Finite Group Databasebeta

← C2×#19146801 #25973399

Subgroups — C2×#19146801 #25973399

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×#14583599C211yesmaximal, characteristic, complemented
2C2×#14583544C211yesmaximal, characteristic, complemented
3#19146801C2116yesmaximal, direct product factor
4C2×#14583254C211yesmaximal, characteristic, complemented
5C2×#14583242C211yesmaximal, characteristic, complemented
6C2×#14583214C211yesmaximal, characteristic, complemented
7C2×#14583199C211yesmaximal, characteristic, complemented
8C2×#14583151C211yesmaximal, characteristic, complemented
9C2×#14583144C211yesmaximal, characteristic, complemented
10C2×#14583114C211yesmaximal, characteristic, complemented
11C2×#14583041C211yesmaximal, characteristic, complemented
12C2×#14583031C211yesmaximal, characteristic, complemented
13C2×#14582978C211yesmaximal, characteristic, complemented
14C2×#14582897C211yesmaximal, characteristic, complemented
15C2×#14582902C211yesmaximal, characteristic, complemented
16C2×C4×D8×C43C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×D4×D43C2211yescharacteristic
19C22×#10621883C2211yescharacteristic, complemented
20C22×#10621882C2211yescharacteristic
21C22×#10621872C2211yescharacteristic
22C22×#10621872C2211yescharacteristic, complemented
23#14583599—24no—
24#14583599C2218yescomplemented
25#14583544—24no—
26#14583544C2218yescomplemented
27C2×#13063318—21no—
28C2×#13063317C2211yescharacteristic, complemented
29C2×#13063313C2211yescharacteristic
30C2×#13063309—21no—
31C2×#13063308—21no—
32C2×#13063305C2211yescharacteristic
33C2×#13063300C2211yescharacteristic
34C2×#13063299—21no—
35C2×#13063298—21no—
36C2×#13063296C2211yescharacteristic
37C2×#13063296C2211yescharacteristic, complemented
38C2×#13063295—21no—
39C2×C4×D172C2211yescharacteristic
40C2×C4×C22⋊D43—21no—
41C2×#13063283C2211yescharacteristic
42C2×C4⋊C4×D43C2211yescharacteristic, complemented
43C22×(C2×D43)⋊C4—21no—
44#14583254C2218yescomplemented
45#14583242C2218yescomplemented
46#14583214C2218yescomplemented
47#14583199C2218yescomplemented
48#14583151C2218yescomplemented
49#14583144C2218yescomplemented
50#14583114C2218yescomplemented
51#14583041C2218yescomplemented
52#14583031C2218yescomplemented
53#14582978C2218yescomplemented
54C2×#13063258C2211yescharacteristic, complemented
55C2×#13063256C2211yescharacteristic, complemented
56C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
57#14582902C2218yescomplemented
58#14582897C2218yescomplemented
59C2×#13063250C2211yescharacteristic, complemented
60C2×#13063250C2211yescharacteristic, complemented
61C2×#13063248C2211yescharacteristic, complemented
62C2×#13063247C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
69C22×D8×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic, complemented
72C4×D8×C43C2218yescomplemented
73C2×#107×C43C2211yescharacteristic, complemented
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic, complemented
76C2×C4×C8×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C2×#10621900—24no—
79C2×#10621900—22no—
80C2×#10621900—42no—
81C2×#10621900C2314yes—
