Finite Group Databasebeta

← C2×#19147345 #25976343

Subgroups — C2×#19147345 #25976343

Order 11008.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583631C211yesmaximal, characteristic, complemented
2C2×#14583606C211yesmaximal, characteristic, complemented
3#19147345C2116yesmaximal, direct product factor
4C2×#14583262C211yesmaximal, characteristic, complemented
5C2×#14583258C211yesmaximal, characteristic, complemented
6C2×#14583255C211yesmaximal, characteristic, complemented
7C2×#14583208C211yesmaximal, characteristic, complemented
8C2×#14583197C211yesmaximal, characteristic, complemented
9C2×#14583180C211yesmaximal, characteristic, complemented
10C2×#14583116C211yesmaximal, characteristic, complemented
11C2×#14583092C211yesmaximal, characteristic
12C2×#14583028C211yesmaximal, characteristic, complemented
13C2×#14583009C211yesmaximal, characteristic, complemented
14C2×#14583000C211yesmaximal, characteristic, complemented
15C2×D8×Dic43C211yesmaximal, characteristic, complemented
16C2×C43×#463C211yesmaximal, characteristic, complemented
17C22×#10621882C2211yescharacteristic
18#14583631—24no—
19#14583631C2218yescomplemented
20#14583606—24no—
21#14583606C2218yescomplemented
22C2×#13063325C2211yescharacteristic
23C2×#13063321C2211yescharacteristic
24C2×#13063316C2211yescharacteristic
25C2×#13063316C2211yescharacteristic
26C2×#13063314C2211yescharacteristic
27C2×#13063311—21no—
28C2×#13063309—21no—
29C2×#13063307—21no—
30C2×#13063304—21no—
31C2×#13063302—21no—
32C2×#13063302—21no—
33C2×Q8×Dic43C2211yescharacteristic
34C2×C4×Dic86C2211yescharacteristic
35C2×C4×D172C2211yescharacteristic
36C2×D4×Dic43C2211yescharacteristic
37C2×D4×Dic43C2211yescharacteristic
38C2×D4×Dic43C2211yescharacteristic
39C2×(C22⋊D43)⋊C4—21no—
40C22×C4⋊Dic43—21no—
41#14583262C2218yescomplemented
42#14583258C2218yescomplemented
43#14583255C2218yescomplemented
44#14583208C2218yescomplemented
45#14583197C2218yescomplemented
46#14583180C2218yescomplemented
47#14583116C2218yescomplemented
48#14583092C2218yes—
49#14583028C2218yescomplemented
50#14583009C2218yescomplemented
51#14583000C2218yescomplemented
52D8×Dic43C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063259C2211yescharacteristic
55C2×#13063256C2211yescharacteristic
56C2×Dic43⋊C8C2211yescharacteristic
57C2×Dic43⋊C8C2211yescharacteristic
58C2×#13063249C2211yescharacteristic
59C2×#13063249C2211yescharacteristic
60C2×#13063247C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063246C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×#13063236C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C22×D8×C43C2211yescharacteristic
71C2×#124×C43C2211yescharacteristic
72C2×C4×D4×C43C2211yescharacteristic
73C43×#463C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86D411yescharacteristic
79C22×D172C2311yescharacteristic
80C22×C22⋊D43—21no—
81C22×C22⋊D43—21no—
82C23×Dic43—21no—
83C23×Dic43—21no—
84C23×Dic43—21no—
85C22×C4×D43—21no—
86C2×#10621882—24no—
87C2×#10621882C2314yes—
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90#13063325—22no—
91#13063325C2314yes—
92#13063321—22no—
93#13063321C2314yes—
94#13063316—22no—
95#13063316—22no—
96#13063316C2314yes—
97#13063316C2314yes—
98#13063314—22no—
99#13063314C2314yes—
100#13063311—28no—
