Finite Group Databasebeta

← C2×#20255635 #27093125

Subgroups — C2×#20255635 #27093125

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×#15689782C211yesmaximal, characteristic, complemented
2#20255635C2116yesmaximal, direct product factor
3C2×#15689480C211yesmaximal, characteristic, complemented
4C2×#15689447C211yesmaximal, characteristic, complemented
5C2×#15689453C211yesmaximal, characteristic, complemented
6C2×#15689427C211yesmaximal, characteristic, complemented
7C2×#15689374C211yesmaximal, characteristic, complemented
8C2×#15689367C211yesmaximal, characteristic, complemented
9C2×#15689338C211yesmaximal, characteristic, complemented
10C2×#15689266C211yesmaximal, characteristic, complemented
11C2×#15689261C211yesmaximal, characteristic, complemented
12C2×C4×#10625335C211yesmaximal, characteristic, complemented
13C2×#15689201C211yesmaximal, characteristic, complemented
14C2×#15689122C211yesmaximal, characteristic, complemented
15C2×#15689131C211yesmaximal, characteristic, complemented
16C2×C47×#553C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C23×Dic94C2211yescharacteristic
19C22×#10625335C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21C22×#10625334C2211yescharacteristic
22C22×#10625329C2211yescharacteristic
23C22×#10625329C2211yescharacteristic
24#15689782—24no—
25#15689782C2218yescomplemented
26C2×#13094012C2211yescharacteristic
27C2×#13094010—21no—
28C2×#13094003C2211yescharacteristic
29C2×#13094002—21no—
30C2×#13093998C2211yescharacteristic
31C2×#13093996—21no—
32C2×C4×Dic94C2211yescharacteristic
33C2×(C22⋊D47)⋊C4—21no—
34#15689480C2218yescomplemented
35#15689453C2218yescomplemented
36#15689447C2218yescomplemented
37#15689427C2218yescomplemented
38#15689374C2218yescomplemented
39#15689367C2218yescomplemented
40#15689338C2218yescomplemented
41#15689266C2218yescomplemented
42#15689261C2218yescomplemented
43C4×#10625335C2218yescomplemented
44#15689201C2218yescomplemented
45C2×#13093957C2211yescharacteristic
46C2×#13093955C2211yescharacteristic
47C2×#13093955C2211yescharacteristic
48C2×C4⋊(C47⋊C8)C2211yescharacteristic
49#15689131C2218yescomplemented
50#15689122C2218yescomplemented
51C2×#13093947C2211yescharacteristic
52C2×#13093947C2211yescharacteristic
53C2×#13093947C2211yescharacteristic
54C2×#13093947C2211yescharacteristic
55C2×#13093947C2211yescharacteristic
56C2×#13093947C2211yescharacteristic
57C2×#13093945C2211yescharacteristic
58C2×#13093944C2211yescharacteristic
59C2×#13093944C2211yescharacteristic
60C2×#13093944C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×C22⋊(C47⋊C8)C2211yescharacteristic
63C2×C4×C47⋊C8C2211yescharacteristic
64C47×#553—24no—
65C47×#553C2218yescomplemented
66C2×#126×C47—21no—
67C2×#125×C47C2211yescharacteristic
68C2×#123×C47—21no—
69C2×#121×C47—21no—
70C2×#121×C47C2211yescharacteristic
71C2×#121×C47C2211yescharacteristic
72C2×C4×D4×C47—21no—
73C2×C4×D4×C47C2211yescharacteristic
74C2×C4×D4×C47C2211yescharacteristic
75C2×#117×C47C2211yescharacteristic
76C22×C4⋊C4×C47C2211yescharacteristic
77C2×#10625350—22no—
78C2×#10625350—24no—
79C2×#10625350—42no—
80C2×#10625350C2314yes—
