Finite Group Databasebeta

← C2×#20255388 #27092974

Subgroups — C2×#20255388 #27092974

Order 12032.

2242 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689794C211yesmaximal, characteristic, complemented
2#20255388C2116yesmaximal, direct product factor
3C2×#15689489C211yesmaximal, characteristic, complemented
4C2×#15689447C211yesmaximal, characteristic, complemented
5C2×#15689436C211yesmaximal, characteristic, complemented
6C2×#15689427C211yesmaximal, characteristic, complemented
7C2×#15689374C211yesmaximal, characteristic, complemented
8C2×#15689357C211yesmaximal, characteristic, complemented
9C2×#15689318C211yesmaximal, characteristic, complemented
10C2×#15689266C211yesmaximal, characteristic, complemented
11C2×#15689266C211yesmaximal, characteristic, complemented
12C2×#15689223C211yesmaximal, characteristic, complemented
13C2×#15689195C211yesmaximal, characteristic, complemented
14C2×#15689122C211yesmaximal, characteristic, complemented
15C2×#15689117C211yesmaximal, characteristic, complemented
16C2×C47×#553C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×#10625350C2211yescharacteristic
19C22×#10625335C2211yescharacteristic
20C22×#10625334C2211yescharacteristic
21C22×#10625334C2211yescharacteristic
22C22×#10625329C2211yescharacteristic
23C23×C47⋊C8C2211yescharacteristic
24#15689794—24no—
25#15689794C2218yescomplemented
26C2×#13094021C2211yescharacteristic
27C2×#13094020—21no—
28C2×#13093998C2211yescharacteristic
29C2×#13093998C2211yescharacteristic
30C2×#13093997—21no—
31C2×#13093997—21no—
32C2×C4×Dic94C2211yescharacteristic
33C2×#13093986—21no—
34#15689489C2218yescomplemented
35#15689447C2218yescomplemented
36#15689436C2218yescomplemented
37#15689427C2218yescomplemented
38#15689374C2218yescomplemented
39#15689357C2218yescomplemented
40#15689318C2218yescomplemented
41#15689266C2218yescomplemented
42#15689266C2218yescomplemented
43#15689223C2218yescomplemented
44#15689195C2218yescomplemented
45C2×#13093957C2211yescharacteristic
46C2×#13093957C2211yescharacteristic
47C2×#13093955C2211yescharacteristic
48C2×C4⋊(C47⋊C8)C2211yescharacteristic
49#15689122C2218yescomplemented
50#15689117C2218yescomplemented
51C2×#13093947C2211yescharacteristic
52C2×#13093947C2211yescharacteristic
53C2×#13093947C2211yescharacteristic
54C2×#13093945C2211yescharacteristic
55C2×#13093944C2211yescharacteristic
56C2×#13093944C2211yescharacteristic
57C2×#13093944C2211yescharacteristic
58C2×#13093944C2211yescharacteristic
59C2×#13093944C2211yescharacteristic
60C2×#13093944C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×C22⋊(C47⋊C8)C2211yescharacteristic
63C2×#13093935C2211yescharacteristic
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—22no—
79C2×#10625350—24no—
80C2×#10625350—24no—
81C2×#10625350—42no—
82C2×#10625350—42no—
83C2×#10625350C2314yes—
