Finite Group Databasebeta

← C2×#19146774 #25973340

Subgroups — C2×#19146774 #25973340

Order 11008.

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×#14583613C211yesmaximal, characteristic, complemented
2C2×#14583560C211yesmaximal, characteristic, complemented
3#19146774C2116yesmaximal, direct product factor
4C2×#14583260C211yesmaximal, characteristic, complemented
5C2×#14583239C211yesmaximal, characteristic, complemented
6C2×#14583224C211yesmaximal, characteristic, complemented
7C2×#14583182C211yesmaximal, characteristic, complemented
8C2×#14583150C211yesmaximal, characteristic, complemented
9C2×#14583125C211yesmaximal, characteristic, complemented
10C2×#14583116C211yesmaximal, characteristic, complemented
11C2×#14583043C211yesmaximal, characteristic, complemented
12C2×#14583000C211yesmaximal, characteristic, complemented
13C2×#14582973C211yesmaximal, characteristic, complemented
14C2×#14582908C211yesmaximal, characteristic, complemented
15C2×#14582894C211yesmaximal, characteristic, complemented
16C2×C43×#448C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21#14583613—24no—
22#14583613C2218yescomplemented
23#14583560—24no—
24#14583560C2218yescomplemented
25C2×#13063324C2211yescharacteristic
26C2×#13063314—21no—
27C2×#13063314C2211yescharacteristic
28C2×#13063312—21no—
29C2×#13063311—21no—
30C2×#13063301—21no—
31C2×#13063301C2211yescharacteristic
32C2×#13063299—21no—
33C2×#13063299C2211yescharacteristic
34C2×#13063297—21no—
35C2×#13063296C2211yescharacteristic
36C2×Q8×Dic43C2211yescharacteristic
37C2×D4×Dic43C2211yescharacteristic
38C2×C4×C22⋊D43—21no—
39C2×C4×C22⋊D43C2211yescharacteristic
40C2×#13063284C2211yescharacteristic
41C2×#13063283C2211yescharacteristic
42C2×#13063281—21no—
43#14583260C2218yescomplemented
44#14583239C2218yescomplemented
45#14583224C2218yescomplemented
46#14583182C2218yescomplemented
47#14583150C2218yescomplemented
48#14583125C2218yescomplemented
49#14583116C2218yescomplemented
50#14583043C2218yescomplemented
51#14583000C2218yescomplemented
52#14582973C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063257C2211yescharacteristic
55C2×#13063256C2211yescharacteristic
56C2×Dic43⋊C8C2211yescharacteristic
57#14582908C2218yescomplemented
58#14582894C2218yescomplemented
59C2×#13063249C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C23×Q8×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C22×SD16×C43C2211yescharacteristic
72C2×#121×C43C2211yescharacteristic
73C43×#448C2218yescomplemented
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—24no—
79C2×#10621902—42no—
80C2×#10621902C2314yes—
81C22×Dic86—21no—
82C22×D172—21no—
83C22×D172C2311yescharacteristic
84C22×C22⋊D43—21no—
85C22×C22⋊D43—21no—
86C22×C22⋊D43D411yescharacteristic
87C23×Dic43—21no—
88C22×C4×D43—21no—
89C22×C4×D43C2311yescharacteristic
90C2×#10621882—42no—
91C2×#10621882C2314yes—
92C2×#10621877—42no—
93C2×#10621877C2314yes—
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96C2×C8×D43—42no—
97C2×C8×D43C2314yes—
98#13063324—22no—
99#13063324C2314yes—
100#13063314—28no—
101#13063314—22no—
102#13063314C2314yes—
103#13063312—28no—
104#13063311—28no—
105#13063301—22no—
106#13063301—28no—
107#13063301C2314yes—
108#13063299—22no—
109#13063299—28no—
110#13063299C2314yes—
111#13063297—28no—
112#13063296—22no—
113#13063296C2314yes—
114Q8×Dic43—22no—
115Q8×Dic43C2314yes—
116D4×Dic43—22no—
