Finite Group Databasebeta

← C2×#20256472 #27097304

Subgroups — C2×#20256472 #27097304

Order 12032.

2066 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689858C211yesmaximal, characteristic, complemented
2#20256472C2116yesmaximal, direct product factor
3C2×#15689513C211yesmaximal, characteristic, complemented
4C2×#15689510C211yesmaximal, characteristic, complemented
5C2×#15689505C211yesmaximal, characteristic, complemented
6C2×#15689345C211yesmaximal, characteristic, complemented
7C2×#15689342C211yesmaximal, characteristic, complemented
8C2×#15689338C211yesmaximal, characteristic, complemented
9C2×#15689335C211yesmaximal, characteristic, complemented
10C2×#15689318C211yesmaximal, characteristic, complemented
11C2×#15689315C211yesmaximal, characteristic, complemented
12C2×#15689254C211yesmaximal, characteristic, complemented
13C2×#15689223C211yesmaximal, characteristic, complemented
14C2×#15689221C211yesmaximal, characteristic, complemented
15C2×C4×#10625334C211yesmaximal, characteristic, complemented
16C2×C47×#559C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625335C2211yescharacteristic
19C22×#10625335C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×#10625336C2211yescharacteristic
22C22×#10625334C2211yescharacteristic
23C22×#10625334C2211yescharacteristic
24C22×#10625334C2211yescharacteristic
25C22×#10625334C2211yescharacteristic
26#15689858—24no—
27#15689858C2218yescomplemented
28C2×#13094021C2211yescharacteristic
29C2×#13094013—21no—
30C2×#13094012C2211yescharacteristic
31C2×#13094012C2211yescharacteristic
32C2×#13094009—21no—
33C2×#13094009—21no—
34C2×C4×Dic94C2211yescharacteristic
35C2×C4×D188C2211yescharacteristic
36C2×C4×D188C2211yescharacteristic
37C2×#13093986—21no—
38#15689513C2218yescomplemented
39#15689510C2218yescomplemented
40#15689505C2218yescomplemented
41#15689345C2218yescomplemented
42#15689342C2218yescomplemented
43#15689338C2218yescomplemented
44#15689335C2218yescomplemented
45#15689318C2218yescomplemented
46#15689315C2218yescomplemented
47#15689254C2218yescomplemented
48#15689223C2218yescomplemented
49#15689221C2218yescomplemented
50C4×#10625334C2218yescomplemented
51C2×#13093957C2211yescharacteristic
52C2×C4⋊(C47⋊C8)C2211yescharacteristic
53C2×C4⋊(C47⋊C8)C2211yescharacteristic
54C2×C4⋊(C47⋊C8)C2211yescharacteristic
55C2×#13093948C2211yescharacteristic
56C2×#13093947C2211yescharacteristic
57C2×#13093945C2211yescharacteristic
58C2×#13093945C2211yescharacteristic
59C2×#13093944C2211yescharacteristic
60C2×#13093944C2211yescharacteristic
61C2×#13093935C2211yescharacteristic
62C2×#13093935C2211yescharacteristic
63C2×C4×C47⋊C8C2211yescharacteristic
64C47×#559—24no—
65C47×#559C2218yescomplemented
66C2×#127×C47C2211yescharacteristic
67C2×#124×C47—21no—
68C2×#124×C47C2211yescharacteristic
69C2×#124×C47C2211yescharacteristic
70C2×#123×C47—21no—
71C2×#123×C47—21no—
72C2×C4×Q8×C47C2211yescharacteristic
73C2×C4×Q8×C47C2211yescharacteristic
74C2×C4×D4×C47—21no—
75C2×C4×D4×C47C2211yescharacteristic
76C2×C4×D4×C47C2211yescharacteristic
