Finite Group Databasebeta

← C2×#20255376 #27092849

Subgroups — C2×#20255376 #27092849

Order 12032.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689785C211yesmaximal, characteristic, complemented
2C2×#15689776C211yesmaximal, characteristic, complemented
3#20255376C2116yesmaximal, direct product factor
4C2×#15689485C211yesmaximal, characteristic, complemented
5C2×#15689460C211yesmaximal, characteristic, complemented
6C2×#15689438C211yesmaximal, characteristic, complemented
7C2×#15689370C211yesmaximal, characteristic, complemented
8C2×#15689360C211yesmaximal, characteristic, complemented
9C2×#15689339C211yesmaximal, characteristic, complemented
10C2×#15689271C211yesmaximal, characteristic, complemented
11C2×#15689263C211yesmaximal, characteristic, complemented
12C2×#15689221C211yesmaximal, characteristic, complemented
13C2×#15689193C211yesmaximal, characteristic, complemented
14C2×#15689123C211yesmaximal, characteristic, complemented
15C2×#103×D47C211yesmaximal, characteristic, complemented
16C2×C47×#477C211yesmaximal, characteristic, complemented
17C22×#10625354—21no—
18C22×#10625354C2211yescharacteristic
19C22×Q8×D47C2211yescharacteristic
20C22×#10625325C2211yescharacteristic
21C22×#10625336C2211yescharacteristic
22C22×D376C2211yescharacteristic
23C22×#10625324C2211yescharacteristic
24C22×C8×D47C2211yescharacteristic
25#15689785—24no—
26#15689785C2218yescomplemented
27#15689776—24no—
28#15689776C2218yescomplemented
29C2×#13094012—21no—
30C2×#13094012C2211yescharacteristic
31C2×#13094009—21no—
32C2×#13094009—21no—
33C2×#13094004—21no—
34C2×#13094004C2211yescharacteristic
35C2×#13094000—21no—
36C2×#13093999—21no—
37C2×#13093999C2211yescharacteristic
38C2×#13093999C2211yescharacteristic
39C2×#13093999C2211yescharacteristic
40C2×C4×D188—21no—
41C2×C4×D188C2211yescharacteristic
42C2×C4×D188C2211yescharacteristic
43C2×C4⋊C4×D47C2211yescharacteristic
44C2×C4⋊C4×D47C2211yescharacteristic
45#15689485C2218yescomplemented
46#15689460C2218yescomplemented
47#15689438C2218yescomplemented
48#15689370C2218yescomplemented
49#15689360C2218yescomplemented
50#15689339C2218yescomplemented
51#15689271C2218yescomplemented
52#15689263C2218yescomplemented
53#15689221C2218yescomplemented
54#15689193C2218yescomplemented
55C2×#13093957C2211yescharacteristic
56#15689123C2218yescomplemented
57C2×#13093949C2211yescharacteristic
58C2×#13093948C2211yescharacteristic
59C2×#13093947C2211yescharacteristic
60C2×#13093947C2211yescharacteristic
61#103×D47C2218yescomplemented
62C2×#13093946C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093935C2211yescharacteristic
69C2×C4⋊Q8×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C47×#477C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#107×C47C2211yescharacteristic
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C2×#10625354—28no—
78C2×#10625354—22no—
79C2×#10625354—24no—
80C2×#10625354—42no—
81C2×#10625354—48no—
82C2×#10625354C2314yes—
83C22×Dic94—21no—
84C22×Dic94C2311yescharacteristic
85C2×Q8×D47—22no—
86C2×Q8×D47—24no—
87C2×Q8×D47—42no—