117D4×Dic43C2314yes—
118C4×C22⋊D43—28no—
119C4×C22⋊D43D414yes—
120C4×C22⋊D43C2314yes—
121#13063284—22no—
122#13063284C2314yes—
123#13063283—22no—
124#13063283C2314yes—
125#13063281—28no—
126C2×C4⋊Dic43—21no—
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2311yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4D411yescharacteristic
133C2×C22⋊Dic43—21no—
134C2×C22⋊Dic43—21no—
135C2×C22⋊Dic43—21no—
136C2×C22⋊Dic43D411yescharacteristic
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4D411yescharacteristic
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43C2311yescharacteristic
147#13063259C2314yes—
148#13063257C2314yes—
149#13063256C2314yes—
150Dic43⋊C8C2314yes—
151#13063249C2314yes—
152#13063249C2314yes—
153#13063249C2314yes—
154#13063249C2314yes—
155#13063247C2314yes—
156#13063247C2314yes—
157#13063246C2314yes—
158#13063245C2314yes—
159(C2×D43)⋊C8C2314yes—
160#13063235C2314yes—
161C22×Q8×C43—22no—
162C22×Q8×C43—21no—
163C22×Q8×C43—24no—
164C22×Q8×C43—42no—
165C22×Q8×C43C2311yescharacteristic
166C22×Q8×C43C2314yes—
167C22×Q8×C43C2311yescharacteristic
168C22×D4×C43—21no—
169C22×D4×C43C2311yescharacteristic
170C23×C4×C43—21no—
171C23×C4×C43C2311yescharacteristic
172C2×SD16×C43—24no—
173C2×SD16×C43—42no—
174C2×SD16×C43C2314yes—
175C2×SD16×C43C2314yes—
176C22×C8×C43C2311yescharacteristic
177C22×C8×C43C2311yescharacteristic
178#121×C43—22no—
179#121×C43C2314yes—
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43—21no—
182#103×C43C2314yes—
183#103×C43C2314yes—
184C22⋊C8×C43C2314yes—
185C24×C43—21no—
186C24×C43C2×D411yescharacteristic
187C23×D43—21no—
188C23×D43C2×D411yescharacteristic
189C2×Q8×C43—21no—
190C2×Q8×C43—24no—
191C2×Q8×C43—21no—
192C2×Q8×C43—22no—
193C2×Q8×C43—28no—
194C2×Q8×C43—22no—
195C2×Q8×C43—22no—
196C2×Q8×C43—44no—
197C2×Q8×C43—44no—
198C2×Q8×C43—48no—
199C2×Q8×C43#4114yes—
200C2×Q8×C43C2412yes—
201C2×Q8×C43C2412yes—
202C2×D4×C43—21no—
203C2×D4×C43—24no—
204C2×D4×C43—22no—
205C2×D4×C43—22no—
206C2×D4×C43—82no—
207C2×D4×C43C2412yes—
208C22×C4×C43—22no—
209C22×C4×C43—22no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—24no—
214C22×C4×C43—44no—
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D412yes—
217C22×C4×C43C2412yes—
218C22×C4×C43C2411yescharacteristic
219C2×C22⋊D43—24no—
220C2×C22⋊D43—24no—
221C2×C22⋊D43—42no—
222C2×C22⋊D43—44no—
223C2×C22⋊D43—82no—
224C2×C22⋊D43C2×D414yes—
225C22×Dic43—24no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—44no—
230C22×Dic43C2×D411yescharacteristic
231C22×Dic43C2×D411yescharacteristic
232C22×Dic43C2×D411yescharacteristic
233#10621902—28no—
234#10621902—44no—
235#10621902—48no—
236C2×D172—21no—
237C2×D172—24no—
238C2×D172—22no—
239C2×D172—22no—
240C2×D172—44no—
241C2×D172C2412yes—
242C2×C4×D43—22no—
243C2×C4×D43—22no—
244C2×C4×D43—24no—
245C2×C4×D43—44no—
246C2×C4×D43C2×D412yes—
247C2×C4×D43C2412yes—
248C2×Dic86—24no—
249C2×Dic86—82no—
250SD16×C43—28no—
251SD16×C43—44no—
252C2×C8×C43—22no—
253C2×C8×C43—22no—
254C2×C8×C43C2412yes—
255C2×C8×C43C2412yes—
256C4⋊C4×C43—21no—
257C4⋊C4×C43C2412yes—
258C22⋊C4×C43—24no—
259C22⋊Dic43—24no—
260C22⋊Dic43—24no—
261C22⋊Dic43—24no—
262C22⋊Dic43C2×D414yes—
263#10621882—44no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4C2×D414yes—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43—24no—
274C4⋊Dic43C2412yes—
275C4⋊Dic43C2412yes—
276C4⋊Dic43C2412yes—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4C2×D414yes—
