Finite Group Databasebeta

← C2×#19135116 #25098569

Subgroups — C2×#19135116 #25098569

Order 11008.

1686 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583665C211yesmaximal, characteristic
2C2×#14583475C211yesmaximal, characteristic
3C2×#14582909C211yesmaximal, characteristic, complemented
4C2×#14582907C211yesmaximal, characteristic, complemented
5C2×#14582872C211yesmaximal, characteristic
6#19135116C218yesmaximal, direct product factor
7C2×#14582655C211yesmaximal, characteristic, complemented
8C2×C43×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C23×Dic86C2211yescharacteristic
11#14583665—22no—
12#14583665—22no—
13#14583665—22no—
14#14583665C2214yes—
15C2×#13063333—22no—
16C2×#13063331—22no—
17C22×#10621877C2211yescharacteristic
18C2×M16×D43—22no—
19#14583475—22no—
20#14583475—22no—
21#14583475C414yescomplemented
22#14583475C2214yes—
23C2×#13063325C412yescomplemented
24C2×#13063313C412yescomplemented
25C2×#13063309—22no—
26C2×#13063305—22no—
27C2×#13063284C2211yescharacteristic
28#14582909—22no—
29#14582909C2214yescomplemented
30#14582907—22no—
31#14582907C2214yescomplemented
32C2×#13063250—22no—
33C2×#13063248—22no—
34#14582872—22no—
35#14582872C2214yes—
36C2×#13063239—22no—
37#14582655C2214yescomplemented
38C22×M16×C43C2211yescharacteristic
39C2×#117×C43C2211yescharacteristic
40C2×#117×C43C2211yescharacteristic
41C43×H(3,ℤ/4)C2214yescomplemented
42C2×#10621898—21no—
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898C2×C412yes—
51C2×#10621898D412yes—
52C2×#10621898D412yes—
53C2×#10621898C2312yes—
54C22×Dic86—21no—
55C22×Dic86—21no—
56C22×Dic86—21no—
57C22×Dic86—21no—
58C22×Dic86—21no—
59C22×Dic86—21no—
60C22×Dic86—21no—
61C22×Dic86—21no—
62C22×Dic86—21no—
63C22×Dic86—21no—
64C22×Dic86—21no—
65C22×Dic86C2×C412yes—
66C22×Dic86C2×C412yes—
67C22×Dic86C2×C411yescharacteristic
68C22×Dic86C2312yes—
69C22×D172C2×C411yescharacteristic
70C22×C22⋊D43D412yes—
71C23×Dic43—21no—
72C22×C4×D43D412yes—
73#13063333—28no—
74#13063333—28no—
75#13063331—28no—
76#13063331—28no—
77C2×#10621877—21no—
78C2×#10621877—21no—
79C2×#10621877—21no—
80C2×#10621877—21no—
81C2×#10621877D412yes—
82C2×#10621877C2312yes—
83C2×#10621872—24no—
84M16×D43—28no—
85M16×D43—28no—
86C22×C43⋊C8D412yes—
87C2×C8×D43—24no—
88#13063325—24no—
89#13063325C2×C418yescomplemented
90#13063313—24no—
91#13063313C2×C418yescomplemented
92#13063309—28no—
93#13063309—28no—
94#13063305—28no—
95#13063305—28no—
96#13063284—21no—
97#13063284—21no—
98#13063284—21no—
99#13063284C2312yes—
100C2×C4⋊Dic43—24no—
101C2×C4⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×(C2×D43)⋊C4—24no—
104C2×C4×Dic43—21no—
105#13063250—28no—
106#13063248—28no—
107#13063239—28no—
108C23×C4×C43C2311yescharacteristic
109C2×M16×C43—21no—
110C2×M16×C43—21no—
111C2×M16×C43—21no—
112C2×M16×C43—21no—
113C2×M16×C43D412yes—