101#13063309—28no—
102#13063307—28no—
103#13063304—28no—
104#13063302—28no—
105#13063302—28no—
106Q8×Dic43—22no—
107Q8×Dic43C2314yes—
108C4×Dic86D414yes—
109C4×Dic86C2314yes—
110C4×D172—22no—
111C4×D172C2314yes—
112D4×Dic43—22no—
113D4×Dic43—22no—
114D4×Dic43—22no—
115D4×Dic43C2314yes—
116D4×Dic43C2314yes—
117D4×Dic43C2314yes—
118(C22⋊D43)⋊C4—28no—
119C2×C4⋊Dic43—21no—
120C2×C4⋊Dic43—21no—
121C2×C4⋊Dic43—21no—
122C2×C4⋊Dic43—21no—
123C2×C4⋊Dic43—28no—
124C2×C4⋊Dic43D411yescharacteristic
125C2×C4⋊Dic43C2311yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4D411yescharacteristic
131C2×Dic43⋊C4D411yescharacteristic
132C2×C22⋊Dic43—21no—
133C2×C22⋊Dic43—21no—
134C2×C22⋊Dic43—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43C2311yescharacteristic
140C2×C4×Dic43C2311yescharacteristic
141#13063259C2314yes—
142#13063259C2314yes—
143#13063256C2314yes—
144Dic43⋊C8C2314yes—
145Dic43⋊C8C2314yes—
146#13063249C2314yes—
147#13063249C2314yes—
148#13063247C2314yes—
149#13063247C2314yes—
150#13063246C2314yes—
151#13063246C2314yes—
152#13063246C2314yes—
153#13063245C2314yes—
154#13063236C2314yes—
155#13063235C2314yes—
156C8×Dic43C2314yes—
157C22×Q8×C43C2311yescharacteristic
158C22×D4×C43C2311yescharacteristic
159C22×D4×C43C2311yescharacteristic
160C23×C4×C43—21no—
161C2×SD16×C43—24no—
162C2×SD16×C43C2314yes—
163C2×D8×C43—24no—
164C2×D8×C43C2314yes—
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167#124×C43—22no—
168#124×C43C2314yes—
169C4×D4×C43—22no—
170C4×D4×C43C2314yes—
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C22⋊C4×C43—21no—
173C2×C22⋊C4×C43—21no—
174C2×C22⋊C4×C43—21no—
175C2×C42×C43C2311yescharacteristic
176C4⋊C8×C43C2314yes—
177#103×C43C2314yes—
178#102×C43C2314yes—
179C24×C43—21no—
180C24×C43—21no—
181C23×D43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—22no—
184C2×Q8×C43—22no—
185C2×Q8×C43C2412yes—
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—22no—
189C2×D4×C43—22no—
190C2×D4×C43—22no—
191C2×D4×C43#4114yes—
192C2×D4×C43C2412yes—
193C2×D4×C43C2412yes—
194C22×C4×C43—24no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—44no—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2411yescharacteristic
201C2×C22⋊D43—24no—
202C2×C22⋊D43—24no—
203C2×C22⋊D43—44no—
204C2×C22⋊D43—82no—
205C22×Dic43—24no—
206C22×Dic43—24no—
207C22×Dic43—24no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—82no—
212C22×Dic43—82no—
213C22×Dic43—82no—
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218C2×D172—21no—
219C2×D172—22no—
220C2×D172—22no—
221C2×D172C2412yes—
222C2×C4×D43—24no—
223C2×C4×D43—82no—
224C2×Dic86—24no—
225C2×Dic86—42no—
226C2×Dic86—82no—
227C2×Dic86C2×D414yes—
228SD16×C43—28no—
229D8×C43—28no—
230C2×C8×C43—22no—
231C2×C8×C43—22no—
232C2×C8×C43C2412yes—
233C2×C8×C43C2412yes—
234C4⋊C4×C43—21no—
235C4⋊C4×C43C2412yes—
236C22⋊C4×C43—24no—
237C22⋊C4×C43—24no—
238C22⋊C4×C43—24no—
239C42×C43C2×D412yes—
240C42×C43C2412yes—
241C22⋊Dic43—24no—
242C22⋊Dic43—24no—
243C22⋊Dic43—24no—
244#10621882—28no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248C4⋊Dic43—24no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43—24no—
253C4⋊Dic43—24no—
254C4⋊Dic43—24no—
255C4⋊Dic43C2×D414yes—
256C4⋊Dic43C2412yes—
257C4⋊Dic43C2412yes—
