Finite Group Databasebeta

← C2×#20255574 #27093028

Subgroups — C2×#20255574 #27093028

Order 12032.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689838C211yesmaximal, characteristic, complemented
2#20255574C2116yesmaximal, direct product factor
3C2×#15689482C211yesmaximal, characteristic, complemented
4C2×#15689461C211yesmaximal, characteristic, complemented
5C2×#15689444C211yesmaximal, characteristic, complemented
6C2×#15689408C211yesmaximal, characteristic, complemented
7C2×#15689374C211yesmaximal, characteristic, complemented
8C2×#15689354C211yesmaximal, characteristic, complemented
9C2×#15689335C211yesmaximal, characteristic, complemented
10C2×#15689268C211yesmaximal, characteristic, complemented
11C2×#15689262C211yesmaximal, characteristic, complemented
12C2×#15689221C211yesmaximal, characteristic, complemented
13C2×#15689195C211yesmaximal, characteristic, complemented
14C2×#15689132C211yesmaximal, characteristic, complemented
15C2×#15689119C211yesmaximal, characteristic, complemented
16C2×C47×#548C211yesmaximal, characteristic, complemented
17C22×#10625336C2211yescharacteristic
18C22×#10625336C2211yescharacteristic
19C22×#10625334C2211yescharacteristic
20C22×#10625329C2211yescharacteristic
21C23×C47⋊C8C2211yescharacteristic
22#15689838—24no—
23#15689838C2218yescomplemented
24C2×#13094024C2211yescharacteristic
25C2×#13094010—21no—
26C2×#13094010—21no—
27C2×#13093998C2211yescharacteristic
28C2×#13093998C2211yescharacteristic
29C2×#13093995—21no—
30C2×C4×D188C2211yescharacteristic
31C2×#13093983C2211yescharacteristic
32C2×#13093983C2211yescharacteristic
33C2×#13093982—21no—
34#15689482C2218yescomplemented
35#15689461C2218yescomplemented
36#15689444C2218yescomplemented
37#15689408C2218yescomplemented
38#15689374C2218yescomplemented
39#15689354C2218yescomplemented
40#15689335C2218yescomplemented
41#15689268C2218yescomplemented
42#15689262C2218yescomplemented
43#15689221C2218yescomplemented
44#15689195C2218yescomplemented
45C2×#13093957C2211yescharacteristic
46C2×#13093955C2211yescharacteristic
47C2×#13093955C2211yescharacteristic
48C2×C4⋊(C47⋊C8)C2211yescharacteristic
49#15689132C2218yescomplemented
50#15689119C2218yescomplemented
51C2×#13093948C2211yescharacteristic
52C2×#13093948C2211yescharacteristic
53C2×#13093948C2211yescharacteristic
54C2×#13093948C2211yescharacteristic
55C2×#13093948C2211yescharacteristic
56C2×#13093948C2211yescharacteristic
57C2×#13093945C2211yescharacteristic
58C2×#13093945C2211yescharacteristic
59C2×#13093945C2211yescharacteristic
60C2×#13093944C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×C22⋊(C47⋊C8)C2211yescharacteristic
63C2×#13093935C2211yescharacteristic
64C22×#41×C47C2211yescharacteristic
65C23×Q8×C47C2211yescharacteristic
66C47×#548—24no—
67C47×#548C2218yescomplemented
68C2×#124×C47—21no—
69C2×#124×C47C2211yescharacteristic
70C2×C22⋊Q8×C47—21no—
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×#121×C47—21no—
73C2×#121×C47C2211yescharacteristic
74C2×C4×Q8×C47C2211yescharacteristic
