Finite Group Databasebeta

← C2×#19135121 #25098575

Subgroups — C2×#19135121 #25098575

Order 11008.

1878 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583665C211yesmaximal, characteristic, complemented
2C2×#14583468C211yesmaximal, characteristic
3C2×#14582905C211yesmaximal, characteristic, complemented
4C2×#14582903C211yesmaximal, characteristic, complemented
5C2×#14582872C211yesmaximal, characteristic, complemented
6#19135121C218yesmaximal, direct product factor
7C2×#14582655C211yesmaximal, characteristic, complemented
8C2×C43×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C23×D172C2211yescharacteristic
11#14583665—22no—
12#14583665—22no—
13#14583665—22no—
14#14583665C2214yescomplemented
15C2×#13063333—22no—
16C2×#13063331—22no—
17C22×#10621877C2211yescharacteristic
18C2×M16×D43—22no—
19#14583468—22no—
20#14583468—22no—
21#14583468C414yescomplemented
22#14583468C2214yes—
23C2×#13063322C412yescomplemented
24C2×#13063313C412yescomplemented
25C2×#13063300—22no—
26C2×#13063295—22no—
27C2×#13063284C2211yescharacteristic
28#14582905—22no—
29#14582905C2214yescomplemented
30#14582903—22no—
31#14582903C2214yescomplemented
32C2×#13063247—22no—
33C2×#13063245—22no—
34#14582872—22no—
35#14582872C2214yescomplemented
36C2×#13063239—22no—
37#14582655C2214yescomplemented
38C22×M16×C43C2211yescharacteristic
39C2×#117×C43C2211yescharacteristic
40C2×#117×C43C2211yescharacteristic
41C43×H(3,ℤ/4)C2214yescomplemented
42C24×D43—21no—
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898—21no—
51C2×#10621898C2×C412yes—
52C2×#10621898D412yes—
53C2×#10621898D412yes—
54C2×#10621898C2312yes—
55C22×Dic86C2×C411yescharacteristic
56C22×D172—21no—
57C22×D172—21no—
58C22×D172—21no—
59C22×D172—21no—
60C22×D172—21no—
61C22×D172—21no—
62C22×D172—21no—
63C22×D172—21no—
64C22×D172—21no—
65C22×D172—21no—
66C22×D172—21no—
67C22×D172—24no—
68C22×D172C2×C412yes—
69C22×D172C2×C412yes—
70C22×D172C2×C411yescharacteristic
71C22×D172C2312yes—
72C22×C22⋊D43D412yes—
73C22×C4×D43D412yes—
74#13063333—28no—
75#13063333—28no—
76#13063331—28no—
77#13063331—28no—
78C2×#10621877—21no—
79C2×#10621877—21no—
80C2×#10621877—21no—
81C2×#10621877—21no—
82C2×#10621877D412yescomplemented
83C2×#10621877C2312yes—
84C2×#10621872—24no—
85M16×D43—28no—
86M16×D43—28no—
87C22×C43⋊C8D412yescomplemented
88C2×C8×D43—24no—
89#13063322—24no—
90#13063322C2×C418yescomplemented
91#13063313—24no—
92#13063313C2×C418yescomplemented
93#13063300—28no—
94#13063300—28no—
95#13063295—28no—
96#13063295—28no—
97#13063284—21no—
98#13063284—21no—
99#13063284—21no—
100#13063284C2312yes—
101C2×C4⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×(C2×D43)⋊C4—24no—
104C2×C4×Dic43—21no—
105#13063247—28no—
106#13063245—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×C43D412yescomplemented
114C2×M16×C43C2312yes—
115C22×C8×C43D412yescomplemented
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×D43—22no—
132C23×D43—22no—