77C22×Dic94C2311yescharacteristic
78C22×D188—21no—
79C22×D188—21no—
80C22×D188C2311yescharacteristic
81C22×D188C2311yescharacteristic
82C22×C4×D47—21no—
83C22×C4×D47—21no—
84C2×#10625337—42no—
85C2×#10625337C2314yes—
86C2×#10625335—24no—
87C2×#10625335—42no—
88C2×#10625335C2314yes—
89C2×#10625335C2314yes—
90C2×#10625336—24no—
91C2×#10625336—42no—
92C2×#10625336C2314yes—
93C2×#10625336C2314yes—
94C2×#10625334—24no—
95C2×#10625334—42no—
96C2×#10625334—42no—
97C2×#10625334—42no—
98C2×#10625334C2314yes—
99C2×#10625334C2314yes—
100C2×#10625334C2314yes—
101C2×#10625334C2314yes—
102C22×C47⋊C8C2311yescharacteristic
103C22×C47⋊C8C2311yescharacteristic
104C22×C47⋊C8C2311yescharacteristic
105C22×C47⋊C8C2311yescharacteristic
106#13094021—22no—
107#13094021C2314yes—
108#13094013—28no—
109#13094012—22no—
110#13094012—22no—
111#13094012C2314yes—
112#13094012C2314yes—
113#13094009—28no—
114#13094009—28no—
115C4×Dic94—22no—
116C4×Dic94C2314yes—
117C4×D188—22no—
118C4×D188—22no—
119C4×D188C2314yes—
120C4×D188C2314yes—
121#13093986—28no—
122C2×C4⋊Dic47C2311yescharacteristic
123C2×Dic47⋊C4—21no—
124C2×(C2×D47)⋊C4—21no—
125C2×(C2×D47)⋊C4—21no—
126C2×(C2×D47)⋊C4—21no—
127C2×(C2×D47)⋊C4—21no—
128C2×(C2×D47)⋊C4—21no—
129C2×(C2×D47)⋊C4—21no—
130C2×C4×Dic47—21no—
131#13093957C2314yes—
132C4⋊(C47⋊C8)C2314yes—
133C4⋊(C47⋊C8)C2314yes—
134C4⋊(C47⋊C8)C2314yes—
135#13093948C2314yes—
136#13093947C2314yes—
137#13093945C2314yes—
138#13093945C2314yes—
139#13093944C2314yes—
140#13093944C2314yes—
141#13093935C2314yes—
142#13093935C2314yes—
143C4×C47⋊C8C2314yes—
144C22×Q8×C47D411yescharacteristic
145C22×Q8×C47C2311yescharacteristic
146C22×D4×C47—21no—
147C22×D4×C47—21no—
148C22×D4×C47C2311yescharacteristic
149C22×D4×C47C2311yescharacteristic
150C23×C4×C47—21no—
151C23×C4×C47—21no—
152#127×C47—22no—
153#127×C47C2314yes—
154#124×C47—28no—
155#124×C47—22no—
156#124×C47—22no—
157#124×C47C2314yes—
158#124×C47C2314yes—
159#123×C47—28no—
160#123×C47—28no—
161C4×Q8×C47—22no—
162C4×Q8×C47D414yes—
163C4×Q8×C47C2314yes—
164C4×Q8×C47C2314yes—
165C4×D4×C47—28no—
166C4×D4×C47—22no—
167C4×D4×C47—22no—
168C4×D4×C47C2314yes—
169C4×D4×C47C2314yes—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47D411yescharacteristic
172C2×C4⋊C4×C47D411yescharacteristic
173C2×C4⋊C4×C47D411yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176C2×C22⋊C4×C47—21no—
177C2×C22⋊C4×C47—21no—
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180C2×C22⋊C4×C47—21no—
181C2×C42×C47—21no—
182C2×C42×C47C2311yescharacteristic
183C2×C42×C47C2311yescharacteristic
184C2×C42×C47C2311yescharacteristic
185C24×C47—21no—
186C24×C47—21no—
187C23×D47—21no—
188C23×D47—21no—
189C2×Q8×C47—21no—
190C2×Q8×C47—22no—
191C2×Q8×C47—22no—
192C2×Q8×C47—42no—
193C2×Q8×C47C2×D414yes—
194C2×Q8×C47C2412yes—
195C2×D4×C47—21no—
196C2×D4×C47—21no—
197C2×D4×C47—24no—
198C2×D4×C47—24no—
199C2×D4×C47—22no—
200C2×D4×C47—22no—
201C2×D4×C47—22no—
202C2×D4×C47—22no—
203C2×D4×C47—44no—
204C2×D4×C47—82no—
205C2×D4×C47C2412yes—
206C2×D4×C47C2412yes—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—24no—