258C4⋊Dic43C2412yes—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4C2×D414yes—
262Dic43⋊C4C2×D414yes—
263C4×Dic43—24no—
264C4×Dic43C2×D412yes—
265C4×Dic43C2×D412yes—
266C4×Dic43C2412yes—
267C4×Dic43C2412yes—
268C2×C43⋊C8—22no—
269C2×C43⋊C8—22no—
270C2×C43⋊C8C2412yes—
271C2×C43⋊C8C2412yes—
272C23×C43—24no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—42no—
276C23×C43—42no—
277C23×C43—42no—
278C23×C43—42no—
279C23×C43—42no—
280C23×C43C22×D411yescharacteristic
281C22×D43—22no—
282C22×D43—42no—
283C22×D43—42no—
284C22×D43—42no—
285Q8×C43—22no—
286Q8×C43—22no—
287Q8×C43—42no—
288D4×C43—24no—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43—22no—
292D4×C43—42no—
293D4×C43C2×#4114yes—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—48no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43C22×D412yes—
302C2×C4×C43C22×D412yes—
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C2×#4112yes—
305C2×C4×C432−1+412yes—
306C2×C4×C43C2511yescharacteristic
307C22⋊D43—48no—
308C22⋊D43—84no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—84no—
320C2×Dic43—84no—
321C2×Dic43—84no—
322C2×Dic43C22×D412yes—
323C2×Dic43C22×D412yes—
324C2×Dic43C22×D412yes—
325C2×Dic43C22×D412yes—
326D172—22no—
327D172—22no—
328D172—42no—
329C4×D43—84no—
330Dic86—44no—
331Dic86—84no—
332C8×C43—22no—
333C8×C43—22no—
334C43⋊C8—22no—
335C43⋊C8—22no—
336C2×#3370—431nomaximal, Sylow
337C22×C43—24no—
338C22×C43—48no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—42no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—84no—
345C22×C43#54812yes—
346C22×C43#57512yes—
347C22×C43#57612yes—
348C22×C43C23×D411yescharacteristic
349C2×D43—42no—
350C2×D43—42no—
351C2×D43—42no—
352C2×D43—84no—
353C4×C43—22no—
354C4×C43—22no—
355C4×C43—42no—
356C4×C43—42no—
357C4×C43#54812yes—
358C4×C43C22×#4111yescharacteristic
359C4×C43C2×2−1+411yescharacteristic
360Dic43—22no—
361Dic43—22no—
362Dic43—22no—
363Dic43—22no—
364Dic43—42no—
365Dic43—42no—
366Dic43—42no—
367C2×#559—431no—
368C2×#554—431no—
369#3370—4316no—
370C2×#490—431no—
371C2×#489—431no—
372C2×#488—431no—
373C2×#479—431no—
374C2×#478—431no—
375C2×#474—431no—
376C2×#463—431no—
377C2×#463D4311yescharacteristic, complemented
378C2×#459—431no—
379C2×#446—431no—
380C2×#442—431no—
381C2×#440—431no—
382C2×C4×D8—431no—
383C2×C43—44no—
384C2×C43—82no—
385C2×C43#337014yescomplemented
386C2×C43C2×#54811yescharacteristic
387C2×C43C2×#57511yescharacteristic
388C2×C43C2×#57611yescharacteristic
389D43—82no—
390C22×SD16C2×D4311yescharacteristic
391C22×D8—431no—
392C22×D8C2×D4311yescharacteristic
393#559—438no—
394#559—864no—
395#554—438no—
396#554—864no—
397C2×C4⋊Q8—431no—
398C2×#127—431no—
399C2×#125—431no—
400C2×#125—431no—
401C2×#124—431no—
402C2×#124—861no—
403C2×#124C2×D4311yescharacteristic
404C2×#123—861no—
405C2×#123—861no—
406C2×C22⋊Q8—861no—
407C2×C22⋊Q8—861no—
408C2×C22⋊Q8—861no—
409C2×C4×Q8—431no—
410C2×C4×Q8—431no—
411C2×C4×D4—431no—
412C2×C4×D4—431no—
413C2×C4×D4—431no—
414C2×C4×D4—431no—
415C2×C4×D4—861no—
416C2×C4×D4C2×D4311yescharacteristic
417C22×C4⋊C4—861no—
418#490—438no—
419#489—438no—
420#488—438no—
421#479—438no—
422#478—438no—
423#474—438no—
424#463—438no—
425#463C2×D4318yescomplemented
426#459—438no—
427#446—438no—