133C23×D43—22no—
134C23×D43—41no—
135C23×D43—41no—
136C23×D43—41no—
137C23×D43—41no—
138C23×D43—84no—
139C23×D43C22⋊C412yes—
140C22×C4×C43—22no—
141C22×C4×C43—41no—
142C22×C4×C43C22×C411yescharacteristic
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43#4111yescharacteristic
152C22×C4×C43#4111yescharacteristic
153C22×C4×C43#4111yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—22no—
157C2×C22⋊D43—22no—
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43C22⋊C414yes—
161C2×C22⋊D43C2×D414yes—
162C22×Dic43—41no—
163C22×Dic43C22⋊C412yes—
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—
179#10621898—22no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—22no—
185C2×D172—22no—
186C2×D172—22no—
187C2×D172—216no—
188C2×D172—22no—
189C2×D172—22no—
190C2×D172—22no—
191C2×D172—22no—
192C2×D172—22no—
193C2×D172—22no—
194C2×D172—22no—
195C2×D172—22no—
196C2×D172—22no—
197C2×D172—22no—
198C2×D172—22no—
199C2×D172—22no—
200C2×D172—41no—
201C2×D172—41no—
202C2×D172—41no—
203C2×D172—41no—
204C2×D172—41no—
205C2×D172—41no—
206C2×D172—41no—
207C2×D172—41no—
208C2×D172—41no—
209C2×D172—41no—
210C2×D172—41no—
211C2×D172—41no—
212C2×D172—88no—
213C2×D172C22⋊C412yes—
214C2×D172C22×C414yes—
215C2×D172C22×C412yes—
216C2×C4×D43—22no—
217C2×C4×D43—22no—
218C2×C4×D43—22no—
219C2×C4×D43—22no—
220C2×C4×D43C22⋊C414yes—
221C2×C4×D43C2×D414yes—
222C2×Dic86—21no—
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86C22⋊C412yes—
227C2×Dic86C22×C412yes—
228M16×C43—22no—
229M16×C43—22no—
230M16×C43—22no—
231M16×C43—22no—
232C2×C8×C43—22no—
233C2×C8×C43—22no—
234C2×C8×C43C2×D414yescomplemented
235C4⋊C4×C43—22no—
236C4⋊C4×C43—22no—
237C4⋊C4×C43—22no—
238C4⋊C4×C43—41no—
239C22⋊C4×C43—22no—
240C22⋊C4×C43—22no—
241C22⋊C4×C43—22no—
242C22⋊C4×C43—41no—
243C42×C43—22no—
244C42×C43—22no—
245C42×C43—41no—
246C42×C43C22×C414yes—
247C22⋊Dic43—22no—
248C22⋊Dic43—41no—
249(C2×D43)⋊C4—216no—
250C4⋊Dic43—22no—
251C4⋊Dic43—41no—
252C4×Dic43—22no—
253C4×Dic43—41no—
254#10621877—22no—
255#10621877—22no—
256#10621877—22no—
257#10621877—22no—
258C2×C43⋊C8—22no—
259C2×C43⋊C8—22no—
260C2×C43⋊C8C2×D414yescomplemented
261#10621872—216no—
262C8×D43—216no—
263C23×C43—42no—
264C23×C43C2×C22⋊C411yescharacteristic
265C23×C43C2×C22⋊C411yescharacteristic
266C23×C43#12111yescharacteristic
267C23×C43#12111yescharacteristic
268C23×C43#12111yescharacteristic
269C23×C43#12111yescharacteristic
270C23×C43C22×D411yescharacteristic
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—24no—
274C22×D43—44no—
275C22×D43—48no—
276C22×D43—42no—
277C22×D43—42no—
278C22×D43—42no—
279C22×D43—42no—
280C22×D43—42no—
281C22×D43—42no—
282C22×D43—84no—
283C22×D43—84no—
284C22×D43—84no—
285C22×D43—84no—
286C22×D43—84no—
287C22×D43—84no—
288C22×D43C2×C22⋊C414yes—
289C2×C4×C43—24no—
290C2×C4×C43—44no—
291C2×C4×C43—42no—
292C2×C4×C43—82no—
293C2×C4×C43C2×C22⋊C411yescharacteristic
294C2×C4×C43C2×C22⋊C411yescharacteristic