114C2×M16×C43C2312yes—
115C22×C8×C43D412yes—
116#117×C43—21no—
117#117×C43—21no—
118#117×C43—21no—
119#117×C43—21no—
120#117×C43—21no—
121#117×C43C2×C412yes—
122#117×C43C2312yes—
123#117×C43C2312yes—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C42×C43—21no—
129C2×C42×C43C2×C412yes—
130C24×C43C2×D411yescharacteristic
131C23×D43C22⋊C412yes—
132C22×C4×C43—22no—
133C22×C4×C43—41no—
134C22×C4×C43C22×C411yescharacteristic
135C22×C4×C43C22×C411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43#4111yescharacteristic
144C22×C4×C43#4111yescharacteristic
145C22×C4×C43#4111yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C2×C22⋊D43—22no—
149C2×C22⋊D43—22no—
150C2×C22⋊D43—22no—
151C2×C22⋊D43—22no—
152C2×C22⋊D43C22⋊C414yes—
153C2×C22⋊D43C2×D414yes—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—41no—
158C22×Dic43—41no—
159C22×Dic43—41no—
160C22×Dic43—41no—
161C22×Dic43—41no—
162C22×Dic43C22⋊C412yes—
163#10621898—22no—
164#10621898—22no—
165#10621898—22no—
166#10621898—22no—
167#10621898—22no—
168#10621898—22no—
169#10621898—22no—
170#10621898—22no—
171#10621898—22no—
172#10621898—22no—
173#10621898—22no—
174#10621898—22no—
175#10621898—22no—
176#10621898—22no—
177#10621898—22no—
178#10621898—22no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172C22⋊C412yes—
184C2×D172C22×C412yes—
185C2×C4×D43—22no—
186C2×C4×D43—22no—
187C2×C4×D43—22no—
188C2×C4×D43—22no—
189C2×C4×D43C22⋊C414yes—
190C2×C4×D43C2×D414yes—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—22no—
196C2×Dic86—22no—
197C2×Dic86—22no—
198C2×Dic86—22no—
199C2×Dic86—22no—
200C2×Dic86—22no—
201C2×Dic86—22no—
202C2×Dic86—22no—
203C2×Dic86—22no—
204C2×Dic86—22no—
205C2×Dic86—22no—
206C2×Dic86—22no—
207C2×Dic86—22no—
208C2×Dic86—22no—
209C2×Dic86—22no—
210C2×Dic86—41no—
211C2×Dic86—41no—
212C2×Dic86—41no—
213C2×Dic86—41no—
214C2×Dic86—41no—
215C2×Dic86—41no—
216C2×Dic86—41no—
217C2×Dic86—41no—
218C2×Dic86—41no—
219C2×Dic86—41no—
220C2×Dic86—41no—
221C2×Dic86—41no—
222C2×Dic86C22⋊C412yes—
223C2×Dic86C22×C414yes—
224C2×Dic86C22×C412yes—
225M16×C43—22no—
226M16×C43—22no—
227M16×C43—22no—
228M16×C43—22no—
229C2×C8×C43—22no—
230C2×C8×C43—22no—
231C2×C8×C43C2×D414yes—
232C4⋊C4×C43—22no—
233C4⋊C4×C43—22no—
234C4⋊C4×C43—22no—
235C4⋊C4×C43—41no—
236C22⋊C4×C43—22no—
237C22⋊C4×C43—22no—
238C22⋊C4×C43—22no—
239C22⋊C4×C43—41no—
240C42×C43—22no—
241C42×C43—22no—
242C42×C43—41no—
243C42×C43C22×C414yes—
244C22⋊Dic43—22no—
245C22⋊Dic43—41no—
246(C2×D43)⋊C4—216no—
247C4⋊Dic43—216no—
248C4⋊Dic43—22no—
249C4⋊Dic43—41no—
250C4×Dic43—22no—
251C4×Dic43—41no—
252#10621877—22no—
253#10621877—22no—
254#10621877—22no—
255#10621877—22no—
256C2×C43⋊C8—22no—
257C2×C43⋊C8—22no—
258C2×C43⋊C8C2×D414yes—
259#10621872—216no—
260C8×D43—216no—
261C23×C43—42no—
262C23×C43C2×C22⋊C411yescharacteristic
263C23×C43C2×C22⋊C411yescharacteristic
