Finite Group Databasebeta

← C2×#19146495 #25973018

Subgroups — C2×#19146495 #25973018

Order 11008.

2210 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×#14583597C211yesmaximal, characteristic, complemented
2C2×#14583555C211yesmaximal, characteristic, complemented
3#19146495C2116yesmaximal, direct product factor
4C2×#14583252C211yesmaximal, characteristic, complemented
5C2×#14583243C211yesmaximal, characteristic, complemented
6C2×#14583209C211yesmaximal, characteristic, complemented
7C2×#14583133C211yesmaximal, characteristic, complemented
8C2×#14583129C211yesmaximal, characteristic, complemented
9C2×#14583113C211yesmaximal, characteristic, complemented
10C2×#14583045C211yesmaximal, characteristic, complemented
11C2×#14583040C211yesmaximal, characteristic, complemented
12C2×#14582986C211yesmaximal, characteristic, complemented
13C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
14C2×#14582892C211yesmaximal, characteristic, complemented
15C22×#13063248C211yesmaximal, characteristic, complemented
16C2×C43×#481C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C23×Dic86C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×#10621882C2211yescharacteristic
22C23×C43⋊C8C2211yescharacteristic
23C22×C8×D43C2211yescharacteristic
24#14583597—24no—
25#14583597C2218yescomplemented
26#14583555—24no—
27#14583555C2218yescomplemented
28C2×#13063320—21no—
29C2×#13063316C2211yescharacteristic
30C2×#13063312C2211yescharacteristic
31C2×#13063311—21no—
32C2×#13063310—21no—
33C2×#13063305C2211yescharacteristic
34C2×#13063302—21no—
35C2×#13063300C2211yescharacteristic
36C2×#13063299—21no—
37C2×#13063299C2211yescharacteristic
38C2×#13063297—21no—
39C2×#13063290C2211yescharacteristic
40C2×D4×Dic43—21no—
41C2×#13063287C2211yescharacteristic
42C2×C4×C22⋊D43—21no—
43C2×C4×C22⋊D43C2211yescharacteristic
44C2×#13063283C2211yescharacteristic
45#14583252C2218yescomplemented
46#14583243C2218yescomplemented
47#14583209C2218yescomplemented
48#14583133C2218yescomplemented
49#14583129C2218yescomplemented
50#14583113C2218yescomplemented
51#14583045C2218yescomplemented
52#14583040C2218yescomplemented
53#14582986C2218yescomplemented
54(C22⋊D43)⋊C8C2218yescomplemented
55C2×#13063258C2211yescharacteristic
56C2×Dic43⋊C8C2211yescharacteristic
57#14582892C2218yescomplemented
58C2×#13063250C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063248C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063248C2218yescomplemented
65C2×#13063246C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C2×#121×C43C2211yescharacteristic
70C22×C4⋊C4×C43C2211yescharacteristic
71C43×#481C2218yescomplemented
72C2×#106×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621900—22no—
78C2×#10621900—24no—
79C2×#10621900—42no—
80C2×#10621900C2314yes—
81C22×Dic86—24no—
82C22×Dic86—22no—
83C22×Dic86—21no—
84C22×Dic86—42no—
85C22×Dic86C2311yescharacteristic
86C22×Dic86C2314yes—
87C22×Dic86C2311yescharacteristic