280C4×Dic43—24no—
281C4×Dic43—24no—
282C4×Dic43—24no—
283C4×Dic43C2×D412yes—
284C4×Dic43C2412yes—
285#10621877—44no—
286C2×C43⋊C8—22no—
287C2×C43⋊C8—22no—
288C2×C43⋊C8C2412yes—
289C2×C43⋊C8C2412yes—
290C8×D43—44no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—42no—
296C23×C43—42no—
297C23×C43—42no—
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—
308Q8×C43—24no—
309Q8×C43—22no—
310Q8×C43—22no—
311Q8×C43—22no—
312Q8×C43—48no—
313Q8×C43—42no—
314Q8×C43C2×#4114yes—
315D4×C43—22no—
316D4×C43—22no—
317D4×C43—42no—
318D4×C43—84no—
319C2×C4×C43—24no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—24no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—48no—
328C2×C4×C43—42no—
329C2×C4×C43—42no—
330C2×C4×C43C22×D412yes—
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C2×#4112yes—
333C2×C4×C43H(5,𝔽2)12yes—
334C2×C4×C43C2511yescharacteristic
335C22⋊D43—44no—
336C22⋊D43—48no—
337C22⋊D43—84no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—48no—
345C2×Dic43—42no—
346C2×Dic43—42no—
347C2×Dic43—42no—
348C2×Dic43C22×D412yes—
349C2×Dic43C22×D412yes—
350C2×Dic43C22×D412yes—
351D172—22no—
352D172—22no—
353D172—48no—
354D172—42no—
355C4×D43—24no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—48no—
359Dic86—84no—
360C8×C43—22no—
361C8×C43—22no—
362C43⋊C8—22no—
363C43⋊C8—22no—
364C2×#3321—431nomaximal, Sylow
365C22×C43—22no—
366C22×C43—22no—
367C22×C43—22no—
368C22×C43—44no—
369C22×C43—42no—
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—84no—
373C22×C43#54612yes—
374C22×C43#57512yes—
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—24no—
386C4×C43—22no—
387C4×C43—42no—
388C4×C43—42no—
389C4×C43#54612yes—
390C4×C43C22×#4111yescharacteristic
391C4×C43C2×H(5,𝔽2)11yescharacteristic
392Dic43—22no—
393Dic43—22no—
394Dic43—22no—
395Dic43—42no—
396Dic43—42no—
397Dic43—42no—
398C2×#555—431no—
399C2×#548—431no—
400#3321—4316no—
401C2×#489—431no—
402C2×#485—431no—
403C2×#482—431no—
404C2×#475—431no—
405C2×#469—431no—
406C2×#465—431no—
407C2×#463—431no—
408C2×#449—431no—
409C2×#448D4311yescharacteristic, complemented
410C2×#440—431no—
411C2×#435—431no—
412C2×#419—431no—
413C2×#416—431no—
414C2×C43—42no—
415C2×C43—82no—
416C2×C43#332114yescomplemented
417C2×C43C2×#54611yescharacteristic
418C2×C43C2×#57511yescharacteristic
419C2×C43C2×#57711yescharacteristic
420D43—42no—
421D43—82no—
422C22×#41—431no—
423C23×Q8C2×D4311yescharacteristic
424C22×SD16C2×D4311yescharacteristic
425C22×SD16C2×D4311yescharacteristic
426C22×D8—431no—
427C22×M16—431no—
428C23×C8—431no—
429#555—438no—
430#555—864no—
431#548—438no—
432#548—864no—
433C2×C4⋊Q8—431no—
434C2×#124—431no—
435C2×#124—861no—
436C2×#124—861no—
437C2×#124—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×#117—431no—
450C2×#117—431no—
451C2×#117—861no—
452#489—438no—
453#485—438no—
454#482—438no—
455#475—438no—
456#469—438no—
457#465—438no—
458#463—438no—
459#449—438no—
460#448C2×D4318yescomplemented
461#440—438no—
462#435—438no—
463C2×#107—431no—
464C2×#106—431no—
465C2×#106—431no—
466C2×C4⋊C8—431no—
467#419—438no—
468#416—438no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#103C2×D4311yescharacteristic
474C2×#103C2×D4311yescharacteristic
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×#102—431no—
479C2×C22⋊C8—431no—
480C2×C22⋊C8C2×D4311yescharacteristic
481C2×#97—431no—