264C23×C43#12111yescharacteristic
265C23×C43#12111yescharacteristic
266C23×C43#12111yescharacteristic
267C23×C43#12111yescharacteristic
268C23×C43C22×D411yescharacteristic
269C22×D43—22no—
270C22×D43—22no—
271C22×D43—44no—
272C22×D43C2×C22⋊C414yes—
273C2×C4×C43—24no—
274C2×C4×C43—44no—
275C2×C4×C43—42no—
276C2×C4×C43—82no—
277C2×C4×C43C2×C22⋊C411yescharacteristic
278C2×C4×C43C2×C22⋊C411yescharacteristic
279C2×C4×C43C4×D411yescharacteristic
280C2×C4×C43C4×D411yescharacteristic
281C2×C4×C43C4×D411yescharacteristic
282C2×C4×C43C4×D411yescharacteristic
283C2×C4×C43C4×D411yescharacteristic
284C2×C4×C43C4×D411yescharacteristic
285C2×C4×C43C4×D411yescharacteristic
286C2×C4×C43C4×D411yescharacteristic
287C2×C4×C43#12011yescharacteristic
288C2×C4×C43#12011yescharacteristic
289C2×C4×C43#12011yescharacteristic
290C2×C4×C43#12011yescharacteristic
291C2×C4×C43#12111yescharacteristic
292C2×C4×C43#12111yescharacteristic
293C2×C4×C43#12111yescharacteristic
294C2×C4×C43#12111yescharacteristic
295C2×C4×C43#12311yescharacteristic
296C2×C4×C43#12311yescharacteristic
297C2×C4×C43#12311yescharacteristic
298C2×C4×C43#12311yescharacteristic
299C2×C4×C43C23×C411yescharacteristic
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C22×D411yescharacteristic
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C2×#4111yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C22⋊D43—24no—
306C22⋊D43—24no—
307C22⋊D43—24no—
308C22⋊D43—24no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—24no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—82no—
320C2×Dic43C2×C22⋊C414yes—
321D172—22no—
322D172—22no—
323D172—22no—
324D172—22no—
325C4×D43—24no—
326C4×D43—24no—
327C4×D43—24no—
328C4×D43—24no—
329Dic86—22no—
330Dic86—22no—
331Dic86—22no—
332Dic86—22no—
333Dic86—24no—
334Dic86—24no—
335Dic86—42no—
336Dic86—42no—
337Dic86—42no—
338Dic86—42no—
339Dic86—42no—
340Dic86—42no—
341C8×C43—24no—
342C43⋊C8—24no—
343C2×#1909—431nomaximal, Sylow
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43#38611yescharacteristic
352C22×C43#38611yescharacteristic
353C22×C43#38611yescharacteristic
354C22×C43#38611yescharacteristic
355C22×C43C22×C22⋊C411yescharacteristic
356C22×C43C2×#12111yescharacteristic
357C22×C43C2×#12111yescharacteristic
358C2×D43—24no—
359C2×D43—44no—
360C2×D43—44no—
361C2×D43—82no—
362C4×C43—44no—
363C4×C43—82no—
364C4×C43#38611yescharacteristic
365C4×C43#38611yescharacteristic
366C4×C43#38611yescharacteristic
367C4×C43#38611yescharacteristic
368C4×C43C2×C4×D411yescharacteristic
369C4×C43C2×C4×D411yescharacteristic
370C4×C43C2×#12011yescharacteristic
371C4×C43C2×#12311yescharacteristic
372Dic43—24no—
373Dic43—44no—
374Dic43—82no—
375C2×#568—431no—
376C2×#536—431no—
377C2×#419—431no—
378C2×#419—431no—
379C2×#410—431no—
380#1909—438no—
381C2×H(3,ℤ/4)—431no—