428#442—438no—
429#440—438no—
430C4×D8—438no—
431C2×#107—431no—
432C2×#107—431no—
433C2×#106—431no—
434C2×C4⋊C8—431no—
435C2×C4⋊C8—431no—
436C2×C4⋊C8C2×D4311yescharacteristic
437C2×#103—431no—
438C2×#103—431no—
439C2×#103C2×D4311yescharacteristic
440C2×#102—431no—
441C2×#102—431no—
442C2×#102—431no—
443C2×#102—431no—
444C2×#102—431no—
445C2×#102—431no—
446C2×#102C2×D4311yescharacteristic
447C2×#97—431no—
448C2×#97—431no—
449C2×C4×C8—431no—
450C43C2×#337011yescharacteristic, complemented, Sylow
451C22×Q8—431no—
452C22×Q8—861no—
453C22×Q8C22×D4311yescharacteristic
454C22×D4—431no—
455C22×D4—861no—
456C22×D4—861no—
457C22×D4C22×D4311yescharacteristic
458C22×D4C22×D4311yescharacteristic
459C23×C4—21no—
460C23×C4—861no—
461C23×C4—861no—
462C23×C4—861no—
463C23×C4—861no—
464C2×SD16—24no—
465C2×SD16C22×D4314yes—
466C2×D8—24no—
467C2×D8—434no—
468C2×D8—864no—
469C2×D8C22×D4314yes—
470C22×C8—431no—
471C22×C8—431no—
472C22×C8C22×D4311yescharacteristic
473C22×C8C22×D4311yescharacteristic
474C4⋊Q8—434no—
475C4⋊Q8—862no—
476#127—434no—
477#127—862no—
478#125—434no—
479#125—434no—
480#125—862no—
481#125—862no—
482#124—22no—
483#124—434no—
484#124—862no—
485#124—868no—
486#124C22×D4314yes—
487#123—868no—
488#123—868no—
489C22⋊Q8—868no—
490C22⋊Q8—868no—
491C22⋊Q8—868no—
492C4×Q8—434no—
493C4×Q8—434no—
494C4×Q8—434no—
495C4×Q8—862no—
496C4×D4—22no—
497C4×D4—434no—
498C4×D4—434no—
499C4×D4—434no—
500C4×D4—434no—
501C4×D4—862no—
502C4×D4—862no—
503C4×D4—862no—
504C4×D4—868no—
505C4×D4—862no—
506C4×D4C22×D4314yes—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4—431no—
513C2×C4⋊C4—868no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4C22×D4311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C42—431no—
531C2×C42—431no—
532C2×C42—861no—
533C2×C42C22×D4311yescharacteristic
534#107—434no—
535#107—434no—
536#106—434no—
537C4⋊C8—434no—
538C4⋊C8—434no—
539C4⋊C8C22×D4314yes—
540#103—434no—
541#103—434no—
542#103C22×D4314yes—
543#102—434no—
544#102—434no—
545#102—434no—
546#102—434no—
547#102—434no—
548#102—434no—
549#102C22×D4314yes—
550#97—434no—
551#97—434no—
552C4×C8—434no—
553C24—21no—
554C24—21no—
555C24—861no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—434no—
560C2×Q8—864no—
561C2×Q8—3442no—
562C2×Q8—1722no—
563C2×Q8C23×D4312yes—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—432no—
570C2×D4—864no—
571C2×D4—864no—
572C2×D4—861no—
573C2×D4—862no—
574C2×D4—862no—
575C2×D4—3442no—
576C2×D4—1724no—
577C2×D4#1062190014yes—
578C2×D4C23×D4312yes—
579C2×D4C23×D4312yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—44no—
584C22×C4—431no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—431no—
588C22×C4—864no—
589C22×C4—864no—
590C22×C4—864no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—864no—
595C22×C4—3442no—
596C22×C4—3442no—
597C22×C4—3442no—
598C22×C4—3442no—
599C22×C4D4×D4311yescharacteristic
600C22×C4D4×D4311yescharacteristic
601C22×C4C23×D4311yescharacteristic
602SD16—28no—
603D8—28no—
604D8—868no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—432no—
608C2×C8—432no—
609C2×C8—862no—
610C2×C8—862no—
611C2×C8C23×D4312yes—
612C2×C8C23×D4312yes—
613C4⋊C4—21no—
614C4⋊C4—434no—
615C4⋊C4—434no—
616C4⋊C4—434no—
617C4⋊C4—432no—
618C4⋊C4—432no—