82C22×Dic86C2311yescharacteristic
83C22×D172—21no—
84C22×D172D411yescharacteristic
85C22×D172C2311yescharacteristic
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C2×D4×D43—24no—
91C2×D4×D43—22no—
92C2×D4×D43—42no—
93C2×D4×D43C2314yes—
94C23×Dic43—21no—
95C22×C4×D43—21no—
96C22×C4×D43C2311yescharacteristic
97C22×C4×D43C2311yescharacteristic
98C2×#10621883—42no—
99C2×#10621883C2314yescomplemented
100C2×#10621882—42no—
101C2×#10621882C2314yes—
102C2×#10621872—42no—
103C2×#10621872—42no—
104C2×#10621872C2314yes—
105C2×#10621872C2314yescomplemented
106C22×C43⋊C8C2311yescharacteristic
107C22×C43⋊C8C2311yescharacteristic
108#13063318—28no—
109#13063317—22no—
110#13063317C2314yescomplemented
111#13063313—22no—
112#13063313C2314yes—
113#13063309—28no—
114#13063308—28no—
115#13063305—22no—
116#13063305C2314yes—
117#13063300—22no—
118#13063300C2314yes—
119#13063299—28no—
120#13063298—28no—
121#13063296—22no—
122#13063296—22no—
123#13063296C2314yes—
124#13063296C2314yescomplemented
125#13063295—28no—
126C4×D172D414yes—
127C4×D172C2314yes—
128C4×C22⋊D43—28no—
129#13063283—22no—
130#13063283C2314yes—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43D411yescharacteristic
133C2×C4⋊Dic43C2311yescharacteristic
134C2×C4⋊Dic43C2311yescharacteristic
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C4⋊C4×D43—22no—
139C4⋊C4×D43C2314yescomplemented
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—28no—
148C2×(C2×D43)⋊C4D411yescharacteristic
149C2×(C2×D43)⋊C4D411yescharacteristic
150C2×C4×Dic43—21no—
151#13063258C2314yescomplemented
152#13063256C2314yescomplemented
153C4⋊(C43⋊C8)C2314yescomplemented
154#13063250C2314yescomplemented
155#13063250C2314yescomplemented
156#13063248C2314yescomplemented
157#13063247C2314yes—
158#13063247C2314yes—
159#13063246C2314yes—
160#13063246C2314yes—
161#13063245C2314yes—
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yescomplemented
164C22×D4×C43C2311yescharacteristic
165C22×D4×C43C2311yescharacteristic
166C23×C4×C43—21no—
167C23×C4×C43—21no—
168C2×D8×C43—24no—
169C2×D8×C43C2314yes—
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172C4×D4×C43—22no—
173C4×D4×C43—22no—
174C4×D4×C43C2314yes—
175C4×D4×C43C2314yescomplemented
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C42×C43C2311yescharacteristic
181#107×C43C2314yescomplemented
182#102×C43C2314yes—
183#102×C43C2314yescomplemented
184C4×C8×C43C2314yescomplemented
185C24×C43—21no—
186C24×C43—21no—
187C23×D43—21no—
188C23×D43—24no—
189C23×D43—44no—
190C23×D43—44no—
191C23×D43—82no—
192C23×D43C2×D411yescharacteristic
193C23×D43C2×D411yescharacteristic
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—22no—
197C2×D4×C43—22no—
198C2×D4×C43—22no—
199C2×D4×C43#4114yes—
200C2×D4×C43C2412yes—
201C2×D4×C43C2412yes—
202C22×C4×C43—24no—
203C22×C4×C43—24no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—82no—
207C22×C4×C43—82no—
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2411yescharacteristic
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—24no—
214C2×C22⋊D43—24no—
215C2×C22⋊D43—44no—
216C2×C22⋊D43—44no—
217C2×C22⋊D43—44no—