382C2×H(3,ℤ/4)D4311yescharacteristic, complemented
383C2×C43—21no—
384C2×C43—21no—
385C2×C43—21no—
386C2×C43—21no—
387C2×C43—21no—
388C2×C43—21no—
389C2×C43#190912yescomplemented
390C2×C43C2×#38611yescharacteristic
391D43—44no—
392C22×#41—431no—
393C23×Q8—431no—
394#568—434no—
395#568—862no—
396#568—862no—
397#568—862no—
398C2×#131—862no—
399C2×#131—862no—
400C22×M16—431no—
401C22×M16—862no—
402C22×M16C2×D4311yescharacteristic
403#536—434no—
404#536—434no—
405#536—862no—
406#536—862no—
407C2×C4⋊Q8—432no—
408C2×#124—432no—
409C2×#123—862no—
410C2×C22⋊Q8—862no—
411C2×#117—431no—
412C2×#117C2×D4311yescharacteristic
413C2×#117C2×D4311yescharacteristic
414#419—434no—
415#419—434no—
416#419—862no—
417#419—862no—
418C2×#103—862no—
419C2×#103—862no—
420#410—434no—
421#410—862no—
422C2×#99—862no—
423H(3,ℤ/4)—434no—
424H(3,ℤ/4)C2×D4314yescomplemented
425C43C2×#190911yescharacteristic, complemented, Sylow
426C2×#41—432no—
427C2×#41—432no—
428C2×#41—432no—
429C2×#41—432no—
430C2×#41—861no—
431C2×#41—861no—
432C2×#41—861no—
433C2×#41—861no—
434C2×#41—861no—
435C2×#41—861no—
436C2×#41—861no—
437C2×#41—861no—
438C22×Q8—431no—
439C22×Q8—432no—
440C22×Q8—432no—
441C22×Q8—432no—
442C22×Q8—861no—
443C22×Q8—861no—
444C22×Q8—861no—
445C22×Q8—861no—
446C22×Q8—861no—
447C22×Q8—861no—
448C22×Q8—861no—
449C22×Q8—861no—
450C22×Q8—861no—
451C22×Q8—861no—
452C22×Q8—861no—
453C22×D4—432no—
454C22×D4—431no—
455C23×C4—432no—
456C23×C4—861no—
457C23×C4C22×D4311yescharacteristic
458#131—868no—
459#131—868no—
460#131—868no—
461#131—868no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—21no—
466C2×M16—432no—
467C2×M16—432no—
468C2×M16—864no—
469C2×M16—868no—
470C2×M16—868no—
471C2×M16—861no—
472C2×M16—861no—
473C2×M16—861no—
474C2×M16—861no—
475C2×M16D17212yes—
476C2×M16C22×D4312yes—
477C22×C8—432no—
478C22×C8—864no—
479C22×C8D17212yes—
480C4⋊Q8—438no—
481C4⋊Q8—864no—
482#124—438no—
483#124—864no—
484#123—868no—
485#123—868no—
486C22⋊Q8—868no—
487C22⋊Q8—868no—
488#117—21no—
489#117—21no—
490#117—21no—
491#117—21no—
492#117—21no—
493#117—432no—
494#117—861no—
495#117—861no—
496#117—861no—
497#117C4×D4312yes—
498#117C22×D4312yes—
499#117C22×D4312yes—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—864no—
503C2×C4⋊C4—861no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—864no—
507C2×C22⋊C4—861no—
508C2×C42—21no—
509C2×C42—861no—
510C2×C42C4×D4312yes—
511#103—868no—
512#103—868no—
513#99—868no—
514C24—432no—
515C24D4×D4311yescharacteristic
516#41—862no—
517#41—862no—
518#41—862no—
519#41—862no—
520#41—862no—
521#41—862no—
522#41—862no—
523#41—862no—
524#41—862no—
525#41—862no—
526#41—862no—
527#41—862no—
528#41—862no—
529#41—862no—
530#41—862no—
531#41—862no—
532C2×Q8—432no—
533C2×Q8—432no—
534C2×Q8—434no—
535C2×Q8—862no—
536C2×Q8—862no—
537C2×Q8—861no—
538C2×Q8—861no—
539C2×Q8—861no—
540C2×Q8—861no—
