139. #13093982C23semidirect
154. #13093957C23semidirect
155. Dic47⋊C8C23semidirect
157. #13093946C23semidirect
158. #13093945C23semidirect
161. #13093944C23semidirect
162. #13093944C23semidirect
163. #13093944C23semidirect
164. (C2×D47)⋊C8C23semidirect
165. #13093934C23semidirect
179. C2×C4⋊C4×C47C23semidirect
181. #106×C47C23semidirect
182. #106×C47C23semidirect
183. #102×C47C23semidirect
184. #102×C47C23semidirect
185. C22⋊C8×C47C23semidirect
434. C2×#481D47semidirect
448. C2×C47#3318semidirect
485. C22×C4⋊C4C2×D47semidirect
488. #481C2×D47semidirect
498. C2×#106C2×D47semidirect
499. C2×#106C2×D47semidirect
511. C2×#102C2×D47semidirect
512. C2×#102C2×D47semidirect
514. C2×C22⋊C8C2×D47semidirect
516. C47C2×#3318semidirect
597. C2×C4⋊C4C22×D47semidirect
610. #106C22×D47semidirect
611. #106C22×D47semidirect
621. #102C22×D47semidirect
622. #102C22×D47semidirect
624. C22⋊C8C22×D47semidirect
875. C2#20255527direct (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×#156897572
#202555272
C2×#156894862
C2×#156894492
C2×#156894222
C2×#156893772
C2×#156893572
C2×#156893172
C2×#156892592
C2×#156892582
C2×#156892342
C2×#156891912
C2×#156891262
C22×#130939442
C2×C47×#4812
C2×#331847