482C43C2×#332111yescharacteristic, complemented, Sylow
483C2×#41—434no—
484C2×#41—862no—
485C2×#41—864no—
486C2×#41—1722no—
487C22×Q8—21no—
488C22×Q8—22no—
489C22×Q8—24no—
490C22×Q8—42no—
491C22×Q8—861no—
492C22×Q8C22×D4311yescharacteristic
493C22×Q8C22×D4314yes—
494C22×Q8C22×D4311yescharacteristic
495C22×D4—21no—
496C22×D4—431no—
497C22×D4—431no—
498C22×D4—861no—
499C22×D4—861no—
500C22×D4—861no—
501C22×D4C22×D4311yescharacteristic
502C23×C4—21no—
503C23×C4—431no—
504C23×C4—861no—
505C23×C4—861no—
506C23×C4C22×D4311yescharacteristic
507C2×SD16—24no—
508C2×SD16—42no—
509C2×SD16C22×D4314yes—
510C2×SD16C22×D4314yes—
511C2×D8—434no—
512C2×D8—1722no—
513C2×M16—434no—
514C2×M16—1722no—
515C22×C8—431no—
516C22×C8—431no—
517C22×C8—434no—
518C22×C8—1722no—
519C22×C8C22×D4311yescharacteristic
520C22×C8C22×D4311yescharacteristic
521C4⋊Q8—434no—
522C4⋊Q8—862no—
523#124—434no—
524#124—862no—
525#124—868no—
526#124—868no—
527#124—868no—
528C22⋊Q8—434no—
529C22⋊Q8—868no—
530C22⋊Q8—862no—
531#121—22no—
532#121—434no—
533#121—434no—
534#121—868no—
535#121—862no—
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—
546#117—434no—
547#117—434no—
548#117—868no—
549#117—862no—
550#117—862no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—431no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4C22×D4311yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—431no—
561C2×C22⋊C4—431no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
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×C42—431no—
571C2×C42—861no—
572C2×C42—861no—
573C2×C42—861no—
574#107—434no—
575#106—434no—
576#106—434no—
577C4⋊C8—434no—
578#103—434no—
579#103—434no—
580#103—434no—
581#103—434no—
582#103C22×D4314yes—
583#103C22×D4314yes—
584#102—434no—
585#102—434no—
586#102—434no—
587#102—434no—
588C22⋊C8—434no—
589C22⋊C8C22×D4314yes—
590#97—434no—
591C24—21no—
592C24—431no—
593C24—861no—
594C24D4×D4311yescharacteristic
595#41—868no—
596#41—1724no—
597#41—1728no—
598C2×Q8—21no—
599C2×Q8—24no—
600C2×Q8—21no—
601C2×Q8—22no—
602C2×Q8—28no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—44no—
606C2×Q8—44no—
607C2×Q8—48no—
608C2×Q8—864no—
609C2×Q8—3442no—
610C2×Q8#1062190014yes—
611C2×Q8C23×D4312yes—
612C2×Q8C23×D4312yes—
613C2×D4—24no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—82no—
618C2×D4—434no—
619C2×D4—432no—
620C2×D4—864no—
621C2×D4—864no—
622C2×D4—864no—
623C2×D4—861no—
624C2×D4—862no—
625C2×D4—862no—
626C2×D4—3442no—
627C2×D4—1724no—
628C2×D4—1722no—
629C2×D4—1724no—
630C2×D4C23×D4312yes—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—24no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—44no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—431no—
641C22×C4—432no—
642C22×C4—432no—
643C22×C4—864no—
644C22×C4—864no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—1724no—
651C22×C4—1724no—
652C22×C4D4×D4312yes—
653C22×C4D4×D4311yescharacteristic
654C22×C4C23×D4312yes—
655C22×C4C23×D4311yescharacteristic
656SD16—28no—
657SD16—44no—
658D8—1724no—
659M16—1724no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—432no—
663C2×C8—432no—
664C2×C8—862no—
665C2×C8—862no—
666C2×C8—1724no—
667C2×C8C23×D4312yes—
668C2×C8C23×D4312yes—
669C4⋊C4—21no—
670C4⋊C4—434no—
671C4⋊C4—432no—
672C4⋊C4—432no—
673C4⋊C4—432no—
674C4⋊C4—864no—
675C4⋊C4—864no—
676C4⋊C4—864no—
677C4⋊C4—861no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4C23×D4312yes—