295C2×C4×C43C4×D411yescharacteristic
296C2×C4×C43C4×D411yescharacteristic
297C2×C4×C43C4×D411yescharacteristic
298C2×C4×C43C4×D411yescharacteristic
299C2×C4×C43C4×D411yescharacteristic
300C2×C4×C43C4×D411yescharacteristic
301C2×C4×C43C4×D411yescharacteristic
302C2×C4×C43C4×D411yescharacteristic
303C2×C4×C43#12011yescharacteristic
304C2×C4×C43#12011yescharacteristic
305C2×C4×C43#12011yescharacteristic
306C2×C4×C43#12011yescharacteristic
307C2×C4×C43#12111yescharacteristic
308C2×C4×C43#12111yescharacteristic
309C2×C4×C43#12111yescharacteristic
310C2×C4×C43#12111yescharacteristic
311C2×C4×C43#12311yescharacteristic
312C2×C4×C43#12311yescharacteristic
313C2×C4×C43#12311yescharacteristic
314C2×C4×C43#12311yescharacteristic
315C2×C4×C43C23×C411yescharacteristic
316C2×C4×C43C22×D411yescharacteristic
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C2×#4111yescharacteristic
320C2×C4×C43C2×#4111yescharacteristic
321C22⋊D43—24no—
322C22⋊D43—24no—
323C22⋊D43—24no—
324C22⋊D43—24no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—42no—
328C2×Dic43—82no—
329C2×Dic43C2×C22⋊C414yes—
330D172—22no—
331D172—22no—
332D172—24no—
333D172—24no—
334D172—22no—
335D172—22no—
336D172—42no—
337D172—42no—
338D172—42no—
339D172—42no—
340D172—42no—
341D172—42no—
342D172—816no—
343C4×D43—24no—
344C4×D43—24no—
345C4×D43—24no—
346C4×D43—24no—
347Dic86—22no—
348Dic86—22no—
349Dic86—22no—
350Dic86—22no—
351C8×C43—24no—
352C43⋊C8—24no—
353C2×#1910—431nomaximal, Sylow
354C22×C43—22no—
355C22×C43—22no—
356C22×C43—22no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43#38611yescharacteristic
362C22×C43#38611yescharacteristic
363C22×C43#38611yescharacteristic
364C22×C43#38611yescharacteristic
365C22×C43C22×C22⋊C411yescharacteristic
366C22×C43C2×#12111yescharacteristic
367C22×C43C2×#12111yescharacteristic
368C2×D43—24no—
369C2×D43—44no—
370C2×D43—44no—
371C2×D43—48no—
372C2×D43—44no—
373C2×D43—82no—
374C2×D43—84no—
375C2×D43—84no—
376C2×D43—84no—
377C2×D43—84no—
378C2×D43—84no—
379C2×D43—84no—
380C4×C43—44no—
381C4×C43—82no—
382C4×C43#38611yescharacteristic
383C4×C43#38611yescharacteristic
384C4×C43#38611yescharacteristic
385C4×C43#38611yescharacteristic
386C4×C43C2×C4×D411yescharacteristic
387C4×C43C2×C4×D411yescharacteristic
388C4×C43C2×#12011yescharacteristic
389C4×C43C2×#12311yescharacteristic
390Dic43—24no—
391Dic43—82no—
392C2×#568—431no—
393C2×#535—431no—
394C2×#418—431no—
395C2×#418—431no—
396C2×#410—431no—
397#1910—438no—
398C2×H(3,ℤ/4)—431no—
399C2×H(3,ℤ/4)D4311yescharacteristic, complemented
400C2×C43—21no—
401C2×C43—21no—
402C2×C43—21no—
403C2×C43—21no—
404C2×C43—21no—
405C2×C43—21no—
406C2×C43#191012yescomplemented
407C2×C43C2×#38611yescharacteristic
408D43—44no—
409D43—84no—
410C22×#41—431no—
411C23×D4—431no—
412#568—434no—
413#568—862no—
414#568—862no—
415#568—862no—
416C2×#131—862no—
417C2×#131—862no—
418C22×M16—431no—
419C22×M16—862no—
420C22×M16C2×D4311yescharacteristic
421#535—434no—