84C2×#10625350C2314yes—
85C22×Dic94C2311yescharacteristic
86C22×D188—21no—
87C22×D188—21no—
88C22×D188C2311yescharacteristic
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—21no—
91C22×C22⋊D47—21no—
92C22×C22⋊D47—21no—
93C22×C22⋊D47—21no—
94C22×C4×D47—21no—
95C22×C4×D47—21no—
96C2×#10625335—24no—
97C2×#10625335C2314yes—
98C2×#10625334—42no—
99C2×#10625334—42no—
100C2×#10625334C2314yes—
101C2×#10625334C2314yes—
102C2×#10625329—42no—
103C2×#10625329C2314yes—
104C22×C47⋊C8—42no—
105C22×C47⋊C8C2311yescharacteristic
106C22×C47⋊C8C2311yescharacteristic
107C22×C47⋊C8C2311yescharacteristic
108C22×C47⋊C8C2311yescharacteristic
109C22×C47⋊C8C2314yes—
110#13094021—22no—
111#13094021C2314yes—
112#13094020—28no—
113#13093998—22no—
114#13093998—22no—
115#13093998C2314yes—
116#13093998C2314yes—
117#13093997—28no—
118#13093997—28no—
119C4×Dic94—22no—
120C4×Dic94C2314yes—
121#13093986—28no—
122C2×C4⋊Dic47C2311yescharacteristic
123C2×Dic47⋊C4—21no—
124C2×(C2×D47)⋊C4—21no—
125C2×(C2×D47)⋊C4—21no—
126C2×C4×Dic47—21no—
127#13093957C2314yes—
128#13093957C2314yes—
129#13093955C2314yes—
130C4⋊(C47⋊C8)C2314yes—
131#13093947C2314yes—
132#13093947C2314yes—
133#13093947C2314yes—
134#13093945C2314yes—
135#13093944C2314yes—
136#13093944C2314yes—
137#13093944C2314yes—
138#13093944C2314yes—
139#13093944C2314yes—
140#13093944C2314yes—
141C22⋊(C47⋊C8)C2314yes—
142C22⋊(C47⋊C8)C2314yes—
143#13093935C2314yes—
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—
189C23×D47—21no—
190C2×D4×C47—24no—
191C2×D4×C47—24no—
192C2×D4×C47—21no—
193C2×D4×C47—22no—
194C2×D4×C47—22no—
195C2×D4×C47—42no—
196C2×D4×C47—44no—
197C2×D4×C47—82no—
198C2×D4×C47C2×D414yes—
199C2×D4×C47C2412yes—
200C22×C4×C47—22no—
201C22×C4×C47—22no—
202C22×C4×C47—22no—
203C22×C4×C47—22no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—24no—
208C22×C4×C47—24no—
209C22×C4×C47—82no—
210C22×C4×C47—82no—
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D412yes—
216C22×C4×C47C2×D412yes—
217C22×C4×C47C2412yes—
218C22×C4×C47C2412yes—
219C22×C4×C47C2411yescharacteristic
220C2×C22⋊D47—24no—
221C2×C22⋊D47—24no—
222C2×C22⋊D47—24no—
223C2×C22⋊D47—24no—
224C2×C22⋊D47—44no—
225C2×C22⋊D47—44no—
226C2×C22⋊D47—82no—
227C2×C22⋊D47—82no—
228C22×Dic47—21no—
229C22×Dic47—21no—
230#10625350—28no—
231#10625350—28no—
232#10625350—44no—
233#10625350—44no—
234#10625350—48no—
235#10625350—48no—
236C2×D188—22no—
237C2×D188—22no—
238C2×D188—22no—
239C2×D188—22no—
240C2×D188—24no—
241C2×D188—21no—
242C2×D188—21no—
243C2×D188—24no—
244C2×D188—44no—
245C2×D188—82no—
246C2×D188C2412yes—
247C2×D188C2412yes—
248C2×C4×D47—24no—
249C2×C4×D47—24no—
250C2×C4×D47—44no—
251C2×C4×D47—44no—
252C2×Dic94—21no—
253C2×Dic94—22no—
254C2×Dic94#4114yes—
255C2×Dic94C2412yes—
256C4⋊C4×C47—21no—
257C4⋊C4×C47—21no—
258C4⋊C4×C47—24no—
259C4⋊C4×C47—24no—