88C2×Q8×D47C2314yes—
89C22×D188—21no—
90C22×D188—21no—
91C22×D188—21no—
92C22×D188—21no—
93C22×D188D411yescharacteristic
94C22×D188C2311yescharacteristic
95C22×D188C2311yescharacteristic
96C22×C4×D47—21no—
97C22×C4×D47—21no—
98C22×C4×D47—21no—
99C22×C4×D47—21no—
100C22×C4×D47—21no—
101C22×C4×D47C2311yescharacteristic
102C22×C4×D47C2311yescharacteristic
103C2×#10625325—42no—
104C2×#10625325C2314yes—
105C2×#10625336—24no—
106C2×#10625336C2314yes—
107C2×D376—42no—
108C2×D376C2314yes—
109C2×#10625324—42no—
110C2×#10625324C2314yes—
111C22×C47⋊C8C2311yescharacteristic
112C22×C47⋊C8C2311yescharacteristic
113C2×C8×D47—42no—
114C2×C8×D47C2314yes—
115#13094012—22no—
116#13094012—28no—
117#13094012C2314yes—
118#13094009—28no—
119#13094009—28no—
120#13094004—22no—
121#13094004—28no—
122#13094004C2314yes—
123#13094000—28no—
124#13093999—28no—
125#13093999—22no—
126#13093999—22no—
127#13093999—22no—
128#13093999C2314yes—
129#13093999C2314yes—
130#13093999C2314yes—
131C4×D188—22no—
132C4×D188—28no—
133C4×D188D414yes—
134C4×D188C2314yes—
135C4×D188C2314yes—
136C2×C4⋊Dic47—21no—
137C2×C4⋊Dic47D411yescharacteristic
138C2×C4⋊Dic47C2311yescharacteristic
139C2×Dic47⋊C4—21no—
140C2×Dic47⋊C4—21no—
141C4⋊C4×D47—22no—
142C4⋊C4×D47—22no—
143C4⋊C4×D47C2314yes—
144C4⋊C4×D47C2314yes—
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)⋊C4—21no—
152C2×(C2×D47)⋊C4D411yescharacteristic
153C2×(C2×D47)⋊C4D411yescharacteristic
154#13093957C2314yes—
155#13093949C2314yes—
156#13093948C2314yes—
157#13093947C2314yes—
158#13093947C2314yes—
159#13093946C2314yes—
160#13093944C2314yes—
161#13093944C2314yes—
162#13093944C2314yes—
163(C2×D47)⋊C8C2314yes—
164(C2×D47)⋊C8C2314yes—
165#13093935C2314yes—
166C22×Q8×C47—21no—
167C22×Q8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170C4⋊Q8×C47—22no—
171C4⋊Q8×C47C2314yes—
172C4×Q8×C47—22no—
173C4×Q8×C47C2314yes—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47—21no—
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C42×C47—21no—
180C2×C42×C47C2311yescharacteristic
181#107×C47C2314yes—
182#107×C47C2314yes—
183C4⋊C8×C47C2314yes—
184#103×C47C2314yes—
185#103×C47C2314yes—
186C23×D47—21no—
187C23×D47—21no—
188C23×D47C2×D411yescharacteristic
189C23×D47C2×D411yescharacteristic
190C2×Q8×C47—21no—
191C2×Q8×C47—24no—
192C2×Q8×C47—22no—
193C2×Q8×C47—44no—
194C2×Q8×C47#4114yescomplemented
195C2×Q8×C47C2412yes—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2411yescharacteristic
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47C2×D411yescharacteristic
206C22×Dic47C2×D411yescharacteristic
207#10625354—28no—
208#10625354—44no—
209#10625354—48no—
210#10625354—432no—
211Q8×D47—28no—
212Q8×D47—44no—
213Q8×D47—48no—
214C2×D188—24no—
215C2×D188—22no—
216C2×D188—22no—
217C2×D188—22no—
218C2×D188—22no—
219C2×D188—24no—
220C2×D188—24no—
221C2×D188—24no—
222C2×D188—24no—
223C2×D188—21no—
224C2×D188—21no—
225C2×D188—44no—
226C2×D188—44no—
227C2×D188—44no—
228C2×D188—44no—
229C2×D188C2×D414yes—
230C2×D188C2412yes—
231C2×D188C2412yes—
232C2×C4×D47—22no—
233C2×C4×D47—22no—
234C2×C4×D47—22no—