422#535—434no—
423#535—862no—
424#535—862no—
425C2×#127—432no—
426C2×#124—432no—
427C2×#121—862no—
428C2×#120—862no—
429C2×#117—431no—
430C2×#117C2×D4311yescharacteristic
431C2×#117C2×D4311yescharacteristic
432#418—434no—
433#418—434no—
434#418—862no—
435#418—862no—
436C2×#102—862no—
437C2×#102—862no—
438#410—434no—
439#410—862no—
440C2×#99—862no—
441H(3,ℤ/4)—434no—
442H(3,ℤ/4)C2×D4314yescomplemented
443C43C2×#191011yescharacteristic, complemented, Sylow
444C25—861no—
445C2×#41—432no—
446C2×#41—432no—
447C2×#41—432no—
448C2×#41—432no—
449C2×#41—861no—
450C2×#41—861no—
451C2×#41—861no—
452C2×#41—861no—
453C2×#41—861no—
454C2×#41—861no—
455C2×#41—861no—
456C2×#41—861no—
457C22×Q8—431no—
458C22×D4—432no—
459C22×D4—431no—
460C22×D4—432no—
461C22×D4—432no—
462C22×D4—432no—
463C22×D4—864no—
464C22×D4—861no—
465C22×D4—861no—
466C22×D4—861no—
467C22×D4—861no—
468C22×D4—861no—
469C22×D4—861no—
470C22×D4—861no—
471C22×D4—861no—
472C22×D4—861no—
473C22×D4—861no—
474C22×D4—861no—
475C23×C4—432no—
476C23×C4C22×D4311yescharacteristic
477#131—868no—
478#131—868no—
479#131—868no—
480#131—868no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—21no—
484C2×M16—21no—
485C2×M16—432no—
486C2×M16—432no—
487C2×M16—864no—
488C2×M16—868no—
489C2×M16—868no—
490C2×M16—861no—
491C2×M16—861no—
492C2×M16—861no—
493C2×M16—861no—
494C2×M16D17212yescomplemented
495C2×M16C22×D4312yes—
496C22×C8—432no—
497C22×C8—864no—
498C22×C8D17212yescomplemented
499#127—438no—
500#127—864no—
501#124—438no—
502#124—864no—
503#121—868no—
504#121—868no—
505#120—868no—
506#120—868no—
507#117—21no—
508#117—21no—
509#117—21no—
510#117—21no—
511#117—21no—
512#117—432no—
513#117—861no—
514#117—861no—
515#117—861no—
516#117C4×D4312yes—
517#117C22×D4312yes—
518#117C22×D4312yes—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—861no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—864no—
525C2×C22⋊C4—861no—
526C2×C42—21no—
527C2×C42—861no—
528C2×C42C4×D4312yes—
529#102—868no—
530#102—868no—
531#99—868no—
532C24—432no—
533C24—862no—
534C24—862no—
535C24—862no—
536C24—3444no—
537C24—1721no—
538C24—1721no—
539C24—1721no—
540C24—1721no—
541C24D4×D4311yescharacteristic
542#41—862no—
543#41—862no—
544#41—862no—
545#41—862no—
546#41—862no—
547#41—862no—
548#41—862no—
549#41—862no—
550#41—862no—
551#41—862no—
552#41—862no—
553#41—862no—
554#41—862no—
555#41—862no—
556#41—862no—
557#41—862no—
558C2×Q8—432no—
559C2×Q8—432no—
560C2×Q8—861no—
561C2×Q8—861no—
562C2×Q8—861no—
563C2×Q8—861no—
564C2×D4—434no—
565C2×D4—434no—
566C2×D4—432no—
567C2×D4—432no—
568C2×D4—434no—
569C2×D4—8616no—
570C2×D4—862no—
571C2×D4—862no—
572C2×D4—862no—
573C2×D4—862no—
574C2×D4—862no—
575C2×D4—862no—
576C2×D4—861no—
577C2×D4—861no—
578C2×D4—862no—
579C2×D4—862no—
580C2×D4—862no—
581C2×D4—862no—
582C2×D4—861no—
583C2×D4—861no—
584C2×D4—862no—
585C2×D4—862no—
586C2×D4—862no—
587C2×D4—862no—
588C2×D4—862no—
589C2×D4—862no—
590C2×D4—862no—