88C22×D172—21no—
89C22×D172C2311yescharacteristic
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C22×C22⋊D43D411yescharacteristic
93C23×Dic43—21no—
94C23×Dic43—21no—
95C22×C4×D43—21no—
96C22×C4×D43C2311yescharacteristic
97C2×#10621873—24no—
98C2×#10621873—42no—
99C2×#10621873C2314yes—
100C2×#10621873C2314yes—
101C2×#10621882—42no—
102C2×#10621882C2314yes—
103C22×C43⋊C8—42no—
104C22×C43⋊C8C2311yescharacteristic
105C22×C43⋊C8C2311yescharacteristic
106C22×C43⋊C8C2314yes—
107C2×C8×D43—42no—
108C2×C8×D43C2314yes—
109#13063320—28no—
110#13063316—22no—
111#13063316C2314yes—
112#13063312—22no—
113#13063312C2314yes—
114#13063311—28no—
115#13063310—28no—
116#13063305—22no—
117#13063305C2314yes—
118#13063302—28no—
119#13063300—22no—
120#13063300C2314yes—
121#13063299—22no—
122#13063299—28no—
123#13063299C2314yes—
124#13063297—28no—
125#13063290—22no—
126#13063290C2314yes—
127D4×Dic43—28no—
128#13063287—22no—
129#13063287C2314yes—
130C4×C22⋊D43—28no—
131C4×C22⋊D43D414yes—
132C4×C22⋊D43C2314yes—
133#13063283—22no—
134#13063283C2314yes—
135C2×C4⋊Dic43—21no—
136C2×C4⋊Dic43—21no—
137C2×C4⋊Dic43C2311yescharacteristic
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4D411yescharacteristic
141C2×C22⋊Dic43—21no—
142C2×C22⋊Dic43—21no—
143C2×C22⋊Dic43D411yescharacteristic
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4D411yescharacteristic
150C2×C4×Dic43—21no—
151C2×C4×Dic43—21no—
152C2×C4×Dic43C2311yescharacteristic
153#13063258C2314yes—
154Dic43⋊C8C2314yes—
155#13063250C2314yes—
156#13063250C2314yes—
157#13063248C2314yes—
158#13063248C2314yes—
159#13063248C2314yes—
160#13063248C2314yes—
161#13063246C2314yes—
162#13063245C2314yes—
163(C2×D43)⋊C8C2314yes—
164C8×Dic43C2314yes—
165C22×D4×C43—21no—
166C22×D4×C43C2311yescharacteristic
167C23×C4×C43—21no—
168C23×C4×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171#121×C43—22no—
172#121×C43C2314yes—
173C2×C4⋊C4×C43—22no—
174C2×C4⋊C4×C43—21no—
175C2×C4⋊C4×C43C2314yes—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C22⋊C4×C43—21no—
180#106×C43C2314yes—
181#106×C43C2314yes—
182#102×C43C2314yes—
183#102×C43C2314yes—
184C22⋊C8×C43C2314yes—
185C24×C43—21no—
186C24×C43C2×D411yescharacteristic
187C23×D43—21no—
188C23×D43C2×D411yescharacteristic
189C2×D4×C43—21no—
190C2×D4×C43—24no—
191C2×D4×C43—22no—
192C2×D4×C43—22no—
193C2×D4×C43—44no—
194C2×D4×C43C2412yes—
195C22×C4×C43—22no—
196C22×C4×C43—22no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—24no—
201C22×C4×C43—82no—
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D412yes—
204C22×C4×C43C2412yes—
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—24no—
207C2×C22⋊D43—24no—
208C2×C22⋊D43—24no—
209C2×C22⋊D43—44no—
210C2×C22⋊D43—44no—
211C2×C22⋊D43C2×D414yes—
212C22×Dic43—24no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—24no—
217C22×Dic43—44no—
218C22×Dic43—44no—
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222#10621900—28no—
223#10621900—44no—