541C2×Q8—862no—
542C2×Q8—862no—
543C2×Q8—862no—
544C2×Q8—862no—
545C2×Q8—862no—
546C2×Q8—862no—
547C2×Q8—862no—
548C2×Q8—862no—
549C2×Q8—862no—
550C2×Q8—862no—
551C2×Q8—862no—
552C2×Q8—862no—
553C2×Q8—862no—
554C2×Q8—1721no—
555C2×Q8—1721no—
556C2×Q8—1721no—
557C2×Q8—1721no—
558C2×Q8—1721no—
559C2×Q8—1721no—
560C2×Q8—1721no—
561C2×Q8—1721no—
562C2×Q8—1721no—
563C2×Q8—1721no—
564C2×Q8—1721no—
565C2×Q8—1721no—
566C2×D4—434no—
567C2×D4—434no—
568C2×D4—432no—
569C2×D4—432no—
570C2×D4—862no—
571C2×D4—862no—
572C2×D4—862no—
573C2×D4—862no—
574C2×D4—861no—
575C2×D4—861no—
576C2×D4—861no—
577C2×D4—861no—
578C22×C4—22no—
579C22×C4—41no—
580C22×C4—432no—
581C22×C4—434no—
582C22×C4—434no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—1721no—
591C22×C4—1721no—
592C22×C4—1721no—
593C22×C4—1721no—
594C22×C4—1721no—
595C22×C4C2×C4×D4311yescharacteristic
596C22×C4C2×C4×D4311yescharacteristic
597C22×C4C2×D17211yescharacteristic
598C22×C4C2×D17211yescharacteristic
599C22×C4#1062189811yescharacteristic
600C22×C4#1062189811yescharacteristic
601C22×C4D4×D4311yescharacteristic
602C22×C4D4×D4311yescharacteristic
603C22×C4D4×D4311yescharacteristic
604C22×C4D4×D4311yescharacteristic
605C22×C4D4×D4311yescharacteristic
606C22×C4#1062190211yescharacteristic
607C22×C4#1062190211yescharacteristic
608C22×C4C23×D4311yescharacteristic
609M16—22no—
610M16—22no—
611M16—22no—
612M16—22no—
613M16—8616no—
614M16—862no—
615M16—862no—
616M16—862no—
617M16—862no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—434no—
621C2×C8—8616no—
622C2×C8—862no—
623C2×C8—862no—
624C2×C8C2×D17214yes—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—41no—
629C4⋊C4—8616no—
630C4⋊C4—862no—
631C4⋊C4—1721no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—41no—
636C22⋊C4—8616no—
637C22⋊C4—862no—
638C22⋊C4—1721no—
639C42—22no—
640C42—22no—
641C42—41no—
642C42—862no—
643C42—1721no—
644C42C2×C4×D4314yes—
645C23—42no—
646C23—434no—
647C23—862no—
648C23—862no—
649C23—1724no—
650C23C22⋊C4×D4311yescharacteristic
651C23C22⋊C4×D4311yescharacteristic
652C23#1306329811yescharacteristic
653C23#1306329811yescharacteristic
654C23#1306330011yescharacteristic
655C23#1306330011yescharacteristic
656C23C2×D4×D4311yescharacteristic
657Q8—862no—
658Q8—862no—
659Q8—862no—
660Q8—862no—
661Q8—864no—
662Q8—864no—
663Q8—1722no—
664Q8—1722no—
665Q8—1722no—
666Q8—1722no—
667Q8—1722no—
668Q8—1722no—
669D4—864no—
670D4—864no—
671D4—864no—
672D4—864no—
673D4—862no—
674D4—862no—
675D4—862no—
676D4—862no—
677C2×C4—24no—
678C2×C4—44no—
679C2×C4—42no—
680C2×C4—82no—
681C2×C4—434no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—864no—
685C2×C4—864no—
686C2×C4—864no—
687C2×C4—864no—
688C2×C4—864no—
689C2×C4—3442no—
690C2×C4—1722no—
691C2×C4—1722no—
692C2×C4—1722no—
693C2×C4—1722no—
694C2×C4—1722no—
695C2×C4—1722no—
696C2×C4—1722no—