81C22×Dic94—24no—
82C22×Dic94—22no—
83C22×Dic94—21no—
84C22×Dic94—42no—
85C22×Dic94C2311yescharacteristic
86C22×Dic94C2314yes—
87C22×Dic94C2311yescharacteristic
88C22×D188C2311yescharacteristic
89C22×C22⋊D47—21no—
90C22×C22⋊D47—21no—
91C23×Dic47—21no—
92C22×C4×D47—21no—
93C2×#10625335—24no—
94C2×#10625335—42no—
95C2×#10625335C2314yes—
96C2×#10625335C2314yes—
97C2×#10625334—42no—
98C2×#10625334C2314yes—
99C2×#10625329—42no—
100C2×#10625329—42no—
101C2×#10625329C2314yes—
102C2×#10625329C2314yes—
103C22×C47⋊C8C2311yescharacteristic
104C22×C47⋊C8C2311yescharacteristic
105C22×C47⋊C8C2311yescharacteristic
106C22×C47⋊C8C2311yescharacteristic
107#13094012—22no—
108#13094012C2314yes—
109#13094010—28no—
110#13094003—22no—
111#13094003C2314yes—
112#13094002—28no—
113#13093998—22no—
114#13093998C2314yes—
115#13093996—28no—
116C4×Dic94—22no—
117C4×Dic94C2314yes—
118(C22⋊D47)⋊C4—28no—
119C2×C4⋊Dic47C2311yescharacteristic
120C2×Dic47⋊C4—21no—
121C2×Dic47⋊C4—21no—
122C2×C22⋊Dic47—21no—
123C2×(C2×D47)⋊C4—21no—
124C2×(C2×D47)⋊C4—21no—
125C2×(C2×D47)⋊C4—21no—
126C2×C4×Dic47—21no—
127#13093957C2314yes—
128#13093955C2314yes—
129#13093955C2314yes—
130C4⋊(C47⋊C8)C2314yes—
131#13093947C2314yes—
132#13093947C2314yes—
133#13093947C2314yes—
134#13093947C2314yes—
135#13093947C2314yes—
136#13093947C2314yes—
137#13093945C2314yes—
138#13093944C2314yes—
139#13093944C2314yes—
140#13093944C2314yes—
141C22⋊(C47⋊C8)C2314yes—
142C22⋊(C47⋊C8)C2314yes—
143C4×C47⋊C8C2314yes—
144C22×D4×C47—21no—
145C22×D4×C47—21no—
146C22×D4×C47D411yescharacteristic
147C22×D4×C47C2311yescharacteristic
148C23×C4×C47—21no—
149C23×C4×C47—21no—
150C23×C4×C47C2311yescharacteristic
151C23×C4×C47C2311yescharacteristic
152#126×C47—28no—
153#125×C47—22no—
154#125×C47C2314yes—
155#123×C47—28no—
156#121×C47—28no—
157#121×C47—22no—
158#121×C47—22no—
159#121×C47C2314yes—
160#121×C47C2314yes—
161C4×D4×C47—28no—
162C4×D4×C47—22no—
163C4×D4×C47D414yes—
164C4×D4×C47C2314yes—
165C4×D4×C47C2314yes—
166#117×C47—22no—
167#117×C47C2314yes—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47—22no—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47D411yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C4⋊C4×C47C2314yes—
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—
189C2×D4×C47—24no—
190C2×D4×C47—24no—
191C2×D4×C47—21no—
192C2×D4×C47—22no—
193C2×D4×C47—22no—
194C2×D4×C47—42no—
195C2×D4×C47—44no—
196C2×D4×C47—82no—
197C2×D4×C47C2×D414yes—
198C2×D4×C47C2412yes—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—22no—
202C22×C4×C47—22no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—24no—
207C22×C4×C47—24no—
208C22×C4×C47—82no—
209C22×C4×C47—82no—
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D412yes—
215C22×C4×C47C2×D412yes—
216C22×C4×C47C2412yes—
217C22×C4×C47C2412yes—
218C22×C4×C47C2411yescharacteristic
219C2×C22⋊D47—24no—
220C2×C22⋊D47—24no—
221C2×C22⋊D47—44no—
222C2×C22⋊D47—44no—
223C22×Dic47—21no—
224C22×Dic47—21no—
225C22×Dic47—21no—
226C22×Dic47—24no—
227C22×Dic47—44no—
228#10625350—28no—
229#10625350—44no—
230#10625350—48no—
231C2×D188—22no—
232C2×D188—22no—
233C2×D188—21no—