224#10621900—48no—
225C2×D172—21no—
226C2×D172—24no—
227C2×D172—22no—
228C2×D172—22no—
229C2×D172—82no—
230C2×D172C2412yes—
231C2×C4×D43—22no—
232C2×C4×D43—22no—
233C2×C4×D43—24no—
234C2×C4×D43—82no—
235C2×C4×D43C2×D412yes—
236C2×C4×D43C2412yes—
237C2×Dic86—21no—
238C2×Dic86—22no—
239C2×Dic86—22no—
240C2×Dic86—22no—
241C2×Dic86—28no—
242C2×Dic86—24no—
243C2×Dic86—21no—
244C2×Dic86—44no—
245C2×Dic86—48no—
246C2×Dic86—44no—
247C2×Dic86#4114yes—
248C2×Dic86C2412yes—
249C2×Dic86C2412yes—
250C2×C8×C43—22no—
251C2×C8×C43—22no—
252C2×C8×C43C2412yes—
253C2×C8×C43C2412yes—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—24no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43C2412yes—
259C4⋊C4×C43C2412yes—
260C4⋊C4×C43C2412yes—
261C22⋊C4×C43—24no—
262C22⋊Dic43—24no—
263C22⋊Dic43—24no—
264C22⋊Dic43C2×D414yes—
265#10621882—44no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4C2×D414yes—
272C4⋊Dic43—21no—
273C4⋊Dic43—24no—
274C4⋊Dic43—24no—
275C4⋊Dic43C2412yes—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278Dic43⋊C4C2×D414yes—
279C4×Dic43—24no—
280C4×Dic43—24no—
281C4×Dic43C2×D412yes—
282C4×Dic43C2412yes—
283C2×C43⋊C8—22no—
284C2×C43⋊C8—22no—
285C2×C43⋊C8—44no—
286C2×C43⋊C8C2412yes—
287C2×C43⋊C8C2412yes—
288#10621873—28no—
289#10621873—44no—
290C8×D43—44no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—42no—
295C23×C43—42no—
296C23×C43—42no—
297C23×C43#13514yes—
298C23×C43C22×D412yes—
299C23×C43C22×D411yescharacteristic
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—42no—
305C22×D43—42no—
306C22×D43—42no—
307C22×D43C22×D412yes—
308D4×C43—22no—
309D4×C43—22no—
310D4×C43—48no—
311D4×C43—42no—
312C2×C4×C43—22no—
313C2×C4×C43—24no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—42no—
320C2×C4×C43—42no—
321C2×C4×C43—42no—
322C2×C4×C43—84no—
323C2×C4×C43C22×D412yes—
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C2×#4112yes—
326C2×C4×C43H(5,𝔽2)12yes—
327C2×C4×C43C2511yescharacteristic
328C22⋊D43—28no—
329C22⋊D43—48no—
330C22⋊D43—48no—
331C2×Dic43—24no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—48no—
339C2×Dic43—48no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43C22×D412yes—
343C2×Dic43C22×D412yes—
344C2×Dic43C22×D412yes—
345D172—22no—
346D172—22no—
347D172—42no—
348D172—84no—
349C4×D43—24no—
350C4×D43—22no—
351C4×D43—22no—
352C4×D43—84no—
353Dic86—24no—
354Dic86—22no—
355Dic86—22no—
356Dic86—22no—
357Dic86—48no—
358Dic86—42no—
359Dic86C2×#4114yes—
360C8×C43—22no—
361C8×C43—22no—
362C43⋊C8—22no—
363C43⋊C8—22no—
364C2×#3301—431nomaximal, Sylow
365C22×C43—22no—
366C22×C43—28no—
367C22×C43—22no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—42no—
371C22×C43—84no—
372C22×C43#54612yes—
373C22×C43C2×#13514yes—
374C22×C43C2×#13512yes—
375C22×C43#57712yes—
376C22×C43C23×D411yescharacteristic
377C2×D43—22no—
378C2×D43—22no—
379C2×D43—22no—
380C2×D43—44no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—84no—
385C4×C43—22no—