260C4⋊C4×C47—24no—
261C4⋊C4×C47—21no—
262C4⋊C4×C47C2×D414yes—
263C4⋊C4×C47C2412yes—
264C4⋊C4×C47C2412yes—
265C4⋊C4×C47C2412yes—
266C22⋊C4×C47—24no—
267C22⋊C4×C47—24no—
268C22⋊C4×C47—24no—
269C22⋊C4×C47—24no—
270C22⋊C4×C47C2×D414yes—
271C22⋊C4×C47C2×D414yes—
272C42×C47—24no—
273C42×C47C2×D412yes—
274C42×C47C2412yes—
275#10625335—28no—
276#10625334—44no—
277#10625334—44no—
278(C2×D47)⋊C4—24no—
279(C2×D47)⋊C4—24no—
280C4⋊Dic47—21no—
281C4⋊Dic47C2412yes—
282Dic47⋊C4—24no—
283C4×Dic47—24no—
284#10625329—44no—
285C2×C47⋊C8—22no—
286C2×C47⋊C8—22no—
287C2×C47⋊C8—22no—
288C2×C47⋊C8—22no—
289C2×C47⋊C8—44no—
290C2×C47⋊C8C2412yes—
291C2×C47⋊C8C2412yes—
292C2×C47⋊C8C2412yes—
293C2×C47⋊C8C2412yes—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—22no—
300C23×C47—22no—
301C23×C47—42no—
302C23×C47—42no—
303C23×C47—42no—
304C23×C47C22×D412yes—
305C23×C47C22×D412yes—
306C23×C47C22×D411yescharacteristic
307C22×D47—22no—
308C22×D47—22no—
309C22×D47—42no—
310C22×D47—42no—
311C22×D47—42no—
312C22×D47—42no—
313C22×D47—42no—
314C22×D47—42no—
315D4×C47—22no—
316D4×C47—22no—
317D4×C47—44no—
318D4×C47—48no—
319D4×C47—42no—
320D4×C47—84no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—24no—
326C2×C4×C47—24no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—42no—
335C2×C4×C47—42no—
336C2×C4×C47—42no—
337C2×C4×C47—84no—
338C2×C4×C47—84no—
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—48no—
348C22⋊D47—48no—
349C22⋊D47—84no—
350C22⋊D47—84no—
351C2×Dic47—24no—
352C2×Dic47—22no—
353C2×Dic47—22no—
354C2×Dic47—42no—
355D188—22no—
356D188—22no—
357D188—22no—
358D188—22no—
359D188—48no—
360D188—42no—
361D188—42no—
362D188—84no—
363C4×D47—48no—
364C4×D47—48no—
365Dic94—24no—
366Dic94—22no—
367Dic94C2×#4114yes—
368C47⋊C8—22no—
369C47⋊C8—22no—
370C47⋊C8—22no—
371C47⋊C8—22no—
372C2×#3309—471nomaximal, Sylow
373C22×C47—22no—
374C22×C47—22no—
375C22×C47—22no—
376C22×C47—22no—
377C22×C47—22no—
378C22×C47—22no—
379C22×C47—44no—
380C22×C47—44no—
381C22×C47—42no—
382C22×C47—42no—
383C22×C47—42no—
384C22×C47—84no—
385C22×C47#54612yes—
386C22×C47#57512yes—
387C22×C47#57612yes—
388C22×C47C23×D411yescharacteristic
389C2×D47—42no—
390C2×D47—42no—
391C2×D47—42no—
392C2×D47—42no—
393C2×D47—42no—
394C2×D47—42no—
395C2×D47—84no—
396C2×D47—84no—
397C4×C47—22no—
398C4×C47—22no—
399C4×C47—22no—
400C4×C47—22no—
401C4×C47—42no—
402C4×C47—42no—
403C4×C47—42no—
404C4×C47#54612yes—
405C4×C47C22×#4111yescharacteristic
406C4×C47C2×H(5,𝔽2)11yescharacteristic
407Dic47—24no—
408Dic47—42no—
409C2×#553D4711yescharacteristic, complemented
410C2×#550—471no—
411#3309—4716no—
412C2×#490—471no—
413C2×#482—471no—
414C2×#480—471no—
415C2×#479—471no—
416C2×#469—471no—
417C2×#466—471no—
418C2×#459—471no—
419C2×#449—471no—
420C2×#449—471no—
421C2×#440—471no—
422C2×#435—471no—
423C2×#417—471no—
