Finite Group Databasebeta

← C2×#19146802 #25973400

Subgroups — C2×#19146802 #25973400

Order 11008.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583596C211yesmaximal, characteristic, complemented
2C2×#14583540C211yesmaximal, characteristic, complemented
3#19146802C2116yesmaximal, direct product factor
4C2×#14583255C211yesmaximal, characteristic, complemented
5C2×#14583237C211yesmaximal, characteristic, complemented
6C2×#14583214C211yesmaximal, characteristic, complemented
7C2×#14583202C211yesmaximal, characteristic, complemented
8C2×#14583151C211yesmaximal, characteristic, complemented
9C2×#14583116C211yesmaximal, characteristic, complemented
10C2×#14583043C211yesmaximal, characteristic, complemented
11C2×#14583032C211yesmaximal, characteristic, complemented
12C2×#14582979C211yesmaximal, characteristic, complemented
13C2×#14582975C211yesmaximal, characteristic, complemented
14C2×#14582899C211yesmaximal, characteristic, complemented
15C2×#14582905C211yesmaximal, characteristic, complemented
16C2×C43×#468C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C23×D172C2211yescharacteristic
19C22×#10621882C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21C22×#10621872C2211yescharacteristic, complemented
22#14583596—24no—
23#14583596C2218yescomplemented
24#14583540—24no—
25#14583540C2218yescomplemented
26C2×#13063318—21no—
27C2×#13063316C2211yescharacteristic, complemented
28C2×#13063314C2211yescharacteristic
29C2×#13063310—21no—
30C2×#13063306—21no—
31C2×#13063300—21no—
32C2×#13063300C2211yescharacteristic
33C2×#13063296—21no—
34C2×#13063296C2211yescharacteristic, complemented
35C2×#13063295—21no—
36C2×D4×Dic43C2211yescharacteristic, complemented
37C2×#13063287C2211yescharacteristic
38C2×C4×C22⋊D43C2211yescharacteristic
39C2×(C22⋊D43)⋊C4—21no—
40C2×#13063284C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic, complemented
42C2×C22⋊C4×D43—21no—
43#14583255C2218yescomplemented
44#14583237C2218yescomplemented
45#14583214C2218yescomplemented
46#14583202C2218yescomplemented
47#14583151C2218yescomplemented
48#14583116C2218yescomplemented
49#14583043C2218yescomplemented
50#14583032C2218yescomplemented
51#14582979C2218yescomplemented
52#14582975C2218yescomplemented
53C2×#13063258C2211yescharacteristic, complemented
54C2×#13063256C2211yescharacteristic, complemented
55C2×Dic43⋊C8C2211yescharacteristic, complemented
56#14582905C2218yescomplemented
57#14582899C2218yescomplemented
58C2×#13063249C2211yescharacteristic, complemented
59C2×#13063249C2211yescharacteristic, complemented
60C2×#13063247C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
68C2×C8×Dic43C2211yescharacteristic, complemented
69C22×SD16×C43C2211yescharacteristic, complemented
70C22×M16×C43C2211yescharacteristic
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×#121×C43C2211yescharacteristic
73C43×#468C2218yescomplemented
74C2×#107×C43C2211yescharacteristic, complemented
75C2×#103×C43C2211yescharacteristic, complemented
76C2×#102×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C2×#10621902—22no—
79C2×#10621902—24no—
80C2×#10621902—42no—
81C2×#10621902C2314yes—
82C22×D172—24no—
83C22×D172—21no—
84C22×D172—21no—
85C22×D172—22no—
86C22×D172—21no—
87C22×D172—42no—
88C22×D172C2311yescharacteristic
89C22×D172C2314yes—
90C22×D172C2311yescharacteristic