210C22×C4×C47—24no—
211C22×C4×C47—82no—
212C22×C4×C47—82no—
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2411yescharacteristic
220C22×Dic47—21no—
221C22×Dic47—21no—
222C2×D188—22no—
223C2×D188—22no—
224C2×D188—22no—
225C2×D188—22no—
226C2×D188—24no—
227C2×D188—21no—
228C2×D188—21no—
229C2×D188—24no—
230C2×D188—44no—
231C2×D188—82no—
232C2×D188C2412yes—
233C2×D188C2412yes—
234C2×C4×D47—24no—
235C2×C4×D47—24no—
236C2×C4×D47—82no—
237C2×C4×D47—82no—
238C2×Dic94—22no—
239C2×Dic94—22no—
240C2×Dic94—21no—
241C2×Dic94C2412yes—
242C4⋊C4×C47—24no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47C2×D414yes—
245C4⋊C4×C47C2×D414yes—
246C4⋊C4×C47C2×D414yes—
247C4⋊C4×C47C2412yes—
248C22⋊C4×C47—24no—
249C22⋊C4×C47—24no—
250C22⋊C4×C47—24no—
251C22⋊C4×C47—24no—
252C22⋊C4×C47—24no—
253C22⋊C4×C47—24no—
254C42×C47—24no—
255C42×C47C2×D412yes—
256C42×C47C2×D412yes—
257C42×C47C2×D412yes—
258C42×C47C2412yes—
259C42×C47C2412yes—
260C42×C47C2412yes—
261#10625337—44no—
262#10625336—28no—
263#10625336—44no—
264#10625335—28no—
265#10625335—44no—
266#10625334—28no—
267#10625334—44no—
268#10625334—44no—
269#10625334—44no—
270(C2×D47)⋊C4—24no—
271(C2×D47)⋊C4—24no—
272(C2×D47)⋊C4—24no—
273(C2×D47)⋊C4—24no—
274(C2×D47)⋊C4—24no—
275(C2×D47)⋊C4—24no—
276C4⋊Dic47—21no—
277C4⋊Dic47C2412yes—
278Dic47⋊C4—24no—
279C4×Dic47—24no—
280C2×C47⋊C8—22no—
281C2×C47⋊C8—22no—
282C2×C47⋊C8—22no—
283C2×C47⋊C8#4114yes—
284C2×C47⋊C8C2412yes—
285C2×C47⋊C8C2412yes—
286C2×C47⋊C8C2412yes—
287C2×C47⋊C8C2412yes—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—42no—
291C23×C47—42no—
292C23×C47—42no—
293C23×C47—42no—
294C23×C47—42no—
295C23×C47—42no—
296C23×C47C22×D411yescharacteristic
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—42no—
300C22×D47—42no—
301C22×D47—42no—
302C22×D47—42no—
303C22×D47—42no—
304C22×D47—42no—
305Q8×C47—22no—
306Q8×C47—22no—
307Q8×C47—44no—
308Q8×C47—42no—
309D4×C47—22no—
310D4×C47—22no—
311D4×C47—22no—
312D4×C47—22no—
313D4×C47—48no—
314D4×C47—42no—
315D4×C47—42no—
316D4×C47—84no—
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—22no—
324C2×C4×C47—22no—
325C2×C4×C47—42no—
326C2×C4×C47—42no—
327C2×C4×C47—84no—
328C2×C4×C47—84no—
329C2×C4×C47C22×D412yes—
330C2×C4×C47C22×D412yes—
331C2×C4×C47C22×D412yes—
332C2×C4×C47C22×D412yes—
333C2×C4×C47C22×D412yes—
334C2×C4×C47C22×D412yes—
335C2×C4×C47C22×D411yescharacteristic
336C2×C4×C47C2×#4112yes—
337C2×C4×C47H(5,𝔽2)12yes—
338C2×C4×C47C2511yescharacteristic
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—42no—
342C2×Dic47—42no—
343D188—22no—
344D188—22no—
345D188—22no—
346D188—22no—
347D188—48no—
348D188—42no—
349D188—42no—
350D188—84no—
351C4×D47—84no—
352C4×D47—84no—
353Dic94—22no—
354Dic94—22no—
355Dic94—42no—
356C47⋊C8—22no—
357C47⋊C8—22no—
358C47⋊C8—22no—
359C47⋊C8C2×#4114yes—
360C2×#3403—471nomaximal, Sylow
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—42no—
364C22×C47—42no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47—84no—
368C22×C47—84no—
369C22×C47#55012yes—