424C2×#416—471no—
425C2×C47—42no—
426C2×C47—42no—
427C2×C47—82no—
428C2×C47#330914yescomplemented
429C2×C47C2×#54611yescharacteristic
430C2×C47C2×#57511yescharacteristic
431C2×C47C2×#57611yescharacteristic
432D47—82no—
433D47—82no—
434C22×#41—471no—
435C22×#41—471no—
436C22×SD16—471no—
437C22×D8—471no—
438C22×D8—471no—
439C22×M16—471no—
440C23×C8—471no—
441#553—24no—
442#553C2×D4718yescomplemented
443#550—478no—
444#550—944no—
445C2×#127—471no—
446C2×#127—941no—
447C2×#126—21no—
448C2×#125C2×D4711yescharacteristic
449C2×#123—21no—
450C2×#121—21no—
451C2×#121—471no—
452C2×#121—471no—
453C2×#121—941no—
454C2×#121—941no—
455C2×#121C2×D4711yescharacteristic
456C2×#121C2×D4711yescharacteristic
457C2×C4×Q8—471no—
458C2×C4×D4—21no—
459C2×C4×D4—941no—
460C2×C4×D4C2×D4711yescharacteristic
461C2×C4×D4C2×D4711yescharacteristic
462C2×#117C2×D4711yescharacteristic
463C22×C4⋊C4C2×D4711yescharacteristic
464#490—478no—
465#482—478no—
466#480—478no—
467#479—478no—
468#469—478no—
469#466—478no—
470#459—478no—
471#449—478no—
472#449—478no—
473#440—478no—
474#435—478no—
475C2×#107—471no—
476C2×#107—471no—
477C2×#106—471no—
478C2×C4⋊C8—471no—
479#417—478no—
480#416—478no—
481C2×#103—471no—
482C2×#103—471no—
483C2×#103—471no—
484C2×#102—471no—
485C2×#102—471no—
486C2×#102—471no—
487C2×#102—471no—
488C2×#102—471no—
489C2×#102—471no—
490C2×#102—471no—
491C2×C22⋊C8—471no—
492C2×C22⋊C8—471no—
493C2×#97—471no—
494C47C2×#330911yescharacteristic, complemented, Sylow
495C2×#41—474no—
496C2×#41—474no—
497C2×#41—944no—
498C2×#41—944no—
499C2×#41—942no—
500C2×#41—942no—
501C2×#41—1882no—
502C2×#41—1882no—
503C22×Q8—471no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—471no—
507C22×D4—471no—
508C22×D4—941no—
509C22×D4—941no—
510C22×D4—941no—
511C22×D4—941no—
512C22×D4—941no—
513C22×D4—941no—
514C22×D4C22⋊D4711yescharacteristic
515C22×D4C22×D4711yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—941no—
519C23×C4—941no—
520C23×C4C22×D4711yescharacteristic
521C23×C4C22×D4711yescharacteristic
522C2×SD16—474no—
523C2×SD16—944no—
524C2×D8—474no—
525C2×D8—474no—
526C2×D8—1882no—
527C2×D8—1882no—
528C2×M16—474no—
529C2×M16—1882no—
530C22×C8—471no—
531C22×C8—471no—
532C22×C8—471no—
533C22×C8—471no—
534C22×C8—474no—
535C22×C8—1882no—
536#127—474no—
537#127—948no—
538#127—942no—
539#126—28no—
540#125—22no—
541#125C22×D4714yes—
542#123—28no—
543#121—28no—
544#121—22no—
545#121—22no—
546#121—474no—
547#121—474no—
548#121—942no—
549#121—942no—
550#121—948no—
551#121—948no—
552#121C22×D4714yes—
553#121C22×D4714yes—
554C4×Q8—474no—
555C4×Q8—942no—
556C4×D4—28no—
557C4×D4—22no—
558C4×D4—948no—
559C4×D4C22⋊D4714yes—
560C4×D4C22×D4714yes—
561C4×D4C22×D4714yes—
562#117—22no—
563#117C22×D4714yes—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—471no—
569C2×C4⋊C4—941no—