386C4×C43—42no—
387C4×C43—42no—
388C4×C43—42no—
389C4×C43#54612yes—
390C4×C43C22×#4111yescharacteristic
391C4×C43C2×H(5,𝔽2)11yescharacteristic
392Dic43—24no—
393Dic43—22no—
394Dic43—22no—
395Dic43—22no—
396Dic43—42no—
397Dic43—42no—
398C2×#553—431no—
399C2×#548—431no—
400#3301—4316no—
401C2×#488—431no—
402C2×#481D4311yescharacteristic, complemented
403C2×#485—431no—
404C2×#479—431no—
405C2×#466—431no—
406C2×#465—431no—
407C2×#463—431no—
408C2×#449—431no—
409C2×#448—431no—
410C2×C4×SD16—431no—
411C2×C8×D4—431no—
412C2×#416—431no—
413C22×#103—431no—
414C2×C43—24no—
415C2×C43—82no—
416C2×C43#330114yescomplemented
417C2×C43C2×#54611yescharacteristic
418C2×C43C22×#13511yescharacteristic
419C2×C43C2×#57711yescharacteristic
420D43—42no—
421D43—82no—
422C22×#41—431no—
423C23×Q8—431no—
424C22×SD16—431no—
425C22×SD16—431no—
426C22×D8—431no—
427C23×C8—431no—
428C23×C8—431no—
429#553—438no—
430#553—864no—
431#548—438no—
432#548—864no—
433C2×#126—861no—
434C2×#125—431no—
435C2×#124—431no—
436C2×#124—861no—
437C2×#123—861no—
438C2×C22⋊Q8—431no—
439C2×C22⋊Q8—861no—
440C2×#121—431no—
441C2×#121—431no—
442C2×#121—861no—
443C2×#121—861no—
444C2×#121C2×D4311yescharacteristic
445C2×C4×Q8—431no—
446C2×C4×D4—431no—
447C2×C4×D4—431no—
448C2×C4×D4—861no—
449C2×C4×D4—861no—
450C2×#117—431no—
451C22×C4⋊C4C2×D4311yescharacteristic
452#488—438no—
453#485—438no—
454#481C2×D4318yescomplemented
455#479—438no—
456#466—438no—
457#465—438no—
458#463—438no—
459#449—438no—
460#448—438no—
461C4×SD16—438no—
462C8×D4—438no—
463C2×#107—431no—
464C2×#106C2×D4311yescharacteristic
465C2×#106C2×D4311yescharacteristic
466C2×C4⋊C8—431no—
467#416—438no—
468C2×#103—431no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#103—431no—
474C2×#103—438no—
475C2×#102—431no—
476C2×#102—431no—
477C2×#102C2×D4311yescharacteristic
478C2×#102C2×D4311yescharacteristic
479C2×C22⋊C8—431no—
480C2×C22⋊C8C2×D4311yescharacteristic
481C2×C4×C8—431no—
482C43C2×#330111yescharacteristic, complemented, Sylow
483C2×#41—434no—
484C2×#41—862no—
485C2×#41—864no—
486C2×#41—1722no—
487C22×Q8—431no—
488C22×Q8—431no—
489C22×Q8—434no—
490C22×Q8—864no—
491C22×Q8—861no—
492C22×Q8—862no—
493C22×Q8—1722no—
494C22×D4—21no—
495C22×D4—431no—
496C22×D4—431no—
497C22×D4—861no—
498C22×D4—861no—
499C22×D4—861no—
500C22×D4C22×D4311yescharacteristic
501C23×C4—21no—
502C23×C4—431no—
503C23×C4—861no—
504C23×C4—861no—
505C23×C4—861no—
506C23×C4C22×D4311yescharacteristic
507C2×SD16—434no—
508C2×SD16—434no—
509C2×SD16—864no—
510C2×SD16—1722no—
511C2×D8—434no—
512C2×D8—1722no—
513C22×C8—431no—
514C22×C8—431no—
515C22×C8—434no—
516C22×C8—434no—
517C22×C8—1722no—
518C22×C8—1722no—
519C22×C8C22×D4311yescharacteristic
520C22×C8C22×D4311yescharacteristic
521#126—868no—
522#125—434no—
523#125—862no—
524#124—434no—
525#124—862no—
526#124—868no—
527#123—868no—
528C22⋊Q8—434no—
529C22⋊Q8—868no—
530C22⋊Q8—862no—
531#121—22no—
532#121—434no—
533#121—434no—
534#121—862no—