218C2×C22⋊D43—82no—
219C22×Dic43—24no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—44no—
224C22×Dic43C2×D411yescharacteristic
225C22×Dic43C2×D411yescharacteristic
226#10621900—28no—
227#10621900—44no—
228#10621900—48no—
229D4×D43—28no—
230D4×D43—44no—
231D4×D43—48no—
232C2×D172—21no—
233C2×D172—24no—
234C2×D172—22no—
235C2×D172—22no—
236C2×D172—42no—
237C2×D172—82no—
238C2×D172C2×D414yes—
239C2×D172C2412yes—
240C2×C4×D43—22no—
241C2×C4×D43—22no—
242C2×C4×D43—22no—
243C2×C4×D43—22no—
244C2×C4×D43—24no—
245C2×C4×D43—82no—
246C2×C4×D43C2×D412yes—
247C2×C4×D43C2×D412yes—
248C2×C4×D43C2412yes—
249C2×C4×D43C2412yes—
250C2×Dic86—22no—
251C2×Dic86—22no—
252C2×Dic86—21no—
253C2×Dic86C2412yes—
254D8×C43—28no—
255C2×C8×C43—22no—
256C2×C8×C43—22no—
257C2×C8×C43C2412yes—
258C2×C8×C43C2412yes—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43C2412yes—
262C4⋊C4×C43C2412yes—
263C22⋊C4×C43—24no—
264C22⋊C4×C43—24no—
265C42×C43C2×D412yes—
266C42×C43C2412yes—
267C22⋊Dic43—24no—
268C22⋊Dic43—24no—
269#10621883—44no—
270#10621882—44no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4C2×D414yes—
277(C2×D43)⋊C4C2×D414yes—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—24no—
281C4⋊Dic43C2×D414yes—
282C4⋊Dic43C2412yes—
283C4⋊Dic43C2412yes—
284Dic43⋊C4—24no—
285Dic43⋊C4—24no—
286Dic43⋊C4—24no—
287C4×Dic43—24no—
288C2×C43⋊C8—22no—
289C2×C43⋊C8—22no—
290C2×C43⋊C8C2412yes—
291C2×C43⋊C8C2412yes—
292#10621872—44no—
293#10621872—44no—
294C23×C43—24no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—42no—
298C23×C43—42no—
299C23×C43—42no—
300C23×C43—42no—
301C23×C43—42no—
302C23×C43C22×D411yescharacteristic
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—48no—
311C22×D43—48no—
312C22×D43—42no—
313C22×D43—42no—
314C22×D43—42no—
315C22×D43—84no—
316C22×D43—816no—
317C22×D43C22×D412yes—
318C22×D43C22×D412yes—
319D4×C43—24no—
320D4×C43—22no—
321D4×C43—22no—
322D4×C43—22no—
323D4×C43—42no—
324D4×C43C2×#4114yes—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—42no—
330C2×C4×C43—42no—
331C2×C4×C43—84no—
332C2×C4×C43—84no—
333C2×C4×C43C22×D412yes—
334C2×C4×C43C22×D412yes—
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C2×#4112yes—
337C2×C4×C43H(5,𝔽2)12yes—
338C2×C4×C43C2511yescharacteristic
339C22⋊D43—48no—
340C22⋊D43—48no—
341C22⋊D43—48no—
342C22⋊D43—84no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—48no—
349C2×Dic43—42no—
350C2×Dic43—42no—
351C2×Dic43—42no—
352C2×Dic43C22×D412yes—
353C2×Dic43C22×D412yes—
354D172—22no—
355D172—22no—
356D172—44no—
357D172—42no—
358D172—84no—
359C4×D43—24no—
360C4×D43—24no—
361C4×D43—22no—
362C4×D43—22no—
363C4×D43—22no—
364C4×D43—22no—
365C4×D43—84no—
366Dic86—22no—
367Dic86—22no—
368Dic86—42no—
369C8×C43—22no—
370C8×C43—22no—
371C43⋊C8—22no—
372C43⋊C8—22no—
373C2×#3322—431nomaximal, Sylow
374C22×C43—24no—
375C22×C43—48no—
376C22×C43—42no—
377C22×C43—42no—
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—22no—
387C2×D43—22no—
388C2×D43—22no—
389C2×D43—22no—
390C2×D43—22no—
391C2×D43—22no—
392C2×D43—44no—
393C2×D43—44no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—42no—