75C2×C4×D4×C47—21no—
76C2×C4×D4×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×D188C2311yescharacteristic
79C22×C22⋊D47—21no—
80C22×C22⋊D47—21no—
81C22×C4×D47—21no—
82C2×#10625336—24no—
83C2×#10625336—42no—
84C2×#10625336C2314yes—
85C2×#10625336C2314yes—
86C2×#10625334—42no—
87C2×#10625334C2314yes—
88C2×#10625329—42no—
89C2×#10625329C2314yes—
90C22×C47⋊C8—42no—
91C22×C47⋊C8C2311yescharacteristic
92C22×C47⋊C8C2311yescharacteristic
93C22×C47⋊C8C2311yescharacteristic
94C22×C47⋊C8C2311yescharacteristic
95C22×C47⋊C8C2314yes—
96#13094024—22no—
97#13094024C2314yes—
98#13094010—28no—
99#13094010—28no—
100#13093998—22no—
101#13093998—22no—
102#13093998C2314yes—
103#13093998C2314yes—
104#13093995—28no—
105C4×D188—22no—
106C4×D188C2314yes—
107#13093983—22no—
108#13093983—22no—
109#13093983C2314yes—
110#13093983C2314yes—
111#13093982—28no—
112C2×C4⋊Dic47—21no—
113C2×C4⋊Dic47C2311yescharacteristic
114C2×C4⋊Dic47C2311yescharacteristic
115C2×C4⋊Dic47C2311yescharacteristic
116C2×C22⋊Dic47—21no—
117C2×C22⋊Dic47—21no—
118C2×(C2×D47)⋊C4—21no—
119C2×(C2×D47)⋊C4—21no—
120C2×(C2×D47)⋊C4—21no—
121C2×C4×Dic47—21no—
122C2×C4×Dic47—21no—
123#13093957C2314yes—
124#13093955C2314yes—
125#13093955C2314yes—
126C4⋊(C47⋊C8)C2314yes—
127#13093948C2314yes—
128#13093948C2314yes—
129#13093948C2314yes—
130#13093948C2314yes—
131#13093948C2314yes—
132#13093948C2314yes—
133#13093945C2314yes—
134#13093945C2314yes—
135#13093945C2314yes—
136#13093944C2314yes—
137C22⋊(C47⋊C8)C2314yes—
138C22⋊(C47⋊C8)C2314yes—
139#13093935C2314yes—
140C2×#41×C47—22no—
141C2×#41×C47—24no—
142C2×#41×C47—42no—
143C2×#41×C47C2314yes—
144C22×Q8×C47—21no—
145C22×Q8×C47—22no—
146C22×Q8×C47—24no—
147C22×Q8×C47—42no—
148C22×Q8×C47C2311yescharacteristic
149C22×Q8×C47C2314yes—
150C22×Q8×C47C2311yescharacteristic
151C22×D4×C47—21no—
152C22×D4×C47—21no—
153C22×D4×C47D411yescharacteristic
154C22×D4×C47C2311yescharacteristic
155C23×C4×C47—21no—
156C23×C4×C47—21no—
157C23×C4×C47C2311yescharacteristic
158C23×C4×C47C2311yescharacteristic
159#124×C47—28no—
160#124×C47—22no—
161#124×C47C2314yes—
162C22⋊Q8×C47—22no—
163C22⋊Q8×C47—28no—
164C22⋊Q8×C47C2314yes—
165#121×C47—28no—
166#121×C47—22no—
167#121×C47C2314yes—
168C4×Q8×C47—22no—
169C4×Q8×C47C2314yes—
170C4×D4×C47—28no—
171C4×D4×C47D414yes—
172C4×D4×C47C2314yes—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47D411yescharacteristic
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C22⋊C4×C47—21no—
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47D411yescharacteristic
182C2×C22⋊C4×C47D411yescharacteristic
183C2×C42×C47—21no—
184C2×C42×C47C2311yescharacteristic
185C24×C47—21no—
186C24×C47C2×D411yescharacteristic
187C24×C47C2×D411yescharacteristic
188C23×D47—21no—
189#41×C47—28no—
190#41×C47—44no—
191#41×C47—48no—
192C2×Q8×C47—21no—
193C2×Q8×C47—24no—
194C2×Q8×C47—21no—
195C2×Q8×C47—22no—
196C2×Q8×C47—28no—
197C2×Q8×C47—22no—
198C2×Q8×C47—22no—
199C2×Q8×C47—44no—
200C2×Q8×C47—44no—
201C2×Q8×C47—48no—
202C2×Q8×C47#4114yes—
203C2×Q8×C47C2412yes—
204C2×Q8×C47C2412yes—