91C22×C22⋊D43—21no—
92C22×C22⋊D43D411yescharacteristic
93C23×Dic43—21no—
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C22×C4×D43—21no—
97C22×C4×D43C2311yescharacteristic
98C2×#10621882—24no—
99C2×#10621882—42no—
100C2×#10621882C2314yes—
101C2×#10621882C2314yes—
102C2×#10621872—42no—
103C2×#10621872C2314yescomplemented
104C22×C43⋊C8C2311yescharacteristic
105C22×C43⋊C8C2311yescharacteristic
106#13063318—28no—
107#13063316—22no—
108#13063316C2314yescomplemented
109#13063314—22no—
110#13063314C2314yes—
111#13063310—28no—
112#13063306—28no—
113#13063300—22no—
114#13063300—28no—
115#13063300C2314yes—
116#13063296—28no—
117#13063296—22no—
118#13063296C2314yescomplemented
119#13063295—28no—
120D4×Dic43—22no—
121D4×Dic43C2314yescomplemented
122#13063287—22no—
123#13063287C2314yes—
124C4×C22⋊D43D414yes—
125C4×C22⋊D43C2314yes—
126(C22⋊D43)⋊C4—28no—
127#13063284—22no—
128#13063284C2314yes—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43C2311yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4D411yescharacteristic
135C4⋊C4×D43—22no—
136C4⋊C4×D43C2314yescomplemented
137C2×C22⋊Dic43—21no—
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43D411yescharacteristic
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4D411yescharacteristic
146C22⋊C4×D43—28no—
147C2×C4×Dic43—21no—
148C2×C4×Dic43C2311yescharacteristic
149#13063258C2314yescomplemented
150#13063256C2314yescomplemented
151Dic43⋊C8C2314yescomplemented
152#13063249C2314yescomplemented
153#13063249C2314yescomplemented
154#13063247C2314yes—
155#13063247C2314yes—
156#13063247C2314yes—
157#13063247C2314yes—
158#13063245C2314yes—
159#13063245C2314yes—
160C22⋊(C43⋊C8)C2314yes—
161(C2×D43)⋊C8C2314yescomplemented
162C8×Dic43C2314yescomplemented
163C22×Q8×C43C2311yescharacteristic
164C22×D4×C43—21no—
165C22×D4×C43C2311yescharacteristic
166C23×C4×C43C2311yescharacteristic
167C2×SD16×C43—42no—
168C2×SD16×C43C2314yescomplemented
169C2×M16×C43—42no—
170C2×M16×C43C2314yes—
171C22×C8×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173C22⋊Q8×C43—22no—
174C22⋊Q8×C43C2314yes—
175#121×C43—22no—
176#121×C43C2314yes—
177C2×C4⋊C4×C43—21no—
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C22⋊C4×C43—21no—
181C2×C22⋊C4×C43—21no—
182#107×C43C2314yescomplemented
183#103×C43C2314yescomplemented
184#102×C43C2314yescomplemented
185C24×C43—21no—
186C24×C43C2×D411yescharacteristic
187C23×D43—21no—
188C23×D43—21no—
189C23×D43—24no—
190C23×D43—44no—
191C23×D43—44no—
192C23×D43—82no—
193C23×D43C2×D411yescharacteristic
194C2×Q8×C43—21no—
195C2×Q8×C43—22no—
196C2×Q8×C43—22no—
197C2×Q8×C43C2412yes—
198C2×D4×C43—21no—
199C2×D4×C43—24no—
200C2×D4×C43—22no—
201C2×D4×C43—22no—
202C2×D4×C43—82no—
203C2×D4×C43C2412yes—
204C22×C4×C43—22no—
205C22×C4×C43—22no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D412yes—
211C22×C4×C43C2412yes—
212C22×C4×C43C2411yescharacteristic
213C2×C22⋊D43—24no—
214C2×C22⋊D43—42no—
215C2×C22⋊D43—44no—
216C2×C22⋊D43C2×D414yes—
217C22×Dic43—24no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—82no—
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224#10621902—28no—
225#10621902—44no—
226#10621902—48no—
227C2×D172—21no—
228C2×D172—22no—
229C2×D172—24no—
230C2×D172—21no—
231C2×D172—24no—
232C2×D172—24no—
233C2×D172—22no—
234C2×D172—22no—
235C2×D172—28no—