591C2×D4—862no—
592C2×D4—862no—
593C2×D4—3448no—
594C2×D4—1721no—
595C2×D4—1721no—
596C2×D4—1721no—
597C2×D4—1721no—
598C2×D4—1721no—
599C2×D4—1721no—
600C2×D4—1721no—
601C2×D4—1721no—
602C2×D4—1721no—
603C2×D4—1721no—
604C2×D4—1721no—
605C2×D4—1721no—
606C22×C4—22no—
607C22×C4—41no—
608C22×C4—432no—
609C22×C4—434no—
610C22×C4—434no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—862no—
614C22×C4—862no—
615C22×C4—1721no—
616C22×C4C2×C4×D4311yescharacteristic
617C22×C4C2×C4×D4311yescharacteristic
618C22×C4C2×D17211yescharacteristic
619C22×C4C2×D17211yescharacteristic
620C22×C4#1062189811yescharacteristic
621C22×C4#1062189811yescharacteristic
622C22×C4D4×D4311yescharacteristic
623C22×C4D4×D4311yescharacteristic
624C22×C4D4×D4311yescharacteristic
625C22×C4D4×D4311yescharacteristic
626C22×C4D4×D4311yescharacteristic
627C22×C4#1062190211yescharacteristic
628C22×C4#1062190211yescharacteristic
629C22×C4C23×D4311yescharacteristic
630M16—22no—
631M16—22no—
632M16—22no—
633M16—22no—
634M16—8616no—
635M16—862no—
636M16—862no—
637M16—862no—
638M16—862no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—434no—
642C2×C8—8616no—
643C2×C8—862no—
644C2×C8—862no—
645C2×C8C2×D17214yescomplemented
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—41no—
650C4⋊C4—862no—
651C4⋊C4—1721no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—41no—
656C22⋊C4—8616no—
657C22⋊C4—862no—
658C22⋊C4—1721no—
659C42—22no—
660C42—22no—
661C42—41no—
662C42—862no—
663C42—1721no—
664C42C2×C4×D4314yes—
665C23—42no—
666C23—434no—
667C23—862no—
668C23—862no—
669C23—864no—
670C23—3444no—
671C23—3444no—
672C23—3444no—
673C23—3444no—
674C23—3444no—
675C23—3444no—
676C23—1728no—
677C23—1724no—
678C23—1722no—
679C23—1722no—
680C23—1722no—
681C23—1722no—
682C23—1722no—
683C23—1722no—
684C23C22⋊C4×D4311yescharacteristic
685C23C22⋊C4×D4311yescharacteristic
686C23#1306329811yescharacteristic
687C23#1306329811yescharacteristic
688C23#1306330011yescharacteristic
689C23#1306330011yescharacteristic
690C23C2×D4×D4311yescharacteristic
691Q8—862no—
692Q8—862no—
693Q8—862no—
694Q8—862no—
695D4—864no—
696D4—864no—
697D4—864no—
698D4—864no—
699D4—862no—
700D4—864no—
701D4—862no—
702D4—864no—
703D4—862no—
704D4—862no—
705D4—34416no—
706D4—1722no—
707D4—1722no—
708D4—1722no—
709D4—1722no—
710D4—1722no—
711D4—1722no—
712C2×C4—24no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—82no—
716C2×C4—434no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—864no—
720C2×C4—864no—
721C2×C4—864no—
722C2×C4—864no—
723C2×C4—3442no—
724C2×C4—1722no—
725C2×C4C22⋊C4×D4311yescharacteristic
726C2×C4C22⋊C4×D4311yescharacteristic
727C2×C4#1306328711yescharacteristic
728C2×C4#1306328711yescharacteristic
729C2×C4#1306328711yescharacteristic
730C2×C4#1306328711yescharacteristic
731C2×C4C4×D17211yescharacteristic
732C2×C4C4×D17211yescharacteristic
733C2×C4C4×D17211yescharacteristic
734C2×C4C4×D17211yescharacteristic
735C2×C4#1306329511yescharacteristic