234C2×D188C2412yes—
235C2×C4×D47—24no—
236C2×C4×D47—44no—
237C2×Dic94—21no—
238C2×Dic94—22no—
239C2×Dic94—22no—
240C2×Dic94—22no—
241C2×Dic94—28no—
242C2×Dic94—24no—
243C2×Dic94—21no—
244C2×Dic94—44no—
245C2×Dic94—48no—
246C2×Dic94—44no—
247C2×Dic94#4114yes—
248C2×Dic94C2412yes—
249C2×Dic94C2412yes—
250C4⋊C4×C47—21no—
251C4⋊C4×C47—21no—
252C4⋊C4×C47—24no—
253C4⋊C4×C47—24no—
254C4⋊C4×C47—24no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47C2×D414yes—
257C4⋊C4×C47C2412yes—
258C4⋊C4×C47C2412yes—
259C4⋊C4×C47C2412yes—
260C22⋊C4×C47—24no—
261C22⋊C4×C47—24no—
262C22⋊C4×C47—24no—
263C22⋊C4×C47—24no—
264C22⋊C4×C47C2×D414yes—
265C22⋊C4×C47C2×D414yes—
266C42×C47—24no—
267C42×C47C2×D412yes—
268C42×C47C2412yes—
269C22⋊Dic47—24no—
270#10625335—28no—
271#10625335—44no—
272#10625334—44no—
273(C2×D47)⋊C4—24no—
274(C2×D47)⋊C4—24no—
275(C2×D47)⋊C4—24no—
276C4⋊Dic47—21no—
277C4⋊Dic47C2412yes—
278Dic47⋊C4—24no—
279Dic47⋊C4—24no—
280C4×Dic47—24no—
281#10625329—44no—
282#10625329—44no—
283C2×C47⋊C8—22no—
284C2×C47⋊C8—22no—
285C2×C47⋊C8—22no—
286C2×C47⋊C8—22no—
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—
308D4×C47—22no—
309D4×C47—22no—
310D4×C47—44no—
311D4×C47—48no—
312D4×C47—42no—
313D4×C47—84no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—24no—
319C2×C4×C47—24no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—42no—
328C2×C4×C47—42no—
329C2×C4×C47—42no—
330C2×C4×C47—84no—
331C2×C4×C47—84no—
332C2×C4×C47C22×D412yes—
333C2×C4×C47C22×D412yes—
334C2×C4×C47C22×D412yes—
335C2×C4×C47C22×D412yes—
336C2×C4×C47C22×D411yescharacteristic
337C2×C4×C47C2×#4112yes—
338C2×C4×C47H(5,𝔽2)12yes—
339C2×C4×C47C2511yescharacteristic
340C22⋊D47—48no—
341C22⋊D47—48no—
342C2×Dic47—24no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—48no—
347C2×Dic47—42no—
348C2×Dic47—42no—
349D188—22no—
350D188—22no—
351D188—42no—
352C4×D47—48no—
353Dic94—24no—
354Dic94—22no—
355Dic94—22no—
356Dic94—22no—
357Dic94—48no—
358Dic94—42no—
359Dic94C2×#4114yes—
360C47⋊C8—22no—
361C47⋊C8—22no—
362C47⋊C8—22no—
363C47⋊C8—22no—
364C2×#3326—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—22no—
388C4×C47—22no—
389C4×C47—42no—
390C4×C47—42no—
391C4×C47—42no—
392C4×C47#54612yes—
393C4×C47C22×#4111yescharacteristic
394C4×C47C2×H(5,𝔽2)11yescharacteristic
395Dic47—24no—
396Dic47—42no—
397Dic47—42no—
398C2×#553D4711yescharacteristic, complemented
399C2×#548—471no—
400#3326—4716no—
401C2×#488—471no—
402C2×#482—471no—
403C2×#483—471no—
404C2×#479—471no—
405C2×#469—471no—
406C2×#468—471no—
407C2×#463—471no—
408C2×#449—471no—
409C2×#448—471no—
410C2×C4×SD16—471no—
411C2×#436—471no—
412C2×#417—471no—
413C2×#419—471no—
414C2×C47—42no—
415C2×C47—42no—
416C2×C47—82no—
417C2×C47#332614yescomplemented
418C2×C47C2×#54611yescharacteristic
419C2×C47C2×#57511yescharacteristic
420C2×C47C2×#57711yescharacteristic
421D47—82no—
422C22×#41—471no—
423C23×Q8—471no—
424C22×SD16—471no—
425C22×SD16—471no—
426C22×D8—471no—
427C22×M16—471no—
428C22×M16—471no—
429#553—24no—
430#553C2×D4718yescomplemented
431#548—478no—
432#548—944no—
433C2×#126—21no—
434C2×#125C2×D4711yescharacteristic
435C2×#124—471no—