570C2×C4⋊C4C22⋊D4711yescharacteristic
571C2×C4⋊C4C22×D4711yescharacteristic
572C2×C4⋊C4C22×D4711yescharacteristic
573C2×C4⋊C4C22×D4714yes—
574C2×C4⋊C4C22×D4711yescharacteristic
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—941no—
580C2×C22⋊C4—941no—
581C2×C22⋊C4C22⋊D4711yescharacteristic
582C2×C22⋊C4C22⋊D4711yescharacteristic
583C2×C42—21no—
584C2×C42—941no—
585C2×C42C22×D4711yescharacteristic
586#107—474no—
587#107—474no—
588#106—474no—
589C4⋊C8—474no—
590#103—474no—
591#103—474no—
592#103—474no—
593#102—474no—
594#102—474no—
595#102—474no—
596#102—474no—
597#102—474no—
598#102—474no—
599#102—474no—
600C22⋊C8—474no—
601C22⋊C8—474no—
602#97—474no—
603C24—21no—
604C24—941no—
605C24—941no—
606C24C2×C22⋊D4711yescharacteristic
607C24C2×C22⋊D4711yescharacteristic
608#41—948no—
609#41—948no—
610#41—1884no—
611#41—1884no—
612#41—1888no—
613#41—1888no—
614C2×Q8—474no—
615C2×Q8—472no—
616C2×Q8—941no—
617C2×Q8—942no—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—21no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—42no—
624C2×D4—44no—
625C2×D4—82no—
626C2×D4—472no—
627C2×D4—472no—
628C2×D4—944no—
629C2×D4—944no—
630C2×D4—944no—
631C2×D4—944no—
632C2×D4—944no—
633C2×D4—944no—
634C2×D4—941no—
635C2×D4—941no—
636C2×D4—942no—
637C2×D4—942no—
638C2×D4—942no—
639C2×D4—942no—
640C2×D4—3762no—
641C2×D4—3762no—
642C2×D4—3762no—
643C2×D4—1884no—
644C2×D4—1884no—
645C2×D4—1884no—
646C2×D4C2×C22⋊D4714yes—
647C2×D4C23×D4712yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—82no—
658C22×C4—82no—
659C22×C4—941no—
660C22×C4—941no—
661C22×C4—944no—
662C22×C4—944no—
663C22×C4—1884no—
664C22×C4—1884no—
665C22×C4C2×C22⋊D4712yes—
666C22×C4C2×C22⋊D4712yes—
667C22×C4C2×C22⋊D4711yescharacteristic
668C22×C4C2×C22⋊D4711yescharacteristic
669C22×C4C2×C22⋊D4711yescharacteristic
670C22×C4C2×C22⋊D4711yescharacteristic
671C22×C4C23×D4712yes—
672C22×C4C23×D4712yes—
673C22×C4C23×D4711yescharacteristic
674SD16—948no—
675D8—1884no—
676D8—1884no—
677M16—1884no—
678C2×C8—472no—
679C2×C8—472no—
680C2×C8—472no—
681C2×C8—472no—
682C2×C8—942no—
683C2×C8—942no—
684C2×C8—942no—
685C2×C8—942no—
686C2×C8—1884no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—21no—
693C4⋊C4—472no—
694C4⋊C4—944no—
695C4⋊C4—941no—
696C4⋊C4C2×C22⋊D4714yes—
697C4⋊C4C23×D4712yes—
698C4⋊C4C23×D4712yes—
699C4⋊C4C23×D4712yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—944no—
705C22⋊C4—944no—
706C22⋊C4C2×C22⋊D4714yes—
707C22⋊C4C2×C22⋊D4714yes—
708C42—24no—
709C42—944no—
710C42C2×C22⋊D4712yes—
711C42C23×D4712yes—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—942no—
723C23—942no—
724C23—1882no—
725C23—1882no—
726C23—1882no—
727C23—1882no—
728C23—1882no—
729C23—1882no—
730C23C22×C22⋊D4712yes—
731C23C22×C22⋊D4712yes—
732C23C22×C22⋊D4711yescharacteristic
733Q8—474no—
734Q8—944no—
735Q8—942no—