397C2×D43—816no—
398C2×D43—84no—
399C4×C43—22no—
400C4×C43—22no—
401C4×C43—42no—
402C4×C43—42no—
403C4×C43#54612yes—
404C4×C43C22×#4111yescharacteristic
405C4×C43C2×H(5,𝔽2)11yescharacteristic
406Dic43—22no—
407Dic43—22no—
408Dic43—42no—
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×#468—431no—
420C2×#463—431no—
421C2×#449—431no—
422C2×#447—431no—
423C2×C4×D8D4311yescharacteristic, complemented
424C2×#436—431no—
425C2×#417—431no—
426C2×#418—431no—
427C2×C43—44no—
428C2×C43—82no—
429C2×C43#332214yescomplemented
430C2×C43C2×#54611yescharacteristic
431C2×C43C2×#57511yescharacteristic
432C2×C43C2×#57611yescharacteristic
433D43—42no—
434D43—42no—
435D43—82no—
436C22×#41—431no—
437C23×D4—431no—
438C22×SD16—431no—
439C22×D8—431no—
440C22×D8C2×D4311yescharacteristic
441C22×M16—431no—
442C22×M16—431no—
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⋊Q8—431no—
453C2×#121—431no—
454C2×#121—431no—
455C2×#121—431no—
456C2×#121—861no—
457C2×#121—861no—
458C2×#120—861no—
459C2×C4×D4—431no—
460C2×C4×D4—861no—
461C2×C4×D4C2×D4311yescharacteristic
462C2×C4×D4C2×D4311yescharacteristic, complemented
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#468—438no—
472#463—438no—
473#449—438no—
474#447—438no—
475C4×D8C2×D4318yescomplemented
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×#103—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102C2×D4311yescharacteristic
492C2×#102C2×D4311yescharacteristic, complemented
493C2×C22⋊C8—431no—
494C2×C22⋊C8—431no—
495C2×C4×C8C2×D4311yescharacteristic, complemented
496C43C2×#332211yescharacteristic, complemented, Sylow
497C25—861no—
498C2×#41—434no—
499C2×#41—862no—
500C2×#41—864no—
501C2×#41—1722no—
502C22×Q8—431no—
503C22×D4—434no—
504C22×D4—431no—
505C22×D4—431no—
506C22×D4—861no—
507C22×D4—862no—
508C22×D4—861no—
509C22×D4—864no—
510C22×D4—861no—
511C22×D4—861no—
512C22×D4—861no—
513C22×D4—1722no—
514C22×D4C22×D4311yescharacteristic
515C22×D4C22×D4311yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—431no—
519C23×C4—431no—
520C23×C4—861no—
521C23×C4—861no—
522C2×SD16—434no—
523C2×SD16—1722no—
524C2×D8—24no—
525C2×D8—434no—
526C2×D8—1722no—
527C2×D8C22×D4314yes—
528C2×M16—434no—
529C2×M16—434no—
530C2×M16—1722no—
531C2×M16—1722no—
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—434no—
544C22⋊Q8—862no—
545#121—434no—
546#121—434no—
547#121—434no—
548#121—868no—
549#121—868no—
550#121—862no—
551#121—862no—
552#121—862no—
553#120—868no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—434no—
557C4×D4—434no—
558C4×D4—868no—
559C4×D4C22×D4314yes—
560C4×D4C22×D4314yescomplemented
561#117—434no—
562#117—862no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—431no—
566C2×C4⋊C4—434no—
567C2×C4⋊C4—862no—
568C2×C4⋊C4—861no—
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—861no—
587C2×C42C22×D4311yescharacteristic
588#107—434no—
589#107C22×D4314yescomplemented
590#106—434no—
591C4⋊C8—434no—
592#103—434no—
593#103—434no—
594#103—434no—
595#102—434no—
596#102—434no—
597#102—434no—
598#102—434no—
599#102—434no—
600#102C22×D4314yes—
601#102C22×D4314yescomplemented