436C2×#124—941no—
437C2×#123—21no—
438C2×C22⋊Q8—471no—
439C2×C22⋊Q8—941no—
440C2×#121—21no—
441C2×#121—471no—
442C2×#121—941no—
443C2×#121C2×D4711yescharacteristic
444C2×#121C2×D4711yescharacteristic
445C2×C4×Q8—471no—
446C2×C4×D4—21no—
447C2×C4×D4—941no—
448C2×C4×D4C2×D4711yescharacteristic
449C2×C4×D4C2×D4711yescharacteristic
450C2×#117C2×D4711yescharacteristic
451C22×C4⋊C4C2×D4711yescharacteristic
452#488—478no—
453#483—478no—
454#482—478no—
455#479—478no—
456#469—478no—
457#468—478no—
458#463—478no—
459#449—478no—
460#448—478no—
461C4×SD16—478no—
462#436—478no—
463C2×#107—471no—
464C2×#106—471no—
465C2×#106—471no—
466C2×C4⋊C8—471no—
467#419—478no—
468#417—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×C4×C8—471no—
482C47C2×#332611yescharacteristic, complemented, Sylow
483C2×#41—474no—
484C2×#41—944no—
485C2×#41—942no—
486C2×#41—1882no—
487C22×Q8—471no—
488C22×Q8—471no—
489C22×Q8—474no—
490C22×Q8—944no—
491C22×Q8—941no—
492C22×Q8—942no—
493C22×Q8—1882no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—471no—
497C22×D4—941no—
498C22×D4—941no—
499C22×D4C22⋊D4711yescharacteristic
500C22×D4C22×D4711yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—941no—
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—474no—
515C2×M16—1882no—
516C2×M16—1882no—
517C22×C8—471no—
518C22×C8—471no—
519C22×C8—471no—
520C22×C8—471no—
521#126—28no—
522#125—22no—
523#125C22×D4714yes—
524#124—474no—
525#124—948no—
526#124—942no—
527#123—28no—
528C22⋊Q8—474no—
529C22⋊Q8—942no—
530C22⋊Q8—948no—
531#121—28no—
532#121—22no—
533#121—22no—
534#121—474no—
535#121—948no—
536#121—942no—
537#121C22×D4714yes—
538#121C22×D4714yes—
539C4×Q8—474no—
540C4×Q8—942no—
541C4×D4—28no—
542C4×D4—22no—
543C4×D4—948no—
544C4×D4C22⋊D4714yes—
545C4×D4C22×D4714yes—
546C4×D4C22×D4714yes—
547#117—22no—
548#117C22×D4714yes—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—471no—
554C2×C4⋊C4—941no—
555C2×C4⋊C4—941no—
556C2×C4⋊C4C22⋊D4711yescharacteristic
557C2×C4⋊C4C22×D4711yescharacteristic
558C2×C4⋊C4C22×D4711yescharacteristic
559C2×C4⋊C4C22×D4714yes—
560C2×C4⋊C4C22×D4711yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—941no—
566C2×C22⋊C4—941no—
567C2×C22⋊C4—941no—
568C2×C22⋊C4—941no—
569C2×C22⋊C4C22⋊D4711yescharacteristic
570C2×C22⋊C4C22⋊D4711yescharacteristic
571C2×C42—21no—
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—
590C4×C8—474no—
591C24—21no—
592C24—941no—
593C24C2×C22⋊D4711yescharacteristic
594C24C2×C22⋊D4711yescharacteristic
595#41—948no—
596#41—1884no—
597#41—1888no—
598C2×Q8—474no—
599C2×Q8—472no—
600C2×Q8—472no—
601C2×Q8—948no—
602C2×Q8—941no—
603C2×Q8—944no—
604C2×Q8—941no—
605C2×Q8—942no—
606C2×Q8—942no—
607C2×Q8—942no—
608C2×Q8—1884no—
609C2×Q8—1884no—
610C2×Q8—1888no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—42no—
617C2×D4—44no—
618C2×D4—82no—
619C2×D4—472no—
620C2×D4—944no—
621C2×D4—944no—
622C2×D4—941no—
623C2×D4—942no—
624C2×D4—942no—
625C2×D4—1884no—
626C2×D4—1884no—
627C2×D4C2×C22⋊D4714yes—
628C2×D4C23×D4712yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—82no—
639C22×C4—82no—
640C22×C4—941no—
641C22×C4—944no—