681C22⋊C4—24no—
682C22⋊C4—434no—
683C22⋊C4—434no—
684C22⋊C4—864no—
685C22⋊C4—864no—
686C22⋊C4—864no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C22⋊C4—864no—
692C42—432no—
693C42—432no—
694C42—864no—
695C42—864no—
696C42—864no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—432no—
705C23—862no—
706C23—862no—
707C23—862no—
708C23—862no—
709C23—1722no—
710C23—1722no—
711C23—1722no—
712C23C2×D4×D4312yes—
713C23C2×D4×D4311yescharacteristic
714Q8—22no—
715Q8—24no—
716Q8—22no—
717Q8—22no—
718Q8—48no—
719Q8—42no—
720Q8—3444no—
721Q8C2×#1062190014yes—
722D4—22no—
723D4—22no—
724D4—42no—
725D4—84no—
726D4—862no—
727D4—862no—
728D4—3444no—
729D4—1728no—
730D4—1724no—
731D4—1728no—
732D4—1722no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—48no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—432no—
745C2×C4—432no—
746C2×C4—432no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—864no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—1728no—
757C2×C4—1728no—
758C2×C4—1722no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4C2×D4×D4312yes—
762C2×C4C2×D4×D4311yescharacteristic
763C2×C4C2×#1062190012yes—
764C2×C4#1306337012yes—
765C2×C4C24×D4311yescharacteristic
766C8—22no—
767C8—22no—
768C8—862no—
769C8—862no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—84no—
778C22—862no—
779C22—862no—
780C22—862no—
781C22—3444no—
782C22—1722no—
783C22—1722no—
784C22—1722no—
785C22—1724no—
786C22#1458353612yes—
787C22#1458369812yes—
788C22#1458370512yes—
789C22C22×D4×D4311yescharacteristic
790C4—22no—
791C4—24no—
792C4—42no—
793C4—42no—
794C4—862no—
795C4—862no—
796C4—862no—
797C4—1722no—
798C4—1722no—
799C4—1722no—
800C4#1458353612yes—
801C4C22×#1062190011yescharacteristic
802C4C2×#1306337011yescharacteristic
803C2—42no—
804C2—82no—
805C2—3442no—
806C2—1722no—
807C2#1914677414yesdirect product factor
808C2C2×#1458353611yescharacteristic
809C2C2×#1458369811yescharacteristic
810C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#448C2
socleC23×C43C22×D4
hypercenterC2×#448D43
hypocenterC43C2×#3321
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×#14583613C2semidirect
2. C2×#14583560C2semidirect
3. #19146774C2direct (N × H)
4. C2×#14583260C2semidirect
5. C2×#14583239C2semidirect
6. C2×#14583224C2semidirect
7. C2×#14583182C2semidirect
8. C2×#14583150C2semidirect
9. C2×#14583125C2semidirect
10. C2×#14583116C2semidirect
11. C2×#14583043C2semidirect
12. C2×#14583000C2semidirect
13. C2×#14582973C2semidirect
14. C2×#14582908C2semidirect
15. C2×#14582894C2semidirect
16. C2×C43×#448C2semidirect
22. #14583613C22semidirect
24. #14583560C22semidirect
43. #14583260C22semidirect
44. #14583239C22semidirect
45. #14583224C22semidirect
46. #14583182C22semidirect
47. #14583150C22semidirect
48. #14583125C22semidirect
49. #14583116C22semidirect
50. #14583043C22semidirect
51. #14583000C22semidirect
52. #14582973C22semidirect
57. #14582908C22semidirect
58. #14582894C22semidirect
73. C43×#448C22semidirect
409. C2×#448D43semidirect
416. C2×C43#3321semidirect
460. #448C2×D43semidirect
482. C43C2×#3321semidirect
807. C2#19146774direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836132
C2×#145835602
#191467742
C2×#145832602
C2×#145832392
C2×#145832242
C2×#145831822
C2×#145831502
C2×#145831252
C2×#145831162
C2×#145830432
C2×#145830002
C2×#145829732
C2×#145829082
C2×#145828942
C2×C43×#4482
C2×#332143