619C4⋊C4—432no—
620C4⋊C4—864no—
621C4⋊C4—864no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—864no—
629C4⋊C4C23×D4312yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C22⋊C4—864no—
639C42—432no—
640C42—432no—
641C42—432no—
642C42—432no—
643C42—864no—
644C42D4×D4312yes—
645C42C23×D4312yes—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—862no—
655C23—1722no—
656C23—1722no—
657C23—1722no—
658C23C2×D4×D4311yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—42no—
662Q8—3444no—
663Q8—1724no—
664D4—24no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—42no—
669D4—862no—
670D4—862no—
671D4—3444no—
672D4—1728no—
673D4—1722no—
674D4C2×#1062190014yes—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—48no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—432no—
683C2×C4—432no—
684C2×C4—432no—
685C2×C4—432no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—3444no—
694C2×C4—3444no—
695C2×C4—3444no—
696C2×C4—3444no—
697C2×C4—1722no—
698C2×C4—1722no—
699C2×C4—1722no—
700C2×C4C2×D4×D4312yes—
701C2×C4C2×D4×D4312yes—
702C2×C4C2×D4×D4311yescharacteristic
703C2×C4C2×#1062190012yes—
704C2×C4#1306337212yes—
705C2×C4C24×D4311yescharacteristic
706C8—22no—
707C8—22no—
708C8—862no—
709C8—862no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22—3444no—
719C22—1722no—
720C22—1722no—
721C22—1722no—
722C22#1458355512yes—
723C22#1458369512yes—
724C22#1458370112yes—
725C22C22×D4×D4311yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—862no—
731C4—862no—
732C4—862no—
733C4—862no—
734C4—1722no—
735C4—1722no—
736C4—1722no—
737C4#1458355512yes—
738C4C22×#1062190011yescharacteristic
739C4C2×#1306337211yescharacteristic
740C2—44no—
741C2—82no—
742C2—3442no—
743C2#1914734514yesdirect product factor
744C2C2×#1458355511yescharacteristic
745C2C2×#1458369511yescharacteristic
746C2C2×#1458370111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#463C2
socleC23×C43C22×D4
prime radicalC2×#14583092C2
hypercenterC2×#463D43
hypocenterC43C2×#3370
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#14583631C2semidirect
2. C2×#14583606C2semidirect
3. #19147345C2direct (N × H)
4. C2×#14583262C2semidirect
5. C2×#14583258C2semidirect
6. C2×#14583255C2semidirect
7. C2×#14583208C2semidirect
8. C2×#14583197C2semidirect
9. C2×#14583180C2semidirect
10. C2×#14583116C2semidirect
12. C2×#14583028C2semidirect
13. C2×#14583009C2semidirect
14. C2×#14583000C2semidirect
15. C2×D8×Dic43C2semidirect
16. C2×C43×#463C2semidirect
19. #14583631C22semidirect
21. #14583606C22semidirect
41. #14583262C22semidirect
42. #14583258C22semidirect
43. #14583255C22semidirect
44. #14583208C22semidirect
45. #14583197C22semidirect
46. #14583180C22semidirect
47. #14583116C22semidirect
49. #14583028C22semidirect
50. #14583009C22semidirect
51. #14583000C22semidirect
52. D8×Dic43C22semidirect
73. C43×#463C22semidirect
377. C2×#463D43semidirect
385. C2×C43#3370semidirect
425. #463C2×D43semidirect
450. C43C2×#3370semidirect
743. C2#19147345direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836312
C2×#145836062
#191473452
C2×#145832622
C2×#145832582
C2×#145832552
C2×#145832082
C2×#145831972
C2×#145831802
C2×#145831162
C2×#145830922
C2×#145830282
C2×#145830092
C2×#145830002
C2×D8×Dic432
C2×C43×#4632
C2×#337043