205C2×D4×C47—24no—
206C2×D4×C47—24no—
207C2×D4×C47—21no—
208C2×D4×C47—22no—
209C2×D4×C47—22no—
210C2×D4×C47—42no—
211C2×D4×C47—44no—
212C2×D4×C47—44no—
213C2×D4×C47C2×D414yes—
214C2×D4×C47C2412yes—
215C22×C4×C47—21no—
216C22×C4×C47—22no—
217C22×C4×C47—22no—
218C22×C4×C47—22no—
219C22×C4×C47—22no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—24no—
223C22×C4×C47—24no—
224C22×C4×C47—44no—
225C22×C4×C47—44no—
226C22×C4×C47C2×D411yescharacteristic
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2×D411yescharacteristic
230C22×C4×C47C2×D412yes—
231C22×C4×C47C2×D412yes—
232C22×C4×C47C2412yes—
233C22×C4×C47C2412yes—
234C22×C4×C47C2411yescharacteristic
235C2×C22⋊D47—24no—
236C2×C22⋊D47—24no—
237C2×C22⋊D47—82no—
238C2×C22⋊D47—82no—
239C22×Dic47—21no—
240C22×Dic47—21no—
241C22×Dic47—21no—
242C2×D188—22no—
243C2×D188—22no—
244C2×D188—21no—
245C2×D188C2412yes—
246C2×C4×D47—24no—
247C2×C4×D47—44no—
248C2×Dic94—24no—
249C2×Dic94—82no—
250C4⋊C4×C47—24no—
251C4⋊C4×C47—24no—
252C4⋊C4×C47—21no—
253C4⋊C4×C47C2×D414yes—
254C4⋊C4×C47C2412yes—
255C22⋊C4×C47—24no—
256C22⋊C4×C47—24no—
257C22⋊C4×C47—24no—
258C22⋊C4×C47—24no—
259C22⋊C4×C47C2×D414yes—
260C22⋊C4×C47C2×D414yes—
261C42×C47—24no—
262C42×C47C2×D412yes—
263C42×C47C2412yes—
264C22⋊Dic47—24no—
265C22⋊Dic47—24no—
266#10625336—28no—
267#10625336—44no—
268#10625334—44no—
269(C2×D47)⋊C4—24no—
270(C2×D47)⋊C4—24no—
271(C2×D47)⋊C4—24no—
272C4⋊Dic47—24no—
273C4⋊Dic47—21no—
274C4⋊Dic47—21no—
275C4⋊Dic47—21no—
276C4⋊Dic47C2412yes—
277C4⋊Dic47C2412yes—
278C4⋊Dic47C2412yes—
279C4×Dic47—24no—
280C4×Dic47—24no—
281#10625329—44no—
282C2×C47⋊C8—22no—
283C2×C47⋊C8—22no—
284C2×C47⋊C8—22no—
285C2×C47⋊C8—22no—
286C2×C47⋊C8—44no—
287C2×C47⋊C8C2412yes—
288C2×C47⋊C8C2412yes—
289C2×C47⋊C8C2412yes—
290C2×C47⋊C8C2412yes—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—42no—
299C23×C47—42no—
300C23×C47—42no—
301C23×C47C22×D412yes—
302C23×C47C22×D412yes—
303C23×C47C22×D411yescharacteristic
304C22×D47—22no—
305C22×D47—42no—
306C22×D47—42no—
307C22×D47—42no—
308Q8×C47—24no—
309Q8×C47—22no—
310Q8×C47—22no—
311Q8×C47—22no—
312Q8×C47—48no—
313Q8×C47—42no—
314Q8×C47C2×#4114yes—
315D4×C47—22no—
316D4×C47—22no—
317D4×C47—44no—
318D4×C47—48no—
319D4×C47—48no—
320D4×C47—42no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—24no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—24no—
328C2×C4×C47—24no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—48no—
336C2×C4×C47—48no—
337C2×C4×C47—42no—
338C2×C4×C47—42no—
339C2×C4×C47C22×D412yes—
340C2×C4×C47C22×D412yes—
341C2×C4×C47C22×D412yes—
342C2×C4×C47C22×D412yes—
343C2×C4×C47C22×D411yescharacteristic
344C2×C4×C47C2×#4112yes—
345C2×C4×C47H(5,𝔽2)12yes—
346C2×C4×C47C2511yescharacteristic
347C22⋊D47—84no—
348C22⋊D47—84no—
349C2×Dic47—22no—
350C2×Dic47—22no—
351C2×Dic47—22no—
352C2×Dic47—42no—
353C2×Dic47—42no—
354C2×Dic47—42no—
355D188—22no—
356D188—22no—
357D188—42no—
358C4×D47—48no—
359Dic94—84no—
360C47⋊C8—22no—
361C47⋊C8—22no—
362C47⋊C8—22no—
363C47⋊C8—22no—
364C2×#3321—471nomaximal, Sylow