235C2×C4×D47—22no—
236C2×C4×D47—24no—
237C2×C4×D47—24no—
238C2×C4×D47—24no—
239C2×C4×D47—24no—
240C2×C4×D47—24no—
241C2×C4×D47—44no—
242C2×C4×D47—44no—
243C2×C4×D47—44no—
244C2×C4×D47—44no—
245C2×C4×D47—44no—
246C2×C4×D47C2×D412yes—
247C2×C4×D47C2×D412yes—
248C2×C4×D47C2412yes—
249C2×C4×D47C2412yes—
250C2×Dic94—22no—
251C2×Dic94—22no—
252C2×Dic94—21no—
253C2×Dic94—24no—
254C2×Dic94—44no—
255C2×Dic94C2412yes—
256C2×C8×C47—22no—
257C2×C8×C47—22no—
258C2×C8×C47C2412yes—
259C2×C8×C47C2412yes—
260C4⋊C4×C47—24no—
261C4⋊C4×C47—24no—
262C4⋊C4×C47—21no—
263C4⋊C4×C47—21no—
264C4⋊C4×C47—21no—
265C4⋊C4×C47C2412yes—
266C4⋊C4×C47C2412yes—
267C4⋊C4×C47C2412yes—
268C42×C47—24no—
269C42×C47C2×D412yes—
270C42×C47C2412yes—
271#10625336—28no—
272(C2×D47)⋊C4—24no—
273(C2×D47)⋊C4—24no—
274(C2×D47)⋊C4—24no—
275(C2×D47)⋊C4—24no—
276(C2×D47)⋊C4—24no—
277(C2×D47)⋊C4—24no—
278(C2×D47)⋊C4—24no—
279(C2×D47)⋊C4C2×D414yes—
280(C2×D47)⋊C4C2×D414yes—
281C4⋊Dic47—21no—
282C4⋊Dic47—24no—
283C4⋊Dic47C2×D414yes—
284C4⋊Dic47C2412yes—
285Dic47⋊C4—24no—
286Dic47⋊C4—24no—
287C2×C47⋊C8—22no—
288C2×C47⋊C8—22no—
289C2×C47⋊C8C2412yes—
290C2×C47⋊C8C2412yes—
291D376—44no—
292#10625325—44no—
293#10625324—44no—
294C8×D47—44no—
295C23×C47C22×D411yescharacteristic
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—22no—
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—42no—
304C22×D47—42no—
305C22×D47—42no—
306C22×D47—42no—
307C22×D47—42no—
308C22×D47—42no—
309C22×D47AGL(1,ℤ/8)14yes—
310C22×D47C22×D412yes—
311C22×D47C22×D412yes—
312Q8×C47—24no—
313Q8×C47—22no—
314Q8×C47—48no—
315Q8×C47C2×#4114yescomplemented
316C2×C4×C47—24no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—42no—
324C2×C4×C47—42no—
325C2×C4×C47—42no—
326C2×C4×C47C22×D412yes—
327C2×C4×C47C22×D412yes—
328C2×C4×C47C22×D411yescharacteristic
329C2×C4×C47C2×#4112yes—
330C2×C4×C47H(5,𝔽2)12yes—
331C2×C4×C47C2511yescharacteristic
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—42no—
337C2×Dic47—42no—
338C2×Dic47C22×D412yes—
339C2×Dic47C22×D412yes—
340D188—28no—
341D188—22no—
342D188—22no—
343D188—22no—
344D188—22no—
345D188—48no—
346D188—48no—
347D188—48no—
348D188—48no—
349D188—42no—
350D188—42no—
351C4×D47—24no—
352C4×D47—24no—
353C4×D47—22no—
354C4×D47—22no—
355C4×D47—22no—
356C4×D47—22no—
357C4×D47—48no—
358C4×D47—48no—
359C4×D47—48no—
360C4×D47—48no—
361C4×D47—48no—
362Dic94—22no—
363Dic94—22no—
364Dic94—48no—
365Dic94—42no—
366C8×C47—22no—
367C8×C47—22no—
368C47⋊C8—22no—
369C47⋊C8—22no—
370C2×#3308—471nomaximal, Sylow
371C22×C47#54612yes—
372C22×C47C2×AGL(1,ℤ/8)12yes—
373C22×C47#57812yes—
374C22×C47C23×D411yescharacteristic
375C2×D47—22no—
376C2×D47—28no—
377C2×D47—22no—
378C2×D47—22no—
379C2×D47—22no—
380C2×D47—22no—
381C2×D47—44no—
382C2×D47—42no—
383C2×D47—42no—
384C2×D47—42no—
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—84no—
389C2×D47—84no—
390C2×D47C2×AGL(1,ℤ/8)14yes—
391C4×C47—24no—
392C4×C47—22no—
393C4×C47—22no—
394C4×C47—42no—
395C4×C47—42no—
396C4×C47—42no—
397C4×C47#54612yes—
398C4×C47C22×#4111yescharacteristic
399C4×C47C2×H(5,𝔽2)11yescharacteristic