602C22⋊C8—434no—
603C22⋊C8—434no—
604C4×C8C22×D4314yescomplemented
605C24—21no—
606C24—21no—
607C24—431no—
608C24—431no—
609C24—864no—
610C24—861no—
611C24—3442no—
612C24—1724no—
613C24—1724no—
614#41—868no—
615#41—1724no—
616#41—1728no—
617C2×Q8—432no—
618C2×Q8—861no—
619C2×Q8—862no—
620C2×Q8—862no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—434no—
627C2×D4—432no—
628C2×D4—864no—
629C2×D4—864no—
630C2×D4—868no—
631C2×D4—864no—
632C2×D4—864no—
633C2×D4—864no—
634C2×D4—861no—
635C2×D4—862no—
636C2×D4—862no—
637C2×D4—3442no—
638C2×D4—3442no—
639C2×D4—1722no—
640C2×D4—1724no—
641C2×D4—1728no—
642C2×D4—1724no—
643C2×D4—1724no—
644C2×D4—1724no—
645C2×D4#1062189814yes—
646C2×D4C23×D4312yes—
647C2×D4C23×D4312yes—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—24no—
651C22×C4—24no—
652C22×C4—82no—
653C22×C4—82no—
654C22×C4—431no—
655C22×C4—431no—
656C22×C4—432no—
657C22×C4—432no—
658C22×C4—432no—
659C22×C4—432no—
660C22×C4—864no—
661C22×C4—864no—
662C22×C4—862no—
663C22×C4—862no—
664C22×C4—862no—
665C22×C4—862no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—3442no—
670C22×C4—1724no—
671C22×C4D4×D4311yescharacteristic
672C22×C4D4×D4311yescharacteristic
673C22×C4C23×D4311yescharacteristic
674SD16—1724no—
675D8—28no—
676D8—1724no—
677M16—1724no—
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—21no—
688C4⋊C4—21no—
689C4⋊C4—434no—
690C4⋊C4—432no—
691C4⋊C4—432no—
692C4⋊C4—864no—
693C4⋊C4—864no—
694C4⋊C4—861no—
695C4⋊C4—861no—
696C4⋊C4—864no—
697C4⋊C4—864no—
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—864no—
712C42D4×D4312yes—
713C42C23×D4312yes—
714C23—22no—
715C23—24no—
716C23—22no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—432no—
723C23—432no—
724C23—862no—
725C23—862no—
726C23—862no—
727C23—862no—
728C23—862no—
729C23—862no—
730C23—862no—
731C23—3444no—
732C23—34416no—
733C23—1728no—
734C23—1728no—
735C23—1722no—
736C23—1722no—
737C23—1722no—
738C23C2×D4×D4311yescharacteristic
739Q8—862no—
740Q8—862no—
741Q8—1722no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—24no—
746D4—42no—
747D4—862no—
748D4—862no—
749D4—3444no—
750D4—3444no—
751D4—1724no—
752D4—1728no—
753D4—1728no—
754D4—1728no—
755D4—1722no—
756D4C2×#1062189814yes—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—84no—
764C2×C4—84no—
765C2×C4—432no—
766C2×C4—432no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—864no—
774C2×C4—864no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—3444no—
779C2×C4—1728no—
780C2×C4—1722no—
781C2×C4—1722no—
782C2×C4—1722no—
783C2×C4C2×D4×D4312yes—
784C2×C4C2×D4×D4312yes—
785C2×C4C2×D4×D4311yescharacteristic
786C2×C4C2×#1062189812yes—
787C2×C4#1306337112yes—
788C2×C4C24×D4311yescharacteristic
789C8—22no—
790C8—22no—
791C8—862no—
792C8—862no—
793C22—24no—
794C22—42no—
795C22—42no—
796C22—48no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—862no—
802C22—862no—
803C22—862no—
804C22—862no—
805C22—862no—
806C22—862no—
807C22—34416no—
808C22—3444no—
809C22—1722no—
810C22—1722no—
811C22—1722no—
812C22—1724no—
813C22—1724no—
814C22#1458354512yes—
815C22#1458369612yes—