365C22×C47—22no—
366C22×C47—22no—
367C22×C47—22no—
368C22×C47—22no—
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—44no—
372C22×C47—44no—
373C22×C47—42no—
374C22×C47—42no—
375C22×C47—42no—
376C22×C47—84no—
377C22×C47#54612yes—
378C22×C47#57512yes—
379C22×C47#57712yes—
380C22×C47C23×D411yescharacteristic
381C2×D47—42no—
382C2×D47—42no—
383C2×D47—42no—
384C2×D47—84no—
385C4×C47—22no—
386C4×C47—22no—
387C4×C47—24no—
388C4×C47—22no—
389C4×C47—22no—
390C4×C47—42no—
391C4×C47—42no—
392C4×C47#54612yes—
393C4×C47C22×#4111yescharacteristic
394C4×C47C2×H(5,𝔽2)11yescharacteristic
395Dic47—42no—
396Dic47—42no—
397Dic47—42no—
398C2×#555—471no—
399C2×#548D4711yescharacteristic, complemented
400#3321—4716no—
401C2×#489—471no—
402C2×#485—471no—
403C2×#482—471no—
404C2×#475—471no—
405C2×#469—471no—
406C2×#465—471no—
407C2×#463—471no—
408C2×#449—471no—
409C2×#448—471no—
410C2×#440—471no—
411C2×#435—471no—
412C2×#419—471no—
413C2×#416—471no—
414C2×C47—42no—
415C2×C47—42no—
416C2×C47—82no—
417C2×C47#332114yescomplemented
418C2×C47C2×#54611yescharacteristic
419C2×C47C2×#57511yescharacteristic
420C2×C47C2×#57711yescharacteristic
421D47—82no—
422C22×#41C2×D4711yescharacteristic
423C23×Q8C2×D4711yescharacteristic
424C22×SD16—471no—
425C22×SD16—471no—
426C22×D8—471no—
427C22×M16—471no—
428C23×C8—471no—
429#555—478no—
430#555—944no—
431#548—24no—
432#548C2×D4718yescomplemented
433C2×C4⋊Q8—471no—
434C2×#124—21no—
435C2×#124—941no—
436C2×#124—941no—
437C2×#124C2×D4711yescharacteristic
438C2×C22⋊Q8—21no—
439C2×C22⋊Q8C2×D4711yescharacteristic
440C2×#121—21no—
441C2×#121—471no—
442C2×#121—471no—
443C2×#121—941no—
444C2×#121C2×D4711yescharacteristic
445C2×C4×Q8C2×D4711yescharacteristic
446C2×C4×D4—21no—
447C2×C4×D4—471no—
448C2×C4×D4C2×D4711yescharacteristic
449C2×#117—471no—
450C2×#117—471no—
451C2×#117—941no—
452#489—478no—
453#485—478no—
454#482—478no—
455#475—478no—
456#469—478no—
457#465—478no—
458#463—478no—
459#449—478no—
460#448—478no—
461#440—478no—
462#435—478no—
463C2×#107—471no—
464C2×#106—471no—
465C2×#106—471no—
466C2×C4⋊C8—471no—
467#419—478no—
468#416—478no—
469C2×#103—471no—
470C2×#103—471no—
471C2×#103—471no—
472C2×#103—471no—
473C2×#103—471no—
474C2×#103—471no—
475C2×#102—471no—
476C2×#102—471no—
477C2×#102—471no—
478C2×#102—471no—
479C2×C22⋊C8—471no—
480C2×C22⋊C8—471no—
481C2×#97—471no—
482C47C2×#332111yescharacteristic, complemented, Sylow
483C2×#41—22no—
484C2×#41—24no—
485C2×#41—42no—
486C2×#41C22×D4714yes—
487C22×Q8—21no—
488C22×Q8—22no—
489C22×Q8—24no—
490C22×Q8—42no—
491C22×Q8—941no—
492C22×Q8C22×D4711yescharacteristic
493C22×Q8C22×D4714yes—
494C22×Q8C22×D4711yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—471no—
498C22×D4—941no—
499C22×D4—941no—
500C22×D4C22⋊D4711yescharacteristic
501C22×D4C22×D4711yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—941no—
505C23×C4C22×D4711yescharacteristic
506C23×C4C22×D4711yescharacteristic
507C2×SD16—474no—
508C2×SD16—474no—
509C2×SD16—944no—
510C2×SD16—1882no—
511C2×D8—474no—
512C2×D8—1882no—