236C2×D172—44no—
237C2×D172—44no—
238C2×D172—44no—
239C2×D172—48no—
240C2×D172—82no—
241C2×D172#4114yes—
242C2×D172C2412yes—
243C2×D172C2412yes—
244C2×C4×D43—22no—
245C2×C4×D43—22no—
246C2×C4×D43—24no—
247C2×C4×D43—24no—
248C2×C4×D43—24no—
249C2×C4×D43—44no—
250C2×C4×D43—82no—
251C2×C4×D43—82no—
252C2×C4×D43C2×D412yes—
253C2×C4×D43C2412yes—
254SD16×C43—44no—
255M16×C43—44no—
256C2×C8×C43—22no—
257C2×C8×C43—22no—
258C2×C8×C43C2412yes—
259C2×C8×C43C2412yes—
260C4⋊C4×C43—24no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43C2412yes—
264C4⋊C4×C43C2412yes—
265C22⋊C4×C43—24no—
266C22⋊C4×C43—24no—
267C22⋊Dic43—24no—
268C22⋊Dic43—24no—
269C22⋊Dic43—24no—
270C22⋊Dic43C2×D414yes—
271#10621882—28no—
272#10621882—44no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4C2×D414yes—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—24no—
281C4⋊Dic43C2412yes—
282C4⋊Dic43C2412yes—
283Dic43⋊C4—24no—
284Dic43⋊C4—24no—
285Dic43⋊C4C2×D414yes—
286C4×Dic43—24no—
287C4×Dic43C2×D412yes—
288C4×Dic43C2412yes—
289C2×C43⋊C8—22no—
290C2×C43⋊C8—22no—
291C2×C43⋊C8C2412yes—
292C2×C43⋊C8C2412yes—
293#10621872—44no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—42no—
299C23×C43—42no—
300C23×C43—42no—
301C23×C43C22×D412yes—
302C23×C43C22×D411yescharacteristic
303C22×D43—22no—
304C22×D43—24no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—22no—
309C22×D43—48no—
310C22×D43—42no—
311C22×D43—42no—
312C22×D43—48no—
313C22×D43—42no—
314C22×D43—42no—
315C22×D43—42no—
316C22×D43—84no—
317C22×D43—816no—
318C22×D43C22×D412yes—
319Q8×C43—22no—
320Q8×C43—22no—
321Q8×C43—42no—
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—42no—
325D4×C43—84no—
326C2×C4×C43—22no—
327C2×C4×C43—24no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—42no—
334C2×C4×C43—42no—
335C2×C4×C43—42no—
336C2×C4×C43C22×D412yes—
337C2×C4×C43C22×D411yescharacteristic
338C2×C4×C43C2×#4112yes—
339C2×C4×C43H(5,𝔽2)12yes—
340C2×C4×C43C2511yescharacteristic
341C22⋊D43—44no—
342C22⋊D43—48no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—42no—
349C2×Dic43—42no—
350C2×Dic43—84no—
351C2×Dic43C22×D412yes—
352C2×Dic43C22×D412yes—
353C2×Dic43C22×D412yes—
354D172—24no—
355D172—22no—
356D172—22no—
357D172—22no—
358D172—48no—
359D172—48no—
360D172—42no—
361D172—84no—
362D172C2×#4114yes—
363C4×D43—24no—
364C4×D43—22no—
365C4×D43—22no—
366C4×D43—48no—
367C4×D43—84no—
368C4×D43—84no—
369C8×C43—22no—
370C8×C43—22no—
371C43⋊C8—22no—
372C43⋊C8—22no—
373C2×#3322—431nomaximal, Sylow
374C22×C43—22no—
375C22×C43—22no—
376C22×C43—22no—
377C22×C43—44no—
378C22×C43—42no—
379C22×C43—42no—
380C22×C43—42no—
381C22×C43—84no—
382C22×C43#54612yes—
383C22×C43#57512yes—
384C22×C43#57612yes—
385C22×C43C23×D411yescharacteristic
386C2×D43—24no—
387C2×D43—22no—
388C2×D43—22no—
389C2×D43—22no—
390C2×D43—44no—
391C2×D43—48no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—42no—
397C2×D43—816no—
398C2×D43—84no—
399C4×C43—22no—
400C4×C43—42no—
401C4×C43—42no—
402C4×C43—42no—
403C4×C43#54612yes—
404C4×C43C22×#4111yescharacteristic
405C4×C43C2×H(5,𝔽2)11yescharacteristic
406Dic43—22no—
407Dic43—22no—
408Dic43—22no—
409Dic43—42no—
410Dic43—42no—
411C2×#553—431no—
412C2×#546—431no—
413#3322—4316no—
414C2×#488—431no—
415C2×#485—431no—
416C2×#480—431no—
417C2×#478—431no—
418C2×#469—431no—
419C2×#468D4311yescharacteristic, complemented