400Dic47—22no—
401Dic47—22no—
402Dic47—42no—
403Dic47—42no—
404C2×#548—471no—
405C2×#547—471no—
406#3308—4716no—
407C2×#489—471no—
408C2×#484—471no—
409C2×#480—471no—
410C2×#477D4711yescharacteristic, complemented
411C2×#468—471no—
412C2×#466—471no—
413C2×#463—471no—
414C2×#449—471no—
415C2×#448—471no—
416C2×#440—471no—
417C2×#435—471no—
418C2×#417—471no—
419C22×#103—471no—
420C2×C47#330814yescomplemented
421C2×C47C2×#54611yescharacteristic
422C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
423C2×C47C2×#57811yescharacteristic
424D47—24no—
425D47—42no—
426D47—82no—
427D47—82no—
428C22×#41—471no—
429C22×#41—941no—
430C23×Q8—471no—
431C22×SD16—471no—
432C22×SD16—471no—
433C22×D8—471no—
434C22×M16—471no—
435C23×C8—471no—
436#548—478no—
437#548—944no—
438#547—478no—
439#547—944no—
440C2×C4⋊Q8C2×D4711yescharacteristic
441C2×#124—471no—
442C2×#124—941no—
443C2×#123—941no—
444C2×#123—941no—
445C2×C22⋊Q8—471no—
446C2×C22⋊Q8—941no—
447C2×C22⋊Q8—941no—
448C2×#121—471no—
449C2×#121—471no—
450C2×#121—471no—
451C2×#121—941no—
452C2×C4×Q8C2×D4711yescharacteristic
453C2×C4×D4—471no—
454C2×C4×D4—471no—
455C2×C4×D4—941no—
456C22×C4⋊C4—471no—
457C22×C4⋊C4—471no—
458#489—478no—
459#484—478no—
460#480—478no—
461#477C2×D4718yescomplemented
462#468—478no—
463#466—478no—
464#463—478no—
465#449—478no—
466#448—478no—
467#440—478no—
468#435—478no—
469C2×#107—471no—
470C2×#107C2×D4711yescharacteristic
471C2×#107C2×D4711yescharacteristic
472C2×C4⋊C8C2×D4711yescharacteristic
473#417—478no—
474C2×#103—471no—
475C2×#103—471no—
476C2×#103—471no—
477C2×#103—471no—
478C2×#103—478no—
479C2×#103C2×D4711yescharacteristic
480C2×#103C2×D4711yescharacteristic
481C2×#102—471no—
482C2×#102—471no—
483C2×#102—471no—
484C2×#102—471no—
485C2×C22⋊C8—471no—
486C2×C22⋊C8—471no—
487C2×#97—471no—
488C47C2×#330811yescharacteristic, complemented, Sylow
489C2×#41—474no—
490C2×#41—942no—
491C2×#41—948no—
492C2×#41—944no—
493C2×#41—1882no—
494C2×#41—1888no—
495C22×Q8—21no—
496C22×Q8—474no—
497C22×Q8—471no—
498C22×Q8—941no—
499C22×Q8—942no—
500C22×Q8—944no—
501C22×Q8—1882no—
502C22×Q8C22×D4711yescharacteristic
503C22×D4—471no—
504C22×D4—471no—
505C22×D4—471no—
506C22×D4—941no—
507C22×D4—941no—
508C22×D4—941no—
509C22×D4—941no—
510C23×C4—471no—
511C23×C4—471no—
512C23×C4—941no—
513C23×C4—941no—
514C23×C4—941no—
515C23×C4—941no—
516C23×C4—941no—
517C2×SD16—474no—
518C2×SD16—474no—
519C2×SD16—944no—
520C2×SD16—1882no—
521C2×D8—474no—
522C2×D8—1882no—
523C2×M16—474no—
524C2×M16—1882no—
525C22×C8—471no—
526C22×C8—471no—
527C22×C8—474no—
528C22×C8—1882no—
529C22×C8C22×D4711yescharacteristic
530C22×C8C22×D4711yescharacteristic
531C4⋊Q8—22no—
532C4⋊Q8C22×D4714yes—
533#124—474no—
534#124—948no—
535#124—942no—
536#123—948no—
537#123—948no—
538C22⋊Q8—474no—
539C22⋊Q8—948no—
540C22⋊Q8—942no—
541C22⋊Q8—948no—
542#121—474no—
543#121—474no—
544#121—474no—
545#121—942no—
546#121—942no—
547#121—942no—
548#121—948no—
549C4×Q8—22no—
550C4×Q8C22×D4714yes—
551C4×D4—474no—
552C4×D4—474no—
553C4×D4—474no—
554C4×D4—948no—