697C2×C4C22⋊C4×D4311yescharacteristic
698C2×C4C22⋊C4×D4311yescharacteristic
699C2×C4#1306328711yescharacteristic
700C2×C4#1306328711yescharacteristic
701C2×C4#1306328711yescharacteristic
702C2×C4#1306328711yescharacteristic
703C2×C4C4×D17211yescharacteristic
704C2×C4C4×D17211yescharacteristic
705C2×C4C4×D17211yescharacteristic
706C2×C4C4×D17211yescharacteristic
707C2×C4#1306329511yescharacteristic
708C2×C4#1306329511yescharacteristic
709C2×C4#1306329511yescharacteristic
710C2×C4#1306329511yescharacteristic
711C2×C4#1306329811yescharacteristic
712C2×C4#1306329811yescharacteristic
713C2×C4#1306330011yescharacteristic
714C2×C4#1306330011yescharacteristic
715C2×C4#1306331011yescharacteristic
716C2×C4#1306331011yescharacteristic
717C2×C4#1306331011yescharacteristic
718C2×C4#1306331011yescharacteristic
719C2×C4C22×C4×D4311yescharacteristic
720C2×C4C2×D4×D4311yescharacteristic
721C2×C4C2×D4×D4311yescharacteristic
722C2×C4C22×D17211yescharacteristic
723C2×C4C2×#1062189811yescharacteristic
724C2×C4C2×#1062190211yescharacteristic
725C8—24no—
726C8—864no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—864no—
735C22—3442no—
736C22—1724no—
737C22—1724no—
738C22#1458277711yescharacteristic
739C22#1458277711yescharacteristic
740C22#1458277711yescharacteristic
741C22#1458277711yescharacteristic
742C22C2×C22⋊C4×D4311yescharacteristic
743C22C2×#1306329811yescharacteristic
744C22C2×#1306330011yescharacteristic
745C4—44no—
746C4—82no—
747C4—864no—
748C4—3442no—
749C4—1724no—
750C4#1458277711yescharacteristic
751C4#1458277711yescharacteristic
752C4#1458277711yescharacteristic
753C4#1458277711yescharacteristic
754C4C2×#1306328711yescharacteristic
755C4C2×C4×D17211yescharacteristic
756C4C2×#1306329511yescharacteristic
757C4C2×#1306331011yescharacteristic
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—1724no—
765C2#1913511612yesdirect product factor
766C2C2×#1458277711yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×H(3,ℤ/4)C2
socleC22×C43#386
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC2×H(3,ℤ/4)D43
hypocenterC43C2×#1909
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
3. C2×#14582909C2semidirect
4. C2×#14582907C2semidirect
6. #19135116C2direct (N × H)
7. C2×#14582655C2semidirect
8. C2×C43×H(3,ℤ/4)C2semidirect
21. #14583475C4semidirect
23. C2×#13063325C4semidirect
24. C2×#13063313C4semidirect
29. #14582909C22semidirect
31. #14582907C22semidirect
37. #14582655C22semidirect
41. C43×H(3,ℤ/4)C22semidirect
89. #13063325C2×C4semidirect
91. #13063313C2×C4semidirect
382. C2×H(3,ℤ/4)D43semidirect
389. C2×C43#1909semidirect
424. H(3,ℤ/4)C2×D43semidirect
425. C43C2×#1909semidirect
765. C2#19135116direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836652
C2×#145834752
C2×#145829092
C2×#145829072
C2×#145828722
#191351162
C2×#145826552
C2×C43×H(3,ℤ/4)2
C2×#190943