420C2×#463—431no—
421C2×#449—431no—
422C2×#447—431no—
423C2×C4×D8—431no—
424C2×#436—431no—
425C2×#417—431no—
426C2×#418—431no—
427C2×C43—42no—
428C2×C43—82no—
429C2×C43#332214yescomplemented
430C2×C43C2×#54611yescharacteristic
431C2×C43C2×#57511yescharacteristic
432C2×C43C2×#57611yescharacteristic
433D43—42no—
434D43—44no—
435D43—82no—
436C22×#41—431no—
437C23×D4—431no—
438C22×SD16C2×D4311yescharacteristic, complemented
439C22×D8—431no—
440C22×D8—431no—
441C22×M16—431no—
442C22×M16C2×D4311yescharacteristic
443#553—438no—
444#553—864no—
445#546—438no—
446#546—864no—
447C2×#126—861no—
448C2×#125—431no—
449C2×#124—431no—
450C2×#123—861no—
451C2×#123—861no—
452C2×C22⋊Q8C2×D4311yescharacteristic
453C2×#121—431no—
454C2×#121—431no—
455C2×#121—861no—
456C2×#121—861no—
457C2×#121C2×D4311yescharacteristic
458C2×#120—861no—
459C2×C4×D4—431no—
460C2×C4×D4—431no—
461C2×C4×D4—431no—
462C2×C4×D4—861no—
463C2×#117—431no—
464C22×C4⋊C4—431no—
465C22×C22⋊C4—861no—
466#488—438no—
467#485—438no—
468#480—438no—
469#478—438no—
470#469—438no—
471#468C2×D4318yescomplemented
472#463—438no—
473#449—438no—
474#447—438no—
475C4×D8—438no—
476#436—438no—
477C2×#107—431no—
478C2×#107C2×D4311yescharacteristic, complemented
479C2×#106—431no—
480C2×C4⋊C8—431no—
481#418—438no—
482#417—438no—
483C2×#103—431no—
484C2×#103—431no—
485C2×#103C2×D4311yescharacteristic, complemented
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102—431no—
492C2×#102C2×D4311yescharacteristic, complemented
493C2×C22⋊C8—431no—
494C2×C22⋊C8—431no—
495C2×C4×C8—431no—
496C43C2×#332211yescharacteristic, complemented, Sylow
497C25—861no—
498C2×#41—434no—
499C2×#41—862no—
500C2×#41—864no—
501C2×#41—1722no—
502C22×Q8C22×D4311yescharacteristic
503C22×D4—21no—
504C22×D4—431no—
505C22×D4—431no—
506C22×D4—431no—
507C22×D4—434no—
508C22×D4—864no—
509C22×D4—861no—
510C22×D4—861no—
511C22×D4—861no—
512C22×D4—861no—
513C22×D4—862no—
514C22×D4—1722no—
515C22×D4C22×D4311yescharacteristic
516C23×C4—431no—
517C23×C4—861no—
518C23×C4—861no—
519C23×C4—861no—
520C23×C4—861no—
521C23×C4C22×D4311yescharacteristic
522C2×SD16—42no—
523C2×SD16C22×D4314yescomplemented
524C2×D8—434no—
525C2×D8—434no—
526C2×D8—864no—
527C2×D8—1722no—
528C2×M16—42no—
529C2×M16—434no—
530C2×M16—1722no—
531C2×M16C22×D4314yes—
532C22×C8—431no—
533C22×C8—431no—
534C22×C8C22×D4311yescharacteristic
535C22×C8C22×D4311yescharacteristic
536#126—868no—
537#125—434no—
538#125—862no—
539#124—434no—
540#124—862no—
541#123—868no—
542#123—868no—
543C22⋊Q8—22no—
544C22⋊Q8C22×D4314yes—
545#121—22no—
546#121—434no—
547#121—434no—
548#121—868no—
549#121—862no—
550#121—862no—
551#121—868no—
552#121C22×D4314yes—
553#120—868no—
554C4×D4—434no—
555C4×D4—434no—
556C4×D4—434no—
557C4×D4—434no—
558C4×D4—862no—
559C4×D4—862no—
560C4×D4—868no—
561#117—434no—
562#117—862no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—431no—
566C2×C4⋊C4—431no—
567C2×C4⋊C4—434no—
568C2×C4⋊C4—862no—
569C2×C4⋊C4—861no—
570C2×C4⋊C4—861no—
571C2×C4⋊C4—861no—
572C2×C4⋊C4C22×D4311yescharacteristic
573C2×C4⋊C4C22×D4311yescharacteristic
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—431no—
577C2×C22⋊C4—431no—
578C2×C22⋊C4—868no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C22⋊C4—861no—
582C2×C22⋊C4—861no—
583C2×C22⋊C4—861no—
584C2×C22⋊C4—861no—