816C22#1458370012yes—
817C22C22×D4×D4311yescharacteristic
818C4—22no—
819C4—22no—
820C4—42no—
821C4—42no—
822C4—862no—
823C4—862no—
824C4—1722no—
825C4—1722no—
826C4—1722no—
827C4#1458354512yes—
828C4C22×#1062189811yescharacteristic
829C4C2×#1306337111yescharacteristic
830C2—44no—
831C2—82no—
832C2—3442no—
833C2—1722no—
834C2—1722no—
835C2#1914680114yesdirect product factor
836C2C2×#1458354511yescharacteristic
837C2C2×#1458369611yescharacteristic
838C2C2×#1458370011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C4×D8×C43C2
socleC23×C43C22×D4
hypercenterC2×C4×D8D43
hypocenterC43C2×#3322
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#14583599C2semidirect
2. C2×#14583544C2semidirect
3. #19146801C2direct (N × H)
4. C2×#14583254C2semidirect
5. C2×#14583242C2semidirect
6. C2×#14583214C2semidirect
7. C2×#14583199C2semidirect
8. C2×#14583151C2semidirect
9. C2×#14583144C2semidirect
10. C2×#14583114C2semidirect
11. C2×#14583041C2semidirect
12. C2×#14583031C2semidirect
13. C2×#14582978C2semidirect
14. C2×#14582897C2semidirect
15. C2×#14582902C2semidirect
16. C2×C4×D8×C43C2semidirect
19. C22×#10621883C22semidirect
22. C22×#10621872C22semidirect
24. #14583599C22semidirect
26. #14583544C22semidirect
28. C2×#13063317C22semidirect
37. C2×#13063296C22semidirect
42. C2×C4⋊C4×D43C22semidirect
44. #14583254C22semidirect
45. #14583242C22semidirect
46. #14583214C22semidirect
47. #14583199C22semidirect
48. #14583151C22semidirect
49. #14583144C22semidirect
50. #14583114C22semidirect
51. #14583041C22semidirect
52. #14583031C22semidirect
53. #14582978C22semidirect
54. C2×#13063258C22semidirect
55. C2×#13063256C22semidirect
56. C2×C4⋊(C43⋊C8)C22semidirect
57. #14582902C22semidirect
58. #14582897C22semidirect
59. C2×#13063250C22semidirect
60. C2×#13063250C22semidirect
61. C2×#13063248C22semidirect
68. C2×(C2×D43)⋊C8C22semidirect
71. C2×C4×D4×C43C22semidirect
72. C4×D8×C43C22semidirect
73. C2×#107×C43C22semidirect
75. C2×#102×C43C22semidirect
76. C2×C4×C8×C43C22semidirect
99. C2×#10621883C23semidirect
105. C2×#10621872C23semidirect
110. #13063317C23semidirect
124. #13063296C23semidirect
139. C4⋊C4×D43C23semidirect
151. #13063258C23semidirect
152. #13063256C23semidirect
153. C4⋊(C43⋊C8)C23semidirect
154. #13063250C23semidirect
155. #13063250C23semidirect
156. #13063248C23semidirect
163. (C2×D43)⋊C8C23semidirect
175. C4×D4×C43C23semidirect
181. #107×C43C23semidirect
183. #102×C43C23semidirect
184. C4×C8×C43C23semidirect
423. C2×C4×D8D43semidirect
429. C2×C43#3322semidirect
462. C2×C4×D4C2×D43semidirect
475. C4×D8C2×D43semidirect
478. C2×#107C2×D43semidirect
492. C2×#102C2×D43semidirect
495. C2×C4×C8C2×D43semidirect
496. C43C2×#3322semidirect
560. C4×D4C22×D43semidirect
589. #107C22×D43semidirect
601. #102C22×D43semidirect
604. C4×C8C22×D43semidirect
835. C2#19146801direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835992
C2×#145835442
#191468012
C2×#145832542
C2×#145832422
C2×#145832142
C2×#145831992
C2×#145831512
C2×#145831442
C2×#145831142
C2×#145830412
C2×#145830312
C2×#145829782
C2×#145828972
C2×#145829022
C2×C4×D8×C432
C2×#332243