535#121—868no—
536#121—868no—
537#121—862no—
538#121C22×D4314yes—
539C4×Q8—434no—
540C4×Q8—862no—
541C4×D4—434no—
542C4×D4—434no—
543C4×D4—434no—
544C4×D4—862no—
545C4×D4—868no—
546C4×D4—868no—
547#117—434no—
548#117—862no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4C22×D4311yescharacteristic
558C2×C4⋊C4C22×D4311yescharacteristic
559C2×C4⋊C4C22×D4314yes—
560C2×C4⋊C4C22×D4311yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—431no—
563C2×C22⋊C4—431no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C42—431no—
572C2×C42—861no—
573C2×C42—861no—
574#107—434no—
575#106C22×D4314yes—
576#106C22×D4314yes—
577C4⋊C8—434no—
578#103—434no—
579#103—434no—
580#103—434no—
581#103—434no—
582#103—434no—
583#103—434no—
584#102—434no—
585#102—434no—
586#102C22×D4314yes—
587#102C22×D4314yes—
588C22⋊C8—434no—
589C22⋊C8C22×D4314yes—
590C4×C8—434no—
591C24—21no—
592C24—431no—
593C24—861no—
594C24D4×D4311yescharacteristic
595#41—868no—
596#41—1724no—
597#41—1728no—
598C2×Q8—434no—
599C2×Q8—432no—
600C2×Q8—432no—
601C2×Q8—868no—
602C2×Q8—861no—
603C2×Q8—864no—
604C2×Q8—861no—
605C2×Q8—862no—
606C2×Q8—862no—
607C2×Q8—862no—
608C2×Q8—1724no—
609C2×Q8—1724no—
610C2×Q8—1728no—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—44no—
616C2×D4—434no—
617C2×D4—432no—
618C2×D4—864no—
619C2×D4—864no—
620C2×D4—864no—
621C2×D4—864no—
622C2×D4—861no—
623C2×D4—862no—
624C2×D4—862no—
625C2×D4—3442no—
626C2×D4—1724no—
627C2×D4—1724no—
628C2×D4C23×D4312yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—24no—
635C22×C4—82no—
636C22×C4—431no—
637C22×C4—431no—
638C22×C4—431no—
639C22×C4—432no—
640C22×C4—432no—
641C22×C4—864no—
642C22×C4—864no—
643C22×C4—861no—
644C22×C4—862no—
645C22×C4—862no—
646C22×C4—864no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—3442no—
650C22×C4—1724no—
651C22×C4—1724no—
652C22×C4D4×D4312yes—
653C22×C4D4×D4311yescharacteristic
654C22×C4C23×D4312yes—
655C22×C4C23×D4311yescharacteristic
656SD16—868no—
657SD16—1724no—
658D8—1724no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—432no—
662C2×C8—432no—
663C2×C8—862no—
664C2×C8—862no—
665C2×C8—1724no—
666C2×C8—1724no—
667C2×C8C23×D4312yes—
668C2×C8C23×D4312yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—21no—
673C4⋊C4—434no—
674C4⋊C4—432no—
675C4⋊C4—864no—
676C4⋊C4—864no—
677C4⋊C4—864no—
678C4⋊C4—864no—
679C4⋊C4—861no—
680C4⋊C4C23×D4312yes—
681C4⋊C4C23×D4312yes—
682C4⋊C4C23×D4312yes—
683C22⋊C4—24no—
684C22⋊C4—434no—
685C22⋊C4—434no—
686C22⋊C4—864no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C22⋊C4—864no—
692C22⋊C4—864no—
693C42—432no—
694C42—432no—
695C42—864no—
696C42—864no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—432no—
704C23—862no—
705C23—862no—
706C23—862no—
707C23—862no—
708C23—1722no—
709C23—1722no—
710C23—1722no—
711C23#1306334614yes—
712C23C2×D4×D4312yes—
713C23C2×D4×D4311yescharacteristic
714Q8—434no—
715Q8—862no—
716Q8—864no—
717Q8—862no—
718Q8—862no—
719Q8—1728no—