370C22×C47#57512yes—
371C22×C47#57612yes—
372C22×C47C23×D411yescharacteristic
373C2×D47—42no—
374C2×D47—42no—
375C2×D47—42no—
376C2×D47—42no—
377C2×D47—42no—
378C2×D47—42no—
379C2×D47—84no—
380C2×D47—84no—
381C4×C47—22no—
382C4×C47—22no—
383C4×C47—22no—
384C4×C47—22no—
385C4×C47—22no—
386C4×C47—22no—
387C4×C47—42no—
388C4×C47—42no—
389C4×C47#55012yes—
390C4×C47C22×#4111yescharacteristic
391C4×C47C2×H(5,𝔽2)11yescharacteristic
392Dic47—42no—
393Dic47—42no—
394C2×#559—471no—
395C2×#559D4711yescharacteristic, complemented
396#3403—4716no—
397C2×#496—471no—
398C2×#496—471no—
399C2×#495—471no—
400C2×#464—471no—
401C2×#464—471no—
402C2×#463—471no—
403C2×#463—471no—
404C2×#459—471no—
405C2×#459—471no—
406C2×#446—471no—
407C2×#440—471no—
408C2×#440—471no—
409C2×C4×D8—471no—
410C2×C47—82no—
411C2×C47—82no—
412C2×C47#340314yescomplemented
413C2×C47C2×#55011yescharacteristic
414C2×C47C2×#57511yescharacteristic
415C2×C47C2×#57611yescharacteristic
416D47—82no—
417D47—82no—
418C22×Q16—471no—
419C22×SD16—471no—
420C22×SD16—471no—
421C22×SD16—471no—
422C22×SD16—471no—
423C22×D8—471no—
424C22×D8—471no—
425C22×D8—471no—
426C22×D8—471no—
427#559—24no—
428#559—478no—
429#559—944no—
430#559C2×D4718yescomplemented
431C2×#127—471no—
432C2×#127C2×D4711yescharacteristic
433C2×#124—21no—
434C2×#124—471no—
435C2×#124—471no—
436C2×#124—941no—
437C2×#124C2×D4711yescharacteristic
438C2×#124C2×D4711yescharacteristic
439C2×#123—21no—
440C2×#123—21no—
441C2×#123—941no—
442C2×#123—941no—
443C2×C4×Q8—471no—
444C2×C4×Q8C2×D4711yescharacteristic
445C2×C4×Q8C2×D4711yescharacteristic
446C2×C4×D4—21no—
447C2×C4×D4—471no—
448C2×C4×D4—471no—
449C2×C4×D4—941no—
450C2×C4×D4C2×D4711yescharacteristic
451C2×C4×D4C2×D4711yescharacteristic
452#496—478no—
453#496—478no—
454#495—478no—
455#464—478no—
456#464—478no—
457#463—478no—
458#463—478no—
459#459—478no—
460#459—478no—
461#446—478no—
462#440—478no—
463#440—478no—
464C4×D8—478no—
465C2×#107—471no—
466C2×C4⋊C8—471no—
467C2×C4⋊C8—471no—
468C2×C4⋊C8—471no—
469C2×#103—471no—
470C2×#103—471no—
471C2×#102—471no—
472C2×#102—471no—
473C2×#102—471no—
474C2×#102—471no—
475C2×#97—471no—
476C2×#97—471no—
477C2×C4×C8—471no—
478C47C2×#340311yescharacteristic, complemented, Sylow
479C22×Q8—471no—
480C22×Q8C22⋊D4711yescharacteristic
481C22×Q8C22×D4711yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—471no—
485C22×D4—471no—
486C22×D4—941no—
487C22×D4—941no—
488C22×D4C22×D4711yescharacteristic
489C22×D4C22×D4711yescharacteristic
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—941no—
493C23×C4—941no—
494C2×Q16—474no—
495C2×Q16—1882no—
496C2×SD16—474no—
497C2×SD16—474no—
498C2×SD16—474no—
499C2×SD16—474no—
500C2×SD16—944no—
501C2×SD16—944no—
502C2×SD16—1882no—
503C2×SD16—1882no—
504C2×D8—474no—
505C2×D8—474no—
506C2×D8—474no—
507C2×D8—474no—
508C2×D8—944no—
509C2×D8—1882no—
510C2×D8—1882no—
511C2×D8—1882no—
512C22×C8—471no—
513C22×C8—471no—
514C22×C8—471no—
515C22×C8—471no—
516#127—22no—
517#127—474no—
518#127—942no—
519#127C22×D4714yes—
520#124—28no—
521#124—22no—