513C2×M16—474no—
514C2×M16—1882no—
515C22×C8—471no—
516C22×C8—471no—
517C22×C8—471no—
518C22×C8—471no—
519C22×C8—474no—
520C22×C8—1882no—
521C4⋊Q8—474no—
522C4⋊Q8—942no—
523#124—28no—
524#124—22no—
525#124—948no—
526#124—948no—
527#124C22×D4714yes—
528C22⋊Q8—22no—
529C22⋊Q8—28no—
530C22⋊Q8C22×D4714yes—
531#121—28no—
532#121—22no—
533#121—474no—
534#121—474no—
535#121—948no—
536#121—942no—
537#121—942no—
538#121C22×D4714yes—
539C4×Q8—22no—
540C4×Q8C22×D4714yes—
541C4×D4—28no—
542C4×D4—474no—
543C4×D4—942no—
544C4×D4C22⋊D4714yes—
545C4×D4C22×D4714yes—
546#117—474no—
547#117—474no—
548#117—942no—
549#117—942no—
550#117—948no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—471no—
554C2×C4⋊C4—471no—
555C2×C4⋊C4—471no—
556C2×C4⋊C4—941no—
557C2×C4⋊C4C22⋊D4711yescharacteristic
558C2×C4⋊C4C22×D4711yescharacteristic
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⋊C4C22⋊D4711yescharacteristic
569C2×C22⋊C4C22⋊D4711yescharacteristic
570C2×C42—21no—
571C2×C42—941no—
572C2×C42—941no—
573C2×C42C22×D4711yescharacteristic
574#107—474no—
575#106—474no—
576#106—474no—
577C4⋊C8—474no—
578#103—474no—
579#103—474no—
580#103—474no—
581#103—474no—
582#103—474no—
583#103—474no—
584#102—474no—
585#102—474no—
586#102—474no—
587#102—474no—
588C22⋊C8—474no—
589C22⋊C8—474no—
590#97—474no—
591C24—21no—
592C24—941no—
593C24C2×C22⋊D4711yescharacteristic
594C24C2×C22⋊D4711yescharacteristic
595#41—28no—
596#41—44no—
597#41—48no—
598C2×Q8—21no—
599C2×Q8—24no—
600C2×Q8—21no—
601C2×Q8—22no—
602C2×Q8—28no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—44no—
606C2×Q8—44no—
607C2×Q8—48no—
608C2×Q8—944no—
609C2×Q8—3762no—
610C2×Q8#1062535214yes—
611C2×Q8C23×D4712yes—
612C2×Q8C23×D4712yes—
613C2×D4—24no—
614C2×D4—24no—
615C2×D4—21no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—472no—
622C2×D4—944no—
623C2×D4—944no—
624C2×D4—941no—
625C2×D4—942no—
626C2×D4—942no—
627C2×D4—3762no—
628C2×D4—3762no—
629C2×D4C2×C22⋊D4714yes—
630C2×D4C23×D4712yes—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—24no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—941no—
643C22×C4—941no—
644C22×C4—941no—
645C22×C4—944no—
646C22×C4—1884no—
647C22×C4C2×C22⋊D4712yes—
648C22×C4C2×C22⋊D4712yes—
649C22×C4C2×C22⋊D4711yescharacteristic
650C22×C4C2×C22⋊D4711yescharacteristic
651C22×C4C2×C22⋊D4711yescharacteristic
652C22×C4C2×C22⋊D4711yescharacteristic
653C22×C4C23×D4712yes—
654C22×C4C23×D4712yes—
655C22×C4C23×D4711yescharacteristic
656SD16—948no—
657SD16—1884no—
658D8—1884no—
659M16—1884no—
660C2×C8—472no—
661C2×C8—472no—
662C2×C8—472no—
663C2×C8—472no—
664C2×C8—942no—
665C2×C8—942no—
666C2×C8—942no—
667C2×C8—942no—
668C2×C8—1884no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—21no—
672C4⋊C4—472no—
673C4⋊C4—472no—
674C4⋊C4—472no—
675C4⋊C4—941no—
676C4⋊C4—941no—
677C4⋊C4—941no—
678C4⋊C4—944no—
679C4⋊C4C2×C22⋊D4714yes—
680C4⋊C4C23×D4712yes—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—944no—
686C22⋊C4—944no—
687C22⋊C4—944no—
688C22⋊C4—944no—
689C22⋊C4—944no—
690C22⋊C4C2×C22⋊D4714yes—