642C22×C4—941no—
643C22×C4—941no—
644C22×C4—944no—
645C22×C4—1884no—
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—
660M16—1884no—
661C2×C8—472no—
662C2×C8—472no—
663C2×C8—472no—
664C2×C8—472no—
665C2×C8—942no—
666C2×C8—942no—
667C2×C8—942no—
668C2×C8—942no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—21no—
675C4⋊C4—472no—
676C4⋊C4—944no—
677C4⋊C4—944no—
678C4⋊C4—941no—
679C4⋊C4C2×C22⋊D4714yes—
680C4⋊C4C23×D4712yes—
681C4⋊C4C23×D4712yes—
682C4⋊C4C23×D4712yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—944no—
688C22⋊C4—944no—
689C22⋊C4—944no—
690C22⋊C4—944no—
691C22⋊C4C2×C22⋊D4714yes—
692C22⋊C4C2×C22⋊D4714yes—
693C42—24no—
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—474no—
715Q8—944no—
716Q8—942no—
717Q8—942no—
718Q8—942no—
719Q8—1888no—
720Q8—1882no—
721D4—22no—
722D4—22no—
723D4—44no—
724D4—48no—
725D4—42no—
726D4—84no—
727D4—942no—
728D4—942no—
729D4—1888no—
730D4—1888no—
731D4—1882no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4—944no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—1888no—
755C2×C4—1888no—
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×C4#41×D4712yes—
764C2×C4#1309407012yes—
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#1568976112yes—
787C22#1568992112yes—
788C22#1568993412yes—
789C22C23×C22⋊D4711yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—944no—
798C4—1882no—
799C4—1882no—
800C4#1568976112yes—
801C4C2×#41×D4711yescharacteristic
802C4C2×#1309407011yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—3762no—
807C2#2025563514yesdirect product factor
808C2C2×#1568976111yescharacteristic
809C2C2×#1568992111yescharacteristic
810C2C2×#1568993411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#553C2
socleC23×C47C22×D4
hypercenterC2×#553D47
hypocenterC47C2×#3326
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#15689782C2semidirect
2. #20255635C2direct (N × H)
3. C2×#15689480C2semidirect
4. C2×#15689447C2semidirect
5. C2×#15689453C2semidirect
6. C2×#15689427C2semidirect
7. C2×#15689374C2semidirect
8. C2×#15689367C2semidirect
9. C2×#15689338C2semidirect
10. C2×#15689266C2semidirect
11. C2×#15689261C2semidirect
12. C2×C4×#10625335C2semidirect
13. C2×#15689201C2semidirect
14. C2×#15689122C2semidirect
15. C2×#15689131C2semidirect
16. C2×C47×#553C2semidirect
25. #15689782C22semidirect
34. #15689480C22semidirect
35. #15689453C22semidirect
36. #15689447C22semidirect
37. #15689427C22semidirect
38. #15689374C22semidirect
39. #15689367C22semidirect
40. #15689338C22semidirect
41. #15689266C22semidirect
42. #15689261C22semidirect
43. C4×#10625335C22semidirect
44. #15689201C22semidirect
49. #15689131C22semidirect
50. #15689122C22semidirect
65. C47×#553C22semidirect
398. C2×#553D47semidirect
417. C2×C47#3326semidirect
430. #553C2×D47semidirect
482. C47C2×#3326semidirect
807. C2#20255635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897822
#202556352
C2×#156894802
C2×#156894472
C2×#156894532
C2×#156894272
C2×#156893742
C2×#156893672
C2×#156893382
C2×#156892662
C2×#156892612
C2×C4×#106253352
C2×#156892012
C2×#156891222
C2×#156891312
C2×C47×#5532
C2×#332647