585C2×C22⋊C4—861no—
586C2×C42—431no—
587C2×C42—861no—
588#107—434no—
589#107C22×D4314yescomplemented
590#106—434no—
591C4⋊C8—434no—
592#103—434no—
593#103—434no—
594#103C22×D4314yescomplemented
595#102—434no—
596#102—434no—
597#102—434no—
598#102—434no—
599#102—434no—
600#102—434no—
601#102C22×D4314yescomplemented
602C22⋊C8—434no—
603C22⋊C8—434no—
604C4×C8—434no—
605C24—21no—
606C24—431no—
607C24—861no—
608C24—864no—
609C24—861no—
610C24—3442no—
611C24—1724no—
612C24—1724no—
613C24D4×D4311yescharacteristic
614#41—868no—
615#41—1724no—
616#41—1728no—
617C2×Q8—21no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8C23×D4312yes—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—82no—
626C2×D4—434no—
627C2×D4—434no—
628C2×D4—432no—
629C2×D4—432no—
630C2×D4—868no—
631C2×D4—864no—
632C2×D4—864no—
633C2×D4—864no—
634C2×D4—861no—
635C2×D4—864no—
636C2×D4—861no—
637C2×D4—862no—
638C2×D4—862no—
639C2×D4—862no—
640C2×D4—3442no—
641C2×D4—1724no—
642C2×D4—1728no—
643C2×D4—1724no—
644C2×D4—1724no—
645C2×D4—1722no—
646C2×D4—1724no—
647C2×D4C23×D4312yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—431no—
654C22×C4—431no—
655C22×C4—431no—
656C22×C4—432no—
657C22×C4—432no—
658C22×C4—864no—
659C22×C4—864no—
660C22×C4—864no—
661C22×C4—864no—
662C22×C4—862no—
663C22×C4—862no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—3442no—
667C22×C4—3442no—
668C22×C4—3442no—
669C22×C4—1724no—
670C22×C4D4×D4312yes—
671C22×C4D4×D4311yescharacteristic
672C22×C4C23×D4312yes—
673C22×C4C23×D4311yescharacteristic
674SD16—44no—
675D8—868no—
676D8—1724no—
677M16—44no—
678M16—1724no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—432no—
682C2×C8—432no—
683C2×C8—862no—
684C2×C8—862no—
685C2×C8C23×D4312yes—
686C2×C8C23×D4312yes—
687C4⋊C4—24no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—434no—
691C4⋊C4—432no—
692C4⋊C4—432no—
693C4⋊C4—864no—
694C4⋊C4—864no—
695C4⋊C4—864no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4C23×D4312yes—
699C4⋊C4C23×D4312yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—434no—
703C22⋊C4—434no—
704C22⋊C4—864no—
705C22⋊C4—864no—
706C22⋊C4—864no—
707C22⋊C4—864no—
708C22⋊C4—864no—
709C22⋊C4—864no—
710C22⋊C4—864no—
711C42—432no—
712C42—432no—
713C42—864no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—432no—
722C23—862no—
723C23—862no—
724C23—862no—
725C23—862no—
726C23—864no—
727C23—862no—
728C23—3444no—
729C23—34416no—
730C23—1728no—
731C23—1728no—
732C23—1722no—
733C23—1722no—
734C23—1722no—
735C23—1722no—
736C23—1722no—
737C23C2×D4×D4312yes—
738C23C2×D4×D4311yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742D4—22no—
743D4—22no—
744D4—42no—
745D4—84no—
746D4—434no—
747D4—862no—
748D4—862no—
749D4—862no—
750D4—864no—
751D4—3444no—
752D4—1728no—
753D4—1728no—
754D4—1724no—
755D4—1728no—
756D4—1722no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—432no—
768C2×C4—432no—
769C2×C4—432no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—864no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—3444no—
779C2×C4—3444no—
780C2×C4—3444no—
781C2×C4—1728no—
782C2×C4—1722no—
783C2×C4—1722no—
784C2×C4C2×D4×D4312yes—
785C2×C4C2×D4×D4311yescharacteristic
786C2×C4#41×D4312yes—
787C2×C4#1306337012yes—
788C2×C4C24×D4311yescharacteristic
789C8—22no—
790C8—22no—
791C8—862no—