736D4—22no—
737D4—22no—
738D4—44no—
739D4—48no—
740D4—42no—
741D4—84no—
742D4—942no—
743D4—942no—
744D4—942no—
745D4—942no—
746D4—3764no—
747D4—3764no—
748D4—3764no—
749D4—1888no—
750D4—1888no—
751D4—1888no—
752D4—1882no—
753D4—1882no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—84no—
771C2×C4—84no—
772C2×C4—944no—
773C2×C4—942no—
774C2×C4—942no—
775C2×C4—1888no—
776C2×C4—1888no—
777C2×C4—1882no—
778C2×C4C22×C22⋊D4712yes—
779C2×C4C22×C22⋊D4712yes—
780C2×C4C22×C22⋊D4712yes—
781C2×C4C22×C22⋊D4712yes—
782C2×C4C22×C22⋊D4711yescharacteristic
783C2×C4#41×D4712yes—
784C2×C4#1309407012yes—
785C2×C4C24×D4711yescharacteristic
786C8—942no—
787C8—942no—
788C8—942no—
789C8—942no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—44no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—84no—
802C22—3764no—
803C22—3764no—
804C22—1882no—
805C22—1882no—
806C22—1882no—
807C22—1882no—
808C22—1882no—
809C22—1882no—
810C22#1568976112yes—
811C22#1568992112yes—
812C22#1568992612yes—
813C22C23×C22⋊D4711yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—944no—
822C4—1882no—
823C4#1568976112yes—
824C4C2×#41×D4711yescharacteristic
825C4C2×#1309407011yescharacteristic
826C2—42no—
827C2—42no—
828C2—82no—
829C2—3762no—
830C2—3762no—
831C2#2025538814yesdirect product factor
832C2C2×#1568976111yescharacteristic
833C2C2×#1568992111yescharacteristic
834C2C2×#1568992611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#553C2
socleC23×C47C22×D4
hypercenterC2×#553D47
hypocenterC47C2×#3309
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×#15689794C2semidirect
2. #20255388C2direct (N × H)
3. C2×#15689489C2semidirect
4. C2×#15689447C2semidirect
5. C2×#15689436C2semidirect
6. C2×#15689427C2semidirect
7. C2×#15689374C2semidirect
8. C2×#15689357C2semidirect
9. C2×#15689318C2semidirect
10. C2×#15689266C2semidirect
11. C2×#15689266C2semidirect
12. C2×#15689223C2semidirect
13. C2×#15689195C2semidirect
14. C2×#15689122C2semidirect
15. C2×#15689117C2semidirect
16. C2×C47×#553C2semidirect
25. #15689794C22semidirect
34. #15689489C22semidirect
35. #15689447C22semidirect
36. #15689436C22semidirect
37. #15689427C22semidirect
38. #15689374C22semidirect
39. #15689357C22semidirect
40. #15689318C22semidirect
41. #15689266C22semidirect
42. #15689266C22semidirect
43. #15689223C22semidirect
44. #15689195C22semidirect
49. #15689122C22semidirect
50. #15689117C22semidirect
65. C47×#553C22semidirect
409. C2×#553D47semidirect
428. C2×C47#3309semidirect
442. #553C2×D47semidirect
494. C47C2×#3309semidirect
831. C2#20255388direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897942
#202553882
C2×#156894892
C2×#156894472
C2×#156894362
C2×#156894272
C2×#156893742
C2×#156893572
C2×#156893182
C2×#156892662
C2×#156892232
C2×#156891952
C2×#156891222
C2×#156891172
C2×C47×#5532
C2×#330947