522#124—22no—
523#124—474no—
524#124—474no—
525#124—948no—
526#124—942no—
527#124—942no—
528#124C22×D4714yes—
529#124C22×D4714yes—
530#123—28no—
531#123—28no—
532#123—948no—
533#123—948no—
534C4×Q8—22no—
535C4×Q8—474no—
536C4×Q8—942no—
537C4×Q8C22⋊D4714yes—
538C4×Q8C22×D4714yes—
539C4×Q8C22×D4714yes—
540C4×D4—28no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—474no—
544C4×D4—474no—
545C4×D4—948no—
546C4×D4—942no—
547C4×D4—942no—
548C4×D4C22×D4714yes—
549C4×D4C22×D4714yes—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—471no—
552C2×C4⋊C4—941no—
553C2×C4⋊C4C22⋊D4711yescharacteristic
554C2×C4⋊C4C22⋊D4711yescharacteristic
555C2×C4⋊C4C22⋊D4711yescharacteristic
556C2×C4⋊C4C22×D4711yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—941no—
564C2×C22⋊C4—941no—
565C2×C22⋊C4—941no—
566C2×C22⋊C4—941no—
567C2×C22⋊C4—941no—
568C2×C22⋊C4—941no—
569C2×C42—21no—
570C2×C42—941no—
571C2×C42C22×D4711yescharacteristic
572C2×C42C22×D4711yescharacteristic
573C2×C42C22×D4711yescharacteristic
574#107—474no—
575C4⋊C8—474no—
576C4⋊C8—474no—
577C4⋊C8—474no—
578#103—474no—
579#103—474no—
580#102—474no—
581#102—474no—
582#102—474no—
583#102—474no—
584#97—474no—
585#97—474no—
586C4×C8—474no—
587C24—21no—
588C24—21no—
589C24—941no—
590C24—941no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—42no—
595C2×Q8—472no—
596C2×Q8—941no—
597C2×Q8—942no—
598C2×Q8—942no—
599C2×Q8C2×C22⋊D4714yes—
600C2×Q8C23×D4712yes—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—44no—
610C2×D4—82no—
611C2×D4—472no—
612C2×D4—472no—
613C2×D4—944no—
614C2×D4—944no—
615C2×D4—941no—
616C2×D4—941no—
617C2×D4—942no—
618C2×D4—942no—
619C2×D4—942no—
620C2×D4—942no—
621C2×D4—3762no—
622C2×D4—1884no—
623C2×D4C23×D4712yes—
624C2×D4C23×D4712yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—82no—
630C22×C4—82no—
631C22×C4—941no—
632C22×C4—941no—
633C22×C4—944no—
634C22×C4—944no—
635C22×C4—3762no—
636C22×C4—3762no—
637C22×C4C2×C22⋊D4711yescharacteristic
638C22×C4C2×C22⋊D4711yescharacteristic
639C22×C4C2×C22⋊D4711yescharacteristic
640C22×C4C2×C22⋊D4711yescharacteristic
641C22×C4C2×C22⋊D4711yescharacteristic
642C22×C4C2×C22⋊D4711yescharacteristic
643C22×C4C23×D4711yescharacteristic
644Q16—1884no—
645SD16—948no—
646SD16—948no—
647SD16—1884no—
648SD16—1884no—
649D8—948no—
650D8—1884no—
651D8—1884no—
652D8—1884no—
653C2×C8—474no—
654C2×C8—472no—
655C2×C8—472no—
656C2×C8—472no—
657C2×C8—472no—
658C2×C8—942no—
659C2×C8—942no—
660C2×C8—942no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—472no—
664C4⋊C4—944no—
665C4⋊C4—941no—
666C4⋊C4C2×C22⋊D4714yes—
667C4⋊C4C2×C22⋊D4714yes—
668C4⋊C4C2×C22⋊D4714yes—
669C4⋊C4C23×D4712yes—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—944no—
677C22⋊C4—944no—
678C22⋊C4—944no—
679C22⋊C4—944no—
680C22⋊C4—944no—
681C22⋊C4—944no—
682C42—24no—
683C42—944no—
684C42C2×C22⋊D4712yes—
685C42C2×C22⋊D4712yes—
686C42C2×C22⋊D4712yes—
687C42C23×D4712yes—
688C42C23×D4712yes—
689C42C23×D4712yes—
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—942no—
699C23—942no—