555C4×D4—942no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—471no—
559C2×C4⋊C4—471no—
560C2×C4⋊C4—474no—
561C2×C4⋊C4—474no—
562C2×C4⋊C4—942no—
563C2×C4⋊C4—942no—
564C2×C4⋊C4—941no—
565C2×C4⋊C4—941no—
566C2×C4⋊C4—941no—
567C2×C4⋊C4C22×D4711yescharacteristic
568C2×C4⋊C4C22×D4711yescharacteristic
569C2×C4⋊C4C22×D4711yescharacteristic
570C2×C22⋊C4—471no—
571C2×C22⋊C4—471no—
572C2×C22⋊C4—941no—
573C2×C22⋊C4—941no—
574C2×C22⋊C4—941no—
575C2×C22⋊C4—941no—
576C2×C22⋊C4—941no—
577C2×C22⋊C4—941no—
578C2×C22⋊C4—941no—
579C2×C42—21no—
580C2×C42C22×D4711yescharacteristic
581#107—474no—
582#107C22×D4714yes—
583#107C22×D4714yes—
584C4⋊C8C22×D4714yes—
585#103—474no—
586#103—474no—
587#103—474no—
588#103—474no—
589#103C22×D4714yes—
590#103C22×D4714yes—
591#102—474no—
592#102—474no—
593#102—474no—
594#102—474no—
595C22⋊C8—474no—
596C22⋊C8—474no—
597#97—474no—
598C24—471no—
599C24—471no—
600C24—941no—
601C24—941no—
602#41—948no—
603#41—1884no—
604#41—1888no—
605#41—18832no—
606C2×Q8—21no—
607C2×Q8—24no—
608C2×Q8—22no—
609C2×Q8—44no—
610C2×Q8—472no—
611C2×Q8—944no—
612C2×Q8—941no—
613C2×Q8—948no—
614C2×Q8—942no—
615C2×Q8—942no—
616C2×Q8—1884no—
617C2×Q8—1884no—
618C2×Q8—1888no—
619C2×Q8#1062535414yescomplemented
620C2×Q8C23×D4712yes—
621C2×D4—474no—
622C2×D4—472no—
623C2×D4—472no—
624C2×D4—944no—
625C2×D4—944no—
626C2×D4—944no—
627C2×D4—944no—
628C2×D4—944no—
629C2×D4—941no—
630C2×D4—941no—
631C2×D4—942no—
632C2×D4—942no—
633C2×D4—942no—
634C2×D4—942no—
635C2×D4—1884no—
636C2×D4—1884no—
637C2×D4—1884no—
638C2×D4—1884no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—471no—
644C22×C4—471no—
645C22×C4—472no—
646C22×C4—472no—
647C22×C4—472no—
648C22×C4—472no—
649C22×C4—944no—
650C22×C4—944no—
651C22×C4—944no—
652C22×C4—944no—
653C22×C4—942no—
654C22×C4—942no—
655C22×C4—942no—
656C22×C4—942no—
657C22×C4—941no—
658C22×C4—941no—
659C22×C4—944no—
660C22×C4—1884no—
661C22×C4—1884no—
662C22×C4—1884no—
663C22×C4—1884no—
664C22×C4—1884no—
665C22×C4D4×D4711yescharacteristic
666C22×C4D4×D4711yescharacteristic
667C22×C4C23×D4711yescharacteristic
668SD16—948no—
669SD16—1884no—
670D8—1884no—
671M16—1884no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—472no—
675C2×C8—472no—
676C2×C8—942no—
677C2×C8—942no—
678C2×C8—1884no—
679C2×C8C23×D4712yes—
680C2×C8C23×D4712yes—
681C4⋊C4—24no—
682C4⋊C4—24no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—474no—
687C4⋊C4—472no—
688C4⋊C4—944no—
689C4⋊C4—944no—
690C4⋊C4—944no—
691C4⋊C4—941no—
692C4⋊C4C23×D4712yes—
693C4⋊C4C23×D4712yes—
694C4⋊C4C23×D4712yes—
695C22⋊C4—474no—
696C22⋊C4—474no—
697C22⋊C4—944no—
698C22⋊C4—944no—
699C22⋊C4—944no—
700C22⋊C4—944no—
701C22⋊C4—944no—
702C22⋊C4—944no—
703C22⋊C4—944no—
704C42—24no—
705C42D4×D4712yes—
706C42C23×D4712yes—
707C23—474no—
708C23—472no—
709C23—472no—
710C23—942no—
711C23—942no—
712C23—942no—
713C23—942no—
714C23—942no—
715C23—942no—
716C23—942no—
717C23—1882no—
718C23—1882no—
719C23—1882no—
720C23—1882no—
721C23—1882no—
722C23—1882no—
723C23C2×D4×D4711yescharacteristic
724Q8—24no—
725Q8—22no—
726Q8—48no—
727Q8—942no—
728Q8—942no—