736C2×C4#1306329511yescharacteristic
737C2×C4#1306329511yescharacteristic
738C2×C4#1306329511yescharacteristic
739C2×C4#1306329811yescharacteristic
740C2×C4#1306329811yescharacteristic
741C2×C4#1306330011yescharacteristic
742C2×C4#1306330011yescharacteristic
743C2×C4#1306331011yescharacteristic
744C2×C4#1306331011yescharacteristic
745C2×C4#1306331011yescharacteristic
746C2×C4#1306331011yescharacteristic
747C2×C4C22×C4×D4311yescharacteristic
748C2×C4C2×D4×D4311yescharacteristic
749C2×C4C2×D4×D4311yescharacteristic
750C2×C4C22×D17211yescharacteristic
751C2×C4C2×#1062189811yescharacteristic
752C2×C4C2×#1062190211yescharacteristic
753C8—24no—
754C8—864no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—864no—
763C22—3444no—
764C22—3444no—
765C22—3444no—
766C22—3444no—
767C22—3444no—
768C22—3442no—
769C22—3444no—
770C22—1728no—
771C22—1724no—
772C22—1724no—
773C22—1724no—
774C22#1458277711yescharacteristic
775C22#1458277711yescharacteristic
776C22#1458277711yescharacteristic
777C22#1458277711yescharacteristic
778C22C2×C22⋊C4×D4311yescharacteristic
779C22C2×#1306329811yescharacteristic
780C22C2×#1306330011yescharacteristic
781C4—44no—
782C4—82no—
783C4—864no—
784C4—3442no—
785C4#1458277711yescharacteristic
786C4#1458277711yescharacteristic
787C4#1458277711yescharacteristic
788C4#1458277711yescharacteristic
789C4C2×#1306328711yescharacteristic
790C4C2×C4×D17211yescharacteristic
791C4C2×#1306329511yescharacteristic
792C4C2×#1306331011yescharacteristic
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—3444no—
800C2—1724no—
801C2#1913512112yesdirect product factor
802C2C2×#1458277711yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×H(3,ℤ/4)C2
socleC22×C43#386
prime radicalC2×#14583468C2
cosocleC22×C4×C43C24
hypercenterC2×H(3,ℤ/4)D43
hypocenterC43C2×#1910
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
1. C2×#14583665C2semidirect
3. C2×#14582905C2semidirect
4. C2×#14582903C2semidirect
5. C2×#14582872C2semidirect
6. #19135121C2direct (N × H)
7. C2×#14582655C2semidirect
8. C2×C43×H(3,ℤ/4)C2semidirect
14. #14583665C22semidirect
21. #14583468C4semidirect
23. C2×#13063322C4semidirect
24. C2×#13063313C4semidirect
29. #14582905C22semidirect
31. #14582903C22semidirect
35. #14582872C22semidirect
37. #14582655C22semidirect
41. C43×H(3,ℤ/4)C22semidirect
82. C2×#10621877D4semidirect
87. C22×C43⋊C8D4semidirect
90. #13063322C2×C4semidirect
92. #13063313C2×C4semidirect
113. C2×M16×C43D4semidirect
115. C22×C8×C43D4semidirect
234. C2×C8×C43C2×D4semidirect
260. C2×C43⋊C8C2×D4semidirect
399. C2×H(3,ℤ/4)D43semidirect
406. C2×C43#1910semidirect
442. H(3,ℤ/4)C2×D43semidirect
443. C43C2×#1910semidirect
494. C2×M16D172semidirect
498. C22×C8D172semidirect
645. C2×C8C2×D172semidirect
801. C2#19135121direct (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×#145834682
C2×#145829052
C2×#145829032
C2×#145828722
#191351212
C2×#145826552
C2×C43×H(3,ℤ/4)2
C2×#191043