720Q8—1722no—
721D4—22no—
722D4—22no—
723D4—48no—
724D4—42no—
725D4—868no—
726D4—862no—
727D4—862no—
728D4—3444no—
729D4—1728no—
730D4—1728no—
731D4—1722no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—84no—
743C2×C4—432no—
744C2×C4—432no—
745C2×C4—432no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—864no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—864no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—3444no—
757C2×C4—1728no—
758C2×C4—1728no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4C2×D4×D4312yes—
762C2×C4C2×D4×D4311yescharacteristic
763C2×C4#41×D4312yes—
764C2×C4#1306337112yes—
765C2×C4C24×D4311yescharacteristic
766C8—22no—
767C8—22no—
768C8—862no—
769C8—862no—
770C22—22no—
771C22—22no—
772C22—28no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—84no—
777C22—862no—
778C22—862no—
779C22—862no—
780C22—3444no—
781C22—1722no—
782C22—1722no—
783C22—1722no—
784C22—1724no—
785C22#1458354112yes—
786C22C2×#1306334614yes—
787C22C2×#1306334612yes—
788C22#1458370912yes—
789C22C22×D4×D4311yescharacteristic
790C4—22no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—862no—
795C4—864no—
796C4—862no—
797C4—862no—
798C4—1722no—
799C4—1722no—
800C4#1458354112yes—
801C4C2×#41×D4311yescharacteristic
802C4C2×#1306337111yescharacteristic
803C2—24no—
804C2—82no—
805C2—3442no—
806C2—1722no—
807C2#1914649514yesdirect product factor
808C2C2×#1458354111yescharacteristic
809C2C22×#1306334611yescharacteristic
810C2C2×#1458370911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#481C2
socleC23×C43C22×D4
hypercenterC2×#481D43
hypocenterC43C2×#3301
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#14583597C2semidirect
2. C2×#14583555C2semidirect
3. #19146495C2direct (N × H)
4. C2×#14583252C2semidirect
5. C2×#14583243C2semidirect
6. C2×#14583209C2semidirect
7. C2×#14583133C2semidirect
8. C2×#14583129C2semidirect
9. C2×#14583113C2semidirect
10. C2×#14583045C2semidirect
11. C2×#14583040C2semidirect
12. C2×#14582986C2semidirect
13. C2×(C22⋊D43)⋊C8C2semidirect
14. C2×#14582892C2semidirect
15. C22×#13063248C2semidirect
16. C2×C43×#481C2semidirect
25. #14583597C22semidirect
27. #14583555C22semidirect
45. #14583252C22semidirect
46. #14583243C22semidirect
47. #14583209C22semidirect
48. #14583133C22semidirect
49. #14583129C22semidirect
50. #14583113C22semidirect
51. #14583045C22semidirect
52. #14583040C22semidirect
53. #14582986C22semidirect
54. (C22⋊D43)⋊C8C22semidirect
57. #14582892C22semidirect
64. C2×#13063248C22semidirect
71. C43×#481C22semidirect
402. C2×#481D43semidirect
416. C2×C43#3301semidirect
454. #481C2×D43semidirect
482. C43C2×#3301semidirect
807. C2#19146495direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835972
C2×#145835552
#191464952
C2×#145832522
C2×#145832432
C2×#145832092
C2×#145831332
C2×#145831292
C2×#145831132
C2×#145830452
C2×#145830402
C2×#145829862
C2×(C22⋊D43)⋊C82
C2×#145828922
C22×#130632482
C2×C43×#4812
C2×#330143