792C8—862no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—862no—
802C22—864no—
803C22—862no—
804C22—862no—
805C22—34416no—
806C22—3444no—
807C22—1722no—
808C22—1722no—
809C22—1722no—
810C22—1722no—
811C22—1722no—
812C22—1724no—
813C22—1728no—
814C22#1458353812yes—
815C22#1458369812yes—
816C22#1458370312yes—
817C22C22×D4×D4311yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—862no—
823C4—862no—
824C4—862no—
825C4—1722no—
826C4—1722no—
827C4#1458353812yes—
828C4C2×#41×D4311yescharacteristic
829C4C2×#1306337011yescharacteristic
830C2—42no—
831C2—82no—
832C2—3442no—
833C2—1722no—
834C2—1724no—
835C2#1914680214yesdirect product factor
836C2C2×#1458353811yescharacteristic
837C2C2×#1458369811yescharacteristic
838C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#468C2
socleC23×C43C22×D4
hypercenterC2×#468D43
hypocenterC43C2×#3322
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#14583596C2semidirect
2. C2×#14583540C2semidirect
3. #19146802C2direct (N × H)
4. C2×#14583255C2semidirect
5. C2×#14583237C2semidirect
6. C2×#14583214C2semidirect
7. C2×#14583202C2semidirect
8. C2×#14583151C2semidirect
9. C2×#14583116C2semidirect
10. C2×#14583043C2semidirect
11. C2×#14583032C2semidirect
12. C2×#14582979C2semidirect
13. C2×#14582975C2semidirect
14. C2×#14582899C2semidirect
15. C2×#14582905C2semidirect
16. C2×C43×#468C2semidirect
21. C22×#10621872C22semidirect
23. #14583596C22semidirect
25. #14583540C22semidirect
27. C2×#13063316C22semidirect
34. C2×#13063296C22semidirect
36. C2×D4×Dic43C22semidirect
41. C2×C4⋊C4×D43C22semidirect
43. #14583255C22semidirect
44. #14583237C22semidirect
45. #14583214C22semidirect
46. #14583202C22semidirect
47. #14583151C22semidirect
48. #14583116C22semidirect
49. #14583043C22semidirect
50. #14583032C22semidirect
51. #14582979C22semidirect
52. #14582975C22semidirect
53. C2×#13063258C22semidirect
54. C2×#13063256C22semidirect
55. C2×Dic43⋊C8C22semidirect
56. #14582905C22semidirect
57. #14582899C22semidirect
58. C2×#13063249C22semidirect
59. C2×#13063249C22semidirect
67. C2×(C2×D43)⋊C8C22semidirect
68. C2×C8×Dic43C22semidirect
69. C22×SD16×C43C22semidirect
73. C43×#468C22semidirect
74. C2×#107×C43C22semidirect
75. C2×#103×C43C22semidirect
76. C2×#102×C43C22semidirect
103. C2×#10621872C23semidirect
108. #13063316C23semidirect
118. #13063296C23semidirect
121. D4×Dic43C23semidirect
136. C4⋊C4×D43C23semidirect
149. #13063258C23semidirect
150. #13063256C23semidirect
151. Dic43⋊C8C23semidirect
152. #13063249C23semidirect
153. #13063249C23semidirect
161. (C2×D43)⋊C8C23semidirect
162. C8×Dic43C23semidirect
168. C2×SD16×C43C23semidirect
182. #107×C43C23semidirect
183. #103×C43C23semidirect
184. #102×C43C23semidirect
419. C2×#468D43semidirect
429. C2×C43#3322semidirect
438. C22×SD16C2×D43semidirect
471. #468C2×D43semidirect
478. C2×#107C2×D43semidirect
485. C2×#103C2×D43semidirect
492. C2×#102C2×D43semidirect
496. C43C2×#3322semidirect
523. C2×SD16C22×D43semidirect
589. #107C22×D43semidirect
594. #103C22×D43semidirect
601. #102C22×D43semidirect
835. C2#19146802direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835962
C2×#145835402
#191468022
C2×#145832552
C2×#145832372
C2×#145832142
C2×#145832022
C2×#145831512
C2×#145831162
C2×#145830432
C2×#145830322
C2×#145829792
C2×#145829752
C2×#145828992
C2×#145829052
C2×C43×#4682
C2×#332243