700C23—1882no—
701C23—1882no—
702C23—1882no—
703C23—1882no—
704C23—1882no—
705C23—1882no—
706C23C22×C22⋊D4711yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—44no—
710Q8—42no—
711Q8—942no—
712Q8—942no—
713Q8—1882no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—48no—
719D4—42no—
720D4—42no—
721D4—84no—
722D4—942no—
723D4—942no—
724D4—942no—
725D4—942no—
726D4—3764no—
727D4—1888no—
728D4—1882no—
729D4—1882no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—942no—
743C2×C4—942no—
744C2×C4—3764no—
745C2×C4—3764no—
746C2×C4—1882no—
747C2×C4—1882no—
748C2×C4C22×C22⋊D4712yes—
749C2×C4C22×C22⋊D4712yes—
750C2×C4C22×C22⋊D4712yes—
751C2×C4C22×C22⋊D4712yes—
752C2×C4C22×C22⋊D4712yes—
753C2×C4C22×C22⋊D4712yes—
754C2×C4C22×C22⋊D4711yescharacteristic
755C2×C4#41×D4712yes—
756C2×C4#1309407012yes—
757C2×C4C24×D4711yescharacteristic
758C8—474no—
759C8—942no—
760C8—942no—
761C8—942no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22—84no—
770C22—3764no—
771C22—3764no—
772C22—1882no—
773C22—1882no—
774C22—1882no—
775C22—1882no—
776C22—1882no—
777C22—1882no—
778C22#1568979212yes—
779C22#1568992112yes—
780C22#1568992612yes—
781C22C23×C22⋊D4711yescharacteristic
782C4—22no—
783C4—22no—
784C4—22no—
785C4—22no—
786C4—22no—
787C4—22no—
788C4—42no—
789C4—42no—
790C4—1882no—
791C4—1882no—
792C4#1568979212yes—
793C4C2×#41×D4711yescharacteristic
794C4C2×#1309407011yescharacteristic
795C2—82no—
796C2—82no—
797C2—3762no—
798C2—3762no—
799C2#2025647214yesdirect product factor
800C2C2×#1568979211yescharacteristic
801C2C2×#1568992111yescharacteristic
802C2C2×#1568992611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#559C2
socleC23×C47C22×D4
hypercenterC2×#559D47
hypocenterC47C2×#3403
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#15689858C2semidirect
2. #20256472C2direct (N × H)
3. C2×#15689513C2semidirect
4. C2×#15689510C2semidirect
5. C2×#15689505C2semidirect
6. C2×#15689345C2semidirect
7. C2×#15689342C2semidirect
8. C2×#15689338C2semidirect
9. C2×#15689335C2semidirect
10. C2×#15689318C2semidirect
11. C2×#15689315C2semidirect
12. C2×#15689254C2semidirect
13. C2×#15689223C2semidirect
14. C2×#15689221C2semidirect
15. C2×C4×#10625334C2semidirect
16. C2×C47×#559C2semidirect
27. #15689858C22semidirect
38. #15689513C22semidirect
39. #15689510C22semidirect
40. #15689505C22semidirect
41. #15689345C22semidirect
42. #15689342C22semidirect
43. #15689338C22semidirect
44. #15689335C22semidirect
45. #15689318C22semidirect
46. #15689315C22semidirect
47. #15689254C22semidirect
48. #15689223C22semidirect
49. #15689221C22semidirect
50. C4×#10625334C22semidirect
65. C47×#559C22semidirect
395. C2×#559D47semidirect
412. C2×C47#3403semidirect
430. #559C2×D47semidirect
478. C47C2×#3403semidirect
799. C2#20256472direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898582
#202564722
C2×#156895132
C2×#156895102
C2×#156895052
C2×#156893452
C2×#156893422
C2×#156893382
C2×#156893352
C2×#156893182
C2×#156893152
C2×#156892542
C2×#156892232
C2×#156892212
C2×C4×#106253342
C2×C47×#5592
C2×#340347