729Q8—1888no—
730Q8—1882no—
731Q8C2×#1062535414yescomplemented
732D4—948no—
733D4—942no—
734D4—942no—
735D4—942no—
736D4—942no—
737D4—1888no—
738D4—1888no—
739D4—1888no—
740D4—1888no—
741D4—1882no—
742D4—1882no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—472no—
754C2×C4—472no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—944no—
758C2×C4—944no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—1888no—
766C2×C4—1888no—
767C2×C4—1888no—
768C2×C4—1888no—
769C2×C4—1888no—
770C2×C4—1882no—
771C2×C4—1882no—
772C2×C4C2×D4×D4712yes—
773C2×C4C2×D4×D4712yes—
774C2×C4C2×D4×D4711yescharacteristic
775C2×C4C2×#1062535412yes—
776C2×C4#1309407012yes—
777C2×C4C24×D4711yescharacteristic
778C8—22no—
779C8—22no—
780C8—942no—
781C8—942no—
782C22—474no—
783C22—942no—
784C22—942no—
785C22—948no—
786C22—942no—
787C22—942no—
788C22—942no—
789C22—3764no—
790C22—3764no—
791C22—1882no—
792C22—1882no—
793C22—1882no—
794C22—1882no—
795C22—1882no—
796C22—1882no—
797C22—1884no—
798C22#1568976412yes—
799C22AGL(1,ℤ/8)×D4712yes—
800C22#1568993612yes—
801C22C22×D4×D4711yescharacteristic
802C4—24no—
803C4—22no—
804C4—22no—
805C4—42no—
806C4—42no—
807C4—42no—
808C4—942no—
809C4—942no—
810C4—1882no—
811C4—1882no—
812C4#1568976412yes—
813C4C22×#1062535411yescharacteristic
814C4C2×#1309407011yescharacteristic
815C2—944no—
816C2—3762no—
817C2—3762no—
818C2—1882no—
819C2#2025537614yesdirect product factor
820C2C2×#1568976411yescharacteristic
821C2C2×AGL(1,ℤ/8)×D4711yescharacteristic
822C2C2×#1568993611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#477C2
socleC23×C47C22×D4
hypercenterC2×#477D47
hypocenterC47C2×#3308
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#15689785C2semidirect
2. C2×#15689776C2semidirect
3. #20255376C2direct (N × H)
4. C2×#15689485C2semidirect
5. C2×#15689460C2semidirect
6. C2×#15689438C2semidirect
7. C2×#15689370C2semidirect
8. C2×#15689360C2semidirect
9. C2×#15689339C2semidirect
10. C2×#15689271C2semidirect
11. C2×#15689263C2semidirect
12. C2×#15689221C2semidirect
13. C2×#15689193C2semidirect
14. C2×#15689123C2semidirect
15. C2×#103×D47C2semidirect
16. C2×C47×#477C2semidirect
26. #15689785C22semidirect
28. #15689776C22semidirect
45. #15689485C22semidirect
46. #15689460C22semidirect
47. #15689438C22semidirect
48. #15689370C22semidirect
49. #15689360C22semidirect
50. #15689339C22semidirect
51. #15689271C22semidirect
52. #15689263C22semidirect
53. #15689221C22semidirect
54. #15689193C22semidirect
56. #15689123C22semidirect
61. #103×D47C22semidirect
71. C47×#477C22semidirect
194. C2×Q8×C47#41semidirect
315. Q8×C47C2×#41semidirect
410. C2×#477D47semidirect
420. C2×C47#3308semidirect
461. #477C2×D47semidirect
488. C47C2×#3308semidirect
619. C2×Q8#10625354semidirect
731. Q8C2×#10625354semidirect
819. C2#20255376direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897852
C2×#156897762
#202553762
C2×#156894852
C2×#156894602
C2×#156894382
C2×#156893702
C2×#156893602
C2×#156893392
C2×#156892712
C2×#156892632
C2×#156892212
C2×#156891932
C2×#156891232
C2×#103×D472
C2×C47×#4772
C2×#330847