691C22⋊C4C2×C22⋊D4714yes—
692C42—24no—
693C42—944no—
694C42—944no—
695C42C2×C22⋊D4712yes—
696C42C23×D4712yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—942no—
708C23—1882no—
709C23—1882no—
710C23—1882no—
711C23C22×C22⋊D4712yes—
712C23C22×C22⋊D4712yes—
713C23C22×C22⋊D4711yescharacteristic
714Q8—24no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—48no—
719Q8—42no—
720Q8—3764no—
721Q8C2×#1062535214yes—
722D4—22no—
723D4—22no—
724D4—44no—
725D4—48no—
726D4—48no—
727D4—42no—
728D4—942no—
729D4—942no—
730D4—3764no—
731D4—3764no—
732D4—1882no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—1888no—
755C2×C4—1882no—
756C2×C4—1882no—
757C2×C4—1882no—
758C2×C4C22×C22⋊D4712yes—
759C2×C4C22×C22⋊D4712yes—
760C2×C4C22×C22⋊D4712yes—
761C2×C4C22×C22⋊D4712yes—
762C2×C4C22×C22⋊D4711yescharacteristic
763C2×C4C2×#1062535212yes—
764C2×C4#1309406912yes—
765C2×C4C24×D4711yescharacteristic
766C8—942no—
767C8—942no—
768C8—942no—
769C8—942no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—3764no—
783C22—1882no—
784C22—1882no—
785C22—1882no—
786C22#1568976712yes—
787C22#1568992112yes—
788C22#1568993112yes—
789C22C23×C22⋊D4711yescharacteristic
790C4—22no—
791C4—22no—
792C4—24no—
793C4—22no—
794C4—22no—
795C4—42no—
796C4—42no—
797C4—1882no—
798C4—1882no—
799C4—1882no—
800C4#1568976712yes—
801C4C22×#1062535211yescharacteristic
802C4C2×#1309406911yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—3762no—
807C2#2025557414yesdirect product factor
808C2C2×#1568976711yescharacteristic
809C2C2×#1568992111yescharacteristic
810C2C2×#1568993111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#548C2
socleC23×C47C22×D4
hypercenterC2×#548D47
hypocenterC47C2×#3321
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#15689838C2semidirect
2. #20255574C2direct (N × H)
3. C2×#15689482C2semidirect
4. C2×#15689461C2semidirect
5. C2×#15689444C2semidirect
6. C2×#15689408C2semidirect
7. C2×#15689374C2semidirect
8. C2×#15689354C2semidirect
9. C2×#15689335C2semidirect
10. C2×#15689268C2semidirect
11. C2×#15689262C2semidirect
12. C2×#15689221C2semidirect
13. C2×#15689195C2semidirect
14. C2×#15689132C2semidirect
15. C2×#15689119C2semidirect
16. C2×C47×#548C2semidirect
23. #15689838C22semidirect
34. #15689482C22semidirect
35. #15689461C22semidirect
36. #15689444C22semidirect
37. #15689408C22semidirect
38. #15689374C22semidirect
39. #15689354C22semidirect
40. #15689335C22semidirect
41. #15689268C22semidirect
42. #15689262C22semidirect
43. #15689221C22semidirect
44. #15689195C22semidirect
49. #15689132C22semidirect
50. #15689119C22semidirect
67. C47×#548C22semidirect
399. C2×#548D47semidirect
417. C2×C47#3321semidirect
432. #548C2×D47semidirect
482. C47C2×#3321semidirect
807. C2#20255574direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898382
#202555742
C2×#156894822
C2×#156894612
C2×#156894442
C2×#156894082
C2×#156893742
C2×#156893542
C2×#156893352
C2×#156892682
C2×#156892622
C2×#156892212
C2×#156891952
C2×#156891322
C2×#156891192
C2×C47×#5482
C2×#332147